Canucks Anonymous

An Asset Price Decline IS a Negative Productivity Shock

2012-02-13T15:28:00.000-08:00

So the Bullard speech caused a stir. I don't much care what the man meant, if he did intend to say something sensible it doesn't appear he said it very well and from the snippets of the speech that I've read, (I haven't read the whole thing), I can see how some people got the idea that he was saying something as simple as - lower household wealth will lead people to spend less and save more thus permanently lowering aggregate demand. If that's what Bullard meant then it was as stupid as everyone says.

Not quite everyone said Bullard's speech was stupid however, David Andolfatto here and here provides an interpretation that actually make sense (and links to the rest of the discussion). Of course, even if Bullard meant what Andolfatto seems to think it's quite absurd for a Fed president to be out there making speeches that require such interpretation and so in a sense Bullard deserves to be dragged over the coals a bit. That said though, while Bullard may or may not have been saying something completely idiotic Andolfatto most certainly isn't.

Limited Commitment and the Costs of Credit Intermediation

It is perhaps an unfortunate fact of life but the reality is that we live in a world of limited commitment and that implies that credit intermediation is an astonishingly costly endeavour, costly in terms of requiring very large inputs of both labour and capital.

To illustrate let's think through an example that most people are familiar with, buying a house with a 30 year loan. Now, let's suppose at first that the bank can't seize your house if you fail to repay the loan. In what circumstances would the bank be willing to loan you the required amount of money?

Actually, it's hard to imagine any circumstance where a bank would loan the average person that kind of money without collateral, but why not? Why can't the borrower just say to the bank that "I commit to pay back the loan out of my future labour income"? After all, that is what the borrower is saying in the normal case of a standard mortgage, but why isn't that enough, why does the bank also want collateral?

Well, it's because from the bank's point of view you aren't really committed. One problem is costly state verification, the bank doesn't necessarily know that state of your finances or of your labour prospects. You might get out of paying back the loan by hiding your income, then you keep the house, you keep your money and when the bank calls you just tell them "leave me alone, there's no money here". Think a bit about the amount of resources governments spend collecting income taxes and finding hidden income and you see how expensive this would be for the bank.

I could go on but I'm getting away from the main point which is that for this and a host of related problems having the loan sufficiently collateralized is the cure for what ails you. If you post the house as collateral on the loan than the bank saves a lot on monitoring you and trying to enforce payment on the loan, so much so that in the bubble when everyone expected house prices to keep rising the people who invested in MBS where basically willing to finance mortgages with essentially no monitoring and enforcement at all. If the borrower defaulted they were just as happy to seize the house, sell it and get all their money back.

Most importantly of all, the basic point that collateral is a cure all for otherwise nearly prohibitive credit intermediation costs is ubiquitous. It applies everywhere that credit is extended and the costs in the absence of collateralization truly are prohibitive, just think how much resource is expanded on intermediating credit even with a high degree of collateralizaion, banks employ a lot of highly educated labour.

The Cost of Credit Intermediation and Aggregate Productivity

Well, an obvious effect of higher credit intermediation costs on aggregate productivity is the diversion of resources. To the extent that more resource is directed at intermediating credit that leaves less for other uses but there's a further point. In all probability the result will be a certain amount of credit rationing Stiglitz-Weiss style.

Stiglitz and Weiss made the point that if it's very expensive (or impossible) for a lender to distinguish good lenders from bad ones then the market may clear by quantity rationing rather than price adjustment, that is the interest rate may not clear the market. The reason is that the guy who offers to pay a high interest rate may be the guy with great investment project but he also may be the guy who knows he's not gone pay anything back anyway. It may be prohibitively expensive for the bank to tell the difference and so the bank may instead simply ration credit as a result. Notice once again that sufficient collateralization is the solution to this problem.

So what if a fall in the value of collateral leads to an equilibrium rationing of credit? Well, the equilibrium capital/labour ratio falls, a notion that Tim Duy and Noah Smith found rediculous.

In sum, in a world of limited commitment where credit intermediation is costly a fall in asset prices increases those costs and consequently reduces aggregate productivity.

A Permanent Fall in Asset Prices or a Monetary Policy Solution?

Of course the idea that the fall in asset prices is permanent is pretty debatable, I think instead that it implies that monetary policy is the answer. Of course this would essentially entail the Fed raising asset prices back to their "bubble" levels and one can reasonably debate whether or not that is either possible or desirable but provided the Fed could do it there is a case to be made that the Fed should do it.

Paul Krugman goes a bit bonkers

2011-11-22T13:45:00.000-08:00

So here's Paul Krugman on the competitive model:

Yet textbook economics says that in a competitive economy, the contribution any individual (or for that matter any factor of production) makes to the economy at the margin is what that individual earns — period. What a worker contributes to GDP with an additional hour of work is that worker’s hourly wage, whether that hourly wage is $6 or $60,000 an hour. This in turn means that the effect on everyone else’s income if a worker chooses to work one hour less is precisely zero. If a hedge fund manager gets $60,000 an hour, and he works one hour less, he reduces GDP by $60,000 — but he also reduces his pay by $60,000, so the net effect on other peoples’ incomes is zip.

Say what? Yeah, I'm gonna have to disagree.

Well, the first two sentences are fine, nothing to complain about there, but the rest? I mean, as the man said in the competitive model you get paid the value of your output! If this guy works an hour less then that means his clients either have to do that hour of work themselves or not get the benefit of a service that they valued so much they'd pay $60,000 per hour for it. In so far as they paid that hourly rate voluntarily it follows that they are necessarily worse off.

Furthermore, there are gains from trade. In the competitive model where you get paid the value of your output that guy only gets that wage if he's really good at his job, if his client has to do that hour himself he may only value his own hour spent investing at, say, $50,000.

[Nick Rowe corrects me on those two paragraphs so I'll try again.

Yes, at the margin the hedge fund manager is paid just the right amount so that his clients are indifferent to having that last hour of his labour and paying $60,000 for it or not having it at all. However, it's also true that the manager is indifferent to working the hour and getting the pay or taking the hour as leisure, at the margin.

The distortion from taxation arises because the hedge fund guy necessarily reduces his labour by more than that one hour, it must be the case because he needs to reduce his labour until he's indifferent between supplying his last hour worked and the new, lower, after tax hourly income. His elasticity of substitution approximates how many hours he'll cut back. Now, for every additional hour, after the first, that he reduces his labour supply there is a deadweight loss to society (basically his clients lose their consumer surplus). For each of those hours his clients were not indifferent to having the service or not, for each of those hours they strictly preferred to have the service and pay $60,000 rather than not have the service, in fact for each of those hours his clients would have willingly paid a bit more that $60,000 (basically they lose their consumer's surplus).]

It appears that in using the example of the hedge fund manager Krugman is really just thinking of a guy who can't possibly be really worth what he gets paid and who knows, maybe in the real world that's even correct. But in the competitive model it most certainly is not correct.

I think Krugman has broken one of his own precepts, he's made an economic argument into a morality play and that just doesn't work. I mean, forget the hedge fund guy, look at Tiger Woods. If ever a man didn't "deserve" his millions it seems like Tiger is him but in our society there are enough people who want to watch the best golfer and few enough top golfers that the market values Tiger highly regardless what kind of guy he is. How do you argue with that? Tiger is paid to play good golf not be a good guy and whatever you want to say about him I don't believe you can reasonably argue that Tiger Woods isn't good a golf.

Now, of course Krugman is saying this because what he really wants to do is tax Tiger and the hedge fund guy more and there surely are good arguments for doing that. It seems the Diamond and Saez paper he links to probably makes some of them. Krugman doesn't.

The Magic of 5: NGDP Targeting and the Natural Rate of Unemployment

2011-11-19T13:33:00.000-08:00

I'm a bit late writing this post, but I think there's more to say on the NGDP targeting argument that I've been having with some of the "market monetarists". (Actually, there will be more still to say. To their credit Nick Rowe and David Beckworth actually give reasoned arguments instead of simply asserting their correctness. I'm not convinced but to give a decent response will entail some long posts, which I hope to find time to do.)

Actually, since I last posted Bill Woolsey has actually come out against stable NGDP growth! Well, actually not but he does agree that NGDP growth in the 70s was very stable around its roughly 10% trend, yet because real output gaps were large during the period he actually concludes that this was a case of "irresponsible out-of-control monetary policy". Apparently it's all down to that magic number again, stable NGDP growth isn't really what we want. It's stable NGDP growth at exactly the right number, and the correct number has been shown by divine revelation to Scott Sumner, it's 5%.

The question I'm asking is really quite simple, Sumner says that historically periods of stable 5% NGDP growth have been considered to be good times while times when NGDP growth fell below that have tended to be recessions, well all that is certainly true. However, does it follow as a logical consequence that during those times that NGDP growth fell below 5% the outcome would have been better if the Fed had kept NGDP on target by pushing inflation higher?

Sumner thinks the answer to this question is obviously yes but that is a non-sequitor, the conclusion does not follow from the facts as a point of logic. You need some theoretical and empirical work to give a good answer to that question and the rigorous work that's been done invariably says the answer is no.

So, when Scott Sumner says "I don’t work with toy models; I try to stay grounded in the real world" he's really saying that he can't actually answer the question.

Inflation Volatility and Optimal Policy

Generally speaking models that give any useful role for monetary policy tend to have some sort of nominal rigidity, price stickiness and/or wage stickiness. The thing about it is that when you ask, within the context of the model, what is the optimal monetary policy none of the models return NGDP targeting. Perhaps this explains all the appeals to pragmatism and simplicity on the part of the market monetarists.

One thing these models do say however is that if prices are sticky then all else equal you want to minimize price volatility. In fact many such specifications imply the "divine coincidence" where stabilizing inflation stabilizes the output gap. Now the divine coincidence is itself a special result that you get from price stickiness in the absence of wage stickiness but there is a general principle at work here. If a negative shock to output is amenable to a monetary solution then it should show up in lower inflation, if it doesn't then there's nothing monetary policy can do to help and any attempt to help will be counter-productive. This principle carries over to other situations, when wages are assumed sticky then optimal policy tries to stabilize wage growth as well as inflation. Nowhere from rigorous theory do you get NGDP targeting as optimal policy.

Natural Rates

One of the points I've been making is that the 1970's are a period that seems to refute the idea that NGDP targeting would be a good idea. After all, in the first few years of the decade after the 1970 recession NGDP grows at a stable 10% and the economic result in terms of real output and unemployment is just fine. Then of course we get the oil shock, real output plummets but the fed responds by pushing up inflation to keep NGDP around it's trend path. Sumner himself acknowledges that in the face of such a shock stable NGDP growth won't prevent a recession. We agree on that but my question is this, is pushing inflation up to keep NGDP growth on trend a good idea? One of the market monetarist's primary arguments in favour of NGDP targeting over inflation targeting is that pushing up inflation in response to an adverse supply shock is a good idea.

My point was simply that in the 1970's this advice was followed and it didn't seem to work out to well. So, how about this question: suppose that in the early 70s NGDP growth had been 5% per year when the oil shock hit. The oil shock sent real GDP growth to -2.5%, in that case would it have been a good idea for the Fed to push inflation to 7.5% to keep NGDP growth at 5%?

The market monetarists say yes.

Finally responding to the poor labour market performance of the 70s Sumner says:

It’s also widely acknowledged that the natural rate of unemployment rose sharply during the 1970s—market monetarist policies have no control over that variable.

Indeed. So what about those natural rate models?

Some International Evidence on Output-Inflation Tradeoffs

Here's a really great paper with a natural rate model in it. In the paper Robert Lucas runs time series regressions of the deviation from trend of real output on nominal income growth. He also runs time series regressions of inflation on NGDP growth. (Both regressions include some lagged dependent variables to improve the fit.)

He then compares the estimated coefficients with the variance of inflation and finds that the countries with high inflation variance (only 2 of the 18 countries) have coefficients on output that are a tenth as large as as the countries with low inflation volatility.

Here's Lucas:

In a stable price country like the United States, then, policies which increase nominal income tend to have a large initial effect on real output, together with a small, positive initial effect on the rate of inflation. Thus the apparent short-term trade-off is favorable, as long as it remains unused. In contrast, in a volatile price country like Argentina, nominal income changes are associated with equal, contemporaneous price movements with no discernible effect on real output.

It's unfortunate for Lucas that he as only 2 countries in his sample that have highly variable inflation rates while the rest have very stable inflation rates, however his results and the theory he develops in the first part of the paper imply strongly that this is not unfortunate for the residents of those other 16 countries.

The point though is that Lucas' data show that, historically, volatile inflation has been associated with monetary policy losing its ability to increase real output, this implies that keeping NGDP stable at the expense of volatile inflation is a bad idea.

In fact, in Lucas' data Austria, Denmark, West Germany, Italy and the Netherlands all have average NGDP growth over 8% and yet all have coefficients on output that are of the same order of magnitude as the one for the US. This suggests that perhaps, just perhaps, the poor response of real output and employment to higher NGDP after the oil shock actually was a result of monetary policy but that the average growth rate of NGDP being too high was not the problem.

More importantly for my purpose it shows that the arguments of the market monetarists that NGDP targeting is a good idea because it's better at handling supply shocks is not consistent with theory or history.

Misreading Graphs, Assuming Your Conclusion and Getting Your Own Argument Wrong

2011-11-12T13:42:00.000-08:00

Scott Sumner replies to this post and catches me making a pretty embarrassing mistake. I claimed that the unemployment rate in the 1960 recession stayed stable at 5% when actually it didn't, it rose to around 7%. My eye had literally read right over the jump in unemployment without seeing it, suffice to say the "Misreading Graphs" part of the title of this post refers to me. However, the thing is that it doesn't matter that much, the reference to the 1960's was an afterthought when the real point of the post was to point out that keeping NGDP growing didn't seem to do any good when faced with a supply shock.

So, what about the "Assuming Your Conclusion and Getting your Own Argument Wrong" part of the title? That part applies to Sumner.

Assuming your conclusion

Sumner begins his discussion of the 1974 oil shock and subsequent economic performance with this:

NGDP growth rises sharply in the early 1970s, from barely over 5% to a peak of 12.5% in 1973. Then it falls to about 8% in the recession. Also recall that market monetarism is a natural rate model. That means even if NGDP growth had remained at 12.5% in 1974, and even if there had been no oil shock, we still would have expected a recession. The preceding demand-side growth certainly pushed unemployment below the natural rate, and hence a relapse was inevitable in 1974

Now, I know that I'm a bit challenged in reading these plots but nonetheless, it's clear that unemployment is above 5% from 1971 to the beginning of 1974 which is the same value it was for the expansionary periods of the 1960s up until about 1966. From 1966 to 1970 the unemployment dips below 5% as nominal growth rises above 5% so one can actually make the argument that unemployment has been pushed to low but then the recession of 1970 was the one that would have restored equilibrium.

After the 1970 recession unemployment is something like 6% and gradually falls back to 5% over the years 1971 to 1973. Is that below the natural rate? Well, NGDP growth does average around 10% for those years and Sumner apparently takes that to imply that whatever level unemployment was at it must be below the natural rate. However, since actual unemployment never falls below 5% that must mean that there has been an unobserved, and unexplained, shift up in the natural rate of unemployment. He's effectively assuming his conclusion, unemployment didn't behave as expected so that must mean that the natural rate had changed.

Getting your own argument wrong

Now, let's suppose for the sake of argument that the Fed began following an NGDP level targeting scheme after the 1970 recession. The scheme is as Sumner calls for now, you set a level target for NGDP that rises at a fixed rate per year. This means that undershoots and overshoots are made up for. However, suppose they'd chosen to raise the target level at 10% per year instead of Sumner's favoured 5%.

Well, in this case the path of NGDP growth might look just as the actual path did. Coming out of the 1970 recession NGDP accelerates quickly to near 10% but the Fed doesn't tighten yet because it is still below target, the Fed needs to make up for the previous undershoot. NGDP growth gets up over 12% and stays there for a bit more than a year by which time the Fed is at or a bit above target so the Fed begins to tighten, bring the growth rate temporarily below 10%. The point is that in the first half at least of the 1974 recession NGDP would have been just about smack on the level target and yet RGDP would be plunging and unemployment spiking.

As I said before, the behaviour of NGDP during this episode is entirely consistent with the Fed following an NGDP level targeting regime, it's exactly as the market monetarists would hope, and yet the economic performance in the face of a supply shock is abysmal.

Arguing my point for me

Here's another quote from Scott:

Now add on the fact that there was a severe real shock to the economy, in the form of a dramatic reduction in OPEC oil production. Also recall that our economy was much more oil intensive back then. The easiest way to consider this case is to assume the AD curve is a hyperbola. Then if aggregate supply shifts left, we’ll have a recession, even with NGDP targeting.

Well yes, we agree that output would fall but Bill Woolsey had explicitly argued that one of the reasons that an NGDP target was preferred was that if a supply shock hit and wages are downwardly sticky then raising prices would maintain employment, this didn't happen. Of course that's because the natural rate of unemployment went up and monetary policy can't prevent that!

But then what advantage was gained by keeping NGDP on target? That's all I'm asking.

The magic number

Finally we have this from Scott:

To add insult to injury, Adam suggests that market monetarism is somehow to blame for the inflation overshoot of the late 1970s. Recall that NGDP grew at an 11% rate from 1972 to 1981. We recommend a 5% rate. Those extra six percentage points pushed inflation from 2% to 8%. There’s no mystery here, inflation rose because the Fed was ignoring the advice of market monetarists, and regular monetarists as well.

Well, I don't see where I ever suggested that market monetarism was to blame for the inflation overshoot. My point was that keeping NGDP on a level target apparently did no good. This passage does however reveal pretty much the entire substance of Scott's argument, it was all because they chose the wrong growth rate for NGDP! Had they grown it at 5% instead of 10% everything would have been fine?

Well, except that unemployment still would have risen because that was the natural rate increasing. Inflation wouldn't have overshot? Oh, but real GDP growth was -2.5% in the depths of the recession and remember this was due to a supply shock so you can't blame the Fed for it. Thus maintaining a 5% NGDP growth rate would have still required pushing inflation to 7.5%. Oh, and Sumner can't save his story by saying the problem was with expectations because the whole problem in the 1970s was that the inflation was expected.

I still think this is an ideal test case, the behaviour of NGDP is perfectly consistent with a level targeting regime and yet the outcome is horrible. Furthermore keeping NGDP on target, even Sumner's preferred target would have required a huge and useless rise in inflation.

This is better than low and stable inflation?

NGDP Targeting and Supply Shocks

2011-11-07T12:47:00.000-08:00

It seems that one of the main arguments in favour of NGDP targeting is that its handling of supply shocks is supposed to be preferable to the outcome under inflation targeting. David Beckworth makes that argument here and Ryan Avent does it here.

To take a more specific example, here's Bill Woolsey saying something that, to my reading appears entirely consistent with what Beckworth and Avent are saying:

The implications of "supply shocks" play a key role in market monetarist thinking. If potential output changes, then firms will need to adjust their prices to clear markets. Adam P. argues that this will create welfare reducing fluctuations in inflation.

Consider what Adam P.'s argument implies. If there is an adverse supply shock, with potential output falling or growing less than the expected amount, then nominal GDP targeting will imply excessive inflation. With nominal GDP remaining on target, the equilibrium level of the prices of output rises. (Nominal incomes, including nominal wage rates, continue to grow at trend.)

How would inflation targeting fix this problem? The monetary authority would slow nominal GDP growth when there is an adverse supply shock, so inflation rate would remain at trend.

Now, consider a specific example--a bad harvest for corn. According to Adam P., what should happen is that the monetary authority slow nominal expenditure in the economy, to keep the inflation implied by the higher price of corn from "reducing welfare" due to its arithmetic impact on the price level. What that really means is that all the other prices in the economy, including nominal incomes like wages, must grow more slowly. The price of corn, then, rises slightly less than it would with nominal GDP targeting, and all the other prices are slightly lower than they would otherwise be. If those other prices, for example, wages, are sticky, then the effort to reduce the "welfare loss" from inflation causes a recession...

To be clear, Bill's post is long with many more details so I risk quoting out of context here but I actually think the whole argument is confused nonsense so I'll leave it to any interested reader to go to Bill's post and read the whole thing.

Now, the thing about supply shocks is that there really isn't anything monetary policy can do to "fix" the problem, one of the reasons that inflation or price level targeting is better is exactly because there is no attempt to fix a problem that is not amenable to a monetary solution.

The part that's really interesting is the last bit that I've cited, "If those other prices, for example, wages, are sticky, then the effort to reduce the "welfare loss" from inflation causes a recession". Bill is apparently claiming that under an NGDP target the recession would be avoided.

Now, the first question is in what sense Bill thinks NGDP targeting would avoid recession, by construction a drop in output is unavoidable since that's what "supply shock" means. I suppose he means that a rise in unemployment would be prevented, that would be consistent with his reference to sticky nominal wages.

So what about that? Would keeping NGDP stable prevent a rise in unemployment after a supply shock? Well, fortunately we have some data available to us and we at least one episode that is nearly universally regarded as a supply shock, the oil shock of the 1970s. This is the supply shock, the one that gave rise to real business cycle theory and the rational expectations revolution.

Below is a time series plot of real GDP growth, nominal GDP growth and the unemployment rate during the 1970s. On the eve of the supply shock NGDP growth is running about 10%, real GDP growth is running around 5% and unemployment is about 5%. Now, 10% NGDP growth is a higher level than you'd typically choose to target but the important thing to notice is that in the preceding 4 years or so the unemployment rate is extremely stable right around 5%, inflation is also very stable as both real GDP growth and NGDP growth are accelerating virtually in parallel. It certainly looks like an economy in equilibrium.

Now, when the shock hits real GDP growth of course plummets as is required for the episode to warrant the name "supply shock", but look at NGDP growth, it is remarkably stable! This is exactly the response of monetary policy and NGDP growth that the market monetarists want, this is supposed to prevent unemployment from rising but if fails miserably! Unemployment rises sharply and remains elevated for several years.

Furthermore, as we all know there was subsequently an acceleration in inflation that got somewhat out of hand, you might even say an inflation overshoot perhaps?

This is an amazingly pure test case, NGDP did exactly as the market monetarists would want and the whole thing is a total failure. Monetary policy does not appeared to have fixed the situation.

An Example of Good Monetary Policy

To conclude lets take a look at another historical episode. The following plot shows NGDP growth, real GDP growth, inflation and unemployment from 1957 to 1967 in the US. Inflation is extremely stable while real output growth varies a lot and thus NGDP growth is very volatile as well (both inflation and NGDP are included because the inflation series is ex food and energy).

Unemployment stays stable around 5% the whole time. So, which outcome do you prefer?

Scott Sumner says "I make no apologies for ignoring these little toy models, and having my policy analysis incorporate a complex mixture of politics, macroeconomic history, well-established basic economic principles, and logic."

I pointed out here that "well-established basic economic principles" shouldn't really be on that list, can we strike "macroeconomic history" as well?

Update: Bill Woolsey has responded with a post that completely misrepresents what I said, again. This is getting tedious....

Here's Bill:

Adam P. shows some charts where he claims that the record of the seventies proves that a stable nominal GDP growth path would have adverse effects due to supply shocks.

Is that what I said? Can someone point to where I said that stable nominal GDP gowth "would have" adverse effects? I'm not claiming to show that maintaining the growth rate of NGDP caused the poor outcome and I don't need to show that to make my argument. I'm only trying to give a counter example in which maintaing NGDP growth failed to prevent the bad outcome. (The comment about the subsequent inflation overshoot was also not a claim that NGDP targeting was its cause since the Fed wasn't actually targeting NGDP at the time, it was just a reference to our previous discussion.)

Bill again:

What is more incredible, is that he counts the sixties as a period of inflation targeting, where unemployment held stable at 5 percent due to the stable inflation rate.

Really? I said that the sixties were a period of inlation targeting? Can somene please show me where? No, the point was that in 1960 there was a very large, sharp drop in NGDP growth, an NGDP shock that had absolutely no adverse effect on employment. The Fed clearly didn't attempt to "fix" the situation and the outcome was just fine.

Now the fact that the better outcome did happen to coincide with low and stable inflation is suggestive but I never claimed that the Fed was targeting inflation at the time. In any event, the real point of the examples is to show that maintaining NGDP growth appears to have nothing at all to do with the quality of the labour market outcome.

The Problems with NGDP Targeting in Theory and Reality

2011-11-06T13:18:00.000-08:00

I've spent the weekend trying to get the market monetarists to actually explain why we should expect nominal GDP targeting, level or growth, to really be the panacea they claim it is (see my last several posts). Thus far, still nothing but assertions of their correctness without much backing it up so I thought I'd do a post summarizing my case against it.

Theory

Any case in favour of NGDP targeting must start with the view that money is non-neutral and that monetary easing is at least partly reflected in increased real output instead of only raising prices. This basically means you must believe in some variant of the Phillips curve. Generally this means believing in some form of sticky prices and/or wages. Scott Sumner for one frequently cites price/wage stickiness as the source of money's non-neutrality.

Well, there's a problem here. When you actually work out the effects of sticky prices/wages you don't find that it implies targeting NGDP as being in any way optimal. The first problem is that in any reasonable description of the world potential output must be allowed to vary, that is there are supply shocks.

The second problem is that variability in inflation is itself welfare reducing because with sticky prices it implies that transactions are taking place at prices that are different from the level that would imply the optimal allocation. Thus extraneous variability in inflation is welfare reducing.

These two points already show that NGDP targeting is suboptimal because keeping NGDP on target while potential output varies implies unnecessary inflation volatility. However, we can go even farther. In such models what you hope to do is stabilize the output gap and inflation separately, however since any variation in the output gap feeds into the Phillips curve and shows up in actual inflation it generally turns out that stabilizing inflation is the way to stabilize the output gap.

So, from the theory there's no support for NGDP targeting. Of course, the market monetarists also tend to appeal to pragmatism in arguing for an NGDP target. So what about that?

Reality

In a paper that has been central to the discussion Laurence Ball showed that if the Phillips curve has any weight on lagged inflation then NGDP targeting has another problem, an overshooting problem. Basically stabilizing NGDP in response to a shock entails inflation and output oscillating inefficiently around their trend values. Again, this extraneous volatility is welfare reducing relative to a first best policy.

The responses to this result have tended to either ignore the optimality issue entirely or to critique Ball's specification of the Phillips curve. I'm not defending Ball's specific model but the important point is that the overshooting problem applies to any specification with any weight on the backward looking inflation term. Now, the theoretical models discussed above don't usually have any weight on lagged inflation and this point featured in prominently in Scott Sumner's response.

Well, here's where reality gets in the way of a good story. The thing is, empirically the Phillips curve is very well studied and it is pretty much universal that in order to get anything like an acceptable fit the lagged inflation term has to be there. That pesky data! There have even been several theoretical attempts to generate a Phillips curve that depends on lagged inflation to be consistent with this fact, (most theoretical models imply that the Phillips curve depends only on expectations of future inflation).

None of the responses to Ball's paper addressed the overshooting issue yet the data demands that they do if they want to claim NGDP targeting to be the cure all for the economy.

It seems to me that NGDP targeting has flaws both in theory and reality.

Monetarists Misunderstanding Other People's Arguments (and misquoting them): Bill Woolsey edition

2011-11-06T03:55:00.000-08:00

So Bill Woolsey also has a response the my Laurence Ball post. It's not any better.

He begins by quoting me out of context, the part where I work out the two period ahead nominal income stabilization rule in Ball's model was in direct response to what Nick Rowe had said, it wasn't central to the point of whether NGDP targeting is a good idea or not. There I was mainly critiquing Nick for failing to at least take the question seriously.

Then Bill goes directly to the dynamic instability point:

Why would any economist take seriously the claim that a constant nominal GDP could possibly cause prices to veer off to infinity and output to zero, and then have output veer off to infinity and prices fall to zero?

Why do all the monetarists want to focus on this instead of the relevant question? I gather it's because to the instability point they have a response while nobody actually has a rigorous argument that NGDP targeting is in any sense optimal.

But seriously, what if an NGDP target causes oscillations of output and inflation, in response to a shock, that die out over time but are still unnecessary? Isn't that almost as bad? And again, doesn't the fact that your rule would consider this situation a success say something about your rule?

It doesn't matter though, the fact is that output variation and inflation variation are different, they have different causes and consequences and it's not a great idea to confound them. As I keep saying, one of the reasons an nominal income target is inferior is because some output fluctuation is efficient and this immediately implies that hitting the target would necessitate inefficient volatility in inflation, and that's something you get out of a completely forward looking model with no backward looking terms in the Phillips curve.

Bill ends with this:

With nominal GDP targeting, the equilibrium price level is the target for nominal GDP (if it actually will be reached,) divided by potential output. If the system is expected to work, the expected equilibrium price level is the target for nominal GDP divided by expected potential output. And, as usual, the equilibrium level of output is potential output. If the price level is set at the expected equilibrium price level, and nominal GDP is on target and potential income is at the expected level, then real expenditure will equal potential output. The price level will clear markets and real expenditures will purchase potential output.

That has to be the where any model begins.

I certainly don't disagree but the problem is that his argument actually implies that an inflation target is superior. The reason is that potential output is neither constant nor observable, as it varies around the value of NGDP that is optimal changes as well unless you want inefficient, and welfare reducing, volatility in inflation. On the other hand, if you stabilize relative prices so that price/wage stickiness doesn't distort the real outcome then you get exactly the outcome Bill describes. If you target NGDP with any variability in all in potential output then you don't get the outcome Bill describes.

A Simple Minded Non-Response from Scott Sumner

2011-11-06T01:47:00.000-07:00

So Scott Sumner has responded to my post on Laurence Ball's paper and to the paper itself. The problem is the response is completely vacuous, the usual assertions but, as always, nothing backing them up.

Sumner starts with an appeal to authority:

I’m especially unlikely to respond if the macroeconomist I most respect (Bennett McCallum) thinks the argument has no validity.

Hmm, is that what McCallum said? I assume that we're again referring to this paper from McCallum, this is the paper that David Beckworth also cited as showing that Ball's result is fragile. Have either of these guys actually read the two papers in question? McCallum shows that dynamic instability result is fragile, that's true but completely irrelevant, Ball even acknowledges that the dynamic instability is special. It's also uninteresting. What matters is what's optimal and Ball claims that nominal income targeting is inferior to inflation targeting in general, nobody seems to want to address that claim.

Sumner then continues, after a bit of complaining about his irritation with the model he gives us this little gem:

I don’t think the real interest rate measures monetary policy. To the extent that interest rates matter at all, I believe it is the nominal rate minus expected NGDP growth. But I’d rather just leave interest rates out of my “simplest imaginable model,” and stick with NGDP shocks and sticky wages as my explanation of changes in real output. And I’d rather model inflation (or better yet NGDP growth rates) via expected future NGDP, and hence expected future monetary policy. The hot potato effect. I’m not saying the output gap plays no role, but it’s much more complicated than the second equation implies.

Come back to me later when Ball has a model in which output fluctuations are caused by NGDP shocks and sticky wages, not real interest rates.

Now it's not an appeal to authority but the assertion of authority. Real interest rates don't matter. So, where does the rest of the economics profession get the idea that real interest rates do matter? From basic economic reasoning! The real interest rate is just a relative price, does Sumner not think that the relative prices of apples and oranges has any effect at all on the relative demands for them? Matt Rognlie here gives a fine explanation of the effects of real interest rates in a different context here. The fact is that it's impossible to write down any economic model with more than one period and agents that actually optimize utility, that is behave rationally, and not have the real interest rate be the most important macroeconomic variable by far.

However, Sumner is getting somewhere when he talks about wage stickiness (price stickiness works as well). So what do actual economic models that incorporate price and/or wage stickiness say?

Well, one thing they don't say is that NGDP targeting is a good policy. In fact such models explicitly imply that NGDP targeting is a lousy idea. The reason for this is that not all real output fluctuations are either inefficient or amenable to a monetary solution, thus stabilizing NGDP necessarily means extraneous volatility in inflation and all of these models would imply that that is welfare reducing.

Furthermore, talking about the importance of expectations of future monetary policy for behaviour today doesn't overturn that result, if anything if reinforces it! In the class of models I'm talking about expectations of the future path of monetary policy is the most important driving factor and yet NGDP stabilization is suboptimal. How is it that Scott Sumner thinks so much of these models yet thinks the conclusion is wrong?

Sumner's response contains a lot of complaining and, as always, a lot of asserting but no real reasoning and no attempt to actually address the issue at hand.

Sumner concludes with this:

I make no apologies for ignoring these little toy models, and having my policy analysis incorporate a complex mixture of politics, macroeconomic history, well-established basic economic principles, and logic.

There we find the biggest problem of all, in Sumner's arguments "well-established basic economic principles" are nowhere to be found.

Fixing what's wrong with NGDP targeting.

2011-11-05T12:44:00.000-07:00

NGDP targeting is getting a lot of attention of late. As I see it there is a major flaw in this idea.

There are good economic reasons why inflation that is too high, too volatile or both reduces welfare. There are good economic reasons why excessive output fluctuations may reduce welfare. Furthermore, the long run is different from the short run, excessively volatile inflation and/or output can potentially reduce long run growth.

Put all that together and it may sound as if targeting NDGP is a good idea. However, there are two, closely related, problems.

1) Not all real output fluctuations can be remedied with monetary policy, the rate of productivity growth is quite variable and their are real frictions.

2) With an NGDP target inflation and output can still be very volatile even while NGDP remains roughly constant.

These problems of course interact, if full employment, potential, output falls below trend then achieving an NGDP target entails increasing inflation and vice versa when potential output rises temporarily above trend thus making inflation at least as variable as productivity growth unnecessarily.

At the same time, to the extent that their is a short run Phillips curve, when potential output rises temporarily above trend the tightening required to hit an NGDP target will tend to reduce both inflation and output causing an unnecessary loss of real income.

Both of these issues suggest that an inflation target might be superior to an NGDP target. However, to the extent that there may be times, like the present, when inflation is around its target value and yet output is depressed due to a lack of demand then additional monetary easing is likely to be welfare improving.

Thus, it seems a rule that has the policy interest rate react to both inflation and output might be optimal but that rule should overweight inflation relative to output. In short, an optimal rule would look a like the original Taylor rule.

I'm sort of responding to this post from Andy Harless a while back arguing that an NGDP target is basically similar to a Taylor rule but preferable for a variety of reasons. It seems to me the opposite is true.

In my last post I discussed a paper from Laurence Ball that shows nominal income targeting to be suboptimal in a standard class of models because they generate unnecessary oscillations in both inflation and output in order to keep nominal GDP on target. The fact that this would count as success under an NGDP targeting regime shows that the target doesn't make any sense at all.

Monetarists Misunderstanding Other People's Arguments (and not really trying): Nick Rowe edition

2011-11-05T05:40:00.000-07:00

Greg Ip refers us to this excellent paper from Laurence Ball which shows that targeting NGDP is a pretty lousy idea. One can see immediately that Ball must be spot on from that fact that none of the usual suspects, Scott Sumner or Nick Rowe for example, has even acknowledged the existence of the paper even though Nick actually did a post responding to Ip's article! Nick just ignored the part of Ip's article where he discusses Ball's paper and pretends not to notice that Ip even provides a link, this is not good. The reason of course is that Ball is right and targeting NGDP is simply a horrible idea, if there was a counter-argument that even sounded coherent those guys would have each done a post on it.

I asked Nick about this in the comment section of his blog and after a couple of off the top of his head sort of retorts he comes back with this:

Adam: I have now read Larry Ball's 1999 paper. OK, I didn't really read it, but I looked at the model. (The math wasn't anyway near as scary as I thought!)

The intuition behind his result is exactly as I guessed. Assume r causes y with a one period lag, and r causes p (inflation in this case) with a two period lag. Larry Ball says that targeting inflation gives you good results, and targeting NGDP gives you bad results.

That is correct. And it will also generalise beyond the strict assumptions in his model.
But that result has nothing to do with whether the target variable is inflation or NGDP.

What his model really shows is that if you target with a 2 period horizon you get better results than if you target with a 1 period horizon.

Suppose half the components of the CPI react to r with a 1 period lag, and the other half of the CPI reacts with a 2 period lag. If you target inflation at a 2 period horizon all is well. If you target inflation with a 1 period lag you will get low variance in total inflation but big oscillations in relative prices.

Oh dear, no that is not correct. None of it. If this is a homework assignment then Nick Rowe gets a failing grade. The worst part is that, as he apparently prepares to give testimony to the BoC on what would be a good framework for monetary policy he can't take the time to actually check if what he's saying makes sense.

The first problem for Nick is that in fact the model in the paper implies that the way to stabilize two period ahead ENGDP is to stabilize one period ahead ENGDP. However, we can ignore that and work out a policy rule on the interest rate that tries to directly stabilize ENGDP two periods ahead which is apparently what Nick has in mind.

Well, I sat down this morning and worked out the implied policy rule for the interest rate that stabilizes expected NGDP two periods ahead (this took just a few minutes) and it generates exactly the large oscillations in real income and inflation that Ball obtained with the rule that actually would be correct in his model.

The Model

Ball writes down the simplest model you can imagine:

y = -b*r(-1) + l*y(-1) + e
pi = pi(-1) + a*y(-1) + n

Here, y is real income, pi is inflation (both as deviations from trend) and e and n are shocks. The notation y(-1) denotes one period lagged income, etc.

This is just an IS curve and an accelerationist Phillips curve. When discussing NGDP targeting Ball solves for the interest rate rule that sets E[y(+1) + pi(+1) - y] = 0, the implied rule for r then implies dynamics for y as:

y = (1-a)*y(-1) + pi(-1) + e

Combining this autoregressive process for y with the Phillips curve generates dynamics in which y and pi have to oscillate persistently in order to keep one step ahead expected NGDP constant at trend.

Now, Nick apparently wants to set r so that E[y(+2) + pi(+2) - y] = 0, as should be obvious, this generates an outcome that is even less desirable. The implied rule sets r according to the autoregressive process:

r = (l+a)*r(-1) + (1/b)*(l*l - 1 + a*(1+l))*y(-1) - (1/b)*pi(-1) + e;

(The coefficient on r is the letter l added to a). Substituting back into the IS equation gives dynamics for income of:

y = -(l+a)*r(-2) - + l*y(-1) - K*y(-2) + e

One can already see that at best you get similar oscillatory behaviour for y and pi but wait, it's actually much worse. For reasonable values of l and a the system has no solution! Ball takes baseline values of l =.8 and a=.4, for these values the coefficient on r(-2) is greater than one and so if one continues the back substitution we see that r must spend most of its time at or very near zero in order to have a finite value for y, but of course if that happens then pi blows up.

So, Nick's response falls flat on its face. What about other potential critiques?

1) The model is backward looking. Ball deals with this in his paper, here is an excerpt:

The result that output and inflation have infinite variances may appear
too extreme to believe. Indeed, recent work by McCallum (1997) and Dennis
(1998) shows that the result is not robust. Reasonable modifications of the
Phillips curve, equation (2), produce finite variances of output and inflation
under income targeting. Dennis, for example, shows that the variances are
finite if inflation depends on both past inflation and expected future inflation.
This is true even if the future-inflation term has a small weight, so the Phillips
curve is close to my purely backward-looking equation.
These results do not, however, overturn the conclusion that income targeting
is an undesirable policy.While infinite variances are a special result, it appears
that income targeting produces finite but large variances under a broad
range of assumptions. The reason is the overshooting phenomenon discussed
above. The overshooting result appears robust; it arises, for example, in Dennis’s
model, as long as the lagged-inflation term in the Phillips curve has a positive
weight. In that model, the oscillations die out over time, implying finite variances.
But the variances are still large relative to efficient policies.4

2) The paper only deals with NGDP growth targeting, NGDP level targeting is still a good idea. Andy Harless tries this one in the comments to Ip's original post.

Nope, Ball deals with that in another paper. Here's another excerpt:

An earlier version of this paper (Ball 1997) considers level targets, and shows that they have equally poor properties.

3) It's all driven by the fact that monetary policy effects output with a one period lag but inflation only with a 2 period lag.

It's true that this assumption drives the result, but no you can't dispense with it to save NGDP targeting as a good policy. That assumption is nothing more than the assumption of some form of price stickiness that you need to get any real effects out of monetary policy. Without such an assumption then money would be neutral and again targeting inflation would be superior to targeting NGDP (growth or level).

4) (Update) Ryan Avent fails worst of all. Here's him addressing Ball's paper:

Again, I fail to see how this is much of a criticism. A central bank that consistently overshoots will fuel instability. Surely the Fed's economists, being sensible men who have done their jobs for long periods of time, recognise that policy impacts both inflation and real output? Surely that's a dynamic they build in to their policy decisions? And surely they therefore recognise that in targeting NGDP they should opt for interventions small enough to keep NGDP from swinging well above or below target?

Ryan, you have to understand the paper to critique it intelligently! What happens in the model is not that NGDP swings above and below the target, NGDP stays basically on target, it's just that this isn't necessarily good! The reason it's bad is because while NGDP stays on target inflation and real output are oscillating above and below target and real output is the thing we actually care about most!

You can't cheat this, inflation targeting is simply better.

A Monetarist Assuming his Conclusion

Now here's Nick looking at Canadian inflation and NGDP growth and concluding that since inflation stayed pretty much on target but is still below target that an NGDP target might be better. Are you sure?

The two time series plots that Nick looks at could just as easily be read as evidence that NGDP targeting would be destabilizing. After all, to raise NGDP back to trend would require monetary easing.

In the Ball model it's easy to see what goes wrong, in the first period y is raised by enough to make up the difference and get NGDP back to its trend line. This however means that in period two inflation increases and so NGDP is above trend, the result is a tightening that brings real income back below trend in period 3, and the process repeats.

With a forward looking Phillips curve things are no better, the monetary ease to bring NGDP back to trend raises expected inflation, this shifts the entire Phillips curve in an adverse way making it necessary to either overshoot inflation, as in the Ball model, or to take persistently depressed real income. This is not a good outcome.

NGDP targeting, level or growth, is just a lousy idea and no amount of repeating the faith on the part of the market monetarists will change that.

[Update: David Beckworth does address the Ball paper in his response to Ip. For the most part he cites the McCallum and Dennis papers that Ball responds to in the passage I quoted after 'other complaint' number 1 above, he then states "Thus, there have been no robust studies that show nominal GDP targeting increases volatility".

Indeed, but isn't the issue optimality? Ball's response is to say yes, the explosive variance result is not robust but that in itself doesn't mean NGDP targeting is superiour inflation targeting. Ball maintains that the superiority of inflation targeting is robust.]

[Update 2: Bill Woolsey also at least acknowledges Ball's paper in his response to Ip but simply says

"I don’t believe this is realistic. That is, Ball did develop a model that has this consequence. His model of the macroeconomy was pretty standard. However, I don’t believe that it is realistic to expect inflation and real output to wander arbitrarily far from their long run levels when nominal GDP grows on a target growth path. Something is wrong with these models"

That is an incredibly weak response, "I don't believe..." is hardly an argument. Where is the reasoning to believe something is wrong with "these models" instead of something being wrong with NGDP targeting?]

Cause and Effect

2011-10-30T04:32:00.000-07:00

Here's a question that everyone who wants to understand economics should ask themselves:

If I flip a coin and it comes up heads, did it come up heads because the tails is facing down or is the tails facing down because it came up heads?

I suppose the most common answer to that question would be to say both (or neither), neither one causes the other. Yet when commenting on macroeconomics both economists and non-economists alike are constantly asserting that in fact it's one or the other.

Here are few examples of what is effectively the same question, just cast into other contexts:

Is Japanese inflation low because the yen is high, or is the yen high because Japanese inflation is low.
Does China have a lot of dollars because they run a trade surplus with the US or does the US run a trade deficit with China because China holds a lot of dollars.
Do we currently suffer from a lack of demand or a lack of supply?
Is there excess demand for money or deficient demand for goods and services?
Does higher expected inflation cause higher nominal wage settlements or do higher nominal wage settlements cause higher expected inflation?

Questions 1 through 5 are basically the same question with the same answer as the coin flip question I asked above, yet many people are quite sure that the answer to 3 is lack of demand, the answer to 4 is there is an excess demand for money and the answer to 2 is that China has dollars because the US consumes too much. Further, much commentary on the implication of rational expectations implicitly assumes that the answer to 5 is unambiguously and always that expected inflation causes higher wage settlements, this is a serious misunderstanding of what rational expectations means.

Endogenous and Exogenous Factors

Before anyone gets the impression that I'm trying to argue that nothing is explainable by economic theory let me come to the point. You can't get cause and effect from entirely endogenous variables, at least not in equilibrium. You need to look for something exogenous to play the role of a causal factor.

To take an example, I strongly believe that the answer to 2 is that the US runs a trade deficit with China because China buys a lot of dollars, however the reason I think I can make a causal statement is becuase Chinese forex policy seems to clearly be an exocgenous factor.

Another example is the answer to question 5 in the 1970's, in that case I think you can say that expected inflation led to higher wages because there had been an exogenous policy shift to attempt to trade off a permanently higher inflation rate for a permanently lower unemployment rate.

The Monetary Transmission Mechanism

The motivation for this post comes from the comments section of this post over at Matt Rognlie's. I'm talking about the exchange Matt has with Nick Rowe on the transmission mechanism of monetary policy.

Here's Matt describing the monetarist version of the transmission story:

So let’s suppose that demand for base money suddenly increases. (And hey, I’d even be happy with M1.) The old monetarist story is hydraulic: everybody wants 10% more money, they can’t possibly achieve this in the aggregate without deflation (impossible due to sticky prices), and in their efforts to privately hoard money by refraining from purchases, they only manage to bring down GDP.

But refraining from purchases isn’t the only way to get more base money. If you have any liquid assets at all (and most people, at least ones with budgets of economically relevant magnitude, do), it is easy to liquidate them and get base money. It seems much more plausible to me that someone will say “hmm, I need more base money, why don’t I take some cash out of my account?” or “I want more money in my checking account, why don’t I transfer some more from my savings account?” than “hmm, I need more base money, so I’m going to refrain from making otherwise useful purchases in an attempt to conserve what I have”. At most the effect on economic activity should be marginal.

Now, in practice it isn’t, but that’s because of the price response: as everyone tries to grab more of the fixed supply of money, the nominal interest rate increases to clear the market, until the marginal investor is no longer interested in money after all. And this higher rate alters incentives for everybody in a substantial way: it makes all kinds of consumption and investment more expensive.

To me the most important thing to notice is that under normal conditions market clearing will require a change in interest rates to reconcile intertemporal utility maximization conditions with the change in consumption/investment behaviour so you can't really say what causes the aggregate effect, the change in money demand or the change in interest rates it causes. The essential thing that makes this story "monetarist" is what's taken to be exogenous, the assumed shock is an exogenous shift in money demand.

The problem of course arises when we find ourselves in a situation, like right now, that doesn't fit with normal conditions. With the nominal interest rate at zero monetary expansion can't lower the real interest rate directly in the manner that Matt describes. Now it suddenly becomes crucial to understand what actually drives the aggregate effect of increasing the current money supply. On this point the body of Matt's post makes it pretty clear that only the interest channel is a plausible transmission mechanism.

Ok, Matt's post actually critiques the "new monetarist" transmission mechanism, not the old monetarist one. However, it's even easier to see that under zero nominal interest rates monetary expansion will have no direct effect on anything. After all, the idea that if you force economic agents to hold more aggregate real balances then they want they'll attempt to shed the excess balances by increasing real expenditures completely breaks down with zero nominal rates, after all the opportunity cost of holding money balances is the foregone interest. That's the one point that monetarists always skip when denying the existence of the liquidity trap, if an agent is happy to hold a short-term bond at zero interest why would he be unwilling to hold currency? (Yet Scott Sumner has explicitly claimed exactly this.)

Now, this is not to say that monetary policy has no effect at the zero bound. Matt gives a nice treatement of it here, but it does say that the only reasonable story for the transmission mechansim is the New Keynesian one. At zero interest rates there is no "hot potato" effect on money, in the liquidity trap money is a cold and raw potato being stored for future consumption.

Conclusion

The point of course is that we need to beware of claims about cause and effect among endogenous variables. The arguments that Nick was making, and the arguments that Scott Sumner continually makes, are based on the idea that you can make unequivocal statements about cause and effect among endogenous variables, but at market clearing values no endogenous variable can be said to cause any other, to say something about causation you need to begin with an exogenous shock to the system.

Furthermore, we need to be careful with stories about the out of equilibrium effects that bring about market clearing, for example the "hot potato" stories about the effect of monetary expansion. We can only make conclusions about the effect of monetary expansion by tracking its effect on all market clearing conditions and if one of those effects breaks down we need to return to first principles, a structural model, to see what effect we should expect.

This last point is important as many seemingly straightforward and plausible stories of the current situation fall apart when you look at their implications for variables not directly part of the story, one equation economics never works! This is true of the idea that our current weal economy is due to an excess demand for money and it's true of the idea that the Fed can hit any level of NGDP it chooses.

Liquidity Provision vs Stimulus: Understanding the difference between QE1 and QE2 (and twist).

2011-10-16T07:04:00.000-07:00

There's been plenty of debate in the blogosphere recently about the IS-LM model. In particular, while Paul Krugman and Brad Delong have been defending it one of its critics has been Matt Rognlie. To my understanding Matt's critique comes down to the assumption of an exogenously fixed money supply, central banks don't fix the money supply anymore (if they ever did) so you can't get reasonable conclusions out of the assumption that they do.

While I tend to side with Krugman and DeLong on this I actually think the model is best saved by re-interpreting the LM curve as the set of (Y,i) pairs that equate the supply and demand for liquidity, not the set of points that equate the supply and demand for money. One thing that needs to be stressed here is that the standard IS-LM model only has two assets, money, which pays no interest but serves a liquidity purpose and bonds, which pay a yield but are relatively less liquid. In the model money demand is liquidity demand and money supply is liquidity supply. That's not true of the real world. So, I tend to think the model always really meant the LM curve to be the set of (Y,i) points that equate the supply and demand for liquidity.

The Aggregate Supply of Liquidity

Holmstrom and Tirole have an entire book (Inside and Outside Money) based on the premise that the aggregate supply of liquidity is limited because there is a limit to how much output can be pledged externally, basically this comes from various things like agency problems and information asymmetries that induce some sort of limited commitment on the part of the insiders to any productive enterprise.

The important point though is that this is basically a technological constraint on the economy. Furthermore, since their are similar limits to the amount of output that the government can extract to back its claims we see that their is effectively an exogenous limit to the aggregate supply of liquidity.

If we combine this sort of market incompleteness with the "liquidity supply = liquidity demand" interpretation of the LM curve then I think we can get back to thinking about the economy in pretty much the original IS-LM framework with an exogenously given liquidity supply.

This framework can then be applied to several issues, in particular to understanding the difference between what the Fed was doing in QE1 versus QE2 and twist.

QE1: Liquidity Provision

The first round of asset purchases, in which the Fed almost entirely bought agency debt was about provision of liquidity. Essentially you had a large stock of claims that were liquid and had ceased to be so, the Fed was attempting to replace some of them with claims that would still serve the liquidity purpose. To see that this is so one only needs to notice that, as Stephen Williamson had pointed out, the Fed was actually a net seller of Treasuries during that time.

In the IS-LM framework this was classic monetary policy, there had been a reduction in aggregate liquidity that shifted the LM curve to the left. The fed responded by increasing the supply of liquidity to shift the LM curve back out to the right.

In so far as the fall in output was quickly arrested and deflation averted I'd say this worked in exactly the way expected. Of course, we haven't returned to full employment, or even much in the way of employment growth. That's what QE2 and twist are about.

The Liquidity Trap

Of course the fall in output didn't go with a rise in the risk-free real interest rate so to be consistent with observation the model must be consistent with the IS curve shifting as well. I think this is a reasonable interpretation of events.

Along with the liquidity shock we had a large increase in risk premia, that means that a given risk-free real interest rate will now imply less aggregate investment than previously and that would show up in the IS-LM model as a shift in the IS curve. In this case the IS curve has shifted so far left that the full employment level of Y corresponds to a negative i, the liquidity trap has sprung.

QE2 and Twist: Stimulus

In the context of IS-LM the second round of QE and twist, where the fed buys up yielding assets with low yielding reserves, are about lowering risk premia and thus shifting the IS curve back out. This is stimulus to investment in the same sense that a lowering of the interest rate is in normal times, this is an attempt at "normal" policy stimulus. Of course getting the amount right is much harder since we don't have so much experience with this, but it's not really any different from normal Fed policy.

PS: I think it's very important to notice that in neither case did QE have anything at all to do with the supply of base money per se. Matt is exactly right when he says "The messy regulatory and technical issues that determine banks’ demand for reserves on the fed funds market have virtually nothing to do with the effects of monetary policy on the economy. Obsessing over money demand is a waste of time." With that I couldn't agree more.

MMT

2011-08-28T10:09:00.000-07:00

Malthusian Monetary Theory, that is.

First a bit about Malthus, the economist magazine from August 6th describes him on page 62 as "a British economist who forecast that population would outstrip food supply". Although this seems to be a common conception of what Mathus predicted it's incorrect, this is not what a Malthusian model predicts. (I should point out that I'm basing this on Clark's book "A Farewell to Alms", I've not read the original Malthus).

The economist's description implies that Malthus predicted falling per capita real incomes as population growth outstripped food supply, what Malthus actually predicted was that in the long run per capita incomes should be constant as population growth offset productivity growth. What Malthus actually proposed was a neutrality proposition, the long-run neutrality of technology.

The Malthusian Neutrality of Technology

Matlthus' data came from a time when food availability was a binding constraint on real income and hence on population growth. What Malthus observed was that increases in food availability, productivity gains in agriculture, led to an increase in the population that continued until per capita food availability had fallen back to its original level. In fact, this observation pretty much directly implies that food availability was a binding constraint on population growth.

The mechanism would be as follows:

There would be an upward sloping relationship between food availability and child survival rates.
Food availability would be constrained by the level of agricultural technology.
If the child survival rate exceeded the population replacement rate so that the population was growing then food availability would be falling, thus lowering the child survival rate.
If the population was shrinking then food availability would be increasing, thus increasing survival rates.
The dynamics of 4 and 5 imply that the population level would find a steady state given the level of food availability and that an increase in food availability would increase the population by exactly the amount necessary to make per capita food availability return to exactly the level it started at.

The point here is that in the long-run technology was neutral, productivity gains were offset exactly so that per capita incomes, as measured by food availability, would stay exactly the same.

The further point is that the neutrality proposition depended on food availability being a binding constraint on income. When you're short of food you don't devote resources to the production of other goods, hence in the time that Malthus' data was generated food availability was a binding constraint on real income. When food ceased to be a binding constraint on real income then technological neutrality ceased to hold and instead technology became the binding constraint on income. Most importantly, the relationship between survival rates and food availability ceased to hold and population growth rates subsequently were determined by other factors.

Malthusian Monetary Theory

It's impossible not to notice the direct analogy between Malthusian technological neutrality and the long-run neutrality of money that comes out of most economic models. If money supply is increased relative to the demand to hold it this is supposed to result, at least in the long-run, in prices rising until the real value of the money stock has returned to the level demanded with no real effects. Furthermore, the quantity theory of money predicts a relationship between nominal income and the money supply that is in direct analogy with the relationship between food availability and population growth in the Malthusian model.

Most importantly, the relationship between the quantity of money and nominal income originates from a time when the gold standard was in operation, the data that motivated it were generated from an economy in which the availability of money was physically constrained and thus could be a binding constraint on economic activity. That is not true of fiat money systems.

Thus, the lesson of Malthus most applicable to the modern world is that there is no reason for the quantity theory to remain useful past the closing of the gold window, that you need to understand why it may be that MV=PY in order to know if the relationship is useful. When nominal interest rates were greater than zero then the money supply was a binding constraint on economic activity, kept that way by the central bank keeping a lid on the supply of money, but with nominal interest rates at zero there doesn't need to be any relationship between the supply of money and anything else.

This means, above all else, that since the relationship between money and activity was being artificially sustained once the gold window closed, it was never really the case that the money supply was fundamental to anything beyond its effect on real interest rates.

The collapse of China's economy

2011-08-07T22:17:00.001-07:00

It started on Friday. I'd guess they'll be broke by 2015.

QE3?????

2011-07-29T11:07:00.000-07:00

I don't think we're anywhere near that yet.

Notice that core inflation is basically right on the Fed's stated (though unofficial) target.

While markets whip themselves into a frenzy anyone who has actually listened to what Bernanke and other Fed officials have said couldn't fail to have noticed that they've been very consistent in doing what they said they would and they've been equally consistent in saying that in the long run stabilizing inflation, in both directions of course, is the only thing they really think monetary policy should try to do.

When core inflation was falling near .5% year over year they bought more stuff, but with core inflation above 1.5%? Not very likely.

Are Rebuplicans trying to get Obama impeached?

2011-07-18T12:23:00.000-07:00

The slapstick comedy routine that is the US government is having its shining moment and though logic still leads me to think they'll increase the debt limit and avoid a default and or closing down of government I actually don't really believe this.

For a while my view has been largely based on what I read in this post from James Hamilton. He gives the following quotation,

Larry Rosenthal, a professor at Chapman University School of Law, said ... a more persuasive argument is that the agreement in April to fund the government through the remainder of the 2011 fiscal year implicitly increased the debt ceiling. By passing that agreement, Congress essentially instructed Obama to spend money in the coming months. To pay for programs Congress authorized, the government will have to borrow money.

"It's basically an order to the executive-- pay this money," Rosenthal said. Even if the debt ceiling would block him from doing so, "when two laws are in conflict, the more recent law is understood to supercede the first law."

That, combined with this from Felix Salmon:

purely as a practical matter, it's far from clear that it's even possible to stop making the 3 million payments that Treasury makes automatically every day. Doing so involves a massive computer-reprogramming effort which I'm sure could not be implemented overnight-- and for political reasons nobody is going to get started on such an effort until after all hope is lost for a deal in Congress.

had lead me to think that congress won't pass the debt ceiling and nothing at all would happen. Payments would still be made as usual. How would such payments be made? Well, as Rajiv Sethi explains the Treasury would go into overdraft on its account with the Fed:

Strictly speaking, the Treasury could continue to make payments on all obligations authorized by Congress, simply by sending out checks as they come due. Commercial banks would undoubtedly accept these from depositors, confident in the knowledge that the Fed would create the reserves necessary to credit their accounts. If the Fed were concerned about the resulting expansion of the monetary base, it could neutralize this by selling bonds on the open market. The result would be an increase in the debt held by the public, with no change in the monetary base, which is exactly what would transpire if the deficit were financed by the issue of new bonds.

But then Sethi makes this ominous observation:

The problem, of course, is that the Treasury's account at the Fed would then be vastly overdrawn and the debt limit thereby exceeded. Instead of borrowing from bondholders, the Treasury would be borrowing, so to speak, from the Federal Reserve. I'm quite certain that in the current political climate this would be treated by Congress as a usurpation of its power, resulting in a constitutional crisis and possible impeachment.

Surely Republicans are aware of the impossibility of not making some of the payments, surely they're aware the Fed would allow the overdraft and surely they're aware that this might, just might, make a case for impeachment.

And really, if you don't think that Republicans would crush the economy to impeach Obama then that just means you don't know any.

How do Fed asset purchases help?

2011-07-14T14:38:00.000-07:00

By raising asset prices. It has nothing at all to do with increasing the money supply.

For the purpose of this post I want to take it as given that Fed purchases can raise asset prices. Casual observation of equity price seems to confirm this. I would point out though that it is often asserted that QE can only affect prices if there is some sort of market segmentation among assets and this is not true. The two trees principle shows that a real friction, adjustment costs to the capital stock, are enough.

The question then becomes, why would raising asset prices help? To answer that we need to ask a more basic question:

What do we lack?

Well, it certainly isn't money or liquidity that we're short of, nor is it safe assets. Basically we're short of nominal wealth. So why do we need more nominal wealth?

Well, for whatever reason the US is going to insist on running a current account deficit. You can blame Chinese and other Asian countries' exchange rate policy or something else, but that is the fact of current life. This implies directly that the US is net borrowing as can be seen from the fact that (X-M) < 0 implies that

Y < C + I + G

Furthermore, this fact of life implies that when demand falls a dollar short it's a low-skilled American worker earning the American real wage that loses his job and not a Chinese worker working at the Chinese real wage.

Now, the fact that the world, and in particular China, is willing to send us so many goods in exchange for paper that we can completely control the value of certainly seems like a good deal for us and it is. We surely don't want to discourage this sort of behaviour on the part of our trading partners! However, there is a catch. In order to maintain full employment the US economy in aggregate, public and private, needs to willingly consume/invest everything our fully employed economy can produce at home plus everything China is sending us, that's a lot of consuming and investing and since it exceeds our income that's also a lot of debt that we'd be issuing.

The problem then is how to get the economy to take on enough leverage to consume the sum of what China sends us and what we can produce at full employment. One answer that you hear a lot is for the government to do this on everyone's behalf, debt financed fiscal expansion. The problem of course is there's no way to get the government to buy the right basket of stuff and distribute it exactly the right way, in short this is a poor answer.

So we are left with the problem of inducing the private sector to willingly take on the debt to income level that is required to maintain full employment and this is where raising asset prices comes in.

The supply and demand for debt

I certainly don't want to go into all the determinants of the supply and demand for debt, only to point out that asset prices are one of them. My point is that asset prices are particularly important determinant of leverage levels because they affect both the supply and demand for debt.

In a world with significant costs to default it stands to reason that both borrowers and lenders would try to avoid defaults as much as possible. This consideration, combined with the substantial uncertainty both parties face, would lead both sides to a debt transaction to want the borrower to posses collateral that partly or wholly secures the loan. I stress that borrowers will generally want to have such collateral just as much as lenders.

The reasons that a borrower would get liquidity by borrowing against an asset rather than selling it are varied but I'd point out that one of the principle reasons is that the asset might provide a convenience yield that accrues to the borrower so long as he retains ownership of the asset. Houses are the obvious example of this but in fact this sort of dynamic is pervasive, for example banks hold most of their capital in high quality yielding assets like government bonds, and for a time unfortunately MBS, that are also used as collateral to settle trades.

The upshot of all this is that high and rising asset prices will facilitate private agents, both corporations and households, taking on increased debt to income levels and this is a necessary condition for reaching full employment. In the aftermath of the housing bubble many people decried the home equity lines of credit that supported consumption but this was silly, without an inducement for at least some set of agents to spend on credit the US would have found itself stuck in the low employment we have now for the entire decade.

Deficient Demand?

The story I'm telling is basically one of deficient demand but it's not the usual one. It's not due to agents hoarding liquidity or a disequilibrium due to an excess demand for money, there is clearly more than enough demand to make use of the output of our fully employed economy, there just isn't enough to make use this plus all the Chinese workers labouring on our behalf and any shortfall costs the job of any American worker who is doing something that can be done more cheaply in China (or Taiwan or...).

In the absence of a change to Chinese exchange rate policy the only route to full employment is to induce Americans to make use of all this potential output, that should be easy enough but this does require them to willingly take on higher and higher levels of debt to income. The only way to facilitate this is to pump the value of the assets that back the debt and that is something Fed asset purchases can do.

Monetarists misunderstanding other people's arguments

2011-07-07T23:29:00.000-07:00

Andy Harless responds to my last post in the comments section, this is a good response:

By your argument, we would have to say that, because wages are going up, there is no excess supply of labor. (To alter your words slightly, "In what economic theory does the value of something that is in excess [supply] actually [rise]?" Is there any reason that your argument should not be symmetrical?) If you want to take that position when the US unemployment rate is close to the highest it has been in 29 years...

The first thing to notice is that we mean real value here, the positive inflation rate means the real value of money is falling, and the wages Andy refers to are the real wages:

And they're rising, well, actually going sideways but they're higher than when the recession began.

Already you can tell a bit of a story here, the initial rise in measured real wages (during the recession) may reflect the fact that those losing their jobs were the lowest earners. Following that initial uptick real wages have been flat so already Andy is on somewhat shaky ground, real wages are a real candidate for the behaviour I said you'd expect of a price being sticky and failing to clear a market that is in excess supply. This price isn't going the wrong way, it's stuck at a level.

But wait, there's more. Productivity growth has continued, actually accelerated:

If you think about the firm's decision to hire an employee or not, it's clearly the unit labour cost that matters, in the formal models labour is supposed to be measured in "efficiency units". Well that fell in the recession and has since been flat:

So, the wage measure that matters has exactly the behaviour I said was needed to make the sticky price story work, it is stuck at a level, not falling but not going in the wrong direction.

Now the clincher, Andy asks "To alter your words slightly, "In what economic theory does the value of something that is in excess [supply] actually [rise]?"".

Is the real value of labour rising?

Seems to be falling.

Monetarists misunderstanding their own argument

2011-07-03T15:24:00.000-07:00

Here's Andy Harless in the comment section of this post trying to preach Milton's gospel:

There is absolutely an excess demand for base money, as evidenced by the many people who are eager to purchase base money with labor and are unable to do so at the current price.

Now you are going to say that this is not an excess demand for base money, because these people would just as willingly purchase bank deposits, or bonds, or perhaps even stock, with their labor. But this is beside the point. Yes, there is an excess demand for other assets as well. But that doesn't change the fact that there is an excess demand for base money. In fact, since bank deposits and high quality bonds trade freely against base money in liquid markets, there could not be an excess demand for base money if there were not also an excess demand for these other assets.

Andy's not off to a good start here. Even in the standard monetarist story it's not the unemployed who have the excess demand for money, it's the people who would buy the output of their labour but don't because they prefer to increase their money holdings.

Andy was actually doing a bit better on the previous post where he says:

The whole point of "excess demand" is that prices are not changing in such a way as to equalize supply and demand. If the price of money fell sufficiently, the excess demand would disappear. Prices as such tell you nothing about whether there is excess demand or excess supply. The point is that the quantity of money demanded is greater than the quantity supplied.

You're apparently assuming that there is some incomplete equlibrating mechanism in place that will lead excess demand to be correlated with a rising price (of money, that is, which means a falling price of goods relative to money). The problem is that the equilibrating mechanism is not working.

This is closer to a coherent story, the idea being that money is in excess demand and the corresponding excess supply is of labour. Sticky prices/wages are why prices are failing to adjust to clear the markets.

Andy also says:

If it could somehow be decreed that all prices and wages must drop by a certain (sufficiently large) percentage, then the output gap would be eliminated.

So basically Andy's story is that safe assets, of which money is one, are in excess demand, prices aren't falling to clear markets and this leaves labour in excess supply. Even if we ignore the problem of whether an excess demand for fruit is the same as an excess demand for oranges, casual observation shows that Andy's story doesn't even have a toehold on reality.

Now, something's price may not tell you if it is in excess demand or not but the rate of change of its price most certainly can. And if that price is sticky? Well, if that price falls then you can certainly say that the thing in question is not in excess demand.

The heart of the problem seems to be confusion between something being in high demand and something being in excess demand. The value of risky assets are below their peak, so we can agree that the demand for safety is higher than it was. The supply of money has increased a lot without causing very much inflation so we can agree the demand for money is higher than it was. However, the value of risky assets are rising, not falling. The price level is rising, not stuck at a level or falling too slowly. So, in what economic theory does the value of something that is in excess demand actually fall?

Now this...

2011-07-01T12:59:00.001-07:00

is a really great post from Stephen Williamson.

The Curious Incident of the Markets that Cleared in the Night (and Day)

2011-06-26T10:05:00.000-07:00

Inspector Friedman: Is there any other point to which you wish to draw my attention?

Sherlock Holmes: To the curious incident of the price of treasury bills in the night.

Inspector Friedman: But the price of T-bills did nothing in the night.

Sherlock Holmes: That was the curious incident.
...

David Andolfatto catches me making a silly mistake in my last post so I'm gonna try this one more time.

I'm arguing against the idea that the current slump is due to a lack of base money relative to the demand to hold it. This idea is quite obviously wrong to anyone not religiously devoted to its truthfulness and those that insist on believing in the excess demand for money story are led immediately to obviously wrong policy conclusions.

So, the question I'm asking is: where's the evidence that anyone who has a claim on base money is having trouble getting it? This is an important question. The idea that base money is in excess demand implies that certain markets are failing to clear. In order for this to be the case there must be some economic actors holding nominal wealth in another form (say bonds or foreign currency) and are unable to trade those claims for base money at market prices yet somehow market prices are failing to adjust so that someone will take the other side of the trade. There is no evidence of this (during the worst of the crisis, just after Lehman went under you could reasonably say this was the case).

So who do we think is demanding money in excess of what's available?

Consumers

Matt Rognlie has made this point several times (in the comment section) that any consumer with positive nominal wealth can have as much base money as they have wealth by simply going to an ATM and withdrawing the money (perhaps preceded by selling their assets into a bank deposit).

There have been no bank runs or freezing of deposit accounts that have left consumers with nominal claims that can't be liquidated into cash, there is clearly no excess demand for base money from consumers.

Banks

The candidate most people seem to have in mind is the banks. It seems to be a strongly held belief that banks aren't lending out their reserves because they want to hold them, presumably to ward off a run, and if they were just given some more they'd start lending out the excess.

It's nonesense. The way to see this is dead simple, banks aren't holding all of their liquid assets in reserves. I rather doubt they're even holding most of their liquid assets in reserves, they still hold T-bills, treasury bonds, and many other liquid assets all of which are easily tradeable into reserves. If any bank wanted more reserves it could have them, the fact that the prices of the liquid assets that banks hold isn't lower shows that banks are happy to hold them at current yields. There is no attempt from banks or anyone else to switch out of T-bills and into reserves, thus there is no excess demand for reserves on the part of banks.

Now, it may well be the case that banks are refusing to lend because they are short capital but that has nothing to do with the supply or demand for base money and can't be solved by the Fed buying T-bills for newly created reserves.

Firms

For firms the same argument as that for banks applies. The demand for liquidity and safety has clearly gone up but this is not the same as the demand for base money.

Policy Responses

In the comment section of a post at WCI Scott Sumner claims that it would be effective for the Fed to simply keep buying T-bills for base money. This is the view that I'm refuting here, this is the poor policy prescription that one gets from viewing the world through the quantity equation. This view is clearly wrong.

Again, to say that there is an excess demand for base money implies that some market is not clearing. Now, we can surely say that the demand for and price of liquidity has gone up. We can say that the demand for and price of safety has gone up. However, neither of these things is in excess demand. This is clear, the price of illiquid and/or risky assets has fallen but these prices are not still falling, their yields went up enough that people are willing to hold them.

To be clear, this not to say that I don't think QE is effective, I do. However, buying T-bills is not effective and it is silly to think it would be.

Is there excess demand for base money?

2011-06-21T15:03:00.000-07:00

For Scott Sumner this is basically a religious belief, he defines "tight money" as any situation where NGDP growth falls short of 5%, which means his view is basically vacuous. If you believe that everything that ever happens does so because it's god's will then what explanation can there ever be for anything other than "it's god's will"?

Nick Rowe also believes that an "excess demand" for money is the only thing that can possibly cause a recession, so again, if there's a recession it must be due to an excess demand for money. In the comment section of this post Andy Harless also makes the claim that "The problem is a lack of base money relative to demand."

What's the evidence?

If we agree to discount the faith based arguments then we are led to apply some basic economics to the question in the title of this post. In the basic supply curve/demand curve diagram an increase in demand, holding the supply curve fixed, is associated with an increase in price and an increase in quantity. On the other hand an increase in supply, holding the demand curve fixed, is associated with an increase in quantity but a decrease in price. Furthermore, if both curves shift then you can determine which one shifted by more by looking at price and quantity, if price decreased while quantity increased then supply increased more than demand.

So, what about money? Well, the first thing we need to ask is, what happened to the price of money?

We can express the price of any good in many ways, for example if apples cost $1 each, bananas $2 each and oranges $3 each then the price of of an apple in oranges is 1/3, in bananas it's 1/2 and in dollars it's 1.

For money the two most reasonable ways to express its price is against some sort of basket of consumption goods, like the CPI basket, or against bonds.

Over the roughly 3 years of the current slump the CPI price index has been roughly stable while the supply of base money has increased dramatically. That seems to point toward an increase in the demand for money but, since the price of money relative to the consumption basket has been roughly unchanged there appears to be no excess demand for base money. Andy Harless got this one wrong. The price of money relative to goods implies that the increased demand for money has been satisfied by the increased supply.

Furthermore, the price of money relative to bonds has fallen. ~~Relative to bonds base money is in excess supply, not excess demand.~~ In fact, during the height of the crisis bond prices, in terms of base money, went up and not down. From the very beginning of the slump money was never in excess demand. ~~and now it's in excess supply.~~

The religion that is monetarism simply failed to lead us to the truth in this episode, asking "what would Milton say?" is unhelpful. Milton would give the wrong answer.

Fiscalist Hyperinflation

2011-06-14T15:00:00.000-07:00

Hoisted from the comments of my second price level determination post here's Andy Harless:

"If all CB assets are government bonds which are all now worthless they have no mechanism for reducing the money supply, ever."

The central bank can reduce the money supply to the public by raising the interest rate that it pays on reserves. Now of course this won't work if money becomes (or is expected to become, within a fixed amount of time) worthless, but as long as there is a chance that money will be worth something in the future, the CB can choose an IOR rate that outbids the expected future value of money by enough to compensate the banks and their depositors for the time value and the risk.

This reminded me of this paper on a fiscalist hyperinflation, here's the abstract:

ABSTRACT: Hyperinflation is usually interpreted as a result of the monetary financing of serious fiscal imbalances. Here, a fiscalist alternative is explored, in which inflation explodes because of the fiscal effects of monetary policy. Higher interest rates cause the outside financial wealth of private agents to grow faster in nominal terms, which in fiscalist models calls for higher inflation. If the monetary authority responds to higher inflation with sufficiently higher nominal interest rates, a vicious circle is formed. The model is particularly advantageous for hyperinflations in which most of the fiscal action concentrates in the interest bill on public debt and debt rollover, rather than seigniorage or primary budget deficits. Brazil in the late 1970s and early 1980s serves as a motivating case.

What does it mean to explain? (And why it matters.)

2011-06-14T14:52:00.000-07:00

In the comments to my last post Nick Rowe, in defense of the quantity equation, says:

The temperature of my house is determined by many things/equations. But it can be explained (within limits) by one equation: where I set the thermostat.

Now, the post in question was about price level determination and so I suppose that in principal he's not saying anything that's inconsistent with what I said. My point was mainly that price level determination required more than the quantity equation. Also, he puts in the "within limits" qualifier so he's being somewhat consistent again, one of the points of my post was basically that one equation may work in most circumstances but it will breakdown and you need to understand why that happens and what to do when it does. If Nick's house were on fire then the thermostat setting wouldn't explain the temperature very well and reacting quickly and effectively would be pretty important.

However, since he's brought it up I think it needs to be asked: does the quantity theory explain anything?

I'm gonna say no. The problem is that velocity is always left unexplained, it's supposed to be basically the reciprocal of money demand but in practice it usually is just taken to be defined by the quantity equation. In just about every application of the quantity theory to the real world all the work goes into explaining velocity, thus the quantity equation itself ends up explaining nothing.

A great example is given by Matt Rognlie:

Consider, for instance, the savage recession of the early 80s, which is near-universally acknowledged as the result of Volcker’s fight against inflation. Can we identify a change in the monetary base that matches the magnitude of the recession, or even comes close? Not at all; it’s barely a blip. What about a higher-level monetary aggregate like M2? Again, nothing. Compare that to the obvious slump in nominal GDP. When it mattered, velocity wasn’t so stable after all.

Why? It’s easy to interpret with the right theory. Consumers desire money balances roughly in proportion to their nominal income, with some adjustments made for the nominal interest rate. Consumers are also sluggish in reoptimizing their portfolios. When the Fed contracts the supply of base money even slightly, slow reoptimization means that a dramatic increase in the nominal interest rate is necessary to clear the market. Since interest rates are now well above the “natural rate”, we see recession and disinflation.
Does velocity-centric monetarism offer any similarly coherent account of the Volcker recession? I don’t see it. What made velocity collapse between mid-1981 and 1983?

In the comment section at Matt's place Nick responds:

Desired velocity depends on the expected rate of inflation. (Witness what happens to velocity in hyperinflations for empirical confirmation). When Volcker started talking about getting inflation down, and showed he was serious by contracting the supply of base money even slightly, expected inflation fell, and so desired velocity fell too.

So, by appealing to expectations Nick can explain the fall in velocity, but without the extra explanation the quantity equation is completely unhelpful. And Matt proved by example that you can give a similar explanation without invoking the quantity equation at all. The quantity equation didn't even help to explain anything.

So why does it matter?

It matters because invoking the quantity equation has a very strong tendency to lead to really bad policy conclusions.

One example is the the liquidity trap, looking at the slump as a sharp fall in velocity appears to imply that increasing M by enough will return the economy to full employment. You need to understand the consumption-saving-investment decisions of economic actors to realize this isn't so, in the liquidity trap velocity falls one for one with increases in M. It's not just that velocity fails to be stable in the sense of having random shocks, it fails to be even well defined. You can't get the right policy conclusion from the quantity equation.

At the same time, those people going out of their minds about quantitative easing also seem to be applying the quantity equation and fearing velocity can increase suddenly at any moment. You need to look beyond the quantity equation to see that this is not so.

Finally, the quantity equation alone would seem to imply that QE works the same regardless of what the central bank buys. Yet there seems to be general agreement that the effect is larger the longer the bond is that the Fed buys, how do you get that from the quantity equation? You can't, even the monetarists don't really think it fully explains nominal GDP.

Price Level Determination with One Equation?

2011-06-13T23:09:00.000-07:00

It's not possible.

In fact, in macro economics you can't determine anything with just one equation. Here's a quote from Paul Krugman that I like a lot:

What determines interest rates? Before Keynes-Hicks - and even to some extent after - there has seemed to be a conflict between the idea that the interest rate adjusts to make savings and investment equal, and that it is determined by the choice between bonds and money. Which is it? The answer, of course - but it is only "of course" once you've approached the issue the right way - is both: we're talking general equilibrium here, and the interest rate and price level are jointly determined in both markets.

My last post talked about price level determination without money. Basically the idea is that government budget constraint/valuation equation can also determine the price level but it doesn't do this in isolation. The rest of the model still matters, for example to endogenously determining discount rates.

Now, in the real world we do in fact have money so perhaps the point is only academic. I say no, I say:

What determines the price level? There seems to be some conflict between the idea that the price level adjusts to make the real money supply equal to the demand for real balances and that it adjusts to enforce the governments budget constraint/satisfy the governemnts valuation equation. Which is it? The answer, of course, is both: we're talking general equilibrium here, and the interest rate and price level are jointly determined in both markets.

This is, of course, not new, I'm just talking about Sargent and Wallace's unpleasant monetartist arithmetic here. Now, from the comments on my last post here's Nick Rowe making the claim that I think most monetarists would agree with:

if the central bank is genuinely independent, the central bank can remain solvent even if the government is insolvent. The liabilities of the central bank are not the same as the liabilities of the government

Basically Nick wants to say that, if the central bank is truly independent, the quantity equation wins out and the price level is determined by one equation. The central bank retains control of the price level.

I don't think that's true. I've already pointed this out in the case of a liquidity trap, now I'll make the argument more generally. Yes the CB can issue cash but in a hyperinflation I'd say the real seignorage revenue is going to zero. That pretty much makes the CB insolvent. Furthermore, the real point here is that even in the QTM the central bank can lose control of the price level. If all CB assets are government bonds which are all now worthless they have no mechanism for reducing the money supply, ever. Furthermore, usually the CB is restricted to only buying government bonds (or taking them on repo), the Fed needed special permission to buy MBS and even then only stuff guaranteed by the treasury.

If all government bonds are worthless than what is the mechansim for the CB to expand the money supply?

I suppose that you could let the CB buy and sell private assets in its OMOs to break the link with the government budget constraint but that doesn't mean we're back to one equation price level determination! It just means the central banks ability to control the price level is now dependent on other valuation equations, each of which is an equilibrium condition. If the value of all private assets crashes then not only does the CB lose the ability to reduce the money supply but, if asset values are low enough, it also has a limited ability to increase the money supply.

Finally, what about the CB just giving people money? Actual printed notes. Well, perhaps that allows them to expand the money supply at will. Perhaps then money supply contractions can be done by taxing the money back. Now are we back to just the quantity equation? No. First off, it's obvious in this case that the government budget constraint matters, if the government is short of money it ends up draining too much money out, thus forcing the CB to replace it. Effectively then the government can money finance itseflt, attempting to earn seignorage, and a loss of inflation control can immediately result.

Further though, velociy is endogenous remember, the risk of the government trying to earn too much seignorage effects things even if the government is behaving. The willingness of private agents to accept CB money depends on them believing they won't be expropriated, otherwise they'll just dump it as fast as possible driving it's value down and the price level up. Further, in an open economy (most of the ones we have) this will crush the foreign exchange value of the currency, thus driving up the domestic price level. In the German hyperinflation the government must have been collecting a lot of taxes in order to pay the repartations, it didn't control the price level that way.

You can't cheat the real economy with purely nominal assets.

Price Level Determination Without Money

2011-06-12T10:22:00.000-07:00

The point of this post is to describe a couple of theories of price level determination that apply to a world without money. On is the cashless New-Keynsian model and the other is the fiscal theory of the price level. The topic came up recently in discussions over at WCI where there was some misunderstanding about the fact that the cashless NK model does in fact determine the price leve, not just inflation, but it is the interest rate rule that does the work, it is different from the fiscal theory.

Setting context: The Quantity Theory of Money

The shortest way to describe the working of the quantity theory is to say that it takes as inputs the nominal stock of money and aggregate demand for real balances, then equilibrium requires that the price level adjust to make the real value of the money stock equal to the amount of real balances demanded.

Of course, stories of the mechanism that makes the price level move can differ but the basics of the model are as described above.

More context: Asset Pricing

The fundamental result of asset pricing theory is that just the absence of arbitrage implies the existence of a stochastic discount factor such that the price of an asset can be written as the discounted sum of expected cashflows weighted by the discount factor.

I bring this up because in the standard models the intertemporal budget constraint of the government has exactly the same form. This makes perfect sense. Imagine a company trying to finance an investment project with a given sequence of cashflows by issuing equity in the project. The value of the equity is the discounted risk-adjusted expected cashflows. Although it's not usually phrased this way this sum of discounted cashflows also effectively acts as a budget constraint, that's maximum amount of money that can be raised by the equity issuance. Any attempt to raise more just lowers the per share price so that the total value is unchanged. If the initial investment cost exceeds this value then the firm can't raise enough funds, it is in this sense a budget constraint.

The same goes for the government, the sum of the discounted risk-adjusted expected primary surpluses (real surpluses) both values the stock of government debt in real terms and gives the maximum amount the government can possibly spend today. Any attempt to spend more by issuing more debt just drives down the real value of the debt.

Price Level Determination in the Cashless NK model

In the cashless NK model the central bank determines inflation through its control of the short-term nominal interest rate. The central bank's ability to control the nominal interest rate combined with the stickiness of nominal prices means that the bank can control real interest rates and hence change aggregate demand.

In the model the government issues nominal bonds, just as in the QTM the stock of nominal government debt is taken as given. The intertemporal government budget constraint is just the real value of this stock of debt, this real value is determined by the discounted value of the real primary surpluses the government can generate.

It's now easy to see how the model determines the price level, the central bank reaction function (usually a Taylor rule but it doesn't have to be) specifies the conditional path of real interest rates and thus determines the real value of the stock of nominal debt. Basically the central bank determines the demand for real bond holdings.

The price level is now determined in a similar way to the quantity theory, it must adjust to make the real value of the stock of nominal government debt equal to the demand for real bond holdings.

The Fiscal Theory of the Price Level

The fiscal theory of the price level is superficially identical to the cashless NK model, it takes as given the stock of nominal government debt and determines the price level as the value of P that makes the real value of the stock of government debt equal to the value as a discounted sum of primary surpluses.

Are the two theories different?

The essential difference between the two theories is that the standard NK model assumes a Ricardian fiscal regime while the fiscal theory doesn't. That is the only difference. So, is it really a difference?

A Ricardian fiscal regime assumes that the government adjusts primary surpluses passively in response to changes in the price level. If a deflation raises the real debt burden the government actually raises the the primary surpluses to pay it off in real terms. In the non-Ricardian regime the government doesn't necessarily do this.

In a non-Ricardian fiscal regime, provided the fiscal authorities don't go and change the sequence of primary surpluses, a central bank that can control real interest rates can still determine the price level through the mechanism described above. On the other hand, in the Ricardian regime the government budget constraint can't determine the price level without the central bank since primary surpluses are determined partly by the price level.

The main difference is that the Ricardian regime completely takes the fiscal authorities out of the picture and leaves the central bank in complete control, there is never a conflict between monetary and fiscal policy. In the non-Ricardian regime there is potential for conflict, the fiscal authorities are determinig the sequence of primary surpluses and if they want to issue a lot of nominal debt not backed by future surpluses then they can create inflation that the central bank can be powerless to stop.

Which Regime is more realistic?

That's not obvious, the fiscal austerity in the US and UK, for example, can be taken as examples of governments trying to be Ricardian. In the US low inflation is raising the real debt burden and the government, through spending cuts, is at least talking about trying to generate more primary surpluses in response. On the other hand, the fiscal stimulus that was passed in 2009 reflects a fiscal regime. In response to the rising real value of the debt, thus relaxing the government budget constraint, the government proposed to take advantage of the relaxed constraint to increase expenditures funded with nominal debt.

The real conclusion is that though governments have an interest in appearing Ricardian lots of the time the truth is somewhere in the middle, fiscal inflations do happen.

Conclusion

The boader point here is that the price level can be determined without any use of the money stock, even in a world where money doesn't exist, and you can get insights into this world that apply fully to a world with money. For example, with or without money the price level can be determined by an interest rate rule. Even in a world with money a fiscal inflation can happen which the central bank is powerless to stop, after all the government budget constraint/valuation equation applies with or without money. Quantity theorists should beware, there's more to the price level than one equation.

It takes two to tango II

2011-06-03T00:47:00.000-07:00

Imagine that their are only two currencies, the domestic currency called dollars and the foreign currency called globos. The idea here is that the entire world outside the domestic country has formed a currency union.

Further, suppose that goods trade is entirely frictionless. No shipping costs or anything to prevent arbitrage of different prices. Thus PPP holds perfectly all the time.

Finally suppose there is absolutely no capital movement between the domestic country and the rest of the world because while the rest of the world is allowed to hold dollars the domestic residents are forbidden from holding globos. Assume that somehow the capital controls are 100% effective.

Now suppose that the rest of the world pegs the nominal globo/dollar exchange rate unilaterally. Suppose that this peg is 100% effective (possible if the capital controls are 100% effective).

Now suppose the rest of the world chooses an inflation rate of -10% per year. That is, they choose 10% deflation.

PPP and the nominally fixed exchange rate mean that the domestic country also gets 10% deflation no matter what the CB does, no matter how many dollars it prints.

It might be wondered how the domestic central bank can print unlimited amounts of dollars without causing inflation somewhere, perhaps not domestically but in the foreign economies.

The mechanism would work as follows:

If domestic prices failed to fall in line with foreign prices then dollars would flow out of the domestic economy. Maintaining the exchange rate peg then forces the foreign authorities to absorb the dollars.

Now, to do this they may well have to issue globos and buy the dollars so how do they maintain their deflation? Well, they then have to tighten monetary policy some other way, higher interest rates or reserve requirements (maybe eventually exceeding 100%) which takes the globos back out of circulation.

The net effect of this sequence of actions is that the dollars have effectively been confiscated. That's why I said they "may" have to issue globos to buy the dollars. The might just directly confiscate the dollars.

Either way, any time the domestic price level tries to move above the foreign price level the goods market arbitrage that enforces PPP will cause all the extra dollars to flow out of the domestic economy where they are simply confiscated and taken out of circulation by the foreign authorities.

The domestic central bank is then powerless to change the domestic rate of inflation through monetary policy.

If the domestic country is unwilling to either put in their own controls on capital (which then prevents trade in goods since the foreigners can't hold dollars) or somehow interferes in the goods market in another way (to break PPP) then they will have no control over their inflation rate at all despinte having complete control of the domestic money supply.

New Keynsian models are models of the Phillips curve, not the business cycle.

2011-05-04T11:16:00.000-07:00

Oh dear, Casey Mulligan really is clueless. I say that not because it's the topic of this post, only because it reminded me to write this post.

The thing is, the canonical NK model really isn't a model of the business cycle, or at least not a new one. The business cycle generated by NK models is a real business cycle, without a real shock there can be no recessions in the model. In fact, in the canonical NK model the labour market is identical to the frictionless RBC labour market.

What NK models add are an explanation for the observed Phillips curve, an (very plausible) explanation of why it shifts and a plausible mechansim for amplifying and transmitting small, sector specific (or local) real shocks into large economy wide shocks and the consequent scope for monetary policy to stabilize output.

In short NK models are the business cycle models that RBC models want to be (or should).

PS: It is worth also mentioning that while RBC models need an actual reduction in productivity to generate a recession NK models can get one with a shock to the rate of productivity growth (that is not observed in real time by the central bank). This is also a much more plausible recession generating mechanism then the standard RBC one.

Stephen Williamson completely stops thinking.

2011-04-30T10:47:00.000-07:00

Here's Stephen Williamson claiming that QE2 is irrelevant, here he is repeating the argument more succinctly. It's all complete nonsense.

Here's his simplified argument:

Suppose a financial intermediary that holds long-maturity Treasury bonds, and finances this portfolio with a sequence of repurchase agreements, with the Treasuries used as the collateral in the repos. Suppose also that this intermediary, and the counterparty in the repo transaction, both have reserve accounts with the Fed. Now, one morning, when the intermediary needs to repurchase the Treasuries, it sells the Treasuries to the Fed in exchange for reserves, then transfers the reserves to the repo counterparty. What has changed here? First, some private economic entity now has reserves instead of a collateralized overnight loan (repo), where the collateral was the Treasury bonds. Second, the Treasuries are now at the Fed instead of at a private intermediary. Nothing of substance has changed. The Treasuries used in the original repos are backed by the full faith and credit of the United States of America, as is the reserve account. Nothing of substance has changed.

Isn't it funny how the backing seems to be the only relevant feature of the assets? (He also, subsequently, mentions liquidity differences of the bond and reserves.) The risk return profile doesn't matter? Really?

He doesn't ask himself why the intermediary is levering to buy treasuries. Presumably the reason would be to earn the carry, the intermediary earns the spread between the yield on the treasury and the overnight repo rate. In return for this the intermediary bears the price risk of the bond, this is a classic carry trade no different from buying the higher yielding currency.

This sort of carry trade was done with various ABS during the boom, particularly backed by mortgage pools. This in turn created a demand for the securitized pools and thus led to a lot of mortgage financing, the point being that this sort of trade was essentially financing real assets, housing, during the boom.

Of course, when it's financing the treasury it doesn't lead to more investment unless the government does the investing, something the US government isn't interested in doing right at the moment.

Now, when the Fed steps in and buys the treasury isn't it reasonable to expect that the intermediary will either find another yielding asset or buy another treasury to put a carry trade back on?

If it buys a new treasury then whoever sold the treasury will presumably reinvest the proceeds in a yielding asset. Either way it's virtually certain that somebody will buy a privately issued security to replace the yield of the treasury bond that the Fed bought (certain because if the intermediary wanted to sit on reserves or make overnight loans it could have already had that, so it clearly wants to take some risk and earn a return).

Of course, that's the point of QE, to ~~force~~ encourage private sector asset holdings into real assets and thus funding real investment and that's why it clearly reflates equity prices even though the Fed isn't buying any equities (see Nik Blanchard here).

Finally, Williamson of all people should be the first to tell you that reflating asset prices is one of the best things the Fed can do to encourage private credit creation and investment.

He apparently just doesn't want to see it.

Is China being bad?

2011-02-13T08:37:00.000-08:00

The answer is going to be yes and the forex peg is the reason, but it won't be for anything they're doing to the US. My last three posts have been a lead up to this one.

This post is also a response to Nick Rowe who asked on my last post

Let's switch to a slightly different thought-experiment. Suppose I, as an individual, tried to create 0% inflation in Canada, because I didn't like the Bank of Canada's 2% inflation target. Could I do it? If not, what's the difference between me and China?

The answer to that question is connected to the answer to the question of whether or not China is being bad.

Size Matters

First Nick's question, clearly the answer is no Nick can't personally change Canada's inflation rate but why not? Well in a perfectly competitive market Nick is a price taker so can't really effect the price of anything. The usual intuition is that Nick is too small a part of the market.

If we move to monopolistic competition then Nick has pricing power in his own output and maybe he can do something to change Canada's inflation rate. Of course, in the international market for manufactured goods if we identify countries as the competing units then we're pretty clearly talking oligopolistic competition where countries can exert substantial price effects.

To take an example, suppose Nick and I were the only two people providing blogging services to Canadians, that there was a paying market for this service and that this sector was, say, 10% of all economic output in Canada and 10% of the CPI basket of goods. Further suppose our two blogs are perfect substitutes for one another (clearly fantasy since I have about 5-10 readers as best I can guess, but humor me). So actually it's not actually monopolistic competition it's straight oligopoly but the argument will carry over. If Nick decided to compete with me by undercutting my prices by say, 20%, then I'd have to match him or lose the whole market.

If this happened then the CPI basket's price would be reduced by 2%, enough to bring down Canada's inflation rate to zero in the absence of a response from the BoC. Essentially China is undercutting US prices in manufactures, a sector that is probably something like 10% of the US economy (I don't know but for this it doesn't matter what the right number is). This puts downward pressure on US inflation.

Now, presumably the BoC would respond by easing so Nick would have to continue lowering his prices to offset this. This is basically what China is doing when they match each Fed easing with a local tightening, the pegged exchange rate means Fed easing is also Chinese easing but also Chinese tightening is US tightening. Notice I haven't mentioned the tradeable vs non-tradeable distinction yet, this will appear soon.

So what rules out this behaviour of Nick in the usual sort of models? Well, optimizing behaviour. In the example Nick and I have some sort of marginal cost of producing the service and to keep Canada's inflation at zero he'd have to very quickly reduce his price below his costs. If the story had an initial condition that was equilibrium then Nick was optimizing and his 20% price reduction was therefore, by construction, suboptimal for him. Nick would not be acting in his own best interest.

China's badness

This leads naturally to the question of China and the connection to my previous posts. China is not acting in their own best interests. So why do they do it? Well, there's only one Nick but lots of Chinese. In particular some Chinese work in the tradeables sector and some in the non-tradeables. China is acting in the interests of those Chinese that work and own capital in the tradeables sector at the the expense of those that work in the non-tradeables sector.

Basically the combination of the forex peg and keeping domestic inflation low has the effect, through the mechanism describe here, of keeping the REAL wages of the workers in the non-tradeables sector below their free market levels. This creates a surplus which accrues to those in the tradeables sector, particularly the capital owners I'd imagine.

This is wrong, it's basically exploitation and it is why I so intensely dislike the Chinese exchange rate peg and their disingenuous wining about Fed policy.

It takes two to tango

2011-01-30T11:53:00.000-08:00

In one of his blurbs Paul Krugman made a comment, he attributed it to Rudi Dornbusch, that it takes two nominals to make a real (I can't remember where I read this so no link).

In the case of a real exchange rate it actually takes three nominals, the home price level, the foreign price level and the nominal exchange rate. My last two posts have been about the interaction of something called the Balassa-Samuelson effect, which predicts that higher relative productivity levels in the tradeables sector should go with higher real price levels, and incomplete nominal adjustment. To the extent that productivity gains tend to be higher in traded goods, like manufatured goods, then the Balassa-Samuelson effect implies that richer countries should have higher price levels in real terms. This last prediction appears to be born out by the data.

The Balassa-Samuelson effect gets translated into an effect on nominal variables by some form of incomplete nominal adjustment, a pegged exchange rate is a good one there.

So, imagine you're Ben Bernanke. Do you have more or less complete control over US inflation or NGDP growth over some horizon, say a year? Seems most monetarists would say yes, Scott Sumner would and I'm pretty sure so would Nick Rowe. Sumner's NGDP targeting ideas are all dependent on the ability of US monetary policy to completely control US NGDP growth.

Now imagine also that the second largest economy in the world, and a huge US trading partner, pegs their nominal exchange rate to the dollar and doesn't allow their price level to rise. Further suppose they are a developing economy with super fast productivity growth in the tradeables sector and possibly little or no productivity growth in the nontradeable sector. Finally, on top of all that suppose they've pegged their nominal exchange rate at a value below that which the equilibrium real exchange rate implies it should be, given the initial values of their nominal price level and the US nominal price level.

Well, US inflation and NGDP growth are going to want to fall and you, the chairman of the Fed, are going to have to work hard to prevent this should you view deflation as undesirable. Furthermore, your attempts to prevent domestic deflation will manifest themselves as much in pressure for inflation in your trading partner's economy as in your own. Your trading partner might even start complaining about this rather loudly.

If the trading partner in question was sufficiently determined to neither change their nominal exchange rate nor accept domestic inflation then they'd meet each additional monetary ease of the Fed's with a tightening of their own. Just as Fed ease was sending inflationary pressures to this trading partner, their tightening would be sending deflationary pressure back to the US. In the end you may well end up in a stalemate, with the Fed embarking on large scale monetary stimulus with little apparent effect.

If you're Bernanke and this is happening to you then you know what may actually be the worst part of all? You may well end up having economists of every stripe criticizing you, all for different reasons. Monetarists claiming you're not doing your job, how could you let NGDP growth fall when stabilizing it is so easy? Just offset those pesky velocity shocks. Others saying that the stimulus you are providing is reckless and crazy, it risks high inflation here yet does nothing but generate inflation in your trading partner's economy that they are powerless to stop! No reasonable person could expect them to float their currency after all. All the while some members of congress are blaming you for pesistently high unemployment while others are screaming bloody murder you dare do anything at all when anything you do so obviously has no effect on anything except foreign inflation!

If you're Ben Bernanke right now, you don't have a fun job.

Nominal stickiness, Balassa-Samuelson and why MV=PY is useless.

2011-01-30T04:20:00.000-08:00

Just a quick note to clear up some potential real/nominal confusion from my last post. The Balassa-Samuelson effect is entirely about real quantities, it says that the country with the higher productivity level in tradeables will have a higher price level in real terms. To turn that into a nominal effect you need some sort of incomplete nominal adjustment, either of a pegged exchange rate (as Andy Harless suggested in the comments) or nominal wage stickinesss (as I had in mind) will work. As an aside, this is a bit weird since it's stickiness causing something real to have a nominal effect, usually we think of it going the other way, of stickiness being the reason nominal things have real effects.

Nonetheless, the point made in that post still stands. If there is incomplete nominal adjustment either in the foreign exchange market, perhaps because another country has pegged their exchange rate to yours, or nominal stickiness in home markets you can have apparent shifts in V that have nothing at all to do with the demand for real balances and the real effects will not be amenable to any of the monetary remedies that interpreting them through the quantity equation would suggest. To me this makes the quantity theory pretty much useless.

As a sort of PS, nominal stickiness is itself a bit of a conundrum. It sort of seems to be there, though the point is certainly not settled, yet it's incredibly hard to tell a good story as to why. It's also a bit funny that the one set of prices that certainly aren't sticky, asset prices, tend often to look like they should be stickier!

Purchasing power parity, real business cycles and why inflation is NOT always and everywhere a monetary phenomenon.

2011-01-25T15:29:00.000-08:00

The blurb below is something I wrote a year or so ago for the benefit of some younger colleagues. I was reminded of it today when I heard an FX strategist making the claim that theory unambiguously predicts that higher inflation currencies should depreciate in nominal terms. This claim is of course patently false, he based it on the assumption of PPP but putting aside the empirical problems with PPP even as a point of theory he's wrong. There is something known as the Balassa-Samuelson effect that implies that if a country has faster productivity growth in its tradeables sector than in its non-tradeables sector its price level should be rising, and if the productivity growth in its tradeables is faster also than that of its trading partners then it would experience both inflation and an appreciating currency. For unmistakable examples of this see Japan in the 60s and 70s or China today.

The original blurb was written to make the point that inflation is sometimes not a monetary phenomenon, it also shows that sometimes inflation is a sign of something good happening. The story is based on a parable of Paul Krugman's that can be found here, in what follows it assumes Krugman's hot dog and bun economy as context. Here's the gist of the parable:

Imagine an economy that produces only two things: hot dogs and buns. Consumers in this economy insist that every hot dog come with a bun, and vice versa. And labor is the only input to production.

Suppose that our economy initially employs 120 million workers, which corresponds more or less to full employment. It takes two person-days to produce either a hot dog or a bun. (Hey, realism is not the point here.) Assuming that the economy produces what consumers want, it must be producing 30 million hot dogs and 30 million buns each day; 60 million workers will be employed in each sector.

Now, suppose that improved technology allows a worker to produce a hot dog in one day rather than two. And suppose that the economy makes use of this increased productivity to increase consumption to 40 million hot dogs with buns a day. This requires some reallocation of labor, with only 40 million workers now producing hot dogs, 80 million producing buns.

Let's extend the discussion to talk about how productivity growth in one sector, but not others, can cause inflation without any base money growth. Krugman doesn’t mention it but the way the transfer of labour into the bun sector is affected goes something like this:

1) since there are more hot dogs then people want and fewer buns the price of the buns rises relative to the price of hot dogs (I haven’t said yet what happens to the absolute price of hot dogs), so far wages haven’t changed yet.

2) Relatively higher margins in the bun market cause employment in the bun sector to want to expand relative to the hot dog sector, thus wages rise in the bun sector (relative to hot dog sector wages)

3) Eventually enough labour has moved from the hot dog sector to the bun sector to restore an equality of wages, otherwise labour would want to keep transferring until there was nobody left making hot dogs.

Now, so far nothing can be said about absolute prices and wages. The relative increase in bun prices/wages could happen by hot dog prices/wages falling or by bun prices/wages rising. However, suppose that hot dogs are tradable internationally and the economy is small relative to the world economy (and a price taker in world markets). Then the hot dog sector can export the surplus so they have no reason to lower prices or wages or employment. Thus the relative price change is entirely in the form of higher bun prices, thus:

4) the higher bun prices mean higher profit margins in the bun sector (wages have not yet changed).

5) To increase bun production they need to hire labour and the higher margins allow for a higher wage to be offered

6) The higher bun sector wage makes ALL labour want to switch, but of course eventually hot dogs become scarce, their prices rise and then their wages rise to match the bun wages.

7) End result is that equilibrium is restored when real wages are equal in the two sectors but both wages have increased in nominal terms.

[Update on Jan. 27]~~An assumption that works just as well but does not require the good with the productivity gain to be tradeable is to assume~~ If we add the assumption that nominal prices and wages are downward sticky then the reasoning implies that prices and nominal wages must rise since real wages have risen. This is empirically an accurate assumption but I chose the other one because a) it is relevant to the current china situation and b) I didn’t want to have to try to explain why prices/wages are downward sticky. What's driving this is the substitutablitly of labour, since labour is equally useful in both sectors the real wages will tend to equalize so the bun sector workers benefit from the hot dog sector productivity gain just as much as hot dog sector workers. Furthermore, this is a good thing for hot dog sector workers as some will need to switch sectors and equality of wages is needed to affect the switch. The real wage though only pins down the ratio of W and P, if W won't fall then one way or the other P will rise.

I said there is no base money growth, the way exchange would be facilitated at the higher prices would be an expansion in the nominal value of credit (broad money growth without an increase in base money) so this is also an example of the real economy causing credit growth instead of vice versa. The leverage increase is no problem because the increase in output will increase incomes to support the increase in debt. The credit will be created when the hot dog sector borrows to finance the capital expenditure that causes the productivity gain in the first place. The increase in credit is spent on capital goods and then circulates in the economy as part of broad money thus facilitating transactions at the eventually higher prices. Thus, this is also an example of the real economy causing credit growth instead of vice versa. But of course, to an outside observer it might appear that the credit expansion caused the inflation but THIS WOULD BE WRONG. This inflation is manifestly not a monetary phenomenon.

It is worth noting as well that if that hypothetical outside observer looked at the economy through the quantity equation lens (MV=PY) it would appear that velocity had risen with the investment boom/inflation. But remember, velocity is just another name for money demand in this equation yet what happened has nothing at all to do with changes in the demand for real balances, it would be equally informative to attribute the boom to the good will of the gods.

Notice also that if the investment fails to increase hot dog sector productivity then the loan is defaulted on and broad money supply goes back to where it was, there doesn’t end up being any inflation. This explains how an economy can have a huge leverage increase with low stable inflation followed by a rash of defaults and contraction in credit, it happens if the investment doesn’t cause productivity gains (because, say, it is all spent on useless housing). I guess this is a story we all know well though. In this case our monetarist from the last paragraph would think that crazy velocity had just randomly fallen back down again, go figure.

I guess it should be clear now why you might have inflation and an appreciating currency, if the productivity growth in the tradeables sector is faster than the world average then the currency will clearly appreciate while the Balassa-Samuelson effect will generate domestic inflation.

Finally then, what about real business cycles? Well, it's simple, if the hot dog producing sector suffers a negative productivity shock instead if the positive productivity growth assumed above then the effect on the bun producing sector is exactly the opposite of the story told above, falling demand and falling real wages.

As David Andolfatto has been pointing out, this is a pure demand shock from the point of view of bun sector and if the bun sector in this parable represents the service sector of the U.S. economy then that's the sector that accounts for most of the employment of labour. What might generate a negative productivity shock to the hot dog sector? it could be something like a disease that kills the cows or pigs that are used for the meat, that would be the typical sort of example. However, as I pointed out before, it could simply a change in tastes. If hot dogs can be made of beef or pork and the capital stock is geared to producing beef hot dogs then a preference shift towards pork hot dogs would reduce hot dog sector productivity. Either way though this generates what appears to be demand shock in the bun producing sector but the shock has nothing whatsoever to do with money demand, nor is the shock amenable to a monetary remedy.

Now, to be clear, I'm a believer in the deficient demand idea though I think the problem is not that demand low relative to any sort of long-run norm but instead that the level of demand needed to maintain full employment is too high. This nonetheless implies that our high unemployment is due to demand being deficient. My point here though is that in reality it can be awfully hard to tell the if you're living through real business cycle or a monetary one.

Does inflation destroy savings?

2011-01-24T10:50:00.000-08:00

A commenter on my Ron Paul post notes:

The problem is not so much with wages as with wealth. Whatever bit of wealth you've accumulated just got sliced in half when prices double.

The sort of flippant response is to ask why you're keeping your savings all in cash? Forget inflation, if the risk-free real interest rate is even greater than zero, which it usually is, you'd be pretty silly to keep your savings all in cash.

I suppose you could say that it's unfair because those that leave their savings in cash are doing it because they don't know any better or because they don't want to pay the fees associated with investing in yielding assets but that's pretty weak. If you're gonna have the sort of free society most Americans seem to want then it's gonna have to be incumbent on those living in that society to figure some things out on their own, it's not really that hard. If you think that financial service providers are cheating the poor then the remedy should be to make them stop somehow.

There is a deeper moral point here though. If short term risk-free real interest rates have been pushed negative, as they are now, then protecting the real value of your savings does entail taking some risk. Pushing wealth holders to take on some aggregate risk in return for higher real returns is (one way to express) the point of generating expected inflation and that's where the economic stimulus comes from.

Nonetheless, this is risk the wealth holders clearly didn't want to bear. It was available before and they preferred to avoid it, only when the yield on their risk-free investments goes sufficiently negative do they take this risk on. Are they being screwed unfairly?

I'm gonna say no but it's pretty much a judgement call. The reason I say no is that you can't cheat aggregate risk, someone has to hold it or investment doesn't get done. If the only way to get investment funded is to make the real yield on risk-free investments negative then so be it. After all, if the fed lowers the short-term real interest rate from 5% to 4% then some who didn't want risky investments when risk-free could be had at 5% return will now take some risk, did these people get screwed? There is no difference really if instead the fed is lowering the real risk-free yield from 0% to -1%.

Now, one can make an argument that intervention by government agencies is always immoral and the Fed is screwing people when they lower risk-free real yields from 5% to 4% but this doesn't seem to be something many people have complained about and I do think that logically if you accept the 5% to 4% intervention then you have to accept the 0% to -1% intervention and so put this way I don't see that very many people have much to complain about.

Furthermore, to extent that getting people to hold this risk generates investment and gets other people a job when they'd be otherwise unemployed well, economics is about trade-offs and this is one where you take the jobs, the investment, the output. So all in all, I still think the Fed is doing the right thing and they should be doing more of it.

Do the Fed and the Treasury work together?

2011-01-22T09:21:00.000-08:00

So Stephen Williamson admits that maybe Bernanke knew what he was talking about on 60 minutes:

When Bernanke said in his 60 Minutes interview that QE2 was not about printing money, that sounded out of context, or misleading, but apparently he was (perhaps unintentionally) correct (so far).

But what about the "perhaps unintentionally" comment? Now here's Williamson a while back talking about the fact that QE2 wasn't increasing the money supply because the Treasury was draining reserves:

During the year, the balance in the Treasury's general account dropped by $31 billion, but the Treasury also accumulated $188 billion in its "supplementary financing account." This supplementary account was created in September of 2008, and is described here. Basically, the Treasury sells T-bills, in exchange for reserves, and deposits the proceeds in this supplementary account. The balance in this account peaked at about $560 billion in November 2008, went to zero for a period late in 2009, and rose to about $200 billion in April 2010, staying constant at that level since. The Fed thinks of this as a reserve-draining operation.

Thus, once we take account of accumulation of reserve balances by the Treasury, and reductions in lending by the Fed, total outside money has increased little in the past year...

So, "the Fed thinks of this as a reserve-draining operation." Doesn't that phrasing seem to strongly imply that Williamson believes the Fed and Treasury are co-ordinating what they're doing? But if that's what Willimason thinks then why not take Bernanke at his word, why the "perhaps unintentionally" comment?

Oh that Bernanke

2011-01-07T08:56:00.000-08:00

Yes the chairman of the Federal reserve is in fact the same Ben Bernanke of the work on credit intermediation with Mark Gertler, for example these pieces.

I only bring it up because Stepen Williamson seems to think that the reason for Fed asset purchases is to increase the money supply.

On the asset side, "securities held outright" has increased by about $300 billion, with an increase of about $230 billion in long-maturity Treasuries, and a net increase of about $70 billion in agency securities and mortgage-backed securities. However, on the liability side, the increase in outside money has been quite small, at about $15 billion ($54 billion increase in currency, $39 billion decrease in reserves). ...Indeed, if we take the Fed seriously that it wants to "quantitatively ease," it is not doing it, since the total quantity of Federal Reserve liabilities in the hands of the private sector declined in real terms during 2010

I think this just reflects the fact that Bernanke knows what he's doing and Williamson doesn't. It also appears to reflect the fact that Ben was telling the truth on the 60 minutes interview. Here's Williamson commenting on that interview:

Further, [Bernanke] says that the notion that QE2 involves printing more money is "a myth." What the Fed is really up to, according to him, is "lowering interest rates by buying Treasury securities." Maybe these comments were lifted out of context, but of course this is not correct.

Hmm, not correct? Indeed.

Sounds as though Bernanke was telling the truth, the Fed wants to lower the required real rate of return on assets, that is lower real interest rates, and is not expanding the money supply, just as Bernanke said. Furthermore this is clearly a sensible thing to do, in a liquidity trap the supply of money over some minimum is entirely irrelevant and this works in both directions, so there is no harm in keeping the money supply stable or even contracting it slightly.

On the other hand anyone who is a believer in the Bernanke-Gertler work, such as yours truly, would think that higher asset prices will facilitate growth. I've explained here that due to global imbalances the only way for the US to reach full employment is to induce the population to take on vastly increased leverage relative to their income, as they were in the bubble. Higher asset prices facilitate this in two ways, it makes borrowers willing to accept a higher debt to income ratio because their asset holdings will cover the debt. At the same time it makes lenders willing to lend to borrowers with high debt to income ratios for the same reason, the assets secure the debt.

Finally, if you're thinking that in QE2 has been a failure because interest rates on longer-term treasuries haven't declined I respond in two ways. Firstly, depending on what's happening to inflation expectations (something we don't observe) it may well be that the perceived real rates on treasuries has declined. Second, and most importantly, equity prices have been reflated substantially. On this you have to compare to equity prices prevailing when QE2 first began to be widely anticipated, not when it was actually announced, thus the relevant time to compare to is something like August 2010 if I recall correctly. But higher prices is just another name for lower required real returns, that is a lower cost of capital for firms. Thus real rates, broadly construed, have come down substantially.

All in all then, I tend to think QE2 has been a success and I think it, and Bernanke, deserve credit for the moderate improvement in the recent data. On the other hand, I think it's still way too small in size. I think higher inflation would be a big help and so would even higher prices of all assets, both treasuries and equities. I also think Ben wants to do more but is perhaps being slightly held back by political considerations and so what I'd like most of all is for Ron Paul to shut up.

Are real wages sticky, or are they stuck?

2011-01-06T15:47:00.000-08:00

Over at MacroMania David Andolfatto reminds us of the great Canadian employment slump of the 90s and warns that nobody can really be certain it won't happen to the US in this decade. This episode in Canada in the 90s is also discussed by Akerlof and Shiller in their book Animal Spirits.

At the same time, if you look out the window to your left you'll find Shimer and Hall suggesting that the data support the hypothesis that real wages are generally sticky. My source on what Shimer and Hall say is not actually Shimer or Hall, it's Andolfatto again speaking in the comment section of his blog. Nonetheless as a believer in stickiness I'm happy to take this at face value though it means I can't tell you what Shimer or Hall's story is about why real wages are sticky.

Suppose we take real wage stickiness as a potential explanation for the Canadian employment slump of the 90s and the current US employment slump. Does it make sense? Well, I'm generally a believer in stickiness but for 10 years? I mean, are real wages supposed to be sticky or stuck? And is there a policy solution to this?

On the other hand Akerlof and Shiller focus on downward stickiness of nominal wages and argue that a moderate increase in the inflation rate would have helped Canada in the 90s. Does this make sense, and which wages are supposed to be sticky, the real ones or the nominal ones?

Here's my attempt at a coherent story.

Near rational behaviour under small adjustment costs

Akerlof and Shiller are using the example of Canada's experience on the 90s to argue that at very low inflation rates (like the roughly 1% that the US has now and Canada had through the 90s) people suffer from a mild form of money illusion even though those same people wouldn't suffer from any money illusion for even moderately higher inflation rates, say above 2%. Akerlof and Shiller also argue for the presence in the data of downward stickiness in nominal wages, and they offer some anecdotal evidence of this from the Canadian slump. All this implies that for very low inflation rates you'd expect to have a Phillips curve type relation between inflation and unemployment that persists in the "long-run", that is you have something stronger than that famous empirical tease that is the classic Phillips curve (stronger since we usually think in the long-run there isn't an inflation-unemployment trade-off).

So why might I think it plausible that workers behave as if they have money illusion for low inflation rates when in general they don't suffer the illusion? Well, one idea I really like is the idea of near rational behaviour under small adjustment costs (though I'm sure this has a literature the paper that comes to mind is this one from John Cochrane). Basically Cochrane calculates the utility costs to an agent of infrequently adjusting their consumption or asset holdings to transient shocks and finds it to be very, very small for empirically relevant shocks. Thus, if there is just a small cost associated with even paying close attention (perhaps you're like me and you'd rather be watching hockey) then you'd expect sluggish responses of a range of endogenous variables to shocks. Thus I find it plausible that for low inflation rates agents pretty much ignore the presence of inflation all together.

Sticky real wages

Finally, to finish setting the context for what I want to say we have the efficiency wage story. The most basic implication of efficiency wages is that the real wage is above the market clearing wage and thus we have unemployment in equilibrium (or higher unemployment than would be implied by the basic matching friction story that gives us the natural unemployment rate in undergrad models). That basic implication of efficiency wages doesn't really speak to stickiness of real or nominal wages but I'm gonna argue that it can lead to downward stickiness of the real wage.

One of the basic reasons you might expect firms to offer efficiency wages is to reduce labour turnover (another is that if there is unemployment in equilibrium it is more costly to the worker to be fired and this reduces the incentive to shirk). I find this very plausible, when a firm hires new workers it generally takes a decent amount of time before the worker is fully integrated into the workings of the firm and until this happens the workers productivity will be lower than its permanent level, of course during this acclimation period the worker usually doesn't work for a lower wage (usually, not always). Thus labour turnover can be quite costly to the firm and gives the firm an incentive to pay wages above the market clearing level. To the extent that workers specifically dislike real wage cuts this also gives the firm an incentive to react to a downturn by firing staff and leaving the wages of those retained unchanged instead of giving everyone a wage cut.

Putting it all together

Suppose we believe Hall and Shimer about the stickiness of real wages, suppose we also believe Akerlof and Shiller about agents ignoring inflation if it is low enough. Then something curious happens, real wage stickiness is transformed into nominal wage stickiness. Agents view nominal wages as if they're real, they ignore a small increase in inflation even though it does in fact very slowly erode their real wage. We end up in a world as Akerlof and Shiller describe where for low inflation rates we get a long-run exploitable Phillips curve!

There we have it, a reason why even slightly higher inflation might be a good idea. It may appear that this argument in favour more inflation is entirely exclusive of my previous arguments, agents can't react to higher expected inflation and ignore it at the same time. The way to reconcile them of course is to notice that the previous arguments were for a reasonably large increase in expected inflation, up to say 4% or even 5%, this is large enough that it wouldn't be ignored by anyone. The arguments in this post are about a small increase to an inflation rate that starts out low, the point is that even getting inflation up from the current 1% to 1.5% can have beneficial effects.

So again, three cheers for Ben Bernanke and bring on the QE. Please Ben may we have some more?

The representative agent is an agent like no other.

2010-12-31T14:12:00.000-08:00

Happy New Year!

Representative agents are not simply typical agents. When economists write down the maximization problem that determines the behaviour of a representative agent the utility function is usually assumed to be the same as for any typical agent in the economy. So then, what's the difference? What's wrong with thinking of the representative agent as just another agent?

Well, the representative agent faces entirely different constraints than does a typical agent. Let's agree to assume the economy is closed, so no imports or exports. In such a situation a typical agent can save more than he invests or invest more than he saves, a representative agent can't. A typical agent can consume more than he produces, a representative agent can't. A typical agent can have an income that is different from the sum of his consumption and investment (ignoring government), a representative agent can't. A typical agent can pay more in taxes then he receives from the government in services and transfers, a representative agent can't.

All these points are pretty important when you try to reason about macroeconomic outcomes by imagining what a typical agent will do. Very often your typical agent will behave in ways that the representative agent can't, but the actual macroeconomic outcome will, by construction, be the result of the representative agent's behaviour.

To take an example I've recently discussed, consider a case where expected inflation has increased but nominal rates (all of them) have stayed the same, perhaps because a central bank is managing them. Thus, real interest rates have fallen. Let's also assume that the economy is at less than full employment. The utility maximization problem of a representative agent says that since current consumption has gotten cheaper in real terms relative to future consumption the optimal response is to increase current consumption demand. In a depressed economy this sounds like a good outcome and so if it's possible to engineer an increase in expected inflation while keeping nominal rates the same that sounds like a good idea.

So, would a typical agent behave this way? Probably not, the typical consumer is likely to move his savings out of cash and into real assets which means equity here (recall the economy is closed so there's no foreign currency). At the same time the representative firm sees that future output has gotten more valuable in real terms and so thinks it would be a good, firm value maximizing, idea to increase future productive capacity. This entails investing more today. At the same time the typical firm has seen it's stock price go up, that is its cost of capital has fallen, and so the typical firm is happy to issue equity to the typical consumer. The increase in investment will employ some idle labour who then, quite reasonably, increases consumption. These agents are increasing consumption because their income increased, not because they're spending their savings.

In the end the result is that the representative agent has increased consumption even though not one typical agent spent a dime of their savings on consumption goods. The funny thing is that the result is exactly what the representative agent's utility function said it should do. The key difference of course is that while a typical agent can move savings from cash to equities the representative agent couldn't in the first place, the representative agent already owned all the equities and held all the cash. Nonetheless, the representative agent ends up behaving as if it is a single person maximizing the postulated utility function and the representative firm behaves as if it is a single firm maximizing firm value. That means that a fall in real interest rates translates into a rise in both consumption and investment demand.

This brings up a more general point, though Nick Rowe already kind of stole my thunder on this one. Consider any fall in real interest rates for any reason. The reasoning of a typical consumer may well involve both substitution and income effects, future consumption has gotten more expensive so you want to substitute away from it towards current consumption. However, if you're saving at all then future consumption is something your spending current income on and thus there may well be an income effect working in the opposite direction, you may feel poorer. However, by the same reasoning as above the typical firm feels as though they want to increase future output and also, the typical firm feels a sort of income effect in the other direction since their future output has gotten more valuable. Furthermore, again from the same logic as before this all shows up in today's prices. Lower real returns means higher asset prices, the typical firm is worth more allowing it to fund the increase in investment. The increased investment expenditure increases employment and so on.

Of course, the representative agent knew none of this but it shows that while income effects can occur in a partial equilibrium analysis, that of the typical agent, they don't in a general equilibrium analysis. After all, the representative agent owns all the capital.

These examples are of course motivated by my last post and one of the main points is also like the last post. For all those like Winterspeak who can't understand the subtleties of the macro economy or macro economic theory but are arrogant enough to be dead certain that most of the economics profession is making obvious, silly mistakes, that Nobel prize winners don't undersand the economy, while only they know that all our economic problems can be solved trivially, all of you would be much better served simply asking an economist how the models work. Over at WCI we have Nick Rowe who is eminently qualified to answer your questions and has an inexhaustible reserve of patience and energy to devote to the task, and unlike yours truly he's also very polite and would never, ever, ridicule you for saying something stupid. All you need do is ask him.

Attacking a straw man in winter.

2010-12-28T07:42:00.000-08:00

Is it really so much to ask that if you're going to attack mainstream economic theory you have some understanding of what it says? Yesterday I posted about Bill Mitchell attacking a straw man, today it's Winterspeak.

Winterspeak offers a simplistic critique of what he (I don't know if the blog author is a man or woman so I'll use the masculine pronoun by default) calls the "inflation expectations hypothesis". In an earlier related piece he begins with

Economic models take it as a given that, in the face of expected inflation, savers start to spend more.

This is not a good start in that the statement is already false, not one economic model takes this as given and not all economic models even imply that it's true. One of the reasons economists go about constructing models, some of which imply that an increase in expected inflation increases consumption and some that don't, but all based on the idea of agents behaving in some consistent fashion (not always rationally) is to understand in what circumstances the statement might be true and when it won't be. It is never just taken as given.

Now those models that do predict that an increase in expected inflation to stimulate demand for domestic production will be ones in which nominal interest rates do not rise, or at least do not rise as much as inflation expectations, so that real rates have in fact fallen. Thus, for this thought experiment we need to agree to maintain the assumption that nominal rates, all of them, stay the same. This is an assumption Winterspeak appears to make:

If inflation expectations increases, then future consumption is discounted more heavily, and inter-temporal substitution begins to favor the present. Or, as Nick says "the increase in expected inflation reduces the real interest rate for any given nominal interest rate".

That would only be true if real interest rates had fallen so I think I can safely assume that Winterspeak is willing to maintain this assumption.

Now here's Winterspeak in the main thrust of his straw man take down:

Primarily, people save for things:
1. They cannot afford currently (and don't want to buy on credit)
2. Unexpected emergencies
3. Old age
4. Bequests for their kids

2-4 cannot be moved forward and so are not inter temporal decisions the way the models treat them. Therefore, if savings are threatened, people will substitute into other stores of value such as fx or gold. They will not move consumption forward, as they cannot. This is not about consumption.

1 is an interesting case. If there's something you cannot afford now, you will not go out and buy it because you'll be able to afford even less of it in the future. There is one big exception to this, which I'll write about in a future post

Ultimately, you need to decide for yourself whether, if your nest egg is going to be hyper inflated away, you'll spend it on a fiber glass kayak or move your savings to another currency. Economists are betting on the kayak.

This last sentence is almost comically wrong, no economist is really betting on a Kayak. Winterspeak is making a couple of classic, elementary, mistakes . One is to apply micro reasoning to a macro problem. A representative agent is not the same thing as a typical agent. The other is the classic inflation fallacy, a mistake exactly like Ron Paul makes.

In fact in an open economy I think the suggestion that people will move their savings into other currencies is a correct one. So why isn't Winterspeak right?

Imagine that savers in an economy, en masse, try to move their savings into a different currency. Surely the foreign exchange value of the domestic currency will fall and might it not be the case that the lower FX value of the domestic currency might increase foreign demand for domestic goods? Might not exports increase? This is the micro/macro mistake that Winterspeak makes. Those economic models that predict that increases in expected inflation that are not accompanied by increases in nominal interest rates of equal or greater magnitude say only that that this will increase demand for domestic goods, they don't restrict that demand to come from the domestic savers. The savers do just as Winterspeak suggests and yet demand increases through other, general equilibrium, channels.

That's not the worst thing that's wrong with Winterspeak's bludgeoning of this particular straw man. Take reason number 1 that people save, for things that "they cannot afford currently (and don't want to buy on credit)." Notice that the decision about whether or not they want to buy on credit seems independent of the terms of said credit. Isn't that a bit odd? Surely if the credit came at zero or negative interest they may be happy to buy on credit. I would be.

The thing to remember here is that it is a maintained assumption that nominal rates of interest have not risen as much as expected inflation (perhaps they haven't risen at all). So, if there is something you want to buy and have been saving for and I told you that its price would soon start rising but that you could obtain credit on the same terms as before, would that change your decision? No? How about if I also told you that your nominal income would also soon start rising but that you could still obtain credit on the same nominal terms as before? If that doesn't make buying on credit more attractive then you're simply being stupid. It's not even necessary to assume that your nominal income rises at the rate of inflation, this still makes buying on credit seem like a really good idea.

So in which inflation did nominal incomes, in aggregate remember, not also increase? That would, by definition, be none. This perhaps is Winterspeak's worst mistake, the classic fallacy of inflation. The main reason why nominal borrowing to buy real goods or real assets becomes more attractive before an expected inflation is that expected future nominal incomes are higher making the debt burden less in the future. In particular, a corporation that can borrow nominally will surely see its nominal income higher in the future because of inflation as it selling the goods whose prices will increase and this is true even if the company realizes that nominal wages will also rise and so its real income won't change. This still makes borrowing and investing more attractive relative to before the increase in expected inflation, and we're talking about the marginal decision remember.

This brings me to the final fallacy in Winterspeak's straw man, the idea that it all works through consumption. In fact we'd expect it to work primarily through investment. Even if savers can't or won't switch to foreign currency saving vehicles they will respond by buying real assets, say equity or housing. The rise in the price of real assets would generate inflation in the sectors that received the extra investment flows.

After all, rising prices of housing caused more houses to be built in the most recent bubble and lot's of people who otherwise wouldn't have bought on credit took advantage of the fact that mortgage rates stayed low to take out mortgages at essentially negative real rates. In the tech bubble before that rising equity prices caused people to employ people in equity financed tech firms. Furthermore, both bubbles generated employment in sectors that serviced the bubble industries, how many people got jobs originating mortgages in the last bubble?

In fact, if agents are behaving even slightly intelligently then they'd respond to expected inflation in conjunction with unchanged nominal interest rates not by spending their savings as Winterspeak believes the models are saying. They would, according to the models, move their savings into foreign currencies and/or real assets and increase credit financed consumption and investment expenditures. So the models would predict the effect working through all the channels discussed above. Winterspeak doesn't provide a counter argument to anything that the mainstream theory actually says.

The conclusion here is that even if you don't believe that increasing expected inflation will work you can't make an intelligent counter argument if you completely fail to understand why it might work. Winterspeak fails to make an intelligent counter argument.

Labour Supply Curves in the Frictionless Model

2010-12-27T10:13:00.000-08:00

So here's Bill Mitchell trashing "mainstream" macro. I haven't read the whole thing because the part I have read is so horribly wrong I struggle to see what Bill could possibly have to say that's intelligent. Nonetheless, in so far that Bill is such a hero in a part of the blogosphere it is maybe worth explaining why the only thing you can learn from reading his post is that Bill himself has a less than zero understanding of "mainstream" macro. (It's less than zero because he not only fails to know how the standard models work but thinks that they say things they don't.)

To be clear, I'm not saying I think the frictionless model of the labour supply is in any way empirically accurate. I'm saying though that it's important to at least try to understand the baseline models so that you can understand how their predictions differ from reality. On this Bill gets a failing grade.

Here's the passage I read that doesn't have one correct argument in it:

The worker is conceived of at all times making very complicated calculations – which are described by the mainstream economists as setting the “marginal rate of substitution between consumption and leisure equals to the real wage”. This means that the worker is alleged to have a coherent hour by hour schedule calibrating how much dissatisfaction he/she gets from working and how much satisfaction (utility) he/she gets from not working (enjoying leisure). The real wage is the vehicle to render these two competing uses of time compatible at a work allocation where the worker maximises satisfaction.

What happens when the relative price between C and L changes? The final result looks scientific but is in actual fact a total fudge.

They isolate two separate “effects” of such a real wage change (say a rise): (a) a substitution effect; and (b) an income effect.

So an increase in the real wage (more corn is foregone for an hour of leisure) leads the worker to consume less leisure and to work more. This is the substitution effect. So if the real wage rises, work becomes relatively cheaper (compared to leisure) and the mainstream theory asserts via the so-called law of demand that people demand less of a good when its relative price rises. So real wage up, less leisure, more work.

But there is another effect to consider – the so-called income effect. When the real wage rises, the worker now has more income for a given number of hours of work.
The mainstream theory of normal goods (as opposed to inferior goods – the distinction is just made up largely) tells us that when income rises a consumer will consume more of all normal goods. The opposite is the case for an inferior good.

Leisure is considered to be a normal good as are other consumption goods the worker might buy with the income he/she earns. So as the real wage rises, the income effect suggests that the worker will demand more of all normal goods (because they have higher incomes for a given number of working hours) including leisure. That is the worker will work less and consume more leisure.

What is the net result? No analytical solution is provided. They just assert that the relative price (substitution) effect is stronger than the income effect and so the labour supply curve is upward sloping. It is totally made up result and no robust empirical analysis has supported this assertion. The reason they need to assert this result is because they also assert the demand curve is downward sloping and for an “equilibrium” they need the curves to cross. Simple as that.

So what's wrong here? Not one bit of Bill's explanation of why the classical model says labour supply is increasing in the real wage is correct. The only part Bill gets right is the fact that yes, the classical labour supply curve slopes up.

First off is the problem that Bill is using a partial equilibrium analysis for a general equilibrium problem. The first order effect of a change in the real wage is to distribute income away from capital and towards labour. However, since households in aggregate own all the capital the effects at the aggregate level is only redistributive, there is no first order change in aggregate income so it's hard to see how the income effect can be very strong. That however, while an elementary mistake is not the worst of it.

So what does "mainstream" economics actually say about the labour supply curve and why it slopes up. Well, the neo-classical theory is fundamentally about intertemporal substitution, in this case intertemporal substitution of labour. Workers are assumed to be maximizing a lifetime utility function that derives utility from consumption and leisure.

Maximizing the lifetime utility function entails solving a dynamic programming problem whose solution will imply that the worker arrange his leisure to be higher when real wages are lower than average and lower when real wages are higher than average. That is he will work more when wages are higher than average and less when they're lower than average. (Since the series is stochastic the solution will be a conditional map from time t information to time t labour supply).

The labour supply curve for time t that results from the solution to this programming problem says trace out his labour supply as w(t) varies while holding the rest of the sequence the same. The conditional rule will say that the higher is w(t) the more labour he should supply at time t.

Notice that even if the positive wage shock increases total lifetime income there is still *no* income effect like Bill thinks.

The reason is that the intertemporal maximization will mean that the reaction to the extra income will be to take more *lifetime* leisure. The worker still won't take the extra leisure when real wages are higher than average!

Any income effect from the higher time t wage will only mean a reduction in labour supply for future times. So the labour supply curve at time t is *unambiguously* upward sloping in the time t real wage!

Any increase in lifetime expected income then shifts some or all *future* labour supply curves down. In just the same way giving the worker more assets, claims on other peoples output, would only shift his labour supply curve, it would still slope up.

The relative strength of income and substitution effects in the labour supply decision would be relevant if what we were talking about was a rise in all present and future real wages but that would constitute a shift in the entire labour supply curve, not a movement along it. In that case the relative strength of the income and substitution effects would determine in which direction the curve shifted. But this has nothing to do with the fact that the curve slopes up.

The only assumption being made is that future leisure and consumption are substitutes for current leisure and consumption. The upward sloping labour supply curves are a direct result of intertemporal utility maximization on the part of workers, none of Bill Mitchell's "critique" is even close to accurate.

I stress again that I'm not defending the empirical accuracy of the classical model, I'm only pointing out Bill Mitchell's complete and utter failure to understand it.

What is Inflation and does Ron Paul have any idea?

2010-12-26T11:02:00.000-08:00

So what exactly is inflation? We usually measure it/define it by rises in the price of a basket of consumption goods. The interesting thing is that it's just the prices of consumption goods, not the price of things like labour. On the other hand, the usual sort of shorthand informal way to define inflation is a proportional rise in "all" prices so that relative prices are unchanged. Presumably "all" prices would include the price of things like labour.

The point here is that the basic theory says that a permanent increase in the money supply should raise all prices by an equal amount so that relative prices are unchanged. This "all" absolutely includes the price of labour, the nominal wage.

This point is important when you read something like this from Ron Paul. It may seem, at first glance, as though he's telling a standard sort of story and that he knows what he's talking about. It seems similar to stories Milton Friedman used to tell but Paul slips in a mistake, perhaps intentionally or perhaps not, that changes things to a story where inflation appears to be a horrible crime. Here's Paul:

The money supply (total amount of money) has doubled! It’s just a one-time event and your regular income remains the same…

Why, if there is all this extra money circulating, does my regular nominal income stay the same? After all, maybe I don't feel like I have enough bargaining power with my employer to extract a raise to compensate for the increased cost of living and any other time I'd be right. Any other time it will be roughly true that my wage is related to my marginal product in such a way as the firm that hired me is roughly indifferent to employing me or not at that real wage.

But not now! Now that all final goods prices have doubled, including whatever good I'm working to produce, I'm working for half the real wage I used to work at and it won't be long before somebody is willing to hire me at a substantial nominal raise.

This is not to say inflation is entirely harmless, it is however to say that the issue has more to it then Paul seems to realize and that there are times when inflation can be beneficial as well as times it can be undesirable or simply benign.

It seems that Ron Paul either doesn't understand the basics of what he's talking about or is being blatantly dishonest, either way this is not a guy we want overseeing the Fed.

Negative Technology Shocks: Forgetting How to do Stuff. Is the Economy Ever That Drunk?

2010-12-23T13:37:00.000-08:00

Has anyone ever noticed that when RBC modelers talk about the shocks driving their models they use the term productivity shocks, when Keynesians or New Keynesians talk about RBC models they usually refer to technology shocks?

Presumably the reason for this is that negative technology shocks are sort of hard to imagine and that's usually one of the main critiques of RBC style models. On the other hand negative productivity shocks are very easy to imagine (more on that below).

So which is it? Well if you look at how the technology/productivity parameter enters the models it's completely clear and unambiguous that productivity is the correct label. The aggregate production function usually is written as A(t)*F(K,L) where K is the capital stock and L the supply of labour input (also dependant on t of course, the function F is not dependant on time). The shocks in question are to the parameter (actually stochastic process) A and it's obvious that shocks to A are shocks to productivity, if A goes up it means we can get more output for the same capital and labour inputs. That's what it means for productivity to increase.

Now, it may well be that most increases in productivity are due to advances in technology but that doesn't change the correct interpretation of the coefficient A above. After all, to the extent that there was ever a technological advance that didn't happen to allow more aggregate output from the same levels of input it is clear that A would not have increased.

The point is that, once the shocks are correctly interpreted as productivity shocks then it is exceedingly easy to imagine negative shocks. After all, we're talking about aggregate quantities here and so a simple shift in the desired composition of output will generally amount to a negative productivity shock. The reason is that capital, both physical and human, tends to be specialized, at least to some degree. Thus, if the capital stock has been installed to produce a particular composition of output and that same capital stock is now asked to produce a different basket of goods then it is virtually certain that it won't be able to produce as much of it.

Moreover, if some capital is completely specialized and can only produce a particular type of output and that output now has less value (in utility terms say) then it did before, this would also count as a reduction in aggregate output. So again, the same capital stock would be unable to produce as much as before.

One conclusion that seems to fall out of the above reasoning is that, to the extent the recent deep recession reflected a shift in the desired composition of production from a basket that included a lot of housing and other fixed structures to a basket that includes much less investment in fixed structures, and to the extent that a large amount of the human, organizational and physical capital built up in the previous 5-7 years was specialized to construction then this shift is a rather severe negative productivity shock.

As David Andolfatto reminds us this can feel to everyone, not just those in construction, as a lack of demand even if the core problem is the sort of real frictions (say time to build or labour search frictions) that translate negative productivity shocks into recessions.

Does Arnold Kling know the basic theories?

2010-12-14T11:39:00.000-08:00

Of course, writing a post with that title means I'm about to suggest that he doesn't. Weighing in on a debate about whether or not a barter economy can have a recession Kling writes this:

If barter were possible, then firms would pay their workers in goods. If you can pay your workers in the goods and services they produce, then you eliminate any wedge between the real wage and the marginal product. So there is full employment. QED.

It's worth pointing out that Kling is going slightly off topic relative to the original debate because what he's saying would imply that barter economies don't have involuntary unemployment. That is a somewhat different question than if they can have a recession, many models have output and employment fluctuations without any involuntary unemployment.

Nonetheless, the QED part is nearly comical in so far as he seems to think this is true regardless of the source of the wedge. In particular Kling thinks the wedge between the real wage and the marginal product comes from the use of money? I suppose Kling has in mind the wedge coming only from a combination of sticky nominal wages and imperfectly anticipated inflation.

I suppose there are actually many theories of where the wedge between marginal product and the real wage comes from (and theories that generate unemployment in the absence of such a wedge) certainly one of the most basic theories is that of efficiency wages (hence the title of this post). The efficiency wage theory is in Blanchard's undergraduate textbook and Romer's graduate textbook, both covering what would have to be considered "standard" theory.

The interesting thing in the context of Kling's remark though is that the efficiency wage model implies that firms choose to pay a higher real wage then would be required to clear the labour market, that is firms choose to pay a higher real wage then necessary to hire workers. Even if the economy were barter, efficiency wage considerations would lead firms to make this choice. It's also interesting to note that it is the firms making this choice in the efficiency wage story, workers are quite willing to do the same job at a lower real wage.

Furthermore, if some shock comes along that opens a wedge between the marginal product and the real wage then efficiency wage concerns may make a firm rationally prefer to fire some workers instead of giving everyone a real wage cut. Again, it's the firms making this choice. It may well be that the fired workers would prefer to take a wage cut and keep their jobs but the firm refuses this deal.

Thus Kling is quite wrong to claim that a barter economy couldn't have unemployment. If efficiency wages are being paid then even a barter economy can have involuntary unemployment and recessions.

What does the world look like if the Fed is doing a really good job?

2010-12-14T07:32:00.000-08:00

Well, it lools like the world we live in. Menzie Chinn notes that various correlations between base money supply growth and inflation look to be about zero. His point is simply to ask where "the idea that money base expansion must necessarily manifest itself in higher inflation" comes from.

However, given that he shows that the data seem to imply not only that base money expansion doesn't have to result in higher inflation, but that in reality it doesn't even usually manifest itself in higher inflation, it is worth asking why the data looks the way it does. After all, a simple reading of most basic macro models would seem to imply that base money expansion should, at least on average, cause higher inflation. Do we have a puzzle here?

No. A zero correlation between money growth and inflation is exactly what you'd expect if your data came from an economy where the central bank was doing a good job at stabilizing inflation.

Increases in money growth would be endogenous reactions of the central bank to accommodate increased demand, decreases in money supply growth would be endogenous central bank responses to decreased demand.

The only puzzle is why nobody can just accept that the data say the Fed has simply been doing a truly incredibly good job? And if you can accept that then clearly you should not expect QE to be inflationary at all, you should believe that the fed know what it's doing and is just responding to an increase in money demand.

[Update: Nick Rowe correctly points out that, of course, if the Fed is really doing such a good job then in fact nothing should forecast inflation. So a zero correlation with money growth is not sufficient to conclude the fed is doing its job, it is necessary though.]

What's the difference between a monetarist and a Keynesian?

2010-11-22T11:05:00.000-08:00

Partly to check if anyone is reading and partly because I want to see the answers I'll give a few days for answers to be put in comments. Then I'll give my answer.

I've recently been asking this question of a few people and all the answers have been the same, and all wrong...

RE does not help Kocherlakota

2010-08-30T23:34:00.000-07:00

One of the defenses of what Kocherlakota said in his now infamous speech is that it is consistent with rational expectations (RE) and thus what he said is sensible in that context. Rajiv Sethi agrees with this and even Andy Harless, in the comments to my last post, agrees that RE may justify Kocherlakota's comments.

I just don't see how that's true in any model that is close to being standard. Certainly all the models with RE allow for the idea that if the Fed expects, rationally, that at the current nominal interest rate inflation will be lower going forward than it has been then they will lower interest rates and agents in the economy who also rationally expect lower inflation will expect the Fed to lower rates. If the amount that the Fed lowers the nominal rate by is exactly equal to the expected reduction in inflation then agents in the economy will not infer that the real rate has fallen, thus aggregate demand would not increase with the lower nominal rate. Instead the lower inflation rate materializes as expected. This is not the same as saying that by lowering nominal rates the Fed can cause expected inflation to fall.

Of course, it appears that what is in the mind of people defending this view is a bit different. Here's Rajiv in the comment section of his blog post:

Suppose the Fed decides to change the Taylor Rule in such a manner as to result in a lower target nominal rate. Suppose that it is common knowledge that this change has been made and that it is permanent. Then nominal rates fall right away, inflation falls by an even greater amount, real rates rise temporarily and then fall back as convergence to a new steady state with lower nominal interest rates is attained.

This sounds to me like Rajiv has in mind a situation where we start in the steady state and the change to the Taylor Rule that results in a lower "target nominal rate" means we change the long-run steady state target for the nominal rate, that is equivalent to simply lowering the inflation target.

If that's the case then the response of inflation depends on whether or not we start in the steady state. If we are in the steady state when the policy rule is changed then yes inflation falls immediately. On the other hand, if target inflation is being reduced from 2% to 1% and current inflation is 1% then inflation doesn't change but yes the nominal rate is increased by the Fed.

If target inflation is reduced from 2% to 1% and current inflation is 0% then neither inflation nor the nominal rate changes today, the Fed simply stands ready to raise the short earlier than under the old policy rule.

This last case seems to best describe what Kocherlakota has in mind but he is still wrong. He is advocating for the policy shift that stands ready to raise the nominal rate earlier but seems to think it constitutes an increase in the target inflation rate, it helps avoid a deflationary steady state.

Of course in fact this constitutes a decrease in the target inflation rate and as such is a tightening, furthermore, this would effectively raise the prevailing real rate in the economy right now. In other words such a shift in the policy reaction function is a tightening of policy today. This would in fact cause more deflation not less, it pushes away from the long-run steady state.

RE doesn't save Kocherlakota here, in no RE model does the Fed raising nominal rates from 0% to 10% cause today's expected inflation to go to 8% or higher.

Two ways to Irving: Along neither is Kocherlakota correct.

2010-08-30T11:06:00.000-07:00

The recent uproar over a speech of Narayana Kocherlakota has been fun, I guess I don't need to do the customary posting of links. If you're reading this you surely know about it. In particular Stephen Williamson has shown himself to be quite silly, something I've already noticed.

I will however link to Nick Rowe because he's one of my favourite bloggers, Nick points out that Kocherlakota appears to make an elementary mistake. One point of this post is to observe that there is an interpretation of what Kocherlakota said in which this is not a mistake, perhaps this what his defenders have in mind. Of course the other point of this post is to observe that under the alternate interpretation Kocherlakota is still making an elementary mistake, a different elementary mistake. Either way you cut it, he said something really dumb.

The defense of Kocherlakota has basically been to say well, in the long run the Fisher effect dominates and when this is combined with an assumed positive real interest rate low nominal rates will go with deflation. This of course is perfectly correct but completely misses what is so, so very stupid about what Kocherlakota actually said. Here's the money quote:

To sum up, over the long run, a low fed funds rate must lead to consistent—but low—levels of deflation. The good news is that it is certainly possible to eliminate this eventuality through smart policy choices. Right now, the real safe return on short-term investments is negative because of various headwinds in the real economy. Again, using our simple arithmetic, this negative real return combined with the near-zero fed funds rate means that inflation must be positive. Eventually, the real economy will improve sufficiently that the real return to safe short-term investments will normalize at its more typical positive level. The FOMC has to be ready to increase its target rate soon thereafter.

That sounds easy—but it’s not. When real returns are normalized, inflationary expectations could well be negative, and there may still be a considerable amount of structural unemployment. If the FOMC hews too closely to conventional thinking, it might be inclined to keep its target rate low. That kind of reaction would simply re-enforce the deflationary expectations and lead to many years of deflation.

Now nobody is disagreeing with the idea that in the long-run low rates go with low inflation and a zero nominal rate would only be consistent with deflation. The problem with what Kocherlakota said is at the end where he advocates for the Fed increasing nominal rates quickly as a way to avoid deflation. The problem with this is of course that it won't work, just about any reasonable macro theory tells you it won't work.

Here's Nick, he says:

If the economy returns to normal, and the natural rate of interest rises, the Fed must raise its target rate of interest. (So far so good). If it doesn't, the result would be....deflation. ("Inflation" would be the right answer).

Nick is correct in the case that the natural rate of interest rises while (expected) inflation is still positive (or not too far below zero, greater than minus the natural rate). In that case the real rate in the economy is below the natural rate and the result is inflation, and if the Fed doesn't respond by raising rates then accelerating inflation.

There is however another possibility for what happens when the natural rate rises back to a normal value. Suppose the natural rate r* is currently -2% and will rise to 2%. If inflation (let's take inflation = expected inflation) is -1% and the nominal rate i = 0 when this happens then the real rate in the economy (call it r) is 1% and the result is inflation as Nick says.

On the other hand, suppose that inflation is -2% when the real rate returns to 2%. In that case i = 0 corresponds to the natural rate being equal to the prevailing real rate, r = r*, and we settle into a long-run deflationary equilibrium. This seems to be the case some of Kocherlakota's defenders may have in mind.

So does that mean that what Kocherlakota said is sensible? No, it's completely idiotic and actually very pernicious. It's idiotic because of the part where he says

The FOMC has to be ready to increase its target rate soon thereafter. That sounds easy—but it’s not. When real returns are normalized, inflationary expectations could well be negative, and there may still be a considerable amount of structural unemployment. If the FOMC hews too closely to conventional thinking, it might be inclined to keep its target rate low. That kind of reaction would simply re-enforce the deflationary expectations and lead to many years of deflation.

This really sounds like he thinks that raising the nominal rate before unemployment has begun to fall or inflation has begun to rise will actually prevent the deflationary outcome and that is just not supported by any theory. Not one, regardless of what Stephen Williamson says.

If the Fed raises i so that the r > r* then inflation will fall, all models agree on this, the only dispute is whether the economy falls into a deflationary trap that is even harder to get out of, a deflationary spiral that is the mirror image of what Nick talks about, or the price level falls to a point where from there it is expected to rise, thus generating the expected inflation that must be in the long-run equilibrium with the new higher i. In no case does a fed that cares at all about the welfare of the citizens it serves actually follow this advice. In no case does raising i mitigate deflation in the short run, it only makes it worse.

Finally, it's actually worse than all that, why is what Kocherlakota says particularly pernicious? Were the Fed to heed his advice then that would basically constitute a tightening right now. Kocherlakota is talking about the Fed's reaction function. If the Fed stands ready to raise rates before inflation has increased (based on other indications of a normalization) then that is a change in the reaction function that constitutes a tightening. (Look at it this way, in Scott Sumner's phrasing it is a statement that the Fed stands ready to reduce the money supply even earlier than we thought, the monetary injection has gotten *less permanent*).

What Kocherlakota said is not defensible in macro theory and it's very, very scary that someone could be the position he is while thinking this way.

The Bank of England's excluded middle.

2010-08-24T13:01:00.000-07:00

A little while ago I recalled Krugman's law of the excluded middle to argue that NGDP futures targeting does not solve the problem of liquidity traps. The idea is that in a liquidity trap it there may be levels of inflation or NGDP that are absolutely impossible to achieve. This is important because the whole way that the futures targeting scheme is supposed to prevent liquidity traps from ever springing is by keeping expectations of NGDP growing at a nice rate, thus stabilizing aggregate demand. No need to cut back on investment spending if you always expect growth.

The law of the excluded middle was a theoretical point but there is another, related, point that comes up. Just because the futures market is balanced and so aggregate "market" expectations equal the target (see the previous post for a description of the market), that does not mean any individual actually expects the target to be hit. To take a simple example, if half the market expects NGDP to fall short of the target, to be 3% say, and the other half expects NGDP growth of 7% the aggregate expected NGDP growth is 5% but you still have an aggregate demand shortfall from half the market.

Now, does the bullish half of the market make up the difference? No, not if they're rational anyway. Since real growth is physically constrained by the growth rate of total factor productivity they must believe the extra 2% nominal growth comes from inflation and the rational response to that is not to increase production or investment, it's to increase price. (As an aside this is another reason to target inflation and not NGDP, the real growth rate is something that monetary policy can't determine even in the best of times and since the growth rate of total factor productivity will never be know ex-ante this will introduce distortions in market allocations).

So is it really plausible for a group to polarize in such a way that they're aggregate expectations are a bi-modal distribution centered on the target but with very little mass on actually hitting the target? Well, the BoE's monetary policy committee is a small but very well informed group. The following is from their most recent quarterly inflation report.

Chart 5.11 Frequency distribution of CPI inflation based on market interest rate expectations and £200 billion asset purchases(a)

I agree with Andy 100%.

2010-08-22T10:53:00.000-07:00

Here's a post from macroblog arguing that the money growth-inflation connection may be strengthening.

Here's Andy Harless blowing them completely out of the water. With the very first comment no less:

I thought that the old "monetary aggregates" version of the quantity theory -- where something like M2 is taken as an exogenous determinant of inflation -- was pretty much discredited by the policy experiment in the early 1980's. The Fed tried to control M1 (which should be easier to control than M2) and found that (1) it couldn't and (2) the correlation became much weaker. It's not a very convincing response just to say they were trying to control the wrong aggregate.

Posted by: Andy Harless
July 28, 2010 at 05:36 PM

The reality of the real interest rate.

2010-08-17T23:33:00.000-07:00

As I was saying last post one of the reasons studying RBC models is a worthwhile endeavour, even though the models don't even have a toehold on reality, is that they make you think about a world without money (or debt of any kind).

One of things that thinking this way reminds you of is the reality of the real interest rate. If we imagine a world with no money or credit of any kind then the only way for individual agents of substituting consumption accross time is by investment (storing up consumption goods for future use counts as inventory investment). This is relevant to reality because in aggregate it applies to the real world, financial assets can't facilitate a trade of less consumption today in return for more tomorrow, only investment can do that. Holding more money certainly accomplishes the less today part but if productive capacity is not expanded by real investment then how can we, in aggregate, have more tomorrow?

So what does this have to do with reality? Well in a world with debt instruments is the real interest rate the real return to financial assets or is it the real return to investment? The answer, as say IS-LM models tell us, is both.

The point here is, the fact that the marginal product of capital is the rate at which we can trade off consumption today against consumption tomorrow is not an equilibrium condition, it's a constraint of physical reality. The equilibrium condition is the fact that that at full employment this rate will also be the (risk-adjusted) real return on financial assets. One way to characterize recessions is that people hold more financial assets than real investment projects because the expected (risk-adjusted) real return to the financial assets is higher than that of the available investment projects.

The solution then is to lower the expected (risk-adjuted) return to the financial assets, raising the real return of available investment is not something monetary policy can do.

Is deleveraging a symptom or a cause (or both)?

2010-08-17T11:35:00.000-07:00

One of the reasons studying RBC models is a worthwhile endeavour, even though the models don't even have a toehold on reality, is that they make you think about a world without money (or debt of any kind). The same goes for endowment economies, Lucas tree models and the like. In an endowment economy intertemporal substitution of consumption is physically impossible but there is still the usual notion of equilibrium, it's just that prices have to adjust until nobody wants to save or dis-save anyway.

The point here with respect to the real world and our current situation is that just because problems are most apparent in the financial sector doesn't mean that banks are the cause of anything. The fact that it in the toy model economies that theoretical economists work with liquidity traps can happen even though there usually is no financial sector is not necessarily a deficiency of the model. It may be that the model is telling you that the underlying causes have nothing to do with leverage, intermediation or balance sheets. So anyway...

Paul Krugman just finished a post on Richard Koo's book The Holy Grail of Macroeconomics, he seems to think the book is ok. I thought it was garbage.

The biggest problem with Koo's book is the empirical fact that his central thesis appears to be wrong. In the book he flat out states that in the mid 2000's when the Japanese economy started to rebound this was because the balance sheets had been finally repaired. He claims to have been told this by some CEO's, he states it like it's soooo obvious.

Yet, remarkably the Japanese recovery happened at a time of relative yen weakness and was pretty much entirely driven by exports. When the export markets collapsed and the yen rallied the recovery vanished, the economy slumped just as badly as before. Were balance sheets suddenly un-repaired? Had they had another bubble burst that nobody noticed?

Seems clear that the lack of investment was due to a lack of demand pretty much as Krugman diagnosed in the late 90s. The deleveraging was a symptom not a cause. I mean surely had the BoJ got the perceived real rate to -5% then even more leverage would have been appropriate.

Which brings me to the title of this post and the next problem with Koo, as a matter of theory his thesis is nonsense. What's worse, the basic idea is also not new yet everything in the book including the title indicates he believes it is. Koo demonstrates a complete lack of understanding of basic economic theory and complete ignorance of the literature that precedes him.

Everything that is sensible in the idea of the balance sheet recession is basically Bernanke-Gertler on the costs of credit intermediation. The basic idea of the balance sheet recession is that firms have stopped maximizing profits and instead turned to minimizing debt, this is already a problem because, other than for first-year undergraduates, no macro models assume that firms maximize current profits. The assumption is that they maximize firm value. This makes a difference, regardless of current debt levels and servicing costs if you can borrow at 5% and invest the money at 8% you would do it.

Furthermore, he argues that many firms in Japan were basically cashflow solvent, they had enough cashflow to service their debt, but balance sheet insolvent in that the value of their assets was lower than the value of their liabilities so they had negative market values of equity capital. Again, if you could borrow at 5% and invest at 8% return why would you not just because your existing assets are worth less than existing liabilities?

This should already tell you that lack of demand for credit reflects something other than firms have stopped maximizing profits. It must have been that either the required returns on investment were too high relative to the returns expected from the available investment projects or something was interfering with the credit intermediation process.

Koo draws the conclusion that lowering interest rates won't stimulate investment demand because anyway firms don't want new credit, they want to pay down existing debt. The question Koo never asks is, why don't firms refinance at the new, lower interest rate? The answer is Bernanke-Gertler, they can't refinance because the value of the assets that secure the debt is too low (clearly this applies to US housing as well). Surely then if monetary policy could reflate asset values then it could potentially have an effect.

Furthermore, if the firm is cashflow solvent and can still service its existing debt why does that make it prefer deleveraging to investment? After all, borrowing to invest adds to the debt and the debt service costs but it also, hopefully, adds to income. The answer again is Bernanke-Gertler, they can't borrow to invest because they don't have the asset values to borrow against. This is a particular problem for the intermediaries, small and mid-size firms can't invest to expand because the banks that would invest in these firms can't borrow the money. The banks can't borrow the money because they can't secure the loan with valuable assets (this is just the MMT statement that banks are capital constrained, not reserve constrained. If they had the assets to use as collateral they can always source liquidity). However, right now the banking system has a fortune in excess reserves. Clearly they have little problem borrowing from the Fed! They are choosing to deleverage, this is a symptom of insufficient investment demand and not a cause of it.

Finally, there is the fact that for large firms most investment tends to be funded out of retained earnings. Why, as right now in the US, do large firms prefer to pay down debt, pay out dividends or accumulate cash instead of investing? Again, for firms in the US right now deleveraging is a symptom of insufficient investment demand, not a cause of it.

So is there a feedback effect, can deleveraging also cause a fall in invesmtent spending? Yes, but again it's Bernanke-Gertler, it works through asset prices. The asset price fall that accompanies the bursting of a bubble can cause a cash crunch and as assets that still have value (perhaps not bubble assets) are sold to raise cash (or because they had been pledged as security for a loan) then this causes a generalized asset price decline that interferes with the creation of new credit (see Gary Gorton's Slapped by the Invisible Hand on that). There is a financial accelerator, the idea just didn't originate with Richard Koo.

The point here is that insufficient investment demand is the cause of our problems (largely insufficient relative to excessively high global savings) and the deleveraging we see is just a reflection of the lowered demand for credit (lowered relative to what happened when we did have enough investment to maintain full employment). However, monetary policy can still gain traction by reflating asset prices both to lower the cost of credit intermediation and to lower the required return on new investment.

Are stock prices too low? (And are they going lower, higher or both?)

2010-08-16T14:21:00.000-07:00

Right now the real cyclically adjusted PE ratio on the S&P500 index is about 19.8 (from Robert Shiller's data). By long term historical standards this is pretty high, the long term average for this ratio, from Shiller's data, is about 15. Historically a number this high for the CAPE has been associated with relatively low subsequent returns, it really doesn't sound like prices are too low does it? If anything they seem too high given the precarious state of the US economy.

On the other hand, our basic situation is a world of excessively high savings and, what's worse, those savings are in large part being imposed on the United States. Large amounts of capital are flowing into the US, which is already capital rich instead of being invested in the high saving countries, like China, who are capital poor. Given the need to invest all these imported savings in a country that already has plenty of capital it makes perfect sense that investment returns should be low, which means it makes sense that asset prices should be high. After all, it is no coincidence that liquidity traps tend to follow asset bubbles. The bubble is the manifestation of the high savings and it takes bubble level asset prices to generate enough investment to spend all the savings. When the bubble breaks employment falls and the liquidity trap springs.

Clearly the US right now is a place of high unemployment and for the first time in a while the US has a positive household savings rate. At the same time China is still sending over plenty of their own saving. Getting the US back towards full employment requires all these savings be spent, so how do you get that done? Here's Krugman writing about Japan way back when:

To build a fully specified model with investment would require a longer and more elaborate paper. However, it is fairly straightforward to see that if we have a "Tobin's q" model of investment, in which periods of high investment are associated with a high real price of assets, a positive marginal product of capital is no guarantee that individuals face a positive real rate of return. To see why, suppose that for whatever reason consumers right now want to save a large fraction of their income. In order to persuade firms to invest that much, q must be high. But in the future, when consumers want to save less, q will be lower. Now while an investor who buys capital now will collect any rents on the capital - which will be positive as long as the marginal product of capital is positive - he must also take into account the prospective real capital loss as q declines from its current high level to a more normal level. As a result, to get the level of investment needed to absorb temporarily very high savings might require that investors be prepared to accept a negative real rate of return, and hence that the real interest rate be negative.

An asset bubble, more or less by definition, is a situation where asset prices are unreasonably high and will eventually fall. Thus, however it's happened, a bubble is a situation where investors have somehow been induced to hold assets at a negative return. In the height of the last boom assets where certainly being held at negative expected return, though perhaps not consciously. Full employment is going to require another bubble.

So, is the Fed up to it? The Fed has come under a lot of criticism over the last bubble, on the other hand lots of people are clamouring for more easing. Personally I'm 100% certain that privately, when he's home alone having a beer, Bernanke wants to expand the size of the Fed's balance sheet to around $5 trillion just for a start. I also think that's exactly what he should do. At the same time he's going to need some political cover, you've got Hoenig and ~~Tosser~~ Plosser vocally calling for a tightening so clearly there's enough stupidity to go around. So that brings me to my market view, for whatever it's worth. I think stocks need to fall, probably the S&P500 below about 850. At that level I'm a buyer because I think that will be enough for the Fed to come out swinging, and I think the Fed won't stop easily once they get started. We all know from his previous writing that Bernanke understands more than anyone the need to reflate asset prices, I have faith in him to eventually do the right thing.

Does Stephen Williamson make any sense at all? (Or Does Modern Monetary Theory make any sense at all, part 2)

2010-08-10T10:57:00.000-07:00

In the comments section of this post from Williamson an anonymous commenter says:

I hope you won't deny that falling prices create a value of waiting/delaying consumption?

and Williamson responds:

The consumption-postponement argument has never made any sense to me. If everyone wants to postpone consumption because there is deflation, how can there be deflation in general equilibrium?

Seriously? I mean as a monetarist (new or otherwise) he presumably believes that the demand for money and other financial assets (bonds) is important. He has said previously that he thinks the problem right now is that the real rate on government bonds is too low, isn't that just another way of saying the demand for government bonds is too high? But, as I've been trying to point out, an increased desire to hold financial assets (money and bonds) is exactly a decreased demand to trade those financial assets for consumption or investment goods.

You can't logically believe that it is possible for the demand for financial assets to increase but it's not possible for the demand for consumption/investment to decrease?

Deflation increases the demand for money and bonds by making their real return higher, this is exactly the same thing as decreasing the demand for consumption and investment. If you want to increase the demand for real goods, consumption or investment, then you need to decrease the real return to holding the financial assets.

Arguing against NGDP futures for monetary policy. Part 1: Multiple equilibria, none on target.

2010-08-08T03:11:00.000-07:00

Basically the point here is that in a liquidity trap we have what Krugman called the law of the excluded middle. If the real interest rate that supports full employment is -4% and the central bank targets an inflation rate of 2% then even at zero nominal rates the economy suffers deficient aggregated demand and unemployment which puts downward pressure on the inflation rate and eventually leads to outright deflation. Effectively, if the central bank sets its inflation target too low then it is impossible to hit the target (my last post explains why generating inflation expectations is a necessary condition for stimulating aggregate demand once short term nominal rates hit zero).

For the case of targeting NGDP lets expand the example by assuming that if full employment is maintained then real GDP growth will be 3% (presumably this along with 2% inflation is where Sumner gets the 5% number he favours). On the other hand, suppose with 2% expected inflation the rate of real GDP growth will be 1% (something like what Japan ended up with and what the US is likely to have as the fiscal stimulus and inventory correction wears off). The result is that 5% NGDP growth is not a possibility for this economy, 7% is possible and 3% is possible but not 5%.

So why is this such a problem for an NGDP futures targeting scheme? The way the scheme is supposed to work is that there are futures contracts on realized NGDP growth with around one year to maturity and a strike price of 5% (or whatever is the target) traded on an open market, the fed conducts open market operations to keep the market balanced. If somebody goes long realized NGDP (betting it will be above target) then the fed contracts the money supply, anytime someone goes short the fed expands the money supply, this continues until the longs and shorts are balanced. The idea is that expected NGDP growth is then kept on target.

So the first problem is that there will be excess volatility in monetary policy as the market oscillates between the possible outcomes. Essentially monetary policy will begin to act in a destabilizing way, creating volatility, instead of a stabilizing way. This is exactly the opposite of what is intended.

The second problem is that you can't change the target! Even if the problem is correctly diagnosed, what happens if you want to change the target? In this scheme you have multiple contracts trading at any given moment, presumably an expiry for each quarterly GDP data release at the minimum. If you attempt to change the target on a new contract to 7% what happens to those who've already traded the contracts struck at 5%? The fed has basically screwed them and this will ruin the functioning of the system going forward as traders begin to price in the possibility of target changes happening before their contracts mature.

The conclusion here is that if the economy is in liquidity trap conditions then an NGDP futures targeting scheme will only make things worse. It does not make the liquidity trap cease to exist as Sumner has repeatedly claimed.

Can printing money really make people stop maximizing utility or make firms stop maximizing profits?

2010-08-03T11:47:00.000-07:00

Here is Scott Sumner describing his view of the monetary transimission process:

If you put more cash into circulation than people want to hold, they’ll try to get rid of it. Individually they can, but collectively they cannot. The attempt to get rid of the cash will drive up AD. I think everyone understands this (excluding post-Keynesians of course) but many economists forget what monetary policy is all about; the supply and demand for money.

In my last post I've already explained why in a liquidity trap this is wrong but the fact that it's wrong is important enough to repeat the story. After all, Sumner's belief that this process applies in a liquidity trap is the basis of his belief in using an NGDP futures market for conducting monetary policy, a bad idea, and his belief that NGDP targeting is superior to inflation targeting, another bad idea.

In a nutshell the problem here is that Sumner is engaging in one equation economics, a big no-no in macro. He bases everthing on the supply and demand for base money ignoring the consumption-saving decision of consumers and the investment decision of firms. In the real world though consumers make both a real balance decision (how much to demand) and a consumption-saving decision.

Let's concentrate on consumers making a consumption-saving decision, an analogous argument will apply to firm's investment decisions. The thing to notice in the following argument is that everthing hinges on changing the real interest rate which in a liquidity trap means increasing inflation expectations. The critical point is that increasing the money supply in a way that somehow doesn't change inflation expectations will do nothing in a liquidity trap. It may seem a trivial distinction since you'd think that the way to increase inflation expectations is to increase the money supply but for a discussion Sumner's NGDP targeting ideas (in future posts) the fact that the real rate does all the work is critical.

So, what happens if the consumption-saving decision is in conflict with the real balance decision because the central bank has supplied more money then people want to hold? (As discussed below the conflict is only possible in a liquidity trap case.) If people spend their excess balances then their consumption is higher than they wanted it to be, if they don't then their money balance is higher than they want it to be. Something's got to give and at zero interest rates it will always be the case that people will choose to willingly hold the excess balances, there will be no attempt to get rid of the extra money. The reason for this is simple, the consumption-saving condition is a utility maximization condition. If people increase their consumption without a corresponding fall in the real interest rate then they have moved to a point of less than maximal utility, they are suffering a utility loss. On the other hand, for no change in nominal interest rates or expected inflation, holding more money then you want is costless.

To flesh out the argument let's first go through the normal case.

When interest rates are above zero you can tell the monetary transmission story one of two ways:

1) Money version: An increase in the money supply leads to people holding excess real balances, the attempts to get rid of the excess balances leads to an increase in expenditures and thus higher consumption and/or prices. Eventually consumption is increased enough that some of the extra real balances are saved and find their way to financial markets, the real interest rate falls to reconcile the higher consumption with intertemporal utility maximization (the consumption Euler equation). In this version the fall in the real rate is not caused by the increase in current consumption but makes it consistent with intertemporal utility maximization. Notice that if interest rates can't fall or inflation doesn't rise then the story never ends, as Sumner says of the excess money, "they’ll try to get rid of it. Individually they can, but collectively they cannot." Clearly AD won't be infinite but if interest rates can't fall and thus increase the demand for real money balances (by lowering the cost to holding them) or prices rise to lower the real value of the money balances down to what is demanded, then how is equilibrium restored? That's our first clue that something is amiss.

2) Interest rate version: An increase in the money supply leads to excess real balances and people at first try to get rid of the extra money by buying financial assets, this puts more liquidity into financial markets and to clear the markets the price of liquidity, the interest rate, falls. The lower interest rate has basically made future consumption more expensive in terms of current consumption so people substitute more current consumption for less future consumption, they save less and consume more today. In this version the fall in interest rates causes the increase in demand and it clearly would not apply if rates are stuck at zero.

So far this is two ways of describing the same story and the economic conditions that describe equilibrium, that is money demand = money supply and the optimal consumption-saving condition don't specify what causes what, they just characterize the equilibrium.

Now the zero interest rate case is clear, if the money supply is increased past what people want to hold but neither interest rates nor expected inflation change then there is a conflict. Either people end up with excess real balances or they consume more than they want to at the prevailing real interest rate. Which will it be? Well, as I said above it will always be that they willingly hold the extra money, the cost to holding money hasn't changed so if they were willing to hold it before then they'll hold whatever extra amount you give them. On the other hand, changing their consumption level does have a cost in utility terms. If people respond to the excess balance by increasing their consumption but the real interest rate doesn't fall then they're no longer maximizing their utility. Can monetary policy really do that?

One final point, Sumner very frequently has stated that the monetary injection in fact needs to be permanent to have any effect but never explains why the story he tells in the cited passage requires this. The reason is exactly that if the extra money is permanent then it raises the expected future price level and thus lowers the real interest rate. However, this story now has absolutely nothing to do with the fact that the extra money comes today. The promise of future inflation both lowers the real rate, thus increasing consumption demand and lowers the demand for money by increasing the cost of holding it. Increasing or not increasing today's money supply is completely irrelevant.

It is worth noting that a very similar story can be told for a firms investment problem but it would basically just repeat what I've said here.

I think the absolutely essential role played by the real interest rate is of paramount importance because understanding it will show that Sumner's focus on NGDP targets for monetary policy and his pet idea, NGDP futures targeting, are not good ideas.

Does Modern Monetary Theory make any sense at all?

2010-08-02T11:49:00.000-07:00

In a recent post Stehphen Williamson wrote:

What's the difference between a New Keynesian and a New Monetarist? This sounds like I'm leading off to tell a joke (a duck walks into a bar...), but I'm not. A New Keynesian thinks that the real interest rate is too high, while a New Monetarist thinks the real interest rate is too low.

I've been meaning for a while now to write a post on Williamson's statement and what's wrong with it.

The crux of Williamson's argument is in this passage:

From a New Monetarist point of view, a key element of the financial crisis relates to the scarcity of liquid assets. There is one type of liquid asset, which is outside money. Currency and bank reserves play their own unique roles as media of exchange in retail and large-scale financial transactions. A second important set of liquid assets are (in the US) Treasury securities, and various intermediated private assets that are implicitly traded through the exchange of various intermediary liabilities. When the Fed conducts an open market purchase of Treasuries, it swaps the first type of liquidity for the second. My view is that one reason this matters is that it increases the scarcity of the the second type of liquidity. The financial crisis also increased the scarcity of the second type of liquidity.

He goes on to point out that in large part the Fed's response to the crisis was to sell treasuries as well as buy private debt with newly created reserves consistent with the idea that both types of assets are in excess demand. The point about a scarcity of liquid assets and the Fed's response is all perfectly correct as far as I see, I completely agree. Williamson isn't really so clear on the policy prescription but presumably the comment about the real rate being too low refers to the high value that treasuries carry, thus the policy prescription would be to supply more treasuries until the excess demand is satisfied and capital will flow to other uses. Satisfying the excess demand would lower the price of treasuries thus increasing their yield. Really this is just old monetarism applied to all government debt instead of money.

So why is the statement about real interest rates so wrong? A couple of things, first a minor point.

1) Why aren't reserves (Federal reserve debt) good substitutes for these second type of liquid assets? If liquidity is the issue then surely money will do the job as well as the various intermediated private assets that are implicitly traded through the exchange of various intermediary liabilities. Moreover, the fact that these type 2 assets where scarce and yet they (for the most part) didn't start trading at negative interest rates shows that money does serve the liquidity function just as well. So why do we need to change the real rate at all, why doesn't increasing the money supply in old monetarist style do the trick?

Really though, the first point is a sidebar. Here's the real problem.

2) The real rate of interest is a real rate of interest. The real interest rate is more than a financial construct, when agents have a choice of buying a treasury or funding a real investment project (something that generates a demand for labour) the relative risk/return characteristics of the potential investments decide where the marginal dollar flows. The real rate of return on default-free debt is the certainty equivalent required return on the marginal available investment project, this required return will not change because the government increases the supply of treasuries. Thus, issuing more treasuries won't actually lower their price. The standard liquidity trap problem applies to treasuries as well.

This last point is worth explaining. Any macro model (that isn't static) has some equilibrium condition that determines aggregate intertemporal substitution of consumption demand and aggregate investment demand (in the IS-LM model it's the IS curve, for consumption it's the consumption Euler equation). Most models also have some sort of supply equals demand for liquidity condition (the LM curve). In older models (or just simpler ones) liquidity just means money but Williamson is correctly generalizing to any security that in some context serves a money like function (for example anything you can repo).

Normally, in non-liquidity trap times these two equilibrium conditions are not in conflict. If the supply of liquidity is increased then this will increase aggregate expenditure. It doesn't matter if the effect works by lowering the interest rate, which feeds into the Euler equation to increase consumption and the firms optimality condition which increases investment demand as a (new) Keynesian would say or if it works by giving people an excess of liquid assets which they try to shed by increasing their expenditures on consumption or investment goods, as a monetarist would say. In the monetarist story the higher current consumption and investment feeds into the optimality equations and lowers the real interest rate that satisfies them, thus their is no tension between the supply and demand for liquidity being equated and the aggregate saving equalling aggregate investment.

However, in a liquidity trap saving persistently exceeds desired investment because the risk/return profile of the marginal investment project is not as good as what is available in liquid assets (it is important to note that interest rates being zero or above zero irrelevant here, Hyman Minsky stressed that liquidity traps can happen with positive nominal rates). So saving is not being equated to investment, can supplying an excess of liquid assets change this condition? Not if it doesn't worsen the risk/return profile of those assets.

Here's the crux, the consumption-saving decision of consumers and the investment decisions of firms are optimality conditions, deviating from them has a cost in terms of their objective functions. That is why even if increased expenditures came from the monetarist channel (in the non-liquidity trap case) the real rate had to change to restore equilibrium. Now, in the liquidity trap can increasing the supply of liquidity make people change their consumption or investment behaviour? No because there is no cost associated with holding the liquidity, you only forgo an investment project whose risk/return profile is less preferred to the liquid assets. On the other hand, spending the excess liquidity on real goods takes you to a sub-optimal point on your objective function, this is a cost. Thus in the tension between equating supply and demand for liquidity and increasing investment/decreasing saving, the supply/demand for liquidity relationship is always the one that breaks.

Of course the point here is that the new monetarists are just wrong and the new Keynesians right with respect to the real interest rate. Furthermore, this has nothing at all to do with new Keynesian theory, it's just what you get from any model that has people making consumption-saving and investment decisions, that is, any model that makes any sense. You need to lower the real return to holding the liquid assets, you need expected inflation.

Mysteries of Deflation: Some theoretical background

2010-07-26T12:29:00.000-07:00

In a recent post Paul Krugman talks about a "mystery" of Japnaese style deflation. Here's Krugman:

But here’s the thing: the inflation-adjusted Phillips curve predicts not just deflation, but accelerating deflation in the face of a really prolonged economic slump. Suppose that the economy is sufficiently depressed that with expected inflation at 3 percent, actual inflation comes out only 1; expectations will actually catch up, so that if the economy remains depressed we’d expect inflation to go to -1; but if the economy remains depressed even longer, we’d expect inflation to go to -3, then -5, and so on.

In reality, this doesn’t happen. Prices fell sharply at the beginning of the Great Depression, when the real economy was collapsing; but they began rising again when the economy began to recover, even though there was still a huge negative output gap. Japan has been depressed since before incoming freshmen were born, but its chronic deflation has never turned into a rapid downward spiral

Krugman doesn't really give much of an explanation of why the inflation-adjusted Phillips curve predicts accelerating deflation. The argument goes like this:

1) Fix an initial value for expected inflation. Now suppose that the nominal interest rate is set higher than the sum of the natural (real) rate plus that expected inflation (perhaps it was right for a few periods but now a shock has changed the value of the natural rate).

2) Now the real rate that prevails is too high and so aggregate demand today is too low to be consistent with those inflation expectations. This puts downward pressure on prices today. However, some sort of friction in the price setting process (menu costs, staggered contracts, Calvo pricing, take your pick) has delayed some of the actual price changes.

3) Rational forward looking agents see that at the current nominal interest rate inflation will be lower than previously expected.

4) Now the crux, (3) implies that the real rate that agents perceive is even higher and thus aggregate demand even lower.

5) The expectational explosion is in progress, it is slow in terms of actual prices because of the friction but expected inflation is now always below the level at which the (fixed) nominal rate is consistent with the real rate being equal to the natural rate, so the deflation keeps accelerating.

Notice though the big caveat at 4, everything stays stable if agents believe that at some future date when the deflation is in progress the CB will make a big loosening, an over reaction so to speak. This belief can put a damper on the explosion today.

Which brings up the most important point, price level determinacy depends on the entire central bank reaction function, not just on what it actually does. Whether or not the price level today is determined depends on what agents think the central bank will do in all states of the world, both states that may occur and states that may never occur. Put another way, private agent behaviour in equilibrium is controlled by beliefs about what the central bank will do out of equilibrium even though that may never happen.

Can't we just stop buying Chinese stuff?

2010-07-25T10:03:00.000-07:00

I claimed in this post that China is effectively forcing a current account deficit on the US by controlling the capital account balance. China can control their capital account balance with the US because China has capital controls in place but the US doesn't. A commenter says:

"the post makes it sound as if the US is forced to consume Chinese goods. It's not. To borrow from the RBA, a current account deficit is a matter for 'consenting adults'. The US was one of those consenting adults."

In the comments to that post Andy Harless has already given the answer, Andy replies:

"As a US citizen, I consent to my own purchases of Chinese goods but not to my neighbors' purchases. So a current account deficit is not a matter for consenting adults, at least if "consent" means active consent. The US does give passive consent by not restricting imports or manipulating capital flows. "

Andy's exactly right but I'll rephrase it in my own words because hey, I want to contribute too. Part of Andy's point is that there is a huge coordination problem here, how can everyone in America all agree to stop buying Chinese goods? This sort of thing has been tried before, there were "Buy American" campaigns against Japanese goods in the 80's. I don't think it had much effect in the 80's but why not?

Well, there is incentive to deviate for everybody individually, it's not an equilibrium outcome. That's what Andy means saying "I consent to my own purchases of Chinese goods but not to my neighbors' purchases". If everyone else boycotts Chinese made goods then the economy gets just as much benefit as it does if I alone deviate and buy the cheaper goods. On the other hand, there is no way to exclude me from sharing in the benefits of higher domestic employment and wages. As long as everyone everyone else avoids the Chinese goods I'm better off buying them, and everyone else goes ahead and buys the Chinese goods then I'm also better off buying them since they are cheaper. Thus, buying from China is a dominant strategy.

There is just no way for the private sector to coordinate reduced purchases of Chinese stuff, the only way is for the government to intervene and affect the coordination.by introducing either capital controls or an import tariff to make the imports more expensive. Neither of these is a good idea though.

If a tree falls in the forest, and only the government hears it, does it make a sound? And if the private sector builds a house that nobody wants to live in...

2010-07-18T08:14:00.000-07:00

Paul Krugman is again despairing about the silliness of reasoning when it comes to fiscal stimulus. I don't really want to advocate for fiscal stimulus, I think monetary policy, in particular a promise of future inflation, is the way. Nonetheless...

Generally, as far as I can understand, the arguments against fiscal stimulus come down to the fact that the government will waste the resources it employs by making something that nobody wants (Update: I have assumed here that it is understood that Ricardian equivalence does not to apply to an explicitly temporary stimulus). That certainly is a pervasive problem with governments and at a basic level it really is what killed the pseudo-communism that was the Soviet Union. Fine, we can all agree that communism sucks and we don't want it.

Still it has to be asked, is that really any different from what the private market produced in the dotcom or housing bubbles? Does anyone now think that funding pets.com type ventures or all the now defunct housing developments in the US or Spain was a good use of resource? Not to mention all the resource devoted to arranging the financing, not wasteful?

Yet those investment booms certainly created employment and the associated high aggregate demand did promote other, more valuable investment as well. Surely the same would apply to the government building infrastructure, even if nobody wants it.

Permanent vs temporary changes to prices and pay

2010-07-17T02:16:00.000-07:00

There has been a debate going on about price stickiness and macro models, see for example Nick over at WCI. This is just my two cents on one possible, partial, explanation for what appears to be going on in the data.

The first point is that, based on my own anecdotal observations, I think you can make a case that what consumers dislike is not so much price variation as permanent price increases (or at least increases perceived to be permanent). This appears to be consistent with the empirical finding of reference prices that change very infrequently while actual traded prices show many temporary changes away from the reference prices. Presumably the temporary changes are largely discounts to the reference price, that is sales. It seems to me that increasing the reference price is something that firms are very hesitant to do while increasing the traded price, discounting the reference price a smaller amount, is something that consumers must not mind so much. So maybe some price variation is ok with consumers.

A couple of things I've observed seem consistent with this idea. One is that there are some things that seem to be discounted most of the time, it is clear in these cases that probably very little exchange takes place at the reference price which means the reference price isn't really a market price at all. This implies that reference prices are chosen intentionally above the intended trading price, possibly to allow room for increasing the trading price without increasing the reference price. Furthermore, I've noticed in the supermarkets where I shop for groceries that there is a strong preference for implementing price increases by reducing package size instead of raising the marked reference price. All this does seem to imply that consumers particularly dislike increases to headline reference prices, somehow more than they dislike increases to traded prices. (Of course if increasing reference prices by reducing package size makes consumers feel better than there is clearly some less than rational behaviour in here somewhere.)

So, why are reference price increases perceived by consumers to be so much worse than simply raising a price that is still a discount to the reference price? Well, perhaps it is the perceived permanence of it. In the book "Animal Spirits" Akerlof and Shiller make a lot of the fact that workers intensely dislike nominal wage cuts, even though wage freezes which usually imply a real wage cut (inflation is usually positive) are fairly commonplace. They attribute this to behavioural reactions, a sense of fairness on the part of workers. However, one thing that is getting more and more common is payment of bonuses as a significant part of total pay (not just in banking where it happens to most of the total pay). Presumably this is so firms can vary the pay of their employees more easily from year to year (that's why it happens in banking). Why might a cut in base salary be far worse than a lower bonus than last year? For bankers it's not, but if the bonus is only 20-30% of you total compensation then a cut this year seems, and is, explicitly temporary while a cut in salary sure seems permanent. (Bankers don't feel this way because the "bonus" is such a high proportion of their pay that they basically just view it as pay, not a "bonus" in the literal sense of the word.)

The connection between base salary and reference price would then be that a cut in salary is basically a permanent cut in pay (for non-bankers bonuses are ofter calculated as percentage of base salary, as are company pension contributions) while an increase in reference price is a permanent increase in price. After all, usually sale prices are a percentage discount to the reference price.

Strong preferences against salary cuts and/or reference price increases could also, in this story, be interpreted as just another example of the people's preference for consumption insurance. Since a company that pays bonuses at all will pay some amount most of the time it follows that the base salary is set intentionally below the intended compensation, just as reference prices are set intentionally above the intended trading prices. Moreover, for better or worse we seem to have found an equilibrium where both reference prices and salaries are sticky, firms set salaries lower than total compensation and reference prices higher than market clearing because they know they can't change them easily. Workers/shoppers accept this because they expect salaries/prices not to be changed easily or frequently. Thus workers/shoppers trade off a lower salary/higher regular price for the stability of knowing it won't change much. It is a stable equilibrium. Whether it's optimal or not? Well, I'd imagine you could make a decent case either way.

Playing the confidence game to win

2010-07-14T12:56:00.000-07:00

A lot has been made recently about the lack of business investment and what's driving it, the universal conclusion is that investment is being constrained by a lack of confidence. Meanwhile Paul Krugman has reiterated his point that the way to break a liquidity trap is through higher expected future prices and in particular that this has nothing to do with how much money is supplied today (since the money can be just as easily taken away tomorrow to prevent any inflation from actually happening). The usual way of describing how inflation helps is that it discourages consumers from saving in the form of cash by lowering the return they can expect, putting consumers in a sort of "use it or lose it" bind with their income.

When it is described in this way it really sounds as though it would take a lot of inflation to achieve sufficient stimulus and it really sounds unfair to use inflation in this way, penalizing those who are prudent. This may well explain some of the resistance to it. However, the stimulative effect of inflation will actually show up in investment far more than in consumption. In large part this is because investment is far more interest rate sensitive than consumption and the way inflation works is by lowering the real interest rate. Moreover, since investment is very interest sensitive it is plausible to have a sufficiently large effect from a relatively small amount of inflation.

This brings me to the point of the post, surely the uncertainty that is holding back investment is a severe doubt that the demand for the output will materialize when the investment starts to bear its fruit. But a promise of future inflation is a promise of high future aggregate demand. Furthermore, the relationship between demand and the real interest rate is something that is abstract and the mechanism is hard to see at the micro level. So it is worth pointing out how amazingly familiar it is to anyone who lived through the last decade. After all, isn't this why there was all this housing being built during the bubble? As long as the prices were rising, and expected to continue rising, the investment in new buildings continued, and was financed, with enthusiasm.

When expressed this way the promise of future inflation clearly isn't screwing anyone out of their hard earned savings. It simply solves a coordination problem, nobody wants to invest if the demand won't be there but the demand won't be there if nobody invests. A promise of future inflation is a promise to that the demand will be there when it's needed.

So why are profits high if demand is really so low?

2010-07-13T12:26:00.000-07:00

Tyler Cowan wants to know how profits of companies can be so high while apparently demand is too low. Tim Duy notes that labour's share of income has been falling for quite a while. I think that these are two symptoms of the same phenomenon and I want to propose what I think is a fairly simple explanation.

If we take the trading world's economy as a whole, as one big closed economy, then the opening of china over the last 10-15 years has basically been a very large increase in the available labour force. This has left the capital:labour ratio in the trading world too low. The appropriate response then is to have an increase in investment spending to build the world's capital stock up to its desired level. The low interest rates and high stock prices that most of the western world has seen since the mid-90s is just the normal market signal for a high level of investment. The increase in capital's share of income is just what you'd expect of the relatively scarce factor.

Now of course there has been a spanner thrown in the works in the form of Chinese capital controls. Clearly, since the added labour is all located in China, the additional capital should also be located in China. However Chinese capital controls, associated with their exchange rate peg, interfere with this. In order to maintain the peg the Chinese are forced to invest a substantial proportion of their savings in the already capital rich west (causing us trouble when we try to invest all those savings) instead of investing them at home where capital is scarce, labour abundant, and thus the marginal product of capital is highest. Finally, and most importantly, the capital formation that has happened in China has been directed by the government into the export sectors and kept out of the rest of the economy.

The result is that in capital rich manufacturing industries in China labour is competing directly with cheaper labour from their general economy and this depresses their real wages. The goods produced in these sectors are exported and thus these low wage workers are competing directly with workers in similar industries in the west. Since labour is substitutable across industries (generally we think capital is specialized and labour is substitutable) this translates into depressed wages even in the more capital intensive industries in the west and since these industries aren't in direct competition with Chinese production the result for them is simply a gift of higher margins and profits. Effectively, by this mechanism, scarce capital at the world level is translating into capital having a higher value and taking a greater share of income, more or less as you'd expect.

Of course, increasing capital's share of income should be a standard price signal that it is scarce and valuable and thus should spur investment but, again, capital controls are preventing this. It is worth pointing out that by most standards it does appear that China is in fact doing a lot of investing but at the same time simply looking at the huge amount of savings that they export to the west shows that they should be investing much more. After all, this is a country with a population that is (I guess) double the population of the US and Europe combined and it is extremely capital poor. China should be investing at unprecedented levels.

Most importantly, if China had the appropriate level of physical capital formation happening then the west would have much less of an unemployment problem, China would send us consumption goods and we'd send back capital goods. What's going on now is better for neither the west nor China, we have unemployment and they remain poorer than they should be. More real capital in China would mean higher wages for the Chinese and less deflationary pressure exported to the west, it would be win-win, just as trade should be.

Why we keep having bubbles

2010-07-10T04:07:00.000-07:00

The point of this post is to argue that, despite what we may naturally think, the reason that our economy is in such a mess can be traced essentially to one source: China. What China is doing with their currency peg is the reason our natural interest rate is negative and so the only way we can maintain full employment is with either an asset bubble, which we've tried twice, or by allowing a higher inflation rate. What this recession is not is a failure of monetary policy.

To explain what China is doing and why it's causing us such trouble let's start with the capital account. Because China has capital controls and the western world doesn't they essentially control our capital account balance with them, if they export capital to us by by buying our bonds or hoarding our currency there is nothing the west can do to bring the capital account into balance. We can't send the capital back by investing in China because we can't buy their currency.

So why does Chinese control of our capital account balance with them matter? Because it basically means they also control our current account balance (exports minus imports). By construction the capital account balance and the current account balance sum to zero, so in the absence of an intervention that prevents markets from clearing (like trade barriers) they can impose a current account deficit just by imposing a capital account surplus on the west and that is what they are doing. Thus, in the national accounts of the west China is forcing the (X-M) term to be negative.

Since Y = C + I + G + (X-M) we see right away that C + I + G must exceed Y which explains why the west is constantly dissaving. Right now it is G that is doing most of the dissaving but before it was in large part C and I that exceeded incomes, basically you could say that our problem is that in order to maintain full employment we have to spend all of the savings that China sends us and this requires more spending on C, I and G then we have income Y.

So what are our options for raising Y back to its full employment level? Well, clearly G can dissave a lot more which is something lots of people are proposing. The only other way is to raise C and I. The problem is, how do you induce the private sector to spend that much? There are basically two possiblities, one is general price inflation to make the real interest rate negative and the second is an asset bubble. It should be said that inflation is the preferred way because it is less distortionary.

Inflation works by making the real interest rate negative and thus spurs spending on C and I without favouring one sector over the other. The only other way to induce all that private spending is to concentrate it in one particular sector, have an asset bubble. The role of the asset inflation is, on one hand to induce a lot of investment in the chosen sector by making prices high and hence required returns low (even negative) while on the other hand it gives consumers a price signal that their future consumption will be high and so it is optimal to raise consumption now, even if it means consuming more than their income.

To show just how simple the problem really is let's now take a look at the real side to the problem we're having while ignoring the financial side.

Basically what is happening is that since the late 90's the Chinese have started sending us lots and lots of stuff (like t-shirts and sneakers). The stuff shows up at our shores and gets distributed. This means though that whomever might have been making that stuff here now needs something else to do.

So, what did they do? (Remember we are ignoring the price signals that co-ordinate what they should do.) The first try was to have them set up Pets.com type ventures, this worked for a while but eventually we stopped wanting to buy things from Pets.com.

The next try was having them all go build stuff, houses and other fixed structures. Eventually though we had too many of those. A lot of them also got into various services (mortgage origination) associated with such building.

Now we are co-ordinating on having them sit and do nothing.

Ok, first of all, what should they be doing? They should be employed producing capital goods for export to China, supplying chinese domestic investment. However, the Chinese forex peg plus capital controls prevents all those chinese savings from being spent on chinese investment.

So, since China is exporting all those savings to us how can we be induced to spend it all? Well, we can have an asset bubble that generates over investment in some sector of our economy like has been tried twice or we can have inflation that maintains expenditures in a balanced way.

Of course, if we introduced either trade barriers to prevent the Chinese goods from arriving or capital controls, essentially to prevent us paying for them, then that solves the problem but in a very, very suboptimal way.

What we simply can't have (without capital controls or trade barriers) is all of full employment, no bubble and no inflation. It is simply false that the fed could have maintained full employment in the middle of the last decade and still tightened enough to prevent a bubble.

Furthermore, until China starts buying stuff from us or stops selling stuff to us at artificially low prices then it will remain impossible for us to maintain full employment without inflation of something (either consumer prices or assets).

Can the Euro be Saved?

2010-02-07T10:48:00.000-08:00

As Simon Johnson points out here and here, the Euro might be in some trouble. One problem is that one or more of the PIIGS might leave the union but the more serious problem is that Germany might and it seems obvious that without Germany there is no Euro.

The first potential problem, that some or all of the PIIGS might leave the monetary union is really, in my opinion, no trouble at all. If they left, as the weaklings of the union, the Euro only would only get stronger and more to the point, leaving the Euro only makes things worse for the PIIGS. On the other hand, if Germany decides to issue its own currency instead of bail these countries out then the Euro would surely dissolve. So what can be done about the weak links?

Well, the point of one of these countries leaving the Eurozone would be that it could begin issuing its own currency. This, of course, would constitute a default on their debt which promise to pay in Euros and in the short to medium run their external payments trouble would only get worse. After all, the new currency would certainly be worth far less than the Euro just for being less liquid and on top of that the whole point of issuing it would be to monetize fiscal deficits. The new currency would have virtually no purchasing power internationally.

So why might a country consider this? Well, one thing a domestically issued currency would accomplish is keeping the domestic banking system liquid. This will soon be a major problem for Greece. Currently the ECB is accepting Greek government bonds on repo but this will soon end and then the Greek banking system will find itself hard up to obtain liquidity.

What about government finance? This works out the same either way, only the language we use to describe it differs. In the Eurozone the Greek government will soon find it can't sell debt externally (probably when the ECB stops accepting it on repo), out of the Euro the same thing will happen so in real terms the only resources available to the Greek government are taxes and domestics buying their bonds. If the Greek government tries to consume more in real terms then it can afford by printing its own currency the result will be hyperinflation, if they try to do this while keeping the Euro the result will be default. In neither case will the government get more resources.

So what's the solution? Well, what the PIIGS need to do is get on with the business of defaulting in a coordinated manner and with German backing. What I have in mind would play out in the following way:

1) The PIIGS get their domestic constituents to agree to a set of austerity measures that reign in government expenditures (this may well be the hardest part). Given those measures, which they commit to going forward, they calculate how much of their existing debt they can afford to pay back. Hopefully it's a decent number, let's say 70% for all of them.

2) They announce that the face value of all outstanding bonds is now reduced to the amount calclulated above, so in our example they write the debt down to 70 cents on the Euro.

3) With the fiscal austerity measures in place and the debt written down to an affordable level we come to the clincher. The rest of the Eurozone, meaning Germany, guarantees the remaining outstanding debt and and any new short-term debt issuance for a period of time. The guarantee is contingent on the respective governments sticking to the austerity measures. This accomplishes the most important part, the ECB can now accept the debt on repo and keeps the domestic banks funded.

The point here is that for the most part the deed is done on the existing debt, they bought stuff with paper that promises Euros, they don't have the Euros. Other than Germany just assuming the debt, something that they would be ill advised to do, default of one sort or another is inevitable. Furthermore, default is only such a disaster for the domestic economy if it leaves the banks without liquidity. This way they can keep the local banks funded, be able to issue more short-term paper to keep their governments running and do it all in a way that should be acceptable to Germany, in particular it shouldn't actually cost the German treausury any money.

Finally, they should do this all at the same time. Far better to get it done once then to have each country get run by the market in sequence with some sort of ad hoc fix applied each time. One of the lessons of the countries leaving gold in the 30s was they were best off when they did it together, otherwise the ones still on gold got squeezed after the others had devalued.

Of course, this is all predicated on the PIIGS being able to get their populations to agree to the auserity measures and this is looking pretty much impossible for Greece. So the prognosis is not that good.

The Phillips Curve in a Liquidity Trap

2009-06-01T10:43:00.000-07:00

This note discusses the Phillips curve with special emphasis on understanding it not as a single equation standing alone but how it interacts with other equilibrium relationships. The modern Phillips curve has a specification that looks something like:

PC: Infl(t) = a*E(infl(t+1)) + b*OutputGap; a > 0, b < 0.

Notice that the first term on the right hand side has expected FUTURE inflation. This is the specification that results from a rigorous derivation based on an economy with forward looking, value maximizing firms that are constrained by nominal frictions, (for example an inability to continuously adjust wages to match fluctuations in the demand for their output). This makes the specification given here different from the empirically derived Phillips curves that failed so badly in the seventies. This version attempts to pre-empt the Lucas critique by explicitly specifying that expected inflation does not increase output, it only increases current inflation. (The specification of the underlying frictions is not fully articulated in the canonical version which leaves it open to a generalized version of the Lucas critique. There are however a variety of proposed improvements in the literature.)

Also notice that having b < 0 implies a definition of OutputGap such that a larger output gap means less output, the gap is how much below potential the economy is operating. However, the gap is allowed to be negative, that is, the economy is allowed to operate above “potential”. As such, “potential” is not a hard constraint but an elastic one. “Above potential” output is understood to mean that there are inflationary pressures.

One thing that is important to understand about the Phillips curve, in any of its theoretical incarnations, is that in no case does it say that high inflation causes higher output, the theory only says that high output and high inflation tend to coincide, generally due to both being caused by strong aggregate demand.

This and other similar considerations imply that to make use of the Phillips curve we need to relate it to the equilibrium determinants of aggregate demand. One of these is the consumption Euler equation, (see here as well), the other is the Fisher equation:

FE: 1+i = (1+r)*(1+E(infl)); i is the nominal interest rate, r is the real interest rate.

It is not correct to base an analysis on the Phillips curve alone, the time path of consumption, inflation and interest rates (both real and nominal) must satisfy all three equations simultaneously.

The Effect of an Increase in Expected Inflation

The first thing to notice is that the equation PC, on its own, implies that increasing expected inflation does not change output at all, it simply raises current inflation. The effect on output of an increase in expected inflation depends on the reaction of the nominal interest rate.

In particular, if the nominal interest rate does not change (perhaps because the central bank is targeting the nominal rate) then the Fisher equation implies that the real rate has fallen and this feeds into the consumption Euler equation to increase aggregate demand.

On the other hand, if the central bank increases the nominal rate one for one with expected inflation then the real rate and AD are unchanged. Finally, if the central bank increases nominal rates more than one for one then the real rate is actually raised and thus AD falls.

Two Important Conclusions for Policy in a Liquidity Trap

The Phillips curve and its relation to the other two equations makes clear two important points.

1) Higher inflation should be expected to precede a real recovery, it is unlikely to be the case that inflation only picks up after the output gap closes.

2) The real recovery will only happens if the central bank keeps nominal rates low for a time after inflation begins to rise. The central bank must accommodate some inflation for a period of time in order to increase output.

The three equations taken together imply that in a liquidity trap there is simply no way for monetary policy to generate a real recovery without accommodating a sufficient amount of inflation.

In a liquidity trap investment is a like a public good

2009-05-27T12:28:00.000-07:00

This post picks up where the last two left off. The idea is that we’ve found ourselves in a situation where the natural real interest rate is negative but there isn’t enough expected inflation to make the real rate that agents believe they are faced with when making their consumption-savings decision as low as the natural rate. Thus, the consumption level that satisfies agent’s consumption Euler equations is lower than the consumption level at full employment or, put a different way, the savings level that satisfies the Euler equation is too high. At the same time, the extra savings does not get spent on real investment due to the marginal returns to investment being too low to compensate for the risk. In particular, with a risk premium the shortfall in investment demand can happen even if the marginal product of capital is still positive.

I’ve argued here http://canucksanonymous.blogspot.com/2009/05/what-do-liquidity-traps-have-to-do-with.html that simply increasing the money supply, without generating expectations of future inflation, accomplishes nothing no matter how much money is printed. The reason for this is that agents are caught in a sort of prisoners dilemma type equilibrium, even if everyone understands what’s happening there is no way to coordinate increased expenditures. Since each agent individually prefers to save rather than consume and each individually is unwilling to fund the available investments then, even if everyone understands it’s better for us all to spend more now, regardless of what you expect the rest of the economy to do you’re better not spending. If everyone else spends you get the benefit whether or not you take part and if nobody else spends you won’t see the benefit even if you do spend. Thus to not spend is the dominant strategy for everyone.

In this sense investment seems like a public good in a liquidity trap, just like a road is. Everyone understands more investment spending is desirable but everyone prefers that someone else actually do the spending. So perhaps the solution is for the government to do the investment spending directly. Well, to the extent that the government issues new debt to finance the expenditures then this can be inflationary and thus break the trap. However, suppose that the central bank remains committed to price level stability and will tighten policy to avoid the inflation. While the government spending would raise income while the economy remains in the trap, without expected inflation it won’t succeed in breaking the trap.

One final possibility is that the central bank buy up the real investment with the intention of selling it back to the private sector. In particular here is the suggestion of a commenter:

the central bank buys the marginal investment project - with a negative return - for money - with zero return - and then re-sells the project in the next period at the purchase price. Everyone who did the switch avoids making a loss, which the central bank ends up with.

The problem here is that if investment truly has negative real returns then the real return to the portfolio of all the money being held by the private sector can’t have a zero real return. Suppose the real return to investment is -3%, well then when tomorrow comes and agents are ready to consume it’s not physically possible for them to all have made zero real return on each dollar they held because productive capacity expanded at less than one for one with the extra money. If the central bank leaves the money supply unchanged then this must necessarily translate into roughly 3% inflation. If the central bank wants to avoid this inflation then they must contract the money supply to keep prices unchanged. Thus, the result is that while each dollar that remains in circulation realizes a zero real return the sum of all the dollars does not. Some of the dollars are simply reclaimed by the central bank, and since the central bank doesn’t exchange these for stored consumption the aggregate real return can’t exceed the -3% that the investment generated.

Thus, if available investment returns are negative the central bank can only accomplish two things by buying it. One is to allow all outstanding currency to share equally in the real loss, that is, allow inflation. The second possibility is to have most of the money in the economy have zero real loss and have some small portion of it bear the entire loss

Euler Equations and the Liquidity Trap

2009-05-26T14:47:00.000-07:00

This post picks up where the last one left off. The natural real rate of interest is the real rate that would obtain at full employment. This rate is determined jointly by the consumption Euler equation and firms profit maximization condition for investment which is that the real interest rate should equal the marginal product of capital.

Suppose that, for whatever reason, the real rate that prevailed in the economy is higher than the natural rate. Well, the Euler equation is just a condition for maximizing utility and so agents individually will always want to choose their consumption to satisfy it. Note that from the point of view of the individual agent today’s consumption level is the choice variable, the real rate is taken as given. Now, if the real rate is too high, relative to the natural rate, then 1/(1+r) is too low, thus in order to satisfy the Euler equation the ratio of marginal utility tomorrow to marginal utility today needs to be lower. The way to lower this ratio is to raise the marginal utility of consumption today and this means choosing less consumption today (since declining marginal utility means marginal utility is lower for higher consumption levels).

This is important in the liquidity trap case because a liquidity trap is manifestly a situation where the real rate prevailing in the economy is too high. If the natural rate is negative then a zero nominal rate will only translate into a negative real rate if inflation is expected. Suppose, on the other hand, that expected inflation is zero and so the real rate that agents infer is zero. Individual agents can’t change the prevailing real rate, thus, since they all want to maximize their utility they will reduce their consumption today to set up a consumption path from today to tomorrow that corresponds to utility maximization. The result is that the economy finds an equilibrium in which the real rate of zero is rationalized with aggregate demand being too low to support full employment.

Consumption Euler Equations Explained

2009-05-26T14:08:00.000-07:00

The consumption Euler equation is nothing more than the intertemporal analogue of a standard result in basic economics that at a point of utility maximization the ratio of the marginal utilities of two goods is equal to the ratio of their prices. The intuition for this result is simple enough, the price ratio tells you how much of one good you need to give up to get an extra bit of the other good. To be concrete let’s say the choice is between pizza and beer (clear complements). If the price of a pizza is 3 time the price of a beer you must give up 3 beers to get a pizza. On the other hand, your marginal utility of pizza measures the utility gained from a pizza or the utility lost from giving up a pizza (taken to be the same because strictly speaking marginal utility refers to a derivative which means it’s the gain or loss from an infinitesimal amount of pizza added or subtracted from your consumption basket).

So, if your terms of trade are 3 beers per pizza and your marginal utility of more pizza was 4 times as high as your marginal utility of a beer, clearly you should make a trade and give up 3 beers to get a pizza. You lose the utility of 3 beers but gain the utility of 4 beers. Since such a trade clearly raises your total utility it means that the original point was not a point of utility maximization. You can only have maximized your utility if the ratio of marginal utilities equals the price ratio. A consumption Euler equation makes the same argument about your choice between consumption now and consumption in the future.

Suppose we normalize so the price of your consumption basket today is 1 and consider a zero coupon bond maturing at time T in the future. If r is the real yield of the bond then the price of a unit of your consumption basket at time T is 1/(1+r) and this is also the price ratio. Thus, by the reasoning above you are only maximizing your utility if the ratio of your marginal utility of consumption today to your marginal utility of consumption at T is equal to 1/(1+r). This remains true for any time T for which you have available a zero coupon bond of that maturity.

Of course, in practice most bonds are coupon bearing bonds. However, since the coupon bond can be seen as just a portfolio of zero coupon bonds their prices are still fundamentally related to the relative prices of consumption today versus consumption in the future.

I've ignored uncertainty here, this complicates matters but doesn't really negate the basic intuition. You just have to apply it even more widely.

Update: Let U(c(t+1), t) denote the utility at time t of c units of consumption consumed on date t+1. The Euler equation relating consumption at date t and consumption at time t+1 is

E[U'(c(t+1),t)]/U'(c(t),t) =1/(1+r);

where the prime denotes differentiation with respect to c(.), the E denotes expected value and the r is the real interest rate between t and t+1.

Usually it is assumed that U(.,t) is related to U(.,s) by a common utility function and discount factor: U(c(t+1),t) = b*U(c(t+1)); b<1.

Micro-foundations of Money

2009-05-20T12:58:00.000-07:00

This post picks up where the IS-LM post left off to discuss two versions of the effects of an increase in the money supply. One version is my view and is based, loosely, on the idea of a cash-in-advance constraint. The other version is my attempt to interpret the view of Nick Rowe as I understand it, I think Nick's view is based, also perhaps loosely, on a money-in-the-utility-function type formulation.

Two versions of what happens when the money supply is increased:

My version: In my version, at the margin money is held to only to fund purchases of consumption goods. Notice I said at the margin, there could be a buffer stock held for unexpected expenditure needs. Thus, once enough real balances are held to cover real purchases (plus the buffer) any marginal extra currency is used to buy an interest bearing asset, that is a bond. Thus, in my story an increase in the money supply shifts the LM curve by the following causal chain:

1) Start at a point on the LM curve were supply and demand for real balances are equated and increase the money supply. Since real balances are high enough to fund desired purchases ALL of the extra money flows to the bond market and thus drives real interest rates down.

2) The lower real interest rates increase consumption demand via the consumption Euler equations as usual. With sticky prices the extra consumption demand increases output.

3) Higher consumption demand increases demand for real balances to fund the extra expenditures and LM equilibrium is re-established.

My interpretation of Nick’s version: Here money (that is, real balances) is held to satisfy a liquidity preference. It is a derived preference in the sense that it is still for the purpose of funding real consumption expenditures plus a buffer for unexpected expenditures, the difference is in the word “preference”. The liquidity preference acts like a standard preference with the usual, smoothly declining marginal utility. Thus, in this version an increase in the money supply shifts the LM curve by this causal chain:

1) Start at a point on the LM curve were supply and demand for real balances are equated and increase the money supply. Since we are at an optimum, at the margin we are indifferent to holding the extra money, buying a bond with it or spending it on consumption goods. Thus, potentially some of the marginal extra money gets spent on consumption goods. To the extent that some of the extra money is invested in bonds the logic is identical to my version. However, since some of the excess also gets spent on consumption goods the extra money can increase aggregate demand directly. (In particular, if interest rates are already zero like right now then the money is entirely spent on consumption goods.) So, assume the marginal dollars are spent on consumption, then:

2) With sticky prices the increased consumption demand increases output. (In the usual case, with nominal rates not stuck on zero, the extra output, relative to future output, lowers the real rate via the consumption Euler equation.)

3) The lower real interest rate (in the non-liquidity trap case) is a lower cost to holding real balances and thus the demand for real balances goes up via the usual maringal benefit equals marginal cost logic. The increased demand for real balances matches the extra supply and equilibrium is restored.

Note the fundamental difference in the two stories, in my version the transmission from increased money supply to higher aggregate demand is entirely due to the lower interest rate. Thus in my story, when nominal rates are at zero the only way to increase aggregate demand is to raise inflation expectations thus lowering the real rate. In Nick’s version, when nominal rates are zero, the increased money supply increases aggregate demand directly.

IS-LM explained

2009-05-20T12:53:00.000-07:00

My purpose here is to explain the IS-LM model as I understand it and to set the context for a subsequent post that will explain a difference I have with Nick Rowe about the microfoundations of monetary theory. The IS-LM model shows how income and the real interest rate are jointly determined in the economy. The model is not really dynamic so I’ll only refer to two periods, today and tomorrow (where tomorrow is just some time in the future, perhaps next year). I’ll ignore government spending so there won’t be any discussion of fiscal stimulus.

The IS Curve.
The IS curve is made up of all combinations of real income Y and the real interest rate r such that real investment demand equals the demand for real savings. The IS curve traces out a downward sloping curve with r on the vertical axis and Y on the horizontal axis. Notice that everything is real, the curve relates the real interest rate to real income.

To begin we need to find one point on the curve. To do this consider the situation an full employment, the real income at full employment is entirely determined by the production technology and the real interest rate is equal to the natural real rate which is determined by expected consumption growth assuming full employment is maintained. Note that the difference between income and consumption is investment since we are ignoring government.

Next I’ll argue that the curve slopes downward:

1) Consumption: Start out in a case where we are in equilibrium so at the current interest rate you are happy with your consumption levels for today and tomorrow (ignore the uncertainty in tomorrow's consumption). Now I give you more income today but hold tomorrow's consumption unchanged (and prices/interest rates have not yet changed). Since you where at a maximum before you were indifferent between an extra bit of consumption today or tomorrow. Now you have extra consumption today and so by the usual declining marginal utility idea your marginal utility of today's consumption has fallen below your marginal utility of tomorrow's consumption. Thus, to re-establish your first order condition you need to reduce today's consumption and increase tomorrow's. Thus, the fact that you want to save some is not an assumption but comes from the fact that you're maximizing utility.

2) Investment: Still assuming prices/rates have not yet changed. A firm’s maximization problem says they want to employ capital until the marginal product of capital (MPK) equals the real interest rate. Since rates haven't yet changed there is no change in investment demand. (Firms also started in an equilibrium where they were happy with current investment plans).

3) We now have a situation where desired savings exceeds desired investment. How are they re-equated? Well, the excess saving starts to drive down the interest rate. This has two effects, it reduces saving demand by making tomorrow's consumption more expensive (in terms of today's) and it increases investment because reducing the real rate means firms need to increase the capital stock to re-establish MPK = r (declining MPK). The real rate falls until savings demand and investment demand are equal.

The LM Curve.

The LM curve gives the set of (Y,r) pairs such that money supply equals money demand. This curve is upward sloping when drawn with Y on the horizontal axis and r on the vertical axis. To derive the curve start at a point where supply and demand for real balances are equated and raise income.

1) Increasing income while holding the real rate constant increases consumption demand by the same utility maximization mechanism as above.

2) The increased demand for consumption purchases increases the demand for real balances to fund the extra expenditures. Recall that the money supply is unchanged.

3) The higher demand for cash prompts sales of bonds and thus raises interest rates.

Why do liquidity traps tend to follow investment booms?

2009-05-18T09:27:00.000-07:00

My last post described my view on how a negative natural real interest rate gets turned into a liquidity trap, in particular, it is not the case that the negative real rate necessarily results in a recession. After all, it could just mean a huge investment boom. I said there that we'd fail to get the required level of real investment if the marginal product of capital was too low to generate a high enough risk premium due to a recent investment boom

My first post described a simple example of how a negative natural real rate can occur. That post was motivated in large part by discussions I've been having over on the WCI blog (http://worthwhile.typepad.com/worthwhile_canadian_initi/2009/05/could-the-natural-rate-of-interest-really-be-negative.html) about whether or not the natural real rate could really be negative. In that discusson Sthephen Gordon pointed out that one way to get a negative real interest rate is if the marginal product of capital was less than the depreciation rate and this could be the result of an overhang of essentially useless capital.

My point here is just that these arguments appear to explain why liquidity traps seem to follow gigantic investment booms. In the great depression, Japan's trap and the current recession, the trap followed a gigantic run up in asset prices.

There are, I think, two ways to interpret the asset price rallies that precede the springing of the traps. One interpretation is that future productivity growth was anticipated to be high and this growth was not regarded as being very uncertain. In this case, despite high asset prices, future returns were still believed to be high enough to compensate for the perceived risk. The trap would then be sprung by some shock, say a large run-up in commodities prices or an otherwise innocuous seeming monetary tightening that might make future output growth seem a bit more uncertain and thus, just slightly, raised risk premia. We then find ourselves in a situation where real investment and asset prices start to decline.

Of course another interpretation is that high prices are just another name for low returns. Thus, it may be that in each case a very low, possibly already negative, natural real rate preceded the liquidity trap by several years. Moreover, the sheer scale of the equity price rallies and valuations that preceded the crashes in all case imply that if future productivity growth was not expected to be enormous then both real rates and risk premia were very low. Again, some shock to the perceived distribution of future growth would raise risk premia and start a decline in real investment.

In either case, from there things would only get worse. The initial decline in asset prices in all cases destroyed the balance sheets of an over leveraged financial system. The sudden freezing of credit interemediation activity further interrupted investment and by reducing future output growth (by reducing the future capital stock) would cause further increases in both desired saving and risk premia.

What do liquidity traps have to do with liquidity?

2009-05-15T10:40:00.000-07:00

The purpose of this post is to discuss my view on the relation between liquidity traps and monetary policy. Throughout I’ll assume that the natural rate of interest is strictly less than zero. I make no claim that a negative natural real rate is necessary or sufficient for the liquidity trap to occur. I claim only that it’s one way to get a liquidity trap and it can be a reasonable interpretation of the current situation (for an explanation of what the “naturnal real interest rate” is and a motivating example of how it can be negative see http://canucksanonymous.blogspot.com/2009/05/purpose-of-this-post-is-to-explain-what.html. )

A negative real interest rate comes about via the consumption Euler equation from some combination of expected consumption growth being low (possibly negative) and (for risk averse agents) consumption growth being perceived as very uncertain (volatile). In particular, a negative natural real rate of interest can occur even in a world without money.

Now, the first thing to notice about the negative real rate is that it doesn’t have to imply deficient aggregate demand and the resulting drop in output. It certainly implies a high demand for real savings, in aggregate agents are willing to trade off one unit less consumption today for only (say) .97 units of consumption tomorrow. However, the standard first order condition for firms to be maximizing profits sets the marginal product of capital (MPK) equal to the real interest rate. Since MPK is usually thought to decline with the amount of capital we should see a huge investment boom. The huge demand for capital goods makes up for the high savings demand and full employment is maintained.

So, what goes wrong in the world with money, nominal frictions and risk premia? Well, the zero bound on nominal rates of course. But:

First of all, the zero bound alone wouldn’t cause a problem with flexible wages and prices. Once the zero bound was hit you’d simply have wages and prices fall today, relative to where they’re expected to be tomorrow, and this sets up expected inflation that delivers the required negative real interest rate and maintains full employment. So, we only have a problem with sticky prices and the zero bound working together.

Secondly, even if the risk-free real interest rate wouldn’t go below zero it’s difficult to argue that there is any limit to the amount of possible investment that at least returns something greater than zero. So why don’t we still get the investment boom? The answer is the risk premium on real investment (equity), even if the risk-free real interest rate of zero the required return on risky real investment could be much higher and thus there may be no real investments that can actually attract capital.

It is in this sense the trap is about liquidity, agents are willing to save at less than zero real return but not willing to fund real investment because, although it offers positive expected returns, it doesn’t offer a high enough return to compensate for the risk. Thus we have deficient aggregate demand and a recession.

Now, suppose we have a situation where the full-employment real interest rate is negative, say it’s -2%, nominal interest rates are zero and expected inflation is also zero. Suppose the equity risk premium is 7% so the required return on real investment is 5%. Finally, suppose that the expected return on the available real investment is only 2% (perhaps because we’ve recently had a time of booming investment). Clearly maintaining full employment requires expected inflation of 5%.

Now the money question:

Does increasing the money supply, without increasing expected inflation, help?
No.

Suppose that the only two agents in the economy are you and I. In full employment we are producing as much as we can and we both would like to substitute more consumption tomorrow for less today. If we devote the savings to real investment then the capital stock tomorrow is higher and this allows us both to consume more tomorrow. In the liquidity trap case we both keep our savings as money (or government bonds) and we don’t fund any real investment. Thus, the capital stock is unchanged (ignore depreciation) and it’s not physically possible for both of us to consume more tomorrow.

Now, increase the money supply for today only. Suppose the extra money goes to both of us in equal amounts. It is understood that the extra money supply will be withdrawn tomorrow so that this doesn't generate any increase in expected inflation. Suppose I spend my share and you save yours. I get extra consumption today (equal to the amount you sacrifice) and you get extra consumption tomorrow. The result is that you've accomplished what you wanted but I've done the opposite. So I also want to save my money today just to keep up with you. This remains true no matter how much money is printed.

To break the trap you have to lower the real return to holding money (and other nominal debt).

There is general agreement that a permanent increase in the money supply will break the trap provided it is believed to be permanent by agents in the economy. The important theoretical point here is that it works by lowering the real return to holding money, it has absolutely nothing to do with satisfying an excess demand for base money.

Lowering the real return to holding money accomplishes two things:
1) Future consumption gets more expensive relative to current consumption and so people start substituting away from future consumption and towards current consumption (savings demand falls).
2) The required return on real investment falls and so demand for real investment increases. Basically the risk-return profile of real investment looks relatively better the lower is the real return to money.

If the real return to holding money is lowered enough then 1 and 2 eventually dominate the demand for real savings.

Negative natural real interest rates

2009-05-14T23:29:00.000-07:00

(Recently updated to correct a silly mistake that was pointed out by a commenter)

The purpose of this post is to explain what it means for the natural real rate of interest to be negative and give an extremely simple example of how it might happen.

First of all, what do we mean by the “natural real rate” of interest. The natural real rate of interest is the interest rate that prevails in the economy when it is at full employment and is producing at full capacity. This natural rate is determined by the consumption path at full capacity and thus has absolutely nothing to do with money, nominal prices or expectations about inflation.

To take an example, consider a world with two periods. In the first period our maximum output is 100.25 units of consumption. In the second period our maximum output grows to 110 units of consumption. Assume there is no investment, the productivity growth is a result of learning by doing.

Now, suppose that another country called “China” offers us a trade, they give us 4.75 units of consumption in the first period and we give them 5 units of consumption in the second period. Assume we can’t default on our debts.

So our choice is between two consumption paths, in one case we consume 100 in the first period and 110 in the second period. In the second case we consume 105 in both periods. Which would we choose? Well, under the standard assumption of declining marginal utility we are better off accepting the trade and consuming 105 in both periods. Thus, let’s assume we take the trade.

Now, what is the natural real interest rate in this world? Since we took the trade our consumption is constant, we consume 105 in both periods, thus the natural real rate of interest is equal to the average subjective discount factor, say 4%. That is the real interest rate that supports a constant consumption path is 4%. Notice that this has nothing to with money or expectations about prices at all. It is entirely determined by our productive capacity and our real net exports in both periods.

So, how can the natural real rate turn negative? Suppose that in the first period a computer virus called ‘CDOsquared.Doom’ destroys all the databases in the country and completely stops our learning by doing productivity growth. Now our productive capacity in the second period has fallen to 100, but we still owe 5 to the Chinese. Thus, our consumption in period 2 has fallen to 95.

We are now in a situation where, assuming we stay at full employment and produce at full capacity, consumption growth is -5% (even though output growth is zero) and our subjective discounting of future consumption, on average, is 4%. Whether or not this actually results in a negative natural rate of interest depends on preferences but it is extremely easy to specify a utility function (say the standard power utility) where this results, via consumption Euler equations, in a negative natural real rate of interest.

I stress again that the natural real interest rate is entirely determined by the path of consumption assuming maximum output and by preferences in the consumption Euler equations. It is not changed in any way, in this example, by monetary policy or inflation expectations. (The time path of monetary policy can only have an effect if it changes investment rates.)

To conclude I would like to point out that I’ve said nothing about whether or not a negative natural real rate of interest actually results in a recession or the dreaded liquidity trap. These questions do hinge on expectations of monetary policy and inflation. I will do a post discussing how the negative natural real rate might result in a liquidity trap, as well as a post explaining what consumption Euler equations are, if I have any indication that anyone would read them.