Thursday, May 21, 2015

Don't get mathy with me, or I'll give you a good shunning.

I had heard Paul Romer is disgruntled, and now that he's written down his thoughts, we can perhaps sort this out. We'll start with his recent blog post on "Protecting the Norms of Science in Economics." Here is Paul's view of science:
My reading of the evidence convinces me that a group of scholars can make progress toward the truth only if they share a commitment to the norms of science, a set of norms that support a reputational equilibrium that encourages trust and that rewards progress toward truth.
Think of truth as existing at the top of a mountain. Once we get to the top of the mountain we'll know it, as we'll be able to see a long way, but while we're climbing the mountain we're in a fog, and we can't see the top of the mountain. But we might be able to discern whether we're moving up, down, or just sitting in one place. Paul thinks that we can't just let scientists run loose to take various paths up the mountain with different kinds of gear, and with different companions of their choosing. According to him, we have to organize this enterprise, and it's absolutely necessary that we write down a set of rules that we will abide by, come hell or high water. And when he says "reputational equilibrium" most economists will know what he has in mind - there will be punishments (imposed by the group) for deviating from the rules.

Paul isn't just throwing this out as a vague idea. He has a specific set of rules in mind. We'll go through them one by one:

1. We trust that what each person says is an honest account of what he or she thinks is true. So, that seems fine. We'll all agree that people are at least trying to be honest.

2. We all recognize that reasonable people can differ and that no one has privileged access to the truth. Sure, people are going to differ. Otherwise it would be no fun. But there's that word "truth" coming up again. I really don't know what truth in science is - if I ever find it the surprise will likely induce cardiac arrest, a stroke, or some such. To my mind, we only have a set of ideas, which we might classify as useful, not-so-useful, and useless. One person's useful idea may be another's useless idea. Particularly in economics, there are many of us who can't be convinced that our works of genius are actually not-so-useful or useless. Truth? Forget it.

3. We take seriously the claims of people who disagree with us. What if the people disagreeing with us are idiots?

4. We are ready to admit that others might be right that each of us might be wrong. At first I thought there was a typo in this one, but I think this is what Paul intended. Sure, sometimes two people are having a fight, and no one else gives a crap.

5. In our discussions, claims that are recognized by a clear plurality of members of the community by as being better supported by logic and evidence are the ones that are provisionally accepted as being true. This is absurd of course. We don't take polls to decide scientific merit. Indeed, revolutionary ideas - the ones that take the biggest steps toward Romerian truth - would be the ones that would fail, by this criterion. Scientists, particularly the older ones, become heavily invested in the status quo, and don't want to give it up. In casting their negative votes, they may even by convinced that they are adhering to (1)-(4).

6. In judging what constitutes a “clear plurality,” we put more weight on the views of people who have more status in the community and are recognized as having more expertise on the topic. The problem with (5) of course kicks in with a vengeance here. What community? Recognized how? What expertise relative to what topic? I get no weight because I work at the University of Saskatchewan and not Harvard, or what?

7. We update the status of a members of our community on the basis of his or her contribution to progress a clearer understanding of what is true, not on the basis of “unwavering conviction” or “loyalty to the team.” This I suppose is intended to answer my concerns from (6) about what "status" might mean. I guess our status is our ranking in the profession, according to goodness. Do a good thing, and you move up. Do a bad thing, and you move down. Who decides what's good and bad, and how good, and how bad? What prevents a promotion based on "loyalty to the team," disguised as a good thing?

8. We shun, or exclude from the community, someone who reveals the he or she is not committed to these working principles. Well, I would be happy to be shunned by this community - it really doesn't look like it's built for success. Faced with these rules, I'll deviate and find my own like-minded community.

So, to me those rules seem strange, particularly coming from an economist who, like the rest of us, is schooled in the role of incentives, the benefits of decentralization, and the virtues of competition. We might wish that things were more clear-cut in economics, but it's not going to happen. Our models have to be so simple that they are guaranteed to be wrong - they're always inconsistent with some phenomena, hopefully the ones we're not focused on when we construct the model. There can be radically different theories, with different implications, that are all consistent with the empirical evidence we have (which is often not so great). This just reflects the technological limitations of science - our ability to construct and analyze models, and our ability to collect data. Why not just embrace the diversity and move on?

At this point, you may be wondering what's bugging Paul. He must have something specific he's concerned about. To get some ideas about that, read Romer's recent AER Papers and Proceedings paper. This paper is in part about "mathiness." What could that mean? It certainly doesn't mean that using mathematics in economics is a bad thing. Paul seems on board with the idea that mathematical precision lends clarity to our economic ideas, while potentially keeping people honest. Once you write your economic argument down in formal mathematical terms, it's hard to cheat. Math, unlike the English language (or any other language on the planet), is unambiguous.

But, in trying to get our ideas across, math can work against us. A sophisticated mathematical argument may be impenetrable to the average reader. And a rigorous, mathematically-detailed, internally consistent model is not necessarily a good model. The model-builder may have left out details that are essential for addressing the economic problem at hand, or there may be blatant inconsistencies between the model and the empirical regularities that are germane to the problem. Even though Paul gives specific examples, however, I'm still not entirely clear on "mathiness." As far as I can tell, it's related to the impenetrability problem. A dishonest economist can construct a mathematically sophisticated model, churn out some results without being too careful, claim success, and hope no one notices the errors and inconsistencies. That would certainly be a problem, and I could imagine recommending rejection to the editor if I were asked to referee such a paper, or rejecting the paper if I were in an editorial position.

Is that what's going on in the growth papers that Paul cites in his AER P&P piece? Are the authors guilty of "mathiness," - dishonesty? I'm not convinced. What McGrattan-Prescott, Boldrin-Levine, Lucas, and Lucas-Moll appear to have in common, is that they think about the growth process in different ways than Paul does, with somewhat different models. Sometimes they come up with different policy conclusions. Paul seems to think that, after 30 years, more or less, of research on the economics of technological change, we should have arrived at some consensus as to whether, for example, Paul's view of the world, or the views of his competitors, are somehow closer to Romerian truth. His conclusion is that there is something wrong with the winnowing-out process, hence his list of rules, and the attempt to convince us that M-G, B-L, L, L-M, and Piketty-Zucman too, are doing crappy work. I'm inferring that he thinks their papers were published in good places (our usual measure of value-added science) because they are well-connected big shots. It could also be that Paul just doesn't like competition - in more ways than one.

Monday, April 13, 2015

Sticky Prices, Financial Frictions, and the Ben Bernanke Puzzle

Noah Smith's Bloomberg post on the wonders of sticky price models caught my eye the other day. I'm going to use that as background for addressing issues on financial stability and monetary policy raised by Ben Bernanke.

First, Noah is more than a little confused about the genesis of sticky-price New Keynesian (NK) models. In particular, he thinks that Ball and Mankiw's "Sticky Price Manifesto" was a watershed in the NK revolution. Far from it. Keynesian economics went in several different directions after the theoretical and empirical revolution in macroeconomics. There was the coordination failure literature - Bryant, Diamond, and Cooper and John, for example. There was the sunspot literature. In addition, Mankiw, and Blanchard and Kiyotaki, among others, thought about menu costs. The "Sticky Price Manifesto" is in part a survey of the menu cost literature, but it reads like a religious polemic. You can get the idea from Ball and Mankiw's introduction to their paper:
There are two kinds of macroeconomists. One kind believes that price stickiness plays a central role in short-run economic fluctuations. The other kind doesn't... Those who believe in sticky prices are part of a long tradition in macroeconomics... By contrast, those who deny the importance of sticky prices depart radically from traditional macroeconomics. These heretics hold disparate views... heretics are united by their rejection of propositions that were considered well-established a generation or more ago. They believe that we mislead our undergraduates when we teach them models with sticky prices and monetary non-neutrality. A macroeconomist faces no greater decision than whether to be a traditionalist or a heretic. This paper explains why we choose to be traditionalists. We discuss the reasons, both theoretical and empirical, that we believe in models with sticky prices...
This is hardly illuminating. There are (were) only two kinds of macroeconomists? I've known (and knew in 1993) more kinds of macros than you can shake a stick at, and most of them don't (didn't) define themselves in terms of how they think about price stickiness. Further, they don't ponder choices about research programs as if, for example, they are living in 1925 in Northfield Minnesota, and choosing between lifetime paths as Roman Catholics or Lutherans. Why should we care what Ball and Mankiw think is going on in the minds of their staw-men opponents, or in the classrooms of those straw-men? Why should we care what Ball and Mankiw "believe?" Surely we are (were) much more interested in figuring out what we can learn from them about recent (at the time) developments in the menu cost literature.

Bob Lucas discussed Ball and Mankiw's paper at the Carnegie-Rochester conference where it was presented, and had this to say:
The cost of the ideological approach adopted by Ball and Mankiw is that one loses contact with the progressive, cumulative science aspect of macroeconomics. In order to recognize the existence and possibility of research progress, one needs to recognize deficiencies in traditional views, to acknowledge the existence of unresolved questions on which intelligent people can differ. For the ideological traditionalist, this acknowledgement is too risky. Better to deny the possibility of real progress, to treat new ideas as useful only in refuting new heresies, in getting us back where we were before the heretics threatened to spoil everything. There is a tradition that must be defended against heresy, but within that tradition there is no development, only unchanging truth.
Noah seems to think that Lucas was being unduly harsh, and that he was somehow feeling threatened by these "upstarts." It's pretty clear, actually, that Lucas just thinks it's a bad paper - religion, not science - and that Ball and Mankiw could do a lot better if they put their minds to it.

Where did NK come from? Which of the three threads in post-macro revolution Keynesian economics - coordination failures, sunspots, menu costs - morphs into Woodfordian NK models? To a first approximation, none of them. Perhaps NK owes a little to the menu cost approach, but it's really a direct offshoot of real business cycle theory. Take a Kydland and Prescott (1982) RBC model, eliminate some bells and whistles, add Dixit-Stiglitz monopolistic competition, and you have Rotemberg and Woodford's chapter from "Frontiers of Business Cycle Research." Add some price stickiness, and you have NK. So, NK basically leapfrogs most of the "Keynesian" literature from the 1980s. It's much more about RBC than about Ball and Mankiw.

Further, it's worth noting that Mike Woodford, the key player in NK macro, was at the University of Chicago from 1986 to 1992, the latter 3 years in the Department of Economics with - guess who - Bob Lucas. Indeed, they wrote a paper together. It's about - guess what - a kind of sticky price model with non-neutralities of money. Later on, Lucas wrote about sticky prices with Mike Golosov. So, I think we could make the case that the influence of Lucas on NK is huge, and that of Ball and Mankiw is tiny. Was it the case, as Noah contends, that Lucas was left, disappointed in the dust, by the purveyors of sticky price economics? Of course not - he was helping it along, and doing his own purveying.

How does a basic NK model - Woodford's "cashless" variety, for example - work? There is monopolistic competition, with multiple consumption goods, and the representative consumer supplies labor and consumes the goods. There's an infinite horizon, and we could add some aggregate shocks to total factor productivity (TFP) and preferences if we want. Without the price stickiness, in a competitive equilibrium there are relative prices that clear markets. There's no role for money or other assets (in exchange or as collateral), no limited commitment (everyone pays their debts) - no "frictions" essentially. Financial crises, for example, can't happen in this world. Then, what Woodford does is to add a numeraire object. This object is a pure unit of account, existing as something to denominate prices in terms of. We could call it "money," but let's call it "stardust," just for fun. So far, this wouldn't make any difference to our model, as it's only relative prices that matter - the competitive equilibrium relative prices and equilibrium quantities don't change as the result of adding stardust. What matters, though, is that Woodford assumes that firms in the model cannot change prices (at least sometimes) without bearing a cost. With Calvo pricing, that cost can either be zero or infinite, determined at random each period. Even better, the central bank now has some control over relative prices, as it has the power to determine the price of stardust tomorrow relative to stardust today.

Then, if there are aggregate shocks in this economy, we can do better with central bank intervention than without it. Shocks produce relative price distortions essentially identical to tax distortions, and central bank intervention can alter relative prices in beneficial ways, by reducing the distortions. Basically, it's a fiscal tax-wedge theory of monetary policy. Why monetary policy can do this job better than fiscal policy is not clear from the theory.

Noah tells us that "sticky-price models have become the dominant models used at central banks." You might ask what "used" means. Certainly Alan Greenspan wasn't "using" NK models. My best guess is that he wouldn't even want to hear about them, as he knows little about modern macroeconomics in the first place. Ben Bernanke, of course, is a different story - he clearly learned modern macro, published papers with serious models in them, and knows exactly what the working parts of an NK model are about. Which brings us to a post of his from last week.

The issue at hand is how central banks should think about financial stability. Is this solely the province of the financial regulators, or should conventional monetary policy intervention take into account possible effects on private-sector risk-taking? I think it's well-recognized, if not blatantly obvious, that there were regulatory failures that helped cause the financial crisis. Whether legislated financial reforms were adequate or not, I don't think any reasonable person would question the need for new types of financial regulation in the wake of the financial crisis. Also, most economists would not question the need for intervention by the central bank in a genuine financial crisis. The Fed was founded in part to correct problems of financial instability during the National Banking era (1863-1913) in the United States, and there was a well-established approach to banking panics by the Bank of England in the 19th century (which Bagehot, for example, wrote about). Friedman and Schwartz wrote extensively about how the failure of the Fed to intervene during the Great Depression helped to exacerbate the depth and length of the Depression.

But should a central bank intervene pre-emptively to mitigate financial instability or, for example, to reduce the probability of a financial crisis? That's an open question, and I don't think we have much to go on at this point in time. In any case, to think about this constructively, we would have to ask how alternative policy rules for the central bank jointly affect financial stability, asset prices, GDP, employment, etc., along with economic welfare, more generally. It would help a lot - indeed it seems it would be necessary - for the model we work with to have some working financial parts to it - credit, banks, collateral, the potential for default, systemic risk, etc. I actually have one of these handy. It's got no sticky prices, but plenty of other frictions. There's limited commitment, collateral, various assets including government debt, bank reserves, and currency, and private information. You can see that I didn't take either of the roads that Ball and Mankiw imagined I should be choosing, and I'm certainly not unique in that regard. The model I constructed tells us that conventional monetary policy can indeed exacerbate financial instability. There is an incentive problem in the model - households and banks may have the incentive to post poor-quality collateral to secure credit - and this incentive problem will tend to kick in when nominal interest rates are low.

Bernanke gives us some evidence from research which he claims informs us about the problem of financial stability and monetary policy. The paper he cites and summarizes is by Ajello et al. at the Board of Governors. Here's what Bernanke learned from that:
As academics (and former academics) like to say, more research on this issue is needed. But the early returns don't favor the idea that central banks should significantly change their rate-setting policies to mitigate risks to financial stability. Effective financial oversight is not perfect by any means, but it is probably the best tool we have for maintaining a stable financial system. In their efforts to promote financial stability, central banks should focus their efforts on improving their supervisory, regulatory, and macroprudential policy tools.
I agree with the first sentence. But what about the rest of it, which is his takeaway from the Ajello et al. paper. Maybe we should check that out.

So, the Ajello et al. model is a kind of reduced-form NK model. For convenience, NK models - which at heart are well-articulated general equilibrium models - are sometimes (if not typically) subjected to linear approximation, and reduced to two equations. One is an "IS curve," which is basically a linearized Euler equation that prices a nominal government bond, and the other is a "NK Phillips curve" which summarizes the pricing decisions of firms. These two equations, given monetary policy, determine the dynamic paths for the inflation rate and the output gap - the deviation of actual output from its efficient level. Often, a third equation is added: a Taylor rule that summarizes the behavior of the central bank. The basic idea is that this reduced form model is fully grounded in the optimizing, forward-looking behavior of consumers and firms, and so conforms to how modern macroeconomists typically do things (for good reasons of course).

If Ajello et al. could get financial crises into a model of monetary policy, that would be very interesting. There is some work on this, for example Gertler and Kiyotaki's Handbook of Monetary Economics chapter, but that's not what Ajello et al. are up to. What they do is to take the first two equations in a standard reduced form NK model, and then append a third equation that captures the effects of financial crises. The financial part of the model isn't grounded in any economic theory - the authors are just taking the express route to the reduced form. There are two periods. The endogenous variables are the current output gap, the current inflation rate, and the probability of a financial crisis in the second period. The second period financial crisis state has exogenous output gap and inflation rate, and the second period non-crisis state has another exogenous output gap and inflation rate. The probability of a financial crisis depends on the first period nominal interest rate, inflation rate, and output gap. That's it. The authors then "calibrate" this model, and start doing policy experiments.

What's wrong with this model? For starters, there's no assurance that, if we actually take the trouble to figure out what a financial crisis is, how to model it at a fundamental level, and then somehow integrate that with basic NK theory, that we're going to get a reduced form in which we can separate the non-financial-frictions NK model from the financial frictions NK model in the way that the authors of the paper have done it. They appeal to a paper by Woodford, but Woodford doesn't help me much, as he's basically taking the express route too. Think about it. We're starting with a model that is frictionless, except for the sticky prices, and we're asking it to address questions that involve default and systemic financial risk. What grounds to we have for arguing that this involves tweaking an NK reduced form in a minor way? But, suppose that I buy the specification the authors posit? What grounds do we have for setting the parameters in the third equation? I'm not sure what the signs of the parameters should be, let alone the magnitudes, and it puzzles me that the authors can be confident about it either.

Bernanke is taking it seriously though, as you can see from the quote above. We can see that Bernanke has strong priors, but there is essentially zero take-away in the paper, so why is he trying to use the paper to convince us he's right?

So, as Noah says, NK models are "used" in central banks, and here's an example of what that can mean. There is nothing inherently offensive about work on sticky prices, just as there's nothing inherently offensive about cats. In fact, there is some very interesting work on sticky prices. Last week, I saw a paper by Fernando Alvarez and Francesco Lippi. They do very sophisticated work, with careful attention to the available data on product pricing, and I think a lot can be learned from what they're up to. But if we want to think about the effects of monetary policy, and how monetary policy should be conducted, we better be thinking about the details of central bank liabilities, central bank assets, the role of the central bank as a financial intermediary, private banks, collateral, government debt, credit, etc. A basic NK model throws all of that out and focuses exclusively on sticky price frictions. Why is that a problem? Well, suppose a financial crisis comes along. What then do you know about malfunctioning credit markets, the role of central bank lending vs. open market operations, the effects of unconventional monetary policies such as quantitative easing? Not much, right? And it's pretty clear that you're not going to learn much about these things by tweaking a reduced form NK model.

Saturday, April 4, 2015

NK Models

Brad DeLong has a post on New Keynesian (NK) models. Things are certainly looking up, as I'm finding DeLong more agreeable by the day. As far as I can tell, we both think there is a deficiency of safe assets in the world, and we're not big fans of NK. Soon Brad will be doing monetary theory and quoting Neil Wallace, I have no doubt.

It's not like Brad has everything right though. He says:
The baseline New Keynesian model was not, originally, intended to become a workhorse. It was intended as a proof-of-concept...
That's definitely not correct. Mike Woodford can correct me on this, but my impression is that he came out of graduate school with a specific goal in mind, which was creating a version of Keynesian economics that would fit into modern macro. Ed Prescott's project left central bankers scratching their heads about what they were supposed to be doing, and Woodford and others stepped into the void. Interest and Prices is, I think, intended as a handbook for central bankers. There was a lot of effort put into marketing the whole NK project to the world's central banks. This is ongoing, and has been institutionalized, for example here.

But then, Brad gets to his criticisms:
But the extraordinary shortcuts needed for tractability were and are a straitjacket that makes it extremely hazardous for policy analysis. It cannot fit the time series. And when it does fit the time series, it does so for the wrong reasons.
He's not specific enough, but I agree with him. And other people do too. For example Chari/Kehoe/McGrattan.

But then we part ways again:
So why require everything to fit in this Procrustean Box? This is a serious question–closely related to the question of why models that are microfounded in ways we know to be wrong are preferable in the discourse to models that try to get the aggregate emergent properties right.
Again, Brad needs to expand on this to make clear what he's thinking, but my understanding is that the "Procrustean Box" of preferences/endowments/technology/information/equilibrium concept is too confining for him. He also might think that post-1970s macroeconomics opened a Pandora's box - setting loose evil forces that ruined much of the profession. Just guessing of course.

In any case, we're left wondering who the "we" is that knows microfounded models to be wrong. What are those microfounded models that are wrong, and how are they wrong in ways that mislead us? What specific "aggregate emergent properties" are there that some other models are trying to get right, and what are those models anyway?

Several points:

1. Saying a macroeconomic model is wrong misses the point. These models are all wrong, in the sense that, with sufficiently good data in sufficiently large quantities, which has in some sense performed the right natural experiments for us, we can reject any model. But that doesn't make these models useless - they can indeed be useful in carrying out the purpose for which they were intended. You could also stick to the letter of the law, and come up with a crappy model, of course.

2. We can address Lucas critique issues if our models are properly "micro-founded" - i.e they use the best available theory. But being explicit also keeps people honest. If you're specific about all the forces at work, and formalize them - as we're expected to do when we publish papers in serious academic journals - it's easier to understand the ideas, and to check them for accuracy and consistency. This is just good science.

3. It takes a model to beat a model. You can say that you don't like NK, but what's your model? Show me how it works. If you've got a model of monetary policy, show it to central bankers. Try to get them to buy into your ideas. Argue about it in public. Publish papers. Go to conferences.

Friday, April 3, 2015

Bernanke and Low Real Interest Rates

As you probably know, Ben Bernanke has a series of blog posts on why we have low interest rates. My two main points are: (i) Bernanke may be missing what is most important about the phenomenon of low real interest rates; (ii) He's giving Larry Summers way too much credit.

Bernanke starts by making a very useful point, which is that conventional macroeconomic theory tells us that monetary policy can affect real rates of interest only in the short run. A couple of implications of this are: (i) Leaving aside any effects of quantitative easing (QE), there has been no change in U.S. monetary policy since late 2008, so any nonneutralities of money dissipated long ago. For example, if the Fed had, in late 2008, gone to a fed funds rate range of 1.0%-1.25% instead of 0-0.25%, and stuck with that, real economic activity in April 2015 in the United States under that alternative policy would not be significantly different from what it actually is now. (ii) If you are looking for reasons why the real rate of interest is currently low, you shouldn't be blaming the Fed.

So where does Bernanke look for solutions to the low-real-interest-rate puzzle? He first contemplates Larry Summers's "secular stagnation hypothesis." I discussed secular stagnation in this blog post. There, I argued that there are two types of stagnation that economists like to talk about. The first is growth stagnation, where the argument is typically framed in the context of the standard workhorse growth theory developed by Solow, Cass, Coopmans, etc., many years ago. While growth theory is very useful in helping us understand cross-country growth experience, and to disentangle the factors contributing to economic growth in an individual country, it tells us little about what growth will be in the next 10 years in the United States, for example. Growth theory tells us that a substantial fraction of the growth in per capita income is accounted for by productivity growth, which in turn is driven by growth in the stock of knowledge. If anyone claims to be able to look into the future and see that, you shouldn't take them seriously. Thus, discussion about growth stagnation is just a guessing game.

The second type of stagnation is Keynesian stagnation. That's Larry Summers's version of secular stagnation, which he seems to have first discussed at an IMF conference in November 2013. Summers wasn't acting as the promoter of some well-developed research program. Indeed, the idea seems to have grown in Summers's brain and emerged from his mouth fully-formed. Most of us are longing for the day when this happens to us. No more fighting with editors, referees, colleagues, and various naysayers over our ideas. Just stand up in public, speak, and wait for the adulation. Taylor Swift never had it so good.

Nevertheless, as good scientists, we should flesh out Summers's idea, and check it for consistency and empirical plausibility. Macroeconomists are much better at this than they used to be - say, 50 years ago. So-called microfoundations - essentially, just using the best available theory in a judicious way - is about more than the Lucas critique. We want our models to include economic agents that are recognizably doing the things that real consumers and goods-producing firms do, interacting in ways that will somehow capture the real-world market interactions that we see going on. If the purveyors of particular theories are explicit, we can better understand what they are getting across, and we can check that their conclusions are correct, and that they are taking the right forces into account.

That's not to say that no one has attempted to formally capture what came out of Larry Summers's mouth. Eggertsson and Mehrotra have a paper about secular stagnation, which I wrote about in this blog post. Summers imagines that there exists a persistent inefficiency, reflected in a low real interest rate, that monetary policy can never fix, but which fiscal policy can. There is indeed an inefficiency in the Eggertsson/Mehrotra paper that will persist forever. But in their model it's easy to fix if the government simply provides an outside asset, as is well known for this class of models. I'm not sure this captures what Summers is getting at.

In any case, Summers summarizes what he means by secular stagnation in this reply to Bernanke:
The essence of secular stagnation is a chronic excess of saving over investment. The natural question for an economist to ask is how can such a chronic excess exist in flexible markets? In particular, shouldn’t interest rates adjust to equate saving and investment at full employment? The most obvious answer is that short term interest rates can’t fall below zero (or some bound close to zero) and this inhibits full adjustment.
So, suppose we consider a world with certainty - that will capture the long-run phenomena Summers is interested in. Then,

(1) r = R - i,

where r is the real rate of interest, R is the nominal rate of interest, and i is the inflation rate. Summers seems to be saying that, for some reason, the marginal product of capital is low, so the payoff from investing is low, and so the economically efficient real interest rate - what Woodford would call the "natural real rate of interest" or what Bernanke calls the "equilibrium interest rate" - is low. We'll let r* denote the natural real rate of interest. Then, if r* < -i, even with the nominal interest rate at the zero lower bound, the real rate of interest can't fall enough to correct Summers's "chronic excess of saving over investment." You should see where this is going now. You might have thought it odd that Summers mentions "flexible markets," but doesn't breathe a word about the flexibility of prices. How come? You tell me.

Summers's secular stagnation world appears to be one where the prices are sticky forever. He doesn't say as much, but I don't know how else he gets this to work. It seems to me that, in equation (1), i should be adjusting in the long run so that r* = R - i, no matter how the central bank sets R, if we think of this as, for example, a Wooford-type world. Further, in terms of conventional asset pricing, again in a world with certainty, we can write the real interest rate (approximately), as:

(2) r(t) = b + ag(t+1),

where r(t) is the real interest rate at time t, b is the subjective rate of time preference, a is the coefficient of relative risk aversion (assumed to be constant), and g(t+1) is the growth rate in consumption between this period and next period. It's hard to know for sure (as, again, Summers has not been explicit), but it seems that the effect he is discussing above is a level effect - the stagnation has to do with the level of output, not its growth rate. This translates in equation (2) into no effect on g(t+1), so in order to have a low real rate of interest, something else has to give. Some New Keynesians are fond of capturing real rate shocks as an increase in the discount factor, or a decrease in b in equation (2). This is hardly satisfactory, though. We're supposed that think that the economy will stagnate due to a contagious attack of patience? Maybe Summers thinks that (2) is not a good place to start in pricing assets? If so, he should tell us.

So, we're left wondering what Summers really has in mind, or if he's even thought about these problems. Why don't the prices adjust? What's the source of the low real natural rate?

Bernanke doesn't like Summers's secular stagnation ideas, but for the wrong reasons, I think. First, he gets a bit tangled up in interest rate logic:
The Fed cannot reduce market (nominal) interest rates below zero, and consequently—assuming it maintains its current 2 percent target for inflation—cannot reduce real interest rates (the market interest rate less inflation) below minus 2 percent.
As Summers points out, assuming that a central bank can maintain a 2% inflation target at the zero lower bound - particularly over an extended period of time - is a big leap. Indeed, if we add a time dimension to equation (1),

(3) r(t) = R(t) - i(t),

then (2) and (3) imply that, at the zero lower bound,

(4) i(t) = -b - ag(t+1)

So, conventional asset pricing theory tells us that, if monetary policy is irrelevant for the growth rate in consumption in the long run, then a central bank will have a hard time hitting an inflation target of 2% at the zero lower bound in the long run, unless there is a large enough sustained decrease in consumption. But, you might say, while many central banks in the world are indeed missing their inflation targets on the low side while at the zero lower bound - or even lower - we haven't yet seen sustained deflations, particularly in the United States. Even Japan, with about 20 years at the zero lower bound, experienced an average inflation rate of about zero over that period.

Now, note that, essentially by definition, the right-hand side of equation (4) is the real interest rate. If we're puzzled why we're not seeing deflation at the zero lower bound, we should also be puzzled by the low real interest rate. And, if we can figure out why the real interest rate is low, we also have a potential explanation for why inflation is higher than the conventional theory tells us it should be.

Here's another issue on which Bernanke seems confused. In the chart in this post, he shows us a real interest rate - the yield on 5-year TIPS. That's a security issued by the Treasury, of course. But when he starts taking issue with Summers, he's discussing the rate of return on investment - the marginal product of capital, in most macro models I know about. Maybe Bernanke is thinking that rates of return on all assets move together, and any differences in those rates of return are due to risk, but I don't think that's correct. For example, in this paper by Gomme, Ravikumar, and Rupert, the after-tax rate of return on business capital is measured. Their notion of capital is standard, but excludes residential capital and consumer durables. Basically, this is the average product of capital, which is proportional to the marginal product of capital with a Cobb-Douglas production function. On page 269 of their paper, they show a time series of their rate of return measure. The average is 5.16% for the period 1954-2008, and the rate of return is fairly smooth - bounded for the most part by 4% and 6%. But the real rate of return on short-term government debt (that's the ex post real rate) has much more variability, as can be seen in the following chart.
As well, there's a substantial downward trend, which we don't see in the time series of rates of return on capital that Gomme et al. calculate. Conclusion: There are some factors affecting the real rate of return on government debt that appear unrelated to what is determining the rate of return on capital.

What to make of this? Long ago, when people were interested in the equity premium puzzle, Mehra and Prescott showed that it was hard to reconcile standard asset pricing theory with observed returns on government debt and equities. Given empirical evidence on risk aversion, and the observed degree of aggregate risk from the time series, standard asset pricing predicts a much smaller risk premium than what we observe. Another way to think about this is that safe rates of interest in frictionless models are much higher than they are in practice. Indeed, in the conclusion to their paper, Mehra and Prescott suggest that people start looking at the frictions:
This is not the only example of some asset receiving a lower return than that implied by Arrow-Debreu general equilibrium theory. Currency, for example, is dominated by Treasury bills with positive nominal yields yet sizable amounts of currency are held.
The fact that certain types of contracts may be non-enforceable is one reason for the non-existence of markets that would otherwise arise to share risk. Similarly, entering into contracts with as yet unborn generations is not feasible. Such non-Arrow-Debreu competitive equilibrium models may rationalize the large equity risk premium that has characterized the behavior of the U.S. economy over the last ninety years.
Of course, most of the asset pricing literature didn't follow Mehra and Prescott's suggestions, but instead stuck to Arrow-Debreu pricing. I think they were missing something, and in the current context, Mehra and Prescott's suggestions are quite useful.

Take currency for starters. Bernanke gives an example of why negative real interest rates don't make sense. Basically, with a very small real interest rate, the present value of a small per-period payoff could be huge, making all kinds of seemingly ludicrous investment projects have positive net present value. But, of course, the real rate of return on currency is typically negative, and has been known to be quite large in absolute value. Why do people hold this asset if its rate of return is low - indeed lower, as Mehra and Prescott point out, than Treasury bills, which have essentially identical risk properties? We could say that the difference in the rates of return on money and T-bills reflects a liquidity premium - currency is more useful in exchange than are T-bills. So, extending the idea, why couldn't government debt bear a liquidity premium relative to other assets - capital for example? Government debt is indeed useful in exchange, in the sense that it is useful in credit contracts, as collateral - particularly in repo markets. This has to do with the non-enforceable contracts that Mehra and Prescott mentioned. Then, instead of equation (2), we can determine the real interest rate as:

(5) r(t) = b + ag(t+1) - l(t),,

where l(t) is a liquidity premium. The more liquid the asset, the higher is l(t), and the lower the real interest rate. Of course, equation (5) is a just a piece of a model. Has anyone written down fully-articulated general equilibrium models that determine such liquidity premia? You bet. Here are some:

Williamson (a)
Williamson (b)

That work isn't coming out of nowhere, of course. It's part of a broader research program involving other people - new monetarists, actually - and building on the work of many others. You can read about that in the papers. What the models show is that l(t) is an endogenous object, that depends in general on monetary policy, fiscal policy, and what is going on in credit markets.

Once we have the liquidity premium to work with, we have a potential explanation for why the real interest rate is so low - the liquidity premium is unusually high. Why would that be? We don't have to look too far to find the reasons. The financial crisis effectively destroyed part of the stock of eligible collateral, as did sovereign debt problems in parts of the world. U.S. government debt then became relatively scarce, and its price went up. Further, note that, at the zero lower bound,

(4) i(t) = -b - ag(t+1) + l(t),

so a higher liquidity premium on government debt also implies that we will tend to see higher inflation at the zero lower bound. In the models in the papers I refer to above, the real interest rate can be low due to suboptimal fiscal policy. If that suboptimal policy persists forever, the real interest rate can be low forever, and there is an inefficiency, reflected in low output, consumption, and employment. Looks a lot like what Summers would call secular stagnation. But it's a financial problem - there's insufficient government debt outstanding, not an insufficiency of government spending on goods and services. Faced with suboptimal fiscal policy, monetary policy matters in unusual ways - it's permanently non-neutral, and a severe shortage of government debt can mean that the central bank wants to be off the zero lower bound.

So, I think it would do Ben Bernanke good to get out more. Stop hanging out with big shots like Larry Summers, and make the acquaintance of some young macroeconomists, and other assorted riff-raff.

Sunday, March 22, 2015

Wren-Lewis Takes a Stab at It

Simon Wren-Lewis will unfortunately have to join Brad DeLong and Nick Rowe in the ranks of not-ready-for-prime-time monetary economists. There is always hope, though. We can allow him a retake of the David Levine's Keynesian economics exam. He could even attempt the same problem, if he wants. Quoting yours truly from my previous post:
If Levine's piece were a prelim question, I'm afraid we would have to fail both Brad and Nick. Brad can't quite get off the ground, as he doesn't understand that Levine's model is indeed a monetary economy and not a barter economy. Nick achieves liftoff, and we can give him points for recognizing the double coincidence problem and that the phone is commodity money. But then he stalls and crashes, walking off in a huff complaining that Levine doesn't know what he's talking about. Levine has posted an addendum to his original post, which I think demonstrates that he does in fact have a clue.
Simon says:
When we allow for the existence of money, it becomes quite clear how the ‘wrong’ real interest rate can lead to a demand deficient outcome. Brad DeLong takes Levine to task for trying to use a barter economy and Say’s Law to refute Keynesian ideas, and Nick Rowe turns the knife.
So, Simon compared notes with Brad and Nick after the exam. Bad idea. Everyone knows that talking to the guys who failed isn't going to help you pass the retake.

What did Simon do on his exam? He followed the time-honored approach of not answering the question he was asked, but answering one he thought he knew the answer to instead. What he gives us is not a critique of what Levine did, but a discussion of New Keynesian (NK) vs. RBC models. To summarize his discussion, Simon thinks that people who work with competitive equilibrium business cycle models (RBC for example) are contradicting themselves. According to him, their models are supposed to be microfounded, but prices are set by some Walrasian auctioneer. That's pretty silly, he thinks. He argues that NK models are superior in this respect, as the suppliers of goods actually set prices in an NK model, just as suppliers do in the real world. He elaborates by saying that NK models
...replace the auctioneer with a more modern macroeconomics - a macroeconomics where firms set prices and central banks change interest rates to achieve a target.
As well, repeating from above:
When we allow for the existence of money, it becomes quite clear how the ‘wrong’ real interest rate can lead to a demand deficient outcome.

First, as I explain in my last post, monetary exchange - whether it's commodity money or fiat money - is critical to how Levine's example works. That's how the "demand shock" propagates itself, and where the big multiplier comes from. Further, in Levine's sticky-price equilibrium, that the real interest rate is wrong is exactly the problem. In fact, the real interest rate is constrained to be zero in the sticky price equilibrium, when efficiency dictates that it should be lower. If you want to call that a "demand deficiency," I guess you can, but part of the point is that that terminology isn't actually descriptive of the basic inefficiency.

Since Simon brought up NK and RBC models, let's discuss that. First, there is in fact no Walrasian auctioneer in a competitive equilibrium. The Walrasian auction was a story thought up by someone (no idea who - anyone know?) to justify focusing attention on equilibrium outcomes - it's entirely outside the model. In a competitive equilibrium, everyone optimizes, markets clear, and that's it. But, does dropping competitive equilibrium make much difference? Well, not really. If we take Prescott's RBC model, and add Dixit-Stiglitz monopolistic competition, what do we get? The model behaves in roughly the same way, except there are some monopoly rents in the production of goods. For a lot of problems, we're not going to care about the difference between monopolistic competition and competitive equilibrium, so we might as well take the easy route, and use competitive pricing. But for Woodford's problem, he can't do that, because he is concerned with sticky prices and relative price distortions. You can't do that in competitive equilibrium, so he needs a technical device, and Dixit-Stiglitz works. He doesn't do that because it's somehow more realistic.

Further, if monetary exchange and central banking are so important to Simon, I'm not sure why he likes NK so much. A Woodford "cashless" model is just that. There's no money in sight, except that people quote prices in terms of some virtual unit of account, and the central bank determines an interest rate in terms of that unit of account. If this is realism, I'm confused. Actual central banks issue some liabilities, hold some assets, and their key policy actions involve swapping some of their liabilities for assets. I don't see that happening in an NK model. What I see is an assumption that the central bank can set a price. I have no idea why this central bank can do that - the model certainly doesn't tell me anything about it.

Here's something Simon says of Levine:
He does not talk about central banks, or monetary policy. If he had, he would have to explain why most of the people working for them seem to believe that New Keynesian type models are helpful in their job of managing the economy.
I work for one of these institutions, and I have a hard time answering that question, so it's not clear why Simon wants David to answer it. Simon posed the question, so I think he should answer it.

Friday, March 20, 2015

No One Expects the Spanish Inquisition: More on D.K. Levine and J.M Keynes

I guess I shouldn't be surprised. David Levine's piece on Keynesian economics appears to have generated plenty of heat. See for example the comments section in my post linking to Levine. I'm imagining an angry mob dressed like the Pythons, as in the photo above, running through the streets of Florence looking for Levine. Each has a copy of the General Theory, and they're aiming to inflict torture by taking turns reciting it to David, until he renounces his heretical writings.

What drew my attention to Levine's piece initially were blog posts by Brad DeLong and Nick Rowe. If Levine's piece were a prelim question, I'm afraid we would have to fail both Brad and Nick. Brad can't quite get off the ground, as he doesn't understand that Levine's model is indeed a monetary economy and not a barter economy. Nick achieves liftoff, and we can give him points for recognizing the double coincidence problem and that the phone is commodity money. But then he stalls and crashes, walking off in a huff complaining that Levine doesn't know what he's talking about. Levine has posted an addendum to his original post, which I think demonstrates that he does in fact have a clue.

In any case, I thought Levine's example was interesting, and I'd like to follow John Cochrane's suggestion of filling in some of the spaces, which will require some notation, and a little algebra. First, adding to David's addendum, let's generalize what he wrote down. This is just a version of an economy with an absence of double coincidence of wants. If any two people in this world meet, it will never be the case that each can produce what the other wants. It's roughly like Kiyotaki and Wright (1989), except with 4 goods instead of 3. And of course there are some very old versions of the double coincidence problem in the work of Jevons and Wicksell, for example. Brad DeLong, who reads the old stuff assiduously, perhaps missed those things.

Commodity Money
Let's first imagine a world with T types of people, indexed by i = 1,2, ..., T. There are many people of each type. Indeed, for convenience assume that there is a continuum of each type with mass 1. A person of type i can produce one indivisible unit of good i at a utility cost c, and receives utility u from consuming one indivisible unit of good i + 1 (mod T) (i.e. T + 1 (mod T) = 1 ). We need n >= 3 for a double coincidence problem, and n will matter for some elements of the problem, as we'll see. A key feature of the problem will be that each person can meet only one other person at a time to trade - that's a crude way to capture the costs of search and exchange. We could allow for directed search, and I think that would make no difference, but we'll just cut to the chase and assume that each person of type 1 meets with a type 2, each type 2 meets with a type 3, etc., until the type T - 1 people meet with the type Ts. Further, we'll suppose that, as in David's example, good 1 is perfectly durable and costless to store, while all the other goods are perishable - they have infinite storage costs. Assume that u - c > 0 (with some modifications later).

A key element of the problem is that the indivisibility of goods fixes the prices - indeed, in a Keynesian fashion - so long as we only permit these people to trade using pure strategies. That is, David assumes that when two people meet they both agree to exchange one unit of a good for one unit of some other good, or exchange does not take place. But let's do something more general. Suppose that 2 people who meet can engage in lotteries. That is, what they agree to is an exchange where a good is transferred with some probability, in exchange for the other good with some probability. Then, the probabilities play the role of prices. That is, with indivisible goods, we can think about an equilibrium with lotteries as a flexible price equilibrium, and the Levine equilibrium, where one thing always trades for one other thing, as a sticky price equilibrium.

This sounds like it's going to be hard, but it's actually very easy. Work backwards, starting with a meeting between a type T - 1 and a type T. Trade can only happen if type T-1 has good 1, which is what type T consumes, so suppose that's the case. We have to assume something about how these two would-be trading partners bargain. The simplest bargaining setup is a take-it-or-leave-it offer by the "buyer," i.e. the person who is going to exchange something he or she doesn't want for something the "seller" produces. The buyer has one unit of good 1, which is of no value to him/her, so the buyer is willing to give this up with probability one. Since u > c, the seller is willing to produce one unit of good T in exchange, so the optimal offer for the seller is in fact the Levine contract - one unit of good 1 in exchange for one unit of good T. And the same applies to the meetings where types 2, 3, ..., T-1 are the buyers.

But, the type 1 people - these are the producers of the commodity money in this economy - are different. Unlike the buyers in the other meetings, they have to produce on the spot. And, since they make a take-it-or-leave it offer, they are in a position to extract surplus from sellers - and they do it. So, the trade they agree to is an exchange where each type 2 person produces one unit of good 2 and gives it to a type 1 person, and the type 1 person agrees to produce good 1 with probability p(1), where
So, in equilibrium, only a fraction c/u of each of types 2, 3,..., T gets to consume, and all the type 1s - the money producers - consume. There is a welfare loss from this commodity money system, in that the money producers are extracting seignorage from everyone else. In the fixed price equilibrium, where everyone has to trade one unit of a good for one unit of another good, the type 1s are worse off, and everyone else is better off.

Now, consider a "demand shock." That is, suppose that all the type T people receive utility u* from consuming, where u* < c, and everyone else is the same as before. A point I want to make here is that the Keynesian failure can come from anywhere in the chain - it need not come from the money producers. If we consider the flexible price, or lottery, equilibrium, now the type T - 1 buyers have to do something different in order to get the type T sellers to produce. It is still best for the buyers in these meetings to offer their commodity money (good 1) with certainty, but the take-it-or-leave-it offer the buyer makes involves the seller producing with probability
Further, now it is possible that, because the type T - 1 buyers get a bad deal, they won't be so willing to work when they are trading with T - 2 buyers. Indeed, in this equilibrium (if there is one - more about that later), we can work backward to determine that a type i person will produce with probability
What the type 1 and type 2 people do is potentially a little different, because this involves the behavior of the type 1s, who are the commodity money suppliers. Again, working backward, we can show that an equilibrium will exist if and only if
If that inequality does not hold, then there is not enough total surplus in this economy to support trade, and everything shuts down. But, if (4) holds, then the solutions for p(1) and p(2) are:
So, the effects of the "demand shock" could be transmitted back in the chain, even to the commodity money supplier if the problem is severe enough, i.e. if u*/c is very small. This is quite interesting, as what is going on is that financial arrangements (albeit crude ones - this is just a commodity money system) propagate "shocks." A decline in demand in one sector gets transmitted to others. And all this interconnection and specialization could in fact shut the economy down - even without sticky prices.

Note that I'm putting "demand shock" in scare quotes. Why? Because, in spite of the fact that the comparative static experiment involved a decline in the utility type Ts receive from consuming, it affects everything a type T does, in particular his or her labor supply. Why work if you don't like to eat? This illustrates why terms like "demand shock" and "demand deficiency" have no meaning in a properly specified general equilibrium model. This is a standard criticism of IS/LM models that goes back to at least the mid-1970s. For example, the IS curve is shifting because the behavior of some consumers changed, but those consumers are the same people who are supplying labor in the labor market, and holding money in the money market. Why don't we take account of that? Why indeed. Spelling these things out in the model means you don't miss that, which could be very important.

The next step is easy, as Levine already did it. If prices are fixed (all trade is one thing for one other thing), then the "demand shock" will shut everything down. The flexible price lottery equilibrium is, as far as I can tell, Pareto efficient, so that's a useful benchmark. So note first that having this economy shut down - in this extreme example - will sometimes be efficient, if (4) does not hold. Thus, in that case, the fixed price equilibrium is actually OK. But that's not what interests us. Suppose u* < c, but (4) holds. Then clearly the fixed price equilibrium is not Pareto efficient. But how would we fix it? David goes through some possibilities, but the key message is that, if the government is going to intervene in this world in a good way, it has to redistribute. Somehow the government has to move surplus to type Ts from everyone else, so that the type T's are willing to trade. If the shocks are causing some inefficiency, we can't correct the problem through some blunt policy which says the government should just buy some stuff, and it really doesn't matter what. Indeed, it does matter, and this crude model is an illustration of that fact.

As well, note that a typical justification for thinking about the sticky price equilibrium rather than the flexible price equilibrium, is that pricing is hard for the people in the model to figure out. Indeed, that's the case here. People sometimes argue that mixed strategies (as in the flexible price equilibrium) are very difficult to implement in practice. But that doesn't let the government off the hook. If it wants to correct the incorrect pricing - the prices are the wrong ones in the sticky price equilibrium - they have to do so by replicating the flexible price equilibrium, and that involves lotteries. That's just an example of a general problem in Keynesian economics.

Fiat Money
So, you might wonder why we would worry about a commodity money economy, if that's not the type of world we currently live in. Well, it's not so hard to extend the idea to a fiat money economy. Some things change in an interesting way, but the basic idea stays intact. We're going to work in an overlapping generations framework. Samuelson's OG model is not used so much anymore, but it was a standard workhorse for monetary economics at the University of Minnesota until about the mid-1980s. For this example, it works nicely.

The people that live in this world look much like the people in the commodity money economy, except they each live for two periods. They can produce an indivisible unit of the current perishable consumption good when young at a cost c, and receive utility u from consuming an indivisible unit of consumption good when old. Each period, a continuum of two-period-lived people with unit mass are born. In period 1, there is a continuum of old people who live only one period. The initial old each receive utility u from consumption of one unit of the consumption good, and each has one unit of indivisible fiat money. We'll make the bold assumptions that fiat money cannot be counterfeited, and that it is perfectly durable. Each period, each young person is matched with one old person.

We'll suppose, as in the commodity money economy, that in a meeting between a young person and an old person with money, the old person makes a take-it-or-leave-it lottery offer to the young person. This is actually easier to analyze than the commodity money equilibrium, as the initial old people want to give up their money no matter what - they're not like the commodity money producers who have a cost of producing money. So, here the flexible price equilibrium and the fixed-price equilibrium are the same thing. Each period, every old person exchanges one unit of money for one good produced by a young person, every young person receives utility -c + u > 0, every initial old person receives utility u, and money circulates forever.

Now, suppose that sometime in the future, in period T, utility from consuming is lower for all the people who are born that period, i.e. they receive u* from consuming when old, and u* < c, just as before. Again, this is easier than in the commodity money case, as this economy will not shut down under flexible pricing. Letting p(i) denote the probability a young person produces in a trade with an old person, we get
which should look familiar from the commodity money case, but now this holds for all t = 1,2,...,T. But for t = T+1, T+2, p(i) = 1 as before. So now we get a temporal interpretation of the idea. Future anticipated shocks propagate backward in time.

As in the commodity money economy, everything shuts down if everyone has to trade at fixed prices. In period T, the young will not accept money, and so by induction no one will. Here, just as with commodity money, the problem in the fixed-price economy is not a monetary problem - it's that the prices are wrong. It's always puzzled me, for example, why Mike Woodford thinks of his models as prescriptions for how central banks should behave, as the relative price distortions that exist in those models look like problems for the fiscal authority to work on. I haven't worked out the details, but I think that a policy that would work in the fixed price equilibrium is to simply replicate the flexible price equilibrium with a sequence of taxes on old agents (random confiscations of money) and subsidies for the young (random transfers of money). You can do something similar in a Woodford model with consumption taxes (see this paper by Correia et al.).

We could also think about unanticipated preference shocks in this model. For example, suppose the utility of consumption for old persons is a random draw, which they learn when they are young. With probability q they receive u*, and with probability 1 - q, they receive u. Then, we can construct an equilibrium in which the young produce with probability s* when their utility when old will be u*, and produce with probability s when their utility from consuming when old will be u. For an equilibrium to exist requires
So the economy shuts down unless the unconditional expected utility of a given agent who always receives his or her consumption good when old is not negative. If an equilibrium exists, then s = 1, and
Therefore, the random preference shocks produce random business cycles in which production and consumption are low in bad states and high in good states. But these cycles are efficient. Low demand for goods means low willingness to work, but note that this doesn't mean that the person with the "demand shock" consumes less. They work less and supply less consumption goods.

As in all the previous cases, if prices are fixed, then this economy shuts down because of these demand shocks. There is always a positive probability that the young next period will not accept money, so it is not valued in equilibrium and there is no trade. Again, the problem is that the prices are wrong. A fix for this is for the government to step in, if it can, and replicate the allocation that was achieved under flexible prices. What should work is that, when a bad shock is realized (the young learn that their utility from consumption when old is u*), the government taxes money away from old people, at random, and gives it to young people, again at random. Note that this doesn't involve running a deficit - it's a tax/transfer scheme with taxes = transfers. Again, the cure is redistribution. Further, note that an optimal allocation has cycles - it's not optimal to smooth the cycle completely, even if that were possible (and I'm not sure it is).

So, I think this is an interesting example. It's obviously special, and we wouldn't take it to the U.S. Treasury and tell them about it, hoping to influence their decisions. The message is that whatever anyone thinks they know about "Keynesian" ideas, and the "Keynesian" policies derived from those ideas, they should reconsider. There's nothing obvious about that stuff. We can write down coherent models in which Keynesian phenomena occur, and the optimal policies don't seem to look like anything like that Paul Krugman recommends. And it's not because his IS/LM model is "right." Far from it. We understood that long ago.

Monday, March 16, 2015

Levine on Keynes

This piece be David Levine is a lot of fun. Paul Krugman refers to Levine as "incompetent" and "ignorant," which I think we can interpret as a strong positive signal.