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.