## Wednesday, November 27, 2013

### Liquidity Premia and the Monetary Policy Trap

There is a wide class of monetary models that boil down to something like the following. We'll confine attention to a deterministic world - extending this to a stochastic environment isn't a big deal. Given intertemporal optimization, the price of a nominal bond, q(t), in dollars, is determined from the first-order condition

(1) q(t) = B[u'(c(t+1))/u'(c(t))][p(t)/p(t+1)],

where B is the discount factor, u(.) is the utility function, c(t) is consumption in period t, and p(t) is the price level. Similarly, for money to be held,

(2) 1 - L(t) = B[u'(c(t+1))/u'(c(t))][p(t)/p(t+1)],

where L(t) is the liquidity premium on money. For example, L(t) is associated with a binding cash-in-advance constraint in a cash-in-advance model, or with some inefficiency of exchange in a deeper model of money. In (1) and (2), the nominal interest rate, 1/q(t) - 1, is positive if and only if there is a liquidity premium on money.

A ubiquitous result is the Friedman rule, which says that an optimal monetary policy eliminates inefficiency by reducing L(t) to zero, which implies a zero nominal interest rate, i.e. q(t)=1. Then, supposing an equilibrium in which consumption is constant over time, (1) and (2) give

(3) p(t+1)/p(t) = 1/B,

so the inflation rate is 1/B - 1 < 0 when the central bank runs the Friedman rule, and there is deflation at the optimum. This is the classic notion of a liquidity trap, and why the zero lower bound on nominal interest rates makes some economists fear deflation. In general there are many different monetary policies that will support a zero nominal interest rate forever in this context. This is the traditional sense in which monetary policy does not matter at the zero lower bound. In a basic New Keynesian model, L(t) is always zero as there is no role for money, and instead of (2) the following condition must hold: (4) 1 >= B[u'(c(t+1))/u'(c(t))][p(t)/p(t+1)],

so that people never want to hold money in equilibrium, and (4) holds as long as q(t)<=1, which is just the zero lower bound. In a New Keynesian model, monetary policy is all about correcting relative price distortions - no Friedman rules in that setting. Of course there's much more to liquidity than currency, or the stuff that Milton Friedman might have wanted to include in some monetary aggregate. Various assets, including government debt and asset-backed securities, may have associated liquidity premia, because those assets are held for insurance purposes, because they are exchanged in some class of non-retail transactions, or because they serve as collateral in credit contracts. For example, incomplete-markets Bewley-type models capture an insurance role for assets (see Aiyagari 1994 for example), and new monetarist models (e.g. work by Ricardo Lagos, Guillaume Rocheteau, Randy Wright,or yours truly) get at how the use of assets in exchange and as collateral give rise to liquidity premia.

Some types of models will give us a liquidity premium on bonds, K(t), so instead of (1) we get

(5) q(t) - K(t) = B[u'(c(t+1))/u'(c(t))][p(t)/p(t+1)]

Now this gets very interesting. What happens at the zero lower bound? From (2) and (5), if q(t)=1 and both assets are held, L(t) = K(t). Then, if L(t)>0 at the zero lower bound (because all government and central bank liabilities are collectively in short supply), in a stationary equilibrium with constant consumption and a constant liquidity premium, L, from (2),

(6) p(t+1)/p(t) = B/(1-L),

so, the larger the liquidity premium, the higher is the inflation rate at the zero lower bound. Indeed, we will not have deflation at the zero lower bound if L>1-B. For the details, you should read this paper or this one.

What's the real rate of interest at the zero lower bound? From (6), the real rate is

(7) r = [(1-L)/B]-1,

which is lower than the rate of time preference, and decreasing in the liquidity premium.

So, this looks promising. An increase in the liquidity premium on government debt, beginning in the financial crisis, can explain: (i) why we do not have deflation in a liquidity trap; (ii) why real interest rates on government debt have been low, post-financial crisis.

The financial crisis involved the destruction of private collateral, in part because of the drop in real estate prices, and the resulting damage in markets for asset-backed securities. Further damage occurred in southern Europe, where the safety of sovereign debt was threatened post-financial crisis. All of this led to a flight to safety - i.e. to U.S. government debt.

Following the logic behind the Friedman rule, the high liquidity premium on government debt reflects an inefficiency. Collateral constraints are tighter, and there is a low stock of liquid assets available for financial exchange and for self-insurance. But the power of monetary policy to mitigate the inefficiency is limited. Basically, it's a fiscal problem. The U.S. government could issue more debt, by temporarily running a higher deficit. But that's not happening, so what can the central bank do about it? In this paper, I assume that the fiscal authority follows a suboptimal policy rule, against which the central bank optimizes, and explore what QE (quantitative easing) does in this context - in particular, swaps of short maturity debt (or reserves) for long-maturity government debt. This can have an effect, which depends on the degree to which short-maturity government debt is better collateral than long-maturity debt. But the effect of QE is to lower the liquidity premium (collateral constraints are relaxed) which , as in equations (6) and (7), will lower inflation and increase the real interest rate. This is a good thing, but if you have been listening to Ben Bernanke, you'll know that this is not the way he thinks QE works. In particular, the thinking at the Fed seems to be that QE will increase inflation and lower real rates. If our problem is indeed a financial inefficiency reflected in a low real interest rate, then the Fed has this turned on its head.

So, suppose we think of the world we're living in now as one where any nonneutralities of money associated with the Fed's interventions during and after the financial crisis have played themselves out. Then, with the nominal interest rate effectively at the zero lower bound, the rate of inflation is being determined primarily by the liquidity premium on government debt. Once we recognize that, it's not surprising that the inflation rate has been falling for the last three years (see the chart).
The situation in Europe is looking more stable, and the private sector is presumably finding new sources of private collateral, all of which reduces the liquidity premium on government debt. Further, we should expect this to continue, for example as the price of real estate and other assets rise. In general, if we think that inflation is being driven by the liquidity premium on government debt at the zero lower bound, then if the Fed keeps the interest rate on reserves where it is for an extended period of time, we should expect less inflation rather than more.

But that's not the way the Fed is thinking about the problem. What I hear coming out of the mouths of some Fed officials is that: (i) Things are bad in the labor market, and the Fed can do something about that; (ii) inflation is low. Thus, according to various Fed officials, the Fed can kill two birds with one stone, so it should: (a) keep doing QE; (ii) make it clear that it wants to keep the interest rate on reserves at 0.25% for a very long period of time.

What I hope the discussion above makes clear is that this is a trap for the Fed. There is not much that the Fed can do on its own about the short supply of liquid assets. They can get some action from QE, but the matter is mostly out of their hands, and more QE actually pushes the Fed further from its inflation goal. If the Fed actually wants more inflation, the nominal interest rate on reserves will have to go up. Of course that will lead to some short-term negative effects because of money nonneutralities.

The Fed is stuck. It is committed to a future path for policy, and going back on that policy would require that people at the top absorb some new ideas, and maybe eat some crow. Not likely to happen. The observation of continued low, or falling, inflation will only confirm the Fed's belief that it is not doing enough, not committed to doing that for a long enough time, or not being convincing enough.

## Thursday, November 21, 2013

### Liquidity Constraints

It's taken me a few days to make something out of this post by Paul Krugman, which is a comment on John Cochrane. See also my previous post.

Krugman is unhappy, and is accusing Cochrane of being a lazy reader. I think the subtext here is that Krugman wants us to read his paper with Gauti Eggertsson. I read the working paper, but that was a while back, so I looked at the published version to remind myself what is going on in their model.

The crux of Krugman's argument in his blog post comes for the most part from the Eggertsson/Krugman (EK) paper. Cochrane's point is that New Keynesian models and Old Keynesian models are very different. In New Keynesian models government spending increases consumption by increasing inflation; in Old Keynesian models government spending increases consumption by way of the multiplier process. Krugman says: hold on a minute. Government purchases in a typical New Keynesian model will actually increase output one-for-one. Add "liquidity-constrained" consumers and you can get multiplier effects, just like with Old Keynes.

Since these arguments come straight out of the EK paper, it's useful to dig into the EK model and figure out what is going on. First, I think anyone who attempts to capture credit and liquidity frictions and their implications for macro policy should be given a pat on the back. Certainly there was far too little work on these things before 2008 - particularly among New Keynesians - and that didn't work out so well. So, EK deserve some credit (no pun intended).

EK want to set up a model with credit and borrowing constraints, but they want it to be tractable. Standard incomplete markets models with such constraints (e.g. Krusell/Smith) are notoriously intractable - typically we're stuck with computational approaches. The trick in EK is to assume two types of economics agents - patient and impatient - who are identical except that they discount the future differently. It's well known that, in an endowment economy like this, with unlimited borrowing and lending, all the wealth goes to the patient agents in the limit. But, if we impose an exogenous debt constraint, then in the steady state the borrowing constraint binds for the impatient agents, and the patient people lend to the impatient ones. EK essentially involves linearizing around that steady state, and considering the effects of shocks to the debt limit when the zero lower bound on the nominal interest rate binds. There are also sticky prices, so the model has some basic New Keynesian features.

Thus, there are two key frictions in the model - sticky prices, which give rise to the possibility of typical Keynesian relative price inefficiencies (i.e. an inefficient real rate of interest); and a credit market friction. The relevant part of the paper for us is the section on policy - especially fiscal policy. The government has access to lump-sum taxes, and EK make some assumptions about the distribution of the tax burden, seemingly just to make life easier for the modelers. What does government spending do? Private goods are converted into public goods, which enter the utility function in a separable fashion.

What happens in the basic New Keynesian model (EK with one type of agent) if government spending increases? Consumption does not change, as that is determined from the Euler equation for the representative consumer. There is no investment, and firms are assumed to service whatever demand comes in the door, so the direct effect is for output to increase one-for-one with government spending. A good thing, right? Not necessarily. The increase in output did nothing to correct the fundamental inefficiency in the model, which is the sticky price friction. If we're at the zero lower bound, and the real interest rate is too high in this environment, then essentially we have a consumption gap, not an "output gap." If the government spends more, that doesn't shrink the consumption gap. There is some optimal quantity of public goods in this model - if government is providing less (more) than that quantity, then it should be spending more (less). A second effect is the one Cochrane discusses. By increasing output, the government can move us up the New Keynesian Phillips curve, inflation increases, this lowers the real interest rate, and the consumption gap falls. So, there's nothing wrong with Cochrane's analysis. Krugman is right in a sense, but he's focusing too much on the output effects, rather than the efficiency effects.

Next, go to the full-blown EK model. What happens here is that we get an additional effect from government spending, which Krugman discusses in his post. More output gets produced, as firms serve whatever demand comes in the door. Then, I think what is happening is that labor income must go up for everyone (higher wage and more employment), including the debt-constrained consumers, who will then consume more. As Krugman points out, that's a kind of standard Old-Keynesian effect coming from the non-Ricardian nature of this economy.

But hold on. This has the flavor of reverse engineering. We're supposed to get excited because we find some result that looks like something we think we already know. If all research proceeded like this, we wouldn't learn anything. Suppose we take this model at face value. What's the inefficiency problem or problems? What's a feasible government policy? Within that feasible set, what is optimal? Answers: (i) The economy is in a state of the world where the zero lower bound binds, consumption is too low for unconstrained agents because the real interest rate is too high, and consumption is too low for constrained agents - because they are constrained. (ii) The government has access to lump-sum taxes. If it can tax lump-sum, we'll suppose it can tax consumption as well. (iii) Policy solution? Easy. Given lump-sum taxation, the borrowing constraints can be relaxed - indeed eliminated - through a tax/transfer program. Then, we're back to the basic New Keynesian world, with a consumption gap. To fix that, all we need is a promise to tax consumption in the future when the zero lower bound threatens to bind. This gives us the correct (after-tax) real interest rate (see Correia et al.).

I think the bottom line is that we want to pay attention to what models tell us, not what we hope they might tell us. The model EK want us to pay attention to indeed has a role for fiscal policy. But that role isn't related to spending, multipliers, and Old Keynesian economics. It's about tax policy.

## Sunday, November 17, 2013

### Larry Summers at the IMF

Miles Kimball seems very excited about Larry Summers's talk at the annual IMF research conference. For me, this just reveals (if it wasn't already clear) that we dodged a bullet when Summers decided he did not want to be a candidate for Chair of the Fed.

There is really nothing new in Summers's talk. It seems to be either the standard Keynesian narrative on the financial crisis and post-crisis sluggishness in the U.S. economy, or borrowed from Paul Krugman. Here's the basic story. According to Summers, the pre-crisis period was not one of "excessive aggregate demand," but an episode in which asset price bubbles masked underlying secular stagnation. Post-crisis, we're in a state where the "real interest rate consistent with full employment" is very low. In this state, according to Summers,
…We may well need, in the years ahead, to think about how we manage an economy in which the zero nominal interest rate is a chronic and systemic inhibitor of economic activity, holding our economies back, below their potential.

Summers is very good on his feet. If you don't listen too carefully, everything fits together nicely, and he doesn't contradict himself. He knows his audience, and gets a chuckle when he jokes about Minnesota/Chicago (whatever he thinks that means). But what he's actually saying is shallow, and unsupported by serious economic research. Who wants a guy running the Fed who thinks like that?

The standard New Keynesian narrative at the core of Summers's talk is outlined in this post. New Keynesians (NKs) argue that we can model the financial crisis as a preference shock - the rate of time preference fell. The optimal monetary policy response to such a shock in a NK model is for the nominal interest rate to fall to zero (if the shock is large enough). The "natural rate of interest" falls, but the actual real rate falls short of that because the zero lower bound binds, according to the story. The problem for this story in replicating recent U.S. data is that New Keynesian (NK) models revert to trend. Ultimately, as prices and wages adjust, real GDP growth will be determined by exogenous TFP (total factor productivity) growth. As I argued here, it seems implausible to argue that there is enough price and wage rigidity to give us the level of NK inefficiency that some want to argue exists, more than 5 years after the Lehman collapse.

Maybe Summers is thinking the same thing, as what he wants to add to the story is some kind of Alvin Hansen "secular stagnation" mechanism. This seems puzzling, as Hansen predicted in the late 1930s that the economy would stagnate forever, without sustained government spending to support it. Given that the U.S. economy returned to its pre-recession growth trend after the big reduction in government spending following World War II, that idea seems not to have panned out. But Summers wants to somehow connect secular stagnation to the zero lower bound. This is even more puzzling, as it runs into the same problem as in the standard Keynesian narrative. In NK theory, the key problem is that wage and price stickiness misaligns relative prices, including intertemporal prices (i.e. the real interest rate), and if the zero lower bound binds, then monetary policy can't correct the problem. Summers seems to want us to think that we can have permanent relative price distortions - that if monetary policy is hemmed in by the zero lower bound we'll have inefficiency forever. Apparently Summers does not think prices will ever adjust, or he's unaware of some of the simple tax policy solutions that are available, even if we buy into the NK framework.

So, secular stagnation does not seem to be consistent with NK models, as we know them. Maybe Summers has something new in mind. If so, I haven't seen it, and he certainly did not make us aware of any such new work in his talk. That's why this is a bad policy talk, representing only the glib ramblings of a man who hasn't addressed the problem at hand in a serious way.

## Thursday, November 14, 2013

### John Cochrane and Keynesian Economics

John Cochrane has been writing stuff recently which is very helpful if you want to understand the difference between Old and New Keynesian economics, and the mysteries of the mechanics of New Keynesian models at the zero lower bound. One example is this working paper, in which he argues that the various "paradoxical" results associated with New Keynesian liquidity traps are artifacts of equilibrium selection, and that the paradoxes go away if we focus our attention on an equilibrium that New Keynesians typically ignore. If we want to take these models seriously, we should at least feel confident about what the models actually have to say.

Another related issue Cochrane raises is in this blog post. The basic point that Cochrane wants to make is that an Old-Keynesian model (i.e. IS/LM AS/AD) and a New Keynesian model are very different animals. Indeed, New Keynesian models would be much more recognizable to Ed Prescott than to John Maynard Keynes, if we chose to resurrect the latter. One way in which these models differ is in how fiscal policy works. Old Keynesians typically assumed that the economy was non-Ricardian, which helped to feed the multiplier process. However, in a New Keynesian model, there is a complete set of contingent claims markets, and Ricardian equivalence holds. Fiscal stimulus works by increasing anticipated inflation, and lowering real interest rates, causing consumers to substitute intertemporally. Current consumption must go up, as it is assumed that consumption reverts to trend in the future.

Cochrane is willing to take the New Keynesian story seriously, but he would like it if the people who are promoting fiscal stimulus were to defend their policy recommendations in terms of that model. Unfortunately the fiscal stimulus folks are either confused, or are deliberately obfuscating. Some people want to argue as if New Keynesian models and Old Keynesian models are indeed the same animal. Policy issues are explained in Old Keynesian language - e.g. stimulus works by way of the multiplier process - and then people appeal to New Keynesian models as if that somehow ratifies these old results, which is false.

Now, predictably, this kind of talk gets Paul Krugman upset, as of course what Cochrane is describing is the way Krugman operates. What gets Krugman particularly upset is this (from Cochrane):
But people love the story. Policy makers love the story. Most of Washington loves the story. Most of Washington policy analysis uses Keynesian models or Keynesian thinking. This is really curious. Our whole policy establishment uses a model that cannot be published in a peer-reviewed journal. Imagine if the climate scientists were telling us to spend a trillion dollars on carbon dioxide mitigation -- but they had not been able to publish any of their models in peer-reviewed journals for 35 years.
The problem here is the the story that people "love" is the Old Keynesian multiplier/paradox-of-thrift story. Somehow the average person finds it appealing, and so the story gets used all the time, in spite of the fact that it does not hold water - in the sense of being grounded in sound economic theory.

Krugman's reply to this is to argue that it's not Washington (or him for that matter) that is screwed up - it's the economics journals.
So consider two hypotheses. One — which Cochrane appears to believe — is that being inside the Beltway has rotted Janet’s and Olivier’s brains, not to mention that of all their researchers, causing them to revert to primitive concepts that “everyone” knows are false. The other — which is what I hear from young economists — is that there is an equilibrium business cycle claque in academic macroeconomics that has in effect blockaded the journals to anyone trying to publish models and evidence that stress the demand side.

Obviously you know which story I believe. The main point, though, is that trying to argue from authority is even sillier here than in most situations. There’s a huge difference between “nobody believes that” and “none of my friends will let that get published in the journals they control”.
Of course, most of those two paragraphs is nonsense. Janet Yellen and Oliver Blanchard are well out in the right tail of the quality distribution of Washington policymakers. To my taste, both are a little too wedded to Old Keynesian economics, but they listen, and I don't think those are the people that Cochrane is concerned with.

On other matters, what is an "equilibrium business cycle claque" anyway? Who exactly would those people be? First, if Krugman were to say the word "disequilibrium" to me, I would know what he meant, but I would have to correct him by pointing out that all the macro models I have seen in my life are equilibrium models. Old Keynesian, New Keynesian, stochastic growth, whatever - all of those models have some equilibrium concept. For example, you can fix the prices and let the quantities adjust - it's still an equilibrium model. I think what Krugman wants to say is that there is some "equilibrium business cycle claque" which is a collection of powerful people who control some important institutions, and reserve the right to filter out people and research they don't like. Here's a story. Long ago there was a group of outsiders, who either could not find jobs on the inside - in Cambridge Massachusetts, for example - or were literally kicked out of the Ivy League. Those people didn't spend their time whining about how badly they were treated, as far as I know. They went to work at out-of-the-way institutions like Carnegie Mellon University and the University of Minnesota, and ultimately remade macroeconomics - for the better, I think. They managed to get their work published, they helped start journals and professional societies, and built research institutions from the ground up.

Krugman's academic life was nothing like that. He was a Cambridge insider from the get-go, and anointed at an early age - not much struggle there I think. If these "young economists" who can't publish their "demand side" work even exist, the papers they can't publish must be real stinkers, as I don't see severe limits to the market for such stuff. The NBER - particularly the Fluctuations group and the "Monetary Economics" group - is very friendly to Keynesian economics. The Society for Economic Dynamics, started by what Krugman might think of as an "equilibrium claque," typically has plenty of New Keynesian economics on the program at its annual meeting. The QJE, where Eggertsson and Krugman just published their paper, is of course notable as an outlet for Keynesian work. The Journal of Monetary Economics, has been edited for years by Bob King, who certainly has Keynesian sympathies. That journal will soon be run by Ricardo Reis and Urban Jermann. I think it's fair to say that the former is a Keynesian. The editor of AEJ Macro (a newer and prominent macro journal) is John Leahy - a prominent Keynesian. In the group of co-editors at the AER, the only macroeonomist appears to be Marty Eichenbaum, who as we all know is now a hardcore Keynesian.

What could Krugman be thinking? We've found better ways to do macroeconomics than twiddling IS-LM models. Get over it.

## Tuesday, November 5, 2013

### GDP Plus

The Philadelphia Fed has a post on an alternative GDP measure, called "GDP Plus." The GDP measure we pay most attention to comes from the expenditure side of the national income and product (NIPA) accounts. As we teach undergraduates, there is also an income side to the NIPA, and in a world without measurement error, we would come up with the same measure of GDP whether we do it from the income side or the expenditure side. However, we live in a world with measurement error, and NIPA reports different estimates of GDP coming from the expenditure approach and income approach to measuring GDP. A paper by Aruoba et al. shows how to use information from the expenditure and income measures of GDP from the NIPA to construct an estimate of GDP which is in principle superior to the expenditure side estimate. The authors use latent variable methods. In the Philadelphia Fed post, you can see that this approach can make a substantial difference for quarterly growth rates of GDP. A key question is whether the alternative measure makes a difference for the cyclical properties of real GDP. Not sure if this is reported in the Aruoba et al. paper, as I haven't read it. Unfortunately the Philly Fed post just gives us a time series of quarterly growth rates - not the levels.

### Randy Wright online course

Randy Wright has an online course that covers search and unemployment, banking, credit, and monetary economics. This is intended for upper-level undergraduates or graduate students. It's zero cost, so you should check it out.