Ivan Werning's paper on liquidity traps
is getting attention in the Federal Reserve System. For example, Narayana Kocherlakota
cited the paper in a recent speech. Ivan presented a version of the paper at the 2011 St. Louis Fed Policy conference,
which was where I saw it.
What's the paper about, and why would the FOMC be interested in it? The basic model Werning uses is a well-worked-over linearized New Keynesian sticky price model, much like what can be found, for example, in Clarida, Gali, and Gertler's survey paper.
The key differences here are that Werning works in continuous time with no aggregate uncertainty, which is going to lend tractability to the problem. Further, he's going to solve an optimal policy problem. Perhaps surprisingly, New Keynesians do not often do that. The typical approach is to assume a Taylor rule for monetary policy, and go from there.
Here's the basic model(changing notation a bit):
(1) dx/dt = a[i(t)-r(t)-p(t)]
(2) dp/dt = bp(t)-kx(t)
(3) i(t) >= 0
x is the output gap, i is the nominal interest rate, r is the natural real rate of interest, and p is the inflation rate. a, b, and k are positive parameters. Equation (1) is an inverted Euler equation, equation (2) is a Phillips curve, and (3) imposes the zero lower bound on the nominal interest rate. Given an exogenous path r(t), the central bank determines i(t), and this determines a solution p(t) and x(t). Werning assumes a typical quadratic loss function, where bliss is taken to be a zero output gap and zero inflation.
What is an optimal monetary policy in this environment? If r(t)>=0 for all t, then the answer is easy. Bliss is attainable for all t. An optimal monetary policy is i(t)=r(t), which implies x(t)=p(t)=0.
The interesting question is what happens if r(t)<0 for some t. A simple example is r(t)=r1 for t<=T and r(t)=r2 for t>T, where r1<0 and r2>0. This will imply that bliss is not feasible for all t, and the zero lower bound (3) must bind at some dates. This is intended to look like the type of monetary policy problem that the Fed is currently faced with, as we'll see.
It will make a big difference whether or not the central bank is able to commit to a policy. With no commitment, we know that the central bank chooses i(t)=r(t) from date T on, with x(t)=p(t)=0 for t>T. Then we can work back to find the dynamic path up to time T. Before time T, we are in a liquidity trap, with i(t)=0, and things can be very bad. The output gap and the inflation rate are increasing, but until the time of liftoff there is a negative output gap and deflation. The problem gets worse the larger is T, i.e. the longer the liquidity trap scenario lasts.
Basically, the problem is that the real rate of interest is too high, and there is nothing the central bank can do about it, being constrained by the zero lower bound on the nominal interest rate. Further, the problem is compounded because of deflation during the liquidity trap period.
But, the central bank can do better if it can commit to a policy different from i(t)=r(t) after date T. After date T, the optimal policy with commitment is for the central bank to generate inflation above zero and an output boom (i.e. a positive output gap) after date T, which feeds back to the liquidity trap period, increasing inflation and output before period T.
You can see why people looking for a rationale for the FOMC's recent policy decisions like this paper. If you buy Werning's results, you might write something like the following in an FOMC statement:
To support continued progress toward maximum employment and price stability, the Committee expects that a highly accommodative stance of monetary policy will remain appropriate for a considerable time after the economic recovery strengthens.
The Fed is under a lot of pressure to "do something" about the weak labor market, and that pressure has been fed (no wordplay intended) by the Fed's confident statements about the efficacy of its policies. Apparently they are looking for serious research that will support what they are doing.
But how seriously do we want to take Werning's paper? Is this a basis for sound monetary policy in the circumstances we find ourselves in? I don't think so.
What's the shock that is driving the policy?
As in much recent Keynesian analysis, the reason for being in a prolonged state with a binding zero lower bound on the nominal interest interest rate is that the "natural real rate of interest" is low (negative, in the model). In the underlying model, the natural interest rate is the real rate of interest under flexible prices. What would cause the real rate to be low? The underlying model is a standard neoclassical growth model, in which the natural rate of interest depends (with a constant relative risk aversion utility function) on the discount factor (from preferences) and consumption growth. The natural real rate goes down if the discount factor rises (people care more about the future) or if efficient consumption growth falls. We're supposed to think that the financial crisis was about everyone simultaneously taking a greater interest in the future? At the optimum, this would make them want to save more. Or maybe the financial crisis shock - whatever it was - should have resulted in lower than average consumption growth coming out of the recession? These things are inconsistent with the Keynesian ideas about intervention that I have been hearing.
In terms of the logic of the model, and what we know about the recent recession, the negative natural real rate shock does not make any sense. More fundamentally, this is a model which does not incorporate any financial factors. There is no credit, no banks, and in fact no money. Monetary policy is about setting a market nominal interest rate, and that's it. The model has nothing to say about quantitative easing, why it may or may not work, and how that policy fits into the forward guidance policy that Werning's paper is about. It seems particularly bizarre to be attempting to address monetary policy in the wake of the financial crisis in a model that can exhibit nothing that looks like a financial crisis.
There are at least a couple of papers in which it is argued that nonlinearities are important at the zero lower bound, one by Villaverde and coauthors,
the other by Braun and coauthors.
Sometimes accounting properly for the nonlinearities doesn't just change the results quantitatively, but gives you qualitatively different results. It's a big deal. Werning uses the standard approach of linearizing around zero inflation, and then using a quadratic loss function to approximate welfare loss. I think the latter is suspect as well. As evidence that approximation may be leading Werning astray, look at his results on the effects of allowing for more price flexibility. Monetary policy in this model is all about correcting the price distortions that arise from price stickiness. Thus, one would expect that any monetary policy problems become less foreboding as prices get less sticky. That's not true in Werning's linearized model. In fact, in the economy without commitment, the output gap goes to minus infinity as price stickiness goes away in the limit. Something wrong there, I'm afraid.
Basic New Keynesian problems.
I've come to think of the standard New Keynesian framework as a model of fiscal policy. The basic sticky price (or sticky wage) inefficiency comes from relative price distortions. Particularly given the zero lower bound on the nominal interest rate, monetary policy is the wrong vehicle for addressing the problem. Indeed, in Werning's model we can always get an efficient allocation with appropriately-set consumption taxes (see Correia et al.,
for example). I don't think the New Keynesians have captured what monetary policy is about.
The original idea about monetary policy and commitment came from an example in Kydland and Prescott's paper.
In that model, in the absence of commitment the central bank is always tempted to use inflation to increase the output gap. The result is a bad equilibrium with high inflation. That model was used to justify commitment to policy rules that would lower long-run inflation with no cost in terms of output. The Werning paper, and related work, is being used to turn that argument on its head. Now, we are supposed to think that committing to high inflation in the future, when the central bank would otherwise choose low inflation, will be a good thing. Whether Kydland and Prescott's monetary policy model was any good (it has its problems), the idea certainly played out well in the policy realm, beginning with the Volcker disinflation.
The forward guidance idea in FOMC policy, backed up by Werning's work (and Woodford's), may prove to be harmless. But maybe not. Some FOMC members, particularly Evans and Kocherlakota, seem bent on writing down explicit numerical criteria for future policy tightening. I hope they run up against resistance.