Managing a liquidity trap

I've been catching up on my new-Keynesian economics and found a little gem by Ivan Werning, "Managing a liquidity trap"

The policy issue is this: we're in a recession. Interest rates are zero, and can't go lower. The Fed is desperately trying to goose the economy. Lots of people (most of the recent Jackson Hole Fed conclave) are advising  "open-mouth operations," and  "managing expectations," that the key to current prosperity is for the Fed to make statements  about what it will do in the future; and these statements on their own, with no concrete action, will "increase demand" and lower today's unemployment. The Fed has been convinced, with more and more "forward guidance" as part of its strategy.  For example, the latest FOMC statement made history by promising zero interest rates as long as unemployment stays above 6 and a half percent and inflation below two and a half.

Does any of this make any sense?

There are piles of complicated new-Keynesian models on this topic. Ivan's paper gets right to the core, giving a very simple model that explains their logic.  The version on p. 20 is the simplest and clearest of all. We only really need one equation

log consumption growth = (substitution elasticity) x real interest rate

$$\frac{dc(t)}{dt} = \sigma^{-1} r(t) $$

(Hang in there, non-economists, you don't really even need the equations; everything is in words too. Also, this is an experiment with Latex macros in blogger. You should see a nice equation above. Let me know if it doesn't work in your browser.) When real interest rates are high, people choose to save more, so consumption is lower today and higher in the future. Thus, high consumption growth goes with high interest rates, and vice versa.

Now, forget about capital, so consumption equals output. Assume the Fed can set the real interest rate to whatever it wants.  Also, think of everything as deviations from "potential output" or "trend." The level of consumption becomes the "output gap." Thus, by controlling interest rates, the Fed controls the growth rate of consumption, output, and the output gap.

Now, here's the key. If the Fed raises the interest rate, and hence the growth rate of consumption, the  level of consumption (now the output gap) falls. New-Keynesian models (correctly) anchor the level in the future; consumption (output) sooner or later must be equal to "potential."   This is the key new-Keynesian mechanism by which higher interest rates lower output, and quite different from the static stories you may remember from old-Keynesian models. (I call this "IS" curve the "interntemporal substitution" curve.)

You might have thought that raising the growth rate of consumption would just be a good thing; implicitly anchoring the level of consumption at last year's value. That would be a mistake. The only way to raise the growth rate of consumption next year is for the level this year to drop. (In this economy without capital.) Then we grow faster by catching up.  

Furthermore, if people expect high interest rates for many years, there will be many years of strong consumption growth, and today's level will be very depressed. In equations, we find the level of consumption (output gap) by  integrating all its future growth rates (bottom of p. 19)

$$x(t) = \sigma^{-1} \int_t^\infty r(t) dt$$

In sum, the level of today's consumption, output, and output gap all depend on today's interest rate and people's expectations of the path of future interest rates.

You can start to see how managing expectations of future interest rates might be an attractive idea. If we can't do anything about today's interest rates, lowering expected future rates will have the same effect on today's consumption. 

In this paper's model, as most new-Keynesian thinking, our current problem is that the "natural rate" of interest, required to keep us at potential output, is sharply negative. (This is all exogenous.) With "only" 2% inflation and nominal interest rates stuck at zero, the Fed cannot deliver anything less than a negative 2% real rate of interest. If the "natural rate" is something like negative 5%, then we are stuck at a 3% "too high" real interest rate.  Taking differences to "trend" or "potential,"  our situation is equivalent to a too-high real interest rate that the Fed can't do anything about.

The solid line in Figure 3 of the paper, reproduced above, shows this situation. The lines plot differences relative to potential output, or "output gaps," so being on the horizontal axis is the best outcome. We have a "negative natural rate" until time T, when the world returns to normal, the Fed regains control, and consumption and output revert to the trend line. You see that the too-high growth of consumption between now and T, and the too-low level of consumption (output gap) now.

Well, says Ivan, why not pull the whole line up? Suppose the Fed could promise now that, at time T, it will set interest rates too low, from the point of view of that time? This will encourage people to consume at time T rather than in periods after that, i.e. it will engineer the negatively sloped dashed line from T onwards. If people knew there was going to be this boom at T, consumption today would be less depressed. (Again, the way the graph works is that you work from right to left, and the Fed controls the output and consumption growth rates from right to left in order to produce today's level.)

More formally, Ivan assumes that the Fed wants to minimize the squared deviations from potential. A policy like the dashed one produces smaller sum-of-squared output deviations than the solid line we're facing now.

This pretty little graph illustrates lots of policy advice you're hearing from inside and outside the Fed. According to this view, the key thing the Fed can do to raise "demand" today is to promise that it will keep interest rates low longer than it normally would do -- in the period after T -- engineering a bout of output that is a little too high (in a bigger model, inflationary).   

But the graph, and the paper, illustrate the central problem: At time T, the Fed will not want to keep rates low. "Too much" consumption means inflation, and in this model too much output (beyond "potential") is just as bad as too little. When time T hits, and the "natural rate" returns to normal, the optimal thing for the Fed to do looking  forward is to set the interest rate equal to the natural rate, and follow the solid green line. In turn, people today know this, which is why their expectation for consumption at time T is at the solid line level, which is why consumption today is depressed.

Chicago Fed Chair Charlie Evans describes the needed policy as "Odyssean." As Odysseus realized in having himself tied to the mast, the ability to commit yourself today that you will do things tomorrow, things that you will not choose tomorrow if you will have the choice, can improve overall performance. This is a deep principle of good policy, and its violation describes many of our current problems. If the government refuses to commit today that it will not bail people out in the future, then people will take risky actions, and  the bailout will recur.

And this is the central problem for this little parable in describing the Fed's actions. Let's read the Fed's Odyssean revelation (the FOMC statement) a little more carefully, with the model in mind: 
"..the Committee expects that a highly accommodative stance of monetary policy will remain appropriate for a considerable time...;"  "currently anticipates that this exceptionally low range for the federal funds rate will be appropriate at least as long as the unemployment rate remains above 6-1/2 percent..." "the Committee will also consider other information."
There is no commitment at all in this. It's a description of how the Fed thinks it will feel in the future, but nowhere in here is what the new-Keynesian model demands: a commitment to do things in the future that the Fed will not want to do when the time comes.

The problem is deep. How can the Fed have the power to take the "discretionary" action today, in response to the current situation, but that action is somehow to commit itself to doing something in the future that it very much will not want to do when the time comes -- that it has so far explicitly and loudly promised that it will not do, and has built up 30 years of reputation against doing -- undershoot and cause inflation? Why can't the Fed 2015 convene another Jackson Hole conference, bring out Charlie Plosser and Jeff Lacker's friends to say "we're heading to a repetition of the 1970s, it's time to become new-Monetarists and promise that we'll be looking at monetary aggregates not unemployment rates?" It's so much hot air, and people know it.

True commitment requires legal, institutional, or constitutional restraints. It at least needs language like "the Committee commits to keep a highly accomodative stance of monetary policy long after it is appropriate" or better an institutional commitment "and to that end no further FOMC meetings will be scheduled until inflation hits 3%." But no institution gives up its discretion easily.  (To be clear, I think this would all be a terrible idea; more below. I'm explaining the central commitment/discretion problem highlighted by Ivan's model.)

The paper, of course achieves the same thing in much greater generality, while also presenting this gorgeously transparent example. This example makes it crystal clear that the reason for "forward guidance" in new-Keynesian models is not to raise inflation and thus lower real interest rates -- it works here with constant inflation. "The reason for holding the interest rate at zero is not to promote inflation [and hence negative real rates] as is commonly assumed."..."The real reason for committing to zero interest rates is to create the expectations of a future consumption boom" (p. 4)

Cautioning implicitly against the Fed's "twist" policies aimed at lowering long-term interest rates "I show that optimal policy... actually raises long run interest rates.... This cautions against simple assessments of monetary policy centered around the lowering of yields at long maturities." In the full model, promising the inflationary boom raises long term rates. I.e. exactly the opposite of the Fed's "quantitative easing" operations.

To be clear, I don't buy any of this: that our current problems would all be solved if interest rates could be negative 5%; i.e. that the "natural rate of interest" is sharply negative; that the economy is being strangled by tight credit; and that committing to a repetition of the late 1970s would be a great way to escape our current troubles. I don't think you can analyze the situation in a model without capital, as saving translates to investment demand when there is capital. (Christiano, Eichenbaum and Rebelo's When is the Government Spending Multiplier Large? makes this point, next on my review list.) I don't think a model that says we are experiencing a low level and high growth rates makes much sense. I think the Fed is even more powerless than these models posit.

But this is the great point of clean, theoretical models. They are not black boxes that make predictions. They are collections of clear "if, then" statements. I see the core of the new-Keynesian forward-guidance argument clearly in Ivan's model. If I disagree with the "then," I have to find what I don't like about the "if." And he very clearly shows the difference between "commitment" in the new-Keynesian model vs. how it is translated to policy practice, for better or worse.

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