I just finished a draft of an academic article, "The New-Keynesian Liquidity Trap" that might be of interest to blog readers, especially those of you who follow the stimulus wars.

New-Keynesian models produce some stunning predictions of what happens in a "liquidity trap" when interest rates are stuck at zero. They predict a deep recession. They predict that promises work: "forward guidance," and commitments to keep interest rates low for long periods, with no current action, stimulate the current level of consumption. Fully-expected future inflation is a good thing. Growth is bad. Deliberate destruction of output, capital, and productivity raise GDP. Throw away the bulldozers, let them use shovels. Or, better, spoons. Hurricanes are good. Government spending, even if financed by current taxation, and even if completely wasted, of the digging ditches and filling them up type, can have huge output multipliers.

Even more puzzling, new-Keynesian models predict that all of this gets worse as prices become more flexible. Thus, although price stickiness is the central friction keeping the economy from achieving its optimal output, policies that reduce price stickiness would make matters worse.

In short, every law of economics seems to change sign at the zero bound. If gravity itself changed sign and we all started floating away, it would be no less surprising.

And of course, if you read the

*New York Times*, people like me who have any doubts about all this are morons, evil, corrupt, and paid off by some vast right-wing conspiracy to transfer wealth from the poor to the secret conspiracy of hedge fund billionaires.

So I spent some time looking at all this.

It's true, the models do make these predictions. However, there is a crucial step along the way, where they choose one particular equilibrium. There is another equilibirum choice, where all of normal economics works again: no huge recession, no huge deflation, and policies work just as they ought to.

I took a setup from Ivan Werning's really nice 2012 paper: There is a negative "natural rate" from time 0 to time T, and the interest rate is stuck at zero. After that, the natural rate becomes positive again, and everyone expects the actual interest rate to follow. I solved the standard new-Keynesian model in this circumstance -- forward-looking "IS" and Phillips curves.

This is Werning's "standard" equilibrium choice, which shows all the new-Keynesian predictions. The liquidity trap lasts until T=5, shown as the vertical line in the middle of the graph.

The thick red line is inflation. As you see, there is huge deflation during the liquidity trap, though deflation is steadily decreasing.

The dashed blue line is output (deviation from "potential".) As you see, there is a huge output gap, though strong expected output growth as it comes back to "trend" at the end of the trap. This is why growth is bad -- in these models you always come back to trend, so if you can lower growth, that raises today's level.

The thin red dashed lines marching toward the vertical axis show what happens as you

*reduce*price stickiness. (I only showed inflation, output does the same thing.) As you reduce price stickiness, it all gets worse -- output at any given date falls dramatically. For price stickiness epsilon away from a frictionless market, output falls to zero and inflation to negative infinity.

I verify in the paper that all the claimed policy magic works in this equilibrium. Even a small amount of "forward guidance" can dramatically raise output, wasted-spending multipliers can be as large as you like, and those policies get more effective as price stickiness gets smaller.

However, for the same interest rate path, there are lots and lots of equilibria.

This graph shows a different equilibrium. I call it the "local-to-frictionless" equilibrium. Again, the thick red line is inflation. Now, during the liquidity trap, there is steady, mild inflation. The inflation pretty much matches the negative natural rate, so the zero interest rate during the trap (from t=0 to t=T=5) produces a the real interest rate near the natural rate.

As the trap ends, inflation slowly declines and then takes a "glide path" to zero -- i.e. zero deviation from trend, or back to the Fed's long-run target.

In this equilibrium, there is a small

*increase*in potential output, shown in the dashed blue output line. The new-Keynesian Phillips curve says that when inflation today is higher than inflation tomorrow, output is above potential.

As we turn down price stickiness, the thin red lines show that inflation smoothly approaches the totally frictionless case, positive inflation from 0 to T and zero inflation immediately thereafter. I didn't have room to show it, but output smoothly approaches a flat line as well.

The paper shows that all the magical policies are absent in this equilibrium: The multiplier is always negative, announcements about the far off future do no good, and deliberately making prices sticker doesn't help.

These are not

*different models*. These are not

*different policies*or

*different expected policies.*Interest rates follow exactly the same path in each case, zero from t until T=5, and following the natural rate thereafter. These are

*different equilibrium choices of the same model.*Each choice is completely valid by the rules of new-Keynesian models. I don't here challenge any of the assumptions, any of the model ingredients, any of the rules of the game for computation. Which outcome you choose is completely arbitrary.

The difference between the calamitous equilibrium and the mild local-to-frictionless equilibirum, in this model, is just expectational mulitple equilibria (with an implicit Ricardian regime.) If people expect the inflation glide path, we get the benign equilibrium. If they expect inflation to be zero the minute the trap ends, we get the disaster.

The paper goes on to compute all the magical policies, consider Taylor rules, and every other objection I can think of. So far.

What do I make of all this? Well obviously, maybe one isn't so dumb, evil, or corrupt for having doubts about changing the sign of all economic principles when interest rates hit zero.

Let me just quote from the conclusion

At a minimum, this analysis shows that equilibrium selection, rather than just interest rate policy, is vitally important for understanding these models' predictions for a liquidity trap and the effectiveness of stimulative policies. In usual interpretations of new-Keynesian model results, authors feel that interest rate policy is central, and equilibrium-selection policy by the Fed, or equilibrium-selection criteria, are details relegated to technical footnotes (as in Werning 2012), game-theoretic foundations, or philosophical debates, which can all safely be ignored in applied research. These results deny that interpretation.If all this just whets your appetite, I hope you will read the paper. Similarly, if you're brimming with objections, take a look at my attempts to anticipate most objections -- what about the Taylor rule, etc. -- in the paper.

....there really are multiple equilibria and choosing one vs. another is simply an arbitrary choice. Since there is an equilibrium with no depression and deflation, and no magical policy predictions, one cannot say that the new-Keynesian model makes a definite prediction of depression and policy impact.

I have not advocated a specific alternative equilibrium selection criterion. Obviously, the local-to-frictionless equilibrium has some points to commend it: It is bounded in both directions, it produces normal policy predictions, it has a smooth limit as price stickiness is reduced, and it does not presume an enormous fiscal support for deflation. But this is not yet economic proof that it is the "right" equilibrium choice.

We might consider which equilibrium choice is more consistent with the data. The US economy 2009-2013 features steady but slow growth, a level of output stuck about 6-7% below the previous trendline and the CBO's assessment of "potential," a stagnant employment-population ratio, and steady positive 2-2.5% inflation.

The local-to-frictionless equilibrium as shown in my second Figure can produce this stagnant outcome, but only if one thinks that current output is about equal to potential, i.e. that the problem is "supply" rather than "demand," and that the CBO and other calculations of "potential" or non-inflationary output and employment are optimistic, as they were in the 1970s, and do not reflect new structural impediments to output.

The standard equilibrium choice as shown in my first Figure cannot produce stagnation. It counterfactually predicts deflation, and it counterfactually predicts strong growth. One would have imagine a steady stream of unexpected negative shocks -- that each year, the expected duration of the negative natural rate increases unexpectedly by one more year -- to rescue the model. But five tails in a row is pretty unlikely.

The problem in generating stagnation is central to the new-Keynesian model. The "IS" curve and the assumption that we return to trend means that we can only have a low level of output and consumption if we expect strong growth. The Phillips curve says that to have a large output gap, we must have inflation today much below expected inflation tomorrow and thus growing inflation (or declining deflation). Thus if we are to return to a low-inflation steady state, we must experience sharp deflation today. If one wants a model with stagnation resulting from perpetual lack of "demand," this model isn't it. Static old-Keynesian models produce slumps, but dynamic intertemporal new-Keynesian models do not.

....

I close with a few kinds words for the new-Keynesian model. This paper is really an argument to save the core of the new-Keynesian model -- proper, forward-looking intertemporal behavior in its IS and price-setting equations -- rather than to attack it. Inaccurate predictions for data (deflation, depression, strong growth), crazy-sounding policy predictions, a paradoxical limit as price stickiness declines, and explosive off-equilibrium expectations, are not essential results of the model's core ingredients. A model with the core ingredients can give a very conventional view of the world, if one only picks the local-to-frictionless equilibrium. That model will build neatly on a stochastic growth model, represented here in part by the forward-looking "IS" equation and changes in "potential." Its price stickiness will modify dynamics in small but sensible ways and allow a description of the effects of monetary policy. This was the initial vision for new-Keynesian models, and it remains true.

Really, the fault is not in the core of the new-Keynesian model. The fault is in its application, which failed to take seriously the fundamental problem of nominal indeterminacy.... Interest rate targets, even those that vary with output and inflation, or money supply control with interest-elastic demand, simply do not determine the price level or inflation. In a model with price stickiness, nominal indeterminacy spills over in to real indeterminacy.

In that context, this paper shows there is an equilibrium choice that leads to sensible results. Alas, those sensible results are non-intoxicating. In that equilibrium, our present (2013) economic troubles cannot be chalked up to one big simple story, a "negative natural rate" (whatever that means) facing a lower bound on short term nominal rates; and our economic troubles cannot be solved by promises, or a sign reversal of all the dismal parts of our dismal science. Technical regress, wasted government spending, and deliberate capital destruction do not work. Growth is good, not bad. That outcome is bad news for those who found magical policies an intoxicating possibility, but good news for a realistic and sober macroeconomics.

(This follows an earlier paper in the JPE (online appendix) looking deeply at multiple equilibria in new-Keynesian models. In that paper, I questioned whether ruling out multiple explosive equilibria made sense. In this paper, I accept that part of the rules of the game, and think about the mulitple non-explosive equilibria.)

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