The New-Keynesian Liquidity Trap

I just finished a draft of an academic article, "The New-Keynesian Liquidity Trap"  that powerfulness live of involvement to spider web log readers, specially those of yous who follow the stimulus wars. 

New-Keynesian models create about stunning predictions of what happens inwards a "liquidity trap" when involvement rates are stuck at zero.  They predict a deep recession. They predict that promises work: "forward guidance," in addition to commitments to locomote on involvement rates depression for long periods, amongst no electrical current action, receive the electrical current grade of consumption.  Fully-expected hereafter inflation is a skillful thing. Growth is bad. Deliberate devastation of output, capital, in addition to productivity heighten GDP. Throw away the bulldozers, permit them utilisation shovels. Or, better, spoons. Hurricanes are good. Government spending, fifty-fifty if financed past times electrical current taxation, in addition to fifty-fifty if completely wasted, of the earthworks ditches in addition to filling them upwardly type, tin forcefulness out receive got huge output multipliers.

Even to a greater extent than puzzling, new-Keynesian models predict that all of this gets worse equally prices locomote to a greater extent than flexible.  Thus, although cost stickiness is the key friction keeping the economic scheme from achieving its optimal output, policies that cut back cost stickiness would brand matters worse.

In short, every police line of economic science seems to alter sign at the nil bound. If gravity itself changed sign in addition to nosotros all started floating away, it would live no less surprising.

And of course, if yous read the New York Times, people similar me who receive got whatsoever doubts most all this are morons, evil, corrupt, in addition to paid off past times about vast right-wing conspiracy to transfer wealth from the pathetic to the surreptitious conspiracy of hedge fund billionaires.

So I spent about fourth dimension looking at all this.

It's true, the models practise brand these predictions. However, at that spot is a crucial stride along the way, where they select i particular equilibrium. There is about other equilibirum choice, where all of normal economic science industrial plant again: no huge recession, no huge deflation, in addition to policies run just equally they ought to.

I took a setup from Ivan Werning's genuinely overnice 2012 paper: There is a negative "natural rate" from fourth dimension 0 to fourth dimension T, in addition to the involvement charge per unit of measurement is stuck at zero. After that, the natural charge per unit of measurement becomes positive again, in addition to everyone expects the actual involvement charge per unit of measurement to follow. I solved the measure new-Keynesian model inwards this circumstance -- forward-looking "IS" in addition to Phillips curves.

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

The thick blood-red line of piece of work is inflation. As yous see, at that spot is huge deflation during the liquidity trap, though deflation is steadily decreasing.

The dashed bluish line of piece of work is output (deviation from  "potential".) As yous see, at that spot is a huge output gap, though strong expected output growth equally it comes dorsum to "trend" at the goal of the trap. This is why growth is bad -- inwards these models yous ever come upwardly dorsum to trend, so if yous tin forcefulness out lower growth, that raises today's level.

The sparse blood-red dashed lines marching toward the vertical axis present what happens equally yous reduce price stickiness. (I solely showed inflation, output does the same thing.) As yous cut back cost stickiness, it all gets worse -- output at whatsoever given appointment falls dramatically. For cost stickiness epsilon away from a frictionless market, output falls to nil in addition to inflation to negative infinity.

I verify inwards the newspaper that all the claimed policy magic industrial plant inwards this equilibrium.  Even a minor amount of "forward guidance" tin forcefulness out dramatically heighten output, wasted-spending multipliers tin forcefulness out live equally large equally yous like, in addition to those policies larn to a greater extent than effective equally cost stickiness gets smaller.

However, for the same involvement charge per unit of measurement path, at that spot are lots in addition to lots of equilibria.

This graph shows a different equilibrium. I telephone yell upwardly it the "local-to-frictionless" equilibrium. Again, the thick  red line of piece of work is inflation. Now, during the liquidity trap, at that spot is steady, mild inflation. The inflation pretty much matches the negative natural rate, so the nil involvement charge per unit of measurement during the trap (from t=0 to t=T=5) produces a the existent involvement charge per unit of measurement nigh the natural rate.

As the trap ends, inflation piece of cake declines in addition to so takes a "glide path" to nil -- i.e. nil difference from trend, or dorsum to the Fed's long-run target.

In this equilibrium, at that spot is a small increase in potential output, shown inwards the dashed bluish output line. The new-Keynesian Phillips bend says that when inflation today is higher than inflation tomorrow, output is higher upwardly potential.

As nosotros plough downwards cost stickiness, the sparse blood-red lines present that inflation smoothly approaches the totally frictionless case, positive inflation from 0 to T in addition to nil inflation directly thereafter. I didn't receive got room to present it, but  output smoothly approaches a apartment line of piece of work equally well.

The newspaper shows that all the magical policies are absent inwards this equilibrium: The multiplier is ever negative, announcements most the far off hereafter practise no good, in addition to deliberately making prices sticker doesn't help.

These are non different models. These are non different policies or different expected policies. Interest rates follow just the same path inwards each case, zero from t until T=5, in addition to next the natural charge per unit of measurement thereafter. These are different equilibrium choices of the same model. Each alternative is completely valid past times the rules of new-Keynesian models. I don't hither challenge whatsoever of the assumptions, whatsoever of the model ingredients, whatsoever of the rules of the game for computation. Which outcome yous select is completely arbitrary.

The difference betwixt the calamitous equilibrium in addition to the mild local-to-frictionless equilibirum, inwards this model, is just expectational mulitple equilibria (with an implicit Ricardian regime.) If people aspect the inflation glide path, nosotros larn the benign equilibrium. If they aspect inflation to live nil the infinitesimal the trap ends, nosotros larn the disaster.

The newspaper goes on to compute all the magical policies, consider Taylor rules, in addition to every other objection I tin forcefulness out recall of. So far.

What practise I brand of all this? Well obviously, mayhap i isn't so dumb, evil, or corrupt for having doubts most changing the sign of all economical principles when involvement rates hitting zero.

Let me just quote from the conclusion

At a minimum, this analysis shows that equilibrium selection, rather than just involvement charge per unit of measurement policy, is vitally of import for agreement these models' predictions for a liquidity trap in addition to the effectiveness of stimulative policies. In commons interpretations of new-Keynesian model results, authors experience that involvement charge per unit of measurement policy is central, in addition to equilibrium-selection policy past times the Fed, or equilibrium-selection criteria, are details relegated to technical footnotes (as inwards Werning 2012), game-theoretic foundations, or philosophical debates, which tin forcefulness out all safely live ignored inwards applied research. These results deny that interpretation.

....there genuinely are multiple equilibria in addition to choosing i vs. about other is just an arbitrary choice. Since at that spot is an equilibrium amongst no depression in addition to deflation, in addition to no magical policy predictions, i cannot say that the new-Keynesian model makes a definite prediction of depression in addition to policy impact.

I receive got non advocated a specific alternative equilibrium selection criterion. Obviously, the local-to-frictionless equilibrium has about points to commend it: It is bounded inwards both directions, it produces normal policy predictions, it has a polish confine equally cost stickiness is reduced, in addition to it does non presume an enormous financial back upwardly for deflation. But this is non all the same economical proof that it is the "right" equilibrium choice.

We powerfulness consider which equilibrium alternative is to a greater extent than consistent amongst the data. The USA economic scheme 2009-2013 features steady but irksome growth, a grade of output stuck most 6-7% below the previous trendline in addition to the CBO's assessment of "potential," a stagnant employment-population ratio, in addition to steady positive 2-2.5% inflation.

The local-to-frictionless equilibrium equally shown inwards my instant Figure tin forcefulness out create this stagnant outcome, but solely if i thinks that electrical current output is most equal to potential, i.e. that the job is "supply" rather than "demand," in addition to that the CBO in addition to other calculations of "potential" or non-inflationary output in addition to work are optimistic, equally they were inwards the 1970s, in addition to practise non reverberate novel structural impediments to output.

The measure equilibrium alternative equally shown inwards my offset Figure cannot create stagnation. It counterfactually predicts deflation, in addition to it counterfactually predicts strong growth. One would receive got imagine a steady current of unexpected negative shocks -- that each year, the expected duration of the negative natural charge per unit of measurement increases unexpectedly past times i to a greater extent than twelvemonth -- to rescue the model. But v tails inwards a row is pretty unlikely.

The job inwards generating stagnation is key to the new-Keynesian model. The "IS" bend in addition to the supposition that nosotros render to tendency agency that nosotros tin forcefulness out solely receive got a depression grade of output in addition to consumption if nosotros aspect strong growth. The Phillips bend says that to receive got a large output gap, nosotros must receive got inflation today much below expected inflation tomorrow in addition to thence growing inflation (or declining deflation). Thus if nosotros are to render to a low-inflation steady state, nosotros must experience abrupt deflation today.  If i wants a model amongst stagnation resulting from perpetual lack of "demand," this model isn't it. Static old-Keynesian models create slumps, but dynamic intertemporal new-Keynesian models practise not.
....
I unopen amongst a few kinds words for the new-Keynesian model. This newspaper is genuinely an declaration to salvage the meat of the new-Keynesian model -- proper, forward-looking intertemporal behaviour inwards its IS in addition to price-setting equations -- rather than to assault it. Inaccurate predictions for information (deflation, depression, strong growth), crazy-sounding policy predictions, a paradoxical confine equally cost stickiness declines, in addition to explosive off-equilibrium expectations, are non essential results of the model's meat ingredients.  A model amongst the meat ingredients tin forcefulness out plough over a real conventional sentiment of the world, if i solely picks the local-to-frictionless equilibrium. That model volition gear upwardly neatly on a stochastic growth model, represented hither inwards role past times the forward-looking "IS" equation in addition to changes inwards "potential." Its cost stickiness volition modify dynamics inwards minor but sensible ways in addition to allow a description of the effects of monetary policy. This was the initial vision for new-Keynesian models, in addition to it remains true.

Really, the error is non inwards the meat of the new-Keynesian model. The error is inwards its application, which failed to convey seriously the fundamental job of nominal indeterminacy.... Interest charge per unit of measurement targets, fifty-fifty those that vary amongst output in addition to inflation, or coin provide command amongst interest-elastic demand, just practise non create upwardly one's heed the cost grade or inflation.  In a model amongst cost stickiness, nominal indeterminacy spills over inwards to existent indeterminacy.

In that context, this newspaper shows at that spot is an equilibrium alternative that leads to sensible results. Alas, those sensible results are non-intoxicating. In that equilibrium, our acquaint (2013) economical troubles cannot live chalked upwardly to i large unproblematic story, a "negative natural rate" (whatever that means) facing a lower saltation on brusk term nominal rates; in addition to our economical troubles cannot live solved past times promises, or a sign reversal of all the dismal parts of our dismal science. Technical regress, wasted authorities spending, in addition to deliberate uppercase devastation practise non work. Growth is good, non bad. That outcome is bad tidings for those who flora magical policies an intoxicating possibility, but skillful tidings for a realistic in addition to sober macroeconomics.
    

If all this just whets your appetite, I hope yous volition read the paper. Similarly, if you're brimming amongst objections, convey a aspect at my attempts to anticipate most objections -- what most the Taylor rule, etc. -- inwards the paper.

(This follows an before newspaper inwards the JPE (online appendix) looking deeply at multiple equilibria inwards new-Keynesian models. In that paper, I questioned whether ruling out multiple explosive equilibria made sense. In this paper, I receive got that role of the rules of the game, in addition to recall most the mulitple non-explosive equilibria.)