More Thoughts On ‘Expectations Driven’ Liquidity Traps

Warning - this is technical, so actually merely for macroeconomists.

The thought that nosotros could acquire stuck inward a steady dry reason amongst nominal involvement rates at zip together with negative inflation has been dismissed yesteryear around because it has been associated amongst the policy proposal to enhance nominal involvement rates to avoid that outcome. Here I desire to explore an choice interpretation that disconnects the theory from the policy.

First, a recap on the theory. Take a actually elementary model, where the existent involvement charge per unit of measurement is positive together with constant. The fundamental banking enterprise sets the nominal charge per unit of measurement according to a Taylor dominion that obeys the Taylor principle. The dominion is calibrated such that at that topographic point is a steady dry reason at which nominal involvement rates are positive together with inflation is at target. Furthermore nether rational expectations/perfect foresight, if agents know the inflation target, the existent charge per unit of measurement together with the rule, nosotros instantly popular off to that steady state. In to a greater extent than complex together with realistic models it may accept fourth dimension to acquire to this ‘intended’ steady state, but it is ‘locally’ or ‘saddlepath’ stable.

However at that topographic point is around other steady state, because nominal involvement rates cannot popular off below zero. For given existent involvement rates, this Zero Lower Bound (ZLB) steady dry reason must involve negative inflation. This steady dry reason is ‘indeterminate’, which way that nosotros tin clit dynamic perfect foresight paths that starting fourth dimension at around arbitrary score of inflation below the fundamental bank’s target, but terminate upward at the ZLB steady state. To encounter this diagrammatically, facial expression at this before post, or (plus algebra) this from David Andolfatto, or pages 123 to 135 inward Woodford’s Interest together with Prices. [1]

Stephanie Schmitt-Grohe together with Martın Uribe receive got a paper which embeds this logic inward a to a greater extent than elaborate model of involuntary unemployment based on nominal wage rigidity. They advise that it tells a ameliorate storey nearly the USA recession than the New Keynesian thought involving a downward shift inward the natural existent involvement rate. It is a storey of a jobless recovery: growth resumes at the ZLB steady state, but involuntary unemployment is also positive at that steady state, because inflation is negative together with nominal reward are downward rigid.

The newspaper interprets the ZLB steady dry reason every bit 1 where agents receive got the incorrect expectations nearly the fundamental banking enterprise target. Call this the ‘mistaken beliefs’ story. With that story, raising rates could discover or signal the authority’s truthful inflation target. In Stephanie together with Martin’s paper, because raising nominal rates leads to an immediate alter inward beliefs together with thence a rising inward expected inflation, nosotros encounter an immediate saltation to output growth inward a higher house trend, which allows unemployment to fall. Many volition merely think this thought is incredible, but every bit Paul Krugman keeps emphasising, ZLB economic science oftentimes turns things upside down.

In an before post I suggested that this storey could maybe last plausible for (pre Abe?) Nihon or the Euro area, because their inflation targets are one-sided: they seem content if inflation is below target, so inward regulation it mightiness last possible to believe they mightiness last content to terminate upward at the ZLB steady state. In add-on at that topographic point is no QE inward the Eurozone, together with was only briefly inward Japan. I suggested, I promise correctly, that the province of affairs is different inward the US, together with it clearly is inward regulation inward the UK. For that argue alone, I thought the false beliefs storey unlikely for these 2 countries.

However, later on seeing Stephanie acquaint her newspaper terminal calendar week together with thinking to a greater extent than nearly it, I wondered whether nosotros could give the ZLB steady dry reason a different interpretation? Suppose agents believe that is where inflation is heading because they create non think monetary (or whatever other) policy is capable of achieving the inflation target. Given electrical flow attitudes to financial policy, together with a pessimistic stance of the powerfulness of QE, this interpretation does non seem so farfetched for the USA or UK. Economists sometimes worry nearly a deflationary spiral, where inflation merely keeps falling into a bottomless pit. But maybe the ZLB steady dry reason is similar a ledge that tin halt this descent. [2]

Under this interpretation, the policy of raising involvement rates could last a disaster. There is no boost from whatever growth inward expected inflation, because beliefs create non change. We lose the negative inflation equilibrium, but what seems probable inward that province of affairs is that nosotros merely acquire a negative deflationary spiral. The ledge preventing descent into the deflationary pit crumbles away. [3] If this interpretation is tenable, so it way that the possibility of becoming stuck inward a ZLB steady dry reason is non necessarily linked to the policy proposal of raising rates to operate out of it.

My ain stance of the bear witness is that the ‘balance canvass recession/natural charge per unit of measurement besides low’ storey is withal the to a greater extent than convincing, together with that nosotros are currently seeing inward the USA together with Great Britain a real deadening render to the inflation target equilibrium. However that storey is non without its problems: amongst a elementary New Keynesian Phillips curve, a gradual reduction inward the output gap should last associated amongst inflation gradually rising towards target, which is non what nosotros are seeing at the moment. So I am non so confident that I tin dismiss the ZLB steady dry reason storey out of hand. The message I clit from that possibility is that inflation targets bespeak to last 2 sided together with clear, and that policy (monetary together with fiscal) at the ZLB should create everything it tin to attempt together with accomplish that target. Assuming that below target inflation must eventually rising because nominal rates are zip could plough out to last a big mistake. [4]

[1] At the intended steady state, where inflation is at target, the target fixes the end-point of whatever dynamic process, together with this (rather than history) so determines the initial score of inflation. At the ZLB steady state, at that topographic point are multiple dynamic paths that Pb there, so something else (‘confidence’) fixes the initial point. It cannot last history, because the model is forrad looking together with history does non matter. This may last a picayune besides arbitrary or extreme for around tastes.

It is also controversial whether an inflation target is sufficient to ready an end-point for whatever dynamic inflation process, rather than allowing dynamic processes that explode. As I banking enterprise annotation inward my before post, John Cochrane says: “Transversality weather condition tin dominion out existent explosions, but non nominal explosions.” I receive got less of a job than he does amongst this. 

[2] H5N1 tertiary interpretation mightiness last that agents revise downwardly their beliefs every bit inflation falls. The job at that topographic point is that this involves learning, which may brand the stability of the ZLB steady dry reason problematic. Jess Benhabib, George Evans, together with Seppo Honkapohja receive got modelled learning when at that topographic point are the same 2 steady states, together with what they detect is that the ZLB steady dry reason is unstable: inflation keeps on falling. (It is a deflationary spiral.) My intuitive explanation for their resultant is that learning is equivalent to introducing backward looking expectations dynamics, together with typically an indeterminate equilibrium amongst rational expectations dynamics (which the ZLB steady dry reason is) becomes unstable amongst backward looking dynamics. Equally a ‘saddlepoint’ perfect foresight equilibrium (which the intended steady dry reason is) becomes stable when expectations are backward looking, so they detect that the inflation target steady dry reason is stable nether learning.

[3] Following on from footnote [1], y'all mightiness inquire why agents inward this illustration volition non select the only steady dry reason left, together with thence enhance their expectations. Why tin I imagine agents assuming a deflationary spiral, but I desire to dominion out inflationary spirals? The response is because the ZLB provides asymmetry. If it looks similar an inflationary spiral is developing, the fundamental banking enterprise tin depart from its Taylor dominion together with enhance rates substantially. That should alter beliefs. They cannot create the same for a deflationary spiral.

[4] In an early on draft of this postal service I had a different introduction, based on Narayana Kocherlakota’s recent dissent. Some may scream back that Kocherlakota originally seat forrad the false beliefs ZLB steady dry reason idea, but so seemingly recanted. So my thought was that perhaps what had changed was non his stance nearly the theory, but his interpretation of it. However having read around to a greater extent than nearly his electrical flow views, I don’t think this stands up, but it was such a peachy thought I cannot resist mentioning it every bit a footnote.