The New-Keynesian Liquidity Trap

Transcription

1 The New-Keynesian Liquidity Trap John H. Cochrane Univeristy of Chicago Booth School of Business, NBER, Hoover, Cato

2 New Keynesian models: Diagnosis I Consensus NK diagnosis: Natural rate r << 2% ) i =, π = 2%, i π too high. I Fix E t c t+. Too high i π ) c grows too fast, level too low. I Why do we not see more π? ) model! 4 35 Consumption 3% trend 2 27 New Keynesian PIH

3 New Keynesian models: Policy I Policy: Many laws of economics change sign at the zero bound. 1. Commitments to future policy raise GDP with no action today. 2. Expected in ation raises output. 3. Wasted government purchases, even if nanced by taxes, can have very large multipliers. 4. Technical regress, lower productivity, broken windows raise output. I These work by by raising π, lowering i π, lowering growth E t c t+j and thus raising the level of consumption and output. c t = E t Z lim t+t T! σ 1 (i t+s s= r t+s π t+s ) ds NK model is not static, income driven Keynesian. MPC =. IS = Intertemporal substitution. r, not Y, equilibrates. I Puzzles: 1. Promises further in the future have larger e ect today. 2. Diagnosis and policy get stronger as frictions diminish, with limit. 3.!Though stickiness is the central friction causing our troubles, don t x it! Making prices sticker is good.

4 New-Keynesian model (Werning 212) From discrete time, dx t dt dπ t dt = σ 1 (i t r t π t ) (1) = ρπ t κx t. (2) r t = natural rate x t = E t x t+1 + σ 1 [i t r t E t π t+1 ] π t = e ρ E t π t+1 + κx t or π t = κ Z s= e ρs x t+s ds

5 Scenario negative natural rate / liquidity trap 6 Scenario 4 2 Interest rate 2 4 Natural rate Time I Task: nd fπ t, x t g. (Taylor rule analysis follows.)

6 The frictionless equilibrium 6 5 Frictionless equilibrium,κ = x π I dπ t /dt = ρπ t κx t. κ ) ; x t = 8π t I dx t /dt = σ 1 (i t r t π t ) ) π t = i t r t I Higher π exactly matches r <. Zero bound has no output e ect.

7 Solution with price stickiness d xt dt π t 1 = κ ρ xt π t irt + I Two eigenvalues, λ m <, λ p > ; two free constants. I t > T : Set e λpt term to zero. t T : Match solutions at t = T. I One-dimensional family of solutions. Index by π T (really E t π T ). 1 Inflation across equilibria

8 The standard equilibrium choice π T = 1 Standard equilibrium, varyingκ x π I Depression (with growth). De ation (rapidly changing). I Backward-explosive λ ) key to big predictions. I Less friction!worse! Limit6=limit point! Less frictions! faster.

9 The backwards-stable equilibrium 6 5 Backward stable equilibrium, varying κ x π I Choice: π T s.t. backward approach to steady state. I No (demand-side) recession. No big growth/de ation & dynamics. I Nice frictionless limit! I Exactly the same interest-rate path.

10 The no-in ation-jump equilibrium 6 5 No jump equilibrium, varyingκ x π I Choose π T so that π =. I Also no de ation, small output e ects. I All equilibria with limited π, x jump have normal frictionless limits, small e ects for small price stickiness.

11 Magical multipliers and paradoxical policies dx t dt dπ t dt = σ 1 (i t r t π t ) = ρπ t κ (x t +g t ). I g = useless spending, technical regress, high wage mandates, capital destruction, etc. I Phillips curve disturbance: All else constant, more g means more π. More π means less i π. I π, intertemporal substitution channel, not consumption function! I fπ t g constant means x/ g = 1. E ect needs π, dπ t /dt. I Consider g t = g > for t < T, then g t = for t > T. Calculate x t / g, private-output multiplier...

12 Magical multipliers 2 18 Standard equilibrium Backward stable Multiplier Years I π T = equilibrium: x t / g t is big! Bigger as frictions decrease! I Other equilibria: x t / g t = 1. I Equilibria without big π, d π/dt do not have big multipliers.

13 Percent Percent Percent Low rate promise standard equilibrium I Interest rate stays at zero for time τ after the trap ends 1 τ =. 1 τ = x π τ = 1. 3 τ = I Far-away promises have huge e ects.

14 Percent Percent Percent Low rate promise backwards-stable equilibrium 6 τ =. 6 τ = x π τ = 1. 6 τ = I Faraway promises have little current e ects!frictionless.

15 So far I Reminder: the (expected, equilibrium) interest rate path is the same for all solutions. I The diagnosis of large recession (with large E t c t+1 ) and de ation (with large dπ t /dt) relies crucially on which equilbrium we choose. I Unusual (magical) policies rely crucially on which equilibrium we choose. I Equilibria that are bounded backwards, bounded impulse-response π, and have frictionless limits do not produce large recessions or unusual policies. I So why pick π T =? What about Taylor rules?...

16 Werning s equilibrium selection Why π T =? Answer: expectations of an equilibrium-selection policy, apart from interest rate policy

17 Taylor rule I Why π T =? I NK: Two Fed policies, interest rate policy it and equilibrium selection policy to pick one πt from fπ t g consistent with it. I Taylor form selection. Fed speci es it and also speci es πt from fπ t g consistent with it, then adds i t = i t + φ π (π t π t ). kφ π k > 1+ no explosive solutions = select π t. I The same as Wicksellian, (optimal) stochastic intercept, intercept reacts to shocks, temporary deviations policy i t = (i t φ π π t ) + φ π π t = ī t + φ π π t I!Expectations about equilibrium-selection policy/stochastic intercept/wicksellian response, not about expected interest rates (we see and expect it only), drive the whole result. I Continuous time: needs partial adjustment rule di t dt = θ [φ (π t πt ) (i t it )] if i t > max fθ [φ (π t πt ) (i t it ; )], g if i t =

18 Taylor rule and the standard solution 1 Inflation across equilibria with a Taylor rule I Not: if π T >, Fed tightens too much, lowers in ation too fast I Yes: if π T > people expect the Fed to explode the economy. Or those equilibria are not ruled out.

19 A Taylor rule could select the glidepath too 1 Inflation across equilibria with a Taylor rule I Equilibrium selection policy to choose πt possible. (glidepath) is just as

20 Precommitment and Dr. Stragelove I Why do people believe the Fed would choose πt =, not a benign glidepath? 1. Werning: it = r, π T = from lack of precommitment. 2. Me: But i t it = φ π (π t πt ) takes a huge (Dr. Strangelove, subgame-imperfect) precommitment. Fed cannot precommit to πt > but can precommit to blow up the economy for π t 6= πt? 3. Conclusion: lack of precommitment makes no sense once we recognize equilibrium selection policy. I Old points: 1. Why rule out non-local equilibria (JPE 211)? 2. Does the Fed do this / do people the Fed does this? 2.1 We never observe π 6= π so cannot learn φ π. 2.2 The Fed loudly says it stabilizes, creating kλk <, not destabilizes creating kλk >. 2.3 The Fed uses the word glidepath when ghting in ation. 2.4 Is there really any such thing as equilibrium selection policy? (No equilibrium selection opeds!)

21 Which equilibrium II/Save the model I Bottom line: 1. NK diagnosis and policy are very sensitive to equilibrium selection. 2. There are many plausible equilibria that do not deliver big recession/de ation or policy magic. I Which equilibrium? 1. Fiscal: Jump to negative in ation means a huge transfer to bondholders. (No-jump equilibrium has zero scal implications.) In ation target is a scal promise, constraint on Treasury. 2. Philosophical? No backward explosions, smooth frictionless limit? 3. Data: which equilibrium selection rule accounts for stagnation? Was there policy magic in 193, 195, 1975? 4. Data: Measure equilibrium selection from time - response π? I Goal: Save the NK model (forward looking, microfounded) by solving multiple equilibrium problem, choosing a sensible one (frictionless limits). 1. Builds nominal distortions on top of real models. 2. Gets rid of the policy magic. Alas, if you like magic.

22 Solution with price stickiness d xt dt π t 1 = κ ρ xt π t irt + I t > T (ir t = ) κxt π t λ p λ = m 1 1 e λ m (t e λp (t T ) z T T ) w T ; λ m < λ p > w T = (no quarrel today). Leaves z T = π T, multiple stable equilibria e λm (t T ) π T, index by π T I t < T : choose z T,w T to paste at π T. κxt π t = ir ρ 1 ir e λ m (t T ) e λp (t T ) + π T λ p 1 e λm (t T ). I Both e λm (t T ) and e λp (t T ) terms are potentially active. e λm (t T ) explode going back in time. fπ T g adds e λm (t T ) terms.

23 Taylor rule and the standard solution 1 Output gap across equilibria with a Taylor rule

24 1 Interest rate across equilibria with a Taylor rule

25 A Taylor rule could select the glidepath too 1 Output gap across equilibria with a Taylor rule