Eco 00, part 3, Fall 004 00L5.tex Lars Svensson /6/04 Liquidity traps, the zero lower bound for interest rates, and deflation The zero lower bound for interest rates (ZLB) A forward-looking aggregate-demand relation The neutral/natural (Wicksellian) (real) interest rate Simple forward-looking price-setting behavior A liquidity trap (LT) Optimal policy w/o and w/ a LT Credibility problems with the optimal policy w/ a LT Open-economy issues: Uncovered interest parity (UIP) and expected medium-run Purchasing Power Parity (PPP) TheexchangerateandtheFoolproofWaytoescapefromaliquiditytrap(FPW) 0 Copyright 004 by Lars E.O. Svensson. This document may be reproduced for educational and research purposes, as long as the copies contain this notice and are retained for personal use or distributed free. Thezerolowerboundforinterestrates(ZLB) i t Money demand Money supply i t 0 M S t /P t M S t /P t M t /P t Given money-demand curve, CB controls i t by setting money supply Mt s. Increasing Mt s lowers i t. But i t can only be lowered to 0. Increasing Mt s beyond that point has no effect on i t (excess liquidity). Zero lower bound for (nominal interest rates) (ZLB): i t 0 ()
A forward-looking aggregate-demand relation Intertemporal consumption choice, representative consumer Two periods, and (each period may be a few years long) C t consumption in period t, t =, W wealth in period, r real interest rate between period and W C wealth in period after consumption in period, invested in period, and consumed with interest in period. Intertemporal budget constraint C = (+r )(W C ) = (+r )W ( + r )C Maximize utility subject to this budget constraint max (C,C ) U(C,C ) 3 C Slope =+ r C Slope = C C C C Slope = C < C Slope =+ r <+ r C U(C,C ) = U > U U(C,C ) = U 0 C C C 4
Relation C,C,r : C /C increasing in r C increasing in C, decreasing in r Simplification C = C ar Consider the economy in period, period expected (a>0) Y t,outputinperiodt, determined by (consumption) demand Y t = C t (t =, ) Y e, output in period expected in period Ȳ e > 0, potential output in period expected in period (exogenous) Assumption: Future output expected to equal future potential output (no LT in future) Aggregate-demand relation in period Y e = Ȳ e. Y = Ȳ e ar () 5 The neutral/natural (Wicksellian) (real) interest rate Neutral/natural (Wicksellian) real interest rate in period, r : The real interest rate at which Y equals potential output in period, Ȳ > 0 (exogenous) r a (Ȳ e Ȳ) r increasing in expected potential output growth Specify output gap. Subtract (3) from () Ȳ Ȳ e a r (3) Y Ȳ = a(r r ) Define output gap Aggregate-demand relation: r r (real) interest rate gap y Y Ȳ Ȳ σ ā Y > 0 y = σ(r r ) (4) 6
π inflation in period (between period and ) P t price level in period t (t =, ) π e inflation in period expected in period P e price level in period expected in period Specify real and nominal interest rate: Combine (4), (5) and ZLB π P P P π e P e P P r i π e (5) y = σ[i π e r ] = σi + σ(π e + r ) σ(π e + r ) For given π e, ZLB implies upper bound for y. Low r (because of low Ȳ e Ȳ) implies stricter upper bound. 7 Simple forward-looking price-setting behavior Price setting (simplification): n identical firms, indexed j =,..., n, sets individual price for period, P j, one period in advance (hence in period ) according to expectations P e of aggregate price level in period : P j = P e (j =,..., n) Actual price level in period : Hence, P n nx j= P j, P = P e Price level in period determined by expectations in period Inflation in period determined by expectations in period π = π e Price level in period, P, given in period (determined by expectations in period 0) 8
Optimal policy w/o liquidity trap Loss function for monetary policy in period (δ =) Ideal equilibrium Possible if L =(π π ) + λy y = 0 π = π r = r i = r + π e 0 = π π e r + π 0 r π 9 A liquidity trap (LT) Suppose that inflation expectations equal inflation target (good credibility), but suppose low r, such that π e = π, r + π < 0 r < π Liquidity trap (LT): r higher than r (recession) when π e = π, even though i =0. Happens when r too low. r = i π e =0 π > r Then, y = σ(r r ) < 0 0
Optimal policy w/ liquidity trap Best tradeoff between π and y (when CB can choose π = π e freely): Set i =0 y = σ(π + r ) (6) Temporarily treat π as control variable, to determine optimal policy 0 = L π = (π π )+λy y π = (π π )+λσy Targeting rule in LT: π π = λσy (7) Optimal policy (use (6) in (7)) π π = λσ[σ(π + r )] π π = λσ [(π π )+( r + π )] ( + λσ )(π π ) = λσ ( r + π ) π π λσ +λσ ( r + π ) y = λσ (π π ) σ = +λσ ( r + π ) Optimal inflation π,outputgapỹ, interest rate ĩ : π π λσ +λσ ( r + π ) > 0, σ ỹ +λσ ( r + π ) < 0, ĩ = 0. Overshoot inflation target in period, reduce recession in period
π y = σi + σ( π + r ) π * ( y, π ) σi 0 σ r y y = σπ ( + r) 3 π π * σi = σ( r + π*) 0 σ r y y = σπ ( + r) 4
Targeting rule π * π = λσy π B O π π * y = σπ ( + r) π = πe = π* σr σr < σπ* y = σπ* 0 y B bad equilibrium in LT, π = π e = π, deeper recession, y < ỹ < 0 O optimal equilibrium in LT, π = π >π, y =ỹ < 0 5 Credibility problems Solution to LT: Increase inflation expectations (Krugman 98) How to increase inflation expectations from π e = π to π e = π? (Reverse) credibility problem, not easy, especially for CB with reputation for low inflation (low π ) (Krugman 98) Promise high money supply in period? No liquidity trap expected for period : i e > 0 Then P e M e Problem: No commitment mechanism, no way to commit to high future money supply Cf. Japan, quantitative easing, monetary base up 60%+ since March 00 No indication of inflation expectations (exchange rate depreciation, long interest rates) Private sector obviously expects future money supply to be contracted 6
Open-economy issues Useexchangerate(FoolproofWay,FPW) Assumption (simplification): Uncovered interest rate parity (UIP) +i =(+i ) Se S S exchange rate =Y/$ in period ; S e exchange rate =Y/$ in period, expected in period i home (Japan) interest rate between period and i foreign (US) interest rate between period and Investment strategy : =Y in period, invest at home (Japan), =Y( + i ) in period Investment strategy : =Y in period, exchangeto$/s,investintheus,$( + i )/S in period, expect to exchange to =YS ( e + i )/S. Same expected return, implies UIP 7 Assumption (simplification): Expected medium-run Purchasing Power Parity (PPP) P e = P e S e P e period- price level (CPI or GDP deflator) in Japan (in =Y),expectedinperiod P e period- price level (CPI or GDP deflator) in the US (in $), expected in period (Simplification, disregard covariance terms) Liquidity trap in Japan, i =0 S =(+i )S e =(+i ) P e P e Assume i and P e (US period- interest rate and expected period- price level) independent of Japan S proportional to P e. 8
TheFoolproofWaytoescapefromaliquiditytrap(FPW). Price-level target: Announce temporary price level target P P ( + π ) >P ( + π ) If credible (P e = P ), yen will depreciate in period, S,so But just announcement may not be credible S = S ( + i ) P P e. Currency depreciation and peg: Depreciate and peg yen, so S = S. Best action in period to induce expectations P e 3. Exit strategy: In period, when P reaches P, float yen and switch to flexible inflation targeting 9