Optimal Inflation Stabilization in a Medium-Scale Macroeconomic Model

Transcription

1 Optimal Inflation Stabilization in a Medium-Scale Macroeconomic Model Stephanie Schmitt-Grohé Martín Uribe Duke University 1

2 Objective of the Paper: Within a mediumscale estimated model of the macroeconomy 1. characterize the optimal inflation target 2. characterize optimal monetary stabilization policy 3. characterize implementation of optimal monetary policy 2

3 A medium-scale macroeconomic model (Altig et al., 25, with minor differences) Nominal Frictions: 1. Sticky product prices (Calvo-Yun without indexation) 2. Sticky nominal wages (Calvo-Yun with indexation to lagged price inflation and long-run growth) 3. Cash-in-advance constraint on wages m f t νw th d t 4. Money demand by households Transaction costs: c t [1 + l(c t /m h t )] 3

4 Real Rigidities: 1. Monopolistically competitive product markets: y it = ( Pit P t ) η y t, 2. Monopolistically competitive labor markets: h j t = W j t W t η h d t 3. Habit persistence in consumption E t= β t U(c j t bcj t 1,hj t ) 4. Investment adjustment costs k t+1 =(1 δ)k t + i t [1 S 5. Variable capacity utilization ( it i t 1 )] +Υ 1 t [i t + a(u t )k t ]+...

5 Government Policy Objectives and Instruments 1. Ramsey optimal stabilization policy 2. Nominal interest rate implements the monetary policy 3. Lump-taxes balance the budget

6 Complete Set of Equilibrium Conditions k t+1 =(1 δ)k t + i t [1 S ( it i t 1 )] U c (t) bβe t U c (t +1)=λ t [1 + l(v t )+v t l (v t )] q t = βe t λ t+1 λ t [ [ ( ) Υ 1 it t λ t = λ t q t 1 S i t 1 r k t+1 u t+1 a(u t+1) Υ t+1 + q t+1 (1 δ) +βe t λ t+1 q t+1 ( it+1 i t v 2 t l (v t )=1 βe t λ t+1 λ t π t+1 r k t =Υ 1 t a (u t ) ( ) ( )] it S it i t 1 i t 1 ) 2 ( ) S it+1 i t ] f 1 t = ( η 1 η ) + αβe t ( ( ) η wt w t λ t h d t w t πt+1 (µ z π t ) χ ) η 1 ( wt+1 w t ) η 1 f 1 t+1, 4

7 f 2 t ( ) η ( wt = U ht h d πt+1 t + αβe t w t (µ z π ) χ t ) η ( wt+1 w t ) η f 2 t+1 f 1 t = f 2 t λ t = βr t E t λ t+1 π t+1 y t = c t [1 + l(v t )] + g t +Υ 1 t [i t + a(u t )k t ] x 1 t = y tmc t λ p 1+η +αβe t+1 t λ t t x 2 t = y t p η t +αβe t λ t+1 λ t ) 1+η ( χ ( pt+1 πt p t π t+1 ) η ( χ ( pt+1 πt p t π t+1 ) η x 1 t+1 ) 1 η x 2 t+1 ηx 1 t =(η 1)x2 t 1=απt η 1 π χ(1 η) t 1 +(1 α) p 1 η t F (u t k t,z t h d t ) ψz t = s t y t s t =(1 α) p η t + α π η t π χ s t 1 t 1

8 mc t z t F 2 (u t k t,z t h d t )=w t [ 1+ν R t 1 R t ] mc t F 1 (u t k t,z t h d t )=rk t s t =(1 α) ( wt w t ) η + α h t = s t h d t ( ) η ( wt 1 w t π t (µ z π t 1 ) χ ) η s t 1 w 1 η t =(1 α) w 1 η t + αw 1 η t 1 ( (µz π t 1 ) χ π t ) 1 η

9 Long-run Policy Tradeoff Price stickiness distortion calls for price stability: inflation = % Money demand distortion calls for Friedman rule: Nominal interest rate = % Wage stickiness distortion plays no role because wages are indexed 5

10 Selected Structural Parameters Parameter Value Description α.8 Fraction of firms with nonreoptimized price α.69 Fraction of labor markets with nonreoptimized wag χ Degree of price indexation χ 1 Degree of wage indexation ν.6 Fraction of wage bill subject to a CIA constraint β 1.3 1/4 Subjective discount factor (quarterly) µ z /4 Quarterly growth rate of output θ.36 Share of capital in value added δ.25 Depreciation rate (quarterly) η 6 Price-elasticity of demand for a specific good variet η 21 Wage-elasticity of demand for a specific labor varie b.69 Degree of habit persistence 6

11 Degree of Price Stickiness and the Optimal Rate of Inflation.5 ACEL CEE π α Macro evidence:.5 α.85 Micro evidence: α.3 7

12 Optimal Distortionary Taxation, Price Stickiness, and the Optimal Rate of Inflation.5 CEE ACEL ACEL 1 π CEE α Lump-Sum Taxes -o-o- Optimal Distortionary Taxes When lump-sum taxes are unavailable, and instead the government must set distortionary taxes optimally, price stability emerges as a robust Ramsey outcome. 8

13 Degree of Price Indexation and the Optimal Rate of Inflation π CEE&ACEL χ 9

14 Money Demand Parameters and the Optimal Rate of Inflation π π φ φ 2 Money demand by HH: m h t = c t φ 1 φ 2 +(1 R 1 t ) 1

15 Sources of Uncertainty 1. Permanent investment-specific technology shocks ˆµ Υ,t = ρ µυˆµ Υ,t 1 + ɛ µυ,t 2. Permanent neutral technology shocks ˆµ z,t = ρ µzˆµ z,t 1 + ɛ µz,t 3. Temporary government purchases shocks ln (ḡt ḡ ) = ρḡ ln ) (ḡt 1 + ɛḡ,t ḡ 11

16 Fraction of variance explained by exogenous disturbances in the data Variable µ Υ,t µ z,t Output Consumption Investment.15.9 Interest Rate.16.4 Inflation Hours Source: ACEL (25) 12

17 Fraction of variance explained by each of the three exogenous disturbances in the Ramsey equilibrium Variable µ Υ,t µ z,t g t ln y t /y t ln c t /c t ln I t /I t ln R t ln π t ln πt W ln h d t

18 Ramsey Optimal Stabilization Policy Variable Standard Deviation (in percentage points per year) Baseline High α Nominal Interest Rate.4.4 Price Inflation.1.4 Wage Inflation Output Growth.8.8 Consumption Growth.5.5 Investment Growth

19 Ramsey Response To A Neutral Productivity Shock Output Consumption Investment 1.5 Hours Real wage 2.5 Capacity Utilization Nominal Interest Rate.2 Inflation Note: The size of the initial innovation to the neutral technology shock is one percent, ln(µ z, /µ z ) = 1%. The 15

20 nominal interest rate and the inflation rate are expressed in levels in percent per year. Output, wages, investment, and consumption are expressed in cumulative growth rates in percent. Hours and capacity utilization are expressed in percentage deviations from their respective steady-state values.

21 Implementing the Ramsey equilibrium with an interest rate rule ˆR t = α π ˆπ t + α W ˆπ W t + α y lny t + α R ˆR t 1 Pick the 4 policy coefficients, (α π,α W,α y,α R ), so as to maximize: E t= β t U(c t bc t 1,h t ) Result: α π α W α y α R

22 Welfare Cost Measure E t= β t U(c a t bc a t 1),h a t )=E t= β t U((1 λ c )(c r t bc r t 1),h r t ) 17

23 The Optimal Operational Rule Baseline Taylor Rule Policy Coefficients α π α π W 1.6 α y α R.4 Welfare Costs in percent of c t.1.14 in 26 dollars $.23 $41.81 The welfare cost of the optimal rule is almost zero. The optimal response to output is zero. Welfare gains from interest rate smoothing are negligible. 18

24 The Wage Phillips Curve ACEL model: ˆπ W t ˆπ t 1 = β(e tˆπ W t+1 ˆπ t) γˆµ W t This paper: ˆπ W t ˆπ t 1 = β(e tˆπ W t+1 ˆπ t) (1 + η)γˆµ W t γ = ( 1 )( (1 α)(1 αβ) 1+ η α ) 19

25 Higher wage stickiness: α =.9 Optimal Rule coefficients: α π α W α y α R Welfare costs in percent of c t :.8 in 26 dollars: $2.5 2

26 Ramsey And Optimized Responses To An Investment-Specific Productivity Shock C t F 2 t h d t I t K t Λ t Y t 5 x 1 3 π t.15 Q t R t 4 x 1 4 s t 2 x 1 15 stilde t u t W t X 2 t Ramsey Policy Optimized Rule 21

27 Ramsey And Optimized Responses To A Neutral Productivity Shock C t F 2 t h d t I t K t Λ t Y t π t Q t R t 15 x 1 4 s t 1 x 1 15 stilde t u t W t X 2 t Ramsey Policy Optimized Rule 22

28 Ramsey And Optimized Responses To A Government Purchases Shock C t F 2 t h d t I t K t Λ t Y t 1 x 1 3 π t.2 Q t R t 2 x 1 4 s t x 1 14 stilde t u t W t X 2 t Ramsey Policy Optimized Rule 23

29 Conclusions This paper characterizes optimal monetary policy in a rich DSGE that mimics well U.S. postwar business cycles. The optimal rate of inflation is negative. Thus, it is puzzling that inflation targets in inflation targeting countries are positive. The zero bound on nominal interest rates does not justify positive inflation targets. Under the optimal policy the variance of inflation is near zero, whereas the variance of wage inflation is about 1 percentage point. The Ramsey equilibrium is well approximated by a simple interest rate feedback rule that is active, moderately inertial, and does not respond to output growth. 24