Optimal Simple And Implementable Monetary and Fiscal Rules

Transcription

1 Optimal Simple And Implementable Monetary and Fiscal Rules Stephanie Schmitt-Grohé Martín Uribe Duke University September

2 Welfare-Based Policy Evaluation: Related Literature (ex: Rotemberg and Woodford, 1999) Two-equation Neo-Keynesian framework Steady state is efficient Subsidies to factor inputs No monetary frictions No fiscal policy No capital accumulation 2

3 This paper: Policy Evaluation in a More Realistic Environment Non-stochastic steady state is not efficient No subsidies to undo monopolistic distortions Demand for money Distortionary taxation Fiscal policy Capital accumulation 3

4 Basic Theoretical Ingredients Monopolistic competition in product markets Sticky prices à la Calvo (JME,1983) and Yun (JME, 1996) Money demand motivated by a cash-in-advance constraint on Wage payments by firms Consumption expenditures Capital accumulation Government finances a stochastic stream of public consumption by: Levying either income or lump-sum taxes Printing money Issuing nominal non-state-contingent debt 4

5 Requirements of the Policy Rule Optimality: Policy must maximize consumers welfare Simplicity: Policy takes the form of rules involving a few, readily available macroeconomic variables (e.g., output, inflation, interest rates) Implementability: Policy must guarantee local uniqueness of RE equilibrium Policy must respect the zero lower bound on nominal rates 5

6 Main Findings 1. Optimal policy features an active monetary stance. (However, the precise degree of responsiveness of interest rates to inflation is immaterial.) 2. Optimal monetary policy features a muted response to output. (And not responding to output is critical.) 3. Optimal fiscal policy is passive. 4. The optimized simple rules attain (almost) the same welfare as the Ramsey policy. 6

7 The Household The Model Preferences: E 0 t=0 β t U(c t,h t ) Cash-in-advance constraint on consumption: Budget constraint: m h t vh c t r t,t+1 x t+1 E t +m h t +c t +i t +τt L = x t + mh t 1 +(1 τt D )[w t h t +u t k t ]+ φ t P t P t π t Evolution of capital: k t+1 =(1 δ)k t + i t 7

8 Firms Prices are sticky as in Yun (JME, 1996). Wage payments are subject to a cash-in-advance constraint: m f it νf w t h it Firm must satisfy demand at the posted price: z t F (k it,h it ) χ ( Pit P t ) η (c t + g t + i t ) Firms have monopoly power. Firms maximize the present discounted value of profits: Real profits: E t s=t r t,s P s φ is. φ it ( Pit P t ) 1 η (c t + g t + i t ) u t k it w t h it (1 R 1 t )m f it 8

9 Firm s Optimality Conditions Labor demand: mc it z t F h (k it,h it )=w t [ 1+ν f R ] t 1 R t Demand for capital services: mc it z t F k (k it,h it )=u t Optimal Pricing Decision: E t s=t r t,s P s α s ( P it P s ) η y s [( η 1 η ) ] P it mc is P s =0 9

10 Sources of Business Cycles Productivity shocks, z t Government spending shocks, g t 10

11 Monetary Policy Level Rule: ln ( ) Rt R = α R ln ( ) Rt 1 R i = 0, contemporaneous rule i = 1, backward-looking rule i = 1, forward-looking rule + α π E t ln ( ) πt i π + α y E t ln ( ) yt i y. Difference Rule: ln ( Rt R t 1 ) = α R ln ( ) Rt 1 R t 2 ( ) πt 1 + α π π + α y ln ( ) yt 1 y t 2. 11

12 Methodology For Policy Evaluation Step 1 Compute Ramsey steady state and Ramsey dynamics Step 2 Pick monetary and fiscal policy rule parameters α π,α y, α R,andγ in [0, 3] so as to maximize: { t=0 Unconditional welfare: E β t } U(c t,h t ) (using second-order approximation package of Schmitt-Grohé and Uribe, 2004) Step 3 Compute (second-order accurate) welfare cost of policy rule relative to Ramsey allocation. 12

13 Welfare Cost Measure, λ E 0 t=0 β t U(c t,h t )=E 0 t=0 β t U(c r t (1 λ),hr t ) = allocation associated with interest rate feedback rule r = Ramsey allocation 13

14 Economy I: A Cashless Sticky-Price Economy ν f = ν h =0 ln ( ) R t R = αr ln ( ) R t 1 R + απ ln ( ) π t π + αy ln ( ) y t y Welf. Cost σ π σ R α π α y α R %ofc t %p.a. %p.a. Ramsey Policy Optimized Rule Taylor Rule Simple Taylor Rule Inflation Targeting

15 Economy I: Implementability and Welfare 3 (α Y =0 ) Implementable Rule Welfare Cost<0.05% α R α π = Implementable Rule. = Welfare cost less than 0.05% of consumption. 15

16 Economy I: Importance of Not Responding to Output welfare cost (λ u 100) α y 16

17 The Cashless Economy Backward- and Forward-Looking Rules Welfare Cost α π α y α R %ofc t σ π σ R Contemporaneous Backward Looking Forward Looking

18 Economy I: Implementability and Welfare with a Backward-Looking Rule 3 (α Y =0 ) Implementable Rule Welfare Cost<0.05% α R α π = Implementable Rule. = Welfare cost less than 0.05% of consumption. 18

19 Economy II: A Monetary Sticky-Price Economy m f t =0.63w th t m h t =0.35c t 19

20 Long-run Policy Tradeoffs Price stickiness distortion calls for price stability: Inflation = 0% Money demand distortion calls for Friedman rule: Nominal interest rate = 0 % Tradeoff resolved in favor of price stability π = 0.55 % p.a. 20

21 A Monetary Sticky-Price Economy ( ) ( ) ( ) ln Rt Rt 1 R = α R ln R + α π ln πt π + α y ln ( ) yt y Welfare Cost σ π σ R α π α y α R %ofc t %p.a. %p.a. Ramsey Policy Optimized Rule Taylor Rule Simple Taylor Rule Inflation Targeting

22 Economy II: Implementability and Welfare 3 (α Y =0 ) Implementable Rule Welfare Cost<0.05% α R α π = Implementable Rule = Welfare cost less than 0.05% of consumption. 22

23 Economy II: Importance of Not Responding to Output welfare cost (λ u 100) α y 23

24 Difference Rule ln ( Rt R t 1 ) =0.77 ln ( Rt 1 R t 2 ) ( πt 1 ) ln π ( yt 1 y t 2 ). Welfare cost: σ π =0.06 σ R =

25 Introducing Fiscal Policy The Government budget constraint: M t + B t = R t 1 B t 1 + M t 1 + P t (g t τ t ) Let l t 1 (M t 1 + R t 1 B t 1 )/P t 1 The Fiscal Feedback Rule: τ t = τ + γ(l t 1 l ). l t =(R t /π t )(1 π t γ)l t 1 + R t (γl τ )+R t g t m t (R t 1) Fiscal policy is passive, if γ (0, 2/π ) 25

26 Economy III: A Monetary Sticky-Price Model with a Fiscal Feedback Rule τ t = τ L t Optimized Fiscal Rule: any γ (0, 2) Optimized Interest Rate Rule: ln ( ) ( ) R t R =3 ln πt π Welfare cost =

27 Economy III: Implementability and Welfare 3 (α Y =0 ) Welfare Cost< 0.05% Implementable Policy γ α π = Implementable Rule = Welfare cost less than 0.05% of consumption 28

28 Economy IV: A Monetary Sticky-Price Economy with Income Taxation Long-run tradeoffs: Money demand: R = 1 Sticky Prices: π = 1 τ t = τ D t y t Distortionary Income Taxation: R>1 (seignorage income) Cash-in-advance on labor (but not capital): R>1 Resolution of those tradeoffs τ D =15.7% π = 0.04% p.a. 29

29 Optimal Distortionary Taxation, Price Stickiness, and the Optimal Rate of Inflation π, Percent per year α 30

30 Optimal Rule-Based Stabilization Policy α π =3 α y =0 γ =0.2 welfare cost = σ π =0.16 σ R =0.5 σ τ =0.7 Optimal monetary policy is active. Optimal fiscal policy is passive. Welfare cost relative to Ramsey virtually nil. 31

31 Economy IV: Implementability and Welfare 3 (α Y =0 ) Welfare Cost < 0.05% Implementable Policy γ α π = Implementable Rule = Welfare cost less than 0.05% of consumption 32

32 Economy IV: Importance of Not Responding to Output welfare cost (λ c 100) α y 33

33 Conclusions 1. Optimal monetary policy is active (α π > 1). But the precise magnitude of α π plays a minor role for welfare. 2. Interest-rate feedback rules that respond to output can be significantly harmful. 3. The optimal fiscal-policy stance is passive. 4. The optimized simple monetary and fiscal rules attain virtually the same level of welfare as the Ramsey optimal policy. 5. The welfare gains associated with interest rate smoothing are negligible. 6. An interest-rate feedback rule that responds only to lagged information performs as well as one that responds to contemporaneous information. 34

34 EXTRAS 35

35 Deep Structural Parameters Value Description σ 2 Preference parameter, U(c, h) ={[c(1 h) γ ] 1 σ 1}/(1 σ) θ 0.3 Cost Share of capital, F (k, h) =k θ h 1 θ β /4 Quarterly subjective discount rate η 5 Price elasticity of demand ḡ Steady-state level of government purchases δ 1.1 (1/4) 1 Quarterly depreciation rate ν f Fraction of wage payments held in money ν h Fraction of consumption held in money α 0.8 Share of firms that cannot change their price each period γ Preference Parameter χ Fixed cost parameter ρ g 0.87 Serial correlation of government spending σ ɛg Standard Deviation of innovation to government purchases ρ z Serial correlation of productivity shock σ ɛz Standard Deviation of innovation to productivity shock 36

36 Complete Set of Equilibrium Conditions k t+1 =(1 δ)k t + i t U c (c t,h t )=λ t [1 + ν h (1 R 1 t )] U h(c t,h t ) U c (c t,h t ) = w tr t (1 τt D) R t + ν h (R t 1) [ ] λ t = βe t λ t+1 (1 τ D t+1 )u t+1 +(1 δ)+δτt+1 D λ t+1 λ t = βr t E t π t+1 [ mc t z t F h (k t,h t )=w t 1+ν f R ] t 1 R t mc t z t F k (k t,h t )=u t m t = ν h c t + ν f w t h t 1=απ 1+η t +(1 α) p 1 η t ( ) 1 η x 1 t = p 1 η λ t+1 t (c t + i t + g t )mc t + αβe t π η pt t+1 x 1 λ t p t+1, t+1 37

37 x 2 t = p η λ t+1 t (c t + i t + g t )+αβe t λ t η η 1 x1 t = x 2 t. π η 1 t+1 y t = 1 s t [z t F (k t,h t ) χ] ( pt p t+1 ) η x 2 t+1 y t = c t + i t + g t s t =(1 α) p η t + απ η t s t 1, l t =(R t /π t )l t 1 + R t (g t τ t ) m t (R t 1) τ t = τ L t + τ D t y t (τ t τ )=γ(l t 1 l ) ln(r t /R )=α R ln(r t 1 /R )+α π E t ln(π t i /π )+α y E t ln(y t i /y) i { 1, 0, 1} either τ L t =0orτ D t =0

38 The Welfare Measure: Conditional expectation of lifetime utility welfare = V t E t j=0 β j U(c r t+j,hr t+j ). Computation: Write V t as: V t = g(x t,σ) Second-order approximation around (x, 0) V t = g(x, 0) + g x (x, 0)(x t x)+g σ (x, 0)(σ 0) (x t x) g xx (x, 0)(x t x)+ g xσ (x, 0)(x t x)(σ 0) g σσ(σ 0) 2 + o 3 Assume that at time t all state variables take their steady-state values: x t = x. 38

39 Grid Search: Given i, search over 3 policy parameters, α π, α y and α R or γ, Grid = [0, 3], step points. need to approximate V t 31 3 =29, 791 times for a given value of i 39

40 The Welfare Cost Measure Let λ denote the welfare cost of adopting policy regime a instead of the reference policy regime r. Then λ is defined as V a t = E 0 j=0 β j U((1 λ)c r t+j,hr t+j ). For the particular functional form for the period utility function assumed λ = 1 ( (1 σ)v a t (1 σ)vt r +(1 β) 1 +(1 β) 1 ) 1/(1 σ) Up to second-order accuracy: λ V σ r ɛ σ ɛ (x, 0) Vσ a ɛ σ ɛ (x, 0) (1 σ)v r (x, 0) + (1 β) 1 σ2 ɛ 2 40