Optimal Simple And Implementable Monetary and Fiscal Rules - PowerPoint PPT Presentation

Optimal Simple And Implementable Monetary and Fiscal Rules Stephanie Schmitt-Groh´ e Mart ´ ın Uribe Duke University September 2007 1

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

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

Basic Theoretical Ingredients • Monopolistic competition in product markets • Sticky prices ` a 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

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

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

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

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

Firm’s Optimality Conditions • Labor demand: � � 1 + ν f R t − 1 mc it z t F h ( k it , h it ) = w t R t • Demand for capital services: mc it z t F k ( k it , h it ) = u t • Optimal Pricing Decision: � ˜ � ˜ � − η ∞ �� � P it η − 1 P it r t,s P s α s � − mc is = 0 E t y s P s η P s s = t 9

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

Monetary Policy • Level Rule: � � � R t � R t − 1 � π t − i y t − i � � � ln = α R ln + α π E t ln + α y E t ln . R ∗ R ∗ π ∗ y i = 0, contemporaneous rule i = 1, backward-looking rule i = − 1, forward-looking rule • Difference Rule: � � � � � � R t R t − 1 � π t − 1 y t − 1 � ln = α R ln + α π + α y ln . π ∗ R t − 1 R t − 2 y t − 2 11

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 , and γ in [0 , 3] so as to maximize: �� ∞ � t =0 β t U ( c t , h t ) Unconditional welfare: E (using second-order approximation package of Schmitt-Groh´ e and Uribe, 2004) Step 3 Compute (second-order accurate) welfare cost of policy rule relative to Ramsey allocation. 12

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

Economy I: A Cashless Sticky-Price Economy ν f = ν h = 0 � R t − 1 � R t � π t � y t � � � � ln = α R ln + α π ln + α y ln R ∗ R ∗ π ∗ y Welf. Cost σ π σ R % of c t % p.a. % p.a. α π α y α R Ramsey Policy – – – 0 0.01 0.27 Optimized Rule 3 0.0 0.8 0.000 0.04 0.29 Taylor Rule 1.5 0.5 – 0.522 3.19 3.08 Simple Taylor Rule 1.5 – – 0.019 0.58 0.87 Inflation Targeting – – – 0.000 0 0.27 14

Economy I: Implementability and Welfare ( α Y =0 ) 3 Implementable Rule Welfare Cost<0.05% 2.5 2 α R 1.5 1 0.5 0 0 0.5 1 1.5 2 2.5 3 α π × = Implementable Rule. ◦ = Welfare cost less than 0.05% of consumption. 15

Economy I: Importance of Not Responding to Output 0.25 0.2 welfare cost ( λ u × 100) 0.15 0.1 0.05 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 α y 16

The Cashless Economy Backward- and Forward-Looking Rules Welfare Cost α π α y α R % of c t σ π σ R Contemporaneous 3 0.0 0.8 0.000 0.04 0.29 Backward Looking 3 0.0 1.7 0.001 0.10 0.23 Forward Looking 3 0.1 1.6 0.003 0.19 0.27 17

Economy I: Implementability and Welfare with a Backward-Looking Rule ( α Y =0 ) 3 Implementable Rule Welfare Cost<0.05% 2.5 2 α R 1.5 1 0.5 0 0 0.5 1 1.5 2 2.5 3 α π × = Implementable Rule. ◦ = Welfare cost less than 0.05% of consumption. 18

Economy II: A Monetary Sticky-Price Economy m f t = 0 . 63 w t h t m h t = 0 . 35 c t 19

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

A Monetary Sticky-Price Economy � R t − 1 � y t � R t � � � π t � � ln = α R ln + α π ln + α y ln R ∗ R ∗ π ∗ y Welfare Cost σ π σ R α π α y α R % of c t % p.a. % p.a. Ramsey Policy – – – 0 0.01 0.27 Optimized Rule 3 0.0 0.8 0.000 0.04 0.29 Taylor Rule 1.5 0.5 – 0.709 3.93 3.76 Simple Taylor Rule 1.5 – – 0.015 0.56 0.85 Inflation Targeting – – – 0.000 0 0.27 21

Economy II: Implementability and Welfare ( α Y =0 ) 3 Implementable Rule Welfare Cost<0.05% 2.5 2 α R 1.5 1 0.5 0 0 0.5 1 1.5 2 2.5 3 α π × = Implementable Rule ◦ = Welfare cost less than 0.05% of consumption. 22

Economy II: Importance of Not Responding to Output 0.12 0.1 0.08 welfare cost ( λ u × 100) 0.06 0.04 0.02 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 α y 23

Difference Rule � R t � � R t − 1 � � y t − 1 � � π t − 1 � ln = 0 . 77 ln + 0 . 75 + 0 . 02 ln . π ∗ R t − 1 R t − 2 y t − 2 Welfare cost: 0.001 σ π = 0 . 06 σ R = 0 . 25 24

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

Economy III: A Monetary Sticky-Price Model with a Fiscal Feedback Rule τ t = τ L t • Optimized Fiscal Rule: any γ ∈ (0 , 2) � R t � π t � � • Optimized Interest Rate Rule: ln = 3 × ln R ∗ π ∗ • Welfare cost = 0.001 27

Economy III: Implementability and Welfare ( α Y =0 ) 3 Welfare Cost< 0.05% Implementable Policy 2.5 2 1.5 γ 1 1 0.5 0 0 0.5 1 1.5 2 2.5 3 α π × = Implementable Rule ◦ = Welfare cost less than 0.05% of consumption 28

Economy IV: A Monetary Sticky-Price Economy with Income Taxation τ t = τ D t y t • Long-run tradeoffs: – Money demand: R = 1 – Sticky Prices: π = 1 – 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

Optimal Distortionary Taxation, Price Stickiness, and the Optimal Rate of Inflation 0 − 0.5 − 1 − 1.5 π , Percent per year − 2 − 2.5 − 3 − 3.5 − 4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 α 30

Optimal Rule-Based Stabilization Policy α π = 3 α y = 0 γ = 0 . 2 welfare cost = 0 . 003 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

Economy IV: Implementability and Welfare ( α Y =0 ) 3 Welfare Cost < 0.05% Implementable Policy 2.5 2 1.5 γ 1 1 0.5 0 0 0.5 1 1.5 2 2.5 3 α π × = Implementable Rule ◦ = Welfare cost less than 0.05% of consumption 32

Economy IV: Importance of Not Responding to Output 0.18 0.16 0.14 0.12 welfare cost ( λ c × 100) 0.1 0.08 0.06 0.04 0.02 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 α y 33