Simple and Robust Rules for Monetary Policy

John B. TaylorStanford University

John C. WilliamsFederal Reserve Bank of San Francisco

The opinions expressed are those of the authors and do not necessarily reflect the views of the management of the Federal Reserve Bank of San Francisco or anyone else in the Federal Reserve System.

Outline

• Historical background• Empirical experience• Characteristics of simple rules • Robustness• Optimal control vs. simple rules

Historical Background

• Smith, Ricardo, Fisher, Wicksell, Friedman• Rules proposed in response to crises and

excesses to reduce monetary shocks and mitigate other shocks– Rules versus chaotic monetary policy

• Rules as guideposts for policy– Monetary growth targets– Policy rules

1980s and 1990s:Finding a Few Good Rules

• Stochastic simulations of alternative policy rules in different estimated models – Instrument choice (interest rate, monetary aggregate, exchange rate)– Formal optimization techniques in simple models– Evaluation of representative policy rules across models (Bryant-

Hooper-Mann)

• Long list of models– 1993: Brookings project (Bryant)– 1999: NBER Monetary Policy Rules (Taylor)– Today: Model data base (Wieland)

Experience with Great Moderation

• Many studies showing monetary policy more systematic and responsive during the Great Moderation than before– Policy well described by policy rule (Clarida-Gali-

Gertler, Judd-Rudebusch, Woodford)– Timing suggestive but not definitive (Cecchetti,

Stock and Watson)• Policy rule presriptions regularly discussed at

central banks.

Evaluating Simple and Robust Rules

• Characteristics of optimal simple rules

• Robust Policies

• Simple rules vs. Optimal policies

Central Bank Objective

• Ad hoc quadratic central bank loss:L = E{ (π- π*) 2 + λy2 + ν(i – i*) 2}where E denotes the unconditional expectation, π is the inflation rate, π* is the inflation target, y is the output gap, and i is the nominal short-term interest rate.

• The central bank loss can also be derived as the second-order approximation to household utility

Simple Policy Rules

• Simple (three-parameter) rules:

it = (1-ρ)(πt + r*) + ρ it-1 + α(πt - π*) + βyt

ρ : policy inertia parameter

• This type of rule inherently “leans against the wind” of deviations of objective variables from target values.

Policy Inertia in RE Models

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Inertial RuleLevel rule

Level vs. Inertial Rules in FRB/US Model

σπ

σy

Price Level Targeting (PLT)• Price-level targeting rules:

it = (1-ρ)(πt + r*) + ρ it-1 + α[ln(pt) – ln(pt*)] + βyt

pt* : price level target (deterministic trend)

• PLT rules perform very well in a wide variety of forward-looking models, especially with ZLB, gap mismeasurement, learning (Eggertsson & Woodford, Reifschneider and Williams(2000), Orphanides and Williams (2002, 2008).

• However, effectiveness of PLT depends critically on rational expectations; PLT rules can perform poorly in models with adaptive expectations (Taylor (1999), Levin and Williams (2003), Reifschneider and Roberts 2005, Williams 2006).

PLT vs. IT in RE Models

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Price level

Inflation rate

Policy Frontiers in the FRB/US Model

σπ

Policy rule responds to:λ=0

λ=1/3λ=1 λ=3 λ→∞

σy

Robust Monetary Policy Rules• Robustness: policy performs well across a wide spectrum

of models and environments

• Methodologies: Bayesian, robust control, minimax regret

• McCallum (1988), Taylor (1993), Levin et al (1999, 2003), Levin and Williams (2003), Orphanides and Williams (2002, 2008); Brock, Durlauf, and West (2003, 2007), Tetlow (2006), Brock, Durlauf, Nason, and Rondina (2007)

Types of Uncertainty

• Mismeasurement of data and gaps

• Parameter values

• Model specification• small-, medium-, large-scale• closed vs. open economy• expectations formation (adaptive, rational, learning)• estimation sample

Gap Mismeasurement

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Optimal Response to Lagged Interest Rate (ρ)

Degree of misperceptions

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0.1

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0.3

0.4

0.5

0 1 2 3

Optimal Response to Inflation (α)

Degree of misperceptions

-2

-1.5

-1

-0.5

0

0 1 2 3

Optimal Response to Unemployment Gap (γ)

Degree of misperceptions

-6

-5

-4

-3

-2

-1

0

0 1 2 3

Optimal Response to Change in Unemployment Rate (δ)

Degree of misperceptions

Robustness to Model Uncertainty

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200

0 0.3 0.6 0.9 1.2 1.5

Coefficient on Lagged Interest Rate (ρ)%ΔL

Woodford

Fuhrer

Rudebusch-Svensson

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0 1 2 3

Coefficient on Output Gap (β)%ΔL

Robustness to Bounded Rationality

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Optimal Coefficient on Inflation Rate (α)

Perfect knowledge

Private learning

Private learning +natural rate misperceprions

%ΔL

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150

200

-6 -5 -4 -3 -2 -1 0

Optimal Coefficient on Unemployment Gap (γ)

Perfect knowledge

Private learning

Private learning + natural rate misperceptions

%ΔL

Optimal Control Policy

• Optimal control policy minimizes loss (Woodford 2003, Svensson-Woodford 2003, Giannoni-Woodford 2005)

• Provides very small stabilization benefits over optimized simple rules.

• Can be less robust to uncertainty than robust simple rules and be difficult to communicate.

Simple Rules vs. Optimal Control

• Simple three-parameter rules perform nearly as well as the fully optimal policy in wide variety of empirical macro models , including the Fed’s large-scale FRB/US model (Levin and Williams 2003, Williams 2003, Orphanides and Williams, 2002, 2008) …

Source: Williams, FRBSF Economic Review (2003).

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Inertial Rule

Optimal Control Policy

Simple Rules vs. Optimal Policies in the FRB/US Model

σπ

σy

Simple Rules vs. Optimal Control• … and medium-

scale DSGE models (Schmitt-Grohe and Uribe, 2005, Levin-Onatski-Williams-Williams 2005)

Source: Levin, Onatski, Williams, Williams, NBER Macro Annual (2005).

Robustness of Optimal Control Policy

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0 0.005 0.01 0.015 0.02 0.025 0.03

Robustness to Learning

κ

L

Modified OptimumControl Policy

Optimum ControlPolicy

Inertial RuleDifference Rule

Counterfactual Simulation of Optimal Control Policy

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1965 1970 1975 1980 1985 1990 1995 2000 2005

Percent

OC policy (λ = 16, ν = 1)

Data

Counterfactual Simulation of Robust Policy Rule

1965 1970 1975 1980 1985 1990 1995 2000 2005-2

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Robust policy rule

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