How stable are monetary policy rules: estimating the time-varying coefficients in monetary policy reaction function for the US

doi:10.1016/j.csda.2004.05.028

Computational Statistics & Data Analysis

Volume 49, Issue 2, 30 April 2005, Pages 575-590

https://doi.org/10.1016/j.csda.2004.05.028 Get rights and content

Abstract

The relation among the federal funds rate and the Federal Reserve's expectations about future values of certain policy relevant variables is considered. The coefficients of this relation are biased (i) when relevant explanatory variables are omitted, (ii) when the included explanatory variables are measured with error, (iii) when the functional form of the relation is misspecified. These biases present obstacles to verifying the conditions for monetary policies to be effective. It is explained how auxiliary variables, called concomitants, can be used to remove some of these biases without assuming that the “true” functional form of the relation is known. An analysis of the US quarterly data on the variables in a reaction function for 1960Q1–2000Q4 is given using our methods with a description of a numerical algorithm for enacting our methods.

Introduction

Considerable recent research on monetary policy has focused attention on examining the extent to which the conduct of monetary policy can be characterized by a simple relationship between a policy instrument and a small set of variables. This work was largely inspired by Taylor (1993), who suggested a rule whereby the Federal Reserve (Fed) sets its target for the federal funds rate in response to deviations of actual inflation from target inflation and the gap between actual and potential output.

Such a rule is usually represented by an equation of the form: $r_{t} = \bar{r} + α_{1} (π_{t} - π^{*}) + α_{2} (y_{t} - y_{t}^{*}) + ε_{t},$ where $r_{t}$ is the policy-determined interest rate, $\bar{r}$ the long-term nominal interest rate, $π$ the inflation rate, $π^{*}$ the target inflation rate, y the real output, $y^{*}$ the potential output, and $ε$ the disturbance term. This approach assumes that the relationship between the interest rate and its determinants is linear. There have been attempts to estimate changes in the coefficients of (1) in the periods before and after Paul Volcker was Chairman of the Fed (see, Clarida et al., 1998, Taylor, 1999), but this work has remained in the context of fixed-coefficient linear model.

Let us assume that the “true” version of Eq. (1) exists. The difficulty is that we do not know the functional form of this version and do not have data on some of its explanatory variables. Also, the data that are available on some of its variables contain errors. Consequently, the problems of omitted variables, measurement errors, and unknown functional form are associated with (1). The linearity assumption about (1) is incorrect because the magnitude, direction, and timing of change the Fed wants to make in the interest rate it controls in response to a given gap between actual and expected inflation, and to the gap between actual and potential output, depend on which one of the five broad (and illustrative) categories of policies: “strongly expansionary,” “mildly expansionary,” “neutral,” “mildly contractionary,” and “strongly contractionary,” it wants to follow in light of its expectations about future economic conditions. There can be a host of factors other than the explanatory variables in (1) that affect the Fed's decision to raise or lower the interest rate and that are unlikely to be fully incorporated in the variables in (1). Thus, the estimation of (1) is subject to biases arising from omitted variables. Finally, accurate data on inflation and output may not be available and errors are inevitably present in the measures used for expected inflation and potential output. Therefore, there are ample reasons to believe that serious errors-in-variables problems are present with (1). The biasing effects of omitting relevant explanatory variables, mismeasuring some or all of the included explanatory variables and of misspecifying the “true” functional forms are a pervasive problem in econometrics. The purpose of this paper is to correct the estimates of the coefficients of (1) for such biases without making strong functional-form assumptions.

Section 2 modifies Eq. (1) in such a way that the modified equation corresponds to the “true” equation. The latter equation is used to state both a necessary and sufficient and a sufficient condition for a monetary policy to be a good policy (defined below). The section also provides the real-world interpretations of the coefficients of the modified equation. Section 3 calculates bias-corrected estimates of the coefficients of the modified equation. Section 4 concludes. Computational details are given in the appendix to the paper.

Section snippets

A model of the Fed's reaction function

In this section, we show that under very general conditions, the following flexible version of Eq. (1) adequately represents the monetary-policy reaction function for the US Fed: $r_{t} = γ_{0 t} + γ_{1 t} x_{1 t} + γ_{2 t} x_{2 t} + γ_{3 t} x_{3 t},$ where $r_{t}$ is the federal funds rate in percent, $x_{1 t}$ the inflation in percent equal to $\log (P_{t} / P_{t - 4}) \times 100$ , $P_{t}$ the GDP implicit price deflator for the US, $x_{2 t}$ the output gap equal to (deviation of the logarithm of US GDP from the least-squares estimates of a quadratic trend) $\times 100$ , $x_{3 t}$ the exchange

Monetary policy rules in the United States during 1960Q3–2000Q4

Before proceeding to describe the estimates of the time-varying coefficients of (2), it is first useful to estimate (2) using the standard fixed-coefficient assumption. The least squares estimates of these coefficients are given in Table 1 for the entire sample period, 1960Q3–2000Q4, as well as for the two sub-periods, 1960Q3–1979Q2 and 1979Q3–2000Q4, described above. It is interesting to note that the coefficient on inflation more than doubles between the two sub-periods, which is consistent

Conclusions

The biasing effects of measurement errors, omitted variables, and misspecifications of “true” functional forms are a pervasive problem in econometrics. A necessary and sufficient and a sufficient condition under which a monetary-policy rule is a good policy can only be stated in terms of the bias-free effects on the federal funds rate of all the determinants of this rate including the Fed's expectations about future inflation, the future gap between actual and potential output, and the future

Acknowledgements

The authors received several helpful comments and suggestions from Peter Clark and Peter von zur Muehlen. Much of the work presented in this paper was done when the first author was visiting scholar in the Research Department, the International Monetary Fund, during June 2001. Very special thanks are due to David Belsley, who carefully read the complete paper and made a number of suggestions to improve the presentation.

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How stable are monetary policy rules: estimating the time-varying coefficients in monetary policy reaction function for the US☆