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Article Excerpt
I. INTRODUCTION
"Uncertainty is not just an important feature of the monetary policy landscape; it is the defining characteristic of that landscape" (Greenspan 2003).
Uncertainty is a central issue in monetary policy, as the quote from Alan Greenspan above illustrates. Empirical models, however, rarely take account of this, effectively assuming that policymakers ignore uncertainty. The evident focus of policymakers on uncertainty suggests that this assumption is invalid and therefore that empirical models of monetary policy must account for uncertainty. This article considers the effects of uncertainty about the true state of the economy on monetary policy, estimating a monetary policy rule that allows for this.
Our empirical model combines elements of Svensson's (1997) model of inflation forecast targeting with models drawn from the theoretical literature on optimal monetary policy when there is uncertainty about the true state of the economy, most prominently Svensson and Woodford (2003, 2004) and Swanson (2004). In existing models of monetary policy under certainty, monetary policy affects inflation and the output gap directly, so it is optimal for policymakers to use these variables in forming monetary policy. This is the basis for the Taylor rule (Taylor 1993) model of monetary policy and its subsequent refinements (e.g., Woodford 2003).
Following the literature on monetary policy under uncertainty, our model assumes instead that monetary policy affects the state of the economy, which in turn affects inflation and the output gap. The optimal monetary policy rule is then a certainty equivalent function of the state of the economy. However, the state of the economy is unobserved, so policymakers must infer this from observations of inflation and the output gap. These latter variables therefore act as indicator variables for monetary policy. The optimal predictor of the true state of the economy is a linear function of inflation and the output gap whose parameters are functions of the variances of these variables, which we assume to be time varying.
The resultant empirical model resembles the familiar Taylor rule but where the coefficients on inflation and the output gap are functions of the variances of these variables. An increase in, for example, the variance of inflation reduces the parameter on inflation and increases the parameter on the output gap in the equation for the expected state of the economy. This leads to a smaller weight on inflation and a larger weight on the output gap in the monetary policy rule. Similarly, an increase in the variance of the output gap reduces the weight on the output gap and increases the weight on inflation in the equation for the expected state of the economy, resulting in a lower weight on the output gap and a corresponding larger weight on inflation. As a result, the model makes two main testable predictions. First, policymakers should respond less vigorously to variables that are more uncertain, so the weight on inflation in the policy rule should be lower when inflation is more uncertain and similarly for the output gap (Peersman and Smets 1999; Rudebusch 2001; Smets 2002; Soderstrom 2002; Srour 2003; Swanson 2004; Walsh 2004). Second, uncertainty about one variable may strengthen the response to the other variable, so the weight on the output gap may be larger when inflation is less certain and vice versa (cf. Peersman and Smets 1999; Swanson 2004). (1)
We estimate a system of equations, comprising a monetary policy rule whose parameters are functions of the variances of inflation and the output gap and equations for inflation and the output gap whose error terms have GARCH processes, from which these variances are derived. We use data since 1983 since this is when the Federal Reserve Bank (Fed) switched to using the interest rate as the tool of monetary policy and since continuity in monetary policy objectives has allowed stable policy rules to be estimated over this period (e.g., Judd and Rudebusch 1998). We find that the behavior of monetary policymakers is consistent with the predictions of the theoretical literature. Monetary policy responds less to inflation and the output gap when these variables are more uncertain. We also find that the response to inflation is stronger when the output gap is more uncertain and vice versa. We quantify the impact of uncertainty by constructing a measure of the counterfactual interest rate, which would have been observed if there had been no uncertainty. We find that the impact of uncertainty was most marked in 1983, when uncertainty increased interest rates by up to 140 basis points, in 1990-1991, when uncertainty reduced interest rates by up to 80 basis points, and in 1996-2001, when uncertainty reduced interest rates by up to 70 basis points over 5 yr.
The remainder of the article is structured as follows. Section II explains our methodology. Section III presents our estimates. Section IV summarizes our findings and offers some conclusions.
II. METHODOLOGY
The central bank has the loss function
(1) [E.sub.t] [[infinity].summation over (i=0)] [[delta].sub.i] {[([[pi].sub.t] + i - [[pi].sup.T]).sup.2]/2}
where we assume
(2) [y.sub.t] + 1 = [[beta].sub.x][X.sub.t] + [[beta].sub.y][y.sub.t] + [[eta].sub.t] + 1
(3) [[pi].sub.t] + 1 = [[pi].sub.t] + [[alpha].sub.x][X.sub.t] + [[upsilon].sub.t] + 1
(4) [X.sub.t] + 1 = [phi][X.sub.t] - [[alpha].sub.r]([i.sub.t] - [E.sub.t][[phi].sub.t] + 1) + [[epsilon].sub.t] + 1
y is the output gap, X is the state of the economy, [pi] is the inflation rate, [[pi].sup.T] is the inflation target, i is the nominal interest rate, and [delta] is the discount factor. (2)
Equation (2) is an aggregate demand equation in which the output gap at time t is affected by the state of the economy. [eta] is a demand shock, assumed to be distributed as N(0, [[sigma].sup.2.sub.[eta]t]). The variance of [eta] evolves as a GARCH(1,1) process, since we assume [[sigma].sup.2.sub.[eta]t] = [[lambda].sub.0] + [[lambda].sub.1] [[eta].sup.2.sub.t-1] + [[lambda].sub.2] [[sigma].sup.2.sub.[eta]t-1] and [[lambda].sub.0], [[lambda].sub.1], and [[lambda].sub.2] are parameters. We use the implied variance of [eta] to measure uncertainty about the output gap (for a similar approach, see Grier and Perry 2000). Equation (3) is a Phillips curve in which inflation at time t is affected by inflation and the state of the economy at time (t - 1). [[upsilon].sub.t], is a...
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