The inflation-output variability tradeoff and monetary policy: evidence from a GARCH model.

• Author: Lee, Jim

1. Introduction

   The Phillips curve tradeoff between inflation and output or between inflation and unemployment has long been central to the design and evaluation of monetary policy. While earlier policy debates emphasized inflation-output tradeoffs in levels, the focus today is on the choice between the variability of inflation and the variability of output. The distinction between variability and the level of economic activity is important for the following reason. Despite the general acceptance of no long-run tradeoff between the level of output and the rate of inflation, some economists believe that stabilization policies do have real consequences. For instance, Fuhrer (1997) argues that when an economy is continually buffeted by economic shocks, a short-run level tradeoff may result in a permanent variability tradeoff.

   Owing to the seminal work of Taylor (1979, 1994), it is now standard to express a central bank's objective as an expected-loss function consisting of both inflation and output volatilities with different relative weights. Accordingly, if policymakers aim at lowering inflation to a predetermined target level over time, then inflation will be less variable, while output will inevitably exhibit larger fluctuations. Cecchetti (1998) asserts that this volatility tradeoff frontier--also known as the Taylor curve--can be very steep, implying that rigid pursuance of low or zero inflation may lead to a sharp rise in output variability.

   Methodologically, the existing work on the output-inflation volatility tradeoff relies on model simulations. Despite the popularity of this new policy tradeoff as an expositional tool in explaining the choices confronting policymakers, its empirical value remains questionable for two reasons. First, as pointed out by Walsh (1998), since there is no consensus regarding which model best represents the economy, these studies inevitably lead to disagreements about the true tradeoff faced by policymakers. Second, the volatility tradeoff frontier is traced out in light of a series of "optimal" policy rules, each of which is simulated in a stable and optimal condition over a long time horizon. In practice, however, the efficacy of policy rules cannot be verified independently and the simulated environment is not likely to hold. Without evidence supporting the existence of a Taylor curve relationship, the empirical significance of simulation-based policy inferences is limited.

   A key factor constraining the empirical evaluation of the Taylor curve is that realizations of volatility behavior are not directly observable. This difficulty has been circumvented using ad hoc measures of volatility, for instance, moving standard deviations and squared residual terms in vector autoregressions (VARs). These measures, however, do not differentiate observed volatility from expected or conditional volatility, the latter of which better represents perceived uncertainty and thus is of particular interest to us. In this light, the present paper departs from the existing literature by empirically modeling time-varying conditional volatility. More specifically, the stochastic properties of inflation and output volatility are examined using a multivariate generalized autoregressive conditional heteroskedasticity (GARCH) model.

   Given the finding of a qualitatively meaningful Taylor curve tradeoff relationship as in Lee (1999), the GARCH model is used to estimate the impact of monetary policy on the conditional variances of output and inflation. Bernanke and Mihov (1995) find that except for the 1979-1982 period associated with a shift in the Federal Reserve's (Fed) operating procedure, movements in the federal funds rate (FFR) since 1960 have provided a good measure of the monetary policy stance. (1) Along these lines, I investigate the effects of observed as well as unanticipated changes in the FFR. Interest rate shocks are generated alternatively by a VAR-based reaction function and a policy rule of current research interest commonly known as the Taylor (1993) rule. In addition, I explore plausible changes in the responses of inflation and output volatility before and after the 1979-1982 regime shift.

   The remainder of the paper is organized as follows. The next section describes the estimation model and provides historical data. The third section discusses empirical results for the GARCH model estimated with observed data on monetary policy actions, and the fourth section compares these results with alternative specifications of the policy reaction function. The final section contains a summary and draws conclusions.

2. Methodology

   Estimation Model

   The joint processes of inflation and output volatility can be modeled by a bivariate GARCH(p, q) process, as discussed in Engle and Kroner (1995). Without loss of generality, I focus on a GARCH(1, 1) model previously implemented by Lee (1999) (i.e., p = 1 and q = 1):

   [H.sub.t] = [GAMMA]'[GAMMA] + A'[H.sub.t-1]A + B'[e.sub.t-1][e'.sub.t-1]B + D'[F.sub.t-1]D [for all] t = 1, ... , T, (1)

   where [H.sub.t] [equivalent to] [[h.sub.1t], [h.sub.2t]]', which is a 2 X 1 vector of the conditional variances of output and inflation; [GAMMA], A, B, and D are 2 X 2 upper-triangular matrices of parameters; e, [equivalent to] [[e.sub.1t], [e.sub.2t]]' is a 2 X 1 vector of output and inflation innovations; and [F.sub.t], is a vector of additional explanatory variables. Equation 1 is to be estimated using the maximum-likelihood method for which the likelihood function is written as

   [FORMULA NOT REPRODUCIBLE IN ASCII] (2)

   where [THETA] is the vector of all parameters for estimation.

   The two innovation series in [e.sub.t] represent deviations of output and inflation from their respective trends (or means), which are modeled in a VAR context:

   [FORMULA NOT REPRODUCIBLE IN ASCII] (3)

   where [X.sub.t], is a 2 X 1 vector of the output and inflation series; [Y.sub.t] is a vector of additional explanatory variables, including the FFR and an aggregate variable capturing movements in commodity prices. Essentially, [e.sub.t] is a vector of forecast errors of the best linear predictor of [X.sub.t] conditional on all available information contained in [[OMEGA].sub.t]. Equation 3 is the conditional mean equation, which can also be viewed as part of a VAR system similar to the one investigated by Balke and Emery (1994), among others:

   [FORMULA NOT REPRODUCIBLE IN ASCII] (4)

   where [Z.sub.t] is a 3 X 1 vector consisting of output, inflation, and the FFR, with their residual terms captured in [e.sup.*.sub.t] [equivalent to], [[e.sub.1t] [e.sub.2t] [e.sub.rt]]', and PCOM, captures movements in commodity prices that are exogenous to the VAR system.

   The FFR serves as a measure of monetary policy, while the commodity price variable is used to control for both the effect of supply shocks on inflation and the response of the Fed to future (or anticipated) inflation. Balke and Emery (1994) have demonstrated the role of commodity prices in explaining the "price puzzle," which concerns rising instead of falling prices in response to monetary tightening, as found in recent studies such as that of Bernanke and Blinder (1992). As discussed in section 4 below, the equation for the FFR represents a reduced-form parameterization of the policy reaction function. With a symmetric lag structure across all variables, least-squares estimation of the VAR system (Eqn. 4) equation by equation yields consistent estimates. Moreover, the estimates for the first two equations should also be consistent with those for Equation 3, which is estimated simultaneously with the conditional variance equation (Eqn. 2).

   Data

   Empirical lessons are drawn from monthly data spanning the period between January 1960 and December 1999. (2) Even though GDP may serve as a better approximation of aggregate output, industrial production (IP) is used instead because of its availability in this particular frequency, which also effectively yields (twofold) more data points than the corresponding quarterly observations. The Consumer Price Index (CPI) is used to measure aggregate prices, and the Conference Research Board index is used to measure movements in commodity prices.

   Fuhrer (1997) argues that changes in monetary policy responses to output and price movements affect the nature of their variability tradeoff. To account for possible structural instability, he divides an observation period similar to mine into two sample periods conditional on the change in the Fed's policy regime between October 1979 and August 1982. The timing of the change also coincides with the onset of the Fed's explicit commitment to controlling inflation, which began in the late 1970s. Along these lines, I examine separate results for the subsamples of...