Evaluating monetary policy options.

• Author: Fackler, James S.

1. Introduction

   One of the critical elements in the formulation of monetary policy is the evaluation of the effects of alternative paths of the policy instrument on the macroeconomy. For example, in Federal Open Market Committee (FOMC) meetings, estimates of the effects of alternative paths of the federal funds rate are presented to policymakers as an input into the policy process; for a discussion, see Meulendyke (1998). The effects of the alternative paths are evaluated within the context of a structural model of the economy; the latest version of the structural model used at the Board of Governors is described in Brayton et al. (1997).

   In this article, we present a procedure for evaluating ex ante the effects of alternative paths of a monetary policy tool (the federal funds rate in our illustrations) on output and the price level. We demonstrate this procedure employing a variant of a widely used vector autoregressive (VAR) model of the U.S. economy. This exercise can be viewed as a supplement to, or even an alternative to, analysis that relies on a particular structural model. Given the lack of general agreement on the appropriate structural model, evaluation of the effects of changes in the policy instrument within a variety of different types of models is appropriate.

   The discussion of the proposed procedure is in the spirit of recent work by Leeper and Sims (1994), who, following earlier work by Sims (1982, 1987), distinguish between normal policymaking and regime changes. For purposes of illustration, we employ a VAR model comprised of the same variables used by Christiano, Eichenbaum, and Evans (hereafter CEE) (1994, 1996) and Bernanke and Mihov (hereafter BM) (1998). We show how to evaluate and compare the current policy path with normal policy alternatives, such as typically sized changes in the federal funds target. We stress that this model is used only for illustrative purposes. Our methodology applies to any generic structural model and thus can easily incorporate alternative models and estimation techniques. For instance, the methodology is easily extended to alternative schemes to identify structural shocks such as those proposed by Bernanke (1986) or Blanchard and Quah (1989), including the adoption of prior information into the estimation. Finally, as argued b y Sims (1987) and Cooley, LeRoy, and Raymon (1984), the analysis of normal policymaking avoids the difficulties of the Lucas critique.

   In section 2, we provide a brief discussion of the VAR model. In section 3, we present a discussion of the econometric technique. In section 4, we present and discuss results that compare the no-change policy with alternatives in which the funds rate target is altered. We conclude in section 5.

2. The VAR Model

   The model of GEE and BM comprises output (Y), the price level (P), a commodity price index (CP), and three reserve market variables--total reserves (TR), nonborrowed reserves (NBR), and the federal funds rate (FFR). (1) The analysis uses quarterly data for the period 1959:1-1999:4. Estimation begins in 1961:2 and ends at different points, depending on the policy experiment considered. Eight quarterly lags are employed, and log levels of all variables except FER are used. (2)

   In performing the policy experiments, it is assumed that FER is the policy variable. Monetary policy shocks, following GEE (1994, 1996) and Strongin (1995), are identified using a Choleski decomposition with the following ordering: Y, P, CP, TR, FFR, and NBR. Following Strongin (1995) and BM (1998), we assume that, because the Federal Reserve accommodated the demand for TR over much of the sample, shocks to TR reflect reserve demand shocks. Ordering TR before FFR thus purges shocks to FFR of any effect of reserve demand shocks. The decomposition implies that monetary policy shocks affect Y, P, CP. and TR only with a lag but affect NBR contemporaneously. It also assumes that monetary policymakers respond in the current period to shocks to Y, P, CP, and TR but respond only with a lag to movements in NBR. (3)

   Figure 1 presents impulse response functions for the model estimated over 1961:2-1999: 4 along with associated 1-SE confidence intervals for a 1-SD positive shock to FFR. The patterns of effects are similar to those reported in the literature and are generally consistent with typical views of the operation of monetary policy in an economy with some rigidities. The only troublesome aspect of the results, which also appears in the recent studies of CEE (1994, 1996), BM (1998), and Leeper and Zha (2001), is the puzzling, long-lived negative effect of a transitory shock to FFR on P, which deserves further investigation. (4) Since we focus on illustrating how to implement our procedure, conditional on a widely used specification, we leave pursuit of model refinements to future research.

3. Methodology

   In a precursor to the current analysis, Fackler and Rogers (1995) demonstrated, in the context of a structural VAR, how to use counterfactual analysis to evaluate policy alternatives, terminology also used by Christiano (1998). For present purposes, we adopt a more intuitive terminology used by Sims (1982) and, more recently, Leeper and Sims (1994), who refer to normal policymaking. In a recent article, Leeper and Zha (2001) refer to modest policy interventions rather than normal policymaking. These papers are compared with ours in section 4.

   Consider a policy feedback equation that might be embedded in a VAR such as f = [alpha]y + [epsilon], where f is the proximate objective of policy (the federal funds rate in our exercise), y is a vector of lagged endogenous variables, [alpha] is an appropriately dimensioned vector of coefficients, and [epsilon] is a random structural shock orthogonal to the other shocks in the model. (5) Normal policymaking is an assessment of alternative [epsilon] paths. In contrast, regime shifts are represented by changes in one or more of the coefficients of [alpha] shifting to an interest rate peg would be one example. (6)

   Our reading of the policy literature, along with assessments in the financial press, suggests that most policy actions represent normal policymaking. Agents are likely aware of continuing debates about optimal policy both inside and outside the monetary authority. While these debates, for purposes of emphasis and clarity, are often presented in terms of regime shifts, few shifts in policy regime seem to occur in practice. Agents may even discount announcements of regime shifts until the authority has pursued the new regime long enough to convince them that a shift has indeed occurred.

   Suppose the policymaker wants to evaluate the prospective impact on the economy of lowering the funds rate one-quarter percentage point below the current setting. Using the funds rate equation of the VAR, f = [alpha]y + [epsilon], in normal policymaking, as suggested by Leeper and Sims (1994, p. 91), "... one would solve for [[epsilon].sub.i] sequences that make the time path of interest rates behave as desired. Because the model implies that there are many potential stochastic influences on interest rates, this kind of projection is generally quite different from simply forecasting conditional on a given time path of the interest rate." As will be derived in Equation 3, the technical expression for the moving average representation of the model in period t + j is

   [y.sub.t+j] = [summation over (j-1/s=0)] [D.sub.s][[epsilon].sub.t+j-s] + [summation over ([infinity]/s=j)] [D.sub.s][[epsilon].sub.t+j-s],

   where [D.sub.s] is the moving average coefficient matrix associated with the structural shocks in the [epsilon] vector, the second term on the right-hand side is the dynamic forecast or base projection, and the first term on the right-hand side is the j-period-ahead forecast error. With n variables in the VAR, for Equation I (the policy equation, say), this forecast error is

   [summation over (j-1/s=0)] [summation over (n/h=1)] [D.sub.s,ih][[epsilon].sub.j,t+j-s].

   A conditional forecast, such as a particular interest rate path for several quarters, can be attained in a wide variety of ways by judicious selection of the elements of the [[epsilon].sub.t+j-s], s = 0, ... , j - 1, vectors; in general, there are multiple constraints for which the target path obtains. (7) As noted in the Leeper-Sims quote above, choosing from among these constraints is generally different from selecting the [epsilon] path as described below.

   Our description of normal policymaking begins with the historical decomposition (HD), which quantifies, given the identification of a model, the period-by-period relative importance of the various structural shocks. The HD is derived from a structural model, (8)

   [y.sub.t] = [A.sub.0][y.sub.t] + [A.sub.1][y.sub.t-1] + ... + [A.sub.p][y.sub.t-p] + [[epsilon].sub.t]. (1)

   In Equation 1, the [A.sub.i] represent the structural coefficients and the [[epsilon].sub.t] are the structural shocks. The elements of [[epsilon].sub.t] are assumed to be mutually orthogonal. Let [e.sub.t] = [(I - [A.sub.0]).sup.-1][[epsilon].sub.t], represent the reduced form shocks and [[PI].sub.i] the reduced-form coefficient mastrices. Define [PI](L) = (I - [[PI].sub.1]L - ... - [[PI].sub.p][L.sup.p]). The moving average matrix is given by C(L) = [[[PI](L)].sup.-1], with [C.sub.0] = I. The moving average representation (MAR) of Equation 1 in terms of structural shocks is

   [y.sub.t] = [summation over ([infinity]/s=0)] [D.sub.s][[epsilon].sub.t-s], (2)

   where [[epsilon].sub.t] = (I - [A.sub.0])[e.sub.t] and [D.sub.s] = [C.sub.s][(I - [A.sub.0]).sup.-1]. For a particular period t + j, Equation 2 may be written as

   [y.sub.t+j] = [summation over (j-1/s=0)] [D.sub.s][[epsilon].sub.t+j-s] + [summation over ([infinity]/s=j)] [D.sub.s][[epsilon].sub.t+j-s], (3)

   which represents the HD.

   Equation 3 shows an in-sample accounting identity for a model estimated through period t + j. Specifically, the actual data is the sum of two...