Policy Evaluation with a Forward-Looking Model

In this paper, we follow the standard two-step approach to policy evaluation. We set out a small structural model and obtain estimates of its parameters, and then evaluate the performance of alternative policy rules while treating estimates of the structural parameters as fixed and known. We break with standard practice in an interesting way. On the assumption that structural-error covariances are fixed and known, we compare the performance of fixed coefficient rules that condition on past state variables, current state variables, and expectations of future state variables. We also compare fixed-coefficient rules to optimal commitment and discretion. Our paper provides evidence on the practical importance to a central bank of obtaining a commitment mechanism and on the loss in performance when the commitment mechanism takes the form of a simple fixedcoefficient policy rule. Monetary policy rules are naturally amenable to modern econometric policy evaluation methods that were developed as part of the rational expectations revolution in macroeconomics in the early 1970's. When using these methods, researchers first build a structural model of the economy, consisting of mathematical equations with estimated numerical parameter values. They then test out different rules by simulating the model stochastically. One monetary policy rule is better than another.if the simulation results show better economic performance. (Taylor, 1998). Modern econometric policy evaluation entails two steps. In the first, the parameters of a structural model are either estimated or obtained through calibration. In the second, the performance of alternative policy rules is studied and conclusions about policy are reached. Fuhrer (1997) is a good example of the two part approach. He fits a small structural model to data for the US economy treating the coefficients of his policy rule as free parameters. He then derives an optimal policy frontier by varying the values of the policy-rule coefficients to minimize a weighted sum of the variance of output and the variance of inflation. He evaluates policy by comparing the variances of output and inflation achieved by the estimated rule with points on the policy frontier. In this paper, we follow standard practice by setting out a small structural model, obtaining estimates of its parameters, and then evaluating the performance of alternative policy rules while treating estimates of the structural parameters as fixed and known. We break with standard practice in an interesting way. Our maintained hypotheses include an auxiliary assumption that permits us to identify the covariance matrix of structural errors. On the assumption that structural covariances as well as structural parameters are known and fixed, we are able to compare the performance of backwardand forward-looking fixed coefficient rules. We are also able to compare the performance of fixed-coefficient rules to the performance of the optimal commitment policy and to the optimal policy under discretion. Our paper thus provides evidence on the practical importance to a central bank of obtaining a commitment mechanism and the loss in performance when the commitment mechanism takes the form of a simple and verifiable fixed-coefficient policy rule. We evaluate the performance of a policy with a loss function with three inputs. The first input is a set of three weights that represent the relative importance to the central bank of 2 stabilizing inflation, output, and interest rates. We compute optimal policies and corresponding loss values for different policy weights in order to determine whether conclusions about the relative performance of policies are sensitive to policy objectives. Policy weights range between zero and one and sum to one. The second input to the loss function is the covariance matrix of structural errors. For fixed-coefficient rules, we use the Klein algorithm to compute the covariance matrix of reduced form errors from the structural error covariance matrix, the structural parameters, and the coefficients of the policy rule. The reduced form error covariance matrix is then used to compute policy loss. The third input to the loss function is the statetransition coefficient matrix. For fixed-coefficient rules, we compute this matrix with the Klein algorithm. For optimal commitment and discretion, we derive the reduced form and compute policy loss with a version of Soderlind’s (1999) algorithm. Our policy analysis supports several interesting findings. First, the original Taylor rule, with a priori coefficient values, performs quite well when stabilizing inflation and stabilizing output are both important objectives. Its performance can, however, be very poor for other sets of weights. Second, for a wide variety of policy-objective weights, backward-looking rules perform as well as or better than rules that permit the central bank to adjust the rate of interest in response to current output and inflation. In fact, a backward looking rule which permits the central bank to condition the rate of interest on the full state vector for the economy is the best performer for more than half of our policy objective weight configurations. Third, when the central bank makes output stabilization its chief objective, a optimized version of the Taylor rule where the interest rate depends on current values of output and inflation and the lagged interest rate is the best performer among the rules we consider. We begin in section 1 with an example that explains how the coefficients of a policy rule are computed when the structure is “backward-looking. ” The example highlights the challenges associated with computing optimal policies for “forward-looking” models. Section 1 also describes the algorithm we use to compute policy loss. In section 2, we set out the forwardlooking structural model that underlies our analysis and explain how we use the Klein algorithm to solve it and compute policy loss. In section 3, we present the results of our policy evaluation for fixed coefficient rules. In section 4, we explain how we compute loss for optimal