اهداف درون زا و ارزیابی هدف قرار دادن قوانین برای سیاست های پولی

Recent research in monetary economics has followed the advice of McCallum [1988. Robustness properties of a rule for monetary policy. Carnegie-Rochester Conference Series on Public Policy 29, 173–203] and investigated the robustness properties of monetary policy rules by evaluating them in a variety of models. Evaluation across models is typically based on an exogenously specified loss function. However, the theory on which many recent monetary policy models are based implies that changes in the structure of the model also have consequences for the policy objectives the central bank should pursue. Objectives are endogenous, not exogenous to the model. In this paper, I investigate the impact of endogenous objectives on the evaluation of targeting rules for monetary policy.

There is a fundamental dichotomy that underlies most monetary policy analysis. On the one hand, there is the model of the economy, consisting of a set of structural equations that characterize the private sector's behavior. On the other hand, there are the preferences of the policy maker. This dichotomy allows economists to provide the policy maker with a menu of alternative choices, leaving it to the policy maker to choose from among the available options. This view is reflected in a recent paper by McCallum and Nelson: Accordingly, it can be useful to explore the way in which difference properties of a modelled economy—e.g., the variances of the endogenous variables—are related to policy rule parameters, leaving it to actual policy makers to assign the relevant weights [to policy objectives]. McCallum and Nelson, 2004a and McCallum and Nelson, 2004b. Recent work in macro, most prominently by Woodford (2003), calls into question this dichotomy between economic structure and policy objectives. He shows that the standard quadratic loss function that has been a common component of much of the monetary policy literature can be, under certain conditions, interpreted as a second-order approximation to the welfare of the representative agent. But critically, this interpretation of the loss function breaks the dichotomy between economic structure and objectives; the relative weights on the variables appearing in the loss function, and even the list of variables that should appear, depend on the structure of the economic model.1 The policy maker cannot find the marginal rate of substitution between the target variables in a manner that is independent of the transmission mechanism that governs the marginal rate of transformation between them. Even the definition of the target variables will depend on the policy maker's views of the transmission mechanism. This has two important implications. First, it will rarely be appropriate to combine the same loss function with different structural models of the economy. Different models will imply different loss functions. Second, in assessing model and parameter uncertainty, uncertainty about key structural parameters will also imply uncertainty about the correct loss function.2 At a practical level, the endogeneity of objectives has implications for the assessment of policy robustness. It may, for example, be inappropriate to take a rule designed to minimize a loss function in one model and evaluate its performance in a different model using the original loss function. The objective function appropriate for one model cannot be used directly to evaluate outcomes in a different model. Thus, McCallum's influential recommendation to use multiple models to explore the robustness of policy rules (McCallum, 1988 and McCallum, 1999) may be less straightforward than it appears. There is another implication of the dependence of objectives on structure. Just as one could follow McCallum and evaluate the consequences of using a rule optimized for one structural model in a different structural model, one similarly needs to investigate the consequences of employing a rule optimized for one objective function when the true social objective is different. To be specific, what are the consequences of implementing a policy rule that is optimal from the perspective of the standard quadratic loss function in inflation and output gap volatility if the economy is actually characterized by a model that implies welfare should be measured by a different loss function? In work closely related to this paper, Levin and Williams (2003b), Kimura and Kurozumi (2003), and Kurozumi (2003) also investigate the consequences of parameter uncertainty for policy when objectives are endogenous and depend on the model's structural parameters. They study Bayesian policies and show how optimal monetary policy is affected when the objective function depends on structural parameters whose values are uncertain.3 Levin and Williams show how Brainard's classic finding that multiplicative uncertainty leads to caution can be overturned when the effects of uncertainty on the loss function are appropriately accounted for. For example, they find that the optimal interest rate response to a cost shock is unaffected by uncertainty about the output elasticity of inflation, once the implications of this uncertainty for the central bank's objective function are incorporated into the analysis. Kimura and Kurozumi show how uncertainty about inflation dynamics can lead to more aggressive policy responses to shocks as the nature of these dynamics alter the weight the central bank places on its price stability objective. In contrast to these paper, I do not deal with optimal policy under uncertainty. Instead, I follow the bulk of the literature on optimal monetary policy and consider policy rules that ignore parameter uncertainty. Monetary policy is represented in terms of targeting rules which are based on the first-order conditions from the central bank's policy decision problem (Svensson, 2003 and Svensson and Woodford, 2005). These targeting rules depend, therefore, on both the nature of the central bank's objectives and the constraints imposed by the economy's structure. I focus on how the failure to recognize the link between structural parameters and the loss function affects the evaluation of alternative targeting rules. I also conduct a form of risk assessment by evaluating the consequences for macroeconomic outcomes of basing policy on incorrect parameter values. I show how conclusions about the consequences of this form of parameter misspecification depend on whether all the implications of the misspecification—on structural equations, on objectives, and on the nature of economic disturbances—are fully accounted for. The model employed in the analysis draws on the recent extension of the basic new Keynesian model by Benigno and Woodford (2004), an extension that explicitly incorporates the case of a distorted steady-state. Cost shocks, normally treated as exogenous in the literature on monetary policy, arise endogenously due to stochastic fluctuations in the wedge between the efficient level of output and the flexible-price equilibrium level of output. Two aspects of the model will be the primary foci of the analysis: the degree of structural inflation inertia and the degree of nominal price stickiness. Both have generated much empirical debate and also appear to be important for the evaluation of alternative policies. One of the earliest criticisms of forward-looking models of inflation was that they were incapable of matching the highly serially correlated nature of actual inflation processes (Nelson, 1998). While the persistence displayed by inflation could result from serially correlated inflation shocks or from the behavior of monetary policy (Goodfriend and King, 2001), there is great uncertainty about the respective roles of forward and backward elements in the inflation process. For example, Rudebusch (2002) estimates the weight on lagged inflation to be over twice that on expected future inflation, while Galí and Gertler (1999) find essentially the reverse. This uncertainty about the degree of structural inflation inertia is unfortunate, since the existing literature has identified it as one of the most critical factors affecting the evaluation of alternative policies.4 The degree of nominal price rigidity, like the degree of structural inflation inertia, is also an issue around which there is great uncertainty. Early structural estimates of forward-looking new Keynesian Phillips curves obtained values for the average period between price adjustments that were very long, on the order of a year or more (Galí and Gertler, 1999, Sbordone, 2002 and Dennis, 2003). This is much longer than is consistent with microevidence (Bils and Klenow, 2002).5 In the next section, the basic model is set out and the optimal targeting rule that minimizes the expected present discounted value of a second-order approximation to the welfare of the representative household is derived. The way in which this objective function depends on the model's structural parameters is discussed. Section 3 then considers the case in which the central bank's model of the economy is correct, but policy is based on the wrong objectives. The purpose of this section is to investigate how conclusions reached in standard models with exogenous objectives might need to be altered once model consistent objectives are employed. Section 4 examines the robustness of the optimal targeting rule to parameter misspecification, focusing on how assessments of robustness are affected by the endogeneity of the objective function. Conclusions are summarized in the final section.

The standard approach to monetary policy analysis treats the objectives of policy as exogenously specified, independent of the model used to represent the economy. Economic theory, however, draws a tight link between the objectives a policy maker concerned with maximizing the welfare of the representative agent should pursue and the underlying structure of the economy. Objectives are endogenous. The purpose of this paper has been to investigate the role of endogenous objectives in the evaluation of monetary policy targeting rules. This has been done is a very simple model, but one in which the link between structural equations, social welfare, and the underlying parameters of the model is quite clear. A variety of comparison were made that indicated the potential for conclusions based on the standard exogenous objectives common in monetary policy analysis to be misleading. Because the representation of social welfare in terms of policy objectives is model dependent, any conclusions will themselves be specific to the model employed. However, several interesting result emerge from the simple new Keynesian model used in this paper. The analysis suggested that the use of ad hoc objectives and the addition of ad hoc disturbances can significantly affect the evaluation of alternative policies. The use of the standard loss function provided misleading guidance on the effects of misspecifying structural inflation inertia, suggesting that a robust policy should assume a high degree of such inertia. In contrast, using the social loss function showed this not to be the case, even under the targeting rule that was optimal for the standard loss function. The link between the economy's distortions and the presence of a disturbance to the inflation adjustment equation also played an important role in assessing alternative targeting rules and the effects of price rigidity. Increased price rigidity reduces the output gap elasticity of inflation, but it also increases the relative weight on inflation objectives in the social loss function and reduces the important of cost shocks. Failing to incorporate these last two effects significantly affects policy evaluations. Finally, it may be useful to note that the analysis here has not focused on policies that would be optimal, given parameter uncertainty. Instead, the focus was on the consequences of using incorrect parameters or objectives in designing and evaluating targeting rules. Optimal policies are unlikely to be represented as time-invariant targeting rules of the type studied in this paper. Rather, optimal policy will need to reflect the learning that occurs as the policy maker adapts to new information about the structure of the economy. 19