سیاست های پولی مقاوم در اقتصاد کوچک باز

We study how a central bank in a small open economy should conduct monetary policy if it fears that its model is misspecified. Using a new-Keynesian model of a small open economy, we solve analytically for the optimal robust policy rule and the equilibrium dynamics, and we separately analyze the consequences of central bank robustness against misspecification concerning the determination of inflation, output, and the exchange rate. We show that an increase in the preference for robustness makes the central bank respond more aggressively or more cautiously to shocks, depending on the type of shock and the source of misspecification.

Good policy design requires a good understanding of private sector behavior. Such an understanding is important not only in order to identify market deficiencies and hence policy objectives, but also when trying to reach objectives in the best possible way. The new-Keynesian model as laid out by Rotemberg and Woodford (1997), Goodfriend and King (1997), and others have been established as the mainstream model for monetary policy analysis. This model captures the sluggish adjustment of prices and the intertemporal consumption decision in a model framework with optimizing households and firms. With only a limited number of equations and clear intuition, the model has been very influential and has provided policymakers with several guiding policy principles in responding to the different disturbances in the economy (see, for example, Clarida et al., 1999; King, 2000). More recently, the new-Keynesian framework has been extended to open economies, for example by Galí and Monacelli (2005) and Clarida et al. (2001). Although the new-Keynesian model has many attractive theoretical properties, it has been criticized by many researchers, most notably for not fitting the data well (see, for example, Ball, 1994; Mankiw, 2001; Estrella and Fuhrer, 2002). One response to such criticism is to design more complex models that are better able to capture the behavior of macroeconomic variables, following Christiano et al. (2005) and others. Such models gain in realism but lose in tractability. An alternative route, explored in this paper, is to acknowledge that the simple model is a misspecified description of reality, and to design policy to be robust against model misspecification. We will assume that the true model of private sector behavior lies in some neighborhood around a reference model, and we analyze how monetary policy should be designed in order to work reasonably well for all models inside this neighborhood. This problem has recently been addressed by Hansen and Sargent (2007) using ‘robust control’ techniques. Assuming that the policymaker is unable to formulate a probability distribution over plausible models, the robust policymaker designs policy for the worst possible outcome within a pre-specified set of models. We apply robust control techniques developed by Hansen and Sargent (2007) and Giordani and Söderlind (2004) to a simple new-Keynesian open-economy model developed by Galí and Monacelli (2005) and Clarida et al. (2001). The simple model structure allows us to find closed-form solutions for the optimal robust policy and the equilibrium behavior of the economy. We also generalize the standard robust control framework by allowing the policymaker's preference for robustness to differ across equations, reflecting the confidence the policymaker has in each relationship. For instance, the policymaker may be quite confident about one of the equations (such as the Phillips curve) and believe that robustness against misspecification in this equation is not very important, but at the same time be uncertain about some other equation (for example, the exchange rate relationship). Our approach allows us to consider each equation in turn and ask what is the effect on the robust policy of misspecification in that particular equation. Thus we will consider several different types of misspecification within the model: misspecification in firms’ price-setting, misspecification in consumer behavior, and misspecification in the model determining the exchange rate.1 The ability to focus on specification errors in particular equations seems important. Policymakers are more confident in some relationships than in others, and so regard some types of specification errors to be more important than others. In open economies, monetary policymakers are particularly uncertain about interactions between monetary policy, the exchange rate, and the economy. Using our approach, we are able to analyze the design of monetary policy under such specific model uncertainty while keeping other potential sources of misspecification fixed. One important part of the analysis will focus on how the central bank's preference for robustness against model misspecification affects its monetary policy. Thus far, there is no consensus about whether increased uncertainty should lead to more aggressive or more cautious policy behavior. Following the seminal analysis of Brainard (1967), it is well-accepted that increased uncertainty about the effects of policy should lead to more cautious policy behavior, at least within a Bayesian treatment of model uncertainty. However, Craine (1979) and Söderström (2002) show that this result does not generalize to all parameters in the model: increased uncertainty about the persistence of inflation instead motivates more aggressive policy.2 Within the robust control literature, several authors (for example, Onatski and Stock, 2002, Hansen and Sargent, 2001 and Giannoni, 2002; Giordani and Söderlind, 2004) have shown that an increased preference for robustness tends to lead to more aggressive policy behavior. These authors rely on numerical methods to solve for the optimal robust policy in a closed economy. In a companion paper, Leitemo and Söderström (2008), we use our analytical approach to show that the aggressiveness result is an inherent feature of robust policy in a closed economy. We show in the present paper that this result does not carry over to the open economy: depending on the source of misspecification and the type of disturbance affecting the economy, the optimal robust policy in an open economy can be either more aggressive or more cautious than the non-robust policy.3 A second set of results concerns the effects on the macroeconomy of the central bank's fear of model misspecification. As the central bank designs policy to do well in the worst-case scenario, this will have important consequences for the economy in other more likely outcomes. We show that the price of being robust to misspecification in the Phillips curve or the output equation comes in the form of higher output and exchange rate variability, whereas robustness against misspecification in the exchange rate equation comes at the cost of higher inflation variability. The robust control approach to model uncertainty is designed to minimize the consequences of the worst-case specification of the policymaker's reference model, and thus focuses exclusively on the worst-case outcome within a set of admissible models.4 In contrast, a central bank following a Bayesian approach would take into account all possible outcomes in the specified model set and assign weights to each competing model according to its perceived probability (see, for instance, Brock et al., 2007; Batini et al., 2006). One reason to focus on the worst-case specification is that the policymaker may face Knightian uncertainty and therefore be unable to assign probabilities to alternative specifications of its model. The paper is organized as follows. We first present our model of a small open economy in Section 2. We then derive the robust policy and the equilibrium under this policy in Section 3, both for the ‘worst-case’ model where misspecification is present and for the ‘approximating’ model where there is no misspecification but the central bank's reference model is correct. We analyze the effects of a stronger central bank preference for robustness in Section 4, and we illustrate these effects using a numerical example in Section 5. Finally, we summarize our findings and conclude in Section 6.

We use a stylized model of a small open economy to analyze how optimal monetary policy and the behavior of the economy are affected by the central bank's desire to be robust against model misspecification. The simple model structure enables us to solve analytically for the optimal robust policy, as well as the central bank's worst-case model and the more likely approximating model. Our framework also allows us to analyze cases when the policymaker is more confident about some equations in the model than others. Our analysis shows that an increase in the central bank's preference for robustness has ambiguous effects on the optimal policy behavior, depending not only on the shock to which the central bank responds, but also on what part of the model the central bank perceives as most prone to misspecification. Although our model is highly stylized, we believe this ambiguity to carry over also to more elaborate models.17 In numerical applications the effects of increased misspecification will therefore depend crucially on the calibration or estimation of the parameters that determine the central bank's relative faith in the different model equations. In a companion paper (Leitemo and Söderström, 2008) we focus on the optimal robust policy in the closed-economy version of our model. There, the results are unambiguous: the robust policy always responds more aggressively to shocks than the non-robust policy, and, as a consequence, inflation is less volatile and output is more volatile under the robust policy. The present paper shows that the effects of robustness in the open economy are more complex, as is the design of monetary policy in general. This is because in an open economy the presence of the exchange rate produces new trade-offs for monetary policy and introduces an additional source of volatility and model misspecification.