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This paper focuses on the design of monetary policy rules for a small open economy. The model features optimizing behavior, general equilibrium and price stickiness. The real exchange rate is shown to affect the firm's real marginal cost, aggregate supply and aggregate demand. The welfare objective depends on the openness of the economy, and the optimal policy rule differs from that which obtains in a closed economy. The inflation versus output gap stabilization trade-off is caused by the real exchange rate. The implied optimal monetary policy regime is domestic inflation target coupled with controlled floating of the real exchange rate.

It is widely recognized that the exchange rate plays an important role in the transmission of the monetary policy in open economies. Recent studies on this issue include Benigno and Benigno (2000), Benigno (2004), Devereux (2004), Gali and Monacelli (2005), Taylor (2001), Svensson (2000), among others. Differently from the closed economy framework, however, where there are some stylized results concerning to an optimal policy built on interest rate rules, several questions remain object of analysis in the open economy. Specifically, there lacks a precise answer as to whether the monetary authority should respond to exchange rate movements. The open economy environment yields additional complications to the optimal monetary policy problem. To see this, assume that the monetary authority follows an interest rate rule, as it is the common practice among central banks of developed countries, and the target variables are inflation and output gap. Exchange rate movements have a direct effect on both aggregate demand (switching demand effect) and prices (consumer price effect) and so have an indirect effect on the monetary policy instrument. On its turn, the exchange rate itself, by no arbitrage in international financial markets, is sensible to interest rate differentials. Thus, the exchange rate channels of transmission affect both private agents' expectations of future variables and optimal response of the monetary policy to stabilize the economy. The goal of this paper is to analyze the role of the exchange rate in the design of monetary policy rules for a small open economy. In the model economy, private agents are forward looking and the monetary policy affects economic activity through an interest rate rule. Nominal product prices are set by individual firms in a staggered manner, a la Calvo (1983). The channels of transmission imply that changes in the country's exchange rate affect firms' marginal cost, aggregate supply, and aggregate demand. The model provides a theoretical background for the inflation versus output gap stabilization trade-off. It is caused by the real exchange rate. The implied policy regime is domestic inflation target, coupled with a dirty floating of the exchange rate. Because of the exchange rate channels, neither the canonical representation, proposed by Gali and Monacelli (2005), nor the isomorphic solution for the interest rate rule, suggested by Clarida, Gali, and Gertler (2001), holds in the present model. In addition, in the welfare loss, the monetary authority places a higher weight on output gap stabilization than in the closed economy counterpart, as derived by Woodford (2003). This finding suggests that an overly aggressive inflation stabilization policy might cause undesirable instability in the small open economy. Previous works, including Aoki (2001), Kollmann (2002), Devereux and Engel (2003), and Svensson (2000), show different findings. Aoki (2001) does not find stabilization trade-off under the optimal policy of complete domestic inflation stabilization. When prices are set in local currency and the law of one price does not hold, Kollmann (2002) also argues that it is optimal to stabilize domestic inflation by assuming a Taylor type of policy rule, though it implies significant exchange rate volatility. Devereux and Engel (2003) claim that prices set in producer's currency (PCP) lead to fully flexible exchange rate. This result also does not hold here because of the terms of trade distortion and exchange rate channels of transmission, which are not considered by those authors. Contrary to the previous findings, Svensson (2000) suggests to target CPI inflation because this regime produces small to moderate variability in inflation, output and exchange rate. This result, however, is determined by the ad hoc structure of Svensson's model, which assumes a variety loss functions. In the present model, where welfare loss is utility-based, the optimal policy is domestic inflation target. The paper is organized as follows. The next section presents the model economy. The structural equations for aggregate demand and aggregate supply are derived in 3 and 4, respectively. Section 5 defines the rational expectations equilibrium. Section 6 derives the welfare objective and the optimal monetary policy rule. Finally, Section 7 is dedicated to the concluding remarks.

This paper focused on the design of a monetary policy rule for a small open economy, with special emphasis on the exchange rate channels of transmission for the monetary policy. The findings showed that, once the transmission mechanisms are in place, the real exchange rate affects the firm's real marginal cost, the aggregate supply, and the aggregate demand. In the model's equilibrium conditions, one has to specify the real exchange rate dynamics and the optimal monetary policy rule has a specific form, distinct from the closed economy counterpart. The openness of the economy has a direct effect on the social welfare objective. The relative weight placed on output gap stabilization is higher than its closed economy counterpart and it is increasing in the degree of openness. This finding reflects the welfare cost, in terms of unemployment, of any arbitrary policy that seeks to promote domestic consumption via gains in the terms of trade. In addition, due to the link between output and real exchange rate, an excessive weight placed on domestic inflation stabilization might generate instability in the economic activity. This result finds a parallel in the recent literature on optimal monetary policy for a closed economy when prices and wages are sticky. The monetary authority faces a trade-off between stabilizing inflation versus output gap. The trade-off, however, is due to the real exchange rate and not to the ad hoc cost-push domestic inflation shock that is appended to the closed economy aggregate supply. The real exchange rate captures the wage inflation that is a component of the firm's real marginal cost. Any shock that requires an increase in the nominal interest rate leads, through the exchange rate, to movements in the firm's real marginal cost in the opposite direction. As a result, the monetary authority is not able to stabilize inflation and output gap simultaneously. From the monetary authority's optimization problem, the implied policy regime is a domestic inflation target coupled with a dirty floating of the exchange rate. In the reaction function, the nominal interest rate responds to domestic inflation and output gap. Those variables, however, are directly affected by the real exchange rate due to the wage inflation and aggregate demand channels of transmission. Thus, foreign shocks that affect the exchange rate are followed by a reaction of the domestic nominal interest rate. This feature of the optimal monetary policy illustrates the absence of a fully floating exchange rate regime in the small open economy.