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This paper analyses the implications of the ‘expenditure switching effect’ for the role of the exchange rate in monetary policy in a small open economy. It is shown that, when the elasticity of substitution between home and foreign goods is not equal to unity, welfare depends on the variances of producer prices and the terms of trade. Producer-price targeting is compared to consumer-price targeting and a fixed exchange rate. It is found that a fixed exchange rate yields higher welfare than the other regimes only when the elasticity of substitution between home and foreign goods is very high.

This paper analyses the implications of the expenditure switching effect for welfare maximising monetary policy in a small open economy. Many previous contributions to the literature have not addressed this issue because they are based on models where the elasticity of substitution between home and foreign goods is restricted to unity.1 The model presented in this paper2 allows for a non-unit elasticity of substitution between home and foreign goods and uses second-order approximation techniques to derive an explicit expression for welfare.3 It is found that allowing for a non-unit elasticity of international substitution implies that terms-of-trade volatility becomes an important consideration for optimal monetary policy. Furthermore, welfare can be written as a weighted sum of two factors: the variance of producer prices and the variance of the terms of trade. The weight on terms-of-trade volatility is found to be increasing in the strength of the expenditure switching effect. Previous literature on the welfare effects of monetary policy in closed economies has tended to suggest that strict targeting of consumer prices will maximise aggregate utility.4 Such a policy minimises relative price distortions when some prices are sticky and unable to respond to shocks in the short run. Open economy contributions to the recent literature suggest that a welfare maximising monetary policy should focus on stabilising internal relative prices. This is achieved by strict targeting of producer prices.5 Further analysis of open economy models, where there is less than perfect pass-through from exchange rate changes to local currency prices, has shown that optimal monetary policy should involve some consideration of exchange rate volatility.6 In this case the monetary authority should allow some flexibility in producer prices in order to achieve some desired degree of volatility in the nominal exchange rate. The results of this paper show that terms-of-trade volatility (and thus exchange-rate volatility) can become an important factor in welfare maximising monetary policy even when there is full pass-through.7 In the model described below the strength of the expenditure switching effect is determined by the elasticity of substitution between home and foreign goods. Before proceeding, it is worth considering the available empirical estimates for the value of this elasticity. Obstfeld and Rogoff (2000b) briefly survey some of the relevant literature. They quote estimates ranging between 1.2 and 21.4 for individual goods (see Trefler and Lai, 1999). Typical estimates for the average elasticity across all traded goods lie in the range 5–6 (see for instance Hummels, 2001). Anderson and van Wincoop (2003) also survey the empirical literature on trade elasticities and conclude that a value between 5 and 10 is reasonable.8 There is thus considerable empirical evidence to suggest that the expenditure switching effect is potentially stronger than assumed in much of the recent open economy literature, where the elasticity between home and foreign goods is often restricted to unity. One feature of more recent contributions to the literature on optimal monetary policy (which is shared by the model of this paper) is that the welfare maximising monetary strategy becomes more complex as more realistic aspects are added to the basic model. It quickly becomes apparent that the optimality of a simple strategy of strict consumer or producer-price targeting does not carry over to more general cases. In addition, even when the optimal monetary strategy can be summarised by a relatively simple loss function, it becomes doubtful that the fully optimal monetary policy can in practice be implemented. The fully optimal policy may involve responding to unobservable or unmeasurable variables or require a complex balance between different targets where the optimal weights to be placed on different targets are unmeasurable or uncertain. It is, therefore, useful to analyse the welfare performance of non-optimal but simple targeting rules. After deriving the theoretically optimal policy regime for the model economy, this paper considers three possible simple targeting rules, namely: strict targeting of producer prices, strict targeting of consumer prices and a fixed nominal exchange rate. It is found that, if the elasticity of substitution is low, producer-price targeting yields the highest welfare of the three simple rules. But for intermediate values of the elasticity of substitution, consumer-price targeting can be the best simple rule. And for (very) high degrees of substitutability, a fixed exchange rate can be the best simple rule. The main focus of this paper is on the welfare effects of policy in a small open economy. Previous contributions to the literature have shown that the international spillover effects of monetary policy imply that the optimal policy from an individual country point of view may be suboptimal from a global perspective. Thus there are potential gains from policy coordination.9 In a two country model, with a structure similar to the model presented here, Benigno and Benigno (2003a) have shown that the optimal coordinated policy involves strict targeting of producer prices in each country. The coordinated policy should not involve any attempt to stabilise the terms of trade. It is, therefore, important to note that the individual country concern for terms-of-trade stability identified in the model presented in this paper is inefficient from a global perspective. This paper proceeds as follows. Section 2 presents the model. Section 3 discusses the welfare measure. Section 4 considers the general form of optimal monetary policy for the small open economy. Section 5 compares the welfare performance of the three simple targeting rules. Section 6 concludes the paper.

This paper has presented a simple model which allows for a non-unit elasticity of substitution between home and foreign goods. It is shown that aggregate welfare for the home economy is a weighted sum of the variances of producer prices and the terms of trade. The fully optimal monetary policy can be achieved by assigning a loss function to the monetary authority which includes these two terms. Three simple non-optimal targeting rules are compared and the implications of the degree of international substitutability are analysed. For low values of substitutability, producer-price targeting is best. At intermediate values of substitutability, consumer-price targeting is best. And for very high values of substitutability, a fixed nominal exchange rate is best. The underlying reason for these results is that terms-of-trade shocks tend to cause inefficiently large fluctuations in the demand for home produced goods, and therefore home work effort, when the expenditure switching effect is strong. This creates an incentive for the home policy maker to stabilise the terms of trade. However, terms-of-trade fluctuations are only inefficient from the point of view of home agents. From the perspective of world welfare, terms-of-trade fluctuations are optimal. So a world policy maker would not attempt to stabilise the terms of trade.31 The model presented in this paper is restricted in a number of respects, and relaxing some of these restrictions is likely to have an impact on the results. For instance, the degree of risk aversion in consumption is fixed by the assumption that utility is logarithmic in consumption. Previous authors have noted that risk aversion is an important parameter in determining the welfare effects of exchange rate volatility.32 The source of shocks can also be important in determining the welfare impact of exchange rate policy. Non-optimal variations in the degree of monopoly power or shocks to foreign monetary policy can have an important impact on the relative performance of different nominal target variables. These topics are likely to form interesting lines of future research.33