تعویض مخارج در مقابل ثبات نرخ ارز واقعی: اهداف رقابت برای سیاست نرخ ارز

This paper develops a view of exchange rate policy as a trade-off between the desire to smooth fluctuations in real exchange rates so as to reduce distortions in consumption allocations, and the need to allow flexibility in the nominal exchange rate so as to facilitate terms of trade adjustment. We show that optimal nominal exchange rate volatility will reflect these competing objectives. The key determinants of how much the exchange rate should respond to shocks will depend on the extent and source of price stickiness, the elasticity of substitution between home and foreign goods, and the amount of home bias in production. Quantitatively, we find the optimal exchange rate volatility should be significantly less than would be inferred based solely on terms of trade considerations. Moreover, we find that the relationship between price stickiness and optimal exchange rate volatility may be non-monotonic.

This paper develops a novel view of exchange rate policy as a trade-off between the desire to smooth fluctuations in real exchange rates in order to achieve smaller cross-country deviations in consumer prices on the one hand, and the need to allow flexibility in the nominal exchange rate so as to facilitate terms of trade adjustment on the other hand. There is a substantial body of empirical evidence establishing that the link between movements in exchange rates and changes in national consumer prices is weak.1 One explanation for this weak link is that prices of all goods are sticky in local currencies (LCP, or local currency pricing), and do not respond to movements in the exchange rate. In this case, nominal exchange rate fluctuations lead to inefficient movements in real exchange rates because they alter relative prices of identical or similar goods across countries. From this perspective, it is desirable to avoid movements in exchange rates because they lead to differences in prices across countries for goods that have similar resource costs.2 But there is separate evidence that relative traded goods prices are linked to movements in exchange rates. Obstfeld and Rogoff (2000) show that exchange rates are highly correlated with the terms of trade, measured as the relative price of imports to exports. This suggests that exported goods tend to have prices set in the producer's currency (PCP, or producer's currency pricing), and a depreciation raises the relative price of foreign to home export goods. In this case, the exchange rate may play a role in facilitating relative price adjustment in face of country specific shocks when nominal prices of traded goods are slow to adjust to the shocks. We present an analysis of exchange rate policy when there is a conflict between the objectives of stabilizing consumption-based real exchange rates and allowing terms of trade adjustment. We build a model consistent with both the evidence of weak exchange rate pass-through to consumer goods prices and high pass-through to imported goods prices. In the model, imports and exports are intermediate goods. The law of one-price holds for these traded products, so nominal price stickiness of these goods is of the PCP variety. Intermediate goods are used to produce final consumer goods, whose prices are sticky in the consumers’ currency. Consistent with the evidence, consumer prices are unresponsive to nominal exchange rate changes. In general, optimal exchange rate movements in this setting do not deliver full terms of trade adjustment. There is a trade-off. Nominal exchange rate movement changes the terms of trade in the desired direction when there is a real shock, as the literature has suggested, but mimicking the optimal terms of trade change may imply undesirable changes in the consumption-based real exchange rate. In our model, the optimal real exchange rate is constant only when the production functions for the final consumption good in the home and foreign country are identical and use only traded inputs. If we consider that special case, then under LCP for final goods, nominal exchange rate changes induce movements in real exchange rates that lead to inefficient consumption allocations. Stabilization of the consumption real exchange rate is a legitimate goal of exchange-rate policy, but it conflicts with the objective of achieving terms of trade adjustment. Moreover, when the production functions are not identical (e.g., exhibiting home bias in the use of traded inputs), or when non-traded inputs are used in production, the optimal real exchange rate is not constant. It is nonetheless true that the optimal policy stabilizes real exchange rates relative to the terms of trade.3 Evidence that the law of one price holds relatively well for traded intermediate goods is consistent with PCP, but is also consistent with nominal price flexibility for these goods. The evidence is not refined enough to distinguish between the two possibilities. Markets for intermediate inputs are not the standard “customer” markets to which models of nominal price stickiness are typically applied. To the extent that traded intermediate prices are flexible, exchange rate adjustment is not needed to adjust the terms of trade because the nominal prices themselves can adjust. Additionally, in the short run, domestically produced products might not be easily substituted for imported intermediate goods. If the substitutability of imported intermediates with domestic goods and services is low, the expenditure-switching role of exchange rates may be secondary. It is the short-run elasticity of substitution that is relevant for exchange-rate policy: when nominal prices have had time to adjust, the real effects of nominal exchange rate changes dissipate. It is well known that the short-run elasticity of substitution for imports is quite low. Even if prices are sticky and set according to PCP, so that nominal exchange rate movements do change the relative price of imported goods, there will be little expenditure switching when substitutability is low. We first present a series of special cases where monetary policy can achieve a first-best outcome – stabilizing the consumption real exchange rate as well as supporting efficient terms of trade adjustment. In our first specification, nominal prices of consumer goods are set in advance of the realization of shocks, while prices of intermediate goods are taken to be perfectly flexible. We find that under an optimal monetary policy, the nominal and real exchange rate has a lower variance than the optimal terms of trade movements. Under some parameterizations, an optimal monetary policy keeps the exchange rate constant. In this case, the fully optimal consumption allocations can be attained. The prices of traded intermediates adjust freely in response to shocks, so the role of monetary policy effectively is to achieve the desired real exchange rate response. We then reverse the assumptions on stickiness – final goods prices are flexible, but intermediate goods prices are set in advance in the producer's currency. Here we find that optimal exchange rate policy is aimed purely at achieving the desired terms of trade adjustment, since flexible final goods prices will ensure a stable real exchange rate. This specification is, of course, at odds with the evidence of non-responsiveness of consumer prices to exchange rate movements. We also solve a version of the model in which the home and foreign inputs must be combined in fixed proportions. We illustrate an example where fixed exchange rates are optimal even when both intermediate and final goods prices are fixed in advance (with PCP for intermediates and LCP for final goods.) There is no expenditure-switching role for exchange rates when there is no substitutability between imports and domestically produced goods. In general, however, monetary policy will not be able to attain simultaneously fully optimal consumption allocations as well as optimal terms of trade adjustment. In particular, when both final goods prices and intermediate goods prices are partially sticky, this will be the case. We go on to present a quantitative analysis of the more general case where there is a real trade-off between these goals. Our analysis finds that when consumer price indices are unresponsive to exchange rate changes, an optimal monetary policy may limit exchange rate volatility substantially relative to that required to achieve terms of trade volatility in a frictionless economy – even when most or all intermediate goods prices are sticky in nominal terms. In addition, we show that the relationship between exchange rate volatility and price stickiness may not be monotonic. While intuitively one would anticipate that reducing the flexibility of intermediate prices would increase the desirability of exchange rate adjustment, this relationship does not necessarily hold, particularly when the elasticity of substitution between home and imported intermediates is low. While reducing the flexibility of intermediate goods prices will first increase desired exchange rate volatility, after a certain point, as a greater share of intermediate goods prices are sticky, it becomes desirable to reduce exchange rate volatility. The paper is organized as follows. Section 2 presents the basic model structure and solves for a flexible price equilibrium. Section 3 analyzes a series of cases under alternative assumptions about price setting and substitution possibilities. Section 4 analyzes the more general case. Some brief conclusions follow.

There is a large body of evidence establishing that pass-through from changes in exchange rates to consumer goods prices is weak or non-existent. When this is the case, exchange rate fluctuations automatically change consumption-based real exchange rates. This means that consumer prices do not allocate goods efficiently across countries, and builds an a priori case for exchange rate stability. On the other hand, exchange rates may have a high pass-through to prices at the intermediate good level, and at this level, exchange rate movements may have a significant allocational role to play through expenditure switching among foreign and domestic intermediate goods. This opens up a trade-off. Exchange rate adjustment is desirable for expenditure switching, but may be costly because it moves around real exchange rates. This paper has identified this trade-off and explored its nature, both qualitatively and quantitatively. In some cases, we show that a welfare evaluation of the trade-off gives a significant emphasis on exchange rate stability. Quantitatively, we find that exchange rate volatility should be significantly less than that which would be inferred based on models that focus exclusively on the expenditure-switching role of exchange rates.