Exchange rates, domestic prices, and central bank actions: recent U.S. experience.

• Author: Parsley, David C.

1. Introduction

   The dramatic swings in currency values that characterize the current floating exchange rate period continue to inspire new research into their consequences for prices. This paper examines those consequences for U.S. domestic prices. The use of domestic price data is central to understanding the transmission of depreciation to inflation, and it distinguishes this research from the many related studies that focus on the prices of imports and exports. In examining the link between the exchange rate and domestic prices, we emphasize the role of the central bank. We note that a central bank that is primarily concerned with prices will act to insulate them from currency fluctuations. If successful, the central bank's actions will dampen the responses of prices to changes in the exchange rate, and the underlying response will be partially masked as a consequence. We provide empirical evidence of this dampening effect in the United States. The prices of many U.S. nondurable goods and even of some services respond modestly to the exchange rate, and their responses emerge most clearly when the role of monetary policy is explicitly considered.

   Our results also provide insight into the interpretation of some related studies of trade and traded goods' prices.(1) Many of those studies have found that both trade and the prices of imports and exports appear to respond sluggishly or incompletely to exchange rate movements. The slow, small responses have been explained alternatively as outcomes of particular characteristics of the structure of markets (such as sunk costs, imperfect competition, and price discrimination) and as a result of data inadequacies and aggregation errors.(2) This paper suggests that a different mechanism also may play a role. Specifically, estimates of the responsiveness of prices to the exchange rate also may reflect the policies of the central bank during the period examined.(3)

   In the next section of the paper, we present a simple description of prices. There, we draw out the implications of the central bank's actions for the observed relationships between exchange rates and prices. In section 3, we provide an empirical study of U.S. domestic prices. We present estimates of the responsiveness of the prices of a sample of nondurable goods and services to exchange rate changes using three alternative estimating strategies: a traditional pass-through equation, an error correction model, and a vector autoregression (VAR). In each case, we explicitly consider the role of the central bank.

2. A Simple Description of Individual and Aggregate Prices

   Consider a simple description of the prices of individual goods in which expectations regarding both the exchange rate and monetary policy play a role. Specifically, suppose that the price of a particular good is determined in the following way: in each period, t,

   [p.sub.it] = E{[f.sub.i][[e.sub.t], m([g.sub.t]), [z.sub.it]] [where] [I.sub.t]}, (1)

   where [p.sub.it] is the price of the ith good; [e.sub.t] is the nominal exchange rate in terms of foreign currency units per domestic currency unit; monetary policy, m([g.sub.t]), is implemented using some instruments, [g.sub.t]; [z.sub.it], summarizes all other factors that affect the individual price; and [I.sub.t] represents the information available when the price is determined.(4)

   This description of prices is quite general. For example, it can be derived from the optimizing behavior of an exporting monopolist or imperfect competitor. In such cases, the relative strength of the effects of the expected exchange rate and monetary policy on the price depends on their relative importance as sources of change in marginal cost or marginal revenue, and [z.sub.it] may reflect, say, changes in the price elasticity of the ith good or other changes in marginal costs or revenue.(5) Implicitly, this specification allows monetary policy to have effects that may differ across goods.(6) Alternatively, the pricing equation can characterize purchasing power parity. In that case, monetary policy by itself is unimportant, the exchange rate enters negatively, and [z.sub.it] reflects changes in the foreign price of the ith good.(7) The price equation is also general enough to be consistent with the pricing of nontraded goods, for which the exchange rate may be of slight importance.

   Because the aggregate price level, [p.sub.t], is simply a weighted sum of the individual prices, it also depends on expectations of the exchange rate, monetary policy, and the other factors, [z.sub.it]. Specifically:

   [p.sub.t] = [integral of] [[Alpha].sub.i]E{[f.sub.i][[e.sub.t], m([g.sub.t]), [z.sub.it] [where] [I.sub.t]} [d.sub.i] between limits 1 and 0 (2)

   where goods are indexed uniformly over the interval from zero to one, and

   [[integral of] [[Alpha].sub.i] di between limits of 1 and 0 = 1.

   Using this description of individual and aggregate prices, the underlying responsiveness of individual and aggregate prices to the exchange rate can be characterized as follows:

   [[Gamma].sub.i] = [Delta]E{[f.sub.i][[e.sub.t], [m.sub.t], [z.sub.it]] [where] [I.sub.t]} / [Delta]e, and [Gamma] = [integral of] [[Alpha].sub.i][[Gamma].sub.i] di between limits of 1 and 0.

   When monetary policy is unrelated to exchange rate movements, these parameters, [[Gamma].sub.i] and [Gamma], can be estimated directly.

   In practice, measuring the impact of exchange rate changes on domestic prices may be complicated by the actions of the central bank. The monetary policies of many countries respond to changes in the exchange rate, even if only implicitly. That is, often dm([g.sub.t]) d[e.sub.t] [not equal to] 0. In such cases, the exchange rate affects prices in two ways. It affects prices directly, through the parameters [[Gamma].sub.i] and [Gamma], and it affects prices indirectly through its influence on monetary policy,

   [Delta][p.sub.it]/[Delta]m([g.sub.t]) dm([g.sub.t)/d[e.sub.t] and [Delta][p.sub.t]/[Delta]m([g.sub.t]) dm([g.sub.t])/d[e.sub.t].

   Ignoring the role of monetary policy will lead to misleading measures of the underlying responsiveness of prices to exchange rate changes. This problem affects estimates of the responsiveness of both individual prices and the aggregate price index.

   Consider a central bank that chooses its policy in order to dampen the effect of the exchange rate on the aggregate price level. If the central bank offsets the aggregate price response by a factor of [Theta], where 0 [less than or equal to] [Theta] [less than or equal to]1, then the monetary policy response to the exchange rate can be expressed easily. To simplify notation, let [[Delta].sub.i] and [Delta] denote the individual and aggregate responses of prices to monetary policy; that is, [[Delta].sub.i] = [Delta][p.sub.it]/[Delta]m([g.sub.t]) and [Delta] = [Delta][p.sub.t]/[Delta]m([g.sub.t]) The monetary response to a change in the exchange rate is then dm([g.sub.t])/d[e.sub.t] = -[Theta][Gamma]/[Delta]. Correspondingly, the apparent responses of prices to exchange rates will differ from their underlying responses. While the underlying aggregate response is [Gamma], the apparent aggregate response will be (1 - [Theta])[Gamma]. In the extreme case, where [Theta] = 1, aggregate prices can appear to be completely unresponsive to the exchange rate.

   The response also may be understated for many individual prices.(8) While the underlying response of the ith price is [[Gamma].sub.i], the apparent response will be: [[Gamma].sub.i] - [[Delta].sub.i][Theta][Gamma]/[Delta], which has a smaller magnitude than [[Gamma].sub.i] when [[Delta].sub.i] and [Delta] are positive. Moreover, for some goods, the apparent response will be positive, despite the underlying negative relationship between prices and the exchange rate. When expected monetary policy is ignored, such a response of the wrong sign can appear among those goods whose prices depend relatively little on the exchange rate. That is, individual prices will appear to respond perversely to exchange rate fluctuations when [absolute value of [[Delta].sub.i]] [less than] [absolute value of [[Delta].sub.i][[Theta].sub.[Gamma]/[Delta]].

   Such understatements of the underlying effects also occur in more general models that treat the exchange rate movements as endogenous. Suppose, for example, that the exchange rate depends on monetary...