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

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 policy in the following way:

[e.sub.t] = h([g.sub.t], [w.sub.t]) (3)

where [w.sub.t], represents those variables other than monetary policy that affect the exchange rate;(9) and [Delta][h.sub.it]/[Delta][w.sub.t] [greater than] 0 and [Delta][h.sub.it]/[Delta][g.sub.t] [less than] 0. Prices now can be represented by:

[p.sub.t] = E{[f.sub.i][h([g.sub.t], [w.sub.t]), m([g.sub.t]), [z.sub.it]] [where] [I.sub.t]}, (4)

and,

[p.sub.t] = [integral of] [[Alpha].sub.i] E{[f.sub.i][E[h([g.sub.t], [w.sub.t]), m([g.sub.t]), [z.sub.it]] [where] [I.sub.t]} [d.sub.i] between limits of 1 and 0 (5)

In this case, monetary policy can moderate aggregate price level fluctuations, not only by offsetting the effect of changes in the exchange rate, but also by influencing the exchange rate itself. To insulate inflation from changes in the exchange rate by a factor of [Theta], the central bank will choose:

dm([g.sub.t])/d[w.sub.t] = [Theta][Gamma]([Delta][h.sub.t]/[Delta][w.sub.t]) / [Delta] + [Gamma]([h.sub.t]/[Delta][g.sub.t])/[[Delta]m([g.sub.t])/[Delta][g.sub.t]].

For example, in response to a change that would cause the exchange rate to, say, depreciate, the central bank might tighten monetary policy enough to strengthen the currency somewhat and to moderate the impact that the remaining depreciation has on prices.(10) Again, if monetary policy is ignored, the effects of the exchange rate on aggregate and individual prices may appear smaller than the underlying effects.

3. Estimation of the Responsiveness of U.S. Domestic Prices to the Exchange Rate

The price expressions given by Equations 1 and 2 provide the basis for an empirical examination of domestic prices. In this section, we study the responses of the U.S. prices of a sample of nondurable consumer goods and services to exchange rate changes. To the extent that these goods and services are nontradeables, the exchange rate influences their prices only indirectly.(11) The indirect influence may come through changes in the prices of imported inputs, through changes in the foreign demand for related products, and through exchange-rate-related changes in aggregate economic conditions.(12) Although one might expect these indirect influences to be small, we nevertheless find a significant empirical role for the exchange rate in all of the price formulations that we examine below - even among the least traded items of all, services. Moreover, as predicted by our discussion in section 2 above, the size and significance of the exchange rate in the price equations depends on the inclusion of a gauge of monetary policy.

We begin by estimating a simple, traditional exchange rate pass-through equation. It is traditional in the sense that, like many related studies, it embodies a partial equilibrium approach to examining the response of prices to exchange rate changes. Unfortunately, the partial equilibrium approach has the drawback that it does not allow for the endogenous determination of expected changes in exchange rates and monetary policy that we described in the preceding section.(13) So, after estimating the relationship in this partial equilibrium framework, we also use two other approaches that are better suited to estimation in the presence of dynamic endogeneity. These additional approaches are (i) an error correction model augmented with leads and lags of the differences in the regressors (following Phillips and Loretan 1991) and (ii) a VAR.

We study a panel of individual, domestic prices sampled quarterly from 1975 through 1992. Individual prices are taken from the American Chamber of Commerce Researchers Association's Cost of Living Index. They include the prices of 32 final goods sold in 48 U.S. cities.(14) The goods include predominantly nondurable consumption items and services, with varying degrees of tradeability. The use of a broad spectrum of domestic goods and services prices (as opposed to import or export prices) should enhance our ability to identify any central bank response to exchange rate movements. The nominal effective exchange rate is taken from the International Monetary Fund's (IMF's) International Financial Statistics. The exchange rate is defined in terms of the trade-weighted value of the dollar, and the weights are determined in the IMF's Multilateral Exchange Rate Model.(15) The domestic aggregate price level is represented by the consumer price index. To gauge monetary policy, we focus on the growth of M2.(16) However, our results do not appear to be dependent on this monetary measure: some experiments using alternative measures, including the Bernanke-Mihov (1995) measure of the stance of monetary policy, led to qualitatively similar results.(17) The vector z includes real gross domestic product (GDP) and the price of oil. Observations of the domestic aggregate price level, real GDP, and monetary aggregates are taken from FAME. In all three approaches, Equations 1 and 2 are assumed to be linear in logs, and we treat each of the variables in the estimation as if it possesses a single unit root.(18) Finally, the expected values of future variables are measured using their realized values.(19)

Beginning with the partial equilibrium approach, we estimate specifications of Equations 1 and 2, both including and excluding a measure of monetary policy. Specifically, we estimate the following equations for individual and aggregate price changes:

[Mathematical Expression Omitted] (6)

[Mathematical Expression Omitted], (7)

where [d.sub.i] and d are matrices of city and seasonal dummies; [Delta][p.sub.it], represents the change in the log of the price of the ith good; [Delta][p.sub.t] is the overall rate of inflation; [Delta][e.sub.t], is the rate of appreciation of the dollar; [Delta][m.sub.t] is the rate of growth of money; and, [Delta][z.sub.t] includes the rate of growth of GDP and the log difference in the price of oil. Lags of two years (L = 8) were included to adequately model the equations' dynamics.(20) We are most interested in the estimated value and significance of the coefficients on the contemporaneous and lagged exchange rate changes and whether the inclusion of [Delta][m.sub.t] affects the estimates.

Table 1 presents results from the estimation of Equations 6 and 7, first excluding money from the equation, then including it. As predicted, the estimates are more negative (and more often significantly so) when money is included. Column 1 gives the estimate of the sum of the coefficients on the contemporaneous and lagged exchange rate change when money is excluded from each price equation; Column 2 gives its standard error. In discussing these estimates, we must keep in mind their partial equilibrium nature, which precludes all but the most tentative inferences. As Table 1 shows, the individual estimates range from -1.78 for potatoes to 0.68 for coffee. Four (out of 32) of the individual estimates are positive (the "wrong" sign) and statistically significant. Among services, only one (dry cleaning) has a significant negative estimate. Finally, the aggregate estimate is -0.08.

The next few columns report the estimates when money is included. The importance of having omitted money growth depends largely on the link between money and the individual prices. Columns 3 and 4 give an indication of these links. Column 3 gives the sum of the coefficients on the contemporaneous and lagged growth of money for each equation, and column 4 gives their standard errors. We would expect price increases and money growth to be positively related. Indeed, although we find negative estimates for some of the items (none is significant), the individual estimates are predominantly positive, and the aggregate estimate is positive and statistically significant.

The exchange rate estimates themselves are given in columns 5 and 6. Overall, the individual price estimates are more negative than they were when money growth was excluded from the equations. The range is now delineated by potatoes and cigarettes. Now the exchange rate estimate in the potato equation is even more negative, -2.54, while the estimate in the cigarettes equation is virtually unchanged at 0.26. The estimate for cigarettes is the only statistically significant estimate that is of the wrong sign. Among services, we find three with significant negative coefficients. Finally, the estimate in the Consumer Price Index (CPI) equation is -0.14, which is considerably more negative than the earlier estimate of -0.08.

The empirical importance of considering monetary policy actions can be seen most directly in the final columns, which give the differences between column 1 and column 5 (the estimates including money less the estimates excluding money), and their significance levels. Having argued that the exchange rate link would be masked when monetary considerations were omitted, we should expect these differences to be negative. We find the differences to be negative for 20 of the 32 individual items. The differences are significant at the 10 percent level for ten of the individual items, of which all but two have negative estimates. The evidence from the CPI equation is also consistent with the argument that ignoring money masks the exchange rate link: the difference is -0.06, which is quite large compared with the original estimate of -0.08, and is significant at all conventional confidence levels.(21)

The results reported in Table 1 give us a clear indication of the implications of omitting the influence of monetary policy from such partial equilibrium equations. However, we cannot interpret them in terms of the influence of exchange rates on prices, even with money growth included in the equations, because the estimates are likely to be biased by the endogeneity of monetary policy and the exchange rate. Moreover, conventional theory tells us that the levels of these variables are linked in the long run, so we would like to estimate the price equations in an error correction framework.(22) One approach to addressing endogeneity problems in such a framework has been examined carefully by Phillips and Loretan (1991). Essentially the endogeneity implies contemporaneous correlation between regressors and the regression error. They demonstrate that leads of the differenced endogenous regressors must be included in order to eliminate the asymptotic estimation bias.(23) Following Phillips and Loretan, we estimate a single equation error correction model in levels, augmented with leads and lags of differences in the regressors.(24)

Specifically, we estimate the parameters in the following equations:

[Mathematical Expression Omitted] (8)

[Mathematical Expression Omitted] (9)

where [p.sub.it], [p.sub.t], [e.sub.t], [m.sub.t] are defined as the logs of the ith price, the CPI, the exchange rate, the money supply; [z.sub.t] includes the logs of real GDP and the price of oil; [d.sub.i] and d are (as before) matrices of city and seasonal dummies; and [x.sub.t] = ([e.sub.t] - [e.sub.t-1], [m.sub.t], - [m.sub.t-1], [z.sub.t] - [z.sub.t-1]).

[TABULAR DATA FOR TABLE 1 OMITTED]

[TABULAR DATA FOR TABLE 2 OMITTED]

We estimate these equations, both with and without money, and we examine the implications for the estimate of the exchange rate coefficients. We focus here on the contemporaneous impact, rather than longer-term links. Although the coefficient on the error correction term captures the long-term links, it also involves more than just a response to exchange rate changes. So, to isolate one aspect of the apparent effect of exchange rates on prices, we examine only the short-term effect. (We use the VAR specification, described at the end of this section, to reconsider the apparent effect over time.)

Table 2 reports these results. Overall, we find that, as predicted, the exchange rate coefficients again are more often negative (and statistically significantly so) when money is included. In both specifications, the estimates are generally smaller in magnitude than those reported in Table 1. This reflects both the focus on the short-term response and the removal of other endogenous influences.(25) As before, we expect the estimates to be most muted when money is excluded. These estimates are given in the first column, and their corresponding standard errors are given in the second column. The estimates now range from -0.64 for hamburger to 0.37 for shortening. The CPI estimate, although statistically significant, is only -0.013.

The next four columns give the estimates that result from including money in Equations 8 and 9. Columns 3 and 4 give the coefficients on contemporaneous money and their standard errors. Like the coefficient on the contemporaneous exchange rate, the coefficients on money are smaller than their counterparts in Table 1, and they are positive in 22 of the 32 individual price equations. The coefficient on contemporaneous money in the CPI equation is positive and statistically significant (0.61).

Columns 5 and 6 give the exchange rate coefficients and their standard errors. Again, the coefficients often are smaller in magnitude than their counterparts in Table 1. However, as before, the inclusion of money lowers the range of estimates: including money, the range extends from -0.88 (bacon) to 0.41 (shortening). Meats and potatoes are again among the items for which the exchange rate coefficients are most negative. Among services, the estimates are slightly smaller, but all of them are negative, and all but one are significant; they range from -0.16 to -0.02. The CPI estimate is -0.11 and is statistically significant.

The final two columns illustrate the importance of considering money growth most clearly. Column 7 gives the differences between columns 1 and 5 (the estimates including money less the estimates excluding money), and column 8 gives the significance level of those differences. As before, we expect these differences to be negative. We find the differences are negative for 23 of the 32 items. Of these, 15 are statistically significant at the 10% confidence level. For the CPI, the change in the exchange rate coefficient, although small in absolute terms, moves strongly in the predicted direction and is highly significant. Overall, the estimates reported in Table 2 confirm the model's prediction that the observed link between exchange rates and prices is muted when the effects of monetary policy are ignored.

The final empirical specification that we use is a VAR. The VAR (like the first specification) allows us to examine the apparent response of price changes to lagged exchange rate fluctuations. At the same time (like the second specification), it also provides a different method for separating the influence of the exchange rate from the influence of changes in other endogenous variables. In this way, the VAR approach combines aspects of each of the first two specifications. Again, we estimate the links between prices and the exchange rate, and as before, we examine whether the estimates are affected by the omission of money.

Specifically, we estimate a three-equation system for each of the 32 goods and services and for the CPI. Each system includes the price of oil and real GDP as deterministic variables, and we include four lags of all variables, as well as city and seasonal dummies in all equations.(26) In keeping with our earlier discussion, we focus on the price equations. We first estimate the VAR with money omitted, then we estimate the full VAR, including money. In each case, we examine the response of each price to an exchange rate innovation. Finally, we compare the two sets of estimated responses.

Figure 1 summarizes the results. Again, the results conform to the prediction that price responses appear smaller when money is omitted. The first two panels show the estimated cumulative impulse responses to an exchange rate disturbance for up to 16 quarters. The panels' solid lines give the median responses of the 32 individual items, the short-dashed lines give the 25th and 75th percentile responses of these items, and the long-dashed lines give the estimated CPI response in each case. Both including and excluding money, the estimated cumulative responses all are substantially smaller in magnitude than those reported in Table 1, even after more than two years.(27) This is to be expected, since the original, partial equilibrium approach does not control for endogenous changes in other variables over time. In contrast, the VAR estimates reflect responses only to those exchange rate movements that are orthogonal to movements in the other variables in the system.

The top panel in Figure 1 gives the responses estimated in the VAR that excludes money. The estimated cumulative responses are predominantly negative, and they intensify for most of the first four years following the exchange rate disturbance. After two years, the estimated median cumulative response is -0.024, and the estimated aggregate response is -0.034. The middle panel gives the estimates from the VAR that includes money. Again, the estimates are predominantly negative, and they intensify for most of the first four years following the disturbance. Consistent with the discussion of the model and with the results reported in Tables 1 and 2, the estimated cumulative responses shown here are stronger than those shown in the top panel. Including money, the median estimated response is -0.036, and the estimated aggregate response is also -0.036. The bottom panel gives the differences between the estimated responses. As predicted, the differences are predominantly negative. Like the underlying cumulative responses, the differences become more negative over time. After two years, the change in the median estimate is -0.010, and the change in the CPI estimate is -0.002. After four years, the differences become -0.030 and -0.008. Like Tables 1 and 2, these panels indicate that the nondurable goods and services we examine respond modestly to exchange rate changes and that the inclusion of a measure of monetary policy makes a difference in our ability to observe those responses.

4. Conclusions

The omitted variable problem described in this paper is a common one. As is well known, the effects of the economic policies that shape economic variables of interest sometimes mask relationships between those variables. Ignoring the policy dependence when examining those variables can lead to misleading inferences. In assessing the impact of exchange rate movements on prices, it is particularly important to consider monetary policy. Central banks that are primarily concerned with domestic prices will use monetary policy to try to insulate those prices from exchange rate changes, so prices can seem correspondingly unresponsive to changes in the exchange rate. The observed relationships between prices and the exchange rate will reflect central bank actions instead of the underlying relationship between exchange rates and prices. Inferences about firm behavior or market structure drawn from the observed relationships between prices and the exchange rate will be incorrect when the observed relationship is an outcome of economic policy. This paper explicitly recognizes the role that policy plays in determining the observable relationships between exchange rates and prices, and in so doing, it illustrates how the underlying relationships can be unraveled. Examining the recent experience of the United States, we find that the prices of various nondurable goods, and even of some services, respond modestly to the exchange rate, and we find that the responses emerge most clearly when the role of monetary policy is explicitly considered. These findings are consistent with the hypothesis that the Federal Reserve acts to mitigate the effects of exchange rate fluctuations on domestic prices.

We would like to thank Menzie Chinn and Ken Kasa for their comments on early drafts of this paper and David Papell for this thoughtful editorial suggestions. We also are grateful for the financial support of the Owen Graduate School off Management and the Leavey School of Business.

1 Menon (1995) provides a recent survey of the exchange rate pass-through literature. See also Kasa (1992), Knetter (1993), and Mann (1986).

2 Dornbusch (1987, p. 93), for example, explains the size of the adjustment of prices "in terms of the degree of market concentration, the extent of product homogeneity and substitutability, and the relative market shares of domestic and foreign firms." Fisher (1989) explores the role of market concentration, and Menon (1996) emphasizes the role of nontariff barriers and multinational corporations. Feenstra, Gagnon, and Knetter (1993) and Marston (1990) also investigate the relationship between pass-through and market structure. Other explanations of less than full adjustment include those of Hooper and Mann (1989), who emphasize the poor quality of data, Froot and Klemperer (1989) and Parsley (1995), who suggest that incomplete pass-through also may stem from the dependence of market share on its past, and Giovannini (1988), who shows that menu costs also lead to incomplete pass-through.

3 The approach of this paper builds on the earlier work of Krugman (1978), Pigott, Rutledge, and Willett (1985), and Hung, Kim, and Ohno (1993), who examine the links between exchange rates and prices in the presence of endogenous monetary policies or exchange rates. Following Krugman, who allows the exchange rate to affect monetary policy, we examine the implications of a monetary authority primarily concerned with price stability. At the same time, like Pigott, Rutledge, and Willett and Hung, Kim, and Ohno, we allow monetary policy to affect the exchange rate.

4 Producers are treated here as though they each have the same information on which to form their expectations of monetary policy. One could allow producers' information sets to differ by an idiosyncratic component with only slight modifications to the approach used here. but that would add little insight into the concerns of this paper.

5 Feenstra, Gagnon, and Knetter (1993) provide a useful specification for the case of a differentiated product.

6 That is, monetary policy may affect demand, hence marginal revenue.

7 Although the direct effect of monetary policy may be unimportant in this case, it may still play a role through its effect on the exchange rate. That possibility is discussed below.

8 The biases we report in section 4 are predominately negative; however, the omitted variable bias arising from excluding monetary policy in principle could be positive. This would be the case when, for example, the exchange rate is a random walk and monetary policy enters linearly into the pricing equation only as an indicator of expected future prices.

9 This vector may include both domestic and foreign variables.

10 Consider an increase in [w.sub.t] when [Delta]h/[Delta][w.sub.t-] [less than] 0. Then, the numerator, -[Theta][Gamma]([Delta][h.sub.t]/[Delta][w.sub.t]) is negative. The denominator is positive because [Delta][h.sub.t]/[Delta][g.sub.t] and [Delta]m/[g.sub.t] are of opposite signs and [Gamma] [less than] 0. So, dm([g.sub.t])/d[w.sub.t] [less than] 0 when [Delta][h.sub.it]/[Delta][w.sub.t] [greater than] 0.

11 Of course, the dividing line between tradeables and nontradeables is indistinct. As Obstfeld and Rogoff (1996, p. 203) write: "Even a seemingly highly traded good, such as a banana at the supermarket, comes bundled with a large component of nontraded inputs: local transportation, supermarket space, check-out clerks, and so on." Our sample includes the prices of numerous such "traded" goods, including bananas, as well as the prices of several services.

12 See Woo (1984) for a clear exposition of the channels by which the exchange rate can affect prices.

13 Nor does it allow for the endogeneity described by Krugman (1978), Pigott, Rutledge, and Willett (1985), Hung, Kim, and Ohno (1993), or Popper and Lowell (1994).

14 This data set is described in detail in Parsley (1996).

15 Many related studies measure the response of prices (whether nominal or relative) to changes in the real exchange rate, rather than the nominal rate. We examine nominal prices and exchange rates here because of our focus on the role of the central hank and its concern with price stabilization. This approach also allows us to avoid imposing the constraint that the impacts on prices of the nominal exchange rate and the foreign price level are the same. However, the extremely high correlation between real and nominal exchange rates diminishes the importance of this distinction. Examining the sensitivity of our estimates to the use of the nominal rate, we find that the results differ little. More details are given in the discussion of each set of results.

16 The work of Feldstein and Stock (1996) supports the use of a monetary aggregate for the period we study.

17 Bernanke and Mihov's gauge is a broader one, reflecting both changes in the federal funds rate and changes in reserves.

18 We rely on the work of others, who have repeatedly failed to reject unit roots in these variables, so we do not repeat those tests here (e.g., Chinn and Meese 1993, Papell 1997).

19 Although in principle, the expected exchange rate may depend on many other variables, there has been little empirical support for more complicated representations. This approach is consistent with both rational expectations and the apparent unit root behavior of the data.

20 Using only four lags has little overall impact on the results.

21 The results are similar when the real exchange rate is used: The differences are negative for 18 of the 32 items; the differences are significant for nine of them (again, only one is positive); and the difference (again, 0.06) is negative and highly significant for the CPI equation.

22 For surveys of the long-run links implied by purchasing power parity (see Breuer 1994; Froot and Rogoff 1995).

23 We focus on specifications using one lead, one contemporaneous first difference, and one lag of the endogenous variables because tests indicate this is sufficient to render the residuals white. Sensitivity tests indicate this choice is not crucial.

24 Note that this estimation is asymptotically equivalent to typical error correction specifications that include first differenced regressand and regressors.

25 See Papell (1994) for a similar finding and discussion.

26 The inclusion of eight lags did not substantively alter the results.

27 That is, this difference in magnitude occurs despite the fact that the estimates in Tables 1 and 3 allow for a link between prices and lagged exchange rates.

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