# DO GERMAN, JAPANESE, AND U.S. EXPORT PRICES ASYMMETRICALLY RESPOND TO EXCHANGE RATE CHANGES? EVIDENCE FROM AGGREGATE DATA.

SAEID MAHDAVI [*]

This article estimates the responses (elasticity coefficients) of the export price index to appreciation and depreciation of the nominal effective exchange rate using quarterly data (1973:1-1997:2) for Japan. Germany, and the United States. Cross-county comparisons of the elasticity magnitudes based on the statistically superior of the estimated models indicate that Japanese exporters, in the aggregate, have the highest tendency to dampen the effects of exchange rate fluctuations on the foreign currency export prices in both directions by adjusting their home currency prices. Intracountry comparisons provide some evidence of an asymmetric adjustment in export prices in the cases of Japan and Germany. (JEL F31)

I. INTRODUCTION

The "Plaza Agreement" among the G-5 finance ministers in 1985 led to a sudden reversal of the U.S. dollar's steep climb during the first half of the 1980s. The agreement was intended to improve the large and rising U.S. trade deficits by depreciating the dollar. However, despite the dollar's equally steep fall from its peak value in 1985, subsequent improvements in the U.S. trade balance turned out to be rather sluggish. In fact, the U.S. trade deficits remained quite large in the second half of the 1980s and the 1990s. This is in sharp contrast to the large trade surpluses of Germany and Japan that persisted even in the face of appreciating (nominal and real) effective exchange rates of mark and yen over much of the modern floating period.

One of the explanations for the sluggish response of the U.S. trade balance to changes in the dollar's exchange rate rests on the incomplete pass-through of the depreciation of the dollar to the U.S. import and export prices. This phenomenon is in turn explained by the dollar invoicing of some U.S. imports, currency hedging, outsourcing by some foreign exporters, and differences in markup adjustment practices between foreign and the U.S. exporters. Several authors (e.g., Kvasnick, 1986; Mann, 1986; Hervey, 1988; Ohno; 1989; Martson, 1990) emphasized the role of markup adjustment in the context of what Krugman (1987) termed the "pricing-to-market" (PTM) behavior. The latter suggests that, to keep stable the dollar price of their export, some foreign exporters use markup/ profit margins to (partially) absorb the shock of fluctuations in the exchange value of their home currency vis-a-vis the dollar. Strategic considerations such as market share in export destinations in the face of both demand and exchange rat e uncertainties may motivate this behavior. In this connection, if the foreign exporters try, for example, to maintain their market share during periods of home currency appreciation and try to increase it during periods of depreciation, then the adjustment in export prices will be asymmetric. PTM is thus expected to be more pronounced during the appreciation periods as the exporters cut the home currency prices of their exports by more than they raise them during the depreciation periods. [1]

In a pioneering study, Mann (1986) provided evidence supporting profit margin adjustments of the type described above by foreign exporters over the 1977-81 period of the dollar's depreciation and the 1982-85 period of the dollar's appreciation. Mann's analysis suggested that, in the aggregate, U.S. exporters were relatively insensitive to the exchange rate changes and did not change their profit margins in either of the two periods. Interestingly enough, evidence from disaggregated data indicated that some U.S. exporters even increased their profit margins as the dollar appreciated.

Subsequent studies of PTM mostly employed industry-level data. Knetter (1989) analyzed the quarterly data on the U.S. and German seven-digit export industries and found evidence of more pronounced country-specific adjustments in reaction to the exchange rate fluctuations by German exporters than U.S. exporters. Moreover, his results indicate that while such adjustments had a dampening (or stabilizing) effect on the foreign currency prices of German exports, they had an amplifying (or exacerbating) effect on foreign currency prices of U.S. exports. Martson's (1990) study focused on the pricing behavior of some Japanese transport and consumer manufacturing firms and found evidence of an asymmetric response for five products as predicted by the "market share" model. Knetter (1994) noted that when exporters face bottlenecks due to marketing capacity constraints and/or binding quantitative restrictions in their export destinations, an asymmetric response pattern that is opposite of the kind predicted by the "mark et share" model may be observed. The underlying argument is that, in order for the exporters to clear a supply-side constrained export market, they need to raise the home currency prices of their exports as the home currency depreciates to (partially) offset the fall in their foreign currency prices. However, since the supply-side constraints are not binding when the home currency appreciates, PTM is expected to be larger during periods of depreciation than appreciation. [2] Knetter's estimates of export price elasticities using panel data on several seven-digit German and Japanese industries did not support an asymmetric response in most cases. But in cases where he found evidence of asymmetry, it was mostly consistent with the market share hypothesis. Finally, based on their analysis of German, Japanese, and U.S. automobile export prices, Gagnon and Knetter (1995) concluded that evidence of markup adjustment behavior was the strongest in the case of Japanese exports and the weakest in the case of U.S. expor ts.

The industry-level studies of the export price response to variations in the exchange rate are helpful in identifying the specific industries that exhibit an asymmetric response. However, due to the narrow scope of the data employed in these studies, the implications of their results for the overall trade balance are rather limited. An empirically interesting question to investigate, therefore, is whether the export price index asymmetrically responds to episodes of appreciation and depreciation in the nominal effective exchange rate. In this article, I use aggregate data from the three major trading countries of Germany, Japan, and the United States to (i) determine the extent to which the exporters in each country collectively tend to neutralize the impact of the exchange rate fluctuations on the foreign currency prices of exports by adjusting the home currency price of their exports and (ii) compare the pattern of asymmetric responses (if any) across the three countries to see if they differ in their emph asis on stabilizing export prices during periods of home currency appreciation ver sus depreciation as some micro-level studies seem to suggest. Our results may help explain the observed differential impacts of currency fluctuations on the trade balance across the three countries. [3]

This article is organized as follows. Section II focuses the analytical framework of the article, which includes the cointegration analysis and error correction modeling of the relationship between the export price index and the effective exchange rate. Section III presents the empirical results. The last section summarizes the empirical findings of the article and provides some concluding remarks.

II. THE ANALYTICAL FRAMEWORK

The building block of our empirical analysis is an export-price equation derived by Hung et al. (1993) from a model in which a profit-maximizing producer is assumed to operate under constant returns and exports exclusively to imperfectly competitive foreign markets:

(1) In [[P.sup.h].sub.t] = [[eta].sub.0] + [[eta].sub.1] In [[C.sup.h].sub.t] + [[eta].sub.2] In [[P.sup.f].sub.t] + [[eta].sub.3] In [E.sub.t] + [V.sub.t].

In Equation (1), the export price in home currency (i.e., the exporter's currency) at time t ([[P.sup.h].sub.t]) is modeled as a function of domestic unit cost of production ([[C.sup.h].sub.t]), the price of foreign competing goods in foreign currency unit ([[P.sup.f].sub.t]), the nominal exchange rate ([E.sub.t]), and an error term ([V.sub.t]). The theoretical model behind Equation (1) establishes that (i) [[eta].sub.1] (i.e., the elasticity [[P.sup.h].sub.t] with respect to changes in [[C.sup.h].sub.t]) is inversely related to the relative price elasticity of markup and (ii) the smaller is [[eta].sub.1] the larger is [[eta].sub.3] (i.e., the elasticity [[P.sup.h].sub.t] with respect to changes in [E.sub.t]). [4] In the case of an economy with a relatively large domestic market and significant price-setting power in the world market (such as that of the United States), the price elasticity of markup is expected to be relatively low. This implies that the export price is more influenced by changes in domestic cost (relatively high [[eta].sub.1]) than changes in the foreign competitors' prices (relatively low [[eta].sub.3]). The opposite is predicted for the exporters from relatively smaller and more open economies (such as those of Germany and Japan) that have less price-setting power in their export markets.

I specify the following aggregate version of Equation (1) using proxies for the export price, domestic unit cost, foreign price, and the exchange rate variables:

(2) ln XPI

= [[beta].sub.0] + [[beta].sub.1] In[(ULC).sub.t] + [[beta].sub.2] In[(FPI).sub.t] + [[beta].sub.3] In[(EXR).sub.t] + [e.sub.t],

where XPI is the export price (or export unit value) index in the exporting country's currency, ULC is unit labor cost (a proxy for the domestic cost of production), FPI is a trade-weighted average of the wholesale price indexes of the exporting country's major trading partners (a proxy for the foreign price level), EXR is an index of effective nominal exchange rate (i.e., a trade-weighted average of the bilateral exchange rates between the exporting country and its major trading partners defined such that an increase in its level is associated with an appreciation of the home currency), and e is an error term. (See Appendix for more detailed explanations and data sources.)

As Hung et al. (1993) have pointed out, Equation (1) (and its aggregate version) can best be interpreted as a long-term relationship, for it does not incorporate dynamic adjustments. To specify a model of dynamic adjustments without losing the information contained in the long-term relationship due to differencing of the levels of the variables, one needs to specify an error correction model (ECM). To this end, I first test the variables in Equation (2) for nonstationarity. If the variables are found to be first-difference stationary, or integrated of degree one, I(1), then there may exist one (or more) linear combination of the variables (referred to as a cointegration equation) that is stationary, or I(0) (Engle and Granger, 1987). A one-period lagged value(s) of the residuals obtained from the cointegration equation can be incorporated into a dynamic version of Equation (2), yielding an ECM of the following form:

(3) [delta] ln[(XPI).sub.t-i]

= [delta] + [[[sigma].sup.k-1].sub.i=1] [[omega].sub.i] [delta] ln[(XPI).sub.t-i]

+ [[[sigma].sup.k-1].sub.i=1] [[phi].sub.i] [delta] 1n[(ULC).sub.t-i]

+ [[[sigma].sup.k-1].sub.i=1] [[gamma].sub.i][delta] ln[(FPI).sub.t-i]

+ [[[sigma].sup.k-1].sub.i=1] [[theta].sub.i] [delta] 1n[(EXR).sub.t-i]

+ [[[sigma].sup.r].sub.j=1] [[phi].sub.j] [([EC.sub.j]).sub.t-1] + [[epsilon].sub.t],

where [EC.sub.j] is the residual from the jth cointegrating equation. In Equation (3), the short-term change in the export price index in part reflects a correction of the deviation from the long-term equilibrium relationship in the previous period. I employ Johansen's maximum likelihood procedure (Johansen, 1988; Johansen and Juselius, 1990) to estimate the parameters of Equation (2). This procedure provides a unified framework for testing the number and parameters of the cointegrating vector(s). Then the parameters of Equation (3) are estimated using the residuals of Equation (2) as the values of the error correction term.

Of particular interest are the signs and magnitudes of the estimated coefficients of the 1n(EXR) variable in Equation (3). If exporters in the aggregate adjust their export prices to stabilize the foreign currency prices of their exports in response to fluctuations in the exchange rate, then the sum of the [theta]s is expected to be negative. As [theta]s are constrained to be the same for both positive and negative changes (appreciation and depreciation, respectively) in the exchange rate variable, Equation (3) implicitly assumes a symmetric response of the export price index to the exchange rate changes. To test for an asymmetric response, we define two new variables, [[delta].sup.+] 1n(EXR) and [[delta].sup.-]1n(EXR), representing positive and negative changes in the exchange rate variable, respectively. More formally,

[[delta].sup.+] ln(EXR) = [delta] 1n(EXR) if [delta] 1n(EXR) [greater than] 0,

0 if [delta] ln(EXR) [less than or equal to] 0;

[[delta].sup.-] ln(EXR) = [delta] ln(EXR) if [delta] ln(EXR) [less than] 0,

0 if [delta] ln(EXR) [greater than or equal to] 0.

Thus, a variant of Equation (3) that allows for asymmetric responses can be specified by replacing the [delta] ln(EXR) variable by the two new variables and conducting tests of hypothesis on the sum of their coefficients (represented by [sigma][[theta].sup.+] or [sigma][[theta].sup.+] for positive and negative changes in the exchange rate, respectively).

Statistical evidence consistent with an asymmetric response is said to exist if either [sigma][[theta].sup.+] or [sigma][[theta].sup.-](or both) is significantly different from zero and the difference between the two sums is also significantly different from zero. If both sums are found to be statistically insignificant (implying that the home currency prices of exports remain unchanged in the face of the exchange rate changes), then changes in the exchange rate are fully passed through to the foreign currency price of exports. Finally, note that the "market share" model of export price behavior implies a large (close to one and statistically significant value of [sigma][[theta].sup.+] and a small (close to zero) and/or statistically insignificant value of [sigma][[theta].sup.-]. The opposite is implied when the export supply is constrained by bottlenecks and/or trade restrictions.

III. EMPIRICAL RESULTS

For each of the three countries of Japan, Germany, and the United States we collected data on the variables in Equation (2) over the period 1973:1-1997:2. Since the time series of the variables are suspected to be nonstationary, we tested them for nonstationarity using the augmented Dickey-Fuller (ADF) tests (Dickey and Fuller, 1979). Table 1 summarizes the results of the ADF unit root tests. The results suggest that in all but two cases the null hypothesis that the variables are nonstationary in level cannot be rejected at the 5% level of significance for the lag lengths indicated. (The first differences of all the variables are stationary; results are not reported here.) The two exceptions are the variables In(XPI) and In(ULG) for Japan that seem to be trend stationary. The ADF test statistics at higher lag lengths for the two variables, however, are not large enough to reject the null of nonstationarity. I proceed to perform the cointegration tests assuming that these variables are I(1). [5,6]

The results of cointegration tests applied to Equation (2) are presented in Table 2. [7] For each country, the table shows the values of likelihood-ratio test statistics ([[lambda].sub.max]) based on the maximal eigenvalue of the stochastic matrix in Equation (3) for the lag lengths indicated (see table note a). Since there are four variables in Equation (2), there can be a maximum of three cointegrating relationships among the variables. Four null hypotheses, therefore, can be tested on the number of cointegrating vector (or r). According to the values of [[lambda].sub.max], the null hypothesis of r = 0 can be rejected in favor of r = 1 for all the three countries. Since the null of r = 2 and 3 are rejected, the test results suggest that there is only one cointegrating vector among the four variables. The normalized value of the estimated coefficient of the exchange rate variable has a negative sign in the cointegrating vector for all the three countries. This is consistent with a response on the part of ex porters aimed at stabilizing the foreign currency price of exports. Note, however, that this coefficient is not statistically significant in the case of United States, suggesting that the exchange rate variable may not be part of a long-term equilibrium relationship represented by Equation (2). Since there is one cointegrating vector for each country, only one error correction term enters Equation (3).

Table 3 presents the estimated parameters of three variants of Equation (3) for each country. Model 1 decomposes changes in the exchange rate variable into positive and negative ones to test for asymmetric responses. Model 2 replaces the last lagged value of all the variables (with the exception of the export price index) by the corresponding contemporaneous value. The inclusion of the contemporaneous values seems to be justified in view of the quarterly nature of the data and the fact that those export prices that are invoiced in foreign currency terms change automatically with the change in the exchange rate. Model 3 presents a parsimonious version of Model 2 by employing the "finite prediction error" (FPE) criterion proposed by Akike (1970) in conjunction with the "specific gravity" criterion proposed by Caines et al. (1981) to select the "best" lag combination. Briefly, the FPE criterion balances the costs of overparameterizing a model with the cost of underparameterizing it and, thus, recognizes the tra de-off between bias and efficiency in the estimation process. The specific gravity criterion uses the FPE criterion to determine the order in which variables enter the model after the lagged values of the dependent variable have been included. Comparisons of the Models 1-3 enable testing for the sensitivity of the estimated results to alternative lag structures. Table 3 also reports the conventional measure of goodness of fit along with the statistics for two diagnostic tests. In what follows, I first briefly point out certain aspects of the estimation results of Models 1-3 and then proceed to discuss the results of the sum tests.

Model I

The lag length for each variable in this model is set at k - 1 [see Equation (2) and Table 2 for the value of k for each country]. The explanatory power of the model is rather low for Japan (adjusted [R.sup.2] = 0.18), but it explains more than half of the change in the export price indexes of Germany and the United States. Given that the dependent variable of the model is the percentage change in the export price index, the model seems to perform satisfactorily. For all the three countries, the model also passes the diagnostic tests for serial correlation and heteroskedasticity. The coefficient of the lagged error correction term has the correct negative sign but is statistically significant only in the case of Japan. It implies that the export price index falls (or corrects) by roughly 0.6% for every 1% deviation (or error) from the long-term equilibrium relationship in the preceding quarter.

Model 2

This model is similar to Model 1 in that it also allows for an asymmetric response. The goodness of fit statistics in Model 2 show substantial improvements for all the three countries. The improvement is dramatic for Japan, suggesting that export pricing in Japan is much more sensitive to concurrent than to past changes in the exchange rate. The model does not pass the diagnostic tests for serially independent and homoskedastic residuals in the case of the United States, implying that estimated standard errors of the coefficients are inefficient. Due to this problem, the variance-covariance matrix of the parameter estimates must be adjusted before performing the sum tests. Thus, the Newey-West (1987) adjustment method was employed to obtain a heteroskedasticity and autocorrelation consistent estimates of the standard errors of the coefficients of the model.

Model 3

The application the FPE criterion significantly reduces the number of estimated parameters. The more parsimonious Model 3, however, seems to fit the data for each country roughly as well as Model 2 based on the conventional goodness of fit statistics. Moreover, as a result of the deletions of some of the lagged variables, the error correction term in the equations for all three countries becomes statistically significant. [8] Table 4 shows the results of the sum tests (all figures are rounded).

Japan

In Model 1, the sum of coefficients of positive changes in the exchange rate has a positive sign, implying an amplifying or exacerbating effect on the foreign currency prices of exports when the yen appreciates. This counterintuitive result, however, corresponds to the statistically weakest of the three estimated models and can be reasonably downplayed. The sum of the positive change coefficients is also significant in Model 2 but displays a negative sign, consistent with an export price adjustment intended to stabilize the foreign currency price of the exports. The sum of coefficients of negative changes in the exchange rate, on the other hand, is statistically insignificant in both models, implying a full pass-through of the yen's depreciation. Note that, as in Model 1, the difference between the two coefficient sums (see column 3) is not significantly different from zero. Therefore, both models imply a symmetric response. Test results corresponding to Model 3, on the other hand, are consistent with an asy mmetric response. They suggest that Japanese exporters tend to raise the yen prices of their exports more when the yen depreciates than to cut them when the yen appreciates (see also Ohno, 1989, for similar result). This is a pattern of asymmetric response that is predicted when exporters face binding quantitative restrictions in their export destinations. [9]

Germany

The evidence from the sum tests associated with Model 1 implies a full pass-through of both appreciation and depreciation of the exchange value of the mark to foreign currency prices of German exports, because the home currency price of exports seems to be insensitive to the mark's fluctuations. The statistically superior Model 2, however, indicates that the increase in the foreign currency of exports is somewhat dampened as German exporters lower the mark price of their exports as the mark appreciates. This response is accompanied by a full pass-through during depreciation periods. Model 3 yields results that are essentially the same as Model 2. Unlike Model 2, however, Model 3 suggests an asymmetric response, as the difference between the positive and negative coefficient sums is significantly different from zero at the 5% level.

United States

The coefficient sum test results for Model 1 accord with a symmetric response of the kind noted in relation to Model 2 for Japan and Germany. The adjustment in the export price index suggested by the statistically superior Models 2 and 3 also seems to be symmetric with respect to appreciation and depreciation in the exchange value of the dollar. Model 3 implies a larger emphasis by U.S. exporters on stabilizing the foreign currency prices of U.S. exports when the dollar appreciates than when it depreciates, but the difference between the two coefficient sums is insignificantly different from zero.

Other Variables

A few words about the coefficients other variables in the models are in order. The sum of the coefficients of [delta] ln(ULC) in Model 2 has a negative sign and is highly significant for Japan and Germany, but not for the United States. Thus, while Japanese and German exporters appear to absorb part of the change in the unit (labor) cost of production by lowering the home currency prices of exports, U.S. exporters seem to fully pass through the higher cost of labor. The sum of the coefficients of [delta] ln(FPI) displays a positive sign and is also highly significant for all the three countries. Although this result is consistent with what one would expect for smaller exporting countries of Japan and Germany, it is somewhat surprising in the case of the United States.

IV. SUMMARY AND DISCUSSION

This article estimated the response (elasticity coefficient) of the export price index (measured in home currency) to appreciation and depreciation in the nominal effective exchange rate using aggregate data for Japan, Germany, and the United States and error correction modeling. The main findings of our empirical analysis based on the statistically superior of the three estimated models for each country may be summarized as follows.

1. For all the three countries, the home currency price of exports changed in the opposite direction of the change in the exchange rate to stabilize the foreign currency price of exports. There was some evidence implying that Japanese exporters tended to limit variations in the foreign currency price of their exports to a larger extent in both directions than did their German and U.S. counterparts.

2. For Japan and Germany, I further found some evidence suggesting that the tendency to dampen the effects of exchange rate fluctuations on export prices was asymmetric. The pattern of asymmetric response for Japan implied that Japanese exporters put a larger emphasis on stabilizing the foreign currency prices of their exports during periods of weak yen than during periods of strong yen. German exporters, on the other hand, seemed to be more inclined to dampen the effect of appreciation of the mark on their export prices than its depreciation. The observed patterns of asymmetric response for Japan and Germany are consistent with what is predicted by the supply-side constrained export market and the market share hypotheses, respectively. As for the United States, the evidence pointed to a symmetric response.

These findings have two major related implications. First, the usual assumption of a symmetric export price response to the exchange rate changes at the aggregate level may not be a valid one, at least in some cases. This is a point worth keeping in mind in assessing the impact of exchange rate fluctuations, due to policy interventions or other factors, on the trade balance. If we take the evidence of asymmetric responses summarized above at face value, then the favorable impact of, for example, a 10% depreciation in the effective exchange rate of the mark (the yen) on Germany's (Japan's) trade balance is expected to be larger (smaller) than unfavorable impact of a 10% appreciation, all else being equal. Second, the role of the exchange rate in determining the size of the trade balance of a country may be less predictable in view of the possibility of asymmetric responses on the part of its major trading partners. Consider, for example, the effect of a substantial appreciation of the dollar's effective excha nge rate (reflecting, as in the recent past, the dollar's gains vis-a-vis the yen and the mark and the currencies of a number of Southeast Asian countries). This may present a challenge to U.S. exporters as they face a "raise prices or cut profits" dilemma. [10] If the downward adjustment in the U.S. export prices during periods of strong dollar is as small as these estimates indicate and the German (and Southeast Asian) exporters pass through all or a large portion of the depreciation of their currency to the export prices, then the deterioration in the U.S. trade balance would tend to be worse than expected, all else being equal. Also, consider the effects of commercial policies intended to reduce U.S. bilateral trade deficits with Japan through pushing for a stronger yen (or "cheaper dollar"). As McKinnon and Ohno (1997), among others, have noted, these policies may turn out to be less effective than their advocates think. [11] Our results for Japan even suggest that periods of a relatively stronger yen ma y be associated more with a smaller reduction in Japanese trade surplus than periods of a relatively weaker yen. [12]

Attempts to achieve a more desirable trade balance by manipulating the exchange rate may be hard to resist in view of perceived economic and political benefits. Such attempts, however, may distract us from addressing the root causes of the deteriorating trend in the U.S. trade deficit such as a low savings rate. With this caveat in mind, the need for adopting a more strategic export pricing policy in response to significant changes in the dollar's exchange rate seems to be more pressing in the case of U.S. exporters. Such policy, through an asymmetric adjustment in the dollar prices of U.S. exports, would attempt to counter any competitive disadvantage that may result from a significant rise in the dollar and allow for the full materialization of any competitive advantage that a weaker dollar may provide.

Mahdavi: Associate Professor of Economics, Division of Economics and Finance, University of Texas, San Antonio, Phone 210-458-5301, Fax 210-458-5837, Email smahdavi@utsa.edu

(*.) This is a substantially revised version of a paper presented at the 73rd annual Western Economics Association International Conference, Lake Tahoe, Nevada, June 29--July 2, 1998. The author thanks session participants and especially two anonymous journal referees for their helpful comments and suggestions. The work on this manuscript was completed during a Faculty Development Leave granted by the University of Texas at San Antonio in the Fall of 1998.

(1.) Throughout this article, it would be helpful to remember the following simple relationship among changes in the exchange rate (e), the home currency price of export (h), and the foreign currency price of export (f): f = h + e. Since h = m + c, where m and c represent changes in markup and cost of production, respectively, it follows that f = (c + m) + e. So, for a given value of c, an appreciation of the home currency (positive e) may be fully or partially offset by a reduction in the profit margin (negative m).

(2.) When the threat of antidumping actions exist, building market share by cutting the foreign currency export prices of exports may turn out to be a costly strategy. A dumping charge, however, is less credible when lower export prices can be justified based on the exporters' depreciated home currency (Knetter, 1994). See Ohno's (1989) results, based on industry-level data for Japan, for evidence consistent with the "bottlenecks" model.

(3.) Hakkio and Roberts (1987) estimated that about 56-66% of the deterioration in U.S. trade balance during first half of the 1980s was due to a stronger dollar. They also noted that after the dollar began to decline in 1985, the pass-through for export prices was larger and quicker than for import prices. More recently, Klitgaard (1996) attributed the surprising resilience of Japanese exports despite a rising yen during the first half of the 1990s, in part, to cuts in the yen price of the exports.

(4.) Specifically, in the restricted (theoretical) version of the model, [[eta].sub.1] = 1 - [[eta].sub.2] and [[eta].sub.2] = [[eta].sub.3]. These restrictions, however, may not necessarily hold at the aggregate level of analysis.

(5.) Hung et al.'s (1993) ADF tests yielded similar results for their proxies of domestic cost and export price in the case of Japan. They justify the assumption of treating these variables as I(1) by arguing that "violation of the assumption is not serious because stationary variables tend to show up in estimating cointegrating relationships" (p. 12).

(6.) We also tested the variables for nonstationarity using the Phillips-Perron (1988) test that imposes less restrictive assumptions on the error process. With one exception, the test statistic corresponding to a version of the Phillips-Perron test equation that allows for a drift and a time trend lead to conclusions similar to those obtained from the ADF test. [The one exception is in the case of Japan where the In(FPI) variable is stationary.] The results of the PP tests are not reported here hut are available from the author.

(7.) Note that since the cointegration equation represents the long-term relationship among the level of the variables, it cannot be specified in terms of the positive and negative changes in the exchange rate.

(8.) Note that the term "error correction" cannot be strictly used in relation to Models 2 and 3, for they both include contemporaneous values of the variables.

(9.) One may recall that Japanese automobile exports to the United States in the 1980s faced such restrictions, which were conveniently referred to as "voluntary export restrictions."

(10.) See "Falling Yen Creates Painful Dilemma for U.S. Marketers in Japan," The Wall Street Journal, June 30, 1998, p. B1.

(11.) McKinnon and Ohno (1997) argue that these policies permeated U.S. trade policy with respect to Japan in the post-Bretton Woods era and, backed by periodic threats of trade wars, contributed to a massive appreciation in the exchange value of the yen against the dollar (the yen rose to an all time high of $1 = [yen]80 in April 1995). The U.S. trade deficit with Japan, however, remained quite large despite such a massive appreciation of the yen.

(12.) This conjecture is compatiable with the actual behavior of Japan's trade (current-account) surplus in the recent past. The yen appreciated significantly against the dollar over the period 1991-95. The overvalued yen and accompanying tight monetary policy depressed domestic demand and widened the trade surplus of Japan. The trade surplus began to fall after early 1995, when the yen reversed course and monetary policy eased. See "Talk Is Cheap and So Is the Dollar," The Economist, September 21, 1996, p. 82.

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_____, "Is Export Price Adjustment Asymmetric? Evaluating the Market Share and Marketing Bottlenecks Hypotheses," Journal of International Money and Finance, 13:1, 1994, 55-70.

Krugman, Paul, "Pricing to Market When the Exchange Rate Changes," in S. W. Arndt and J. D. Richardson, eds., Real Financial Linkages among Open Economies, MIT Press, Cambridge, Mass., 1987, 49-70.

Kvasnick, Joseph G., "The Dollar-Trade Puzzle," International Letter, Federal Reserve Bank of Chicago, 560, July 1986.

Mann, Catherine L., "Prices, Profit Margins and the Exchange Rates," Federal Reserve Bulletin, 72, June 1986, 366-379.

Martson, Richard, "Pricing to Market in Japanese Manufacturing," Journal of International Economics, 29, December 1990, 217-236.

McKinnon, Ronald I., and Kenichi Ohno, Dollar and Yen: Resolving Economic Conflict between the United States and Japan, MIT Press, Cambridge, Mass., 1997.

Newey, W. K., and K. D. West, "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix" Econometrica, 55, 1987, 703-708.

Ohno, Kenichi, "Export Pricing Behavior of Manufacturing: A U.S. Japan Comparison," International Monetary Fund Staff Papers, September 1989, 550-579.

Osterwald-Lenum, M., "A Note with Quintiles of the Asymptotic Distribution of the Likelihood Cointegration Rank Test Statistics: Four Cases," Oxford Bulletin of Economics and Statistics, 54:3, August 1992, 933-948.

Phillips, Peter, and Pierre Perron, "Testing for a Unit Root in Time Series Regression," Biometrica, 75, June 1988, 335-346.

[delta] X = [[alpha].sub.0] + [[alpha].sub.1]T + [[alpha].sub.2][X.sub.t-1] + [[[sigma].sup.h].sub.i=1] [[lambda].sub.i] [delta][X.sub.t-i] + [u.sub.t],

where X is the natural log of the variable, T is a time trend, and u is a white noise error term. The lag lengths in the ADF tests (p) are chosen by setting the maximum lag length equal to eight quarters and then using the maximum Likelihood ratio tests to determine whether last included lag was statistically significant (Campbell and Perron, 1991).

The null hypothesis of the ADF test is [H.sub.0]: the variable has a unit root, i.e., an I(1) series.

(**.)denotes that the null can be rejected at the 5% level of significance.

(a.)k is the lag length k in the vector error correction model

[delta][V.sub.t] = [phi] + [[[sigma].sup.k-1].sub.i=1] [[gamma].sub.i][delta][V.sub.t-i] + [pi][V.sub.t-1] + [[zeta].sub.t],

where [V.sub.t] is an n X 1 vector of 1(1) variables; [[gamma].sub.i] and [pi] are n X n matrices reflecting the short- and long-run effects, respectively; [phi] is a vector of intercept terms; and [[zeta].sub.t] is a vector of white noise error terms. The optimal length of k is chosen on the basis of the last significant lag criterion using likelihood ratio tests.

(b.)r is the hypothesized number of cointegrating vectors. The 5% critical values for the cointegration tests are [[lambda].sub.max] = 27.13, 21.07, 14.90, and 8.18 for [H.sub.0]: r = 0, r = 1, r = 2, and r = 3, respectively. These critical values are taken from Table 1 of Osterwald-Lenum (1992) under the assumptions that the variables have a linear deterministic trend, but there is no trend term in the data generating process.

(c.)[beta]s are the parameters of the cointegrating vector. The figures in parentheses are the values of the [X.sup.2](1) statistic in testing the null hypothesis of [beta] = 0. The 5% critical value of [X.sup.2](1) is 3.84.

(*.)denotes significance at the 5% level.

(a.)Figures in parentheses below estimated coefficients are absolute values of the t-statistic. Figures in brackets are p-values (i.e., the probability of falsely rejecting the null hypothesis).

(b.)The statistic in Ljung-Box test of serial correlation. The null hypothesis is that the residuals are serially uncorrelated.

(c.)The statistic for testing heteroskedasticity based on the regression of squared residuals on squared fitted values. The null hypothesis is that the residuals are homoskedastic.

(*.), (**.), and (***.)denote statistical significance at the 10%, 5%, and 1% level, respectively. All figures are rounded.

(a.)Figures reported in each column are the sum of the coefficients indicated above that column. Figures in parentheses are the absolute values of the t-statistic.

(b.)The values of the t-statistic for the model are calculated using the Newey-West autocorrelation and heteroskedasticity consistent estimates of the variance-covariance matrix of the parameters.

(c.)The sum of coefficients test supports an asymmetric response hypothesis.

(*.), (**.), and (***.)denote statistical significance at the 10%, 5%, and 1% level, respectively. All figures are rounded.

ABBREVIATIONS

ADF: augmented Dickey-Fuller

ECM: error correction model

FPE: finite prediction error

PTM: pricing-to-market

APPENDIX

Data Sources

Export Price Index (XPI, 1990 = 100) [Source: International Financial Statistics (IMF)]. The XPI index is a fixed-weight index of all export prices. Because the data on XPI were not available for the United States, we used an alternative index known as the "export unit value." The latter is obtained by dividing the dollar value of total exports by a measure of total output. The unit value index is a relatively crude measure of average export price, for it may rise due to a shift in the mix of exports in favor of higher quality or luxury items.

Unit Labor Cost Index (ULC, 1990 = 100) [Source: Main Economic Indicators (OECD)]. ULC serves as a proxy for the unit cost of producing one unit of output. The inclusion of raw material or commodity prices would have yielded a more comprehensive measure of production cost. The construction of such an index, however, was hampered by lack of appropriate time series data over the sample period. Another problem arises from the fact that most internationally traded commodity and raw material prices are invoiced in the U.S. dollars and, therefore, are not independent of the exchange rate.

Foreign Price Index (FPI, 1990 100). I constructed the index by calculating the weighted average of the wholesale price indexes (WPI; Source: IMF) of each country's major export markets using bilateral export shares as weights. The export shares, in turn, were calculated as averages for the top 25 markets over the period 1980-85. (Source: Direction of Trade Statistics Yearbook, IMF, 1987). This period roughly corresponds to the middle part of our sample period. Since for a few countries (among the top 25) the data on WPI for the entire sample period were not available, they were dropped in constructing FPI. The remaining countries account for at least 60% of the exports of Japan, Germany, and the United States over the 1980-85 period. A drawback of FPI is that it uses fixed weights (shares).

Nominal Effective Exchange Rate Index (EXR, 1990 = 100) (Source: OECD). This index is constructed by OECD using a weighted average of the bilateral exchange rates of the yen, mark, and dollar versus the currencies of the remaining OECD member countries as well as those of five nonmember countries.

This article estimates the responses (elasticity coefficients) of the export price index to appreciation and depreciation of the nominal effective exchange rate using quarterly data (1973:1-1997:2) for Japan. Germany, and the United States. Cross-county comparisons of the elasticity magnitudes based on the statistically superior of the estimated models indicate that Japanese exporters, in the aggregate, have the highest tendency to dampen the effects of exchange rate fluctuations on the foreign currency export prices in both directions by adjusting their home currency prices. Intracountry comparisons provide some evidence of an asymmetric adjustment in export prices in the cases of Japan and Germany. (JEL F31)

I. INTRODUCTION

The "Plaza Agreement" among the G-5 finance ministers in 1985 led to a sudden reversal of the U.S. dollar's steep climb during the first half of the 1980s. The agreement was intended to improve the large and rising U.S. trade deficits by depreciating the dollar. However, despite the dollar's equally steep fall from its peak value in 1985, subsequent improvements in the U.S. trade balance turned out to be rather sluggish. In fact, the U.S. trade deficits remained quite large in the second half of the 1980s and the 1990s. This is in sharp contrast to the large trade surpluses of Germany and Japan that persisted even in the face of appreciating (nominal and real) effective exchange rates of mark and yen over much of the modern floating period.

One of the explanations for the sluggish response of the U.S. trade balance to changes in the dollar's exchange rate rests on the incomplete pass-through of the depreciation of the dollar to the U.S. import and export prices. This phenomenon is in turn explained by the dollar invoicing of some U.S. imports, currency hedging, outsourcing by some foreign exporters, and differences in markup adjustment practices between foreign and the U.S. exporters. Several authors (e.g., Kvasnick, 1986; Mann, 1986; Hervey, 1988; Ohno; 1989; Martson, 1990) emphasized the role of markup adjustment in the context of what Krugman (1987) termed the "pricing-to-market" (PTM) behavior. The latter suggests that, to keep stable the dollar price of their export, some foreign exporters use markup/ profit margins to (partially) absorb the shock of fluctuations in the exchange value of their home currency vis-a-vis the dollar. Strategic considerations such as market share in export destinations in the face of both demand and exchange rat e uncertainties may motivate this behavior. In this connection, if the foreign exporters try, for example, to maintain their market share during periods of home currency appreciation and try to increase it during periods of depreciation, then the adjustment in export prices will be asymmetric. PTM is thus expected to be more pronounced during the appreciation periods as the exporters cut the home currency prices of their exports by more than they raise them during the depreciation periods. [1]

In a pioneering study, Mann (1986) provided evidence supporting profit margin adjustments of the type described above by foreign exporters over the 1977-81 period of the dollar's depreciation and the 1982-85 period of the dollar's appreciation. Mann's analysis suggested that, in the aggregate, U.S. exporters were relatively insensitive to the exchange rate changes and did not change their profit margins in either of the two periods. Interestingly enough, evidence from disaggregated data indicated that some U.S. exporters even increased their profit margins as the dollar appreciated.

Subsequent studies of PTM mostly employed industry-level data. Knetter (1989) analyzed the quarterly data on the U.S. and German seven-digit export industries and found evidence of more pronounced country-specific adjustments in reaction to the exchange rate fluctuations by German exporters than U.S. exporters. Moreover, his results indicate that while such adjustments had a dampening (or stabilizing) effect on the foreign currency prices of German exports, they had an amplifying (or exacerbating) effect on foreign currency prices of U.S. exports. Martson's (1990) study focused on the pricing behavior of some Japanese transport and consumer manufacturing firms and found evidence of an asymmetric response for five products as predicted by the "market share" model. Knetter (1994) noted that when exporters face bottlenecks due to marketing capacity constraints and/or binding quantitative restrictions in their export destinations, an asymmetric response pattern that is opposite of the kind predicted by the "mark et share" model may be observed. The underlying argument is that, in order for the exporters to clear a supply-side constrained export market, they need to raise the home currency prices of their exports as the home currency depreciates to (partially) offset the fall in their foreign currency prices. However, since the supply-side constraints are not binding when the home currency appreciates, PTM is expected to be larger during periods of depreciation than appreciation. [2] Knetter's estimates of export price elasticities using panel data on several seven-digit German and Japanese industries did not support an asymmetric response in most cases. But in cases where he found evidence of asymmetry, it was mostly consistent with the market share hypothesis. Finally, based on their analysis of German, Japanese, and U.S. automobile export prices, Gagnon and Knetter (1995) concluded that evidence of markup adjustment behavior was the strongest in the case of Japanese exports and the weakest in the case of U.S. expor ts.

The industry-level studies of the export price response to variations in the exchange rate are helpful in identifying the specific industries that exhibit an asymmetric response. However, due to the narrow scope of the data employed in these studies, the implications of their results for the overall trade balance are rather limited. An empirically interesting question to investigate, therefore, is whether the export price index asymmetrically responds to episodes of appreciation and depreciation in the nominal effective exchange rate. In this article, I use aggregate data from the three major trading countries of Germany, Japan, and the United States to (i) determine the extent to which the exporters in each country collectively tend to neutralize the impact of the exchange rate fluctuations on the foreign currency prices of exports by adjusting the home currency price of their exports and (ii) compare the pattern of asymmetric responses (if any) across the three countries to see if they differ in their emph asis on stabilizing export prices during periods of home currency appreciation ver sus depreciation as some micro-level studies seem to suggest. Our results may help explain the observed differential impacts of currency fluctuations on the trade balance across the three countries. [3]

This article is organized as follows. Section II focuses the analytical framework of the article, which includes the cointegration analysis and error correction modeling of the relationship between the export price index and the effective exchange rate. Section III presents the empirical results. The last section summarizes the empirical findings of the article and provides some concluding remarks.

II. THE ANALYTICAL FRAMEWORK

The building block of our empirical analysis is an export-price equation derived by Hung et al. (1993) from a model in which a profit-maximizing producer is assumed to operate under constant returns and exports exclusively to imperfectly competitive foreign markets:

(1) In [[P.sup.h].sub.t] = [[eta].sub.0] + [[eta].sub.1] In [[C.sup.h].sub.t] + [[eta].sub.2] In [[P.sup.f].sub.t] + [[eta].sub.3] In [E.sub.t] + [V.sub.t].

In Equation (1), the export price in home currency (i.e., the exporter's currency) at time t ([[P.sup.h].sub.t]) is modeled as a function of domestic unit cost of production ([[C.sup.h].sub.t]), the price of foreign competing goods in foreign currency unit ([[P.sup.f].sub.t]), the nominal exchange rate ([E.sub.t]), and an error term ([V.sub.t]). The theoretical model behind Equation (1) establishes that (i) [[eta].sub.1] (i.e., the elasticity [[P.sup.h].sub.t] with respect to changes in [[C.sup.h].sub.t]) is inversely related to the relative price elasticity of markup and (ii) the smaller is [[eta].sub.1] the larger is [[eta].sub.3] (i.e., the elasticity [[P.sup.h].sub.t] with respect to changes in [E.sub.t]). [4] In the case of an economy with a relatively large domestic market and significant price-setting power in the world market (such as that of the United States), the price elasticity of markup is expected to be relatively low. This implies that the export price is more influenced by changes in domestic cost (relatively high [[eta].sub.1]) than changes in the foreign competitors' prices (relatively low [[eta].sub.3]). The opposite is predicted for the exporters from relatively smaller and more open economies (such as those of Germany and Japan) that have less price-setting power in their export markets.

I specify the following aggregate version of Equation (1) using proxies for the export price, domestic unit cost, foreign price, and the exchange rate variables:

(2) ln XPI

= [[beta].sub.0] + [[beta].sub.1] In[(ULC).sub.t] + [[beta].sub.2] In[(FPI).sub.t] + [[beta].sub.3] In[(EXR).sub.t] + [e.sub.t],

where XPI is the export price (or export unit value) index in the exporting country's currency, ULC is unit labor cost (a proxy for the domestic cost of production), FPI is a trade-weighted average of the wholesale price indexes of the exporting country's major trading partners (a proxy for the foreign price level), EXR is an index of effective nominal exchange rate (i.e., a trade-weighted average of the bilateral exchange rates between the exporting country and its major trading partners defined such that an increase in its level is associated with an appreciation of the home currency), and e is an error term. (See Appendix for more detailed explanations and data sources.)

As Hung et al. (1993) have pointed out, Equation (1) (and its aggregate version) can best be interpreted as a long-term relationship, for it does not incorporate dynamic adjustments. To specify a model of dynamic adjustments without losing the information contained in the long-term relationship due to differencing of the levels of the variables, one needs to specify an error correction model (ECM). To this end, I first test the variables in Equation (2) for nonstationarity. If the variables are found to be first-difference stationary, or integrated of degree one, I(1), then there may exist one (or more) linear combination of the variables (referred to as a cointegration equation) that is stationary, or I(0) (Engle and Granger, 1987). A one-period lagged value(s) of the residuals obtained from the cointegration equation can be incorporated into a dynamic version of Equation (2), yielding an ECM of the following form:

(3) [delta] ln[(XPI).sub.t-i]

= [delta] + [[[sigma].sup.k-1].sub.i=1] [[omega].sub.i] [delta] ln[(XPI).sub.t-i]

+ [[[sigma].sup.k-1].sub.i=1] [[phi].sub.i] [delta] 1n[(ULC).sub.t-i]

+ [[[sigma].sup.k-1].sub.i=1] [[gamma].sub.i][delta] ln[(FPI).sub.t-i]

+ [[[sigma].sup.k-1].sub.i=1] [[theta].sub.i] [delta] 1n[(EXR).sub.t-i]

+ [[[sigma].sup.r].sub.j=1] [[phi].sub.j] [([EC.sub.j]).sub.t-1] + [[epsilon].sub.t],

where [EC.sub.j] is the residual from the jth cointegrating equation. In Equation (3), the short-term change in the export price index in part reflects a correction of the deviation from the long-term equilibrium relationship in the previous period. I employ Johansen's maximum likelihood procedure (Johansen, 1988; Johansen and Juselius, 1990) to estimate the parameters of Equation (2). This procedure provides a unified framework for testing the number and parameters of the cointegrating vector(s). Then the parameters of Equation (3) are estimated using the residuals of Equation (2) as the values of the error correction term.

Of particular interest are the signs and magnitudes of the estimated coefficients of the 1n(EXR) variable in Equation (3). If exporters in the aggregate adjust their export prices to stabilize the foreign currency prices of their exports in response to fluctuations in the exchange rate, then the sum of the [theta]s is expected to be negative. As [theta]s are constrained to be the same for both positive and negative changes (appreciation and depreciation, respectively) in the exchange rate variable, Equation (3) implicitly assumes a symmetric response of the export price index to the exchange rate changes. To test for an asymmetric response, we define two new variables, [[delta].sup.+] 1n(EXR) and [[delta].sup.-]1n(EXR), representing positive and negative changes in the exchange rate variable, respectively. More formally,

[[delta].sup.+] ln(EXR) = [delta] 1n(EXR) if [delta] 1n(EXR) [greater than] 0,

0 if [delta] ln(EXR) [less than or equal to] 0;

[[delta].sup.-] ln(EXR) = [delta] ln(EXR) if [delta] ln(EXR) [less than] 0,

0 if [delta] ln(EXR) [greater than or equal to] 0.

Thus, a variant of Equation (3) that allows for asymmetric responses can be specified by replacing the [delta] ln(EXR) variable by the two new variables and conducting tests of hypothesis on the sum of their coefficients (represented by [sigma][[theta].sup.+] or [sigma][[theta].sup.+] for positive and negative changes in the exchange rate, respectively).

Statistical evidence consistent with an asymmetric response is said to exist if either [sigma][[theta].sup.+] or [sigma][[theta].sup.-](or both) is significantly different from zero and the difference between the two sums is also significantly different from zero. If both sums are found to be statistically insignificant (implying that the home currency prices of exports remain unchanged in the face of the exchange rate changes), then changes in the exchange rate are fully passed through to the foreign currency price of exports. Finally, note that the "market share" model of export price behavior implies a large (close to one and statistically significant value of [sigma][[theta].sup.+] and a small (close to zero) and/or statistically insignificant value of [sigma][[theta].sup.-]. The opposite is implied when the export supply is constrained by bottlenecks and/or trade restrictions.

III. EMPIRICAL RESULTS

For each of the three countries of Japan, Germany, and the United States we collected data on the variables in Equation (2) over the period 1973:1-1997:2. Since the time series of the variables are suspected to be nonstationary, we tested them for nonstationarity using the augmented Dickey-Fuller (ADF) tests (Dickey and Fuller, 1979). Table 1 summarizes the results of the ADF unit root tests. The results suggest that in all but two cases the null hypothesis that the variables are nonstationary in level cannot be rejected at the 5% level of significance for the lag lengths indicated. (The first differences of all the variables are stationary; results are not reported here.) The two exceptions are the variables In(XPI) and In(ULG) for Japan that seem to be trend stationary. The ADF test statistics at higher lag lengths for the two variables, however, are not large enough to reject the null of nonstationarity. I proceed to perform the cointegration tests assuming that these variables are I(1). [5,6]

The results of cointegration tests applied to Equation (2) are presented in Table 2. [7] For each country, the table shows the values of likelihood-ratio test statistics ([[lambda].sub.max]) based on the maximal eigenvalue of the stochastic matrix in Equation (3) for the lag lengths indicated (see table note a). Since there are four variables in Equation (2), there can be a maximum of three cointegrating relationships among the variables. Four null hypotheses, therefore, can be tested on the number of cointegrating vector (or r). According to the values of [[lambda].sub.max], the null hypothesis of r = 0 can be rejected in favor of r = 1 for all the three countries. Since the null of r = 2 and 3 are rejected, the test results suggest that there is only one cointegrating vector among the four variables. The normalized value of the estimated coefficient of the exchange rate variable has a negative sign in the cointegrating vector for all the three countries. This is consistent with a response on the part of ex porters aimed at stabilizing the foreign currency price of exports. Note, however, that this coefficient is not statistically significant in the case of United States, suggesting that the exchange rate variable may not be part of a long-term equilibrium relationship represented by Equation (2). Since there is one cointegrating vector for each country, only one error correction term enters Equation (3).

Table 3 presents the estimated parameters of three variants of Equation (3) for each country. Model 1 decomposes changes in the exchange rate variable into positive and negative ones to test for asymmetric responses. Model 2 replaces the last lagged value of all the variables (with the exception of the export price index) by the corresponding contemporaneous value. The inclusion of the contemporaneous values seems to be justified in view of the quarterly nature of the data and the fact that those export prices that are invoiced in foreign currency terms change automatically with the change in the exchange rate. Model 3 presents a parsimonious version of Model 2 by employing the "finite prediction error" (FPE) criterion proposed by Akike (1970) in conjunction with the "specific gravity" criterion proposed by Caines et al. (1981) to select the "best" lag combination. Briefly, the FPE criterion balances the costs of overparameterizing a model with the cost of underparameterizing it and, thus, recognizes the tra de-off between bias and efficiency in the estimation process. The specific gravity criterion uses the FPE criterion to determine the order in which variables enter the model after the lagged values of the dependent variable have been included. Comparisons of the Models 1-3 enable testing for the sensitivity of the estimated results to alternative lag structures. Table 3 also reports the conventional measure of goodness of fit along with the statistics for two diagnostic tests. In what follows, I first briefly point out certain aspects of the estimation results of Models 1-3 and then proceed to discuss the results of the sum tests.

Model I

The lag length for each variable in this model is set at k - 1 [see Equation (2) and Table 2 for the value of k for each country]. The explanatory power of the model is rather low for Japan (adjusted [R.sup.2] = 0.18), but it explains more than half of the change in the export price indexes of Germany and the United States. Given that the dependent variable of the model is the percentage change in the export price index, the model seems to perform satisfactorily. For all the three countries, the model also passes the diagnostic tests for serial correlation and heteroskedasticity. The coefficient of the lagged error correction term has the correct negative sign but is statistically significant only in the case of Japan. It implies that the export price index falls (or corrects) by roughly 0.6% for every 1% deviation (or error) from the long-term equilibrium relationship in the preceding quarter.

Model 2

This model is similar to Model 1 in that it also allows for an asymmetric response. The goodness of fit statistics in Model 2 show substantial improvements for all the three countries. The improvement is dramatic for Japan, suggesting that export pricing in Japan is much more sensitive to concurrent than to past changes in the exchange rate. The model does not pass the diagnostic tests for serially independent and homoskedastic residuals in the case of the United States, implying that estimated standard errors of the coefficients are inefficient. Due to this problem, the variance-covariance matrix of the parameter estimates must be adjusted before performing the sum tests. Thus, the Newey-West (1987) adjustment method was employed to obtain a heteroskedasticity and autocorrelation consistent estimates of the standard errors of the coefficients of the model.

Model 3

The application the FPE criterion significantly reduces the number of estimated parameters. The more parsimonious Model 3, however, seems to fit the data for each country roughly as well as Model 2 based on the conventional goodness of fit statistics. Moreover, as a result of the deletions of some of the lagged variables, the error correction term in the equations for all three countries becomes statistically significant. [8] Table 4 shows the results of the sum tests (all figures are rounded).

Japan

In Model 1, the sum of coefficients of positive changes in the exchange rate has a positive sign, implying an amplifying or exacerbating effect on the foreign currency prices of exports when the yen appreciates. This counterintuitive result, however, corresponds to the statistically weakest of the three estimated models and can be reasonably downplayed. The sum of the positive change coefficients is also significant in Model 2 but displays a negative sign, consistent with an export price adjustment intended to stabilize the foreign currency price of the exports. The sum of coefficients of negative changes in the exchange rate, on the other hand, is statistically insignificant in both models, implying a full pass-through of the yen's depreciation. Note that, as in Model 1, the difference between the two coefficient sums (see column 3) is not significantly different from zero. Therefore, both models imply a symmetric response. Test results corresponding to Model 3, on the other hand, are consistent with an asy mmetric response. They suggest that Japanese exporters tend to raise the yen prices of their exports more when the yen depreciates than to cut them when the yen appreciates (see also Ohno, 1989, for similar result). This is a pattern of asymmetric response that is predicted when exporters face binding quantitative restrictions in their export destinations. [9]

Germany

The evidence from the sum tests associated with Model 1 implies a full pass-through of both appreciation and depreciation of the exchange value of the mark to foreign currency prices of German exports, because the home currency price of exports seems to be insensitive to the mark's fluctuations. The statistically superior Model 2, however, indicates that the increase in the foreign currency of exports is somewhat dampened as German exporters lower the mark price of their exports as the mark appreciates. This response is accompanied by a full pass-through during depreciation periods. Model 3 yields results that are essentially the same as Model 2. Unlike Model 2, however, Model 3 suggests an asymmetric response, as the difference between the positive and negative coefficient sums is significantly different from zero at the 5% level.

United States

The coefficient sum test results for Model 1 accord with a symmetric response of the kind noted in relation to Model 2 for Japan and Germany. The adjustment in the export price index suggested by the statistically superior Models 2 and 3 also seems to be symmetric with respect to appreciation and depreciation in the exchange value of the dollar. Model 3 implies a larger emphasis by U.S. exporters on stabilizing the foreign currency prices of U.S. exports when the dollar appreciates than when it depreciates, but the difference between the two coefficient sums is insignificantly different from zero.

Other Variables

A few words about the coefficients other variables in the models are in order. The sum of the coefficients of [delta] ln(ULC) in Model 2 has a negative sign and is highly significant for Japan and Germany, but not for the United States. Thus, while Japanese and German exporters appear to absorb part of the change in the unit (labor) cost of production by lowering the home currency prices of exports, U.S. exporters seem to fully pass through the higher cost of labor. The sum of the coefficients of [delta] ln(FPI) displays a positive sign and is also highly significant for all the three countries. Although this result is consistent with what one would expect for smaller exporting countries of Japan and Germany, it is somewhat surprising in the case of the United States.

IV. SUMMARY AND DISCUSSION

This article estimated the response (elasticity coefficient) of the export price index (measured in home currency) to appreciation and depreciation in the nominal effective exchange rate using aggregate data for Japan, Germany, and the United States and error correction modeling. The main findings of our empirical analysis based on the statistically superior of the three estimated models for each country may be summarized as follows.

1. For all the three countries, the home currency price of exports changed in the opposite direction of the change in the exchange rate to stabilize the foreign currency price of exports. There was some evidence implying that Japanese exporters tended to limit variations in the foreign currency price of their exports to a larger extent in both directions than did their German and U.S. counterparts.

2. For Japan and Germany, I further found some evidence suggesting that the tendency to dampen the effects of exchange rate fluctuations on export prices was asymmetric. The pattern of asymmetric response for Japan implied that Japanese exporters put a larger emphasis on stabilizing the foreign currency prices of their exports during periods of weak yen than during periods of strong yen. German exporters, on the other hand, seemed to be more inclined to dampen the effect of appreciation of the mark on their export prices than its depreciation. The observed patterns of asymmetric response for Japan and Germany are consistent with what is predicted by the supply-side constrained export market and the market share hypotheses, respectively. As for the United States, the evidence pointed to a symmetric response.

These findings have two major related implications. First, the usual assumption of a symmetric export price response to the exchange rate changes at the aggregate level may not be a valid one, at least in some cases. This is a point worth keeping in mind in assessing the impact of exchange rate fluctuations, due to policy interventions or other factors, on the trade balance. If we take the evidence of asymmetric responses summarized above at face value, then the favorable impact of, for example, a 10% depreciation in the effective exchange rate of the mark (the yen) on Germany's (Japan's) trade balance is expected to be larger (smaller) than unfavorable impact of a 10% appreciation, all else being equal. Second, the role of the exchange rate in determining the size of the trade balance of a country may be less predictable in view of the possibility of asymmetric responses on the part of its major trading partners. Consider, for example, the effect of a substantial appreciation of the dollar's effective excha nge rate (reflecting, as in the recent past, the dollar's gains vis-a-vis the yen and the mark and the currencies of a number of Southeast Asian countries). This may present a challenge to U.S. exporters as they face a "raise prices or cut profits" dilemma. [10] If the downward adjustment in the U.S. export prices during periods of strong dollar is as small as these estimates indicate and the German (and Southeast Asian) exporters pass through all or a large portion of the depreciation of their currency to the export prices, then the deterioration in the U.S. trade balance would tend to be worse than expected, all else being equal. Also, consider the effects of commercial policies intended to reduce U.S. bilateral trade deficits with Japan through pushing for a stronger yen (or "cheaper dollar"). As McKinnon and Ohno (1997), among others, have noted, these policies may turn out to be less effective than their advocates think. [11] Our results for Japan even suggest that periods of a relatively stronger yen ma y be associated more with a smaller reduction in Japanese trade surplus than periods of a relatively weaker yen. [12]

Attempts to achieve a more desirable trade balance by manipulating the exchange rate may be hard to resist in view of perceived economic and political benefits. Such attempts, however, may distract us from addressing the root causes of the deteriorating trend in the U.S. trade deficit such as a low savings rate. With this caveat in mind, the need for adopting a more strategic export pricing policy in response to significant changes in the dollar's exchange rate seems to be more pressing in the case of U.S. exporters. Such policy, through an asymmetric adjustment in the dollar prices of U.S. exports, would attempt to counter any competitive disadvantage that may result from a significant rise in the dollar and allow for the full materialization of any competitive advantage that a weaker dollar may provide.

Mahdavi: Associate Professor of Economics, Division of Economics and Finance, University of Texas, San Antonio, Phone 210-458-5301, Fax 210-458-5837, Email smahdavi@utsa.edu

(*.) This is a substantially revised version of a paper presented at the 73rd annual Western Economics Association International Conference, Lake Tahoe, Nevada, June 29--July 2, 1998. The author thanks session participants and especially two anonymous journal referees for their helpful comments and suggestions. The work on this manuscript was completed during a Faculty Development Leave granted by the University of Texas at San Antonio in the Fall of 1998.

(1.) Throughout this article, it would be helpful to remember the following simple relationship among changes in the exchange rate (e), the home currency price of export (h), and the foreign currency price of export (f): f = h + e. Since h = m + c, where m and c represent changes in markup and cost of production, respectively, it follows that f = (c + m) + e. So, for a given value of c, an appreciation of the home currency (positive e) may be fully or partially offset by a reduction in the profit margin (negative m).

(2.) When the threat of antidumping actions exist, building market share by cutting the foreign currency export prices of exports may turn out to be a costly strategy. A dumping charge, however, is less credible when lower export prices can be justified based on the exporters' depreciated home currency (Knetter, 1994). See Ohno's (1989) results, based on industry-level data for Japan, for evidence consistent with the "bottlenecks" model.

(3.) Hakkio and Roberts (1987) estimated that about 56-66% of the deterioration in U.S. trade balance during first half of the 1980s was due to a stronger dollar. They also noted that after the dollar began to decline in 1985, the pass-through for export prices was larger and quicker than for import prices. More recently, Klitgaard (1996) attributed the surprising resilience of Japanese exports despite a rising yen during the first half of the 1990s, in part, to cuts in the yen price of the exports.

(4.) Specifically, in the restricted (theoretical) version of the model, [[eta].sub.1] = 1 - [[eta].sub.2] and [[eta].sub.2] = [[eta].sub.3]. These restrictions, however, may not necessarily hold at the aggregate level of analysis.

(5.) Hung et al.'s (1993) ADF tests yielded similar results for their proxies of domestic cost and export price in the case of Japan. They justify the assumption of treating these variables as I(1) by arguing that "violation of the assumption is not serious because stationary variables tend to show up in estimating cointegrating relationships" (p. 12).

(6.) We also tested the variables for nonstationarity using the Phillips-Perron (1988) test that imposes less restrictive assumptions on the error process. With one exception, the test statistic corresponding to a version of the Phillips-Perron test equation that allows for a drift and a time trend lead to conclusions similar to those obtained from the ADF test. [The one exception is in the case of Japan where the In(FPI) variable is stationary.] The results of the PP tests are not reported here hut are available from the author.

(7.) Note that since the cointegration equation represents the long-term relationship among the level of the variables, it cannot be specified in terms of the positive and negative changes in the exchange rate.

(8.) Note that the term "error correction" cannot be strictly used in relation to Models 2 and 3, for they both include contemporaneous values of the variables.

(9.) One may recall that Japanese automobile exports to the United States in the 1980s faced such restrictions, which were conveniently referred to as "voluntary export restrictions."

(10.) See "Falling Yen Creates Painful Dilemma for U.S. Marketers in Japan," The Wall Street Journal, June 30, 1998, p. B1.

(11.) McKinnon and Ohno (1997) argue that these policies permeated U.S. trade policy with respect to Japan in the post-Bretton Woods era and, backed by periodic threats of trade wars, contributed to a massive appreciation in the exchange value of the yen against the dollar (the yen rose to an all time high of $1 = [yen]80 in April 1995). The U.S. trade deficit with Japan, however, remained quite large despite such a massive appreciation of the yen.

(12.) This conjecture is compatiable with the actual behavior of Japan's trade (current-account) surplus in the recent past. The yen appreciated significantly against the dollar over the period 1991-95. The overvalued yen and accompanying tight monetary policy depressed domestic demand and widened the trade surplus of Japan. The trade surplus began to fall after early 1995, when the yen reversed course and monetary policy eased. See "Talk Is Cheap and So Is the Dollar," The Economist, September 21, 1996, p. 82.

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Augmented Dickey-Fuller Tests of Unit Root (1973:1-1997:2) Variable Country In(XPI) In(FPI) In(EXR) In(ULC) Japan -3.82 [**] -2.57 -3.34 -7.55 [**] h: 1 3 1 1 Germany -1.65 -1.26 -3.26 -2.33 h: 8 5 3 1 UnitedStates -1.89 -1.54 -2.11 -2.30 h: 5 5 3 3 Notes: The hth-order ADF test statistic is the t-value of [[alpha].sub.2] in the equation

[delta] X = [[alpha].sub.0] + [[alpha].sub.1]T + [[alpha].sub.2][X.sub.t-1] + [[[sigma].sup.h].sub.i=1] [[lambda].sub.i] [delta][X.sub.t-i] + [u.sub.t],

where X is the natural log of the variable, T is a time trend, and u is a white noise error term. The lag lengths in the ADF tests (p) are chosen by setting the maximum lag length equal to eight quarters and then using the maximum Likelihood ratio tests to determine whether last included lag was statistically significant (Campbell and Perron, 1991).

The null hypothesis of the ADF test is [H.sub.0]: the variable has a unit root, i.e., an I(1) series.

(**.)denotes that the null can be rejected at the 5% level of significance.

Johansen Cointegration Tests [H.sub.0] ([[lambda].sub.max]) r = 0 r = 1 r = 2 r = 3 Japan, 40.20 [*] 16.94 13.90 0.13 1974:4-1997:2 (k = 7) [a] Germany, 37.70 [*] 13.50 6.97 4.32 1974:3-1997:2 (k = 6) [a] United States, 35.91 [*] 18.21 6.36 1.21 1974:2-1997:2 (k = 5) [a] Estimated Coefficients of the Cointegrating Vector [c] [[beta].sub.XPI] [[beta].sub.FPI] Japan, -1.00 [*] 1.30 [*] 1974:4-1997:2 (k = 7) [a] (19.96) (22.26) Germany, -1.00 -1.48 1974:3-1997:2 (k = 6) [a] (0.01) (0.06) United States, -1.00 [*] 1.07 [*] 1974:2-1997:2 (k = 5) [a] (9.19) (13.00) [[beta].sub.EXR] [[beta].sub.ULC] Japan, -0.609 [*] -1.53 [*] 1974:4-1997:2 (k = 7) [a] (17.81) (23.24) Germany, -4.77 [*] 5.80 [*] 1974:3-1997:2 (k = 6) [a] (14.37) (5.87) United States, -0.030 -.020 1974:2-1997:2 (k = 5) [a] (0.16) (0.02)

(a.)k is the lag length k in the vector error correction model

[delta][V.sub.t] = [phi] + [[[sigma].sup.k-1].sub.i=1] [[gamma].sub.i][delta][V.sub.t-i] + [pi][V.sub.t-1] + [[zeta].sub.t],

where [V.sub.t] is an n X 1 vector of 1(1) variables; [[gamma].sub.i] and [pi] are n X n matrices reflecting the short- and long-run effects, respectively; [phi] is a vector of intercept terms; and [[zeta].sub.t] is a vector of white noise error terms. The optimal length of k is chosen on the basis of the last significant lag criterion using likelihood ratio tests.

(b.)r is the hypothesized number of cointegrating vectors. The 5% critical values for the cointegration tests are [[lambda].sub.max] = 27.13, 21.07, 14.90, and 8.18 for [H.sub.0]: r = 0, r = 1, r = 2, and r = 3, respectively. These critical values are taken from Table 1 of Osterwald-Lenum (1992) under the assumptions that the variables have a linear deterministic trend, but there is no trend term in the data generating process.

(c.)[beta]s are the parameters of the cointegrating vector. The figures in parentheses are the values of the [X.sup.2](1) statistic in testing the null hypothesis of [beta] = 0. The 5% critical value of [X.sup.2](1) is 3.84.

(*.)denotes significance at the 5% level.

Estimated Coeficients of Export Price Index Models (1973:1-1997:2) [a] Japan Germany Model 1 Model 2 Model 3 Model 1 Intercept 4.80 [***] 0.655 0.725 [***] 0.011 (3.13) (1.14) (2.63) (0.86) [delta] ln[(XPI).sub.t-1] -0.289 0.068 0.342 [***] 0.198 (0.78) (0.50) (4.69) (1.19) [delta] ln[(XPI).sub.t-2] 0.092 -0.254 [**] -0.053 0.006 (0.26) (2.15) (0.96) (0.05) [delta] ln[(XPI).sub.t-3] 0.086 0.050 -0.047 -0.191 [*] (0.25) (0.47) (0.88) (1.64) [delta] ln[(XPI).sub.t-4] -0.034 -0.162 -0.145 [***] 0.027 (0.11) (1.60) (3.04) (0.23) [delta] ln[(XPI).sub.t-5] -0.161 -0.058 -- -0.137 (0.52) (0.54) (1.23) [delta] ln[(XPI).sub.t-6] 0.202 -0.020 -- -- (0.73) (0.47) [delta] ln[(ULC).sub.t] -- -0.003 -0.058 -- (0.03) (0.63) [delta] ln[(ULC).sub.t-1] 0.189 0.006 -- - 0.065 (0.63) (0.06) (1.10) [delta] ln[(ULC).sub.t-2] -0.140 -0.038 -- -0.120 [**] (0.53) (0.47) (2.13) [delta] ln[(ULC).sub.t-3] 0.008 -0.221 [***] -- -0.050 (0.03) (2.89) (0.95) [delta] ln[(ULC).sub.t-4] -0.463 [*] -0.154 [*] -- 0.051 (1.90) (1.88) (0.96) [delta] ln[(ULC).sub.t-5] -0.450 [*] -0.158 [**] -- 0.118 [**] (1.83) (2.12) (2.05) [delta] ln[(ULC).sub.t-6] -0.173 -- -- -- (0.75) [delta] ln[(FPI).sub.t] -- 0.374 [**] 0.488 [***] -- (2.53) (4.94) [delta] ln[(FPI).sub.t-1] 0.253 0.109 -- 0.254 [**] (0.58) (0.57) (2.04) [delta] ln[(FPI).sub.t-2] -0.155 0.205 -- 0.080 (0.35) (1.36) (0.57) [delta] ln[(FPI).sub.t-3] 0.129 0.222 -- 0.053 (0.28) (1.41) (0.38) [delta] ln[(FPI).sub.t-4] 0.487 0.243 [*] -- 0.233 (1.30) (1.87) (1.56) [delta] ln[(FPI).sub.t-5] 0.278 0.046 -- -0.080 (0.72) (0.37) (0.59) [delta] ln[(FPI).sub.t-6] -0.080 -- -- -- (0.21) [delta] ln[(EXR).sub.t] -- -0.552 [**] -0.493 [***] -- (13.4) (13.0) [delta] ln[(EXR).sub.t-1] -0.097 0.092 0.245 [***] 0.148 [**] (0.40) (1.05) (4.99) (2.31) [delta] ln[(EXR).sub.t-2] 0.289 -0.094 -- 0.049 (1.24) (1.24) (0.73) [delta] ln[(EXR).sub.t-3] 0.126 0.089 -- -0.190 [**] (0.57) (1.23) (3.03) [delta] ln[(EXR).sub.t-4] 0.154 -0.067 -- -0.045 (0.73) (0.96) (0.75) [delta] ln[(EXR).sub.t-5] 0.102 -0.058 -- 0.035 (0.49) (0.81) (0.71) [delta] ln[(EXR).sub.t-6] 0.272 -- -- -- (1.40) [delta] ln[(EXR).sub.t] -- -0.589 [**] -0.709 [***] -- (9.35) (13.2) United States Model 2 Model 3 Model 1 Intercept 0.032 [***] 0.027 [***] 0.008 (3.51) (3.17) (0.23) [delta] ln[(XPI).sub.t-1] 0.095 0.137 0.452 [***] (0.87) (1.40) (3.30) [delta] ln[(XPI).sub.t-2] 0.020 -0.017 -0.117 (0.24) (0.22) (0.89) [delta] ln[(XPI).sub.t-3] -0.030 -0.044 -0.119 (0.39) (0.60) (0.95) [delta] ln[(XPI).sub.t-4] 0.073 0.116 [*] 0.124 (0.97) (1.78) (1.01) [delta] ln[(XPI).sub.t-5] -0.139 [***] -0.190 [***] -- (2.89) (3.07) [delta] ln[(XPI).sub.t-6] -- -- -- [delta] ln[(ULC).sub.t] 0.071 [*] 0.056 [*] -- (1.83) (1.67) [delta] ln[(ULC).sub.t-1] -0.008 -- 0.030 (0.22) (0.25) [delta] ln[(ULC).sub.t-2] -0.066 [*] -- 0.027 (1.94) (0.23) [delta] ln[(ULC).sub.t-3] -0.038 -- -0.218 [**] (1.07) (1.99) [delta] ln[(ULC).sub.t-4] -0.018 -- 0.173 (0.50) (1.59) [delta] ln[(ULC).sub.t-5] -- -- -- [delta] ln[(ULC).sub.t-6] -- -- -- [delta] ln[(FPI).sub.t] 0.453 [***] 0.472 [***] -- (7.05) (7.72) [delta] ln[(FPI).sub.t-1] 0.005 -0.009 -0.156 (0.06) (0.10) (0.90) [delta] ln[(FPI).sub.t-2] -0.014 -0.001 0.513 [**] (0.15) (0.01) (2.85) [delta] ln[(FPI).sub.t-3] -0.078 -0.091 0.404 [**] (0.79) (1.03) (2.24) [delta] ln[(FPI).sub.t-4] 0.024 -0.055 -0.273 (0.26) (0.63) (1.56) [delta] ln[(FPI).sub.t-5] -- 0.88 -- (1.09) [delta] ln[(FPI).sub.t-6] -- -- -- [delta] ln[(EXR).sub.t] -0.185 [***] -0.174 [***] -- (4.35) (4.56) [delta] ln[(EXR).sub.t-1] 0.052 0.063 [*] 0.208 [**] (1.17) (1.78) (2.22) [delta] ln[(EXR).sub.t-2] -0.027 -0.062 [*] 0.127 (0.66) (1.79) (1.27) [delta] ln[(EXR).sub.t-3] -0.100 [**] -0.116 [***] -0.237 [**] (2.40) (3.38) (2.48) [delta] ln[(EXR).sub.t-4] -0.021 -- -0.040 (0.60) (0.42) [delta] ln[(EXR).sub.t-5] -- -- -- [delta] ln[(EXR).sub.t-6] -- -- -- [delta] ln[(EXR).sub.t] -0.070 -0.078 -- (0.98) (1.18) Model 2 Model 3 Intercept 0.036 0.055 [*] (1.03) (1.85) [delta] ln[(XPI).sub.t-1] 0.313 [**] 0.438 [***] (2.74) (4.00) [delta] ln[(XPI).sub.t-2] -0.147 -0.082 (1.28) (0.71) [delta] ln[(XPI).sub.t-3] -0.003 -0.046 (0.03) (0.42) [delta] ln[(XPI).sub.t-4] -0.016 0.106 (0.16) (1.05) [delta] ln[(XPI).sub.t-5] -- -- [delta] ln[(XPI).sub.t-6] -- -- [delta] ln[(ULC).sub.t] 0.032 -- (0.29) [delta] ln[(ULC).sub.t-1] 0.037 -- (0.35) [delta] ln[(ULC).sub.t-2] 0.047 -- (0.45) [delta] ln[(ULC).sub.t-3] -0.177 [*] -- (1.80) [delta] ln[(ULC).sub.t-4] -- -- [delta] ln[(ULC).sub.t-5] -- -- [delta] ln[(ULC).sub.t-6] -- -- [delta] ln[(FPI).sub.t] 0.857 [***] 0.789 [888] (4.38) (3.97) [delta] ln[(FPI).sub.t-1] -0.423 [**] -0.459 [***] (2.48) (2.74) [delta] ln[(FPI).sub.t-2] 0.377 [**] 0.243 (2.30) (1.54) [delta] ln[(FPI).sub.t-3] 0.341 [**] 0.390 [**] (2.16) (2.47) [delta] ln[(FPI).sub.t-4] -- -0.182 (1.28) [delta] ln[(FPI).sub.t-5] -- -- [delta] ln[(FPI).sub.t-6] -- -- [delta] ln[(EXR).sub.t] -0.107 -0.039 (1.25) (0.47) [delta] ln[(EXR).sub.t-1] -0.136 -0.129 (1.54) (1.52) [delta] ln[(EXR).sub.t-2] -0.185 [**] 0.087 (2.09) (1.12) [delta] ln[(EXR).sub.t-3] -0.153 [*] -0.162 [**] (1.78) (2.14) [delta] ln[(EXR).sub.t-4] -- -- [delta] ln[(EXR).sub.t-5] -- -- [delta] ln[(EXR).sub.t-6] -- -- [delta] ln[(EXR).sub.t] -0.072 -0.121 (0.75) (1.35) [delta] ln[(EXR).sub.t-1] -0.446 1.50 0.283 [***] -0.134 (1.53) (1.30) (3.52) (1.24) [delta] ln[(EXR).sub.t-2] 0.369 -0.083 0.045 -0.151 (1.14) (0.78) (0.57) (1.32) [delta] ln[(EXR).sub.t-3] 0.184 0.209 [**] 0.093 -0.048 (0.58) (2.03) (1.02) (0.44) [delta] ln[(EXR).sub.t-4] 0.299 -0.092 -0.161 [**] 0.249 [**] (0.95) (0.90) (2.30) (2.23) [delta] ln[(EXR).sub.t-5] 0.115 0.083 -- 0.158 (0.39) (0.76) (1.47) [delta] ln[(EXR).sub.t-6] 0.401 -- -- -- (1.37) [(EC).sub.t-1] -0.574 [***] 0.078 -0.087 [***] -0.002 (3.15) (1.15) (2.67) (0.88) Goodness of fit statistics Adjusted [R.sup.2] 0.18 0.90 0.90 0.52 F-statistic 1.7[0.5] 30[.00] 62[.00] 4.8[.00] Standard Error 0.025 0.008 0.009 0.005 of the Regression Diagnostic test statistics Q(30) [b] 23[.80] 23[.83] 22[.87] 32[.36] [X.sup.2](1)ht [c] 0.0[.79] 0.2[.69] 1.3[.24] 1.0[.30] [delta] [ln(EXR).sub.t-1] 0.009 -- 0.026 -0.058 (0.12) (0.25) (0.63) [delta] [ln(EXR).sub.t-2] -0.039 -- -0.174 [*] -0.235 [**] (0.52) (1.76) (2.56) [delta] [ln(EXR).sub.t-3] -0.063 -- -0.020 -0.083 (0.81) (0.20) (0.89) [delta] [ln(EXR).sub.t-4] 0.070 -- -0.020 -- (0.76) (0.19) [delta] [ln(EXR).sub.t-5] -- -- -- -- [delta] [ln(EXR).sub.t-6] -- -- -- -- [(EC).sub.t-1] -0.005 [*] -0.004 [***] -0.008 -0.074 (3.46) (2.97) (0.13) (1.16) Goodness of fit statistics Adjusted [R.sub.2] 0.79 0.80 0.57 0.64 F-statistic 14[.00] 21[.00] 6.7[.00] 9[.00] Standard Error 0.003 0.003 0.010 0.009 of the Regression Diagnostic test statistics Q(30) [b] 20[.90] 14.8[1.0] 31[.43] 43[.06] [X.sup.2](1)ht [c] 1.5[.23] 0.63[.43] 0.4[.51] 8.0[.00] [delta] ln[(EXR).sub.t-1] -0.077 (0.84) [delta] ln[(EXR).sub.t-2] -- [delta] ln[(EXR).sub.t-3] -- [delta] ln[(EXR).sub.t-4] -- [delta] ln[(EXR).sub.t-5] -- [delta] ln[(EXR).sub.t-6] -- [(EC).sub.t-1] -0.103 [*] (1.86) Goodness of fit statistics Adjusted [R.sub.2] 0.62 F-statistic 10.5[.00] Standard Error 0.010 of the Regression Diagnostic test statistics Q(30) [b] 37[.17] [X.sup.2](1) ht [c] 1.7[.19]

(a.)Figures in parentheses below estimated coefficients are absolute values of the t-statistic. Figures in brackets are p-values (i.e., the probability of falsely rejecting the null hypothesis).

(b.)The statistic in Ljung-Box test of serial correlation. The null hypothesis is that the residuals are serially uncorrelated.

(c.)The statistic for testing heteroskedasticity based on the regression of squared residuals on squared fitted values. The null hypothesis is that the residuals are homoskedastic.

(*.), (**.), and (***.)denote statistical significance at the 10%, 5%, and 1% level, respectively. All figures are rounded.

Tests of Asymmetric Response of the Export Price Index to Changes in the Exchange Rate [a] (1) (2) [H.sub.0]:[sigma] [H.sub.0]:[sigma] [[[theta].sup.+].sub.i] = 0 [[[theta].sup.-].sub.i] = 0 [H.sub.1]:[sigma] [H.sub.1]:[sigma] [[[theta].sup.+].sub.i] [[[theta].sup.-].sub.i] [not equal to] 0 [not equal to] 0 Japan Model 1 0.845 [*] 0.903 (1.70) (1.36) Model 2 -0.590 [***] -0.321 (3.27) (1.46) Model 3 [c] -0.249 [***] -0.450 [***] (4.63) (4.08) Germany Model 1 -0.0005 0.074 (0.00) (0.27) Model 2 -0.282 [***] -0.110 (3.02) (0.62) Model 3 [c] -0.289 [***] -0.078 (4.63) (1.18) United States Model 1 -0.358 [**] -0.188 (2.46) (1.03) Model 2 [b] -0.211 [***] -0.449 [***] (3.94) (3.00) Model 3 -0.244 [*] -0.198 [*] (1.85) (1.66) (3) [H.sub.0]:[sigma][[[theta].sup.+].sub.i] - [sigma][[[theta].sup.-].sub.i] = 0 [H.sub.1]:[sigma] [[[theta].sup.+].sub.i] - [sigma][[[theta].sup.-].sub.i] [not equal to] 0 Japan Model 1 -0.058 (0.10) Model 2 -0.269 (1.53) Model 3 [c] 0.201 [*] (1.67) Germany Model 1 -0.074 (0.20) Model 2 -0.172 (0.68) Model 3 [c] -0.210 [**] (1.98) United States Model 1 -0.170 (0.64) Model 2 [b] 0.238 (0.82) Model 3 -0.046 (0.21)

(a.)Figures reported in each column are the sum of the coefficients indicated above that column. Figures in parentheses are the absolute values of the t-statistic.

(b.)The values of the t-statistic for the model are calculated using the Newey-West autocorrelation and heteroskedasticity consistent estimates of the variance-covariance matrix of the parameters.

(c.)The sum of coefficients test supports an asymmetric response hypothesis.

(*.), (**.), and (***.)denote statistical significance at the 10%, 5%, and 1% level, respectively. All figures are rounded.

ABBREVIATIONS

ADF: augmented Dickey-Fuller

ECM: error correction model

FPE: finite prediction error

PTM: pricing-to-market

APPENDIX

Data Sources

Export Price Index (XPI, 1990 = 100) [Source: International Financial Statistics (IMF)]. The XPI index is a fixed-weight index of all export prices. Because the data on XPI were not available for the United States, we used an alternative index known as the "export unit value." The latter is obtained by dividing the dollar value of total exports by a measure of total output. The unit value index is a relatively crude measure of average export price, for it may rise due to a shift in the mix of exports in favor of higher quality or luxury items.

Unit Labor Cost Index (ULC, 1990 = 100) [Source: Main Economic Indicators (OECD)]. ULC serves as a proxy for the unit cost of producing one unit of output. The inclusion of raw material or commodity prices would have yielded a more comprehensive measure of production cost. The construction of such an index, however, was hampered by lack of appropriate time series data over the sample period. Another problem arises from the fact that most internationally traded commodity and raw material prices are invoiced in the U.S. dollars and, therefore, are not independent of the exchange rate.

Foreign Price Index (FPI, 1990 100). I constructed the index by calculating the weighted average of the wholesale price indexes (WPI; Source: IMF) of each country's major export markets using bilateral export shares as weights. The export shares, in turn, were calculated as averages for the top 25 markets over the period 1980-85. (Source: Direction of Trade Statistics Yearbook, IMF, 1987). This period roughly corresponds to the middle part of our sample period. Since for a few countries (among the top 25) the data on WPI for the entire sample period were not available, they were dropped in constructing FPI. The remaining countries account for at least 60% of the exports of Japan, Germany, and the United States over the 1980-85 period. A drawback of FPI is that it uses fixed weights (shares).

Nominal Effective Exchange Rate Index (EXR, 1990 = 100) (Source: OECD). This index is constructed by OECD using a weighted average of the bilateral exchange rates of the yen, mark, and dollar versus the currencies of the remaining OECD member countries as well as those of five nonmember countries.

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Author: | MAHDAVI, SAEID |
---|---|

Publication: | Contemporary Economic Policy |

Geographic Code: | 1USA |

Date: | Jan 1, 2000 |

Words: | 9090 |

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