The effects of exchange-rate volatility on U.S. exports: an empirical investigation.

• Author: Arize, Augustine C.

1. Introduction

   The effects of exchange-rate volatility on real exports have been previously examined in the literature, using export demand models that are very restrictive. These models either force the effects of the regressors to be felt fully contemporaneously, or, as in the case of stock adjustment models, they implicitly force the coefficients of the regressors to have the same lag pattern. In either case, the regressions are probably misspecified, and the resulting parameter estimates are biased. The problem is particularly acute in the case of the exchange-rate volatility and relative price estimates; because the effects of these variables are widely believed to build slowly, trade flows with statistically significant lags. Forcing these effects to be felt immediately, or with the same rapidity as changes in activity, may have contributed to the mixed or statistically insignificant estimates that have been obtained.(1)

   The analysis in this paper is distinguished from most previous studies in at least three respects. First, our dynamic modelling of export demand behavior does not follow the restrictive simple stock adjustment mechanism that has been commonly used in several studies. Instead, a less stringent process is used, based on a modified error-correction procedure [24; 15; 19].

   Second, the level specification used in previous studies has not recognized that real exports and some of its proposed determinants such as real world income are, a priori, potentially non-stationary integrated variables. Failure to consider the nonstationarity of the variables may in part explain the mixed conclusions on the effects of exchange-rate volatility.(2) In this study, we establish initially the properties of the individual time series prior to testing for cointegration. Series that are integrated of a different order cannot be cointegrated. In the second step, we employ the maximum likelihood framework for estimating cointegrating vectors between integrated series suggested by Johansen [24]. In the third step, we introduce the estimated error-correction term from the Johansen procedure into our error-correction model.

   A third distinguishing feature of this paper pertains to the measurement of exchange-rate volatility. Following recent specification suggestions, three separate versions of exchange-rate volatility are computed to proxy for exchange-rate uncertainty.

   In the first equation for estimating the determinants of U.S. real exports, we proxied exchange-rate uncertainty by a five-quarter moving average of the variance of the first difference of exchange rate. Jansen [23] has criticized the use of this unconditional measure on the grounds that it lacks a parametric model for the time-varying variance of exchange rate. Therefore, in the second equation estimated, we proxied exchange-rate uncertainty by the Engle [14] model (now well known as the ARCH, or autoregressive conditional heteroskedasficity model), which specifies the variance of a variable as a linear function of the expected squares of the lagged value of the error term from an auxiliary regression determining the mean of the variable of interest.

   Finally, in the third equation that estimates export demand function for the U.S., we employed exchange-rate volatility generated by a model proposed by Antle [3], which is denoted as the linear moment (LM) model. This model specifies the variance (and higher moments) of a variable as a linear (in the parameters) function of the regressors used in an auxiliary regression that specifies the mean of the variable of interest. Pagan, Hall and Trivedi [36] and Holland [22] are but two examples of a number of studies that have used this approach. As Pagan, Hall and Trivedi [36, 586] noted, "the major difference between the ARCH and LM methodologies lies in the type of alternative set up, with the former allowing the variance to be a function of previous forecast errors and the latter being conditional on past values of the explanatory variables."

   A fourth point highlighted in this study is that the export demand equations require the inclusion of the exchange-rate uncertainty variable in order to exhibit the desired property of structural stability. This may partially explain why analysts such as Moreno [33] found that the U.S. export demand function has become structurally unstable. Much of Hendry's work [19; 20] has been devoted to showing that the parameter instability claimed to prevail in empirical equations is a spurious phenomenon due to incorrect specification. A misspecified model might suffer structural shifts when, in reality, the true underlying structural economic relationship has remained unchanged [19, 219].

   The rest of this paper is organized as follows: Section II describes the error-correction model; section III briefly discusses our alternative measures of exchange-rate volatility; section IV reports the results; and a brief conclusion is presented in section V. The data used here are those of Moreno [33] and cover the floating exchange-rate period 1973:2 through 1991:3.(3)

2. Model Specification

   As is customary, the long-run equilibrium export demand function takes the following form:

   [Mathematical Expression Omitted]

   where [Mathematical Expression Omitted] denotes the logarithm of desired real exports, [w.sub.t] is the logarithm of real foreign income; [P.sub.t] is the logarithm of the exchange-rate-adjusted index of the price of U.S. exports relative to trade-weighted foreign prices; v[(h).sub.t] is a measure of exchange-rate uncertainty; and [z.sub.t] is a disturbance term.

   If foreign income rises, the demand for exports will rise, so [Mathematical Expression Omitted] is expected to be positive. On the other hand, if relative prices rise, the demand for exports will fall, so [Mathematical Expression Omitted] is expected to be negative. Most empirical work treats exchange-rate uncertainty as a risk: Higher risk leads to higher cost for risk-averse traders and also to less trade. There are, however, counter-arguments to this. As Bailey, Tavlas and Ulan [6] point out, traders may anticipate future exchange-rate movements better than the average exchange-market participant, and gains from this knowledge could offset the risk of exchange-rate uncertainty. Moreover, if the exchange-rate volatility is due to fundamentals, efforts by the authorities to reduce it by means of exchange controls or other restrictions on trade could be more harmful to trade and could reduce it more. Hence, the effect of exchange-rate uncertainty on export demand cannot be determined a priori but is, rather, an empirical matter.

   To make equation (1) estimable, we need to replace the desired export demand with actual (observable) levels (i.e., [Mathematical Expression Omitted] = [X.sub.t]). To allow for the adjustment of export demand to changes in the regressors, some studies have employed the simple stock adjustment mechanism whereby the entire adjustment is represented by adding a lagged dependent variable as a regressor. However, several researchers have criticized this stock adjustment structure because of its restrictive assumptions [21]. In addition, such an equation is subject to estimation problems due to (a) the correlation between the errors and the lagged dependent variable, even when adjusted for serial correlation [29]; and (b) the "spurious regression phenomenon," first described in Granger and Newbold [18]. This phenomenon, later formalized in Phillips [38], refers to the possibility that inferences based on ordinary least-squares parameter estimates in such regressions are invalid because the usual t- and F-ratio test statistics do not...