Exchange rate volatility and international trade.

1. Introduction

One of the issues that has received considerable attention in international economics is the effect of exchange rate risk on the volume of international trade (Kawai and Zilcha 1986; Franke 1991; Viaene and De Vries 1992; Gagnon 1993; Dellas and Zilberfarb 1993; Broll, Wong, and Zilcha 1999). It has been argued that higher exchange rate volatility has led to a decrease in international trade. The empirical evidence, however, regarding the effect of exchange rate randomness on international trade has at best been inconclusive (Cushman 1988; Giavazzi and Giovannini 1989; Stein 1991). The large majority of the empirical studies are unable to establish a systematically significant link. As an exception to this rule, De Grauwe (1992) classides 12 major industrial countries into two groups: those that have experienced relatively stable exchange rates (mainly the European Monetary System [EMS] countries) and those that have seen their exchange rates fluctuate a lot (three to five times as much as the former countries), He finds that, during the 1980s, the growth rates of output and exports have on average been significantly lower in the EMS countries than in the non-EMS countries.

The above-mentioned empirical studies are based on aggregate data; that is, they test the hypothesis of a significant negative effect of increased exchange rate risk on aggregate trade flows. This hypothesis is natural and conforms to a large body of theoretical work because a firm can avoid part of the higher foreign revenue risk by reducing its export activity. Yet because no significant negative impact has been found on the aggregate level, one may conjecture that, contrary to economic intuition, industries do exist (e.g., in the export sector) that are effectively able to take advantage of larger exchange rate fluctuations and therefore expand their production. The aggregate data available to the authors do not allow the identification of specific industries meeting this criterion. Yet it appears natural to think of industries that are able to react in a flexible manner to changes of international exchange rate parities because they can easily reallocate their products between different markets. If so, we should expect positive correlations between industry-specific export volumes and exchange rate volatility to be more common in countries like the United States, where companies benefit from a large domestic market that permits them to compensate exchange rate fluctuations more easily. In fact, empirical findings by Cushman (1988) and Peree and Steinherr (1989) lend some support to that view.

Motivated by the above empirically based conjecture, the analysis of this paper describes a specific channel through which exchange rate volatility may affect international trade. If the market structure allows a firm to view its exports as an option, then larger stochastic fluctuations of the exchange rate will increase the value of the export option and hence stimulate the firm's production activity. More specifically, we consider a model of a price-taking, risk-averse international firm which can produce a product for sale in the domestic or the foreign market. All prices are certain except for the foreign exchange rate. The production decision has to be made before the exchange rate uncertainty is resolved. Assume, however, that the firm is flexible enough to postpone its choice between the domestic and foreign market for the sale of its products so as to make the sales decision contingent on the realization of the exchange rate. Thus the timing of events in the model is as follows. At the initial date, t = 0, the production decision is made. At t = 1, all uncertainty is resolved and the produced goods are allocated to the domestic or foreign market.

The export strategy is like an option because the domestic market return is certain whatever the realized exchange rate turns out to be. The domestic price is the "strike price" of the real export option. Therefore the possibility to export when exchange rates are favorable constitutes a real call, optionlike source of profits for the export-flexible firm. As the exchange rate volatility increases, so does the value of the option to export to the world market. This is a standard property of option values. Higher volatility increases the potential gains from international trade by making extremely high realizations of the foreign spot exchange rate more likely. The corresponding higher probabilities of low realizations of the foreign spot exchange rate do not offset these gains because the firm may choose to walk away from the export option. Losses are effectively truncated. We show that increased riskiness affects the volume of international trade, but this effect can be either positive or negative depending on the firm's attitude toward risk.

The intuition behind this result is as follows. Given that the firm is averse to risk, an increase in foreign market uncertainty induced by an increase in exchange rate volatility reduces its expected utility of income. This effect implies a decrease in both production and the volume of international trade. However, larger exchange rate fluctuations make the real option to trade internationally more profitable, which tends to stimulate production and exports. Which of these effects dominates depends on the firm's attitude towards risk. As our analysis demonstrates, an increase in exchange rate volatility increases the volume of production and international trade if relative risk aversion is less than unity. Hence, in contrast to the analysis described in the traditional theoretical literature, exchange rate volatility may have a positive impact on international trade. This may explain part of the mixed empirical findings mentioned above.

The plan of the paper is as follows. In section 2, we present the model of an exporting firm under exchange rate uncertainty with ex post flexibility as to the sale of its products in a domestic or foreign market. The main results are derived and discussed in section 3. The final section 4 contains brief concluding comments.

2. Uncertainty, Sales Flexibility, and Trade

The earlier literature on the interaction between exchange rate risk and international trade generally assumes that an exporter sells all production to the world market, irrespective of the exchange rate. In this work, we generalize that assumption by allowing the firm to adjust the export volume to the level of the foreign exchange rate. When the exchange rate surges to high levels, exports are increasing. When the exchange rate drops below a certain level, exports fall to zero. Exporting is a real option that is exercised if profitable.

Consider a competitive, risk-averse firm that produces a commodity to be allocated to the domestic market and one foreign market. The foreign spot exchange rate is a random variable. The firm is a price taker in the sense that its action does not affect the prices of the goods at home and abroad. While this specification greatly simplifies our analysis, it is not critical for the results derived in section 3. Under suitably modified assumptions, all results remain valid if the firm confronts downward-sloping demand curves for its product in both markets. The chosen specification derives support from the literature on international price dynamics; this literature has demonstrated that exchange rate changes do not affect the prices of traded goods in any systematic or uniform way. The degree to which exchange rate changes are reflected in the destination currency prices of traded goods (exchange rate pass-through) is incomplete and differs across countries and industry sectors. Khosla and Teranishi (1989) find that the pass-through ranges across countries from a high of 96% (Sweden) to a low of 0% (Norway). Studies by Ohno (1989), Kim (1990), and Marston (1990) demonstrate that pricing to market behavior is widely practiced in many countries; that is, exporters pass-through only a very small percentage of rate depreciations and inflate their profit margins instead.

The objective of the firm is to maximize the expected utility of its local-currency profits. We take the von Neumann-Morgenstern utility function, U([center dot]), to be strictly concave, increasing, and differentiable. The production process adopted by the firm gives rise to a cost function, C(y), where y is the quantity of output. We assume that C(0) = 0, that C(y) is strictly convex, increasing, and differentiable, and that prices are such that the firm always produces a positive amount. Hence, for given total production y the firm's random revenues in domestic currency are px + eq(y - x), where p, q are the prices of goods at home and abroad, y is total production, x is domestic supply, and y - x is the export volume.

Production is fixed in the sense that it must be chosen before the spot exchange rate is realized. The allocation decision is variable because it can be postponed until the exchange rate has been observed. For concreteness, let us specify the time structure of the model as follows. In the current period, 0, the firm decides on total production y, which gives rise to the production costs C(y). In period 1, the random exchange rate is realized. At that time, the firm decides on the allocation of the output to the home and foreign goods markets. Thus the allocation decision can be made conditional to the realization of the exchange rate. This feature is reflected in the notion of flexibility.

Real-world examples of industries in which production decisions are typically made in advance of the decision over how to allocate the produced goods across countries include the agricultural sector and firms that have temporarily reached their capacity limits. The framework of the model could also be interpreted in terms of a firm that considers investing in a new factory to meet increased demands on both domestic and foreign markets. The decision to produce is then implicit in the sunk cost of the factory and therefore precedes the realization of uncertainty as well as the firm's action on the export market. Because the law of one price does not hold in this model, the markets across which goods can be allocated are assumed to be segmented in the sense that the market arbitrage of goods is either impossible or unprofitable. Examples include the markets for brand-name products such as California wine, French cognac, Dutch flowers, German cars, etc.

ASSUMPTION A.1. The exchange rate is random where [Mathematical Expression Omitted] and [Gamma] are the expected value and standard deviation, respectively; that is,

[Mathematical Expression Omitted], E[Epsilon] = 0, [Mathematical Expression Omitted], [Gamma] [greater than] 0

with mean-zero uncertainty [Epsilon].

The parity exchange rate for the internationally traded goods is [Mathematical Expression Omitted]; [Gamma] is a shift parameter. An increase in [Gamma] leads to an increased spread of the probability distribution around the constant mean, and this will be taken as the definition of an increase in the riskiness of the foreign spot exchange rate.

Ex Post Decision

Because the allocation of the produced goods is chosen after the exchange rate has been observed, it is clear that the allocation decision will be made on the basis of a comparison of the sales prices (in home currency) on the home and foreign goods market. The firm's profit at date 1 is given by

[Pi] = px + eq(y - x) - C(y).

The optimal decision rule at date 1 is found by maximizing profit with respect to the optimal allocation of production for realized e and given y. With Assumption A.1, for any realization [Epsilon] [greater than] 0, the firm's exports are equal to the total production. The export volume equals zero for all realization [element of] [less than] 0. In this model, rational behavior implies that the whole production of the firm will be shifted from the foreign to the domestic market if the foreign currency weakens. Because market switching costs can be substantial in reality, and because criteria other than profits (e.g., market shares) can matter, a firm's reaction to price differentials may be far less pronounced than our model suggests. Yet it is clearly robust that the basic idea of market switching, viewed as an option, is an opportunity the value of which is positively related to the volatility on the foreign exchange market; market switching tends to produce the same qualitative effects even in more general frameworks. At the realization [Epsilon] = 0, the firm is indifferent between selling in the domestic market and selling in the foreign market. Our decision rule assumes that, in this case, the output will be allocated to the domestic market. Thus we obtain the following contingency rule for the optimal allocation of output:

[Mathematical Expression Omitted].

This condition implies that the optimal allocation depends on the realized foreign exchange rate e. If eq [less than] p, the option to export is left unexercised. Hence the payoff resulting from the opportunity to shift one unit of production from the domestic market to the foreign market is eq - p if eq [greater than] p, and zero otherwise. This payoff, which may be written as max (eq - p, 0), is identical to that of a call option which gives the option holder the right to buy a financial asset at the exercise price p if the asset's spot price, eq, happens to be above the exercise price.

The time-0 value of the export option may therefore be valued using standard option-pricing techniques (Black and Scholes 1973; Rubinstein 1976; Drees and Eckwert 1995). Leaving aside this pricing problem, the aim of our study was to analyze the interaction between production and exchange rate volatility in the presence of an export option.

Ex Ante Decision

At date 0, the firm maximizes the expected utility of profit by choosing total production y, given the probability distribution of [Epsilon] and the optimal decision rule (contingency rule) for the allocation of production at date 1. Thus, the decision problem can be written

[Mathematical Expression Omitted], (1)

where [Mu] is the probability measure of the random variable [Epsilon].

The necessary and sufficient first-order condition for optimal output at date 0 reads

[Mathematical Expression Omitted], (2)

where U[prime]([center dot]) is the marginal utility, and an asterisk indicates an optimum level. From this condition (Eqn. 2) we can show that, with low relative risk aversion, a positive effect of exchange rate volatility on production and international trade exists.

3. Exchange Rate Volatility, Production, and Trade

In this section, we demonstrate that the volume of exports and total output may depend positively on the variance of the foreign spot exchange rate. This property holds if the degree of relative risk aversion is not too high.

PROPOSITION. Consider a firm acting under exchange rate uncertainty and sales flexibility as described above. The firm's total production is increasing in exchange rate volatility, d[y.sup.*]/d[Gamma] [greater than] 0, if the degree of relative risk aversion is less than unity; that is, R([Pi]) [equivalent to] - U[double prime] ([Pi])[Pi]/U[prime]([Pi]) [less than] 1, [for every] [Pi] [greater than] 0.

PROOF. In view of the first order condition (Eqn. 2), optimal output [y.sup.*] is a function of exchange rate volatility [Gamma]. Implicit differentiation of Equation 2 yields:

d[y.sup.*]/d[Gamma] = -[Gamma]/[Delta] (3)

where

[Mathematical Expression Omitted], (4)

and

[Mathematical Expression Omitted].

Direct inspection shows that the denominator, [Delta], is less than zero.

Regarding the sign, [Gamma], observe that C([y.sup.*]) [less than] [y.sup.*]C[prime]([y.sup.*]) holds by the strict convexity of the cost function. Thus,

[Mathematical Expression Omitted]. (5)

The claim in the proposition now follows from Equation 3.

The proposition states a sufficient condition for a positive link between exchange rate volatility and exports that may not, however, be necessary. In fact, starting from [Gamma] = 0 (constant exchange rate), greater exchange rate volatility always stimulates exports. This is implied by Equation 3 if we use the equality p = C[prime]([y.sup.*]) from Equation 2 to derive a positive sign for F in Equation 4. In economic terms, the marginal disutility of risk at [Gamma] = 0 is zero because the firm does not bear any risk. Thus, at the margin, higher exchange rate volatility increases the value of the option to export without causing utility costs associated with higher risk exposure.

Premium for the Export Option

What is the export option worth? In the absence of an export option the firm attains the utility level

U[p[C[prime].sup.-1](p) - C([C[prime].sup.-1](p))].

If the firm were to pay K dollars for the right to export, the expected utility of net profits, [[Pi].sup.*] - K, is

[Mathematical Expression Omitted].

Thus the premium, K, that firms are willing to pay for the export option is implicitly defined by

W(K, [Gamma]) = U [p[C[prime].sup.-1]' (p) - C ([C[prime].sup.-1](p))].

Because W(K, [Gamma]) is strictly increasing in [Gamma] and strictly decreasing in K, the export option premium is non-negative and depends positively on the volatility of the exchange rate.

The firm's exports are equal to the production volume, y, for any realization [Epsilon] [greater than] 0 and are independent of y for all realization [Epsilon] [less than] 0. Therefore the proposition implies a positive link between exchange rate volatility and average exports (volume of international trade) in economies with low aversion to risk. This is summarized as follows.

COROLLARY. The average export volume of the firm considered in the proposition is increasing in exchange rate volatility if the degree of relative risk aversion is less than unity.

4. Concluding Remarks

In this paper, we have explored some of the implications of exchange rate uncertainty for the behavior of a competitive firm. In particular, we have analyzed the impact of exchange rate volatility on the optimal export policy of this firm and have found some indication that exports might get stimulated. In our example, an international firm decides upon production before the exchange rate uncertainty materializes. However, the decision whether to sell in the domestic market or in the world market can be made contingent on the realization of the spot exchange rate. This feature is intended to capture the idea of sales flexibility on the part of the firm in international markets. In practice, multinational firms can be especially regarded as firms with some degree of sales flexibility because of their worldwide distribution system.

The specification of the firm's decision problem implies an extreme allocation of sales. The whole production will either be sold on the domestic market or entirely be shifted to the foreign market. This somewhat peculiar feature of the model could be generalized by assuming that exports decline when the foreign currency weakens but do not drop to zero. With this modification, the firm's profits continue to be a convex function of the exchange rate; this is sufficient to ensure that, qualitatively, the results in section 3 remain valid.

The aim of our study is to establish that a positive link between exchange rate volatility and international trade has a theoretical basis. The economic intuition for the mechanism derived in this paper is the following: As the exchange rate volatility increases, so does the value of the option to export to the world market. Higher volatility increases the potential gains from international trade, which makes production more profitable. However, a more volatile exchange rate implies a higher risk exposure for international firms. This effect works in the opposite direction and tends to decrease production and the volume of international trade. The net effect of exchange rate uncertainty on production and exports depends on the degree of relative risk aversion of the firm. This effect may explain part of the mixed empirical findings in the applied economic literature regarding the effects of exchange rate risk on international trade.

In our static approach, the timing of the allocation by producers is exogenous. An extended dynamic version of the model that allows for storage activity could explain the time path of production and production allocation. In such a dynamic context, the character of exports as an optional activity is likely to further enhance the positive link between exchange rate volatility and production because the possibility to pile up inventories delays the export option's time-to-expiration, thereby further increasing the option's value.

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