Exchange Rate Shocks and the Speed of Trade Price Adjustment.

• Author: Ran, Jimmy

Jimmy Ran [+]

Ronald Balvers [*]

A quantity adjustment cost model is developed in the context of international trade along the lines proposed by Krugman (1987). The model implies that prices adjust dynamically to exchange rate fluctuations. The price adjustment speed is determined as a function of foreign demand responsiveness, the appropriate discount rate, and an adjustment cost parameter. Passthrough is incomplete and increases over time and with the speed of price adjustment. A preliminary empirical analysis finds that the speed of price adjustment from the time series by industry and then in a cross-sectional regression tentatively relates the obtained adjustment speeds to their theoretical determinants.

1. Introduction

   Theoretical and empirical work in the international trade literature dealing with the relationship between exchange rate and trade prices has been dominated and guided by the static pass-through and profit markup model [1] (see, e.g., Feinberg 1986; Mann 1986; Fisher 1989; Hooper and Mann 1989; Knetter 1989; Gagnon and Knetter 1995; Feenstra, Gagnon, and Knetter 1996; and Lee 1997). The shortcoming of such models is well captured by William Branson (1989, p. 333):

   Difference in adjustment response signals to me the need for a reconsideration of the theoretical framework for the analysis of the pass-through question. By now, we should be thinking about optimizing price policy for investors and exporters who know that they face an exchange rate that follows some sort of stochastic process over time. These differences call for a revision of pass-through theory along the lines of time series analysis.

   Our explicit incorporation of profit-maximizing firms facing adjustment costs develops the model introduced by Krugman (1987). It transforms the traditional markup and pass-through model to explain from first principles a dynamic markup and a price adjustment speed, both depending on fundamental characteristics of the firms involved. Krugman (1989) concludes his paper on pricing to market by calling for further research on the adjustment cost model. Regarding the adjustment cost approach, he states (Krugman 1989, p. 44),

   It is still a speculative idea, not grounded in solid empirical tests; but it is a good story, and if it is correct, it has extremely important implications for economic policy.

   The present paper provides the quantity adjustment cost approach that Krugman calls for. As such, it complements the work of Gagnon (1989) and Kasa (1992). While Gagnon and Kasa employ quantity adjustment cost models with many of the same features as the model developed here, they provide only approximate solutions and focus on a quite different set of issues. Gagnon examines the effect of exchange rate variability on trade volume. Kasa investigates the importance of mean reversion in exchange rates as an explanation for the pricing to market hypothesis. In contrast, our focus is on the relation between adjustment speeds and pass-through. Thus, our contribution relative to Gagnon (1989) and Kasa (1992) is that we provide the passthrough issue in a dynamic context with exact analytical solutions that relate the degree of passthrough to adjustment speeds and identify the determinants of commodity-specific adjustment speeds in response to exchange rate shocks.

   The remainder of the paper is organized as follows. In section 2 we develop a partial equilibrium model, taking exchange rates as given, of the pricing policies of a profit-maximizing firm competing in foreign markets and subject to a convex quantity adjustment cost. Section 3 develops testable implications directly from the model. Section 4 discusses the data and empirical methodology for preliminary two-stage time-series and cross-sectional tests. Section 5 provides the tentative estimation, and section 6 concludes.

2. A Simple Partial Equilibrium Model

   Consider a representative firm producing for export that maximizes the expected discounted value of infinite horizon real profits. The firm generates its revenue abroad in foreign currency. It has no influence on the exchange rate, may adjust its price at any point in time, but is subject to a convex cost of quantity adjustment. The firm maximizes

   [pi] = E [[[integral of].sup.[infty]].sub.0] [e.sup.-rt][xpq - c([w.sub.D], x[w.sub.F])q - [frac{1}{2}]xh[(q').sup.2]]dt, (1)

   where x is the exogenously given real exchange rate at time t. We define x as the units of domestic currency per unit of foreign currency multiplied by the export destination country's price index and divided by the home country's price index. Instantaneous profits are discounted at a rate r, which is specific to the firm; this rate accounts for a standard risk premium inherent in the riskiness of the firm's activities. Price p is the real foreign currency-denominated sales price in the foreign market at time t. Quantity q represents the firm's export delivery at time t. The first term inside the integral is the revenue obtained in the foreign country converted back into home currency by the exchange rate. The second term is the firm's (indirect) cost function. For simplicity, we assume that production exhibits constant returns to scale in domestic inputs with exogenous price [w.sub.D] and foreign inputs with exogenous foreign price [w.sub.F] (which becomes x[w.sub.F] in home currency terms). We thus consider a constant (i.e., independent of the production level) marginal production cost c (which may include a transportation cost) as a function of these input prices.

   The last term in Equation 1 represents the convex quantity adjustment cost (with parameter h), which is here assumed quadratic for simplicity. In our continuous-time formulation, the change in quantity is indicated conventionally by q'. Note that the adjustment cost is viewed as incurred abroad so that its cost must be premultiplied by the real exchange rate to convert back to domestic currency units. A motivation for this adjustment cost formulation is provided by Krugman (1987, p. 63): Temporary bottlenecks occur because of changing trade volume. Sales cannot be expanded without an expansion of the "infrastructure" related to sales, distribution, and service. Thus, while production costs occur domestically, the quantity adjustment costs may be viewed as occurring abroad and should be adjusted for real exchange rate fluctuations.

   For purposes of tractability, we consider a linear form for the foreign demand curve

   q = a - bp, (2)

   where a and b are positive and finite-valued constants. The finiteness of b reflects the assumption of price-setting power on the part of the firms. The firm is assumed to compete monopolistically only with foreign firms producing for their own market. [2] Strategic interactions are ignored, not only for tractability but also because it is difficult to choose one particular strategic game to be relevant for the whole spectrum of industries we consider. As noted by Dornbusch (1987), who employs a similar linear demand curve, all nonprice determinants of demand are captured by the constant.

   The decision problem for the exporting firm thus is to choose the pricing process to maximize Equation 1 subject to Equation 2. The model's functional form assumptions here are quite similar to the assumptions in the models used in the related literature by Krugman (1987), Gagnon (1989), and Kasa (1992), in particular, the partial equilibrium formulation, the constant marginal production cost, the monopolistic market form, the quadratic adjustment cost, and a specific functional form for the demand curve. A dynamic programming approach (derivation in the Appendix) produces the following solution:

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