Pricing-to-market: price discrimination or product differentiation?

Movements in exchange rates can have an important influence on an imperfectly competitive exporter's pricing behavior. Exchange rates create a wedge between the price set by the exporter and the price paid by the importer, and can be used as an instrument of price discrimination. The idea that an exporter can adjust destination-specific markups to accommodate changes in exchange rates was first documented in Dunn (1970) and Mann (1986) and later was termed "pricing-to-market" (PTM) by Krugman (1987). Knetter (1989) developed an empirical model to analyze the presence of PTM. Knetter's model has since been used extensively, due to its simplicity and data availability, to determine the presence of price discrimination in international trade. This approach has been particularly popular in the study of food and agricultural exports (e.g., Pick and Park 1991; Pick and Carter 1994; Griffith and Mullen 2001; Carew and Florkowski 2003; and Glauben and Loy 2003), automobile exports (e.g., Knetter 1989, 1993; Marston 1990; Gagnon and Knetter 1995), and in a wide range of other industries)

Most PTM studies, such as those listed above, use export unit values as the price variable. (2) Export unit values are calculated as the ratio of value to volume of exports for a specific product category and destination country. Market- or customer-specific price information is typically confidential, making export unit values the next best alternative. The disadvantage of unit values is that they often aggregate data on products employed for very different uses. (3) Thus, findings of PTM that are attributed to price discrimination might alternatively indicate product differentiation when unit values are used (Sexton and Lavoie 2001). It is important to understand the effect of unit value data on PTM testing because evidence, or lack of evidence, of PTM can be used for policy purposes (e.g., Carter 1993; Gil-Pareja 2003). Moreover, PTM can have important effects on the international transmission of monetary and fiscal policy, and can increase exchange rate volatility, relative to a situation where markets are integrated (Betts and Devereux 2000). The objective of our study is to examine the potential bias in pricing-to-market results when using unit values aggregating differentiated products.

Product differentiation has been explicitly modeled in studies evaluating the extent of exchange rate pass-through (e.g., Dornbush 1987; Feenstra, Gagnon, and Knetter 1996; Yang 1997; Bodnar, Dumas, and Marston 2002). (4) In these studies, substitution occurs between a good produced by the home firm and a good produced by the foreign firm. Our analysis of product differentiation differs from the above studies in two respects. First, substitution occurs between a set of vertically differentiated goods produced in the home country and sold to the home and a foreign market. Second, we specifically examine how product differentiation affects the test of PTM.

The disadvantages of unit values are acknowledged in many PTM studies using Knetter's model. Common criticisms of unit values are that they do not account for different qualities shipped to different markets and for changes in product quality over time (Gil Pareja 2002). (5) However, authors, like Knetter (1989), typically argue that systematic differences in product quality, such as shipping different qualities to different markets, can be captured by country dummies. Similarly, changes in the quality of the product that is common across countries can be captured by time effects. Thus, the impact of product differentiation on the evaluation of PTM is typically argued to be minimal. (6)

While prior authors acknowledge the problems associated with unit values when they reflect different qualities shipped to different countries or across time, we address an issue that to our knowledge has not been studied before in the PTM literature. Namely, we examine destination-specific changes in the product-quality mix and the false PTM findings that may result when unit values aggregate differentiated products. False PTM findings occur because fluctuations in exchange rates cause a change in the product-quality mix exported, which in turn affect the unit values. We demonstrate that this relationship between exchange rate and unit values can be mistakenly interpreted as PTM in empirical work. We also show that the magnitude of the bias in PTM results depends on the level of product differentiation. (7)

To examine the incidence of spurious PTM results, we introduce a conceptual model where a monopolist sells vertically differentiated products to a domestic and a foreign market. Two polar scenarios are analyzed. In the first one, there is perfect and costless consumer arbitrage, and the law of one price (LOP) holds for individual products (i.e., before aggregation). In the second scenario, consumer arbitrage is not feasible and markets are segmented. In both scenarios, we find "pseudo PTM," i.e., PTM that is purely the result of data aggregation and product differentiation rather than price discrimination across markets. In the first scenario, there is pseudo PTM only. In the second scenario, there is "real PTM" as well because markets are segmented, and we show that the extent of pseudo PTM increases with the level of product differentiation. (8) To evaluate the implication of these findings for empirical work, we employ Monte Carlo simulations analyzing the relationship between PTM and the level of product differentiation. The results indicate the presence of pseudo PTM for a sufficiently high level of product differentiation when the LOP holds. In both scenarios, a higher level of product differentiation is more likely to lead to a statistically significant evidence of PTM.

The rest of the article is organized as follows. First, we present the conceptual model and the analysis of the two scenarios. This is followed by a simulation study and the conclusion.

The Model

Consider two countries: country 1 and 2. A monopolist in country 1 produces two vertically differentiated products with exogenous qualities [q.sub.l] and [q.sub.h] (0 < [q.sub.l] < [q.sub.h]). The two goods are sold domestically and exported to country 1 2 for the product of 2. The marginal cost is 1/2 [q.sub.2.sub.j] quality [q.sub.j] (j = l, h). (9)

We model vertical differentiation a la Mussa and Rosen (1978). Consumers are heterogeneous in their valuation of quality. The conditional indirect utility of a consumer with a marginal willingness to pay for quality of [theta] and income y is given by y + [[theta].sub.q] - p if she buys one unit of the product of quality q at price p, and y if she does not buy the differentiated product. There is a continuum of consumers with total mass of one distributed uniformly in each country. In other words, [theta] [member of] U[0, [[theta].sub.i]] with density 1/[[theta].sub.i] in country i (i = 1, 2).

Let [[theta].sub.il] (i = 1, 2) denote the consumer in market i who is indifferent between buying the low-quality product or not buying the differentiated product. In other words, that consumer obtains the same level of indirect utility from either option. Thus, [[theta].sub.il] is the value of [theta] that solves y + [theta] [q.sub.l] - [[lambda].sub.i] x [p.sub.il] = y, where [[lambda].sub.1] = 1 and [[lambda].sub.2] = e, and e is the exchange rate expressed in units of country 2's currency per unit of country l's currency. (10) Similarly, [[theta].sub.ih] is the consumer in market i who is indifferent between buying the low--or high-quality product, i.e., [[theta].sub.ih] is the value of [theta] that solves y + [theta][q.sub.h] - [[lambda].sub.i] x [p.sub.ih] = y + [theta] [q.sub.l] - [[lambda].sub.i] x [q.sub.il] with [[lambda].sub.1] = 1 and . Thus, consumers with [theta] [member of] [0, [[theta].sub.il] will not buy the differentiated product, those with [theta] [member of] [[[theta].sub.il], [[theta].sub.ih]] will buy the low-quality product and the others ([theta] [member of] ([[theta].sub.ih], [[theta].sub.i]]) will buy the high-quality product. (11) Accordingly, the demand for each quality is the length of the consumer interval buying the given quality multiplied by the density of consumers along that interval (1/[[theta].sub.i]) times the total number of consumers, N = 1. The demands for the low- and high-quality products in country i = 1, 2 are

(1) [d.sub.il] (p.sub.ih], [p.sub.il]) = [[theta].sub.ih] - [[theta].sub.il]/[[theta].sub.i] = [[lambda].sub.i] ([p.sub.ih] [q.sub.l] - [p.sub.il] [q.sub.h])/[[theta].sub.i] ([q.sub.h] - [q.sub.l]) [q.sub.l],

(2) [d.sub.ih] ([p.sub.ih], [p.sub.il]) = [[theta].sub.i] - [[theta].sub.ih]/[[theta].sub.i] = 1 - [[lambda].sub.i])[p.sub.h] - [p.sub.l])/[[theta].sub.i] ([q.sub.h] - [q.sub.l]).

When there is pricing-to-market, a firm with market power will set different prices (in the same currency) in different markets based on their respective market conditions. Accordingly, Marston (1990) examines PTM by forming the ratio of the export to the home price set by a domestic monopolist and evaluating how it varies with the exchange rate. Similarly, we use the domestic-export price ratio

(3) X = [P.sub.1]/P.sub.2],