ANY PLAUSIBLE THEORY of real exchange rate determination must be able to resolve two prominent stylized facts regarding international relative prices. First, at an aggregate level, real exchange rate movements tend to be very persistent. Second, at the micro level, individual prices tend to be sticky in terms of local currency.¹ Of course, open-economy models in the Keynesian tradition have long since emphasized sticky prices in goods and labor markets. Perhaps the best-known example is the Dornbusch (1976) overshooting model, wherein sticky goods prices in conjunction with flexible, forward-looking exchange rates lead to real exchange rate overshooting and transitory deviations from purchasing power parity (PPP).

However, by invoking the law of one price, this literature incorporates price stickiness at the point of origin rather than at the market destination. In other words, the standard Keynesian approach generates price-level inertia in terms of national currency (seller’s currency) rather than local currency (buyer’s currency). Furthermore, by relying on the law of one price, these models typically cannot generate the degree of persistence that is observed in actual real exchange rate time series. Not only do real and nominal exchange rates move together over the short term, they often move together over much longer horizons as well—sometimes over many years.

The law of one price has of course had a long-standing tradition in international economics. Interpreted as a condition for spatial arbitrage, the law of one price requires that the price of a good be the same in all locations when measured in a common currency. Extending this condition to all traded goods, PPP theory posits an aggregate version of the law of one price, applied at the level of national price indices. The theory maintains that the price of entire baskets of goods should be equal (or proportional) across countries. Together, PPP and the law of one price have served as the basis for some of the most widely-held theories in international economics, greatly influencing the discourse on exchange rate determination.

Meanwhile, empirical evidence supporting the law of one price has remained elusive. Numerous empirical studies have consistently documented the absence of “one price” in practice, net of transport costs, tariffs, and other trade impediments.² In combination with the very mixed evidence on PPP,³ some have begun to call into question those theories that rely upon the concept of spatial arbitrage in goods.⁴ Given its dubious validity, the law of one price has been subject to various modifications,⁵ including the allowance of systematic violations to one price as manifested by the phenomenon of pricing to market.

With pricing to market, forces that would normally assure spatial arbitrage are absent, allowing corresponding prices to diverge across markets. This view—which is adopted in this paper—essentially breaks from standard models by favoring market segmentation rather than integration, and thereby acknowledging the presence of economic barriers and structural rigidities that restrict convergence in intermarket prices. Pricing to market may thus provide an alternative to the traditional view that differential rates of adjustment in goods prices versus asset prices alone underlie persistence in the real exchange rate.

Much of the empirical evidence on market segmentation has drawn from the experience of United States in the 1980s. In particular, several studies have focused on the behavior of U.S. import prices during the period of massive appreciation⁶ and subsequent depreciation⁷ of the dollar. For example, Krugman (1987) examines U.S. import prices during the period of the dollar’s rise. Constructing dollar price indices for U.S. import bundles and comparing them with the dollar price of the same bundle exported to third-country markets, he concludes that more than 30 percent of the real appreciation of the dollar was reflected in a divergence between these prices.

In light of the empirical support for the proposition that certain markets may be segmented, the theoretical avenues regarding the issue of pricing to market have not yet been fully developed. Typically, models of pricing to market present static, partial equilibrium results from the perspective of an exporting industry or firm.⁸ Hence, these models cannot address the dynamic price interactions and adjustment underlying the evolution of relative prices and the real exchange rate at the macroeconomic level.

Using a general equilibrium model of monopolistic competition and market segmentation, this paper investigates the macroeconomic consequences of pricing to market for real exchange rate behavior across different patterns of trade. Allowing producers to price discriminate between local and foreign markets, the monetary model examines exchange rate pass-through and pricing-to-market behavior under segmented markets, and relative-price dynamics under nominal rigidities. By also incorporating the structure of trade, the paper examines the cross-sectional implications of intersectoral versus intraindustry trade for macroeconomic adjustment.⁹

The central result can be summarized as follows. The pattern of industry specialization and trade largely determines the degree of strategic complementarity or price linkage between producers from different countries. In particular, under intraindustry trade—wherein home and foreign products are close substitutes—there exists a higher degree of linkage between domestic and foreign prices prevailing in the same market than under intersectoral (cross-industry) trade. Consequently, domestic and export prices exhibit greater responsiveness to exchange rate fluctuation, a lower degree of pass-through, and a greater degree of pricing to market under two-way trade.

In a setting of imperfect integration,¹⁰ a greater degree of price linkage across borders translates into stronger mean reversion in the real exchange rate. The intuition is as follows. With menu costs and price staggering, prices display inertia in terms of national currency (unit of account) through a lack of coordination among decentralized price setters. In an open economy, however, producers are concerned with relative prices both at home and abroad. With the law of one price, the added concern with the foreign currency price of output compels price setters to partly overcome the coordination failure underlying domestic price inertia. Prices become less sticky in terms of national currency in order to reduce variation in terms of foreign currency. Hence, the stronger international linkage in prices under two-way trade reduces the variability and persistence of real exchange rate fluctuation compared with inter-sectoral trade.¹¹ However, once the assumption of spatial arbitrage is removed, this comparative result no longer holds true.

Once export prices detach from domestic prices with segmented markets, prices are in effect set in terms of local currency rather than national currency, and price linkages predominantly exist within a particular market rather than across markets. If home and foreign prices are inertial in the same unit of account, the pattern of trade no longer affects the comparative degree of variability and persistence in relative prices. Instead, the level of persistence becomes solely a function of the frequency and timing of price adjustment. As a result, market segmentation allows international relative prices to exhibit equally persistent deviations across diverse patterns of trade, despite inherent differences in the substitutability between home and foreign goods.

Comparative issues aside, pricing to market ensures greater price stability in terms of local currency than otherwise, regardless of the trade pattern. Consequently, segmented markets allow greater inertia in the price level domestically and slower adjustment in relative prices internationally than under the law of one price. Thus, pricing to market provides an important propagation mechanism for explaining the large and protracted swings in real exchange rates characteristic of the post-Bretton Woods era. Moreover, in the presence of market segmentation, monetary shocks have lasting effects on relative prices. Without goods arbitrage, absent are the economic forces that would otherwise guarantee the equivalent price of a basket of goods across countries. Instead of long-run PPP, monetary disturbances have permanent effects on the real exchange rate in the absence of one price.

Persistence and permanence in relative prices have important time-series implications for exchange rates. When monetary shocks have persistent effects on relative prices as a result of price level inertia, nominal and real exchange rates move together in the short run, as has been emphasized in earlier sticky-price models. When monetary shocks have “permanent” effects on relative prices, nominal and real exchange rates move together over the longer run as well—so long as markets remain segmented and the law of one price systematically fails.

The paper is organized as follows. Section I develops a two-country model of monopolistic competition and market segmentation under intraindustry and intersectoral trade. Using this static framework, Section II addresses the issues of exchange rate pass-through and pricing to market. A dynamic version of the model is developed in Section III. Incorporating nominal rigidities into the analysis, this section examines the dynamic adjustment of relative prices and the time-series behavior of the real exchange rate. Section IV offers some concluding remarks.

I. Model of Pricing to Market

Consider a world economy consisting of a home and a foreign country, with each country composed of Nproducer-consumers. These individual agents produce and sell a differentiated good in order to purchase and consume the variety of goods made by all agents, taking others’ prices as given. Meanwhile, each agent acts as a monopolistic competitor, setting a price and choosing a level of production depending on the demand that the individual producer faces. Building on the constant elasticity of substitution (CES) approach of Dixit and Stiglitz (1977), the model focuses on two basic variants of this central framework: the cases of intersectoral and intraindustry trade.¹²

Under intersectoral trade, countries specialize and trade at the industry level according to international differences in comparative advantage. This pattern of trade—often associated with the exchange between north and south—emerges as a result of underlying differences in relative factor proportions and gains from cross-industry trade. Thus, this framework essentially embodies the traditional Heckscher-Ohlin view of international trade, although, in this context, each sector is characterized by monopolistic competition rather than by perfect competition.

Under intraindustry trade, the premise is quite different. Countries are now essentially identical with respect to factor composition, yet they still gain from specialization and trade at the variety level because of scale economies and product differentiation. This modern interpretation of trade offers an explanation for the two-way, intraindustry exchange often observed between OECD countries, but left unaccounted for under the standard factor proportions theory. Thus, the second case draws from some recent developments in the noncompetitive theory of international trade.¹³

Under both trade patterns, the local and export demands facing an individual home producer i are given in Table 1.¹⁴ Note that monetary variables with asterisks are expressed in units of foreign currency, and E is the nominal exchange rate expressing the domestic price of foreign currency. Also in Table 1, ϵ > 1 represents the constant elasticity of substitution between any two varieties from the same industry, while α and β are taste parameters, measuring the extent to which countries symmetrically favor their own goods in consumption. These latter two measures roughly capture the nominal expenditure shares allocated to locally produced goods from each country.¹⁵ Assuming that countries predominantly consume the goods that they produce themselves, the model assumes that 0.5 < α,β < 1 under local goods preference.

Table 1.

Domestic and Export Demand Functions Under Monopolistic Competition

Table 1.

Domestic and Export Demand Functions Under Monopolistic Competition

Pattern of trade	Home market	Foreign market
Intersectoral trade	$Y_i=(\frac{P_i}{P}{)}^{-\in }\left(\alpha \frac{M}{P}\right)$	$Y_i=(\frac{P_i}{P}{)}^{-\in }\left((1-\alpha )\frac{{\mathrm{EM}}^{*}}{P}\right)$
Intraindustry trade	$Y_i=(\frac{P_i}{Q}{)}^{-\in }\left(\beta \frac{M}{Q}\right)$	$Y_i=(\frac{P_i}{{\mathrm{EQ}}^{*}}{)}^{-\in }\left((1-\beta )\frac{M}{{\mathrm{EQ}}^{*}}\right)$

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Table 1.

Domestic and Export Demand Functions Under Monopolistic Competition

Pattern of trade	Home market	Foreign market
Intersectoral trade	$Y_i=(\frac{P_i}{P}{)}^{-\in }\left(\alpha \frac{M}{P}\right)$	$Y_i=(\frac{P_i}{P}{)}^{-\in }\left((1-\alpha )\frac{{\mathrm{EM}}^{*}}{P}\right)$
Intraindustry trade	$Y_i=(\frac{P_i}{Q}{)}^{-\in }\left(\beta \frac{M}{Q}\right)$	$Y_i=(\frac{P_i}{{\mathrm{EQ}}^{*}}{)}^{-\in }\left((1-\beta )\frac{M}{{\mathrm{EQ}}^{*}}\right)$

From Table 1, demand for output Y_t in each market under interindustry trade is a function of two components: relative price and aggregate demand. Demand for a particular variety is a decreasing function of its price P_i relative to other prices in the industry, where P is the relevant index of producer prices set by producer i and his (n - 1) compatriots. Second, product demand for each variety depends on aggregate demand facing the industry in each country, where real money balances measure real aggregate demand in each market through a simple quantity equation relationship (see Appendix).

In the case of intraindustry trade, variety demand is once again a function of relative price and aggregate demand. However, since foreign goods now compete in the same industry, the relative-price component is a function of the individual price relative to other home and foreign industry prices. This modification in demand is seen by the ratio of P, to the domestic CPI Q at home and the foreign CPI EQ* abroad, where the consumer price indices and producer price indices naturally coincide under trade in one industry. Moreover, real money balances also reflect the appropriate deflator to capture real aggregate demand in the relevant market. Note that the demands under two-way trade assume from the outset that country size is not an issue (n = n*). Otherwise, a measure of relative country size would also enter the demand under intraindustry trade, further distinguishing it from the case of intersectoral trade.¹⁶

Introducing market segmentation into the analysis, the model also assumes that each producer can price discriminate across markets, setting a different price in each location if the agent so chooses. This assumption represents the critical point of departure from Faruqee (1994), where the law of one price applied. Now, with segmented markets, the implicit arbitrage mechanisms that assured the law of one price are absent. Consequently, each home and foreign producer can price to each market separately, depending on the market conditions that prevail in each location.

In standard models of market segmentation, firms price to market by making destination-specific adjustments to price-cost margins in response to exchange rate changes. However, in this CES framework, markups are constant, closing the usual channel through which prices may systematically differ. Hence, to ensure that producers have an incentive to price discriminate given their ability to do so, it is also assumed that costs are separable (and convex) in the production of domestic and export goods.¹⁷ Otherwise, producers would always choose the same price for each market under either pattern of trade.¹⁸

Qualitatively, pricing behavior under cost separability is similar to the pricing-to-market responses under differential markups. Usually, firms reduce markups in markets where the currency has weakened in order to stabilize price in terms of the local currency.¹⁹ In this context, exchange rate movements elicit a very similar response. For example, a depreciation of the foreign currency lowers demand for home exports, which are now more expensive abroad. Consequently, faced with reduced demand and cost, home producers respond by lowering export prices in units of home currency in order to offset the price increase in terms of foreign currency. Producers still desire local price stability, but now through a marginal cost channel rather than the markup channel.

Note that this simple representation of price discrimination places no boundaries on the degree of divergence between prices for the same good. Clearly, this is an extreme assumption. More likely, there would exist some neutral band—based upon the level of transport or adjustment costs—within which price differentials would persist. Beyond that range, “gray markets” would emerge as agents found it profitable to circumvent the producer’s own distribution channels. However, for small enough demand discrepancies (large enough adjustment costs) this representation is certainly a reasonable assumption.

As for notation, the home and foreign destinations are designated as market 1 and 2, respectively. So, for example, the prices set by home producer i and foreign producer j for the home market are denoted by $P_i^1$ and $P_j^{1*}$ expressed in units of national currency. Solving the producer’s problem, by maximizing real revenues from domestic and export sales minus the utility costs of production (see Appendix), yields the optimal price for each agent for each market destination.

Table 2 presents the optimal price-setting rule (ignoring constants) for each market and under both trade patterns from the perspective of the representative home producer. Note that lowercase letters denote logarithms of variables (q ≡ 1n Q). From Table 2, note that in every case the optimal (log) price ${\overline{p}}_i$ in units of home currency²⁰ is a weighted average of local money, consumer prices at home, and local producer prices for the industry, with all weights being strictly positive.²¹

Table 2.

Optimal Price-Setting Rules

Table 2.

Optimal Price-Setting Rules

Pattern of trade	Destination
	Home market	Foreign market
Intersectoral trade	${\overline{p}}_t^1=\mathrm{\pi m}+\mathrm{\theta q}+(1-\pi -\theta )p^1$	${\overline{p}}_i^2=\pi (e+m^{*})+\mathrm{\theta q}+(1-\pi -\theta )p^2$
Intraindustry trade	${\overline{p}}_i^1=\mathrm{\pi m}+(1-\pi )q$	${\overline{p}}_i^2=\pi (e+m^{*})+\mathrm{\theta q}+(1-\pi -\theta )(e+q^{*})$

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Table 2.

Optimal Price-Setting Rules

Pattern of trade	Destination
	Home market	Foreign market
Intersectoral trade	${\overline{p}}_t^1=\mathrm{\pi m}+\mathrm{\theta q}+(1-\pi -\theta )p^1$	${\overline{p}}_i^2=\pi (e+m^{*})+\mathrm{\theta q}+(1-\pi -\theta )p^2$
Intraindustry trade	${\overline{p}}_i^1=\mathrm{\pi m}+(1-\pi )q$	${\overline{p}}_i^2=\pi (e+m^{*})+\mathrm{\theta q}+(1-\pi -\theta )(e+q^{*})$

Under intersectoral trade, the price rule for the home market places a weight, π, on domestic money, which represents nominal aggregate demand in that market. An increase in aggregate demand raises demand for each individual variety, effecting an increase in price. The weight placed on domestic consumer prices captures a real-income effect. Since each producer is also a consumer—ultimately concerned with utility—an increase in domestic consumer prices translates into a loss of real purchasing power in general and a desire to raise nominal price in response. The weight placed on industry prices, 1 - π - θ, captures a relative-price effect. An increase in industry prices lowers producer <’s relative price, raising the agent’s product demand and price.

Under intraindustry trade, the price rule for domestic prices has the same general form. Once again, producers are concerned about domestic consumer prices to the extent reflected by θ. Now, however, the relative-price coefficient 1 - π - θ, capturing the positive interaction between industry prices, is also placed on the home CPI under two-way trade. Together with the real-income effect, the weight placed on q sums to 1 - π in Table 2. So whereas price setters place a weight 1 - π - θ on p¹ under cross-industry trade, that weight now falls on p¹, p^1*, and e (subsumed in q). Hence, there exists a greater degree of linkage between home and foreign producer prices prevailing in the domestic market. In the terminology of Cooper and John (1988), there is a greater degree of strategic complementarity between home and foreign pricing decisions under intraindustry trade.²²

The intuition behind this result is relatively straightforward. Home and foreign varieties are closer substitutes under two-way trade, so that movements in international relative prices have larger consequences for individual demands. Hence, home price setters are more concerned with foreign prices set for the home market when choosing their own price. The same conclusion holds true for export prices as well. Home export prices under two-way trade display greater influence and interaction with foreign local prices, since the relative-price effect also includes foreign industry prices and the nominal exchange rate.

II. Pass-Through and Pricing to Market

Using the static framework of the previous section, the effects of various disturbances on nominal prices can be measured given a particular calibration of the model. These comparative static exercises are carried out in this section. In particular, the responsiveness of the optimal price to an exchange rate disturbance in all four cases, given that all other variables remain unchanged, is calculated.

The first measure of interest is the degree of exchange rate pass-through. Pass-through is defined as the percentage change in home prices—measured in terms of foreign currency—resulting from a change in the nominal exchange rate. If the foreign-currency price of a good changes one for one with the exchange rate, the degree of pass-through is one. In other words, the exchange rate change is fully reflected in the price change while the home-currency price remains unaffected. At the other extreme, if a price responds fully to offset the change in the exchange rate, leaving the foreign-currency price unaffected, the degree of pass-through is zero. Mathematically, this sensitivity measure is calculated (in absolute value) by $|\partial {\overline{p}}_i^m/\partial e-1|ϵ(0,1)$, for m = 1,2.

Figure 1 displays the degree of pass-through in home prices, holding expenditure shares fixed and allowing the elasticity of substitution to vary; dashed and solid lines represent intraindustry and intersectoral trade, respectively. Note that the pass-through responses shown also apply to foreign producers as well through symmetry.²³ When the elasticity of substitution is exactly one, the two types of trade are identical. This result follows from the characterization of international trade subsumed in consumer preferences.

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Exchange-Rate Pass-Through and the Pattern of Trade

Citation: IMF Staff Papers 1995, 004; 10.5089/9781451930900.024.A006

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Explicitly, preferences are Cobb-Douglas across goods from different industries, while CES preferences apply to goods within an industry. Hence, when countries engage in one-way trade across sectors there exists a low degree of substitutability between home and foreign goods. Meanwhile, with two-way intraindustry trade, the CES specification posits that home and foreign goods are closer substitutes—unless e equals unity, in which case the distinction in utility vanishes.²⁴ Conversely, as ϵ increases, the disparity between the patterns of trade widens in terms of how agents perceive domestic goods compared to foreign goods.

This characterization of preferences embodies the basic idea behind the Armington model.²⁵ The separability assumption under the Cobb-Douglas specification in utility makes the distinction that goods from different industries—appropriately defined—belong to separate commodity classes, representing distinct products. At the industry level, each product is then further differentiated into many varieties with a constant elasticity of substitution between them.

Several results from this framework can be inferred from Figure 1. Naturally, the degree of pass-through is lower in export prices regardless of the trade structure since export demand is always more sensitive to exchange rate fluctuation than is domestic demand. In contrast, note that in case of the law of one price, pass-through in domestic and export prices must be identical in each case, by definition.

Also in Figure 1, as ϵ increases, the degree of pass-through generally declines under two-way trade, but increases under intersectoral trade. The intuition behind the latter result follows from the previous discussion of preferences and trade. As the elasticity of substitution increases, producers display greater strategic complementarity with their industry rivals. This stronger linkage in prices translates into greater sensitivity to any changes in relative prices. Under intersectoral trade, as industry varieties become closer substitutes, price setters become increasingly concerned with keeping prices in line with other resident producers. At that margin, exchange rate fluctuations are of no consequence for relative prices as industry prices are set in the same currency (same unit of account). Hence, producers are more content to allow a greater degree of exchange rate pass-through.

As for intraindustry trade, as the elasticity of substitution increases, price setters prefer to keep prices more closely in line with those of industry competitors, as before, but now the industry includes foreign producers in each destination. Consequently, home producers display a greater responsiveness to exchange rate fluctuations by making offsetting changes in their home-currency prices to minimize movements in relative prices. Figure 2 displays the degree of price discrimination under each trade pattern resulting from an exchange rate disturbance. This degree of pricing to market is measured as the percentage deviation between the domestic price and export price for the same good as a percentage of the change in exchange rate.²⁶ Mathematically, this measure is given (in absolute value) by $|\partial {\overline{p}}_i^1/\partial e-\partial {\overline{p}}_i^2/\partial e|$.

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Pricing to Market and the Pattern of Trade

Citation: IMF Staff Papers 1995, 004; 10.5089/9781451930900.024.A006

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Once again, when ϵ = 1, the two patterns of trade are really the same and the degree of pricing to market is also identical. As the elasticity of substitution increases, producers under intraindustry trade decide to price discriminate across markets to a greater extent. The reasoning follows as before. Stronger price linkages within the industry motivate home price setters to keep price more closely in line with competitors, including foreign producers, in each destination (see again dashed lines in Figure 1). However, since demand abroad for the domestic product is more sensitive to the rate of exchange, movements in the value of currency induce a greater response in prices set for the foreign market than for the home market, increasing the extent of price discrimination. This result is seen in Figure 2 by an increasing degree of pricing to market under two-way trade.

As for intersectoral trade, the total absence of an import-competing industry in each country greatly limits producer concerns about international relative prices. Furthermore, as ϵ increases, closer ties between industry price setters who happen to be from the same country further reduce the level of price discrimination. This is seen by a decreasing degree of pricing to market in Figure 2. As the relative-price effect receives greater weight compared to the aggregate demand and income effects, exchange rate changes are increasingly ignored in both market destinations under intersectoral trade. This finding is clearly at one extreme.

From the setup of the model, complete specialization at the industry level characterizes intersectoral trade between two nations that could not be more different. In sharp contrast, complete overlap in industry production represents intraindustry trade between identical trading partners. In an intermediate structure between these two boundary cases, each country would produce predominantly in one sector or the other, but would at least have some presence in both. In that instance, the typical degree of pricing to market would likely be increasing in ϵ, lying somewhere in between the limiting cases shown in Figure 2.

Interpreted as a boundary range, Figure 2 illustrates the significant variation in pricing-to-market behavior associated with various patterns of international trade. In a multisector setting, the same general result would obtain. In those sectors where the degree of intraindustry trade is high, price setters would display a greater degree of pricing to market and a lower degree of pass-through. Recent empirical evidence documenting the degree of cross-industry variation in pricing-to-market behavior is reported by Knetter (1993). Examining various export prices for Germany, Japan, the United Kingdom, and the United States, Knetter (1993) finds that industry is the critical dimension explaining the variation in the pattern of pricing-to-market practices within and across countries.

III. Relative Prices and Dynamics

This section extends the model to incorporate dynamics. In the presence of nominal frictions such as menu costs, producers do not adjust prices continuously. Instead, price setters respond to changing market conditions only intermittently. Moreover, when decentralized producers adjust, they do so at different times because of a lack of coordination. This lack of synchronization in pricing decisions and revisions induces inertia in the overall price level. When price setters move at different times, agents who respond and change their prices do not adjust completely in an effort to maintain relative prices with those who wait. Consequently, the repercussion of demand shocks may extend long after the initial impulse through this overlapping nature of price adjustment.

To capture this overlapping adjustment process, a simple staggered timing structure for price setting is imposed. Specifically, it is assumed that half of all firms, home and foreign, revise their domestic and export prices in even periods when necessary, while the remaining half adjust in odd periods.²⁷ Taking the frequency and timing of intermittent price changes as given, the comparative dynamics that emerge from this common staggering structure under contrasting patterns of trade and market segmentation can then be examined.

Dropping the i subscript and representing price setters by their time location instead, the dynamic optimal price rule (without discounting) for a particular market—domestic or export—under both trade patterns is

where x_t is the actual price²⁸ set for the periods t and t + 1 by home firms moving at time t.²⁹ Also in equation (1), ${\overline{p}}_t$ and ${{}_t\overline{p}}_{t-1}$ represent the actual and expected optimal price at time t and t + 1, where expectations are formed rationally, based on all the information available at time t. Hence, time-dependent pricing leaves prices predetermined for two periods. Furthermore, the even-odd timing structure introduces asynchronized adjustment similar to that in Taylor (1980). Illustrating the overlapping nature of prices, the index of home producer prices prevailing in the domestic market takes the (approximate) form: $p_t^1=0.5x_{t-1}^1+0.5x_t^1$.

Substituting the static price rules from Table 2 and their corresponding foreign counterparts into the dynamic price-setting equation (1) defines a system of equations with four state variables, consisting of home and foreign local prices and export prices, where each price equation takes the form of a second-order stochastic difference equation as a result of the simple two-period overlapping structure of price adjustment. However, with the focus on real exchange rate dynamics, the four-variable system can be reduced to one difference equation in relative prices, given the behavior of the three forcing variables consisting of home and foreign money and the nominal exchange rate.³⁰ See the Appendix for details.

In the case where home and foreign money follow a random walk,³¹ the dynamic equation for the CPI-based (log) real exchange rate r under either trade pattern can be written compactly as

Note that the simple even-odd staggering structure in nominal price adjustment gives rise to a simple first-order autoregressive process in relative prices, where the coefficient λ in equation (2) can be interpreted as a measure of persistence or inertia in the real exchange rate.³²

As alluded to, the dynamics governing the behavior of the real exchange rate in equation (2) apply to both patterns of trade. At first glance, this equivalency result may seem a bit surprising given the comparative differences shown earlier in Section II. However, the findings are mutually consistent. In fact, the differences regarding the response of nominal prices described earlier are what guarantee the equivalence result regarding the behavior of relative prices.

For illustration, compare the optimal price rules for the home exporter shown in Table 2. The single difference across trade patterns is found in the relative price component. Under intraindustry trade, the home producer is concerned with competing foreign prices, the exchange rate, and other home export prices, whereas that same agent under cross-industry trade is concerned only with other home export prices.

Under the law of one price, the added concern with the foreign-currency price of output would compel price setters in the first instance to reduce the degree of domestic price inertia resulting from menu costs and price staggering. Prices would be less sticky in terms of national currency in order to reduce variation in terms of foreign currency, leading to less variable and persistent deviations in the real exchange rate under two-way trade.³³ However, as indicated by equation (2), once the assumption of spatial arbitrage is removed, this comparative difference regarding the behavior relative prices no longer holds true.

Instead, once export prices detach from domestic prices, goods prices are in effect set in terms of local currency rather than national currency since price linkages predominantly exist within market destinations rather than across them. As a result, under two-way trade, the destination prices set by industry rivals from different countries are inertial in the same unit of account, as if they were from the same country, which just happens to be the case of intersectoral trade. Consequently, real exchange rate dynamics are the same across differing patterns of trade, ceteris paribus, and depend only upon the timing structure of price adjustment.

Overall, pricing-to-market behavior increases the degree of persistence in the real exchange rate compared with the setting of one price. Regardless of the trade pattern, if price setters effectively stabilize price in terms of local currency, destination prices become less responsive to exchange rate disturbances. Pricing to market in effect allows price setters to keep export prices more stable in terms of foreign currency without requiring that domestic prices be more flexible in terms of home currency, unlike the law of one price. Consequently, the real exchange rate displays greater variability and persistence.³⁴ For example, with an import share equal to one quarter, the degree of persistence under intersectoral trade would be twice that under the law of one price, and the corresponding increase under two-way trade would be even larger.³⁵

Based on equation (2), Table 3 presents a sample of computed persistence values for the real exchange rate across different degrees of openness α and substitutability ϵ. Note that a decrease in α, representing an increase in expenditure on imports as a share of national income, reflects an increase in openness. The last column measures the long-run impact of a monetary shock on the real exchange rate. This permanence factor measures the change in the steady-state value of the real exchange as a percentage of the change in the equilibrium nominal exchange rate.³⁶ So, for example, if a = 0.9, a permanent 10 percent increase in the domestic money stock (and proportional nominal depreciation) would induce a steady-state real depreciation of 2 percent.³⁷

Table 3.

Real Exchange Rate Dynamics

Table 3.

Real Exchange Rate Dynamics

	Persistence λ
Openness α	ϵ = 2	ϵ = 6	ϵ = 10	Permanence
0.99	0.40	0.51	0.57	0.02
0.95	0.35	0.46	0.52	0.10
0.90	0.29	0.40	0.47	0.20
0.80	0.21	0.33	0.40	0.40
0.70	0.14	0.26	0.34	0.60
0.60	0.09	0.21	0.29	0.80

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Table 3.

Real Exchange Rate Dynamics

	Persistence λ
Openness α	ϵ = 2	ϵ = 6	ϵ = 10	Permanence
0.99	0.40	0.51	0.57	0.02
0.95	0.35	0.46	0.52	0.10
0.90	0.29	0.40	0.47	0.20
0.80	0.21	0.33	0.40	0.40
0.70	0.14	0.26	0.34	0.60
0.60	0.09	0.21	0.29	0.80

In Table 3, note that persistence declines with increasing openness. The basic reasoning is as follows. As the import share rises, a nominal depreciation leads to greater CPI inflation, and real income is thus affected more by exchange rate changes. Since producers are also consumers concerned with their purchasing power, greater concern with the foreign-currency value of revenue reduces price stickiness in terms of local currency, thereby reducing inertia in the real exchange rate $\left(\theta (1-\alpha )\uparrow \Rightarrow \lambda \downarrow \right)$.

Table 3 also shows that persistence increases with the elasticity of substitution between goods. The argument follows similarly to that above, but via the relative-price channel rather than the income channel. A higher degree of substitutability between varieties implies that demand is more sensitive to a change in relative price (see Table 1). As producers become more concerned with their price relative to the industry, efforts to stabilize price in terms of local currency in each market intensify. The resulting increase in local price stickiness induces greater overall persistence in the real exchange rate.

Lastly, Table 3 illustrates that permanence is an increasing function of openness. As import expenditure shares increase, the asymmetric effects of a lasting domestic monetary expansion on prices across segmented markets become larger. More simply, this result can be interpreted in the context of tradability. If the product is essentially not traded (α → 1), the effects of pricing to market on the long-run real exchange rate are small. Conversely, the degree of permanence rises with increasing openness since the effects of pricing to market are more pronounced with a higher degree of international trade. Finally, note that the permanent effects of monetary shocks are a result of market segmentation and not nominal rigidity and would exist even if prices were perfectly flexible (λ = 0; see Appendix).

Persistence and permanence in relative price responses have important time-series implications for exchange rates. As with earlier sticky-price models, differential rates of adjustment in goods prices versus asset prices allow nominal and real exchange rates to move closely together in the short term. Following an initial impulse, the real exchange rate then eventually self-corrects toward equilibrium, reflecting the persistent effects of monetary disturbances on relative prices. The current framework also predicts that the nominal and real exchange rate move together over the longer run as well,³⁸ since monetary shocks have permanent effects on the nominal rate of exchange and on equilibrium relative prices to the extent that goods markets remain segmented. Alternatively, if the law of one price ultimately holds in the long run, the “permanence” factor can be viewed as long-term persistence in the real exchange rate, extending beyond the period required for prices to adjust.

IV. Concluding Remarks

With the collapse of Bretton Woods and the abandonment of fixed exchange rates in 1973, the two decades since have seen a great deal of turbulence in foreign exchange markets. Yet the large swings in exchange rates under the era of floating rates have not brought about large movements in inflation or disinflation as one would expect with pass-through. Instead, volatile nominal exchange rates have translated into volatile real exchange rates in the post-Bretton Woods world, while local prices have remained remarkably stable.

In an attempt to understand these developments, this paper develops a model of market segmentation and pricing to market, with important macroeconomic consequences for the behavior of international prices broadly in line with the stylized facts. Motivated by a preponderance of the empirical evidence disavowing the law of one price, the model details some of the economic implications of pricing-to-market behavior. The results include both cross-sectional implications regarding nominal prices and time-series implications regarding relative prices.

Across different patterns of trade, significant variation exists in the degree of pass-through and pricing to market depending upon the degree of intraindustry trade and the substitutability between home and foreign goods. Across time, dynamic adjustment in prices suggests that nominal and real exchange rates move together over the short run, as well as over the longer run to the extent that markets remain segmented. Overall, pricing to market provides a potentially important source of local price stickiness and real exchange rate persistence.