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Article Excerpt
EXCHANGE RATE MOVEMENTS have several potentially important implications for the domestic macroeconomy, including inflation variability, monetary policy effectiveness, and current account adjustment. But the importance of these implications depends in part on how much of the exchange rate movements are passed through to changes in import prices. A number of recent papers have found evidence indicating a decline in exchange rate pass-through to import prices in the United States. While there appears to be agreement within the literature surveyed in Goldberg and Knetter (1997) that the pass-through in the 1980s was around 0.5, several papers find much lower estimates for recent years. Marazzi et al. (2005) estimate that the pass-through coefficient for U.S. imports has declined gradually from 0.5 to around 0.2, and similar results are found in Olivei (2002) and Gust et al. (2006). It is less clear how this decline in pass-through applies to other countries and how it applies to prices at the consumer level. (1)
Several potential explanations have been proposed for how pass-through might decline. Taylor (2000) suggested that an environment of lower inflation might discourage firms from adjusting import prices. Campa and Goldberg (2005) suggest and find evidence in support of the idea that the composition of imports has shifted toward goods that are less sensitive to exchange rates, that is, away from energy and toward manufactures. Others have suggested that the competitive environment for imports has changed. Included in this group are Gust et al. (2006), who propose that increased trade integration has made exports more responsive to the prices of their competitors. They develop a dynamic model with endogenous entry decisions and markups that respond endogenously to entry. Also in this category would be the proposition by Marazzi et al. (2005) that the increased role of China as a source of U.S. imports has lowered pass-through, both due to the direct effect of its stable exchange rate against the dollar and by inducing a competitive response in the exporters of other countries.
Evidence varies regarding which of these types of channels is relevant. Campa and Goldberg (2005) find in their multicountry study that pass-through tends to be stable within industry categories but that the change in composition can account for much of any overall fall in aggregate pass-through. While the evidence in Marazzi et al. (2005) agrees that a falling share of oil imports plays a role, evidence is found that pass-through has fallen across a wide range of goods. Further, they also find a correlation between industries that experienced a fall in pass-through and those that experienced the strongest increase in Chinese imports. (2)
The primary purpose of this paper is to provide a theoretical framework for exploring how the rise of China as a supplier to the United States could have altered the competitive environment for U.S. imports and thereby generate time variation in pass-through. More broadly, the lessons developed in our model are relevant for understanding the effects of changing market share of all trading partners with fixed exchange rates. The theory draws upon recent developments in trade theory to shed light on this issue, including endogenous entry and markup decisions by firms. The explanation we develop is similar in spirit to that in Dornbusch (1987) in that the market share of the fixed-exchange rate country in our model affects pass-through in the same manner as the market share of domestic firms does in Dornbusch's model. (3) Gust et al. (2006) also draw similar inspiration from the trade literature in their study of pass-through. We differ from both of these papers in our use of translog preferences to generate time-variation in markups and pass-through. In fact, we regard the extension of the translog expenditure function to be a theoretical contribution that could be of use in studying a range of other issues.
We consider a three-country model with the United States and two representative trading partners. The first trading partner has a floating exchange rate, and for concreteness we will refer to this country as Mexico; the second trading partner has a fixed exchange rate, and we will refer to this country as China. We eliminate any role for U.S. competing firms to affect the pass-though of exchange rates by supposing that the United States only sells a homogeneous exported good. Our focus is on the interplay of exporters to the United States from the fixed and floating countries, both of whom sell a differentiated good. In Section 1, we give a basic outline of the monetary model, which features wages that are fixed in the short run. Beyond the simple distinction between the short run (with fixed wages) and the long run (with flexible wages), we do not introduce any further dynamics into the model.
In Section 2, we analyze the pricing decisions of exporters from both types of countries. We use a translog expenditure function to model U.S. demand. As previously analyzed by Bergin and Feenstra (2000, 2001), this expenditure function allows for endogenous markups that vary with the exchange rate, thereby leading to incomplete pass-through. When the number of firms varies due to free entry, under monopolistic competition it is necessary to solve for the reservation prices of goods that are not available (i.e., prices when demand is zero). In this paper, we extend the results of Feenstra (2003) in solving for reservation prices, obtaining a reduced-form expenditure function that allows for a taste bias in favor of some goods. In particular, we shall suppose that U.S. buyers have a "local bias" that favors Mexican goods over Chinese goods due to Mexico's proximity to the United States, common border, and NAFFA.
In Section 3, we analyze the pass-through of exchange rates treating the number of firms as fixed. Competition from China diminishes the pass-through of the Mexican exchange rate to the price of U.S. imports from Mexico. We show that when we aggregate up to multilateral import prices and exchange rates--by aggregating over both of these countries--then pass-through is still incomplete (even though we have assumed no competing U.S. firms). The incomplete pass-through is related to our assumed taste bias in favor of Mexico and becomes more pronounced as the number of competing Chinese exporters grows. So, competition between China and Mexico--in the presence of a U.S. taste bias--results in incomplete pass-through.
In Section 4, we examine the empirical implication using disaggregate U.S. import data from the 1990s. Like Marazzi et al. (2005, pp. 21-23), we test whether having more competition from China results in lower pass-through coefficients at an industry level and find support for this hypothesis. (4) Panel regressions over 1993-2006 indicate that the rising share of trade from China, or from all countries with fixed exchange rates, can explain a decline in pass-through of between one-sixth and one-third of its initial value, or as much as one-half of the observed decline for the United States. Section 5 extends the model by allowing for the free entry of firms, which can occur in response to monetary and exchange rates shocks. In that case we simulate the model and find a further reason for incomplete pass-through: a monetary expansion in the United States leads to greater entry of firms in the country with fixed exchange rates, creating an extra competitive effect that leads to lower import prices. So, the free entry of firms lowers the pass-through of the dollar further. Section 6 concludes, and proofs are in the Appendix.
1. COUNTRIES, COMMODITIES, AND CURRENCIES
There are three countries: Mexico (denoted by x), China (denoted by y), and the United States (denoted by z). More broadly, China here can be thought of as representing the range of U.S. trading partners with fixed or stabilized exchange rates relative to the dollar. Mexico can be thought of as representing trading partners with essentially floating exchange rates. The United States produces a homogeneous good denoted by z and exports it to both Mexico and China. One unit of labor produces one unit of the z good, so the price of the U.S. good equals the wage, [w.sub.z]. China and Mexico produce a differentiated good that is sold back to the United States. (5) Their prices are [p.sub.x] (in pesos) and [p.sub.y] (in yuan), which are common across all the varieties sold by each country. The dollar--peso exchange rate is [e.sub.x], so the dollar price of imports from Mexico is [e.sub.x][p.sub.x], and the dollar--yuan exchange rate is [[bar.e].sub.y], so the dollar price of imports from China is [[bar.e].sub.y] [p.sub.y]. Note that [[bar.e].sub.y] is a fixed exchange rate, whereas [e.sub.x] is flexible.
We model the cash-in-advance constraint as in Bacchetta and van Wincoop (2000). Each government provides a money transfer of [M.sub.i], i = x, y, z to home residents at the beginning of the period, and imposes an identical tax at the end of the period after all transactions are made. Money will then serve as a unit of account in each country but does not have any distortionary effect by itself. We presume that expenditure in each country equals the money supply from the cash-in-advance constraints. Under balanced trade, expenditure in turn equals the value of output. With labor as the only factor of production, and with zero profits (due to free entry, discussed in Section 5), the money supply in each country therefore equals wage income:
[M.sub.i] = [w.sub.i][L.sub.i], i = x, y, z. (1)
Each country spends a fraction [beta] of wage income on its own, homogeneous good. In the United States, the remaining fraction (1 - [beta]) of expenditure is spent on the differentiated good, imported from either China or Mexico. For Mexico and China, the remaining (1 - [beta]) of income is spent on the U.S. homogeneous good. For example, Mexican spending on the U.S. good is (1 - [beta])[[bar.w].sub.x][L.sub.x] = (1 - [beta])[M.sub.x]. The peso price of the U.S. good equals the dollar price [w.sub.z] (since one unit of labor produces one unit of output) divided by the peso exchange rate [e.sub.x]:
Mexican demand for U.S. good = (1 - [beta])[M.sub.x]/[w.sub.z]/[e.sub.x] = [e.sub.x](1 - [beta])[M.sub.x]/[w.sub.z].
Likewise, Chinese demand is:
Chinese demand for U.S. good = (1 - [beta])[M.sub.y]/[w.sub.z][[bar.e].sub.y] = [[bar.e].sub.y] (1 - [beta])[M.sub.y]/[w.sub.z],
where the yuan exchange rate, [[bar.e].sub.y], is fixed. Finally, U.S. demand for its own good is:
U.S. demand for U.S. good = [beta][M.sub.z]/[w.sub.z].
Summing all the demands we get the U.S. equilibrium condition,
[e.sub.x](1 - [beta])[M.sub.x]/[w.sub.z] + [[bar.e].sub.y] (1 - [beta])[M.sub.y]/[w.sub.z] + [beta][M.sub.Z][w.sub.z] = [L.sub.z]. (2)
While (2) has been derived as the goods market equilibrium condition for the United States, it can also be interpreted as asset market equilibrium condition for dollars. Multiplying both sides of the equation by [w.sub.z], the right of (2) is the U.S. money supply [M.sub.z]. On the left, the first term is the U.S. dollars that Mexican consumers would need to purchase from the United States, the second term is the dollars that Chinese consumers would need, and the third term is the dollars that U.S. consumers need to purchase their local good. So under the assumption that consumers use the currency of the selling country, (2) can be interpreted as the asset market equilibrium condition for dollars.
We assume that wages are fixed at the beginning of the period and that labor supply is demand determined. We can model the specifics of the wage-setting mechanism as in Obstfeld and Rogoff (2000), which leads to a nominal wage [[bar.w].sub.i] that is fixed in the short run. (6)
1.1 Determining the Mexican Exchange Rate
In the short run, wages are fixed, so using (1) we write (2) as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (3)
A 1% increase in the U.S. money supply can be accommodated by a 1% increase in [e.sub.x] (a depreciation of the dollar) and a 1% increase in the Chinese money supply (to keep [[bar.e].sub.y] fixed). In the background, there is 1% more of the U.S. good produced, which is consumed both in the United States (due to increased expenditure), in China (due to increased expenditure), and in Mexico (due to an appreciation of the peso and lower prices there).
Notice that if China does not accommodate the U.S. monetary expansion by increasing its money supply in the same proportion, then the peso will appreciate by a different amount. In general, given some assumption on the responsiveness of [M.sub.y] to [M.sub.z], then (3) is enough to determine the peso exchange [e.sub.x] in the short run. In Sections 3 and 4, we will not need to make any particular assumption on the responsiveness of [M.sub.y] to [M.sub.z], and hence on the movement in the peso rate [e.sub.x]. In Section 5, however, we will use the asset market equilibrium condition for yuan to show how the Chinese money supply My changes in response to the U.S. money supply [M.sub.z], and therefore solve the equilibrium change in the peso rate [e.sub.x].
2. TRANSLOG EXPENDITURE FUNCTION
A fraction (1 - [beta]) of expenditure in the United States is spent on imported differentiated goods produced by Mexico and China. Since the work of Dixit and Stiglitz (1977), a common choice for the utility function defined over the differentiated products has been the constant elasticity of substitution (CES) form. Despite its tractability, this functional form has serious drawbacks for the analysis of firm's pricing. Since optimal prices are a constant markup over marginal costs, there is no strategic interaction between the firms.
This special feature of the CES need not carry over to other choices of the subutility function. We will consider a subutility function defined by the dual expenditure function, which is assumed to have a translog form. (7) That is, given nominal expenditure E, the subutility from consumption of the differentiated products 1, ..., N is u = E/e(p), where the unit-expenditure function e(p) is defined by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (4)
with [[gamma].sub.ij] = [[gamma].sub.ji]. The parameter [??] is the maximum number of possible products, but many of these might not be produced: the prices used for products not available should equal their reservation prices (where demand is zero). Notice that in the...
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