In recent years, a new line of research on exchange rate determination, pioneered by the seminal work of Obstfeld and Rogoff (1995), has developed. The new approach examines exchange rate dynamics within dynamic general-equilibrium (DGE) sticky-price models. Examples of studies that use this approach include Betts and Devereux (2000), Chari, Kehoe, and McGrattan (2000a), Bergin and Feenstra (2001), and Kollmann (2001). In each of these studies, price stickiness is motivated through monopolistic competition in the goods market, while departures from the purchasing-power parity (PPP) are due to the failure of the law of one price (LOP) in traded goods. The latter feature arises from pricing to-market behaviour by monopolistic firms that segment markets by country.
A primary objective of the literature on exchange rate determination is to account for the well-documented volatility and persistence of the real exchange rate. Figure 1 illustrates these stylized facts in the case of the Can$/US$ real exchange rate. The logged and Hodrick-Prescott (H-P) filtered Can$/US$ real exchange rate has a relative standard deviation of 2.09 with respect to Canadian real GDP, and a serial correlation of 0.86. Other bilateral real exchange rates with the U.S. dollar exhibit a similar degree of persistence and even higher volatility. Overall, the above-noted studies have been successful in generating high real exchange rate variability.
In particular, using a careful parameterization of risk aversion, Chari, Kehoe, and McGrattan (2000a) closely replicate the volatility observed in the data. But unless they assume an unreasonable level of price rigidity (for example, via excessively long nominal contracts), standard DGE sticky-price models fail to match real exchange rate persistence. Additional features such as the incompleteness of the financial market and labour market frictions are shown by Chari, Kehoe, and McGrattan (2000a) to be quantitatively ineffective in generating more persistence. Furthermore, Bouakez (2002) finds that habit formation in consumer preferences is irrelevant to exchange rate persistence.
In this paper, I construct a DGE sticky-price model in the spirit of Obstfeld and Rogoff (1995). Departing from their model where the elasticity of demand is assumed to be constant, I allow this elasticity to be time-varying. More specifically, I consider a variety aggregator that yields an elasticity of demand that is increasing in relative price. This assumption may reflect search costs that cause a typical firm to lose more customers when it raises its price than it gains when it reduces its price by the same amount. As Stiglitz (1979), Woglom (1982), and Ball and Romer (1990) point out, this information imperfection leads to kinked (or bent) demand curves. Ball and Romer (1990), Kimball (1995), Bergin and Feenstra (2000), and Rotemberg and Woodford (1999) show that a demand function with a time-varying elasticity exacerbates the real effects of monetary shocks.
Intuitively, an elasticity of demand that is increasing in relative price means that the desired markup is decreasing in relative price. Because a monopolistic firm will lower its desired markup whenever it raises its relative price, the increase in the relative price will be smaller than it would be if the elasticity of demand was constant. Hence, allowing for desired markup variations leads to additional price stickiness beyond that resulting from the exogenously imposed frictions. A corollary is that a large degree of nominal rigidity may be rationalized with a reasonable exogenous length of nominal contracts.
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Nominal Rigidity, Desired Markup Variations, and Real Exchange Rate Persistence
