The considerable variability of real exchange rates since the advent of floating rates has been extensively documented and analyzed. The large and persistent movement of real exchange rates has been characterized by substantially greater movements in nominal exchange rates than in national price levels.1 Such exchange rate behavior is consistent with the popular view—as exemplified by the Dornbusch (1976) model—that national price levels are sticky, often reflecting the existence of past contracts, whereas exchange rates, like other asset prices, are flexible and forward looking. Numerous models incorporating these stylized facts have been developed.2 However, despite the widespread incorporation of the assumption of sticky goods price adjustment in models of exchange rate determination, little effort has been devoted to examining the relationship between measures of the degree of price stickiness, or the speed of goods price adjustment, and the variability of the real exchange rate and, hence, of output.3 Such a link is important, since a plausible inference often drawn is that the greater the degree of price stickiness, the more variable are the real exchange rate and output. Indeed, fluctuations in aggregate output are often attributed to the short-run rigidity of wages and prices, and various proposals and pleas to make wages and prices more flexible have often been advanced.
The link between the degree of price flexibility and the variability of output presents a fundamental question. The two standard textbook static models are the classical model and the Keynesian model. In the Keynesian model prices are assumed to be perfectly rigid, and output adjusts. In the classical model prices are completely flexible and output is perfectly stable. The two models suggest that as prices become more flexible, output should become less variable. Since Mundell (1963) pointed it out, it has been well known that the price level and the rate of change of the price level—that is, the expected inflation rate—exert opposing forces on the level of output in a static Keynesian model.4 Because inflation is essentially a dynamic phenomenon, the static Mundell effect prompts a natural consideration of the link between the degree of price flexibility and the variability of output in a dynamic context. Tobin (1975) presented a formal model where lower prices work to move the economy toward full employment, but an expectation of falling prices raises the real interest rate and moves the economy away from full employment.
DeLong and Summers (1986a, 1986b), Driskill and Sheffrin (1986), and, more recently, King (1988) and Chadha (1989) have examined the question of whether increased price flexibility or inflexibility will stabilize or destabilize output in a closed economy. Whereas Driskill and Sheffrin (1986) and King (1988) find no possibility of destabilizing price flexibility, DeLong and Summers (1986b) present simulations of Taylor’s (1979, 1980) staggered wages model to show that increased flexibility could be destabilizing. This paper examines the question for an open economy with flexible exchange rates and perfect capital mobility. It establishes that, in general, for such an economy a critical degree of price inflexibility exists, below which increased inflexibility of prices is stabilizing in that it reduces the variance of output around capacity, and above which increased inflexibility is destabilizing. It also shows that, as prices become more inflexible, the relationship between the variability of the real exchange rate and that of output will be nonmonotonic; that is, as the variability of the real exchange rate increases, the variability of output will decline up to a point and only then increase. Moreover, it is shown that the existence of a nonmonotonic relationship between the variability of output and the degree of price stickiness does not depend solely on the presence of the real interest rate in the aggregate demand function, as is implied in the closed economy literature.
Section I develops a simple and traditional sticky goods price, flexible exchange rate model with capital mobility. In Section II the model is solved for the time paths of the price level and the exchange rate, and the response of these variables to innovations in the money supply is examined. Section III then examines the variability of the real exchange rate and output as a function of the degree of price stickiness. Section IV contains concluding remarks.
Proof of Unique, Convergent Solution of the Model
This Appendix provides a proof for the existence of a unique, convergent solution of the model developed in the text. The dynamics of the system may be described by a pair of stochastic difference equations in the price level and the exchange rate:
In solving the model, as is traditional in rational expectations models, the condition is imposed that the solution be convergent in the expected value sense, constrained on information when the forecast is made. The existence of a unique, convergent solution to (41) requires that matrix A possess exactly one characteristic root inside the unit circle, given that there is one predetermined variable, the domestic price level, in the system.
Proposition. The matrix A possesses exactly one characteristic root inside the unit circle.
Proof. The characteristic equation of the matrix A may be written as
Denoting the roots by Xt, note that
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Bankim Chadha is an Economist in the External Adjustment Division of the Research Department. He holds a doctorate from Columbia University. The author thanks Richard Barth, Guillermo Calvo, Fabrizio Coricelli, Jeffrey Davis, Susan Jones, Reva Krieger, Ichiro Otani, and Ranjit Teja for their comments.
For a wide-ranging review of the experience under floating rates, see Goldstein (1984) and Obstfeld (1985). For a recent extensive empirical study of the behavior of real exchange rates, see Mussa (1986).
Obstfeld and Rogoff (1984) discuss various contributions.
An exception is Calvo (1987), who links real exchange rate overshooting to the average length of a price quotation in the economy.
An increase in the price level lowers real money supply, creating an excess demand for money and resulting in higher interest rates and lower output. An increase in the rate of inflation, through the Fisher effect, lowers money demand, creating an excess supply of money, lowering interest rates, and raising output.
See Obstfeld and Rogoff (1984) for a discussion of appropriate, forward-looking, sticky goods price adjustment rules.
The reduced-form solution for the aggregate price level generated as a consequence of adopting (5) is exactly the solution in Chadha (1987), where a much more complicated and appealing two-part price-setting mechanism is employed; it corresponds to the reduced-form solution in Rotemberg (1982), where the aggregate price adjustment rule is derived from microfoundations.
Whether the exchange rate overshoots or undershoots is an empirical matter. Papell (1985) finds empirical cases of exchange rate overshooting and undershooting.