Long-Run Purchasing Power Parity with Asymmetric Adjustment

Abstract

1. Introduction Despite its intuitive appeal, there is inconclusive evidence supporting purchasing power parity (PPP) between countries with low inflation rates during the post-Bretton Woods period. For example, Enders (1988), Taylor (1988), and MacDonald (1993) use various forms of cointegration tests-called stage-three tests-and find that real exchange rates exhibit large fluctuations with slow rates of decay toward a long-run mean. Froot and Rogoff's (1995) literature review presents a consensus estimate that deviations from long-run PPP have a half-life of about three years. This is somewhat disappointing since stage-three tests seem to be well suited to the task-they require no assumptions concerning exogeneity and they imply a sensible dynamic relationship among price levels and the exchange rate. The vast literature on PPP is indicative of the importance of the issue and the ambiguity of the findings. It is well recognized that standard cointegration tests have low power to reject the null hypothesis of no cointegration. This observation is especially relevant for PPP since any mean reversion in real rates is very gradual and the length of the post-Bretton Woods period sample period is relatively short. Efforts to increase the power of unit-root and stage-three tests have had mixed success. For example, Lothian and Taylor (1996) and Mark (1990) have tried to circumvent the low power of stage-three tests by using long spans of time-series data. Unfortunately, the use of long time spans raises the possibility of structural changes occurring during the period being examined. Panel unit-root tests are generally more supportive of PPP than are bilateral tests of real exchange rate behavior. For example, Oh (1996), Wei and Parsley (1995), and Wu (1996) have used panel data in order to enhance the power of standard unit-root tests. Although these particular articles are supportive of PPP, panel studies must deal with the thorny issues of cross-sectional correlation and the choice of the nations to include in the panel. Papell (1997) finds that allowing for serial correlation substantially weakens the evidence in favor of long-run PPP. O'Connell (1998) applies generalized least squares to panel data to eliminate any contemporaneous correlation in the error structure and finds no evidence supporting PPP The second problem with the standard unit-root and cointegration tests is that they implicitly assume symmetric adjustment. However, official intervention in the foreign exchange market means that nominal exchange rate adjustment may be asymmetric. Under a managed float, for example, one of the monetary authorities might be more willing to tolerate currency appreciation than depreciation. Similarly, a currency band mitigates exchange rate movements until the level of the band is altered. Furthermore, the slow adjustment of real exchange rates is often explained by the stickiness of national price levels. For example, in the well-known Dornbusch (1976) overshooting model, prices and the exchange rate move in the same proportion as the money supply in the very long run. However, in the short run, prices are sticky and monetary shocks cause PPP deviations since the exchange rate moves proportionately more than prices. Rhee and Rich (1995) and Madsen and Yang (1998) provide empirical evidence corroborating the implications of the asymmetric price adjustment models. The key point to note is that, if prices are primarily sticky in the downward direction, there is no reason to presuppose that real exchange rate adjustment is symmetric. In spite of the evidence supportive of asymmetric exchange rate and price adjustments, there are only a few nonlinear tests of PPP Although they do not explicitly test for PPP, Michael, Nobay, and Peel (1997) and Taylor and Sarno (1998) estimate real exchange rates as smooth-- transition threshold adjustment processes. Enders and Falk (1998) formally apply various nonlinear unit-root tests to real exchange rates and find little evidence of PPP. …