On the relationship between nominal exchange rates and domestic and foreign prices

Abstract

A number of authors have found significant cointegrating relationships between spot exchange rates and domestic and foreign price levels for the major currencies where the magnitude of the coefficients makes economic interpretation of PPP cumbersome. Using theoretically well motivated nonlinear models for ‘artifitially’ created real exchange rates, this paper investigates the properties of two alternative cointegration procedures, namely the Johansen and Saikkonen methodologies. The latter procedure appears to outperform the former one in terms of finding the ‘true’ cointegrating coefficients. The new weights obtained with the Saikkonen method are then used to estimate non-linear ESTAR model for the real exchange rate. The ‘new’ real exchange rates exhibit, in most cases, much lower half-life shocks than the ones predicted by the Rogoff (1996) puzzle.

Acknowledgements

Ivan Paya acknowledges financial support from the IVIE.

Notes

¹ If it is assumed that some goods are non-traded and that the consumer price index is a weighted average of traded and non-traded prices then it is, of course, well known that the real exchange rate in terms of consumer prices is given by

where s_t is the exchange rate, p_t , are domestic and foreign consumer pricers, , are domestic and foreign non-traded prices, α, β are the weight of traded goods in the domestic and consumer price index. Clearly cointegration between the exchange rate and domestic and foreign consumer prices requires that the prices of non-traded goods are stationary or cointegrated.

² Cheung and Lai (1993) report similar coefficients, 4.97 and −7.64.

³ Baum et al . (2001) report results for several other countries where the coefficients are incorrectly signed. They do not comment on this.

⁴ In this paper, the sample on spot exchange rates and prices used in the MacDonald (1993) and Baum et al. (2001) studies are extended from January 1973 to May 2001 for consumer prices. The PPP hypothesis is then estimated using the same multivariate cointegration methodology. There is no evidence for cointegration at 5% in the dollar/DM exchange rate.

Table

⁵ See also Anderson (1997) for an empirical application of agent heterogeneity and smooth transition in the bond market.

⁶ Estimations of 2 were done for a number of other real exchange rates. To preserve space the five currencies mentioned above are concentrated on because results were qualitatively similar (for a full discussion, see Venetis et al., 2001).

⁷ The scaling factor is (n/n − k)⁁0.5

⁸ The max-statistic was also computed in the test but the percentage of times that was significant at 5% was the same than with the trace statistic.

⁹ The Shin test is a modification of the Kwiatkowski et al. (1992) (KPSS) test for stationarity where I(1) regressors are added in the cointegration regression as described in Equation 4. The KPSS test uses the components model

where y_t is the sum of the deterministic trend t, a random walk X_t , and a stationary error v_t . Under the null hypothesis that y_t is trend stationary, v_t is assumed to be stationary and then it is only needed to test that . It is also possible to consider the case where y_t is stationary around a level α, so the parameter δ is set equal to 0. Following Shin, let S_t be the partial sum processes of the residuals v_t from Equation 4. Let s ²(l) be the consistent semiparametric estimator of the long-run variance of the regression error using the Newey–West correction. The Shin statistic is then

The critical values will depend on the number of regressors, in this case two, domestic and foreign price level, and on the deterministic components, constant, trend or none. The Shin statistic is then

The critical values will depend on the number of regressors, in this case two, domestic and foreign price level, and on the deterministic components, constant, trend or none.

¹⁰ For the Newey-West (1987) semiparametric corrections used in the Shin test to remove persistent serial correlation of the residual process we chose l = 12 as the appropriate choice for the lag parameter.

¹¹ See Effron and Tibshirani (1993, ch.10) for full discussion of bias estimation under bootstrap.

¹² It was found that the difference with using 500 repetitions was quantitatively insignificant.

¹³ The correlations between the real exchange rates using unit coefficients (labelled as Unity), the Saikkonen weights obtained in Table 5 (labelled as Sa), and the Saikkonen weights bias-corrected (labelled as SaBC) for the five different exchange rates are presented in the table below.

Table