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Weekly UpdatesThe paper reports diagnostic test results for autocorrelation, heteroskedasticity, autoregressive conditional heteroskedasticity (ARCH) effects, the regression specification error test (RESET), and the Chow test. The Godfrey-Breusch test is applied to test for serial correlation up to the 12th order. The Lagrange multiplier test proposed by Engle [1982] is used to test for ARCH up to the 12th order. White's [1980] test for general heteroskedasticity is also performed. The Ramsey RESET is employed to test for misspecification. Finally, the Chow test is used to check for structural stability. (3) If none of the diagnostic tests reported are significant at the 95 percent critical value, there is nothing to suggest that the model is mis-specified.
In Table 5, the Dornbusch-Frankel model shows the parsimonious equation and diagnostic test results. The coefficient of the error correction term is negative and statistically significant. The speed-of-adjustment coefficient suggests that approximately 1.3 percent of the change in the exchange rate per month can be attributed to the disequilibrium between actual and equilibrium levels. Changes in some of the lagged exchange rates, money stock, real income, interest rate, and expected inflation differentials have significant short-run effects on the exchange rate. The adjusted coefficient of determination is 12 percent. No problems can be seen on diagnostic test results.
Also in Table 5, the Dornbusch-Frankel model with share price shows the parsimonious equation and diagnostic test results. The coefficients of the error-correction terms are negative and statistically significant. The speed of adjustment coefficient suggests that approximately 3.1 percent of the change in the exchange rate per month can be attributed to the disequilibrium between actual and equilibrium levels. Changes in some of the lagged exchange rates, money stock, real income, expected inflation differentials, and share price have significant short-run effects on the exchange rate. The adjusted coefficient of determination is 20 percent. No problems are seen on diagnostic test results.
Finally, the final parsimonious equation is used to forecast the exchange rate for four forecasting horizons-one, three, six, and twelve months ahead over the period 1999:1 to 2000:12. The estimated values of the level of exchange rate are fed back into the error-correction term and a further set of forecasts made. Thus, forecasts are fully dynamic. These forecasts will be continued for all remaining observations and RMSE statistics are calculated over the four forecasting horizons.
Table 6 reports the RMSE statistic of the monetary models and random walk model for all forecasting horizons. First of all, the random walk model dominates the Dornbusch-Frankel model at every forecasting horizon like Meese and Rogoff [1983] results. In addition, the random walk model outperforms the Dornbusch-Frankel model with the modified money demand function at every forecasting horizon except one month. When the forecasting errors of two models are compared, the Dornbusch-Frankel model with share price performs better than the Dornbusch-Frankel model at all forecasting horizons. It means that share price variable improves forecasting errors in the short-run.
Conclusion
This paper has examined the Dornbusch-Frankel sticky-price exchange rate model for the U.S. or Canadian dollar exchange rate from 1980:1 to 2000:12. It is shown that there are up to three cointegrating vectors between the exchange rate and economic fundamental variables. Using these cointegrating vectors, the error correction model was established to estimate the out-of-sample forecasting errors. The random walk model dominates the Dornbusch-Frankel model at all forecasting horizons. This result contrasts with the results of a number of other researchers [MacDonald and Taylor, 1993, 1994; Reinton and Ongena, 1999; Tawadros, 2001].
The random walk model also outperforms the Dornbusch-Frankel model with the modified money demand function at every forecasting horizon except one month. In other words, the Dornbusch-Frankel model with share price predicts exchange rate better than the random walk model at the very short-run horizon. When the forecasting errors of two models are compared, the Dornbusch-Frankel model with share price shows lower forecasting errors than the Dornbusch-Frankel model. The main finding suggests that the share price variable can improve the accuracy of forecasts of exchange rates at short-run horizons.
For the further research, empirical works on more exchange rates might be necessary to support the results of this paper. Also, it would be worth to examine the statistical significance of forecasting accuracy because simply comparing the values of the RMSE does not give any idea of significance of the differences.
Footnotes
(1.) Goldberg and Frydman [1996] showed that "the large forecasting errors reported in Meese and Rogoff [1983] were the result of allowing the forecasting experiment to run past the end of one exchange rate regime and into the next." They presented that the important factor for the failure of empirical exchange rate models is periodic shifts in the long-run relationship governing the exchange rate and macroeconomic fundamentals.
(2.) The ADF test is comparable to the simple DF test but it involves adding an unknown number of lagged first differences of the dependent variable to capture the autocorrelated omitted variables that would otherwise enter the error term. However, it is very important to select the appropriate lag length; too few lags may result in over-rejecting the null when it is true, while too many lags may reduce the power of the test.
(3.) Another important aspect of diagnostic checking is testing for structural breaks in the model that would be evidence that the parameter estimates are non-constant. The null hypothesis is one of structural stability: coefficients are the same over different subsamples. The break point in January 1985 is also used because the U.S. trade deficit and the dollar had climbed so high by the first quarter of 1984 that the stated Reagan policy was changed to try to get the dollar down.
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