# Dynamic forecasting of sticky-price monetary exchange rate model

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<ul><li><p>Dynamic Monetary Forecasting of Sticky-Price Exchange Rate Model </p><p>JAE-KWANG HWANC* </p><p>Abstract </p><p>The Dornbusch-FrankeI monetary model is used to estimate the out-of-sample fore- casting perfo~rnanee ]or the U.S. or Canadian dollar exchange rate. By using Johansen's multivariate cointegration, up to three comtegrating vectors were found between the ex- change rate and macroeeonomic fundamentals. This means that there is a long-run re- lationship between exchange rate and economic fundamentals. Based on error-correction models, the random-walk model outperforms the Dornbusch-Frankel model at every fore- casting horizon. The random-walk model also dominates the Dornbusch-Frankel model with the modified money demand function at every forecasting horizon except one month. However, this paper shows that the share price variable can improve the accuracy of fore- Casts of exchange rates at short-run horizons. (JEL F31) </p><p>I n t roduct ion </p><p>It has long been believed that nominal exchange rate behavior is welt described by the naive random-walk model. This means that there are no systematic economic forces in deter- mining the exchange rates. Meese and Rogoff [1983] show that none of the structural models (Frenkel-Bilson's flexible-price monetary model, Dornbusch-Frankel's sticky-price monetary model, Hooper-Morton's sticky-price asset model) outperform a simple random walk on the basis of the root-mean-square-error (RMSE) and mean-absolute-error criteria for forecast evaluation. The poor empirical performance of these structural exchange rate models could be the result of simultaneous equation bias, sampling error, stochastic movement in the true underlying parameters, and mis-specification of the underlying models. 1 </p><p>However, not all writers present results that reject structural exchange rate models. Woo [1985] incorporates a money demand function with a partial adjustment mechanism, and finds that a reformulated monetary approach can outperform the random-walk model in an out-of-sample forecast exercise. Somanath [1986] also finds that a monetary model with a lagged endogenous variable forecasts better than the naive random-walk model. Finn [1986] finds that the simple flexible-price monetary model is not supported by the data while the rational-expectations monetary model is supported and performs as well as the random-walk model. </p><p>MacDonald and Taylor [1993; 1994] also claim some predictive power for the monetary model. MacDonald and Taylor [1993] examine the monetary model of the exchange rate between the Deutsche mark and the U.S. dollar over the period January 1976 to December 1990. They find that a dynamic error-correction model outperforms the random walk forecast at every forecast horizon. MacDonald and Taylor I1994] also find, using a multivariate cointe- </p><p>*Ouachita Baptist University--U.S.A. The author would like to thank James P. Cover for his help and useful suggestions on earlier drafts. </p><p>103 </p></li><li><p>104 AEJ: JUNE 2003, VOL. 31, NO. 2 </p><p>gration technique, that an unrestricted monetary model outperforms the random walk and other models in an out-of-sample forecasting experiment for the sterling-dollar exchange rate. </p><p>Reinton and Ongena [1999] show that monetary exchange rate models outperform the random walk model at six and 12 months horizons by using Norwegian Krone vis-h-vis four major currencies from 1986-96. Tawadros [2001], using a cointegration and error correction model, examines the predictive power of monetary exchange rate model for the Australian dollar or the U.S. dollar. He presents that an unrestricted monetary model dominates the random wail model at all forecasting horizons. </p><p>This paper examines the forecasting performance of Dornbusch-Frankel's sticky-price monetary model vis-~t-vis the random-wail model for the U.S. dollar-Canadian dollar ex- change rate over the period January 1980 to December 2000. The motivation for this re- examination is to study the effect of the share prices on the demand for money. As men- tioned above, a potential problem with the structural models might be the instability of their underlying money-demand specifications. </p><p>Choudhry [1996] finds that share prices are a statistically significant variable in the long- run real M1 and M2 demand functions in U.S. and Canada. Also, according to Friedman [1988], movements in share prices may have two kinds of effects on money demand: a positive wealth effect and a negative sUbstitution effect. Therefore, if share prices do enter the money demand function, structural exchange rate models that do not include it are mis-specified. </p><p>In addition, some writers report a significant positive relationship between equity prices and exchange rates [Smith, 1992; Solnik, 1987], while others report a strong negative re- lationship between share prices and exchange rates [Soenen and Hennigar, 1988]. Ma and Kao [1990] find that domestic currency appreciation negatively affects domestic share prices for an export-dominant economy and positively affects share prices in an import-dominant economy. </p><p>Bahmani-Oskooee and Sohrabian f1992] show that there is a bidirectional causality be- tween share prices and exchange rates in the short-run but not in the long-run. On the other hand, Abdalla and Murinde [1997] show unidirectional cansahty from exchange rates to share prices in three out of four developing countries. Ajayi and Mougoue [1996] show that an increase in aggregate domestic share prices has a negative short-run effect on the value of domestic currency but in the long-run increases in share prices have a positive effect on the value of domestic currency. However, currency depreciation has a negative short-run and long-run effect on share prices. These results suggest that including the effect of share prices on money demand might result in an improved structural exchange rates model. </p><p>The purpose of this paper is to determine whether Dornbusch-Frankel model with a modified money demand specification performs better than the random-walk model in an out-of-sample forecasting exercise at short horizons. If it does, then share prices become one of the macroeconomic fundamentals in exchange rate models. It is especially interesting to see whether Dornbuseh-Frankel model outperforms the random-walk model at short-run horizons. </p><p>This paper uses the multivariate cointegration technique proposed by Johansen [1988] and Johansen and Jnselius [1990] to determine the long-run multivariate relationship between our variables. This allows the specification of a dynamic error-correction model of the exchange rates. To construct out-of-sample forecasts, the short-run dynamic forecasts are made over four forecasting horizons, namely one, three, six, and twelve months for the period 1999:1- 2000:12. RMSE is the principal criterion to test the out-of-sample forecast performance and when comparing the Dornbusch-Frankel model with the random-wail model. </p><p>Up to three cointegrating vectors are found in the Dornbusch-Frankel exchange rate mod- els. In other words, there is a stable long-run relationship between the exchange rate and </p></li><li><p>HWANG: DYNAMIC FORECAST ING 105 </p><p>macroeconomic fundamental variables. The random walk model outperforms the Dornbusch- Frankel model by showing a lower value of the RMSE statistic. Also, the random walk model dominates the Dornbusch-Frankel model with modified money demand specification in forecasting exchange rates, except one month horizon. 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. As a result, this paper shows that the share price variable could improve the out-of-sample forecasting of the exchange rate at short-run horizons. </p><p>The organization of this paper is as follows. The second section discusses the basic models of exchange rate determination and methodology. The third section presents the empirical results, and the fourth section concludes. </p><p>Exchange Rate Mode ls </p><p>This paper employs the fundamental analysis to forecast the exchange rate instead of the technical analysis. This paper is based on Dornbusch-Frankel's sticky price monetary model. A money demand function with share prices [Choudhry, 1996] can be represented as: </p><p>(M/P) d = f(y+, r - , sp ?) (1) </p><p>This function assumes that demand for the real money balances is positively related to real income, negatively related to interest rate, and is positively or negatively related to share prices. If the real share prices are found to be a part of the money demand function, then we can estimate the size and the direction of the effects of stock returns on the money demand function. But any change in money demand must affect the exchange rate. This is why this paper considers share prices in money-demand specifications. The following section uses this modified money demand function rather than common money demand function in an empirical exchange rate model. </p><p>With Dornbusch-Frankel sticky-price monetary model and modified money demand func- tion, this paper specifies the fundamentals for nominal exchange rate determination in two ways. The quasi-reduced form of two models can be subsumed under the general specification of: </p><p>s = 7(m - m*) + (y - y*) + ~( r - ~*) +/3(~ - ~*) + ~(sp - sp*) + c , (2) </p><p>where 7,/3 > 0; , a < 0; and ~ >< 0; * denotes a variable of the foreign country, s is the logarithm of the spot exchange rate (U.S. $ or Canadian $), m is the logarithm of money supply M2, y is the logarithm of real income, r is the short-term interest rate, r is the expected inflation rate, sp is the logarithm of real share price, and e is the disturbance term. </p><p>The first model is the Dornbusch-Frankel model. It posits the coefficient restrictions as: </p><p>7,/3 >0; , a 0 ; ,a < 0; ~ >< 0 </p></li><li><p>106 AEJ: JUNE 2003, VOL. 31, NO. 2 </p><p>Then the economic fundamental, ft, can be specified as: </p><p>ft : v(m -- m*) + (y - y*) + c~(r -- r*) +/~(Tr -- 7r*) + 6(sp -- sp*) (4) </p><p>Testing for Cointegration: Methodology and Empi r i ca l Resu l ts </p><p>Cointegration methodology allows researchers to test for the presence of equilibrium re- lationships between economic variables. If the separate economic time series are stationary after differencing, but a linear combination of their levels is stationary, then the series are said to be cointegrated. This paper implements a cointegration technique to detect whether a stable long-run relationship between exchange rates and fundamental variables exists, then uses an error correction model to detect dynamic short-run relationships between exchange rates and fundamental variables, and the short-run dynamic equations are used to construct out-of-sample forecasts. </p><p>Data Data used in this paper, relating to the U.S. or Canadian dollar exchange rate and U.S. </p><p>and Canada macroeconomic variables, are taken from International Financial Statistics and run from January 1980 to December 2000. The chosen monetary aggregate is seasonally unadjusted M2. The income measure is seasonally adjusted industrial production. The three-month treasury bill rate is used for the short-term interest rate, and the logarithmic change of the consumer price index over the preceding 12 months is used for the unobservable expected inflation rate. SAP 500 stock index and Toronto Stock Exchange 300 index are used for the share price. To get the real share prices, they are divided by the CPI with the base year of 1990. All data are expressed in logarithm except the interest rate. </p><p>Preliminary Test: Unit Roots Prior to testing for cointegration, one needs to examine the time series properties of </p><p>the variables. They should be integrated of the same order to be cointegrated. In other words, variables should be stationary after differencing each time series the same number of times. Most macroeconomic variables have been found to be non-stationary in their levels and stationary in first differences, which means that they are I(1). </p><p>In testing for stationarity, the augmented Dickey-Fuller [1979] (ADF) test and the Kwiatk- owski, Phillips, Schmidt, and Shin [1992] (KPSS) test are implemented. The Dickey-Yhller type unit root tests are criticized because their failure to reject the null hypothesis may be attributed to their low power against weakly stationary alternatives. However, KPSS tests the null hypothesis of stationary against the alternative of a unit root. Thus the KPSS test is a complement procedure to the ADF test. To implement the ADF test, 2 one estimates the regression: </p><p>k </p><p>axe , (5) j= l </p><p>where A is the difference operator, X is the series being tested, k is the number of lagged differences, and ~ is an error term. If the t-statistics is less than the critical values, then the null hypothesis of a unit root (fl - O) cannot be rejected. However, ff the t-ratio is larger than the critical value, the null hypothesis of non-stationarity can be rejected. KPSS test statistics is: </p><p>~ = T 2 ~ (S2/s2(L)) , (6) </p></li><li><p>HWANG: DYNAMIC FORECAST ING 107 </p><p>where </p><p>t </p><p>St -~ ~ et i=1 </p><p>and </p><p>T L T </p><p>S2:T - I~- '~e2- t -2T - I~ 1 (L+I) ~ etet-s t= l s~-1 t -~sT l </p><p>St is the partial sum process of the residual e, T is the number of observations, and L is the lag length. If the test statistic is greater than the critical values, the null hypothesis of stationarity is rejected in favor of the unit root alternative. </p><p>Table 1 and 2 present that all series are first-difference stationary. When these series are also tested with a trend term for non-stationary test, none of the variables axe trend stationary. Hence, all variables are non-stationary in levels. </p><p>TABLE 1 Unit Root Test </p><p>Variables Levels First-differences LEX -1.04 -16.66" MM -0.46(12) -3.01(11)** YY -1.19(4) -9.92(3)* RR -2.47 -16.64" EE -2.51(11) -8.84(10)* SS -1.50 -18.77" </p><p>Notes: * and ** denotes significance at the 1 and 5 percent levels, respectively. The variables except interest rates are expressed in logarithm. LEX is the ratio of exchange rate between the U.S. and Canada, MM is the ratio of the money supply M2, YY is the ration of income, RR is the difference of the short-run interest rates between two countries, EE is the ratio of the expected inflation rates, and SS is the ratio of real share price. Figures are the pseudo t-statistics for testing the null hypothesis that the series is non-stationary. The critical values of the ADF test statistics with a constant are -3.44, -2.87, and -2.57 at the 1, 5, and the 10 percent levels, respectively. Lag length in parenthesis is selected such that the Ljung-Box Q-statistic fails to reject the null hypothesis of no serial correlation of the residuals. </p><p>TABLE 2 KPSS Test </p><p>Levels of Variables Lags LEX MM YY RR EE SS </p><p>0 10.916" 20.877* 16.782" 8.522 ~ 1.803" 23.146" 1 5.519" 10.484" 8.576* 4.381" 1.601" 11.658" 2 3.713" 7.013" 5.978* 2.983* 1.482" 7.818" 3 2.807* 5.276* 4.399* 2.283* 1.400" 5.895* 4 2.263* 4.234* 3.558* 1.862" 1.324" 4.740* 5 1.900" 3.539* 2.995* 1.580"...</p></li></ul>

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