Stock Prices and the Monetrary Model of Exchange Rate: An Empirical Investigation.

Stock Prices and the Monetary Model of the Exchange Rate: An Empirical Investigation Simon Broome Economics Department National University of Ireland Maynooth and Bruce Morley* Economics Group University of Wales Aberystwyth October 2003 *Address for correspondence: Economics Group, SMB. University of Wales Aberystwyth, Aberystwyth, Ceredigion, SY23 3DB. E-mail: [email protected]. Tel. 0044 1970 622522. Stock Prices and the Monetary Model of the Exchange Rate: An Empirical Investigation Abstract This paper develops an alternative version of the monetary model of exchange rate determination, which incorporates a stock price measure. This model is then tested using data from Canada and the USA, applying the cointegration and error correction methodology. In contrast to many previous tests of the monetary model, this version produces evidence of cointegration and stock prices have a highly significant effect on the exchange rate in both the short and long run. In addition the restricted version of the model outperforms a random walk in out of sample forecasting. (JEL Classification: F 32) 2 1. Introduction Although the asset market approach to exchange rate determination dominates theoretical exchange rate modelling, attempts to construct empirical models based on the asset approach have met with limited success. This is especially true of the flexible price monetary model, which was shown by Meese and Rogoff (1983) to provide inferior out-of-sample forecasts compared to a random walk. Furthermore attempts to produce the valid long-run equilibrium relationship implied by the monetary model have generally met with mixed success, particularly when the implicit restrictions of the model are applied. For example Meese (1986) and McNown and Wallace (1989), fail to find a valid long-run relationship for the conventional monetary model1. This paper develops and tests a version of the monetary model that incorporates stock prices. The analysis is motivated by earlier work by Friedman (1988) and Boyle (1990) that shows how the demand for money is determined in part by the level of the stock market. To date the only attempt to test the role of stock prices on the exchange rate is Smith (1992) who uses a Portfolio Balance approach2. We show that including the level of the stock market produces a valid long-run equilibrium relationship and correctly specified dynamic error correction model (ECM). The implicit restrictions of the model are then examined and it is shown that the ECM out-performs a random walk in out-of-sample forecasting. The remainder of the paper is as follows. Section 2 outlines the theoretical case for including equities in the monetary model and discusses the econometric methodology 3 used in the paper. Section 3 describes the data set and presents the time series results. Section 4 contains the conclusions and considers some implications for the integration of capital markets. 2. Stock prices and money demand In the conventional monetary model the exchange rate adjusts to balance the international demand and supply of monetary assets. The demand for money is usually considered to be a function of the level of interest rates and income. However there is an increasingly good case for including equity prices as separate determinants of the demand for money. In particular Friedman (1988) and Boyle (1990)3 provide empirical evidence describing the relationship between money demand and the level of the stock market, including a specific lag structure to the relationship, which due to a different methodology we do not attempt. On the theoretical side, Friedman (1988) suggests four possible channels through which stock prices might directly effect money demands. Firstly as stock market fluctuations tend to outweigh fluctuations in income, stock market movements are generally associated changes in the wealth to income and hence money to income ratios. Secondly a rise in stock prices reflects an increase in the expected return from risky assets relative to safe assets. The implied increase in portfolio risk can be offset by an adjustment away from other risky assets such as long term bonds toward safer assets including money. Thirdly a rise in stock prices reflects an increased level of financial transactions and thus an increase in the demand for money. The above three ‘wealth effects’ all suggest a positive relationship between the level of the stock 4 market and money demand. However as the real stock price rises equities become more attractive to investors causing a ‘substitution effect’ from equities for money. The relationship between equity prices, the demand for money and exchange rate is therefore an empirical question. As with Friedman (1988) we expect the wealth effect to dominate and thus we expect the demand for money and stock prices to be positively related. To capture these effects we incorporate a stock market variable into the standard money demand function, ttttt siypm       (1) Where m is the nominal demand for money, p is the price level, y is the real income level, i is the nominal rate of interest and s is the real level of the stock market (following Friedman (1988), a market index is used). All variables except the interest rate are in logarithms. Foreign money demands are given by, **** *ttttt siypm   (2) Where * denotes a foreign variable. It is assumed that absolute PPP holds, so that, (3) ppe tt  *t Where e is the log of the exchange rate, defined as the domestic price of foreign currency. PPP is used only as a long-run equilibrium condition in this model, in the short run the error correction model allows deviations from PPP. The evidence on 5 PPP as a long-run equilibrium condition is generally positive (Culver and Papell, 1999). Straightforward rearrangement of (1) - (3) yields, emmyyiis tttttttt            01 2 3 4 ()()()( *** s t ) * ) (4) The monetary approach assumes that domestic and foreign bonds are perfect substitutes so that Uncovered Interest Parity (UIP) holds, (5) ])|([ 1 *ttttt eIeEii   Where is the rational expectation of the exchange rate one period into the future, conditional on the currently available information set . Denoting the set of forcing variables as , substituting (5) into (4) and solving for the exchange rate yields, Ee I tt (/ 1 It ( 4  )])()([ 210   ttttttt ssyymmX     tt tjt tIeE IXE e1 3 3 311          Solving this equation by forward iteration gives,  tnt n tjt j n j tIeEIXEe             3 3 3 03 1 31 )|()]1/([)1(     6 Letting , j or assuming that the solution is free from arbitrary speculative bubbles gives the forward-looking solution for the monetary exchange rate4 (FLME), (6) )|()]1/([)1( 3 03 1 3tjt j j tIXEe       As in Campbell and Shiller (1987) and Macdonald and Taylor (1993) the exchange rate should be cointegrated with the forcing variables . This is illustrated by subtracting from both sides of (6) to obtain, Xt Xt             ........ 11 12 3 3 2 3 1 2 3 3 3 3ttttttt IXEIXEXXe       Rearranging into first differences yields,              ........ 11 12 3 3 2 3 1 2 3 2 3 1 3 3ttttttttt IXEIXEXIXEXe       and,                             ........ 1 11 2 3 3 3 2 2 3 3 1 3 3tttttttt IXEIXEIXEXe       Which for all   j gives, (7) )|()]1/([ 3 13tjt j j tt IXEXe       7 Under rational expectations the forecasting errors are stationary, thus if the forcing variables in are I(1), then the right hand side of (7) must also be stationary. Consequently if is also I(1), then the exchange rate must be cointegrated with the variables . Thus a test for the FLME is to test for cointegration between the exchange rate and forcing variables Xt mm tt ,, et yy s s ttt t ,, ** and * 5 : (8) ttttttt ussyytmme  * 65 * 43 * 210  Where is a random error term and, ut       12345   ,, 6 0    14 23 56 00,,,,,  The sign on the stock market differential depends on the relative strengths of the income and substitution effect, although as with Friedman (1988), the wealth effect is assumed to dominate, producing a negative relationship. Bahmani-Oskooee and Sohrabian (1992), provide a further explanation of why exchange rates and domestic stock prices are negatively related. They suggest that an exogenous increase in domestic stock prices should result in a rise in domestic wealth. According to the portfolio approach, the rise in wealth ought to facilitate an increase in the demand for money and a rise in the interest rate. Higher interest rates should encourage a capital inflow, increased demand for the domestic currency, which results in an appreciation of the domestic currency. To represent dynamic market adjustments, we can rewrite the equilibrium model of (8) as an error correction model (ECM) to give; 8 tttttttt ttttttt vssyymm sbsbybybmbmbbe   1 * 65 * 43 * 21t * 65 * 43 * 210 ][e-  (9) Where all terms must be stationary, that is integrated of order zero, denoted I(0), is a random error term with a zero mean. vt  is the first difference operator and the speed of adjustment is given by  . For values of  close to unity, adjustment is very rapid, with the disequilibrium being totally eliminated within one period of time. For 10   the dynamic adjustment path will be monotonically convergent. If there is evidence that the foreign and domestic coefficients satisfy the implicit restrictions of the monetary model, then the following restricted model is subsequently estimated: (10) ttttt ussyymme  )()()( * 3 * 2 * 10  Where: 0 ,0 ,0 321     To represent dynamic market adjustments, we can again write the equilibrium model of (10) as an error correction model (ECM) to give; ttt tttt ussyymme ssayyammaae   1 * 3 * 2 * 1 * 3 * 2 * 10 )]()()([( )()()(  (11) 3. Empirical Results 9 although more research on the monetary class of exchange rate models is still required. End Notes 1Chrystal & Macdonald (1995) find evidence of a valid long-run relationship using divisia money. Choudhry & Lawler (1997) find evidence of a long-run relationship for the restricted monetary model using Canadian/US data for the 1950’s float. 2 Gavin (1989) provides a nice theoretical version of the sticky price monetary model of exchange rates in which stock prices have wealth effects on the demand for money and exchange rate. 3 This contrasts with Friedman’s (1956) paper that relates money demand to the rate of return on equities. 4 An advantage of using the FLME, is that it produces a model in which stock prices are the explanatory variables along with income and money. If the conventional monetary model, with static expectations or Frankel real interest rate model had been used, both long and short interest rates would have been incorporated into the model, which could have produced problems of collinearity between the interest rates and stock price returns in the ECMs. In general the conventional FLME (without stock prices) has not been widely used as it generally fails to produce evidence of a valid long-run equilibrium relationship and is not a good predictor of the exchange rate. 5 Testing for cointegration between the exchange rate and forcing variables is also a test for the presence of bubbles in the exchange rate. If cointegration is found and certain restrictions proved to hold, then the speculative bubble hypothesis is rejected. However this line of investigation is beyond the scope of this paper. Assuming UIP means the interest rate differential equals the expected rate of depreciation. In the absence of arbitrary bubbles, the rate of expected epreciation is some function of expected movements in fundamentals and so equation (8) must be true. 16 17 6 Canada and the USA were used as both countries have financial systems based around financial markets, rather than the banking sector as in Germany or France. The UK was not used as in 1982 it changed the way in which it’s main monetary aggregates were calculated. 7 Stock market indexes are as follows: US; Standard and poor Composite index; Canada; Toronto stock market composite index. 8 Given that the Johansen maximum Likelihood procedure is essentially a vector autoregression (VAR) based technique, it is more appropriate to produce the complete ECM rather than a parsimonious specification , in which the non-significant lags are omitted. 9 The results for the Frankel real interest model are not included here, as this model has been tested on Canada and the USA over the 1950’s float and the recent float in a number of other studies (Mcnown and Wallace, 1989, Choudhry and Lawler, 1997). The unrestricted Frankel real interest model did provide evidence of cointegration, however the restrictions on the domestic and foreign explanatory variables were rejected, so the restricted version of this model was not estimated. 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Table 1The Augmented Dickey-Fuller (ADF) and Phillips-Perron Test for Unit roots ADF Test Phillips-Perron Test Variables Test for I(0) Test for I(1) Test for I(0) Test for I(1) E CM1 UM1 CY UY CS US DM1 -2.586 0.688 -1.663 -2.485 -2.870 -0.824 1.502 -0.470 -3.007 -4.211 -2.213 -2.916 -2.767 -15.110 -15.272 -2.686 -2.590 1.000 -1.997 -2.656 -1.931 -0.942 2.089 0.051 -28.894 -25.294 -24.645 -12.527 -5.640 -17.471 -19.717 -20.287 20 DY DS -2.944 0.191 -3.704 -7.987 -1.922 0.464 -28.361 -18.292 Notes:. E is the exchange rate, CM1 and UM1 are Canadian and US M1 respectively, CY and UY are Canadian and US real income respectively, CS and US are Canadian and US real stock prices respectively, DM1, DY and DS are the differential between Canadian and US M1, real income and real stock prices respectively. For each variable the first column of statistics tests the null hypothesis that the series is I(1) against the alternative that it is I(0). The second column tests the null that the series is I(2) against the alternative that it is I(1). The critical values for both these tests at the 10% and 5% levels of significance are -2.56 and -2.89 respectively. The Phillips Perron test uses 40 Bartlett lags in each test. Using the same tests with a trend included does not materially change the results. Table 2Johansen Maximum Likelihood Test for Cointegration of the Unrestricted and Restricted models. Unrestricted Model Restricted Model Vectors Trace Test Eigenvalue Test Trace Test Eigenvalue Test r 0 r  1 r  2 r  3 r  4 r  5 177.92* 127.41* 84.09 53.63 31.11 14.75 50.52* 43.31 30.47 22.51 16.36 9.80 78.00* 31.98 15.07 5.32 46.01* 16.92 9.75 5.32 21 r  6 4.96 4.96 Notes: Critical values of Johansen’s Trace and Eigenvalue tests at the 95% level of significance are: r 0; 147.27 and 49.32. r  1, 115.85 and 43.61. r  2, 87.17 and 37.86. r  3, 63.00 and 31.79. r  4, 42.34 and 25.42. r  5, 25.77 and 19.22. r  6, 12.39 and 12.39 respectively. A * indicates significance at the 5% level. For the Restricted Model: r  0, 63.00 and 31.79. r  1, 42.34 and 25.42. r  2, 25.77 and 19.22. r  3, 12.39 and 12.39. Both tests included seasonal dummy variables. Table 3Normalised Equations of the cointegrating vectors. Unrestricted Model Restricted model Variable Coefficient Significance Variable Coefficient Significance E CM1 UM1 CY UY CS US -1.000 1.318 0.139 4.394 -6.360 -1.942 1.594 0.651 0.513 0.024 4.724* 5.904* 5.963* 1.866 CE DM DY DS -1.000 -1.015 0.858 -3.138 0.237 1.117 0.036 11.129* 22 Notes: The significance of the coefficients were tested using the LM statistic which tests the restriction that the coefficient is equal to zero.( . A * indicates significance at the 5% level. ((). .  05 213841) Table 4Restriction Tests on the coefficients of the following variables Null Hypothesis Chi-square statistic H1: CM1=1,UM1=-1 H3: CY=-UY H4: CS=-US H5: CM1=-UM1; CY=-UY; CS=-US 0.372 1.412 0.144 4.312 Notes: Critical Values are 3.84 and 7.815 (5%) Table 5Error Correction Model Results for the Unrestricted Model  E  CS U S Constant rest1 0.017 [0.305] -0.004 [0.328] -0.126 [0.607] 0.035 [0.736] 0.481 [2.529]* -0.107 [2.452]* E  CM 1 0.096 (0.619) 0.084 (0.343) -0.090 (1.900) 1.022 (2.774) -0.031 (0.938) 1.581 (8.594)* UM1  CY  0.187 (0.645) -0.318 (3.994)* -0.478 (0.030) 1.161 (4.283)* 1.504 (0.191) -0.001 (0.073) UY  CS  0.324 (1.274) 0.147 (8.931)* -1.606 (4.839)* -0.068 (0.745) -1.082 (1.236) -0.376 (3.840)** 23 US  R 2 SC(12) SC(6) Reset Heteroskedasticity ARCH(12) -0.103 (4.924)* 0.187 1.658 1.417 0.077 0.522 0.482 0.147 (0.131) 0.206 2.022 1.019 0.232 0.204 0.155 0.047 (0.026) 0.213 0.827 1.021 1.573 0.122 0.989 Notes: res denotes the error correction term; R 2 is the coefficient of determination; DW is the DurbinWatson statistic; SC(i) are the ith order tests for serial correlation; ARCH(i) is Engle’s (1982) test for the i’th autoregressive conditional heteroskedasticity. These test statistics all follow the F-distribution, critical values are: F(6,222)=2.14, F(12,216)=1.80, F(1,227)=3.89. The values in square brackets represent t-statistics for the constant and ect. The values in ordinary brackets represent Wald statistics, which follow a chi-square distribution, critical value 3.842. All equations include seasonal dummies. A * indicates significance at the 5% level, ** 10% level. Table 6Error Correction Model for the Restricted Model  E D S Constant rest1 0.003 (0.705) -0.001 (0.678) 0.034 (4.112)* 0.147 (4.921)* E  DM  -0.075 (0.418) 0.073 (0.545) -0.691 (1.208) 0.035 (1.311) DY  DS  0.061 (0.064) 0.101 (3.733)** 1.266 (0.253) -0.129 (13.055)* R 2 SC(12) 0.08 1.592 0.189 0.746 24 SC(6) Reset Heteroskedasticity ARCH(12) 0.320 1.510 1.025 0.795 0.524 3.913 0.007 0.920 Notes: See Table 4 Table 7RMSE Statistics for Forecasts using the Competing models Models 3 Months 6 Months 9 Months 12 Months Random Walk Unrestricted Model Restricted Model Frankel Model 0.010 0.013 0.009 0.011 0.017 0.017 0.016* 0.016* 0.017 0.018 0.016* 0.016* 0.016 0.017 0.015* 0.015* Notes: A * indicates a significant Diebold-Mariano test statistic at the 5% level. The test uses the standard Newey-West adjustment, with Bartlett weights and a lag window of 2. Figure 1Persistence Profiles of the Effect of a System Wide Shock on the Cointegrating Vector. 25