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Real stock prices and the long-run money demand function: evidence from Canada and the USA
Pergamon
Yournal oflnternational Money and Finance, Vol. 15, No. 1, pp. 1-17, 1996
0261-5606(95)00041-0
Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0261-5606/96 $15.00 + 0.00
Real stock prices and the long-run money demand function: evidence from Canada and the USA TAUFIQ CHOUDHRY*
Department of Economics, Universityof Wales, Swansea SA2 8PP, UK This paper investigates the relationship between stock prices and the long-run money demand function in Canada and the USA during the post WWlI period (1955-1989). The empirical investigation is conducted by means of the Johansen method of cointegration and the error correction modelling strategy. Results show that stock prices play a significantrole in the determination of stationary long-run real M1 and real M2 demand functions in both countries. The direction and magnitude of the role of stock prices depends upon the definition of the money and the country. Error correction results provide evidence of causality between the real money stock and the determinants of the money demand (including real stock prices). (JEL E41, E44).
The research on the money demand function assumes that there exists an underlying stationary long-run equilibrium relationship between real money balances, real income or real wealth, and the opportunity cost of holding real money balances (Friedman, 1956). Stock market prices are usually not associated with the money demand function. 1 According to Friedman (1988) movements in stock prices may have two kinds of effects on money demand, a positive wealth effect and a negative substitution effect. The positive wealth effect may be due to three different reasons. First, an increase in stock prices implies an increase in nominal wealth, producing a positive effect. Second, an increase in stock prices reflects an increase in the expected return from risky assets relative to safe assets. According to Friedman this change in relative valuation does not have to be accompanied by a decrease in risk aversion or an increase in risk preference. Thus, the resulting increase in relative risk may induce economic agents to hold larger amounts of safer assets, such as money, in their portfolio. Third, an increase in stock prices may induce a rise in the * I thank D. N. Manning for numerous helpful comments and suggestionson an earlier draft. I also thank the editor of this journal and two anonymous referees for several valuable comments. All remaining errors and omissions are my responsibility alone.
Stock prices and money demand: T Choudhry
volume of financial transactions. Such an increase in financial transactions will require higher money balance in order to facilitate these transactions. As stated earlier, stock prices also impose a negative substitution effect on money demand. The substitution effect implies that as stock prices rise, equities become more attractive when compared to other components in a portfolio. Thus, there may be a shift from money to stocks. In summary, the net effect of stock market prices on demand for money may be positive or negative. A money demand function that includes stock market prices may be represented as:
(M/P) d =f( y, i, sp). +-? This function states that demand for real money balances (M/P)awhere M is nominal money and P is the price level, is positively related to real income (y), negatively related to the rate of interest (i), and may be positively or negatively related to stock prices (sp). There are three purposes to this paper. First, to determine whether there exists a stationary long-run relationship between money demand and real stock prices in Canada and the USA. Tests are first conducted without the real stock prices in the money demand function. In this manner it can be evaluated if real stock prices truly belong in the money demand function. If real stock prices are found to be a part of the money demand function, the second objective is to determine the size and the direction of the effect of stock prices on demand for money. The third objective is to examine the temporal causality between the real money stock and the determinants of the long-run real money demand. Tests are conducted using both a narrow definition of money (real M1) and a broad defmition of money (real M2). The time period applied ranges from 1955 to 1989 for both countries, except that when using the real M2 for Canada the time period ranges from 1970 to 1989. 2 The Johansen method of cointegration tests is used to test the hypothesis of a stationary long-run money demand function. Results obtained indicate that real stock prices do play a significant role in the money demand function in both Canada and the USA, though the size and the direction of the effect is not identical in each case examined. Error correction models are applied towards the study of the temporal causality between money demand determinants and the real money stock. Results from these models provide evidence of causality between the real money stock and determinants of real money demand in both countries, including real stock prices. In previous studies of the relationship between stock prices and money demand, stock prices are either related to the volume of transactions, or the return on securities is considered as a variable in the money demand function (Hamburger, 1966; Hamburger and Kochin, 1972; Hamburger and Keran, 1987; Keran, 1971). Friedman (1988) provides a study of the direct relationship between stock prices and money demand. Using quarterly data from 1961 to 1986 and annual data from 1886 to 1985, he finds suggestive but non-conclusive results for the USA. Depending upon the time period and the data set, Friedman is able to find both the positive wealth effect and the negative
Stock prices and money demand: T Choudhry
substitution effect. Similar results are obtained by McCornac (1991) using Japanese data from 1975 to 1988. These studies used standard normal regression procedures. However, these procedures are inappropriate if the data are nonstationary; in those cases cointegration constitutes the proper statistical estimation technique. A detailed analysis of the concept of cointegration is provided in Dickey and Rossana (1994). Put simply, two or more nonstationary time series are cointegrated if a linear combination of these variables is stationary. Thus, if the money demand function describes a stationary long-run relationship among real money balances, real income, the opportunity cost of holding money and real stock prices, it can be interpreted to mean that the stochastic trend in real money balances is related to the stochastic trends in real income, the opportunity cost of holding money, and real stock prices. In this paper, the cointegration tests are carried out using the Johansen procedure. This procedure provides more robust results when there are more than two variables (Gonzalo, 1994). Cointegration also implies that the transitory components of the series can be given a dynamic specification by means of the error correction models. In other words, a constrained error correction model that captures the short-run dynamic adjustment of cointegrated variables can be applied. A detailed analysis of the error correction modelling strategy that is based on the information provided by cointegrated variables is provided in Engle and Granger (1987), Miller and Russek (1990) and Miller (1991). In this study, such models are applied to investigate the temporal causality between determinants of the long-run money demand in Canada and the USA, and the real money stock in these countries. Application of error correction models in the short-run dynamic adjustment of the money market is analyzed in Miller (1991). I. The data and the unit root tests
Since cointegration tests require a certain stochastic structure of the time series involved, the first step in the estimation procedure is to determine if the variables are stationary or nonstationary in levels. For our purposes all variables should be nonstationary in levels (i.e. they should contain a unit root). Two different tests, the ADF test (Dickey and Fuller, 1979; Said and Dickey, 1984) and the KPSS test (Kwiatkowski et al., 1992) are conducted to check for the time series properties of data. In the ADF test the null hypothesis is nonstationary (single unit root), while in the KPSS test the null hypothesis is stationary (zero unit root). Fuller (1976) provides the critical values required in the ADF test, while Kwiatkowski et al. (1992) provide the required critical values for the KPSS test. Six variables are tested for unit roots: seasonally unadjusted quarterly series of real M1, real M2, real income, two different types of opportunity cost of holding money (short-term and long-term interest rate), and real stock prices. 4 All variables are transferred to logarithmic form except for the two interest rates. 5 For Canada real money balances are created by dividing the nominal balances by the CPI. Similarly for the United States, nominal balance are
Stockprices and money demand: T Choudhry divided by the G N P deflator to create the real m o n e y balances. R e a l G D P r e p r e s e n t s the real i n c o m e for C a n a d a and for the U S A real G N P r e p r e s e n t s the real income. T h r e e - m o n t h T r e a s u r y bill rates r e p r e s e n t the s h o r t - t e r m interest rate for b o t h countries. Similarly, for b o t h countries rates on the l o n g - t e r m g o v e r n m e n t b o n d s r e p r e s e n t the l o n g - t e r m interest rates. D a t a used are o b t a i n e d f r o m the St Louis F e d e r a l R e s e r v e Bank, the Surrey o f Current Business and the O E C D Main Economic Indicator Historical Statistics. All statistical analyses are c o n d u c t e d using R A T S version 4.10. T a b l e 1 presents the A D F tests and the KPSS tests results using the C a n a d i a n data. B a s e d o n the evidence p r e s e n t e d by Schwert (1987, 1989), up to twelve lags are used in the A D F test. Insignificant lags (standard F-test) w e r e d r o p p e d f r o m the regressions. I f the elimination of lags p r o d u c e d serial correlation, t h e n the lags w e r e a d d e d b a c k on. Following the suggestion by Dickey and P a n t u l a (1987) the unit r o o t tests are first c o n d u c t e d for two roots and, if two roots are rejected, t h e n a single unit r o o t is tested for. W h e n the null hypothesis is two roots the t i m e trend is excluded f r o m the A D F test. Both the constant a n d the time t r e n d are included w h e n the null hypothesis is o n e unit root. In this m a n n e r , the two unit r o o t test allows for an alternative hypothesis o f stationary with a n o n z e r o intercept on the differenced series, while the single unit r o o t test allows for the alternative hypothesis of t r e n d stationary and a n o n z e r o intercept on the series in levels. T r e n d stationary
TABLE 1. Unit root test. Canada. Augmented Dickey-Fuller test Variables
Two unit roots
Real M1 Real M2 Real income Short-term interest rate Long-term interest rate Real stock prices
-
Single unit root
3.09b/(9) 6.88a/(0) 5.12b/(6) 3.54a/(12) 4.96a/(6) 9.43a/(0)
-- 1.77/(12) - 2.24/(9) -- 2.48/(12) - 2.77/(12) - 1.86/(12) - 1.64/(12) KPSS test
Lags Real M1 Real M2 Income Short rate Long rate Stock prices 0 1 2 3 4 5 6
2.70 ~ 1.40 ~ 0.95 a 0.73 ~ 0.58 a 0.49 ~ 0.43 ~
1.76 ~ 0.90 a 0.6P 0.46 a 0.38 a 0.32 a 0.28 ~
1.18 ~ 0.65 a 0.48 ~ 0.37 a 0.30 a 0.25 a 0.22 a
0.54 ~ 0.29 a 0.2P 0.16 b 0.14 c 0.12 c 0.11c
0.75 a 0.40 a 0.28 a 0.22 ~ 0.18 b 0.15 b 0.14 ¢
1.49~ 0.78 a 0.54 a 0.43 ~ 0.36 a 0.31a 0.28 ~
Note: a, b and c imply rejection of the null at 1%, 5% and 10% level respectively. Significant lags in parentheses.
Stock prices and money demand: T Choudhry
implies that the deviation of the series from a linear function of time follows a stationary process. All tests include quarterly seasonal dummies in order to eliminate seasonality. The seasonal dummies enter the relationship exogenously. As Table 1 shows, all variables from Canada are able to reject the null hypothesis of two unit roots but are unable to reject the null hypothesis of a single unit root. Thus, according to A D F tests all variables are stationary after first differencing, but are nonstationary in levels. In other words, all variables contain a single unit root. Table 1 also contains the KPSS tests results using the Canadian data. The KPSS tests are only conducted to check for one unit root. The KPSS tests includes a trend, thus the null is trend stationary. Based on the evidence presented by Kwiatkowski et al. (1992) the maximum number of lags used is six. All six variables are able to reject the null at all lags (0 to 6). Thus, results from the KPSS tests also indicate that the Canadian data are nonstationary in levels. In summary, both unit root tests show that all variables from Canada are nonstationary in levels. 6 Table 2 contains the A D F tests and the KPSS tests using the US data. Both the A D F tests and the KPSS tests are conducted in the same way as above. Results obtained for the USA are similar to the ones found for Canada. From both tests, all the US variables are shown to be nonstationary in levels.
II. Cointegration tests results Cointegration tests in this paper are conducted using the method developed by Johansen (1988), and Johansen and Juselius (1990). The Johansen method applies the maximum likelihood procedure to determine the presence of cointegrating vectors in nonstationary time series. This method detects the number of cointegrating vectors and allows for tests of hypotheses regarding elements of the cointegrating vector. 7 According to Dickey et al. (1991) cointegrating vectors are obtained from the reduced form of a system where all of the variables are assumed to be jointly endogenous. Thus, cointegrating vectors cannot be interpreted as representing structural equations. However, cointegrating vectors may be due to constraints that an economic structure (such as the money demand function) imposes on the long-run relationship among the jointly endogenous variables. Osterwald-Lenum (1992) provides the appropriate critical values required for these cointegration tests. A likelihood ratio test and the Akaike Information Criterion (AIC) is used to select the number of lags required in the cointegration test. 8 As in the unit root tests, lags are not omitted if their exclusion introduces serial correlation. In all cases except one, four lags were indicated for the cointegration tests. Six lags are required in the estimation of the Canadian real M1 demand function that includes the long-term interest rate. Since there seems to be a linear trend in all the nonstationary series, cointegration tests are conducted with the inclusion of a deterministic trend. 9 Seasonality is eliminated by including quarterly seasonal dummies in all regressions. As stated earlier cointegration tests were first conducted without the real
Stock prices and money demand: T Choudhry
TABLE2. Unit root test. USA. Augmented Dickey-Fuller test Variables Real M1 Real M2 Real income Short-term interest rate Long-term interest rate Real stock prices
Two unit roots
Single unit root
- 6.23a/(0) - 11.5l a / ( 0 ) - 8.82a/(0) - 3.88a/(12) - 4.96a/(3) - 4.88~/(9)
- 1.42/(12) - - 1.26/(0) - 1.73/(12) - 2.51/(12) - 1.70/(6) - 0.60/(12)
KPSS test Lags Real M1 Real M2 Income Short Rate Long Rate Stock Prices 0 1 2 3 4 5 6
1.29 ~ 0.65 ~ 0.44 ~ 0.34 a 0.28 ~ 0.24 a 0.21b
0.98 a 0.54 ~ 0.40 ~ 0.33 a 0.28 a 0.25 a 0.23 a
2.02 ~ 1.02 a 0.69 ~ 0.53 a 0.43 a 0.37 ~ 0.32 a
0.64 a 0.34 ~ 0.24 a 0.19 b 0.16 b 0.14 c 0.12 c
0.75 a 0.39 a 0.27 a 0.21b 0.17 b 0.15 b 0.13 c
1.39 ~ 0.74 ~ 0.52 a 0.41a 0.34b 0.30 ~ 0.26 c
See note to Table 1.
stock prices in the d e m a n d function. F o r b o t h C a n a d a and the U S A , real M1 does not cointegrate with real i n c o m e and any o n e of the interest rates. In the case o f real M2, w e a k evidence of cointegration is f o u n d at the 10 p e r c e n t level b e t w e e n C a n a d i a n real M2, real income, and the l o n g - t e r m interest rate. Similarly, at the 10 p e r c e n t level cointegration is indicated b e t w e e n the U S A real M2, real income, and the l o n g - t e r m interest rate. Applying the s h o r t - t e r m rate in the real M 2 function, no stationary relationship is f o u n d for b o t h countries. 1° T h e s e results are not p r e s e n t e d in o r d e r to conserve space, but are available on request. T a b l e s 3 and 4 p r e s e n t results f r o m cointegration tests (trace test and the m a x i m u m eigenvalue test) that include real stock prices along with the traditional variables for C a n a d a and the U S A , respectively. F o r b o t h countries, two different relationships are tested for cointegration for each definition of money. First, cointegration b e t w e e n log of real m o n e y balances (real M1 or real M2), log of real income, log of real stock prices, and the s h o r t - t e r m interest rate is examined. T h e n in the second relationship, the l o n g - t e r m interest rate replaces the s h o r t - t e r m rate in the function. Thus, four different relationships are e x a m i n e d for e a c h country. Results f r o m the C a n a d i a n data are shown in T a b l e 3. B o t h the trace test a n d the m a x i m u m eigenvalue test confirm o n e n o n z e r o vector b e t w e e n real m o n e y balances (real M1 and real M2), real income, real stock prices, and the s h o r t - t e r m interest rate. Thus, t h e r e exists a stationary relationship b e t w e e n
Stock prices and money demand: T Choudhry
real M1 or real M2, real income, the s h o r t - t e r m interest rate, and real stock prices in C a n a d a in the post W W l I period. R e p l a c i n g the s h o r t - t e r m rate with the l o n g - t e r m rate, a stationary long-run d e m a n d function is only f o u n d for real M2. Results do not p r o v i d e a stationary long-run real M1 d e m a n d function which includes l o n g - t e r m interest rate as the o p p o r t u n i t y cost of holding money, and also includes real stock prices. F o r C a n a d a t h r e e out of four relationships are f o u n d to b e cointegrated. Results f r o m the U S d a t a are p r e s e n t e d in T a b l e 4. In the case of the U S A also, t h r e e out four relationships are f o u n d to be stationary. W e fail to find a stationary relationship b e t w e e n real M2, real income, real stock prices and the s h o r t - t e r m interest rate. T w o n o n z e r o vectors are indicated in the real M1 function that includes the l o n g - t e r m interest rate. 11 T h e r e exists a possibility of two stationary relationships b e t w e e n the US real M1, real income, real stock prices, and the l o n g - t e r m interest rate. In s u m m a r y , cointegration results show that in the post W W l I period a stationary long-run real m o n e y (M1 and M2) d e m a n d function in C a n a d a and the U S A requires the inclusion of real stock prices in the relationship along with the s t a n d a r d variables, such as real income and s o m e definition of the o p p o r t u n i t y cost of holding money. W i t h o u t the real stock prices we either fail or we find a w e a k evidence of a stationary m o n e y d e m a n d function in b o t h countries.
TABLE 3. Cointegration test results. Canada. A. Real balances, real income, long-term interest rate and real stock prices Lags in the VAR = 6
Lags in the VAR = 4
Real M1
Real M2
Vectors r r r r
= < < <
0 1 2 3
Trace test
Eigenvalue
52.61b 18.61 8.00 0.50
34.00 b 10.60 7.50 0.50
Vectors r r r r
= < < <
0 1 2 3
Trace test
Eigenvalue
58.17 a 26.00 8.82 0.20
32.18 b 17.18 8.62 0.20
B. Real balance, real income, short-term interest rate and real stock price Lags in the VAR = 4
Lags in the VAR = 4
Real M1 Vectors r r r r
= < < <
0 1 2 3
Real M2
Trace test
Eigenvalue
29.36 14.81 6.03 0.37
14.55 8.78 5.66 0.37
Vectors r r r r
= < < <
0 1 2 3
Trace test
Eigenvalue
55.36 a 26.34 8.60 0.24
29.02 b 17.74 8.36 0.24
Note: a, b and c imply significantly different from zero at 1%, 5% and
10% level respectively.
Stock prices and money demand: T Choudhry
TABLE4. Cointegration test results. USA. A. Real balance, real balance, short-term interest rate and real stock prices Lags in the VAR -- 4
Lags in the VAR = 4
Real M1 Vectors r r r r
= < < <
0 1 2 3
Real M2
Trace test
Eigenvalue
52.94b 20.36 4.44 0.15
32.58b 15.92 4.28 0.15
Vectors r r r r
-- 0 <1 <2 <3
Trace test
Eigenvalue
37.74 18.11 6.22 0.10
19.63 11.90 6.12 0.10
B. Real balance, real income, long-term interest rate and real stock prices Lags in the VAR = 4
Lags in the VAR = 4
Real M1
Real M2
Vectors r r r r
= < < <
0 1 2 3
Trace test
Eigenvalue
53.46b 27.28 4.63 0.20
26.17c 22.65b 4.43 0.20
Vectors r r r r
= < < <
0 1 2 3
Trace test
Eigenvalue
49.26b 22.47 9.53 0.40
26.78c 12.94 9.14 0.40
See note at the end of Table 3.
III. Long-run elasticities T h e estimated cointegrating vectors are given e c o n o m i c meaning by means of normalizing o n the real m o n e y balances. Normalization is only c o n d u c t e d if n o n z e r o vector or vectors are confirmed by the cointegration test. T h e normalized equations are obtained by dividing each cointegrating vector by the negative o f the cointegrating vector o n real m o n e y balances. T h e s e normalized equations are obtained f r o m r e d u c e d forms, and may represent m o n e y demand, m o n e y supply, or some m o r e complicated interaction (Johansen and Juselius, 1990; and Dickey et al., 1991); these normalized equations a p p e a r to be m o n e y d e m a n d functions and they show signs on the variables that are consistent with m o n e y demand. Table 5 presents the implied long-run elasticities obtained f r o m these normalized equations for C a n a d a and the U S A respectively. Using the chi-square test, all variables are tested for significance. In such a test the null hypothesis is that the coefficient on the relevant variable is equal to zero. N o r m a l i z e d equations indicate that out of the six stationary relationships real stock prices have a positive effect (wealth effect) on the d e m a n d for real balances in four of the relationships. In b o t h of the Canadian real M2 d e m a n d functions, real stock prices impose a negative effect (substitution effect). T h e sizes of the coefficient o n stock prices are almost identical, - 0 . 1 9 w h e n the function includes the short-term rate and - 0 . 2 0 when the long-term rate is applied. Real stock prices are significant in all the six relationships. 8
Stock prices and money demand: T Choudhry
T ~ t ~ 5. Long-run elasticities. Canada Variables
Real M1
Real M2
Real income Short-term interest rate Real stock prices
0.45 - 0.03 a 0.30 a
1.22 a - 0.009 - 0.19 b
Real income Long-term interest rate Real stock prices
----
1.32 a -0.012 a - 0.20 ~ USA
Variables
Re~M1
Real M2
Real income Short-term interest rate Real stock prices
0.008 - 0.03 a 0.27 a
--
Real income Long-term interest rate Real stock-prices
0.23 ~ - 0.05 a 0.20 a
1.01a - 0.008 c 0.05 c
-
-
--
Null hypothesis: income elasticity is equal to unity Canada Real M1 0.45/(7.09)* --
Real M2 1.22/(2.23) 1.32/(5.34)*
USA Real M1 0.008/(13.65)* 0.23/(19.42)*
Real M2 1.01/(0.02)
Note: a, b and c imply significantly different from zero at 1%, 5% and 10% respectively. Chi-square statistics in parentheses. * imply rejection of the null at 5% level.
I n s u m m a r y , t h e r e s u l t s s h o w t h a t t h e size a n d t h e d i r e c t i o n o f t h e e f f e c t produced by real stock prices on money demand depends upon the definition o f m o n e y , e s p e c i a l l y in t h e c a s e o f C a n a d a . I n a b s o l u t e v a l u e , r e a l s t o c k p r i c e s h a v e a l a r g e r e f f e c t o n t h e d e m a n d f o r r e a l M 1 t h a n r e a l M 2 b o t h in C a n a d a a n d t h e U S A . O n l y in t h e d e m a n d f u n c t i o n f o r r e a l M 2 in C a n a d a , is t h e r e l a t i o n s h i p b e t w e e n m o n e y d e m a n d a n d r e a l s t o c k p r i c e s i n v e r s e . S i n c e M 2 is more of an investment-oriented definition of money, the negative substitution
Stock prices and money demand: T Choudhry
effect may be justified. 12 An increase in the price of stocks increases the attractiveness of equities as part of the portfolio and this may cause a movement from money holding to equity holding. The effect imposed by real stock prices on real M1 demand is found to be positive in both countries. Since M1 is used as a transaction medium, Friedman's (1988) third reason for a positive effect of real stock prices on real money demand may well be able to justify this particular result. As pointed out by Friedman, increases in stock prices produce a rise in the volume of financial transactions. Demand for money will increase in order to facilitate this higher number of financial transactions. Whenever both the real income and real stock prices are significant in a function, real income elasticity is larger in size (absolute value) than real stock price elasticity. The chi-square test is further used to check if the equilibrium real income elasticity of real money balance is equal to unity (Table 5). In this test the null hypothesis is that the coefficient on real money balance is equal to the coefficient on the real income. If the implied elasticity of real income is equal to unity, this indicates a stationary linear combination between the income velocity of money, and other relevant variables. Once again these tests are only conducted if the cointegration test confirms a nonzero vector or vectors. For Canada, the coefficient on real income is equal to unity in one of the relationships. This result implies that the cointegrating vector indicates a stationary relationship between the Canadian income velocity of M2, the short-term rate of interest, and real stock prices. For the USA also only one of the relationships shows a unit real income elasticity of money demand. A stationary relationship is found between the US income velocity of M2, the long-term rate, and the real stock prices. 13
IV. Causality between money stock and money demand determinants Granger (1986) and Engle and Granger (1987) provide a test of causality which takes into consideration the information provided by the cointegrated properties of variables. Specifically, this test considers the possibility that the past level of a variable (Y) may help explain the current changes in the other variable or variables (X), even though the past changes in Y do not. All this is conditional on the assumption that X and Y are cointegrated and thus share a common trend(s). As long as variables involved are cointegrated, causality has to exist at least in one direction. TM Tables 6 and 7 present results from the error correction estimations for Canada and the USA, respectively. In these tables, the sum of coefficients on the lagged difference is presented in the first line and the chi-square statistics indicating the significance level of the sum of coefficients are shown in parentheses. Significance of the error correction term(s) is presented by means of the t-statistics, thus the data in the parentheses below the error term(s) is the t-ratio. A significant error correction term implies causality from variable Y to variable X. Within an error correction model causality may rise from two sources (Granger, 1988). Short-run dynamics in the model are captured by the 10
Stock prices and money demand: T Choudhry TABLE 6. C a n a d a . Error correction estimations.
Dependent variables A M1 ASR Ay ASP
A M2 ASR Ay ASP
AM2 ALR AY ASP
ECt- 1
EASR
Y"AY
Y~'ASP
~aM1
0.034 a (3.19) 1.07 ~ (2.93) 0.026 a (4.57) - 0.007 ( - 0.31)
- 0.015 a (17.71) -0.16 (1.72) 0.005 b (6.17) - 0.006 (0.59)
1.08 ~ (47.06) 0.75 (0.02) - 0.68 a (70.0) - 0.51 (2.44)
0.017 (0.09) 3.63 c (3.68) 0.057 c (3.82) 0.20 c (3.08)
- 0.84 ~ (26.68) -3.18 (0.33) - 0.29 a (11.39) 0.58 c (2.89)
ECt- 1
F'aSR
EAr
'V-'ASP
Y"aM2
- 0.074 a (-4.00) - 0.86 ( - 0.62) - 0.05 b ( - 2.53) - 0.044 ( - 0.60)
0.006 a (8.08) - 0.29 (2.64) 0.005 b (4.06) - 0.009 (0.96)
- 0.25 a (7.13) - 3.93 (0.31) - 0.9V (75.85) - 0.38 (1.04)
ECt- 1
EALR
-0.08 ( - 1.48) 5.37 a (2.78) - 0.06 ( - 1.11) 0.26 (1.47)
0.001 (0.17) -0.23 (1.76) 0.005 (1.16) 0.05 ~ (9.60)
0.023 (0.31) 4.44 (2.17) 0.13 (0.62) 0.34 b (4.50)
0.048 (0.10) 5.76 (0.27) - 0.04 (0.06) - 0.45 (0.59)
EAy
EASP
~'~'aM2
-0.23 c (2.94) -0.50 (0.01) 0.89 a (45.0) 0.08 (0.03)
0.04 (0.39) 0.10 (0.003) 0.15 b (5.64) 0.056 (0.08)
0.32 b (4.02) 2.84 (0.25) 0.14 (0.72) - 0.12 (0.05)
Notes: a, b a n d c imply significantly different from zero at 1%, 5 % a n d 10%, respectively. Numbers in parentheses present chi-square statistics. N u m b e r s in parentheses under the E C term represent t-statistics. Variables: E C = Error correction term, S R = Short-term rate, L R = Longt e r m rate, Y = R e a l i n c o m e a n d SP = R e a l stock prices.
lagged differences, and conventional tests of causality may be based on the significance of these terms. The error correction term represents the potential effects of departures from the long-run equilibria. The size and the significance of the error correction term in each equation show the tendency of each variable to restore equilibrium in the money market. In this paper, the main interest is the adjustment of the money market to a long-run equilibrium due to changes in the real stock prices. The lag structure in the error correction 11
Stock prices and money demand: T Chondhry TABLE 7. U S A : Error correction estimations. Dependent variable
6M1 ASR Ay ASP
ECt- 1 -0.05 a (-3.12) - 0.62 ( - 0.36) - 0.08 a (-4.51) 0.068 (0.55) EClt- 1
AM1 ALR AY ASP
A LR Ay ASP
EAy
-0.004 a -0.06 (10.39) (0.26) - 0.08 27.31b (0.23) (4.89) 0.002 0.027 (1.14) (0.044) -0.019 -0.37 (2.64) (0.17) EC2t- 1
)'~'ALR
EASP
EAM1
0.016 (1.24) 1.79 (1.23) 0.027 (2.46) 0.21 ¢ (3.29)
0.5P (38.60) - 7.97 (0.77) 0.009 (0.088) 0.96 (2.13)
~,'ty
EASP
0.003 b - 0.05' - 0.016' 0.073 (2.60) ( - 3 . 0 2 ) (38.66) (0.48) -0.13 b - 1.44 0.438 a - 5 . 5 8 (-2.57) (-1.57) (9.30) (0.97) - 0.002 - 0.038 ¢ 0.0004 0.15 ( - 1.50) ( - 1.96) (0.019) (1.66) 0.004 0.029 b - 0.07 a 0.046 (0.06) (2.33) (11.74) (0.004) ECt- 1
A M2
EASR
- 0.28 a ( - 2.94) - 2.20 ( - 1.10) 0.14 a (3.51) 0.32 (1.22)
Y"ALR
~"~Ay
- 0.02" 0.16 (12.65) (0.37) 0.22 c 1.82 (2.74) (0.11) 0.00 0.18 (0.0002) (2.60) -0.06 a -0.34 (10.03) (0.21)
EAM1
- 0.002 0.33" (0.01) (12.60) 1.43 2.24 (2.66) (0.22) 0.035 e 0.17 ¢ (3.47) (3.74) 0.20 ¢ 0.30 (2.73) (0.208)
~ASP
Y~'8M2
0.07V (2.81) 1.30 (2.20) 0.05 a (7.20) 0.18 (2.49)
0.34 (1.61) 0.26 (0.002) 0.09 (0.68) 0.57 (0.602)
S e e note at the end o f Table 6.
model is determined by means of the Akaike's FPE criteria. For each of the models a possible combination of one to eight lags are examined and the lag structure that minimizes the FPE is chosen. The majority of the models required the use of four to six lags. Interpretation of the error correction estimation depends upon whether real money stock is exogenous or endogenous. If the real stock of money is endogenous, then the error correction equation represents the endogenous response of real money growth rate to adjustment in the economy. Results presented in this section show that both the real M1 stock and the real M2 stock are endogenous in both countries. Positive signs are expected on the error correction term in the real income equation, while negative signs are expected on the error term in the real money and the interest rate equations. The error term in the real stock prices 12
Stock prices and money demand: T Choudhry
equation may be negative or positive. These signs are expected because excess supply of money will result in an increase of real income and a decrease in the interest rate, and if the purpose of the monetary policy is stabilization, then the growth rate of money stock should decrease. For Canada (Table 6) the error correction term is significant in two of the money equations, two of the interest rate equations, two of the real income equations, and none of the real stock prices equations. In one of the relationships, real stock prices are econometrically exogenous. In this particular stock price equation only the lagged changes in dependent variable (real stock prices) provide explanatory power. In general, the results suggest feedback effects between the real money stock, both definitions of the interest rate, real income and real stock prices. On causality between the real money stock and real stock prices, only a unidirectional effect is found from real M1 to stock prices. In most of the equations the signs on the error correction terms are not the expected signs. For the USA (Table 7) the error correction term(s) are significant in all three money equations. 15 The error correction term is also significant in all three real income equations and in only one out of the interest rate equation and the stock price equation. For the USA there also is evidence of feedback effects between real money supply, interest rates, real income and real stock prices. There is some evidence of a unidirectional causality from real stock prices to real money stock. Real stock prices are exogenous when the real M1 function includes the short-term interest rate. Similarly, the long-term rate is exogenous in the real M2 demand function. Except for two of the real income equations, the signs on the error correction terms are as expected. For both Canada and the USA results from error correction estimations indicate that both the goods and the financial markets may have adjusted to the disequilibrium in the money market. The error correction term is generally significant in both the real income and the interest rate (short- and long-term) equations. Generally, the error term is not found to be significant in the stock price equations. 16
Conclusion This paper provides a study of the relationship between the long-run money demand function and stock market prices in Canada and the USA for the post WWII period (1955-89). For both countries two different definitions of money are used in the study, a narrow defmition (real M1) and a broad definition (real M2). The Johansen procedure of cointegration is used to test the hypothesis of a stationary relationship between real money balances, real income, the opportunity cost of holding money (the short- or long-term interest rate) and real stock prices. Normalized equations and chi-square tests are used to determine the significance, the size and the direction of the effects produced by each variable on money demand. Results obtained indicate that real stock prices do play a significant role in the money demand function both in Canada and the USA, though the size and the direction of the effect is not identical in every relationship. Without the real stock prices, we either fall, or we find only weak evidence of a stationary money demand function. In absolute value, stock 13
Stock prices and money demand: T Choudhry
prices have a larger effect on the demand for real M1 both in the case of Canada and of the USA. Only in the Canadian demand for real M2 do stock prices produce a negative effect. Whenever real income and real stock prices are significant in the relationship, the real income elasticity is larger in size (absolute value) than the real stock price elasticity. Thus, the results overall suggest that the real money demand function in Canada and the USA in the post WWII period requires the inclusion of real stock prices in the relationship. Error correction models are applied to investigate the temporal causality between the real money stock and real money demand determinants (including real stock prices). These results show that evidence exists of feedback between the real money stock, real income, the interest rate (short- or long-term), and real stock prices in both countries. Notes 1. According to Friedman (1988) direct studies of the relationship between stock prices and money demand function are not very common. Indirectly stock prices are included in the total nonhuman wealth, which plays a role in money demand function. 2. Lack of M2 data before 1970 made it impossible to use a longer period. 3. As stated earlier, for Canada real M2 data is only available from 1970. All test involving real M2 of Canada are confined to the period 1970-89. All Canadian variables are also tested for unit roots for the period 1970-89. These results are not presented here, but are available on request. 4. Analyses of the difference between and construction of seasonally adjusted and unadjusted data are provided in Ghysels and Perron (1993) and Ericsson et al. (1994). Ghysels and Perron (1993) show how linear seasonal adjustment filters, such as US Census X-11 and Statistics Canada X-11 A R I M A methods, which apply a set of moving averages' are used to convert unadjusted (raw) data to seasonally adjusted data. In general, it may be preferable to use seasonally unadjusted data. Ghysels (1990) claims that seasonal-adjustment filters have at least three adverse effects on the power of the unit root test. First, the power of unit root tests may be reduced due to the smoothing effects fo the filters. Second, the long leads and lags used in the filters may produce distant autocorrelation in the adjusted series. The third and final problem is induced by the nonlinear properties of seasonal-adjustment filters. Ghysels and Perron (1993) also provide analyses of the adverse effects of seasonal-adjustment filters on the power of the unit root tests. 5. Application of interest rates rather than their logarithms assumes that the absolute rather than the percentage change in interest rates is what matters for money demand. Friedman and Schwartz (1982) describe the advantages of using the interest rate in absolute values rather than in logarithms in the estimation of money demand functions. 6. When Canadian variables are tested for unit roots for the period 1970-89, similar results are obtained. Thus all Canadian variables are also nonstationary in levels during 1970-89 period. These results are not provided but are available on request. 7. More detailed analysis of the Johansen procedure is provided in Dickey et al. (1991). 8. Starting with a maximum length of 12 lags, lags were eliminated if they were insignificant (as a group of 4) at the 10 percent level. 9. We tested the hypothesis that the linear trend is absent as suggested by Johansen and Juselius (1990, p. 192). The result indicates that the null hypothesis is rejected at the 1 percent level. This result is available on request. 14
Stock prices and money demon&"T Choudluy 10. Haler and Jansen (1991) and Miller (1991) fail to find a stationary long-run real M1 demand function for the USA in the post WWII period. Both studies provide weak support for a stationary long-run real M2 demand function for the USA in the stated period. Both studies only use the standard variables in the demand function and apply the cointegration technique in their empirical estimation. Our results from the US data are similar though not identical to the findings of the studies just described. The difference arises mainly because those studies apply seasonally adjusted data while our paper uses seasonally unadjusted data. Also, the time periods in all three papers are similar but not identical. To our knowledge, no such study has been conducted for Canada in the post WWII period. 11. According to Dickey et aL (1991) and Johansen and Juselius (1990) the larger the number of nonzero vectors, the more stable is the system. More than one nonzero vector implies that the economic systems are stationary in more than one direction. 12. Using the US real M2, only one relationship was found to be stationary. Even though the coefficient on stock prices is positive, it is small (0.05) in size and significant only at the 10 percent level. Real income seems to dominate this particular relationship. 13. Cointegration tests were also conducted to confirm these results involving the income velocity of money. These tests indicate a stationary long-run relationship between the income velocity of M2, the short-term interest rate, and real stock prices in Canada. A similar result was found for the USA using the income velocity of M1, the long-term rate, and real stock prices. Normalized equation have the proper sign on the variables and chi-square tests confirm the significance. Unti root tests (ADF) were also conducted to check for the stochastic structure of M2 income velocity in Canada and the USA in the post WWII period. Both series were found to be nonstationary in levels. This result implies that M2 and income are not cointegrated by themselves in Canada and the USA in the post WWII period. These results are available on request. 14. Miller and Russek (1990) and Miller (1991) describe in detail the application of cointegration-oriented causality tests. 15. Two nonzero cointegrating vectors are found in the real M1 demand function that includes the long-term interest rate. The error correction equation in this case includes two error correction terms. 16. The standard Granger causality test with the VAR model (without the cointegration constraint was conducted for the two relationships where we failed to find cointegration. Results from these tests also imply feed back between the real money stock and the money demand determinants, including the real stock prices. These results are available on request.
References
DICKEY, DAVIDAND WAYNE FULLER,'Distribution of the estimator for autoregressive time series with a unit root,' Journal of the American Statistical Association, June 1979, 74: 427-431. DICKEY, DAVID AND SASTARY PANTULA, 'Determining the order of differencing in autoregressive process,' Journal of Business and Economic Statistics, October 1987, 5: 455-461.O DICKEY,DAVIDAND ROBERTROSSANA,'Cointegrated time series: A guide to estimation and hypothesis testing,' Oxford Bulletin of Economics and Statistics, August 1994, 56: 325-353. DICKEY, DAVID,DENNISJANSENAND DANIELTHORNTON,'A primer on cointegration with an application to money and income,' Review, Federal Reserve Bank of St. Louis, March/April 1991, 73: 58-78. ENGLE, ROBERTAND CLIVEGRANGER,'Co-integration and error correction: Representation, estimation, and testing,' Econometrica, March 1987, 55: 251-276. 15
Stockprices and moneydemand: T Choudhry EmcSSON, NELL, DAVm HEZ~RY AND HONO ANn T ~ , 'Cointegration, seasonality, encompassing, and the demand for money in the UK,' in Colin Hargreaves, ed, Nonstationary Time Series Ana~sis and Cointegration, Oxford: Oxford University Press, 1994. FRIEDMAN,MILTON,'The quantity theory of money: A restatement,' in Milton Friedman, ed, Studies in the Quantity Theory of Money, Chicago: University of Chicago Press, 1956. FRIEDMAN,MILTON,'Money and the stock market,' Journal of PoliticalEconomy, April 1988, 96: 221-245. FRIEDMAN, MILTON AND ANNA SCHWARTZ,'Monetary trends in the United States and the United Kingdom: Their relation to income, prices, and interest rates, 1867-1975' Chicago: University of Chicago Press, 1982. FULLER, WAYNE, Introduction to Statistics Time Series, New York: John Wiley & Sons, Inc, 1976. GHYSFA.S,ERIC, 'Unit-root tests and the statistical pitfalls of seasonal adjustment: The case of U.S. postwar real Gross National Product,' Journal of Business and Economics Statistics, April 1990, 8: 145-152. GHYSELS,ERIC Am) PmggE PERRON,'The effects of seasonal adjustments filters on tests for a unit root,' Journal of Econometrics, January-February 1993, 55: 57-98. GONZALO,JESUS, 'Five alternative methods of estimating long run equilibrium relationship,' Journal of Economeaics, January-February 1994, 60: 203-233. GRANGER,CLIVE,'Developments in the study of cointegrated economic variables,' Oxford Bulletin of Economics and Statistics, August 1986, 48: 213-228. GRANGER,CLIVE,'Development in a concept of causality,' Journal of Econometrics, 1988, 39: 199-211. HAFER, R AND DENNIS JANSEN,'The demand for money in the United States: Evidence from cointegration tests,' Journal of Money, Credit and Banking, May 1991, 23: 155-168. HAMBURGER,MICHAEL,'The demand for money by households, money substitutes, and monetary policy,' Journal of PoliticalEconomy, December 1966, 74: 600-623. HAMBURGER, MICRAEL ANt) MICHAEL KERAN, 'A stable money demand function,' Contemporary Policy Issues, 1987, 5: 34-40. HAMBURGER, MICHAEL AND LEVIS KOCHIN, 'Money and stock prices: The channels of influence,' Journal of Finance, Papers and Proceedings, May 1972, 27: 231-249. JOHANSE~,SOREN,'Statistical analysis of cointegration vectors,' Journal of Economic Dynamic and Control, June-September 1988, 12: 231-254. JOHANSEN, SORENAND KATARINAJUSELIUS,'Maximum likelihood estimation and inference on cointegration-with application to the demand for money,' Oxford Bulletin of Economics and Statistics, May 1990, 52: 169-210. KEP,AN, MICHAEL, 'Expectations, money, and the stock market,' Review, Federal Reserve of St. Louis, January 1971, 53: 16-32. KWIATKOWSKI,DENIS, PETER PHIl.LIPS,PETER SCHMIDTAND YONGCHEOLSHIN, 'Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root,' Journal of Econometrics, October-December 1992, 54: 159-178. McCORNAC, D, 'Money and the level of stock market prices: Evidence from Japan,' Quarterly Journal of Business and Economics, 1991, 30: 42-51. MILLER,STEPHEN,'Monetary dynamics: An application of cointegration and error-correction modeling,' Journal of Money, Creditand Banking, May 1991, 23: 139-154. MILLER, STEPHEN AND FRANK RUSSEK, 'Co-integration and error-correction models: Temporal causality between government taxes and spending,' Southern Economic Journal, July 1990, 57: 221-229. 16
Stockprices and moneydemand: T Choudhry
OSTERWALD-LENUM,MICHAEL,'A note with quantiles of the asymptotic distribution of the maximum likelihood cointegration rank test statistics: Four cases,' Oxford Bulletin of Economics and Statistics, August 1992, 54: 461-472. SAID, SAm AND DAVID DICKEY, 'Testing for unit roots in autoregressive moving average models with unknown order,' Biometrika, December 1984, 71: 599-607. SCHWERT, G. WmLIAM, 'Effects of model specification on tests for unit root in macroeconomics data,' Journal of Monetary Economics, July 1987, 20: 73-103. SCHWERT, G. WILLIAM, 'Tests for unit roots: A Monte Carlo investigation,' Journal of Business and Economics Statistics, April 1989, 7: 147-159.
17
Yournal oflnternational Money and Finance, Vol. 15, No. 1, pp. 1-17, 1996
0261-5606(95)00041-0
Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0261-5606/96 $15.00 + 0.00
Real stock prices and the long-run money demand function: evidence from Canada and the USA TAUFIQ CHOUDHRY*
Department of Economics, Universityof Wales, Swansea SA2 8PP, UK This paper investigates the relationship between stock prices and the long-run money demand function in Canada and the USA during the post WWlI period (1955-1989). The empirical investigation is conducted by means of the Johansen method of cointegration and the error correction modelling strategy. Results show that stock prices play a significantrole in the determination of stationary long-run real M1 and real M2 demand functions in both countries. The direction and magnitude of the role of stock prices depends upon the definition of the money and the country. Error correction results provide evidence of causality between the real money stock and the determinants of the money demand (including real stock prices). (JEL E41, E44).
The research on the money demand function assumes that there exists an underlying stationary long-run equilibrium relationship between real money balances, real income or real wealth, and the opportunity cost of holding real money balances (Friedman, 1956). Stock market prices are usually not associated with the money demand function. 1 According to Friedman (1988) movements in stock prices may have two kinds of effects on money demand, a positive wealth effect and a negative substitution effect. The positive wealth effect may be due to three different reasons. First, an increase in stock prices implies an increase in nominal wealth, producing a positive effect. Second, an increase in stock prices reflects an increase in the expected return from risky assets relative to safe assets. According to Friedman this change in relative valuation does not have to be accompanied by a decrease in risk aversion or an increase in risk preference. Thus, the resulting increase in relative risk may induce economic agents to hold larger amounts of safer assets, such as money, in their portfolio. Third, an increase in stock prices may induce a rise in the * I thank D. N. Manning for numerous helpful comments and suggestionson an earlier draft. I also thank the editor of this journal and two anonymous referees for several valuable comments. All remaining errors and omissions are my responsibility alone.
Stock prices and money demand: T Choudhry
volume of financial transactions. Such an increase in financial transactions will require higher money balance in order to facilitate these transactions. As stated earlier, stock prices also impose a negative substitution effect on money demand. The substitution effect implies that as stock prices rise, equities become more attractive when compared to other components in a portfolio. Thus, there may be a shift from money to stocks. In summary, the net effect of stock market prices on demand for money may be positive or negative. A money demand function that includes stock market prices may be represented as:
(M/P) d =f( y, i, sp). +-? This function states that demand for real money balances (M/P)awhere M is nominal money and P is the price level, is positively related to real income (y), negatively related to the rate of interest (i), and may be positively or negatively related to stock prices (sp). There are three purposes to this paper. First, to determine whether there exists a stationary long-run relationship between money demand and real stock prices in Canada and the USA. Tests are first conducted without the real stock prices in the money demand function. In this manner it can be evaluated if real stock prices truly belong in the money demand function. If real stock prices are found to be a part of the money demand function, the second objective is to determine the size and the direction of the effect of stock prices on demand for money. The third objective is to examine the temporal causality between the real money stock and the determinants of the long-run real money demand. Tests are conducted using both a narrow definition of money (real M1) and a broad defmition of money (real M2). The time period applied ranges from 1955 to 1989 for both countries, except that when using the real M2 for Canada the time period ranges from 1970 to 1989. 2 The Johansen method of cointegration tests is used to test the hypothesis of a stationary long-run money demand function. Results obtained indicate that real stock prices do play a significant role in the money demand function in both Canada and the USA, though the size and the direction of the effect is not identical in each case examined. Error correction models are applied towards the study of the temporal causality between money demand determinants and the real money stock. Results from these models provide evidence of causality between the real money stock and determinants of real money demand in both countries, including real stock prices. In previous studies of the relationship between stock prices and money demand, stock prices are either related to the volume of transactions, or the return on securities is considered as a variable in the money demand function (Hamburger, 1966; Hamburger and Kochin, 1972; Hamburger and Keran, 1987; Keran, 1971). Friedman (1988) provides a study of the direct relationship between stock prices and money demand. Using quarterly data from 1961 to 1986 and annual data from 1886 to 1985, he finds suggestive but non-conclusive results for the USA. Depending upon the time period and the data set, Friedman is able to find both the positive wealth effect and the negative
Stock prices and money demand: T Choudhry
substitution effect. Similar results are obtained by McCornac (1991) using Japanese data from 1975 to 1988. These studies used standard normal regression procedures. However, these procedures are inappropriate if the data are nonstationary; in those cases cointegration constitutes the proper statistical estimation technique. A detailed analysis of the concept of cointegration is provided in Dickey and Rossana (1994). Put simply, two or more nonstationary time series are cointegrated if a linear combination of these variables is stationary. Thus, if the money demand function describes a stationary long-run relationship among real money balances, real income, the opportunity cost of holding money and real stock prices, it can be interpreted to mean that the stochastic trend in real money balances is related to the stochastic trends in real income, the opportunity cost of holding money, and real stock prices. In this paper, the cointegration tests are carried out using the Johansen procedure. This procedure provides more robust results when there are more than two variables (Gonzalo, 1994). Cointegration also implies that the transitory components of the series can be given a dynamic specification by means of the error correction models. In other words, a constrained error correction model that captures the short-run dynamic adjustment of cointegrated variables can be applied. A detailed analysis of the error correction modelling strategy that is based on the information provided by cointegrated variables is provided in Engle and Granger (1987), Miller and Russek (1990) and Miller (1991). In this study, such models are applied to investigate the temporal causality between determinants of the long-run money demand in Canada and the USA, and the real money stock in these countries. Application of error correction models in the short-run dynamic adjustment of the money market is analyzed in Miller (1991). I. The data and the unit root tests
Since cointegration tests require a certain stochastic structure of the time series involved, the first step in the estimation procedure is to determine if the variables are stationary or nonstationary in levels. For our purposes all variables should be nonstationary in levels (i.e. they should contain a unit root). Two different tests, the ADF test (Dickey and Fuller, 1979; Said and Dickey, 1984) and the KPSS test (Kwiatkowski et al., 1992) are conducted to check for the time series properties of data. In the ADF test the null hypothesis is nonstationary (single unit root), while in the KPSS test the null hypothesis is stationary (zero unit root). Fuller (1976) provides the critical values required in the ADF test, while Kwiatkowski et al. (1992) provide the required critical values for the KPSS test. Six variables are tested for unit roots: seasonally unadjusted quarterly series of real M1, real M2, real income, two different types of opportunity cost of holding money (short-term and long-term interest rate), and real stock prices. 4 All variables are transferred to logarithmic form except for the two interest rates. 5 For Canada real money balances are created by dividing the nominal balances by the CPI. Similarly for the United States, nominal balance are
Stockprices and money demand: T Choudhry divided by the G N P deflator to create the real m o n e y balances. R e a l G D P r e p r e s e n t s the real i n c o m e for C a n a d a and for the U S A real G N P r e p r e s e n t s the real income. T h r e e - m o n t h T r e a s u r y bill rates r e p r e s e n t the s h o r t - t e r m interest rate for b o t h countries. Similarly, for b o t h countries rates on the l o n g - t e r m g o v e r n m e n t b o n d s r e p r e s e n t the l o n g - t e r m interest rates. D a t a used are o b t a i n e d f r o m the St Louis F e d e r a l R e s e r v e Bank, the Surrey o f Current Business and the O E C D Main Economic Indicator Historical Statistics. All statistical analyses are c o n d u c t e d using R A T S version 4.10. T a b l e 1 presents the A D F tests and the KPSS tests results using the C a n a d i a n data. B a s e d o n the evidence p r e s e n t e d by Schwert (1987, 1989), up to twelve lags are used in the A D F test. Insignificant lags (standard F-test) w e r e d r o p p e d f r o m the regressions. I f the elimination of lags p r o d u c e d serial correlation, t h e n the lags w e r e a d d e d b a c k on. Following the suggestion by Dickey and P a n t u l a (1987) the unit r o o t tests are first c o n d u c t e d for two roots and, if two roots are rejected, t h e n a single unit r o o t is tested for. W h e n the null hypothesis is two roots the t i m e trend is excluded f r o m the A D F test. Both the constant a n d the time t r e n d are included w h e n the null hypothesis is o n e unit root. In this m a n n e r , the two unit r o o t test allows for an alternative hypothesis o f stationary with a n o n z e r o intercept on the differenced series, while the single unit r o o t test allows for the alternative hypothesis of t r e n d stationary and a n o n z e r o intercept on the series in levels. T r e n d stationary
TABLE 1. Unit root test. Canada. Augmented Dickey-Fuller test Variables
Two unit roots
Real M1 Real M2 Real income Short-term interest rate Long-term interest rate Real stock prices
-
Single unit root
3.09b/(9) 6.88a/(0) 5.12b/(6) 3.54a/(12) 4.96a/(6) 9.43a/(0)
-- 1.77/(12) - 2.24/(9) -- 2.48/(12) - 2.77/(12) - 1.86/(12) - 1.64/(12) KPSS test
Lags Real M1 Real M2 Income Short rate Long rate Stock prices 0 1 2 3 4 5 6
2.70 ~ 1.40 ~ 0.95 a 0.73 ~ 0.58 a 0.49 ~ 0.43 ~
1.76 ~ 0.90 a 0.6P 0.46 a 0.38 a 0.32 a 0.28 ~
1.18 ~ 0.65 a 0.48 ~ 0.37 a 0.30 a 0.25 a 0.22 a
0.54 ~ 0.29 a 0.2P 0.16 b 0.14 c 0.12 c 0.11c
0.75 a 0.40 a 0.28 a 0.22 ~ 0.18 b 0.15 b 0.14 ¢
1.49~ 0.78 a 0.54 a 0.43 ~ 0.36 a 0.31a 0.28 ~
Note: a, b and c imply rejection of the null at 1%, 5% and 10% level respectively. Significant lags in parentheses.
Stock prices and money demand: T Choudhry
implies that the deviation of the series from a linear function of time follows a stationary process. All tests include quarterly seasonal dummies in order to eliminate seasonality. The seasonal dummies enter the relationship exogenously. As Table 1 shows, all variables from Canada are able to reject the null hypothesis of two unit roots but are unable to reject the null hypothesis of a single unit root. Thus, according to A D F tests all variables are stationary after first differencing, but are nonstationary in levels. In other words, all variables contain a single unit root. Table 1 also contains the KPSS tests results using the Canadian data. The KPSS tests are only conducted to check for one unit root. The KPSS tests includes a trend, thus the null is trend stationary. Based on the evidence presented by Kwiatkowski et al. (1992) the maximum number of lags used is six. All six variables are able to reject the null at all lags (0 to 6). Thus, results from the KPSS tests also indicate that the Canadian data are nonstationary in levels. In summary, both unit root tests show that all variables from Canada are nonstationary in levels. 6 Table 2 contains the A D F tests and the KPSS tests using the US data. Both the A D F tests and the KPSS tests are conducted in the same way as above. Results obtained for the USA are similar to the ones found for Canada. From both tests, all the US variables are shown to be nonstationary in levels.
II. Cointegration tests results Cointegration tests in this paper are conducted using the method developed by Johansen (1988), and Johansen and Juselius (1990). The Johansen method applies the maximum likelihood procedure to determine the presence of cointegrating vectors in nonstationary time series. This method detects the number of cointegrating vectors and allows for tests of hypotheses regarding elements of the cointegrating vector. 7 According to Dickey et al. (1991) cointegrating vectors are obtained from the reduced form of a system where all of the variables are assumed to be jointly endogenous. Thus, cointegrating vectors cannot be interpreted as representing structural equations. However, cointegrating vectors may be due to constraints that an economic structure (such as the money demand function) imposes on the long-run relationship among the jointly endogenous variables. Osterwald-Lenum (1992) provides the appropriate critical values required for these cointegration tests. A likelihood ratio test and the Akaike Information Criterion (AIC) is used to select the number of lags required in the cointegration test. 8 As in the unit root tests, lags are not omitted if their exclusion introduces serial correlation. In all cases except one, four lags were indicated for the cointegration tests. Six lags are required in the estimation of the Canadian real M1 demand function that includes the long-term interest rate. Since there seems to be a linear trend in all the nonstationary series, cointegration tests are conducted with the inclusion of a deterministic trend. 9 Seasonality is eliminated by including quarterly seasonal dummies in all regressions. As stated earlier cointegration tests were first conducted without the real
Stock prices and money demand: T Choudhry
TABLE2. Unit root test. USA. Augmented Dickey-Fuller test Variables Real M1 Real M2 Real income Short-term interest rate Long-term interest rate Real stock prices
Two unit roots
Single unit root
- 6.23a/(0) - 11.5l a / ( 0 ) - 8.82a/(0) - 3.88a/(12) - 4.96a/(3) - 4.88~/(9)
- 1.42/(12) - - 1.26/(0) - 1.73/(12) - 2.51/(12) - 1.70/(6) - 0.60/(12)
KPSS test Lags Real M1 Real M2 Income Short Rate Long Rate Stock Prices 0 1 2 3 4 5 6
1.29 ~ 0.65 ~ 0.44 ~ 0.34 a 0.28 ~ 0.24 a 0.21b
0.98 a 0.54 ~ 0.40 ~ 0.33 a 0.28 a 0.25 a 0.23 a
2.02 ~ 1.02 a 0.69 ~ 0.53 a 0.43 a 0.37 ~ 0.32 a
0.64 a 0.34 ~ 0.24 a 0.19 b 0.16 b 0.14 c 0.12 c
0.75 a 0.39 a 0.27 a 0.21b 0.17 b 0.15 b 0.13 c
1.39 ~ 0.74 ~ 0.52 a 0.41a 0.34b 0.30 ~ 0.26 c
See note to Table 1.
stock prices in the d e m a n d function. F o r b o t h C a n a d a and the U S A , real M1 does not cointegrate with real i n c o m e and any o n e of the interest rates. In the case o f real M2, w e a k evidence of cointegration is f o u n d at the 10 p e r c e n t level b e t w e e n C a n a d i a n real M2, real income, and the l o n g - t e r m interest rate. Similarly, at the 10 p e r c e n t level cointegration is indicated b e t w e e n the U S A real M2, real income, and the l o n g - t e r m interest rate. Applying the s h o r t - t e r m rate in the real M 2 function, no stationary relationship is f o u n d for b o t h countries. 1° T h e s e results are not p r e s e n t e d in o r d e r to conserve space, but are available on request. T a b l e s 3 and 4 p r e s e n t results f r o m cointegration tests (trace test and the m a x i m u m eigenvalue test) that include real stock prices along with the traditional variables for C a n a d a and the U S A , respectively. F o r b o t h countries, two different relationships are tested for cointegration for each definition of money. First, cointegration b e t w e e n log of real m o n e y balances (real M1 or real M2), log of real income, log of real stock prices, and the s h o r t - t e r m interest rate is examined. T h e n in the second relationship, the l o n g - t e r m interest rate replaces the s h o r t - t e r m rate in the function. Thus, four different relationships are e x a m i n e d for e a c h country. Results f r o m the C a n a d i a n data are shown in T a b l e 3. B o t h the trace test a n d the m a x i m u m eigenvalue test confirm o n e n o n z e r o vector b e t w e e n real m o n e y balances (real M1 and real M2), real income, real stock prices, and the s h o r t - t e r m interest rate. Thus, t h e r e exists a stationary relationship b e t w e e n
Stock prices and money demand: T Choudhry
real M1 or real M2, real income, the s h o r t - t e r m interest rate, and real stock prices in C a n a d a in the post W W l I period. R e p l a c i n g the s h o r t - t e r m rate with the l o n g - t e r m rate, a stationary long-run d e m a n d function is only f o u n d for real M2. Results do not p r o v i d e a stationary long-run real M1 d e m a n d function which includes l o n g - t e r m interest rate as the o p p o r t u n i t y cost of holding money, and also includes real stock prices. F o r C a n a d a t h r e e out of four relationships are f o u n d to b e cointegrated. Results f r o m the U S d a t a are p r e s e n t e d in T a b l e 4. In the case of the U S A also, t h r e e out four relationships are f o u n d to be stationary. W e fail to find a stationary relationship b e t w e e n real M2, real income, real stock prices and the s h o r t - t e r m interest rate. T w o n o n z e r o vectors are indicated in the real M1 function that includes the l o n g - t e r m interest rate. 11 T h e r e exists a possibility of two stationary relationships b e t w e e n the US real M1, real income, real stock prices, and the l o n g - t e r m interest rate. In s u m m a r y , cointegration results show that in the post W W l I period a stationary long-run real m o n e y (M1 and M2) d e m a n d function in C a n a d a and the U S A requires the inclusion of real stock prices in the relationship along with the s t a n d a r d variables, such as real income and s o m e definition of the o p p o r t u n i t y cost of holding money. W i t h o u t the real stock prices we either fail or we find a w e a k evidence of a stationary m o n e y d e m a n d function in b o t h countries.
TABLE 3. Cointegration test results. Canada. A. Real balances, real income, long-term interest rate and real stock prices Lags in the VAR = 6
Lags in the VAR = 4
Real M1
Real M2
Vectors r r r r
= < < <
0 1 2 3
Trace test
Eigenvalue
52.61b 18.61 8.00 0.50
34.00 b 10.60 7.50 0.50
Vectors r r r r
= < < <
0 1 2 3
Trace test
Eigenvalue
58.17 a 26.00 8.82 0.20
32.18 b 17.18 8.62 0.20
B. Real balance, real income, short-term interest rate and real stock price Lags in the VAR = 4
Lags in the VAR = 4
Real M1 Vectors r r r r
= < < <
0 1 2 3
Real M2
Trace test
Eigenvalue
29.36 14.81 6.03 0.37
14.55 8.78 5.66 0.37
Vectors r r r r
= < < <
0 1 2 3
Trace test
Eigenvalue
55.36 a 26.34 8.60 0.24
29.02 b 17.74 8.36 0.24
Note: a, b and c imply significantly different from zero at 1%, 5% and
10% level respectively.
Stock prices and money demand: T Choudhry
TABLE4. Cointegration test results. USA. A. Real balance, real balance, short-term interest rate and real stock prices Lags in the VAR -- 4
Lags in the VAR = 4
Real M1 Vectors r r r r
= < < <
0 1 2 3
Real M2
Trace test
Eigenvalue
52.94b 20.36 4.44 0.15
32.58b 15.92 4.28 0.15
Vectors r r r r
-- 0 <1 <2 <3
Trace test
Eigenvalue
37.74 18.11 6.22 0.10
19.63 11.90 6.12 0.10
B. Real balance, real income, long-term interest rate and real stock prices Lags in the VAR = 4
Lags in the VAR = 4
Real M1
Real M2
Vectors r r r r
= < < <
0 1 2 3
Trace test
Eigenvalue
53.46b 27.28 4.63 0.20
26.17c 22.65b 4.43 0.20
Vectors r r r r
= < < <
0 1 2 3
Trace test
Eigenvalue
49.26b 22.47 9.53 0.40
26.78c 12.94 9.14 0.40
See note at the end of Table 3.
III. Long-run elasticities T h e estimated cointegrating vectors are given e c o n o m i c meaning by means of normalizing o n the real m o n e y balances. Normalization is only c o n d u c t e d if n o n z e r o vector or vectors are confirmed by the cointegration test. T h e normalized equations are obtained by dividing each cointegrating vector by the negative o f the cointegrating vector o n real m o n e y balances. T h e s e normalized equations are obtained f r o m r e d u c e d forms, and may represent m o n e y demand, m o n e y supply, or some m o r e complicated interaction (Johansen and Juselius, 1990; and Dickey et al., 1991); these normalized equations a p p e a r to be m o n e y d e m a n d functions and they show signs on the variables that are consistent with m o n e y demand. Table 5 presents the implied long-run elasticities obtained f r o m these normalized equations for C a n a d a and the U S A respectively. Using the chi-square test, all variables are tested for significance. In such a test the null hypothesis is that the coefficient on the relevant variable is equal to zero. N o r m a l i z e d equations indicate that out of the six stationary relationships real stock prices have a positive effect (wealth effect) on the d e m a n d for real balances in four of the relationships. In b o t h of the Canadian real M2 d e m a n d functions, real stock prices impose a negative effect (substitution effect). T h e sizes of the coefficient o n stock prices are almost identical, - 0 . 1 9 w h e n the function includes the short-term rate and - 0 . 2 0 when the long-term rate is applied. Real stock prices are significant in all the six relationships. 8
Stock prices and money demand: T Choudhry
T ~ t ~ 5. Long-run elasticities. Canada Variables
Real M1
Real M2
Real income Short-term interest rate Real stock prices
0.45 - 0.03 a 0.30 a
1.22 a - 0.009 - 0.19 b
Real income Long-term interest rate Real stock prices
----
1.32 a -0.012 a - 0.20 ~ USA
Variables
Re~M1
Real M2
Real income Short-term interest rate Real stock prices
0.008 - 0.03 a 0.27 a
--
Real income Long-term interest rate Real stock-prices
0.23 ~ - 0.05 a 0.20 a
1.01a - 0.008 c 0.05 c
-
-
--
Null hypothesis: income elasticity is equal to unity Canada Real M1 0.45/(7.09)* --
Real M2 1.22/(2.23) 1.32/(5.34)*
USA Real M1 0.008/(13.65)* 0.23/(19.42)*
Real M2 1.01/(0.02)
Note: a, b and c imply significantly different from zero at 1%, 5% and 10% respectively. Chi-square statistics in parentheses. * imply rejection of the null at 5% level.
I n s u m m a r y , t h e r e s u l t s s h o w t h a t t h e size a n d t h e d i r e c t i o n o f t h e e f f e c t produced by real stock prices on money demand depends upon the definition o f m o n e y , e s p e c i a l l y in t h e c a s e o f C a n a d a . I n a b s o l u t e v a l u e , r e a l s t o c k p r i c e s h a v e a l a r g e r e f f e c t o n t h e d e m a n d f o r r e a l M 1 t h a n r e a l M 2 b o t h in C a n a d a a n d t h e U S A . O n l y in t h e d e m a n d f u n c t i o n f o r r e a l M 2 in C a n a d a , is t h e r e l a t i o n s h i p b e t w e e n m o n e y d e m a n d a n d r e a l s t o c k p r i c e s i n v e r s e . S i n c e M 2 is more of an investment-oriented definition of money, the negative substitution
Stock prices and money demand: T Choudhry
effect may be justified. 12 An increase in the price of stocks increases the attractiveness of equities as part of the portfolio and this may cause a movement from money holding to equity holding. The effect imposed by real stock prices on real M1 demand is found to be positive in both countries. Since M1 is used as a transaction medium, Friedman's (1988) third reason for a positive effect of real stock prices on real money demand may well be able to justify this particular result. As pointed out by Friedman, increases in stock prices produce a rise in the volume of financial transactions. Demand for money will increase in order to facilitate this higher number of financial transactions. Whenever both the real income and real stock prices are significant in a function, real income elasticity is larger in size (absolute value) than real stock price elasticity. The chi-square test is further used to check if the equilibrium real income elasticity of real money balance is equal to unity (Table 5). In this test the null hypothesis is that the coefficient on real money balance is equal to the coefficient on the real income. If the implied elasticity of real income is equal to unity, this indicates a stationary linear combination between the income velocity of money, and other relevant variables. Once again these tests are only conducted if the cointegration test confirms a nonzero vector or vectors. For Canada, the coefficient on real income is equal to unity in one of the relationships. This result implies that the cointegrating vector indicates a stationary relationship between the Canadian income velocity of M2, the short-term rate of interest, and real stock prices. For the USA also only one of the relationships shows a unit real income elasticity of money demand. A stationary relationship is found between the US income velocity of M2, the long-term rate, and the real stock prices. 13
IV. Causality between money stock and money demand determinants Granger (1986) and Engle and Granger (1987) provide a test of causality which takes into consideration the information provided by the cointegrated properties of variables. Specifically, this test considers the possibility that the past level of a variable (Y) may help explain the current changes in the other variable or variables (X), even though the past changes in Y do not. All this is conditional on the assumption that X and Y are cointegrated and thus share a common trend(s). As long as variables involved are cointegrated, causality has to exist at least in one direction. TM Tables 6 and 7 present results from the error correction estimations for Canada and the USA, respectively. In these tables, the sum of coefficients on the lagged difference is presented in the first line and the chi-square statistics indicating the significance level of the sum of coefficients are shown in parentheses. Significance of the error correction term(s) is presented by means of the t-statistics, thus the data in the parentheses below the error term(s) is the t-ratio. A significant error correction term implies causality from variable Y to variable X. Within an error correction model causality may rise from two sources (Granger, 1988). Short-run dynamics in the model are captured by the 10
Stock prices and money demand: T Choudhry TABLE 6. C a n a d a . Error correction estimations.
Dependent variables A M1 ASR Ay ASP
A M2 ASR Ay ASP
AM2 ALR AY ASP
ECt- 1
EASR
Y"AY
Y~'ASP
~aM1
0.034 a (3.19) 1.07 ~ (2.93) 0.026 a (4.57) - 0.007 ( - 0.31)
- 0.015 a (17.71) -0.16 (1.72) 0.005 b (6.17) - 0.006 (0.59)
1.08 ~ (47.06) 0.75 (0.02) - 0.68 a (70.0) - 0.51 (2.44)
0.017 (0.09) 3.63 c (3.68) 0.057 c (3.82) 0.20 c (3.08)
- 0.84 ~ (26.68) -3.18 (0.33) - 0.29 a (11.39) 0.58 c (2.89)
ECt- 1
F'aSR
EAr
'V-'ASP
Y"aM2
- 0.074 a (-4.00) - 0.86 ( - 0.62) - 0.05 b ( - 2.53) - 0.044 ( - 0.60)
0.006 a (8.08) - 0.29 (2.64) 0.005 b (4.06) - 0.009 (0.96)
- 0.25 a (7.13) - 3.93 (0.31) - 0.9V (75.85) - 0.38 (1.04)
ECt- 1
EALR
-0.08 ( - 1.48) 5.37 a (2.78) - 0.06 ( - 1.11) 0.26 (1.47)
0.001 (0.17) -0.23 (1.76) 0.005 (1.16) 0.05 ~ (9.60)
0.023 (0.31) 4.44 (2.17) 0.13 (0.62) 0.34 b (4.50)
0.048 (0.10) 5.76 (0.27) - 0.04 (0.06) - 0.45 (0.59)
EAy
EASP
~'~'aM2
-0.23 c (2.94) -0.50 (0.01) 0.89 a (45.0) 0.08 (0.03)
0.04 (0.39) 0.10 (0.003) 0.15 b (5.64) 0.056 (0.08)
0.32 b (4.02) 2.84 (0.25) 0.14 (0.72) - 0.12 (0.05)
Notes: a, b a n d c imply significantly different from zero at 1%, 5 % a n d 10%, respectively. Numbers in parentheses present chi-square statistics. N u m b e r s in parentheses under the E C term represent t-statistics. Variables: E C = Error correction term, S R = Short-term rate, L R = Longt e r m rate, Y = R e a l i n c o m e a n d SP = R e a l stock prices.
lagged differences, and conventional tests of causality may be based on the significance of these terms. The error correction term represents the potential effects of departures from the long-run equilibria. The size and the significance of the error correction term in each equation show the tendency of each variable to restore equilibrium in the money market. In this paper, the main interest is the adjustment of the money market to a long-run equilibrium due to changes in the real stock prices. The lag structure in the error correction 11
Stock prices and money demand: T Chondhry TABLE 7. U S A : Error correction estimations. Dependent variable
6M1 ASR Ay ASP
ECt- 1 -0.05 a (-3.12) - 0.62 ( - 0.36) - 0.08 a (-4.51) 0.068 (0.55) EClt- 1
AM1 ALR AY ASP
A LR Ay ASP
EAy
-0.004 a -0.06 (10.39) (0.26) - 0.08 27.31b (0.23) (4.89) 0.002 0.027 (1.14) (0.044) -0.019 -0.37 (2.64) (0.17) EC2t- 1
)'~'ALR
EASP
EAM1
0.016 (1.24) 1.79 (1.23) 0.027 (2.46) 0.21 ¢ (3.29)
0.5P (38.60) - 7.97 (0.77) 0.009 (0.088) 0.96 (2.13)
~,'ty
EASP
0.003 b - 0.05' - 0.016' 0.073 (2.60) ( - 3 . 0 2 ) (38.66) (0.48) -0.13 b - 1.44 0.438 a - 5 . 5 8 (-2.57) (-1.57) (9.30) (0.97) - 0.002 - 0.038 ¢ 0.0004 0.15 ( - 1.50) ( - 1.96) (0.019) (1.66) 0.004 0.029 b - 0.07 a 0.046 (0.06) (2.33) (11.74) (0.004) ECt- 1
A M2
EASR
- 0.28 a ( - 2.94) - 2.20 ( - 1.10) 0.14 a (3.51) 0.32 (1.22)
Y"ALR
~"~Ay
- 0.02" 0.16 (12.65) (0.37) 0.22 c 1.82 (2.74) (0.11) 0.00 0.18 (0.0002) (2.60) -0.06 a -0.34 (10.03) (0.21)
EAM1
- 0.002 0.33" (0.01) (12.60) 1.43 2.24 (2.66) (0.22) 0.035 e 0.17 ¢ (3.47) (3.74) 0.20 ¢ 0.30 (2.73) (0.208)
~ASP
Y~'8M2
0.07V (2.81) 1.30 (2.20) 0.05 a (7.20) 0.18 (2.49)
0.34 (1.61) 0.26 (0.002) 0.09 (0.68) 0.57 (0.602)
S e e note at the end o f Table 6.
model is determined by means of the Akaike's FPE criteria. For each of the models a possible combination of one to eight lags are examined and the lag structure that minimizes the FPE is chosen. The majority of the models required the use of four to six lags. Interpretation of the error correction estimation depends upon whether real money stock is exogenous or endogenous. If the real stock of money is endogenous, then the error correction equation represents the endogenous response of real money growth rate to adjustment in the economy. Results presented in this section show that both the real M1 stock and the real M2 stock are endogenous in both countries. Positive signs are expected on the error correction term in the real income equation, while negative signs are expected on the error term in the real money and the interest rate equations. The error term in the real stock prices 12
Stock prices and money demand: T Choudhry
equation may be negative or positive. These signs are expected because excess supply of money will result in an increase of real income and a decrease in the interest rate, and if the purpose of the monetary policy is stabilization, then the growth rate of money stock should decrease. For Canada (Table 6) the error correction term is significant in two of the money equations, two of the interest rate equations, two of the real income equations, and none of the real stock prices equations. In one of the relationships, real stock prices are econometrically exogenous. In this particular stock price equation only the lagged changes in dependent variable (real stock prices) provide explanatory power. In general, the results suggest feedback effects between the real money stock, both definitions of the interest rate, real income and real stock prices. On causality between the real money stock and real stock prices, only a unidirectional effect is found from real M1 to stock prices. In most of the equations the signs on the error correction terms are not the expected signs. For the USA (Table 7) the error correction term(s) are significant in all three money equations. 15 The error correction term is also significant in all three real income equations and in only one out of the interest rate equation and the stock price equation. For the USA there also is evidence of feedback effects between real money supply, interest rates, real income and real stock prices. There is some evidence of a unidirectional causality from real stock prices to real money stock. Real stock prices are exogenous when the real M1 function includes the short-term interest rate. Similarly, the long-term rate is exogenous in the real M2 demand function. Except for two of the real income equations, the signs on the error correction terms are as expected. For both Canada and the USA results from error correction estimations indicate that both the goods and the financial markets may have adjusted to the disequilibrium in the money market. The error correction term is generally significant in both the real income and the interest rate (short- and long-term) equations. Generally, the error term is not found to be significant in the stock price equations. 16
Conclusion This paper provides a study of the relationship between the long-run money demand function and stock market prices in Canada and the USA for the post WWII period (1955-89). For both countries two different definitions of money are used in the study, a narrow defmition (real M1) and a broad definition (real M2). The Johansen procedure of cointegration is used to test the hypothesis of a stationary relationship between real money balances, real income, the opportunity cost of holding money (the short- or long-term interest rate) and real stock prices. Normalized equations and chi-square tests are used to determine the significance, the size and the direction of the effects produced by each variable on money demand. Results obtained indicate that real stock prices do play a significant role in the money demand function both in Canada and the USA, though the size and the direction of the effect is not identical in every relationship. Without the real stock prices, we either fall, or we find only weak evidence of a stationary money demand function. In absolute value, stock 13
Stock prices and money demand: T Choudhry
prices have a larger effect on the demand for real M1 both in the case of Canada and of the USA. Only in the Canadian demand for real M2 do stock prices produce a negative effect. Whenever real income and real stock prices are significant in the relationship, the real income elasticity is larger in size (absolute value) than the real stock price elasticity. Thus, the results overall suggest that the real money demand function in Canada and the USA in the post WWII period requires the inclusion of real stock prices in the relationship. Error correction models are applied to investigate the temporal causality between the real money stock and real money demand determinants (including real stock prices). These results show that evidence exists of feedback between the real money stock, real income, the interest rate (short- or long-term), and real stock prices in both countries. Notes 1. According to Friedman (1988) direct studies of the relationship between stock prices and money demand function are not very common. Indirectly stock prices are included in the total nonhuman wealth, which plays a role in money demand function. 2. Lack of M2 data before 1970 made it impossible to use a longer period. 3. As stated earlier, for Canada real M2 data is only available from 1970. All test involving real M2 of Canada are confined to the period 1970-89. All Canadian variables are also tested for unit roots for the period 1970-89. These results are not presented here, but are available on request. 4. Analyses of the difference between and construction of seasonally adjusted and unadjusted data are provided in Ghysels and Perron (1993) and Ericsson et al. (1994). Ghysels and Perron (1993) show how linear seasonal adjustment filters, such as US Census X-11 and Statistics Canada X-11 A R I M A methods, which apply a set of moving averages' are used to convert unadjusted (raw) data to seasonally adjusted data. In general, it may be preferable to use seasonally unadjusted data. Ghysels (1990) claims that seasonal-adjustment filters have at least three adverse effects on the power of the unit root test. First, the power of unit root tests may be reduced due to the smoothing effects fo the filters. Second, the long leads and lags used in the filters may produce distant autocorrelation in the adjusted series. The third and final problem is induced by the nonlinear properties of seasonal-adjustment filters. Ghysels and Perron (1993) also provide analyses of the adverse effects of seasonal-adjustment filters on the power of the unit root tests. 5. Application of interest rates rather than their logarithms assumes that the absolute rather than the percentage change in interest rates is what matters for money demand. Friedman and Schwartz (1982) describe the advantages of using the interest rate in absolute values rather than in logarithms in the estimation of money demand functions. 6. When Canadian variables are tested for unit roots for the period 1970-89, similar results are obtained. Thus all Canadian variables are also nonstationary in levels during 1970-89 period. These results are not provided but are available on request. 7. More detailed analysis of the Johansen procedure is provided in Dickey et al. (1991). 8. Starting with a maximum length of 12 lags, lags were eliminated if they were insignificant (as a group of 4) at the 10 percent level. 9. We tested the hypothesis that the linear trend is absent as suggested by Johansen and Juselius (1990, p. 192). The result indicates that the null hypothesis is rejected at the 1 percent level. This result is available on request. 14
Stock prices and money demon&"T Choudluy 10. Haler and Jansen (1991) and Miller (1991) fail to find a stationary long-run real M1 demand function for the USA in the post WWII period. Both studies provide weak support for a stationary long-run real M2 demand function for the USA in the stated period. Both studies only use the standard variables in the demand function and apply the cointegration technique in their empirical estimation. Our results from the US data are similar though not identical to the findings of the studies just described. The difference arises mainly because those studies apply seasonally adjusted data while our paper uses seasonally unadjusted data. Also, the time periods in all three papers are similar but not identical. To our knowledge, no such study has been conducted for Canada in the post WWII period. 11. According to Dickey et aL (1991) and Johansen and Juselius (1990) the larger the number of nonzero vectors, the more stable is the system. More than one nonzero vector implies that the economic systems are stationary in more than one direction. 12. Using the US real M2, only one relationship was found to be stationary. Even though the coefficient on stock prices is positive, it is small (0.05) in size and significant only at the 10 percent level. Real income seems to dominate this particular relationship. 13. Cointegration tests were also conducted to confirm these results involving the income velocity of money. These tests indicate a stationary long-run relationship between the income velocity of M2, the short-term interest rate, and real stock prices in Canada. A similar result was found for the USA using the income velocity of M1, the long-term rate, and real stock prices. Normalized equation have the proper sign on the variables and chi-square tests confirm the significance. Unti root tests (ADF) were also conducted to check for the stochastic structure of M2 income velocity in Canada and the USA in the post WWII period. Both series were found to be nonstationary in levels. This result implies that M2 and income are not cointegrated by themselves in Canada and the USA in the post WWII period. These results are available on request. 14. Miller and Russek (1990) and Miller (1991) describe in detail the application of cointegration-oriented causality tests. 15. Two nonzero cointegrating vectors are found in the real M1 demand function that includes the long-term interest rate. The error correction equation in this case includes two error correction terms. 16. The standard Granger causality test with the VAR model (without the cointegration constraint was conducted for the two relationships where we failed to find cointegration. Results from these tests also imply feed back between the real money stock and the money demand determinants, including the real stock prices. These results are available on request.
References
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