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Money supply growth, stock returns and the direction of causality
Socio-Econ. P/am. Sci. Vol. 21, No. 5, pp. 321-325, Printed in Great Britain. All rights reserved
1987 Copyright 0
0038-0121/87 $3.00 + 0.00 1987 Pergamon Journals Ltd
MONEY SUPPLY GROWTH, STOCK RETURNS AND THE DIRECTION OF CAUSALITY JONATHAN ‘Department ‘Bureau
of Economics of Economic
D. JONES’
and NOEL
URI’
and Business, Catholic University of America, Washington, DC 20064 and Analysis, Federal Trade Commission, Washington, DC 20580, U.S.A.
(Received
Abstract-This paper employs the Granger returns and growth in the money supply The test results support the notion that the information with regard to the money supply are not able to develop profitable trading Moreover, the results here suggest that the
3 September
1986)
direct test to assess the causal relationship between stock in the U.S. over the period May 1976December 1983. stock market is efficient in the sense that current and past is fully reflected in current security prices. Hence, investors rules with information on changes in the money supply. stock market in fact anticipates future monetary growth.
examine again the lead-lag nature of the relationship between money and stock returns for the postwar U.S. This paper extends previous empirical work in several ways. First, the sample period used for analysis, May 1974 to December 1983, includes observations which are more recent than previously used (the most recent study-that by Davidson and Froyen-used data only through 1977). The middle and latter 1970s and early 1980s witnessed a relatively rapid rise in the money supply over part of the period, a recession over part of the period, and a relatively high rate of inflation over part of the period. It will be of interest to note what the empirical results reveal concerning the causal nature of the relationship between the money supply and stock returns when this period is included. Second, attention is paid in this paper to the robustness of the empirical results across the various monetary aggregates used. Kraft and Kraft [7], for example, make the claim that causal inferences are not sensitive to the choice of monetary measures used in analysis. As we will see, this cannot be substantiated. The remainder of this paper is organized as follows. Section 2 provides a brief review of the recent literature dealing with money and stock prices in the postwar U.S. Section 3 discusses the Granger direct test procedure. In addition, comments are made concerning various details involved in the implementation of the test. Section 4 presents the empirical results of the test. Finally, Section 5 offers a summary and conclusion.
I. INTRODUCTION
Much has been written about the relationship between the money supply and stock returns for the postwar U.S. during the past two decades [l, 21. The empirical work has concentrated to a large extent on the timing of the relationship between various money supply measures and aggregate stock returns. There are essentially two categories in which this literature falls. On-the-one-hand, there are those studies which show a significant relationship between various measures of stock returns and various measures of lagged monetary policy (measured as changes in the money supply). For example, studies by Sprinkel [3], Hamburger and Kochin [4], and Keran [5] indicate a lag in the adjustment of stock returns to changes in money growth rates. On-the-other-hand, there are those studies which reject this lagged effect and lend support to the claim that the stock market is efficient with respect to various monetary aggregates. Studies by Rozeff [l], Cooper [6], Kraft and Kraft [7,8], Rogalski and Vinso [9], Tanner and Trapani [lo], and Davidson and Froyen [2] fail to find a significant relationship between stock returns and past money movements. Some of these studies, however, show a significant relationship between current stock returns and changes in future money growth rates which is characteristic of a stock market with a forward-looking propensity (a stock market that manifests a forwardlooking propensity is one in which the current stock return incorporates the market’s expectation of future money movements). Given the disparity in these two views of the relationship between stock returns and changes in the supply of money, the purpose of this paper is to
2. REVIEW
OF THE
LITERATURE
There are essentially two competing hypotheses with regard to the nature of the relationship between stock returns and changes in the money supply. One hypothesis, nominally referred to as the monetary portfolio (MP) hypothesis suggests that, in equilibrium, an investor holds a number of assets including money in his or her portfolio. A monetary
The views expressed are those of the authors and do not necessarily represent the policies of the organizations with which they are affiliated. 321
322
JONATHAN D. JONES and NOEL URI
disequilibrium such as an unexpected (or abnormal) increase or decrease in the rate of growth of the money supply causes a disequilibrium in asset portfolios by making actual money balances depart from desired money balances. The attempt by investors as a group to attain their desired money position then transmits the monetary changes to markets at large. Investors respond to the wealth effect of increased money supply growth by exchanging money for a variety of assets in asset markets such as short and long term bonds, stocks, real estate, durable goods, capital goods and human capital. The time response of investors is viewed in this hypothesis that asset prices respond to the monetary disturbance with lags typically characterized as long, variable, and positive on average.? The hypothesis which has been suggested as an alternative to the MP hypothesis is the efficient market (EM) hypothesis. This hypothesis suggests that the lag (if any) between changes in the money supply and adjustments in the stock returns cannot, on average, be positive and cannot allow for the formulation of trading rules which will enable an investor to earn excess profits. Competition among profit-maximizing investors in an efficient market will insure that current and past information is fully reflected in current security prices so that investors will not be able to develop profitable trading rules with the information. The time sequence of prices conditioned on current and past information will consist of competitively determined equilibrium prices which fully reflect available information and leave investors able to earn only normal rates of return, on average. Monetary policy will not have a systematic lagged effect of any economic importance in an efficient market. Consistent with this efficient market hypothesis is that stock returns will accurately and adequately anticipate future monetary growth. The MP hypothesis was the first (in a temporal sense) one posited [1 l-131. Sprinkel [3] provided the first effort to empirically verify the hypothesis. Using data covering the period 1918 to 1960, he graphically related the money supply level to the level of stock prices. His subjective (i.e. eyeball) analysis lead him to conclude that changes in stock prices lagged tin addition
it is argued that increased money supply growth increases prices of durable goods relative to non-durable goods and makes the latter relatively more desirable. $The Granger direct test was chosen for use here because its statistical performance has been shown to be very good in finite sample Monte Carlo studies dealing with tests of predictive relationships between time series variables [see Nelson and Schwert (1982)]. Also, degrees of freedom are maximized with its use, since it is a one-sided distributed lag causality test and not a two-sided distributed lag test such as the Sims test procedure [20]. #Formally, one covariance stationary time series {a,}, is said to cause another covariance stationary time series {b,} if knowledge of {a,}, for t < 0, results in a smaller error variance in predicting {b,} than would result from a prediction based solely on an autoregressive model. A covariance stationary time series is one for which the following conditions hold: E(q) = @a, + ,) = p and E [(q-p) (a,,, -p)] = y, where p denotes a constant mean, y denotes the autocovariance function and r denotes a discrete time period.
behind changes in the rate of growth in the money supply. Palmer [14] updated Sprinkel’s graphical analysis using 1960 to 1969 data and reached an analogous conclusion to Sprinkel. Subsequent to this, Reilly and Lewis [15], Keran [5], Homa and Jaffee [16] and Hamburger and Kochin [4] used simple regression techniques (including the Almon polynomial distributed lag approach) to conclude that stock prices depend upon both the level of the money supply and the rate of growth of the money supply. The EM hypothesis was first put forward by Fama [17]. Subsequently, Rozeff [I], using data sets covering the period 1916 to 1972 finds empirical evidence to conclude that for the static market, the lag in the effect of monetary policy on stock prices is essentially zero. He suggests that stock prices immediately reflect changes in monetary policy and that, moreover, the stock market actually anticipates future monetary growth. Subsequent to this, Kraft and Kraft [7,8], using seasonally adjusted monthly data and seasonally adjusted quarterly data find that changes in the Standard and Poor Price Index does affect the narrowly defined money supply (i.e. Ml), although the extent of this effect is not detailed. Rogalski and Vinso [9], using four different stock price measures that are seasonally unadjusted, monthly, and measured as percentage changes over the period 1963 to 1974 and the narrow definition of money found, in the aggregate, that percentage changes in stock prices impact the money supply and hence conclude that there is in fact a forward-looking propensity and that the stock market is efficient. Most recently, Davidson and Froyen [2] investigated the lead-lag nature of the relationship between stock returns and the money supply using the New York Stock Exchange Index and narrow definition of the money supply (i.e. Ml) and the monetary base (i.e. MB) on both a weekly and monthly basis. Their results supported the efficient market hypothesis. The conclusion, then, is that the majority of the more recent studies tend to support the efficient market hypothesis. One must still be concerned, however, whether their support is an artifact of the data used, or of the empirical techniques employed, or a combination of both. In what follows, we propose to examine the issue more carefully by employing a test for causality (attributed to Granger 1969) and using several different data series.$ The test is very general and imposes no a priori restrictions in endeavoring to determine whether a statistically identifiable relationship exists between stock returns and changes in the money supply. Before proceeding with its implementation, it is useful to briefly review the methodology. 3. METHODOLOGY
Causality in the present context is defined in terms of predictability. Specifically, one series is said to cause another series if knowledge of this first series results in a smaller error variance in predicting the second series than would result from a prediction based solely on past observations on the second series.0 Based on a Monte Carlo study of eight alternative tests for directional causality, Geweke et al. [19]
Money supply growth recommended the use of the regression-F Granger direct test. In the Granger direct test, prefiltering procedures based on either time domain or frequency domain methods to correct for serial correlation are obviated by including lagged values of the dependent variable on the right-hand side of the equations estimated. The incorporation of lagged values of the dependent variable in the list of regressors corrects for autocorrelation that would otherwise be captured by the regression residuals (as is well-known, serial correlation results in biased standard errors which makes valid inference in the least squares model highly unlikely). Now, let Z$! denote the_ return on the jth stock measure in period t, and M,, denote the percentage change in the. ith money supply variable in period t. Then (R,,, M,,) represents a linearly non-deterministic, possibly non-stationary bivariate time series vector for the pairwise relationships between stock returns and the growth in the money supply. In order to assess the causal relationship(s) between stock returns and changes in the growth rate of the money supply, the use of the Granger test entails classical least squares estimation of the following pairs of restricted and unrestricted equations:
(1)
k=l
NI
Rj,t=
N2
1 a;&-,+
k=,
c bkMi,,_k-i-U: k=l
(2)
NI
Mt.,=
c
k=l
e&f,,-k+v,
Ml.!=
1 k=l
(3)
I
NI e;Mi,,-ki-
F k-1
dkRj,j.r_k+V;
(4)
where ak, a;, bk, ck, CL and dk are coefficients to be estimated, u,, u;, v,, vi are identically and independently distributed random error terms, and N, and N2 are the lengths of the lags (appropriately determined) used in the estimation process. Equations (1) and (2) represent the equations to be estimated in testing the null hypothesis of a lack of causality running from money to stock prices, while the absence of causality from stock prices to money is tested using eqns (3) and (4). With Granger causality, under the null hypothesis of no causal relationship running from &Zi,,to R,,, the tBoth stock price series include dividends. For a discussion of the use of the percentage change in the stock price index as a measure of the stock return, see Froyen and Davidson (1982). .$In order to determine whether the DJIA and NYSE price indices were non-autocorrelated, autocorrelation functions were analyzed for both stock prices, expressed as percentage changes, so as to determine the autocorrelation properties of each. There was some indication of the presence of autocorrelation in each stock price series. For the DJIA price index, a significant spike in the autocorrelation function appeared at lag 1, and a large though insignificant spike appeared at lag 7. For the NYSE price index, significant spikes appeared at lags I and 7, and a large though insignificant spike appeared at lag 6. The use of 12 lags of each price index was deemed adequate to pick up the non-seasonal autocorrelation in the two stock prices for those equations in which the stock prices were the dependent variables.
323
coefficients on the lagged values (which correspond to positive lags) of ti,,, (i.e. bk,for k = 1, . . . , Nt) should not be significantly different from zero as a group. Similarly, under the null. hypothesis of no causal relationship from Rj,! to M,,, the coefficients on the lagged values of R,:, (I.e. dk for k = 1, . . . , NZ) should not be jointly signrficantly different from zero. The data used in the estimation are for two stock price indices (representing stock returns) and three measures of the money supply. The stock price indices include the Dow Jones Industrial Average (DJIA) and the New York Stock Exchange Composite Index (NYSE).t To translate these indices into nominal equity returns, percentage changes were computed. The three money supply growth rates are given by the unweighted first difference of the natural logarithms in successive time periods. The three money measures include the nominal money supply narrowly defined (Ml), the sum of Ml and time deposits (M2), and the monetary base (MB). All five series are measured monthly and are seasonally unadjusted. The data cover the period May 1974 through December 1983. All of the data were obtained from the Federal Reserve Board. In order to empirically implement the test, any deterministic elements in the data must be removed. To do so, the stock return and money growth series were first regressed on a constant, linear time trend, and seasonal dummies. The residuals from these regressions are the data used in estimating the equations for the Granger test. Moreover, the data used in carrying out the Granger test used here were not prefiltered as a means of correcting for serial correlation. Recent Monte Carlo findings have shown that prefiltering as a means of correcting for serial correlation should be avoided in implementing the test. Tests which require prefiltering to correct for serial correlation in general behave unfavorably under the null hypothesis of a lack of one-way causality [19]. Of particular interest to the problem at hand is the finding that regression-F causality tests that require prefiltering as a serial correlation correction yield statistics that are too large and reject the null hypothesis too often. In the implementation of the test, the value of N, was set at 12 in order to capture any non-seasonality that might be present in the data series. To set N, at a smaller value would introduce the possibility that any non-seasonality in the dependent variable would be captured in the regression residua1s.t Next, the truncation of the lag polynomial associated with the independent variable (denoted by N2) was set at 6. Kraft and Kraft [7] suggest that this is appropriate when using monthly data. In addition, it has been suggested that the number of lags associated with the independent variable should be kept smaller than the number of lags associated with the dependent variable in the equations estimated so as to retain power of the causality test [18]. Finally, seasonally unadjusted data were used in this paper to avoid smoothing problems inherent in purging seasonality from raw data (Wallis, 1974). Wallis has shown that the various procedures used by federal government agencies to remove the seasonal component can result in distortion of the information content of the data, making valid causal inferences somewhat difficult.
324
JONATHAN Table
1. Empirical
Regressiont R, on MI on RNY on Ml on Ro, on M2 on RNY on M2 on Ro, on MB on R,.,, on MB on
results of Granger
F-Statistic
Ml Rp, Ml RNY M2 Ro, M2 RNY MB Ro, MB R,,
D. JONESand NOEL URI
direct test
Significance
1.85 2.46 1.29 2.38 1.72 1.60 1.70 1.69 0.77 3.24 0.59 3.50
level$
NS 5% NS 5% NS NS NS NS NS 1% NS 1%
tTbe dependent variable is listed first and the independent variable is listed second. $The critical values for the F6,8O distribution are 2.21 and 3.04 at the 5 and 1% significant levels, respectively. Note: NS denotes not significant.
4.
EMPIRICAL RESULTS
The empirical results of the Granger direct test for the sample period May 1974 to December 1983 are presented in Table 1. The growth rates of Ml, M2, and MB are denoted Ml, M2, and MB respectively. While Rn, and R,, denote the stock returns computed (as described above) for the Dow Jones Industrial Average and the New York Stock Exchange Composite Index, respectively. Inspection of the partial F-statistics (as reported in Table 1) for the
Granger direct test reveals the absence of causality running from each of the three money growth rates to each of the two stock returns. The results also show that both stock return measures cause (in the sense being used here) &I1 and h;lB at the 5 and 1% significance levels, respectively. Neither of the stock return measures is found to have explanatory power for M2. This is particularly interesting because it implies that by judicious choice of the measure of stock returns and the measure of the money supply can yield support for either the acceptance of the efficient market hypothesis (if either Ml or MB are selected as the money supply measure) or the rejection of the hypothesis (if M2 is selected as the money supply measure). In any case, the monetary portfolio hypothesis is unequivocally rejected. These results while consistent with some of the previously referenced studies lending support to the efficient market hypothesis are at odds with the Kraft and Kraft [7,8] papers where it is suggested that the tRozeff [l] describes a stock market with a forward-looking propensity as one which is characterized by reverse causality with correct expectations. IThe presence of serial correlation, either positive or negative, results in a bias in the standard error of the regression, making valid inference virtually impossible. For positive serial correlation, the bias is downward, while for negative serial correlation, the bias can be upward or downward. In general, when serial correlation is a problem in regressions using time series data, residuals usually display positive serial correlation which results in inflated test statistics. It would appear then that the explanatory power of the independent variables in those equations for which serial correlation seems to be a problem is probably overstated. However, there is no way to be certain since the Q-statistic does not provide information as to whether positive or negative serial correlation exists.
detection of the presence or absence of a lead-lag relationship is insensitive to the choice of the money supply measure employed (they both use Ml and M2). The difference in results lies in the suggestion here that stock returns do not have an impact on the money supply measured as M2, while Kraft and Kraft argue otherwise. One can only suppose. that the use of more current data in the current investigation (Kraft and Kraft use data only through 1974) then lead to the anomalous results. Given that the results show the existence of causality running from both the DJIA and the NYSE indices to change in Ml and MB, support is given to the notion that the stock market displayed a forwardlooking propensity with respect to future movements of these two monetary aggregates, at least for the period May 1974 to December 1983 (as noted earlier, a stock market that manifests a forward-looking propensity with respect to monetary changes is one in which the current stock return incorporates the market’s expectation of future money movements).? One should be cautious in interpreting these forgoing results if it turns out that autocorrelation is present in the residuals in the estimated equations. To examine the issue, the Box-Pierce Q-statistics were computed. They are reported in Table 2.$ None of the residuals from the 24 equations are autocorrelated when examined at the 99% level of confidence. Consequently, the F-statistic used in the Granger direct test can be interpreted without fear of misinterpretation. There is an identifiable relationship running from stock returns to the money supply lending credence to the efficient market hypothesis. Table 2. Box-Pierce
Q-statistics
(Granger
R,
on &il
Ml on R, R,,
on Ml
Ml on R,, R,
on M2
M2 on R,, R,, ti2
on M2 on R,,
R,, on MB MB on R, R,,
on MB
MB on R,, tThe Box-Pierce given by:
direct test)t Q-statistic1
Regression Restricted Unrestricted Restricted Unrestricted Restricted Unrestricted Restricted Unrestricted Restricted Unrestricted Restricted Unrestricted Restricted Unrestricted Restricted Unrestricted Restricted Unrestricted Restricted Unrestricted Restricted Unrestricted Restricted Unrestricted Q-statistic
follows a chi-square
42.6 (35) 41.8(29) 37.4 (35) 42.5 (29) 42.9 (35) 37.0 (29) 37.4 (35) 40.5 (29) 42.6 (35) 44.2 (29) 44.9 (35) 48.4 (29) 42.9 (35) 42.4 (29) 44.9 (35) 46.7 (29) 42.6 (35) 35.6 (29) 41.0 (35) 40.5 (29) 42.9 (35) 42.9 (29) 41.0 (35) 44.3 (29) distribution
and is
Q=+;-& I-1 where T is the number of observations on the time series, K denotes the number of autocorrelations considered, Pj represents the squared sample autocorrelation at lag j, and I* denotes the chi-square distribution with K degrees of freedom. IThe critical values for the x2 distribution with 29 and 35 degrees of freedom at the 99% confidence level are 49.6 and 57.2, respectively. Degrees of freedom for the Q-statistics are in parentheses.
Money supply growth 5. CONCLUSION This paper has used the Granger direct test to assess the causal relationship between stock returns and the growth in the money supply over the period May 1974 through December 1983. The results support the notion that the stock market is efficient in the
sense that current and past information with regard to the money supply is fully reflected in current security prices. Hence investors are not able to develop profitable trading rules with information on changes in the money supply. Moreover, the results here suggest that the stock market defacto anticipates future monetary growth.
REFERENCES 1. M. Rozeff, Money and stock prices: market efficiency and the lag in effect of monetary policy. J Financial Econ. 245-302 (1974). 2. L. S. Davidson and R. T. Froyen, Monetary policy and stock returns: are some markets efficient? Fed. Res. Bank SI Louis 3-12 (March 1982). 3. B. Sprinkel, Money and Stock Prices. Irwin, 111.(1964). 4. M. Hamburger and L. Kochin, Money and stock prices: the channels of influence. J. Finance 231-249 (1972). 5. M. Keran, Expectations, Money and the Stock Market. Fed. Res. Bank St Louis 1631 (1971). 6. R. V. L. Cooper, Efficient capital markets and the quantity theory of money. J. Finance 887-908 (1974).
325
I. J. Kraft and A. Kraft, Determinants of common stock prices: a time series analysis. J. Finance 417425 (1977a). 8. J. Kraft and A. Kraft, Common stock prices: some observations. Southern Econ. J. 136>1367 (1977b). 9. R. Rogalski and J. Vinso, Stock returns, money supply, and the direction of causality. J Finance 887-904 (1977). 10. J. E. Tanner and J. Trapani, Can the quantity theory be used to predict stock prices--or is the stock market efficient? Southern Econ. J. 261-270 (1977). ll. K. Brunner, Some major problems in monetary theory. Am. Econ. Rev. 47-56 (1961). 12. M. Friedman, The lag in the effect of monetary policy. J. Pal. Econ. 447466 (1961). 13. P. Cagan, The Channels of Monetary Efects on Interest Rates. Columbia Univ. Press, New York (1972). 14. M. Palmer, Money supply, portfolio adjustments, and stock prices. Financial Analysts J. 19-22 (1970). 15. F. K. -Reilly and J. E. Lewis, Monetary Variables and Stock Prices, Working Paper #38, Carnegie-Mellon University (1971). 16. K. Homa and D. Jaffee, The supply of money and common stock orices. J. Finance 10561066 (1971). 17. E. F. Fama, Efficient capital markets: a reviewbf th&y and empirical work. J. Finance 383417 (1970). 18. J. Geweke, Testing the exogeneity specification in the complete dynamic simultaneous _equation model. J. Econometrics 7. 163-185 (1978). 19. J. Geweke, R. Meese and w. dent, Comparing alternative tests of causality in temporal systems: analytic results and experimental evidence. J. Econometrics 21, 161-194 (1983). 20. C. Sims, Money, income and causality. Am. Econ. Rev. 62, 5&552 (1972).
1987 Copyright 0
0038-0121/87 $3.00 + 0.00 1987 Pergamon Journals Ltd
MONEY SUPPLY GROWTH, STOCK RETURNS AND THE DIRECTION OF CAUSALITY JONATHAN ‘Department ‘Bureau
of Economics of Economic
D. JONES’
and NOEL
URI’
and Business, Catholic University of America, Washington, DC 20064 and Analysis, Federal Trade Commission, Washington, DC 20580, U.S.A.
(Received
Abstract-This paper employs the Granger returns and growth in the money supply The test results support the notion that the information with regard to the money supply are not able to develop profitable trading Moreover, the results here suggest that the
3 September
1986)
direct test to assess the causal relationship between stock in the U.S. over the period May 1976December 1983. stock market is efficient in the sense that current and past is fully reflected in current security prices. Hence, investors rules with information on changes in the money supply. stock market in fact anticipates future monetary growth.
examine again the lead-lag nature of the relationship between money and stock returns for the postwar U.S. This paper extends previous empirical work in several ways. First, the sample period used for analysis, May 1974 to December 1983, includes observations which are more recent than previously used (the most recent study-that by Davidson and Froyen-used data only through 1977). The middle and latter 1970s and early 1980s witnessed a relatively rapid rise in the money supply over part of the period, a recession over part of the period, and a relatively high rate of inflation over part of the period. It will be of interest to note what the empirical results reveal concerning the causal nature of the relationship between the money supply and stock returns when this period is included. Second, attention is paid in this paper to the robustness of the empirical results across the various monetary aggregates used. Kraft and Kraft [7], for example, make the claim that causal inferences are not sensitive to the choice of monetary measures used in analysis. As we will see, this cannot be substantiated. The remainder of this paper is organized as follows. Section 2 provides a brief review of the recent literature dealing with money and stock prices in the postwar U.S. Section 3 discusses the Granger direct test procedure. In addition, comments are made concerning various details involved in the implementation of the test. Section 4 presents the empirical results of the test. Finally, Section 5 offers a summary and conclusion.
I. INTRODUCTION
Much has been written about the relationship between the money supply and stock returns for the postwar U.S. during the past two decades [l, 21. The empirical work has concentrated to a large extent on the timing of the relationship between various money supply measures and aggregate stock returns. There are essentially two categories in which this literature falls. On-the-one-hand, there are those studies which show a significant relationship between various measures of stock returns and various measures of lagged monetary policy (measured as changes in the money supply). For example, studies by Sprinkel [3], Hamburger and Kochin [4], and Keran [5] indicate a lag in the adjustment of stock returns to changes in money growth rates. On-the-other-hand, there are those studies which reject this lagged effect and lend support to the claim that the stock market is efficient with respect to various monetary aggregates. Studies by Rozeff [l], Cooper [6], Kraft and Kraft [7,8], Rogalski and Vinso [9], Tanner and Trapani [lo], and Davidson and Froyen [2] fail to find a significant relationship between stock returns and past money movements. Some of these studies, however, show a significant relationship between current stock returns and changes in future money growth rates which is characteristic of a stock market with a forward-looking propensity (a stock market that manifests a forwardlooking propensity is one in which the current stock return incorporates the market’s expectation of future money movements). Given the disparity in these two views of the relationship between stock returns and changes in the supply of money, the purpose of this paper is to
2. REVIEW
OF THE
LITERATURE
There are essentially two competing hypotheses with regard to the nature of the relationship between stock returns and changes in the money supply. One hypothesis, nominally referred to as the monetary portfolio (MP) hypothesis suggests that, in equilibrium, an investor holds a number of assets including money in his or her portfolio. A monetary
The views expressed are those of the authors and do not necessarily represent the policies of the organizations with which they are affiliated. 321
322
JONATHAN D. JONES and NOEL URI
disequilibrium such as an unexpected (or abnormal) increase or decrease in the rate of growth of the money supply causes a disequilibrium in asset portfolios by making actual money balances depart from desired money balances. The attempt by investors as a group to attain their desired money position then transmits the monetary changes to markets at large. Investors respond to the wealth effect of increased money supply growth by exchanging money for a variety of assets in asset markets such as short and long term bonds, stocks, real estate, durable goods, capital goods and human capital. The time response of investors is viewed in this hypothesis that asset prices respond to the monetary disturbance with lags typically characterized as long, variable, and positive on average.? The hypothesis which has been suggested as an alternative to the MP hypothesis is the efficient market (EM) hypothesis. This hypothesis suggests that the lag (if any) between changes in the money supply and adjustments in the stock returns cannot, on average, be positive and cannot allow for the formulation of trading rules which will enable an investor to earn excess profits. Competition among profit-maximizing investors in an efficient market will insure that current and past information is fully reflected in current security prices so that investors will not be able to develop profitable trading rules with the information. The time sequence of prices conditioned on current and past information will consist of competitively determined equilibrium prices which fully reflect available information and leave investors able to earn only normal rates of return, on average. Monetary policy will not have a systematic lagged effect of any economic importance in an efficient market. Consistent with this efficient market hypothesis is that stock returns will accurately and adequately anticipate future monetary growth. The MP hypothesis was the first (in a temporal sense) one posited [1 l-131. Sprinkel [3] provided the first effort to empirically verify the hypothesis. Using data covering the period 1918 to 1960, he graphically related the money supply level to the level of stock prices. His subjective (i.e. eyeball) analysis lead him to conclude that changes in stock prices lagged tin addition
it is argued that increased money supply growth increases prices of durable goods relative to non-durable goods and makes the latter relatively more desirable. $The Granger direct test was chosen for use here because its statistical performance has been shown to be very good in finite sample Monte Carlo studies dealing with tests of predictive relationships between time series variables [see Nelson and Schwert (1982)]. Also, degrees of freedom are maximized with its use, since it is a one-sided distributed lag causality test and not a two-sided distributed lag test such as the Sims test procedure [20]. #Formally, one covariance stationary time series {a,}, is said to cause another covariance stationary time series {b,} if knowledge of {a,}, for t < 0, results in a smaller error variance in predicting {b,} than would result from a prediction based solely on an autoregressive model. A covariance stationary time series is one for which the following conditions hold: E(q) = @a, + ,) = p and E [(q-p) (a,,, -p)] = y, where p denotes a constant mean, y denotes the autocovariance function and r denotes a discrete time period.
behind changes in the rate of growth in the money supply. Palmer [14] updated Sprinkel’s graphical analysis using 1960 to 1969 data and reached an analogous conclusion to Sprinkel. Subsequent to this, Reilly and Lewis [15], Keran [5], Homa and Jaffee [16] and Hamburger and Kochin [4] used simple regression techniques (including the Almon polynomial distributed lag approach) to conclude that stock prices depend upon both the level of the money supply and the rate of growth of the money supply. The EM hypothesis was first put forward by Fama [17]. Subsequently, Rozeff [I], using data sets covering the period 1916 to 1972 finds empirical evidence to conclude that for the static market, the lag in the effect of monetary policy on stock prices is essentially zero. He suggests that stock prices immediately reflect changes in monetary policy and that, moreover, the stock market actually anticipates future monetary growth. Subsequent to this, Kraft and Kraft [7,8], using seasonally adjusted monthly data and seasonally adjusted quarterly data find that changes in the Standard and Poor Price Index does affect the narrowly defined money supply (i.e. Ml), although the extent of this effect is not detailed. Rogalski and Vinso [9], using four different stock price measures that are seasonally unadjusted, monthly, and measured as percentage changes over the period 1963 to 1974 and the narrow definition of money found, in the aggregate, that percentage changes in stock prices impact the money supply and hence conclude that there is in fact a forward-looking propensity and that the stock market is efficient. Most recently, Davidson and Froyen [2] investigated the lead-lag nature of the relationship between stock returns and the money supply using the New York Stock Exchange Index and narrow definition of the money supply (i.e. Ml) and the monetary base (i.e. MB) on both a weekly and monthly basis. Their results supported the efficient market hypothesis. The conclusion, then, is that the majority of the more recent studies tend to support the efficient market hypothesis. One must still be concerned, however, whether their support is an artifact of the data used, or of the empirical techniques employed, or a combination of both. In what follows, we propose to examine the issue more carefully by employing a test for causality (attributed to Granger 1969) and using several different data series.$ The test is very general and imposes no a priori restrictions in endeavoring to determine whether a statistically identifiable relationship exists between stock returns and changes in the money supply. Before proceeding with its implementation, it is useful to briefly review the methodology. 3. METHODOLOGY
Causality in the present context is defined in terms of predictability. Specifically, one series is said to cause another series if knowledge of this first series results in a smaller error variance in predicting the second series than would result from a prediction based solely on past observations on the second series.0 Based on a Monte Carlo study of eight alternative tests for directional causality, Geweke et al. [19]
Money supply growth recommended the use of the regression-F Granger direct test. In the Granger direct test, prefiltering procedures based on either time domain or frequency domain methods to correct for serial correlation are obviated by including lagged values of the dependent variable on the right-hand side of the equations estimated. The incorporation of lagged values of the dependent variable in the list of regressors corrects for autocorrelation that would otherwise be captured by the regression residuals (as is well-known, serial correlation results in biased standard errors which makes valid inference in the least squares model highly unlikely). Now, let Z$! denote the_ return on the jth stock measure in period t, and M,, denote the percentage change in the. ith money supply variable in period t. Then (R,,, M,,) represents a linearly non-deterministic, possibly non-stationary bivariate time series vector for the pairwise relationships between stock returns and the growth in the money supply. In order to assess the causal relationship(s) between stock returns and changes in the growth rate of the money supply, the use of the Granger test entails classical least squares estimation of the following pairs of restricted and unrestricted equations:
(1)
k=l
NI
Rj,t=
N2
1 a;&-,+
k=,
c bkMi,,_k-i-U: k=l
(2)
NI
Mt.,=
c
k=l
e&f,,-k+v,
Ml.!=
1 k=l
(3)
I
NI e;Mi,,-ki-
F k-1
dkRj,j.r_k+V;
(4)
where ak, a;, bk, ck, CL and dk are coefficients to be estimated, u,, u;, v,, vi are identically and independently distributed random error terms, and N, and N2 are the lengths of the lags (appropriately determined) used in the estimation process. Equations (1) and (2) represent the equations to be estimated in testing the null hypothesis of a lack of causality running from money to stock prices, while the absence of causality from stock prices to money is tested using eqns (3) and (4). With Granger causality, under the null hypothesis of no causal relationship running from &Zi,,to R,,, the tBoth stock price series include dividends. For a discussion of the use of the percentage change in the stock price index as a measure of the stock return, see Froyen and Davidson (1982). .$In order to determine whether the DJIA and NYSE price indices were non-autocorrelated, autocorrelation functions were analyzed for both stock prices, expressed as percentage changes, so as to determine the autocorrelation properties of each. There was some indication of the presence of autocorrelation in each stock price series. For the DJIA price index, a significant spike in the autocorrelation function appeared at lag 1, and a large though insignificant spike appeared at lag 7. For the NYSE price index, significant spikes appeared at lags I and 7, and a large though insignificant spike appeared at lag 6. The use of 12 lags of each price index was deemed adequate to pick up the non-seasonal autocorrelation in the two stock prices for those equations in which the stock prices were the dependent variables.
323
coefficients on the lagged values (which correspond to positive lags) of ti,,, (i.e. bk,for k = 1, . . . , Nt) should not be significantly different from zero as a group. Similarly, under the null. hypothesis of no causal relationship from Rj,! to M,,, the coefficients on the lagged values of R,:, (I.e. dk for k = 1, . . . , NZ) should not be jointly signrficantly different from zero. The data used in the estimation are for two stock price indices (representing stock returns) and three measures of the money supply. The stock price indices include the Dow Jones Industrial Average (DJIA) and the New York Stock Exchange Composite Index (NYSE).t To translate these indices into nominal equity returns, percentage changes were computed. The three money supply growth rates are given by the unweighted first difference of the natural logarithms in successive time periods. The three money measures include the nominal money supply narrowly defined (Ml), the sum of Ml and time deposits (M2), and the monetary base (MB). All five series are measured monthly and are seasonally unadjusted. The data cover the period May 1974 through December 1983. All of the data were obtained from the Federal Reserve Board. In order to empirically implement the test, any deterministic elements in the data must be removed. To do so, the stock return and money growth series were first regressed on a constant, linear time trend, and seasonal dummies. The residuals from these regressions are the data used in estimating the equations for the Granger test. Moreover, the data used in carrying out the Granger test used here were not prefiltered as a means of correcting for serial correlation. Recent Monte Carlo findings have shown that prefiltering as a means of correcting for serial correlation should be avoided in implementing the test. Tests which require prefiltering to correct for serial correlation in general behave unfavorably under the null hypothesis of a lack of one-way causality [19]. Of particular interest to the problem at hand is the finding that regression-F causality tests that require prefiltering as a serial correlation correction yield statistics that are too large and reject the null hypothesis too often. In the implementation of the test, the value of N, was set at 12 in order to capture any non-seasonality that might be present in the data series. To set N, at a smaller value would introduce the possibility that any non-seasonality in the dependent variable would be captured in the regression residua1s.t Next, the truncation of the lag polynomial associated with the independent variable (denoted by N2) was set at 6. Kraft and Kraft [7] suggest that this is appropriate when using monthly data. In addition, it has been suggested that the number of lags associated with the independent variable should be kept smaller than the number of lags associated with the dependent variable in the equations estimated so as to retain power of the causality test [18]. Finally, seasonally unadjusted data were used in this paper to avoid smoothing problems inherent in purging seasonality from raw data (Wallis, 1974). Wallis has shown that the various procedures used by federal government agencies to remove the seasonal component can result in distortion of the information content of the data, making valid causal inferences somewhat difficult.
324
JONATHAN Table
1. Empirical
Regressiont R, on MI on RNY on Ml on Ro, on M2 on RNY on M2 on Ro, on MB on R,.,, on MB on
results of Granger
F-Statistic
Ml Rp, Ml RNY M2 Ro, M2 RNY MB Ro, MB R,,
D. JONESand NOEL URI
direct test
Significance
1.85 2.46 1.29 2.38 1.72 1.60 1.70 1.69 0.77 3.24 0.59 3.50
level$
NS 5% NS 5% NS NS NS NS NS 1% NS 1%
tTbe dependent variable is listed first and the independent variable is listed second. $The critical values for the F6,8O distribution are 2.21 and 3.04 at the 5 and 1% significant levels, respectively. Note: NS denotes not significant.
4.
EMPIRICAL RESULTS
The empirical results of the Granger direct test for the sample period May 1974 to December 1983 are presented in Table 1. The growth rates of Ml, M2, and MB are denoted Ml, M2, and MB respectively. While Rn, and R,, denote the stock returns computed (as described above) for the Dow Jones Industrial Average and the New York Stock Exchange Composite Index, respectively. Inspection of the partial F-statistics (as reported in Table 1) for the
Granger direct test reveals the absence of causality running from each of the three money growth rates to each of the two stock returns. The results also show that both stock return measures cause (in the sense being used here) &I1 and h;lB at the 5 and 1% significance levels, respectively. Neither of the stock return measures is found to have explanatory power for M2. This is particularly interesting because it implies that by judicious choice of the measure of stock returns and the measure of the money supply can yield support for either the acceptance of the efficient market hypothesis (if either Ml or MB are selected as the money supply measure) or the rejection of the hypothesis (if M2 is selected as the money supply measure). In any case, the monetary portfolio hypothesis is unequivocally rejected. These results while consistent with some of the previously referenced studies lending support to the efficient market hypothesis are at odds with the Kraft and Kraft [7,8] papers where it is suggested that the tRozeff [l] describes a stock market with a forward-looking propensity as one which is characterized by reverse causality with correct expectations. IThe presence of serial correlation, either positive or negative, results in a bias in the standard error of the regression, making valid inference virtually impossible. For positive serial correlation, the bias is downward, while for negative serial correlation, the bias can be upward or downward. In general, when serial correlation is a problem in regressions using time series data, residuals usually display positive serial correlation which results in inflated test statistics. It would appear then that the explanatory power of the independent variables in those equations for which serial correlation seems to be a problem is probably overstated. However, there is no way to be certain since the Q-statistic does not provide information as to whether positive or negative serial correlation exists.
detection of the presence or absence of a lead-lag relationship is insensitive to the choice of the money supply measure employed (they both use Ml and M2). The difference in results lies in the suggestion here that stock returns do not have an impact on the money supply measured as M2, while Kraft and Kraft argue otherwise. One can only suppose. that the use of more current data in the current investigation (Kraft and Kraft use data only through 1974) then lead to the anomalous results. Given that the results show the existence of causality running from both the DJIA and the NYSE indices to change in Ml and MB, support is given to the notion that the stock market displayed a forwardlooking propensity with respect to future movements of these two monetary aggregates, at least for the period May 1974 to December 1983 (as noted earlier, a stock market that manifests a forward-looking propensity with respect to monetary changes is one in which the current stock return incorporates the market’s expectation of future money movements).? One should be cautious in interpreting these forgoing results if it turns out that autocorrelation is present in the residuals in the estimated equations. To examine the issue, the Box-Pierce Q-statistics were computed. They are reported in Table 2.$ None of the residuals from the 24 equations are autocorrelated when examined at the 99% level of confidence. Consequently, the F-statistic used in the Granger direct test can be interpreted without fear of misinterpretation. There is an identifiable relationship running from stock returns to the money supply lending credence to the efficient market hypothesis. Table 2. Box-Pierce
Q-statistics
(Granger
R,
on &il
Ml on R, R,,
on Ml
Ml on R,, R,
on M2
M2 on R,, R,, ti2
on M2 on R,,
R,, on MB MB on R, R,,
on MB
MB on R,, tThe Box-Pierce given by:
direct test)t Q-statistic1
Regression Restricted Unrestricted Restricted Unrestricted Restricted Unrestricted Restricted Unrestricted Restricted Unrestricted Restricted Unrestricted Restricted Unrestricted Restricted Unrestricted Restricted Unrestricted Restricted Unrestricted Restricted Unrestricted Restricted Unrestricted Q-statistic
follows a chi-square
42.6 (35) 41.8(29) 37.4 (35) 42.5 (29) 42.9 (35) 37.0 (29) 37.4 (35) 40.5 (29) 42.6 (35) 44.2 (29) 44.9 (35) 48.4 (29) 42.9 (35) 42.4 (29) 44.9 (35) 46.7 (29) 42.6 (35) 35.6 (29) 41.0 (35) 40.5 (29) 42.9 (35) 42.9 (29) 41.0 (35) 44.3 (29) distribution
and is
Q=+;-& I-1 where T is the number of observations on the time series, K denotes the number of autocorrelations considered, Pj represents the squared sample autocorrelation at lag j, and I* denotes the chi-square distribution with K degrees of freedom. IThe critical values for the x2 distribution with 29 and 35 degrees of freedom at the 99% confidence level are 49.6 and 57.2, respectively. Degrees of freedom for the Q-statistics are in parentheses.
Money supply growth 5. CONCLUSION This paper has used the Granger direct test to assess the causal relationship between stock returns and the growth in the money supply over the period May 1974 through December 1983. The results support the notion that the stock market is efficient in the
sense that current and past information with regard to the money supply is fully reflected in current security prices. Hence investors are not able to develop profitable trading rules with information on changes in the money supply. Moreover, the results here suggest that the stock market defacto anticipates future monetary growth.
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