Influences of selected macroeconomic variables on U.S. stock market returns and their predictability over varying time horizons.

Guru-Gharan, Kishor Kumar ; Rahman, Matiur ; Parayitam, Satyanarayana 等

INTRODUCTION

Numerous studies have been documented during last two decades in the empirical literature of financial economics that investigated the predictability of stock returns by lagged regressors. The regressors include financial, macroeconomic and demographic variables. The empirical knowledge regarding the predictability of stock returns has been subjected to continual updating over time mainly driven by new econometric methods. But little consensus regarding the set of appropriate regressors has emerged [e.g., Mankiw and Shapiro (1986), Nelson and Kim (1993), Goetzman and Jorion (1993), Cavanagh, Elliot & Stock, (1995), Stambaugh (1999), Lanne(2002), Lewellen (2003), Campbell and Yogo (2003), Janson and Moreira (2004), and Polk et al. (2004) ]. The recent studies that examined the effects of demographic changes on stock market return include, e.g., Donaldson and Maddaloni (2002), Campbell et al. (2001), Goyal (2004), and Ang and Maddaloni (2005).

Efficient Market Hypothesis (EMH) rooted in the pioneering work of Gibson (1889) made academicians believe for many years that stock prices follow random walk. According to the EMH, the best prediction of the next period's stock price is today's price plus a drift term implying that stock returns are not predictable. Attempts to verify the validity of this assertion sparked enormous interest in studying stock market returns predictability. There is growing evidence that stock market returns are predictable to some degree. The literature documents predictability of stock index returns from lagged returns, lagged financial and macroeconomic variables, and calender or event dummies. However, stock return predictability does not necessarily mean that markets are not reasonably efficient since time-varying expected returns due to changing business conditions and risks can be partly predictable even when the EMH holds. Evidence of stock index returns predictability implies that markets can be beaten by using the above variables. According to Cutler, Poterba, and Summers (1990), "The Efficient Market Hypothesis was probably the right place for serious research on asset valuation to begin, but it may be the wrong place for it to end".

Sudden increases or decreases in wealth result in large stock price movements. Traditional financial theory suggests that such movements are caused by macroeconomic fundamentals. But empirical attempts to link large stock movements to macroeconomic news have been only marginally successful. Chen, Roll, and Ross (1986) consider the weak link a "rather embarrassing gap".

The familiar Gordon (1962) growth model is extensively applied to determine expected stock price that used future dividend stream discount rate and dividend growth rate as explanatory variables. These variables, in turn, are influenced by macroeconomic performance and policy-induced changes in market environment. In general, expected changes in economic environment influence future cash flows and the rate of discount that determine the present value of a firm. Intuitively, macroeconomic variables or state -of-the economy variables are presumed to influence stock returns. At the same time, there is no consensus on the appropriate set of macroeconomic variables that would largely and more precisely explain and predict stock market returns. The theory is silent in this regard leaving the selection of appropriate macroeconomic variables to researchers' judgment and experimentations.

Numerous prior empirical studies investigated the causal linkages between stock market returns and a host of macroeconomic variables that included GDP growth, industrial production rate, short-term interest rate, inflation rate, interest rate spread, changes in monetary aggregates, among others. Stock market returns are usually directly tied with the business cycle, while financial variables (e.g., dividend growth, discount rate, and cash flows) produce perverse effects on stock prices.

In addition to the stock market and macroeconomy linkage empirics, there is a growing amount of empirical literature on time series return predictability which can be divided into three categories: i) return predictability using historical prices or returns investigates whether today's return is related to historical returns at various frequencies; ii) return predictability using lagged financial and macroeconomic variables, and iii) return predictability using calendar dummies for seasonality.

The studies in category (i) include [e.g., Fama and French (1988), Petorba and Summers (1988), Lo and MacKinlay (1997), Lo, Mamaysky and Wang (2000)]. The studies in category (ii) include [e.g., Fama and French (1988), Breen, Glosten and Jagannathan (1989), Harvey (1991), Solnik (1993), Pesaran and Timmermann (1995, 2000)]. The studies in category (iii) include [e.g., Keim (1989), Hawanini and Keim (1995), French (1980), Keim and Stambaugh (1984), Chang, Pinegar and Ravichandran (1998), Ariel (1990)].

Notwithstanding the large number of empirical studies on stock returns, it appears that the studies that focus on the explanatory power of macroeconomic variables with regard to U.S. stock market returns and their predictability on varying time horizons are scant. This paper seeks to fill in this void by investigating the above using monthly data from January 1970 to December 2003 within the VAR (Vector Autoregressive) framework.

LITERATURE REVIEW

Fama (1981) and Kaul (1987) found a puzzling result that real activity explains larger fractions of return variation for longer return horizons. Fama (1990) explains this by arguing that regressions of shorter-horizon returns on production growth rates understate explanatory power because information about the production of a given period spreads over preceding periods. But the number of observations in Fama (1990) varies from 420 in monthly regressions to only 140 in quarterly and 137 in annual. This is equivalent to using two sets of data. In the present study, we examine such impact using the same set of data and number of observations (except for a very small change due to end point adjustments). Similarly, Gesky and Roll (1983), Barro (1990), and Shah (1989) find that larger fractions (often exceeding 50 %) of annual stock-return variables can be traced to forecasts of variables such as real GNP, industrial production, and investment. Apart from these studies, the other studies cited below explore various other aspects of the relationship between stock returns and macroeconomic variables. Chen et al. (1986) examined equity returns relative to a set of macroeconomic variables and found that the set of macroeconomic variables which can significantly explain sock returns includes growth in industrial production, changes in the risk premium, twists in the yield curve, measures of unanticipated inflation and changes in expected inflation during periods of volatile inflation. More recent examples of studies involving a number of macroeconomic variables include Chen (1991), Peseran and Timmermann (1995), and Flanery and Protopapadakis (2002).

The empirical literature in which aggregate output is related to stock returns includes Cutler, et al. (1989), Balvers, et al. (1990), Marathe and Shanky(1994). Examples of studies relating inflation to stock returns are Bodis (1976), Jaff and Mandelker (1976), Nelson (1976), Fama and Schwert (1977), Geske and Roll (1983), DeFine (1991), Boudoukh and Richardson (1993), Bealduzzi (1995), Grahman (1996), Siklos and Kwok (1991), and Adams , et al. (2004). Studies relating money supply to stock returns include Hamburger and Kochin (1972), Pesando (1974), Ragalski and Vinso (1977). Examples of studies relating stock returns to interest rate /term spread variables include Campbell (1987), Fama and French (1989), Hodrick (1992), Jensen and Johnson (1995) and Ang and Bekaert (2001). Examples of studies done outside US are Darrat and Mukherjee (1987), Darrat (1990), Poon and Taylor (1991), Mukherjee and Naka (1995), Brown and Otsuki (1990), Gjerde and Saettem (1999), Naka, et al. (1999), Pethe and Karnik (2000), Mayasami and Koh (2000), and Panda and Kamaiah (2001). Examples of studies involving many countries are Gultekin (1983), Solnick (1984), Mandelker and Tandon (1985), Mookerjee (1989), Wasserfallen (1989), Jeng , et al. (1990), Ferson andHarvey (1993), Lin (1993), Kaneko and Lee (1995), Ely and Robinson (1997), Conover, et al. (1990), and Durham (2001).

In contrast, there have been numerous studies showing reverse causality running from stock returns towards macroeconomic variables. Nevertheless, as remarked by Chen, et al., (1986)," ... Stock prices are usually considered as responding to external forces (even though they may have a feedback on the other variables)". The present study too assumes unidirectional causality from macroeconomics variables towards stock returns because most theoretical models involving macroeconomic variables rarely include stock prices (or stock returns) in their argument as a significant determinant. Therefore, this literature survey excludes the studies investigating the reverse causality. It should be noted, however, that some of the studies mentioned above treat all variables as endogenous in their application of estimating techniques such as VAR models.

Some studies also find that the predictive ability of certain macroeconomic variables with respect to stock returns is quite uneven over time, e.g., Durham (2001). On the other hand, there is no dearth of studies, which fail to support the ability of macro variables to predict stock returns. Chen , et al. (1998) concludes, " The macroeconomic factors generally make a poor showing. Put more bluntly, in most cases, they are as useful as a randomly generated series of numbers in picking up return covariation. We are at loss to explain this poor performance." Flannery and Protopapadakis (2002) argue that tests based on monthly data may have lower power because the impact of macroeconomic variables on monthly stock returns may be obscured by other events occurring during the month. Therefore, they apply high frequency data (daily returns) to minimize such impacts of other omitted variables. Moreover, they evaluate the impact on stock price volatility instead of realized returns with respect to real variables.

SELECTION OF MACROECONOMIC VARIABLES IN THE PRESENT STUDY

Stock market is assumed endogenous relative to other markets in line with Chen, et al. (1986). The S & P 500 Index is selected as a proxy for the aggregate stock market and percentage changes are used to represent stock market returns. Four macroeconomic variables are selected as likely explanatory variables following the simple and intuitive financial theory as suggested by Chen, et al. (1986). As a proxy for overall economic activity, Total Industrial Production (IP) Index (seasonally adjusted) with base year 1997 instead of GNP or GDP is selected because of availability of monthly data. As argued by Chen, et al. (1986), "Insofar as the risk premium measure does not capture industrial production uncertainty; innovations in the rate of productive activity should have an influence on stock returns through their impact on cash flows." Many empirical studies, cited above, have found positive relation between contemporaneous stock returns and industrial activity, while some other studies have found positive contribution of lagged changes in industrial production.

The Consumer Price Index (CPI) and percentage change therein is used to measure inflation. The rate of inflation is a likely determinant of stock returns due to the systematic effect of unanticipated price-level changes as well as impact on asset valuation caused by relative price change associated with inflation as argued by Chen, et al. (1986). Actual inflation can be expected to be positively related to unanticipated inflation and thus have negative impact on asset prices and returns. On the other hand, inflation may have positive impact on cash flows to dampen some or all of this negative impact. Some authors argue, however, that such impact on revenues and cost will not be large , because of pre-existing contracts (for example, DeFina; 1991). Similarly, money supply growth may have important direct effects through portfolio changes and indirect effects through their effect on real economic activity as well as on rate of inflation. While the positive correlation of money supply growth with inflation might suggest negative influence on stock returns, the stimulus provided to overall economic activity might lead to positive impact. The net effect is thus an empirical question.

Finally, rate of interest is supposed to influence stock prices mainly through its impact on the expected rate of discount for future cash flows. Strong positive correlation of interest rate with the discount rate suggests that surges in interest rate will have negative effect on stock returns. Federal Funds Rate (FF) has been selected in this paper to proxy short term interest rate. However, selection of these four macroeconomic variables is not exhaustive by any means.

EMPIRICAL METHODOLOGY

The theoretical model in general functional form is as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where, Y = rate of return on S& P 500, X = percentage change in U.S. industrial production index, Z = inflation rate (percentage change in consumer price index), V = federal funds rate and L = Percentage change in U.S. broad money supply. The expected sign on the top of each explanatory variable is already mentioned in the preceding section. Causality is investigated using Granger's procedure. Causality in the Granger sense implied that for a variable x to cause another variable Y, X must precede Y. The Granger-causality equation can thus be formulated in levels as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

Akaike's information criterion (AIC) is used to obtain the appropriate lag length for all variables. This paper follows the method outlined by Hsio (1981). The Granger causality test uses an F-test to determine whether lagged information on variable X gives statistically significant information about a variable Y in the presence of lagged values of Y. If the F-test fails to provide such evidence, it is then concluded that the variable X does not cause the variable Y. The null hypothesis that X does not causes Y is rejected when the test statistic F is greater than the critical value at the most commonly used 5 percent level of significance.

Contemporaneous values of regressors have not been used considering the reporting delays or lags in the release of information and the lags in the incorporation of information about them into prices. In addition to the consideration of lags in information and the lags in the incorporation of information about them into prices, the lagged value of the endogenous variable indicates autoregressive process. An additional benefit of using only lagged values of explanatory variables is that it enables us to make unconditional or ex post forecasts for stock returns (Pindyck and Rubindeld, 1990). Three versions of the basic regression model have been used. First, all monthly rates of change are measured relative to the value in the previous month. Second, quarterly rates of change are measured relative to the value in the preceding quarter. Third, annual rates of change are measured relative to the value in the same month of the preceding year. Thus, the three versions differ only in the methods of calculations of rates of change but use the same set of monthly data for 35 years spanning from January 1970 through December 2004. [The relevant data are available from www.economagic.com]

To examine the time series property of each variable, the well-known augmented DickeyFuller (ADF) test for unit root (nonstationaity) against its alternative of stationarity around a fixed time trend is applied. The ADF statistics are generated by estimating the following equation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where, T is a time trend.

The ADF test is implemented to avoid the so-called" spurious regression" problem (Granger and Newbold, 1974, Dickey and Fuller, 1979 and 1981).

To forecast out-of-sample for the next 12 months of 2004, the estimates of equation (2) with data for January 1970 through December 2003 are used. The forecasting accuracy is tested by Theil's inequality coefficient and the decomposition into bias, variance and covariance proportions (Maddala, 1977). The plots of actual and predicted values of stock returns are also graphically presented to display out-of-sample prediction accuracy. All estimations are done by EVIEWS.

EMPIRICAL RESULTS AND ANALYSES

To study the nature of the distributions of each variable for monthly, quarterly and annual data, the numeric of mean, median, standard deviation, skewness and kurtosis are reported in Appendix -I panels A, B, and C, respectively. A cursory inspection of the results shows that the respective means and medians are within close proximity. The standard deviation of S& P 500 returns is consistently much higher than that of any other variable and the data distribution of this variable is uniformly skewed to the left. The distributions of X are also skewed to the left excepting monthly data. The distribution of V (federal funds rate) is skewed to the left only for monthly data. Distributions of Z (inflation rate) and L (growth in board money supply) are consistently skewed to the right for monthly, quarterly and annual data. In most cases, there is evidence of excess kurtosis.

Next, the simple correlation coefficients are reported in Appendix-II using monthly, quarterly and annual data ordered in panels A, B and C, respectively to determine the presence and the extent of multicollinearity between explanatory variables. The general conclusion emerges that the pair-wise correlation coefficients are mild to moderate (above 0.5) posing no serious multicollinearity problems to generate inefficient parametric estimates. Moreover, the presence of mild to moderate multicollinearity is not necessarily bad since another important objective of this paper is out-of-sample forecasting.

To ascertain the time series property of each variable, the ADF unit root test results are reported in Table1.

Table 1 depicts stationarity of each variable for monthly and quarterly data uniformly at 5 percent and higher levels of significance. The same also applies to annual data for each variable with the exception of the growth in U.S. broad money supply. However, this variable has not been retained in the final analysis because of its low statistical significance.

Equation (1) is estimated with lagged -values of all four explanatory variables with monthly, quarterly and annual data. The comparative results are reported in Table 2.

Table 2 shows dramatic improvements in the explanatory power and the overall statistical significance of the model in terms of [[bar.R].sup.2]'s and the F-statistics as the frequency of data switches from monthly to quarterly and then from quarterly to annual. The appropriate lag length is 1 (one) as determined by the AIC criterion. Other higher order lagged values do not have statistically significant coefficients. As a result, they have not been reported here.

The coefficients of V(-1) and L (-1) are statistically highly insignificant, although they have the expected negative sign. The redundancy test also shows that these two variables have no discernible influences on stock returns and they do not contribute to the explanatory power of the model in terms of [[bar.R].sup.2] and its overall statistical significance in terns of F-statistic. The F-statistic for redundancy test is 0.5823 with p-value of 0.5591 and the log-likelihood ratio is 1.1803 with p-value of 0.5543. Consequently, the model has been re-estimated only with annual data with exclusions of the lagged redundant variables (V and L). The estimates are presented in Table 3.

As observed in Table 3, virtually there are no changes in the numerics of [[bar.R].sup.2] and DW statistic, but the F-statistic improves significantly from 436.5051 to 728.6307. All the coefficients have the expected sign excepting industrial production rate. Again, the appropriate lag length is determined by the AIC criterion.

The sign of the coefficient of Y (-1) in Table 3 shows positive autoregressive process and its value is significantly below unity showing dynamic stability. The estimated equation shows negative impact of inflation as expected and found in several empirical studies cited earlier. The associated t-statistic, however, shows significance only at 12.83% level. This may be the result of conflicting negative influence of inflation and positive influence through its impact on cash flows. This is also the result of structural changes in the economy. On the other hand, although highly significant, the sign of the coefficient of lagged growth rate in industrial production is negative, contrary to apriori expectation and findings of several empirical studies cited earlier. The examination of structural change helps in explaining this unexpected result.

ANALYSES OF STRUCTURAL CHANGE AND OUT-OF-SAMPLE FORECASTING

The possible structural changes during the post-oil-shock period of 1980's, the stock-market-boom (or Clinton-era) period after 1992 and the period following the tragedy of September 11 of 2001 have been examined. The calculated Chow test statistic for structural breaks at January 1980, January 1992 and October 2001 are calculated as 0.2393, 4.1104 and 0.8434 with corresponding p-values of 0.9160, 0.0028 and 0.4983, respectively. Thus, only the period after 1992 seems to exhibit significant structural break. Following this lead, a slope dummy has been introduced with value 0 before 1992 and 1 thereafter. The resulting equation seems to fit the data well with the slope dummies for annual data as in Table 4.

Table 4 shows that the slope of lagged industrial growth is negative before 1992 and positive after 1992. In other words, the growth in industrial production before 1992 unleashed negative influences on S &P 500, while after 1992 industrial production growth appears to boost stock market returns. The negative impact of inflation seems to have increased further after 1992. Moreover; all coefficients are now more significant as compared to the associated t-values in Table 3.

The model is re-estimated further with slope dummies using 12-month, 18-month and 24-month moving averages. The comparative results are reported in Table 5.

Table 5 unveils gradual significant improvements in [[bar.R].sup.2]'s and F -statistics. As observed, the 2 R estimates with 24-month moving averages produce the best overall results, although some of the associated t-values decline as compared to those relating to 12-month and 18-month averages.

Since the model with slope dummy variables appears to be highly successful, it is used in the forecasting exercise. To implement the out-of-sample forecasting, the entire sample period is divided into January 1970 to December 2003 and January 2004 to December 2004.

The sub-sample for the period of January 1970 to December 2003 is used for estimation of the regression equation with slope dummy variables. The estimated equation is used to forecast stock market returns for out-of-sample period of January 2004 to December 2004. Since the estimated coefficients are very close to those in Table (4), they are no more reported here. The calculated test statistics for out-of-sample error are as follows:

Root Mean Squared Error = 4.8728;

Mean Absolute Error =4.0790;

Mean Absolute Percent Error = 26.8455;

Theil's Inequality Coefficient = 0.1188;

Bias Proportion = 0.0225;

Variance Proportion = 0.0325; and

Covariance Proportion = 0.9449.

These statistics show that the out- of -sample forecasting power of the model is quite high. In particular, Covariance Proportion is quite high while Bias and Variance proportions are low and the Theil's Inequality Coefficient is small. Appendixes III and IV show the graphs of actual and predicted stock returns that closely correlate with each other.

CONCLUSIONS AND REMARKS

This study arrives at an interesting conclusion that the time horizon for calculating stock market returns makes a very large impact on the explanatory power of macroeconomic variables using the same set of monthly data. When stock market returns are calculated over a month, the model fails to capture even 1 percent of variance. In contrast, the model captures more than 84 percent of variance when stock market returns are calculated over the year using the same set of monthly data. As such, there is no need to search for higher frequency data only to improve the explanatory power of the model. The more important step is to calculate stock market returns in line with investors' general attitude which seems to be much longer than a month.

Out of the four macroeconomic variables with presumptive linkages to stock market returns, the rate of growth in industrial production and the rate of inflation seem to be highly significant, while the rate of change in broad money supply and the change in federal funds rate seem to contribute insignificantly. The investigation of structural change shows that the stock-market-boom period after 1992 exhibits significant shift in the slope of the explanatory variables while the post-oil-shock period after 1980 and the period after September 11, 2001tregedy show little change.

Appendix-I: Descriptive Statistics

Panel A: Monthly Data

(January 1970-December 2004)

Descriptors Y X Z

Mean 0.732257 0.220566 0.387357
Median 0.907647 0.267195 0.317797
Std. Dev. 4.463956 0.722525 0.314443
Skewness -0.369232 0.769313 0.929301
Kurtosis 4.826096 6.609577 4.477363

Panel B: Quarterly Data

Descriptors Y X Z

Mean 2.177878 0.668009 1.170113
Median 2.209438 0.852499 0.945068
Std. Dev. 7.744188 1.636548 0.826333
Skewness -0.420173 -1.247963 1.103310
Kurtosis 4.113378 7.444116 4.090962

Panel C: Annual Data

Descriptors Y X Z

Mean 9.279876 2.797704 4.806700
Median 10.57650 3.260724 3.667071
Std. Dev. 16.45477 4.514919 3.099999
Skewness -0.244591 -0.654629 1.332394
Kurtosis 2.752072 3.599568 3.944062

Panel A: Monthly Data

(January 1970-December 2004)

Descriptors V L

Mean -0.016277 0.571366
Median 0.010000 0.571366
Std. Dev. 0.647478 0.379067
Skewness -1.969196 0.654680
Kurtosis 34.245610 5.790072

Panel B: Quarterly Data

Descriptors V L

Mean 0.161825 1.734501
Median -0.181159 1.696773
Std. Dev. 15.63967 0.980526
Skewness 0.478690 0.421388
Kurtosis 5.364808 3.883736

Panel C: Annual Data

Descriptors V L

Mean -0.171520 7.187903
Median -0.255000 7.324172
Std. Dev. 2.539753 3.317056
Skewness 0.257376 0.012370
Kurtosis 4.614925 2.463416

Appendix-II: Correlation Matrices

Panel A: Monthly Data

Descriptors Y X Z

Y 1.000000 -0.055669 -0.163406
X -0.055669 1.000000 -0.082640
Z -0.163406 -0.082640 1.000000
V -0.167707 0.338491 0.072045
L 0.026964 -0.005502 0.053184

Panel B: Quarterly Data

Descriptors Y X Z

Y 1.000000 -0.051101 -0.220252
X -0.051101 1.000000 -0.144781
Z -0.220252 -0.144781 1.000000
V -0.193841 0.432143 0.204371
L 0.077390 -0.002386 0.065618

Panel C: Annual Data

Descriptors Y X Z

Y 1.000000 0.142713 -0.271819
X 0.142713 1.000000 -0.287419
Z -0.271891 -0.287419 1.000000
V -0.125554 0.537450 0.323948
L 0.046661 0.029809 0.199346

Panel A: Monthly Data

Descriptors V L

Y -0.167707 0.026964
X 0.338491 -0.005502
Z 0.072045 0.053184
V 1.000000 -0.114016
L -0.114016 1.000000

Panel B: Quarterly Data

Descriptors V L

Y -0.193841 0.077390
X 0.432143 -0.002386
Z 0.204371 0.065618
V 1.000000 -0.165035
L -0.165035 1.000000

Panel C: Annual Data

Descriptors V L

Y -0.125554 0.046661
X 0.537450 0.029809
Z 0.323948 0.199346
V 1.000000 -0.164699
L -0.164699 1.000000

Appendix III: Forecasting With Annual Data

[ILLUSTRATION OMITTED]

Appendix IV: Forecasting With 12 Month Moving Average

[ILLUSTRATION OMITTED]

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Kishor Kumar Guru-Gharan, McNeese State University

Matiur Rahman, McNeese State University

Satyanarayana Parayitam, University of Massachusetts Dartmouth

Table 1: ADF Statistic for Unit Root

Variables ADF-Statistic (1) ADF-Statistic (2) ADF-Statistic (3)
 (Monthly data) (Quarterly data) (Yearly data)

Y -20.20626 -4.920376 -3.859466
X -9.497868 -5.273363 -3.417938
Z -3.712944 -3.437696 -3.134817
V -13.60964 -4.288197 -3.794280
L -10.63056 -3.560017 -1.510097

Where, (1) for ADF critical values of monthly data are -3.445814,
-2.868252 and -2.570410 at 1,5 and 10 percent levels of
significance, respectively; (2) for ADF critical values of
quarterly data are -3.446122, -2.868387 and -2.570483 at
1,5 and 10 percent levels of significance, respectively and 3
for ADF critical values of annual data are -3.446692,
-2.868638 and -2.570617 at 1,5, and 10 percent levels of
significance, respectively.

Table 2: Regression Results * (All variables included)

Variables Coefficients Coefficient
 (Monthly data) (Quarterly data)

Intercept 1.2294 1.4197
 (2.5402) (1.9752)
Y(-1) -0.0155 0.6486
 (-0.3085) (17.1507)
X(-1) 0.0049 -0.1339
 (0.0153) (-0.6732)
Z(-1) -1.0621 -0.1984
 (-1.4920) (-0.5354)
V(-1) -0.5867 -0.0413
 (-1.5999) (-1.9068)
L(-1) -0.1663 -0.1769
 (-0.2860) (-0.6000)

 [[bar.R].sup.2]=0.0012 [[bar.R].sup.2]=0.4520
 DW=2.0085 DW=1.6756
 F=1.1029 F=69.4655
 AIC=5.8429 AIC=6.3454

Variables Coefficients
 (Yearly data)

Intercept 2.0801
 (2.0402)
Y(-1) 0.9164
 (44.3036)
X(-1) -0.1761
 (-1.5529)
Z(-1) -0.0608
 (-0.3999)
V(-1) -0.2175
 (-1.0371)
L(-1) -0.0795
 (-0.7141)

 [[bar.R].sup.2]=0.8429
 DW=2.0014
 F=436.5051
 AIC=6.6055

* The associated t-value is reported in parenthesis underneath
each coefficient.

Table 3. Regression Results (Yearly Data) (Excluding V and L)

Variables Coefficients t-statistic

Intercept 2.3160 3.0412
Y(-1) 0.9178 44.8254
X(-1) -0.2659 -3.5473
Z(-1) -0.1712 -1.5239

[[bar.R].sup.2] = 0.8432, DW = 1.9963, F = 728.6307, AIC = 6.5986

Table 4: Regression Results with Slope Dummies

Variables Coefficients t-statistic

Intercept 4.2235 4.0814
Y(-1) 0.8769 38.8035
X(-1) -0.4052 -4.9554
Z(-1) -0.3444 -2.6120
D.X (-1) 0.7767 3.8325
D.Z (-1) -1.3112 -3.3751

[[bar.R].sup.2] = 0.8484, DW = 1.9873, F = 455.36, AIC = 6.5697

Table 5: Regression Results With Moving Averages of Monthly Returns

Variables Coefficients Coefficient
 (12-Month (18-Month
 moving average) moving average)

Intercept 0.3045 0.1825
 -3.7382 -2.8114
Y(-1) 0.8840 0.9204
 -39.0786 -44.8463
X(-1) -0.3766 -0.2573
 (-4.9581) (-3.9196)
Z(-1) -0.3018 -0.1584
 (-2.3252) (-1.5816)
D.X(-1) -0.8476 0.5750
 -4.3549 -3.6399
D.Z(-1) -1.3997 -0.8315
 (-3.7395) (-2.9141)

 [[bar.R].sup.2]=0.8574 [[bar.R].sup.2]=0.8964
 DW=2.0070 DW=2.0875
 F=460.3684 F= 652.0145
 AIC=1.4256 AIC=0.7400

Variables Coefficients
 (24-Month
 moving average)

Intercept 0.1222
 -2.2744
Y(-1) 0.9394
 -50.1202
X(-1) -0.1991
 (-3.9382)
Z(-1) -0.0873
 (-1.0942)
D.X(-1) 0.4430
 -3.5430
D.Z(-1) -0.5589
 (-2.7507)

 [[bar.R].sup.2]=0.9215
 DW=1.9890
 F=869.9209
 AIC=0.1352