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dissertation entitled

DIVIDEND POLICY: RELATIONSHIPS WITH INVESTMENT AND RISK

presented by

DAVID A. LOUTON

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DIVIDEND POLICY: RELATIONSHIPS WITH INVESTMENT AND RISK

BY

David A. Louton

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Finance and Insurance
Eli Broad Graduate School of Management

1991

ABSTRACT

DIVIDEND POLICY: RELATIONSHIPS WITH INVESTMENT AND RISK

BY
David A. Louton

This study consists of two related parts. The first is
an examination of the possible empirical relationship
between dividends and investment. In particular,
simulations are used to examine the limits of the
discriminatory power of Smirlock and Marshall’s [1983] study
employing Granger causality methods on a series of 20 annual
observations per firm. Their empirical work is updated
using series of 38 annual observations per firm rather than
the 20 previously available. Granger causality from
dividends to investment, significant at the a=0.05 level, is
found in approximately 28 percent of the sample. The
implication is that many of the largest domestic firms have
been managed in a way that is directly opposed to accepted
theory within the field of corporate finance. Although it
would be impossible to accurately assess the opportunity
cost of such potentially suboptimal decision making, the
magnitude of the variables involved suggests that it would
be substantial.

The second part of this study consists of tests of the

hypothesis that dividend payout causally precedes price

risk. Although causality at statistically significant
levels is not found in any substantial proportion of the
firms in the sample, there are some interesting observations
to be made. Specifically, when longer time series are
employed, there is a stronger relationship between changes
in OLS beta and changes in dividend payout, than there is
between changes in standard deviation of returns and changes
in dividend payout. One inference that could be drawn from
these findings is that changes in dividend payout policy may

contribute to increased systematic risk.

Copyright by
DAVID A . LOUTON
19 9 1 i

To

Marcie, Shaina, Daniel and Corrie

ACKNOWLEDGEMENTS

I would like to thank the members of my dissertation
committee for their critical insights and many helpful
suggestions.

TABLE OF CONTENTS

List of Tables

List of Figures

CQQQEQ; I:

Introduction

Chapper II:

Review of Literature Common to Empirical Chapters

Qhapte; III:
Methodology

Chapper IV:

An Examination of Dividend-Investment Interdependence
Review of the Literature
Simulated Dividends and Investment
Initial Simulation Results
Fama and Babiak Revisited
Further Simulation Results
Empirical Tests for Dividend-Investment Causality
Conclusions

Appendix IV.A: Listing of code used to
generate simulations

vi

ix

xi

16

26
27
37
4o
42
44
45

52

55

cpaptg; V:

Causality Tests of the Relationship Between
Dividend Payout and Risk

Review of the Literature
Dividend Payout and Risk

The Model

The Sample

Initial Test Results

Tests with Extended Data Series

Conclusion

Endnotes

References

vii

126

127

131

133

135

136

143

146

165

166

Eta—bis W192

II.1 Dividend Policy and Value Literature

IV.1 Stationarity: Simulation, T=20, E=0.10

IV.2 Stationarity: Simulation, T=20, E=0.15

IV.3 Stationarity: Simulation, T=20, E=0.20

IV.4 F-statistics: Simulation, T=20, E=0.10

IV.5 F-statistics: Simulation, T=20, E=0.15

IV.6 F-statistics: Simulation, T=20, E=O.20

IV.7 F-statistics: Simulation, T=20, 020%)=0.001
IV.8 F-statistics: Simulation, T=20, ozhu)=0.010
IV.9 F-statistics: Simulation, T=20, ozhu)=0.100
IV.10 Dividend Prediction 1952-1989

IV.11 Dividend Prediction 1952-1970 and 1971-1989
IV.12 Stationarity: Sim with 1952-1989 parameters
IV.13 Stationarity: Sim with 1952-1970 parameters
IV.14 Stationarity: Sim with 1971-1989 parameters
IV.15 F-statistics: Sim with 1952-1989 parameters
IV.16 F-statistics: Sim with 1952-1970 parameters
IV.17 F-statistics: Sim with 1971-1989 parameters
IV.18 Div-Inv Causality: Levels, 1953-1989

IV.19 Div-Inv Causality: lst Diff, 1953-1989
IV.20 Div-Inv Causality: Segmented, 1953-1989
IV.21 Firms Exhibiting Dividenqunvestment Causality
v.1 Payout-Risk Causality: 1st Diff, 1969-1988
v.2 Payout-Risk Causality: Levels, 1953-1989
v.3 Payout-Risk Causality: lst Diff, 1953-1989

viii

LI§I_QI_IA§L!§

79

148
149
150

IV.1

IV.2

IV.3

IV.4

IV.5

IV.6

IV.7

IV.8

IV.9

IV.10
IV.11
IV.12
IV.13
IV.14
IV.15
IV.16
IV.17
IV.18
IV.19
IV.20
IV.21
IV.22
IV.23
IV.24
IV.25
IV.26
IV.27
IV.28
IV.29
IV.30
IV.31
IV.32
IV.33
IV.34
IV.35
IV.36
IV.37
IV.38
IV.39
IV.4O
IV.41
IV.42
IV.43
IV.44

Description _3_Pa e
Simulated Dividend Series 82
Actual Dividend Series 83
Dividend Prediction 1952-1989 : Lagged Dividends 84
Dividend Prediction 1952-1989 : Earnings 85
Dividend Prediction 1952-1989 : AR(1) Coefficient 86
Dividend Prediction 1952-1989 : Sigma 87
Dividend Prediction 1952-1970 : Legged Dividends 88
Dividend Prediction 1952-1970 : Earnings 89
Dividend Prediction 1952-1970 : AR(1) Coefficient 90
Dividend Prediction 1952-1970 : Sigma 91
Dividend Prediction 1971-1989 : Lagged Dividends 92
Dividend Prediction 1971-1989 : Earnings 93
Dividend Prediction 1971-1989 : AR(1) Coefficient EM:
Dividend Prediction 1971-1989 : Sigma 95
Sim 1952-1989 (med): F-Stat Dividends (diff) 96
Sim 1952-1989 (med): F-Stat Investment (diff) 97
Sim 1952-1989 (mode): F-Stat Dividends (diff) 98
Sim 1952-1989 (mode): F-Stat Investment (diff) 99
Sim 1952-1989 (mean): F-Stat Dividends (diff) 100
Sim 1952-1989 (mean): F-Stat Investment (diff) 101
Sim 1952-1970 (med): F-Stat Dividends (diff) 102
Sim 1952-1970 (med): F-Stat Investment (diff) 103
Sim 1952-1970 (mode): F-Stat Dividends (diff) 104
Sim 1952-1970 (mode): F-Stat Investment (diff) 105
Sim 1952-1970 (mean): F-Stat Dividends (diff) 106
Sim 1952-1970 (mean): F-Stat Investment (diff) 107
Sim 1971-1989 (med): F-Stat Dividends (diff) 108
Sim 1971-1989 (med): F-Stat Investment (diff) 109
Sim 1971-1989 (mode): F-Stat Dividends (diff) 110
Sim 1971-1989 (mode): F-Stat Investment (diff) 111
Sim 1971-1989 (mean): F-Stat Dividends (diff) 112
Sim 1971-1989 (mean): F-Stat Investment (diff) 113
Dividends (level) 1953-1989: DF Statistics 114
Investment (level) 1953-1989: DF Statistics 115
Dividends (level) 1953-1989: F-Statistics 116
Investment (level) 1953-1989: F-Statistics 117
Dividends (diff) 1953-1989: DF Statistics 118
Investment (diff) 1953-1989: DF Statistics 119
Dividends (diff) 1953-1989: F-Statistics 120
Investment (diff) 1953-1989: F-Statistics 121
Dividends (diff) 1953-1989: F-Stat. DF<-2.95 122
Investment (diff) 1953-1989: F-Stat. DF<-2.95 123
Dividends (diff) 1953-1989: F-Stat. DF>-2.95 124
Investment (diff) 1953-1989: F-Stat. DF>-2.95 125
Payout (Diff) 1969-1988: DF Statistics 151
OLS Beta (Diff) 1969-1988: DF Statistics 152
Std. Dev. (Diff) 1969-1988: DF Statistics 153

LI§I_QI_IIQEBIQ

ix

<‘=<:<:d<:<‘=<:
Hrau>m~qaxma>

Payout: Payout-OLS Beta, 1969-1988: F-Stat.
OLS Beta: Payout-OLS Beta, 1969-1988: F-Stat.
Payout: Payout-Std.Dev., 1969-1988: F-Stat.

Std. Dev.: Payout-Std. Dev.,

1969-1988: F-Stat.

Payout (Diff) 1953-1989: DF Statistics

OLS Beta (Diff) 1953-1989: DF Statistics

Std. Dev. (Diff) 1953-1989: DF Statistics
Payout: Payout-OLS Beta, 1953-1989: F-Stat.
OLS Beta: Payout-OLS Beta, 1953-1989: F-Stat.
Payout: Payout-Std.Dev., 1953-1989: F-Stat.

Std. Dev.: Payout-Std. Dev.,

1953-1989: F-Stat.

154
155
156
157
158
159
160
161
162
163
164

Wise

Introduction

This study consists of two related parts. The first is
an examination of the possible empirical relationship
between dividends and investment. In particular simulations
are used to examine the limits of the discriminatory power
of Smirlock and Marshall's [1983] study employing Granger
causality methods on a series of 20 annual observations per
firm. Their empirical work is then updated using series of
38 annual observations per firm rather than the 20
previously available. Granger causality from dividends to
investment, significant at the a=0.05 level, is found in
approximately 28 percent of the sample.

The second part of this study consists of tests of the
hypothesis that dividend payout causally precedes price
risk. In the process the converse hypothesis is also
tested. Although causality at statistically significant
levels is not found in any substantial proportion of the
firms in the sample, there are some interesting observations
to be made. Specifically, when longer time series are
employed, there is a stronger relationship between changes
in OLS beta and changes in dividend payout, than there is
between changes in standard deviation of returns and changes
in dividend payout. One inference that could be drawn from
these findings is that changes in dividend payout policy may

contribute to increased systematic risk.

Assuming perfect capital markets Miller and Modigliani
[1961] demonstrate that the value of the firm depends only
on investment policy and not on the method of financing
investments. Thus, although we would expect higher
investment to lead to higher dividends we would not expect
to find a similar intertemporal correlation going from
dividends to investment. Fama and Miller [1972] call this
the separation principle. Although several attempts have
been made to test the empirical validity of this proposition
(see for example Fame [1974], Smirlock and Marshall [1983]
and Partington [1985]), data and methodological problems
have prevented an effective resolution of this issue. Since
a finding that dividend policy influences investment would
clearly imply that suboptimal investment choices are being
made, tests of the separation principle are crucially linked
to the question of how dividend policy affects value.

A somewhat related question involves the relationship
between dividend payout and risk. The importance of
controlling for systematic risk in empirical studies of
dividend policy has long been understood (see for example
Friend and Puckett [1964] and Black and Scholes [1974]).
However, although Rozeff [1982] documented a strong negative
correlation between dividend payout and risk, little has
been done to investigate the specific nature of this
relationship, and in particular, its direction. This is the

focus of the second part of the current study. Since risk

has been shown to be a determinant of share value, this part
of the study is essentially another avenue by which the
empirical validity of Miller and Modigliani’s dividend-
irrelevance proposition can be examined. Once again we are
only concerned with a specific sort of causality. That is,
a causal relationship running from dividend policy to risk
is of concern because it has implications for value. In
contrast, a causal relationship running from risk to
dividend policy, while presenting certain points of
interest, does not imply that any suboptimal policy
decisions have been made.

Both segments of the current study have in common the
dividend policy / value literature, a brief review of which
is presented in Chapter II. Table 11.1 provides a schematic
representation of the development of the literature up to
the point where the two investigative fronts in this study
became distinctly identifiable as separate sub-topics.

Chapter III provides a description of the Granger
causality methodology employed in both parts of this study,
along with some observations on its specific requirements
and limitations. Chapters IV and V each relate to one of
the two empirical questions examined in this study. In
each, the literature and methodology relating to the
appropriate part of the current study is further developed
and empirical results are presented. These two sections are

designed to stand alone in the sense that each includes its

own discussion of the conclusions to be drawn from the

empirical work.

O

cpppte; II

to: ture Co 0

ca Cha ers

ev o v o c a d V In t ature

Since Miller and Modigliani’s [1961] landmark work
demonstrating that dividend policy is irrelevant in perfect
capital markets, the dividend policy debate has focused on
the documentation of market imperfections and the
examination of their implications. Early empirical studies,
some prior to Miller and Modigliani, typically regressed
share prices on dividends per share and retained earnings
(see Graham and Dodd [1934], Gordon [1959], and Benishay
[1961]). The consensus arising from these studies was that
dividends are significantly more important in explaining
prices than are retained earnings. Friend and Puckett
[1964] point out that this effect could be explained by a
negative correlation between earnings uncertainty and
dividend payout ratio. Furthermore, Friend and Puckett
[1964], as well as Beaver, Kettler and Scholes [1970], note
that the tendency of management to resist dividend cuts
could produce just such a negative correlation between
earnings uncertainty and dividend payout ratio. As a result
of this work it became clear that in future empirical
studies of dividend policy, particularly those involving
cross-sectional regressions, it would be necessary to
control for risk explicitly. With the development of the
capital asset pricing model (Sharpe [1964]) the tools with
which to operationalize a control of this sort became

available.

The first study of dividend policy to control for risk
through the capital asset pricing model was conducted by
Black and Scholes [1974]. In their classical empirical work
on the capital asset pricing model Black, Jensen and Scholes
[1972] had found evidence suggesting that the intercept term
in the market model is significantly different from zero.

As shown by the following quote, the search for an
explanation for the non-zero intercept in the market model
was a major motivating factor behind Black and Scholes

[1974]:

"... Black, Jensen and Scholes have found evidence
that high 3 securities tend to be overvalued and
low 6 securities tend to be undervalued. One
possible interpretation of this result is that
high 8 stocks tend to be low yield stocks, and
what is really happening is that low yield stocks
are overvalued and high yield stocks are
undervalued. If this were the case, then the
result should be associated with corporate
dividend policy rather than with factors such as
capital structure that affect the 8 of a
corporation’s common stock."

(Black and Scholes [1974], p. 8)

Thus, Black and Scholes’s study could be seen as an attempt
to explain perceived deficiencies in the performance of the
capital asset pricing model by including a term capturing
dividend policy effects. Black and Scholes attempt to
control for the various sorts of bias often present in
cross-sectional studies by constructing 25 portfolios with
stocks ranked on the basis of both dividend yield and 8.

The obvious issue of tax effects is avoided by arguing that

8

if corporations are able to adjust the relative supplies of
shares at different dividend yields to meet investor demand,
then they will respond by doing so until the possibility of
any advantage has been removed. Using data spanning the
period 1936 through 1966, Black and Scholes find that the
dividend policy coefficient is not significantly different
from zero. Thus, after adjusting for risk, the expected
returns on common stocks in the sample do not appear to be
further differentiable on the basis of dividend yield.
Although this work does not link dividend policy to the
anomalies observed by Black, Jensen and Scholes, it provides
more direct evidence regarding the linkage between dividend
policy and risk than had previously been available.

Litzenberger and Ramaswamy [1979] use the tax-adjusted
capital asset pricing model derived by Brennan [1970] to
critique the results presented by Black and Scholes. The
Brennan model is derived under assumptions of:

i) proportional individual taxes (non-progressive);

ii) certain dividends:

iii) unlimited borrowing at the riskless rate of

interest.

The model can be stated as:

E(Ri) - rf = hei + r(di-rf) (1)

where: E(Ri) = expected before-tax return on security i;

r} = before-tax return on the risk free asset;

i the systematic risk of security i;

i = the dividend yield on security i:
b = the marginal effect of systematic risk:

1 = the marginal effect of taxes.

Litzenberger and Ramaswamy assert that the tests performed
by Black and Scholes lack sufficient power to discriminate
between hypotheses of the form H5: r=0 and H5: r=0.5. They
concur with Rosenberg and Marathe [1979] that the portfolio
technique used to reduce bias, and the estimation method
(OLS), were major factors contributing to this problem.
Litzenberger and Ramaswamy modify the Brennan model to allow
for the taxation of dividend and interest income under a
progressive tax scheme. Although the derivation is lengthy
(see Litzenberger and Ramaswamy [1979] pp. 165-170), the
result is identical to the above model except that an
intercept is included and the tax coefficient, 1, takes on a
more explicit interpretation as "the weighted average of
individual's marginal tax rates less the weighted average of
the individual’s ratios of the shadow price on the income
related borrowing constraint and the expected marginal
utility of mean portfolio return" (see Litzenberger and
Ramaswamy [1979] p.171). Rather than using portfolio
grouping or instrumental variables to control for

measurement error in Bi, as in previous studies,

10

Litzenberger and Ramaswamy derive a maximum likelihood
estimator to obtain more efficient coefficient estimates
incorporating information contained in the estimated sample
variance of observed betas. A further refinement introduced
by Litzenberger and Ramaswamy is the use of an expected
dividend yield based on prior information in ex-dividend
months rather than a simple average monthly yield.

The results obtained by Litzenberger and Ramaswamy
indicate a strong positive relationship between before-tax
expected returns and dividend yields of common stocks. This
implies that, after adjusting for risk, the tax effect is
significant enough to make dividends undesirable, thus
causing investors to require a premium to induce them to
hold high dividend yield stocks. Litzenberger and Ramaswamy
construct a test to determine whether this effect is absent
in non-ex-dividend months, but no significant differences
are found.

Miller and Scholes [1982] take issue with Litzenberger
and Ramaswamy's handling of the information effect
associated with dividend announcements. When the
announcement date and the ex-dividend date occur in the same
month a potential problem arises because the return contains
both the information effect (the timing and magnitude of
actual dividends as compared to expected dividends) and the
tax effect, if in fact such an effect exists. Litzenberger

and Ramaswamy attempted to eliminate this source of bias by

11

introducing a revised dividend variable constructed as

follows:

i) If a firm declared prior to month t and went ex-
dividend in month t, then the expected dividend
yield was computed using the actual dividend paid
in t divided by the price at the end of the
previous month:

ii) If the firm both declared and went ex-dividend in
the same month, then the expected dividend yield
was computed using the last regular dividend,
going back as far as one year. If no such regular
dividend is found, or if the dividend was an extra
dividend, then the expected dividend yield was set
equal to zero.

Miller and Scholes argue, however, that there is an

additional category of firms not taken into account by the

screen described above: those that were expected to pay a

dividend and did not. They call this the case of "the dog

that didn’t bark." Two alternative methods of correcting
for this possibility are proposed:

i) use the dividend yield from 12 months previous as
the expected dividend yield;

ii) include only firms which declared their dividend
in advance.

Running the same regressions after screening the data in

this fashion Miller and Scholes find that the dividend

12

coefficient is much smaller and statistically insignificant
in both cases. Thus, they conclude that the correlation
between dividend policy and expected return found by
Litzenberger and Ramaswamy is spurious and may actually
reflect a signalling phenomenon instead.

Responding to these concerns, Litzenberger and
Ramaswamy [1982] reconstructed their original study taking
information effects into account in a more explicit way. In
order to achieve this, they developed an alternative method
of estimating expected dividends using a pooled time series-
cross sectional regression with the most recent dividend
yield as an explanatory variable, and a system of dummy
variables to capture the periodicity of the dividend
payments. The prediction rule is constructed in such a way
that it relies entirely on information that would be
available to investors ex-ante. Since it more closely
approximates the system by which individuals are thought to
generate expectations, this method has considerably more
intuitive appeal than the naive model used in Miller and
Scholes. The results obtained by Litzenberger and Ramaswamy
using this model suggest once again that the dividend policy
coefficient is positive, less than unity, and statistically
significant. These findings are consistent with a possible
tax-clientele effect. Further evidence presented in this
study suggests that the relationship between expected return

and dividend yield is non-linear. This is consistent with

13

the findings of Litzenberger and Ramaswamy [1979,1980].

The studies presented here constitute the mainstream of
the literature dealing with the relationship between
dividend policy and value. The issues dealt with in the
current study are off-shoots of this body of literature. As
such they are impacted by, and have an impact on, the
continuing debate concerning dividend policy and value.
Reviews of the literature specific to the dividend-
investment and dividend-risk questions are presented in the
respective empirical sections in which each of these

empirical issues is taken up.

14

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Methodolo

16

ed a n o Ca t

The methodology developed by Granger [1969,1980],
applied in the context of vector autoregressions on a firm
by firm basis, provides a way of testing for both the
direction and magnitude of causal relationships between two
or more time series. Since this methodology does not
require the specification of a structural model it is not
subject to many of the criticisms which have plagued
ysimultaneous equations models employed in similar
situations.

Chow [1983] begins his treatment of Granger causality
by noting that: "A favorite saying in regression analysis is
that regression can measure the degrees of association
between variables but cannot confirm causation" (see Chow
[1983], p.212). Nevertheless, in economics and other areas
of research this is a topic of sufficient importance that a
great deal of effort has been devoted to providing an
operationally useful definition of causality. Clearly, one
must expect that in order to be operational within the
framework of regression analysis any such definition must
involve restrictions on both its use and interpretation.

Granger [1969,1980] provides a definition of causality
based on three underlying principles which are reiterated
and expanded in Granger and Newbold [1986]:

Axiom A: The future cannot cause the past. Strict

causality can only occur with the past

17

causing the present or future.
Axiom B: A cause contains unique information about an
effect that is not available elsewhere.
Axiom c: All causal relationships remain constant in
direction throughout time.
Then, following the notation of Granger and Newbold, if we
let F(BIA) denote the conditional distribution of B given A,
and we let {It denote all the information in the universe at
time t, it is possible to construct a probabilistic
definition of causality.
In an analytical sense the proposition that At causes
In is associated with the following inequality (Granger and

Newbold equation 7.3.1):

F(Bmlnt) 7e F(Bmlnt-At) for all k>0 (2)

If inequality (2) holds, and (it-At denotes all the
information in the universe except Arr then A.t is said to
"cause" Bt in the Granger [1969,1980] sense.

Although this definition is intuitively pleasing, the
fact that we cannot incorporate all the information in the
universe into an empirical study means that it can only be
made operational in an empirical context after great
simplification. Granger [1980] suggests the following
solution. Suppose there is available at time t a limited

information set.J} consisting of terms of the vector series

18

2t. Then.J} can be considered a proper information set with
respect to Bt if Bt is included in 2,. Suppose also that 2,
does not include any elements of Aqiand that the augmented
information set J}' consisting of the union of ztiand At

exists. Then we can phrase an operational definition of

causality as follows:

F(BMIJt') 7e F(BmIJt) for all k>0 (3)

In this case we have simply agreed to limit all the
information in the universe to a subset J}' which can
reasonably be expected to have a bearing on the situation
under study. If inequality (3) holds then AW can be said to
be a EMILE cause of 8,. That is, the series At
contains unique information which helps to characterize
future realizations of 8,. This particular limited form of
causality is referred to throughout the literature as
’Granger causality’ or ’Wiener-Granger causality’. It is
usual to implement equation (3) with k=1.

It should be noted that an important precondition for
appropriate implementation of this methodology is that the
processes generating time series At and Bt are stationary.
The type of stationarity referred to here is sometimes
called weak stationarity or covariance stationarity. Harvey
[1990] defines a covariance stationary process as one which

exhibits the following characteristics:

19

i) The mean is independent of t:

ii) The variance is independent of t;

iii) Each autocovariance, E(ete.) , depends only on the

difference between t and 8.
Thus, a stationary process has a mean and variance which are
not time dependent, and the covariance between values
generated by the process at any two points in time depends
only on the time between these two realizations of the
process and not on time itself. Among other things, these
conditions imply that the time series under consideration
must not have trends or fixed seasonal patterns. In
general, covariance stationarity can be achieved by
differencing, log-differencing, or applying a Box-Jenkins
filter with a suitable number of autoregressive, moving
average and differencing terms. Non-stationarity can give
rise to spurious causality findings if a trend is involved
(see Kang [1985]), or can obscure a causal relationship even
in the absence of a trend.

Several alternative tests for stationarity have been
proposed in the literature. Initially, the possibility of
non-stationarity was investigated in a rather ad hoc way by
examining autocorrelation coefficients in an attempt to
verify that there were no systematic trends in the data.
More comprehensive methods of testing for non-stationarity,
based on the fact that the autoregressive (AR)

representation of covariance stationary processes can

20

contain no roots less than unity, were developed by Dickey
and Fuller [1979]. The ’augmented' Dickey-Fuller test} is
the method of choice in much of the empirical literature
(see for example Rose [1988], or Wilcox [1989]). This test
may include a drift term (intercept), and, by including
additional lags, can be made robust to autocorrelation of
order greater than one. The test statistic is computed from

the following regression:

P
(l-L)3{t = a + B)!“ +:12:::"i(1-L)YH + 6‘: (4)

where Y, is the series being tested, L is the lag operator,
and p is the number of lags of order greater than one
included in the test. Then, modeling Y} as an AR(p+1)
process, the hypothesis that one of the p+1 roots of the
characteristic equation is one can be tested by computing a
’t-like’ statistic consisting of fl/SE(B). An alternative
test statistic that is sometimes used is 3 x T, where T is
the number of observations in the time series. The
distribution of both these statistics is tabulated in Fuller
[1976]. More recently, Schmidt [1990] has shown that the
critical values of these statistics are also sensitive to
drift, and converge to the t distribution as the drift
parameter increases. Using Monte Carlo simulations, he
retabulates the critical values by series length and
standardized drift. Since the critical values of the test

21

statistics are strictly decreasing with respect to drift, a
stationary process exhibiting some drift may not 'look’
stationary when evaluated against Fuller's original critical
values.

Phillips [1987] has demonstrated that for certain kinds
of dependence in the error term in equation (4), such as
that generated by an autoregressive integrated moving
average process (ARIMA), the Dickey-Fuller statistic may be
biased. He suggests modifications which produce statistics
with the same asymptotic distribution, but which are robust
to ARIMA processes and those exhibiting conditional
heteroskedasticity.

Although the modifications Suggested by Phillips have
been shown to be effective, higher order lags are required
in order to detect such differences. Since the lengths of
the data series in the current study are at most 38 (i.e.
depending on differencing and the number of lags chosen),
the possible gains resulting from application of the test
suggested by Phillips are outweighed by the obvious decline
in estimational efficiency which would result. Under these
circumstances the ordinary Dickey-Fuller test (equation (4)
with p=1) is a more appropriate choice. Furthermore, to
avoid having to compare the results for each firm to a
potentially different critical value, zero drift is assumed
in evaluating the test statistics. As noted above, this

actually amounts to the imposition of a more stringent

22

stationarity condition.

Although Granger’s axioms establishing a basis for
identifying causality in a multiple regression framework
have stood the test of time, there have been several
attempts to improve the operational framework for causality
testing. For example, Sims [1972] suggests regressing Bt<n1
past and future values of A‘,‘the suspected causal variable.
If unidirectional causality exists from At to Bt then, by
Axiom A, we would expect that the coefficients of the
forward shifted.A& series would be insignificantly different
from zero. Thus, the hypothesis that At causes Bt can then
be tested by computing a block F-statistic for the
significance of the coefficients of the leads of At.
Although this approach provides a useful additional
perspective on causality testing techniques, is not adopted
in the current study because: i.) a data series of greater
length would be required to achieve sufficient degrees of
freedom for statistical significance; and ii.) the direction
of causality can be adequately established in the framework
of Granger's original vector autoregressive parameterization
of the causality testing model.

Nevertheless, Granger’s method of testing for causality
has not been without its detractors. Granger and Newbold
[1986] note that:

"It has been suggested, for example, that

causation can only be accepted if the empirical

evidence is associated with a complete and

23

convincing theory explaining how the cause
produces the effect. If this viewpoint is taken
then ’smoking causes cancer’ would not be
accepted."

(Granger and Newbold [1986], p.222)

While this view may impose too restrictive a standard, the
possibility that a variable that is in the dataset may proxy
for something else that is not in the dataset and is the
real cause of observed behavior does impose limitations on
the interpretation of results. Granger [1980] suggests an
alternative, middle of the road, essentially Bayesian
viewpoint. This approach recognizes that in any
investigation one generally has some prior belief about the
theory under consideration based on past information. If
data is gathered, screened and hypotheses tested, then as a
result one may update one’s belief regarding the validity of
the theory in question. It is unlikely, however, that one’s
posterior probability estimate will go to precisely unity,
or for that matter, precisely zero. Rather, the evidence
that emerges from the analysis tends to move one’s belief
some undisclosed positive or negative distance along a
continuum, with the result never quite attaining either
unconditional extreme. Thus, the results of Granger
causality tests are most appropriately viewed simply as
evidence, without imposing an ’if and only if’ condition.
The strength of this evidence should be evaluated not only

on the basis of statistical significance, but also in the

24

broader context of appropriateness of model specification
given the data environment in question.

This methodology has been widely used in empirical work
both in economics (see for example Sims [1972], Thornton and
Batten [1985] and Christiano and Ljungqvist [1988]) and in
finance (see Smirlock and Marshall [1983] and Bar-Yosef,

Callen and Livnat [1987]).

25

26

nt de nde ce

 

V' In 119‘

Since Miller and Modigliani [1961] put forward the
proposition that in perfect capital markets the investment
and financing decisions of firms are independent, there have
been many attempts to test the empirical validity of this
principle. Some of the significant early work in this area
was performed by Dhrymes and Kurz [1967], and Fama [1974].
The conclusions of these studies, however, are very
different.

Dhrymes and Kurz [1967] developed a theoretical model
consisting of three simultaneous equations representing the
dividend, investment and external financing decisions.
Their sample consists of 181 firms for which data were
available between 1947 and 1960. Data sources consist of
balance sheets and income statements appearing in Moody’s
Manuals. A detailed argument for the use of full
information estimation techniques is presented. Although
one of the objectives of this study is ostensibly to test
the dividend-investment separation principle empirically,
the dependence of these relationships is assumed a priori,
as evidenced by the following statement:

"Clearly dividend disbursals and investment

outlays represent competing demands on the

resources available to the firm; thus it would be

quite plausible to suppose that the investment

activities of the firm will be affected by its

27

dividend activities; postponement or curtailment

of investment could conceivably result because of

inability of the firm to carry out a given

investment program, ’optimally’ determined by some

’rational’ criteria, and at the same time continue

to make ’satisfactory’ dividend payments."

(Dhrymes and Kurz [1967], p. 435)
This dependence is also explicitly assumed in the
specification of the model. Although some theoretical
assumptions are necessary within the context of a
simultaneous equations model in order to allow for parameter
identification, they should not relate to anything integral
to the question under study. Allowing presuppositions of
this sort to affect the specification of the model
constitutes a serious error, and may lead to some bias in
the interpretation of results. Dhrymes and Kurz [1967]
reject the results obtained from single equation techniques,
accepting instead those obtained using a simultaneous
equations approach. They conclude that:

"the dividend impact on investment is quite

pronounced and consistently negative and

significant (except for 1957 and 1960, both peak

years)."

(Dhrymes and Kurz [1967], p. 460)
The investment term is also found to be significant in the
dividend equation. These conclusions are extremely suspect
due to the concerns raised above. However, if one accepts
the assumptions under which these results were obtained, bi-
directional causality is implied.

Fama [1974] argues that the Dhrymes and Kurz model is

28

misspecified. He points out that both the theory and the
data used by Dhrymes and Kurz are more consistent with time-
series models applied to individual firms. Dhrymes and
Kurz, however, use cross-sectional regressions, reestimating
the parameters annually. The coefficients of the
explanatory variables are therefore the same for all firms.
Fama contends that:

"If dividends are correlated with other

explanatory variables in their investment

equation, then including dividends in the

investment regressions may just be a way to adjust

in part for differences among firms in the

coefficients of other variables. A similar

phenomenon may arise when investment is included

in the cross sectional dividend regressions."

(Fama [1974], p. 315)
Using Compustat data on 298 firms for which complete
information was available for the entire 1946-1968 period,
Fama applies both simultaneous and single equation methods
to data for individual firms and finds no significant
dividend policy effects in either case. In terms of
efficiency, the single equation technique is marginally
superior. Fama interprets these results to support the
conclusion that:

"...there is no systematic evidence for the type

of jointness or interdependence in the year-by-

year dividend and investment decisions of firms

that requires a simultaneous equations model."
(Fama [1974], p. 315)

Thus, Fama rejects both the methodology and the conclusions

29

of Dhrymes and Kurz. Instead he concludes that whatever
imperfections are present in the capital market are not
sufficient to justify the rejection of the hypothesis that
dividend and investment decisions are independently
determined.

In a more recent, frequently cited study, Smirlock and
Marshall [1983] use Granger [1969,1980] causality methods,
discussed above in Chapter III, to test for the presence of
a causal relationship between dividends and investment. If
we assume symmetric lags, this methodology is best
operationalized in the context of a vector autoregression.
We can state the two lag specification of the model in

vector autoregressive (VAR) form as follows:

yt = A + 81 yt-I + 02 Yt-z + Ct (5)
Where:
INV 0 <2 8. e
t o i t
yt= A: OI: ‘ C:
DIVt r0 6i I‘i p,

In the bivariate case, this reduces to the following two

regression equations:
2 2

INVt = a0 + z az,mvH + .2 aonvH. + 6t (6)
i=1 j=1

30

2 2
DIV, = r0 +.2 erIvM. + 2 6,INV,_, + u, (7)
j=1 i=1

The two lag specification of the model appears
justifiable both on the grounds of theory and of data
availability. Since the relationship being tested is one
which theoretically should not exist at all, and which, if
it does exist is most likely to be strictly contemporaneous,
it would seem that two lags of the annual data series should
be more than sufficient to detect any causal relationship
which might exist. Furthermore, in light of the fact that
the data series is extremely short for time series work,
i.e. n=20, increasing the number of lags in the model is not
a viable alternative. Thus, there is nothing to cavil at in
the setup of the Granger causality model and the same
specification of the model is carried over to the empirical
testing performed in the current study.

There may be cause for concern, however, in Smirlock
and Marshall’s contention that this methodology is
appropriate even though, as Granger [1980] points out, it is
incapable of identifying causal relationships that are
strictly contemporaneous. Smirlock and Marshall dismiss the
possibility that there may be a contemporaneous underlying
causal relationship on the grounds that:

"As a practical matter, contemporaneous causality

from dividends to the investment decision is

virtually impossible since a lengthy evolution

31

from planned to actual expenditures has been

verified in studies of capital investment."

(Smirlock and Marshall [1983], p.1661)

The sample used consists of firms included in the
Standard and Poor’s 400 index and which met the following
criteria for each of the years in the sample period 1958-
1977:

i) data were available for dividends, investment

and common shares outstanding for every year;

ii) dividends were paid in every year;

iii) the firm had positive investment expenditures

in every year;
iv) the firm did not change its fiscal year
during the sample period.
These screens resulted in a sample consisting of 20 annual
observations for each of 194 firms.

Smirlock and Marshall conduct Granger causality tests
on both firm specific and aggregate data. Aggregate data is
obtained by simply summing the dividend and investment
variables across the firms in the sample for each year in
the study. Causality tests are then conducted by estimating
equations (6) and (7) above on the individual firm series
and on the aggregate series. They report the following
fractiles of the F-statistic for block exclusion tests of

dividends from equation (6) and investment from equation

(7):

32

d M ° 0 Te 3
a - t c
Critical Value of Fwwmzzn3== 3.81
2121512119.: v me
10 0.05 0.04
25 0.18 0.12
Percentile 50 0.59 0.39
75 1.22 1.07
90 2.19 2.04

(Smirlock and Marshall [1983], p. 1664, Table II)

In the aggregate case Smirlock and Marshall report much

lower F-statistics:

i ck nd ° e e Tests
a s t - at c
Critical Value of Fa=0.05,2,13 = 3.81

pigidends ves nt
F-Statistics 0.32 0.04

(Smirlock and Marshall [1983], p. 1663, Table I)

Thus, Smirlock and Marshall find no statistically
significant evidence of Granger causality in either
direction. For the individual firm data Smirlock and

Marshall state unequivocally:

"The F-statistic corresponding to the null hypothesis
of no Granger-causality achieves significance at the
0.05 level for no more firms than would be expected by
chance, for either direction of Granger-causality. At
the 90th percentile the null hypothesis is always
[emphasis added] accepted. These results provide
strong support for the view that the firm’s dividend
and investment decisions are separable."

(Smirlock and Marshall [1983], p.1664)

There are several troubling questions, however, which remain

33

unanswered. First, the small number of degrees of freedom
suggest that these tests may lack discriminatory power. The
seriousness of this concern is not immediately clear,
however, this question is addressed later in the current
study by means of simulations. It should be noted that at
the time of Smirlock and Marshall’s study, additional time
series observations were not available, so this problem
could not have been easily remedied. A second area of
concern is the fact that, although statistically
insignificant, the test statistics given are systematically
stronger in the direction of Dividend-Investment causality
than in the direction of Investment-Dividend causality. The
failure of this study to detect what we expect on the basis
of theory, i.e. causality running from investment to
dividends, casts doubt on its ability to detect that which
we may suspect, i.e. causality running in the opposite
direction, but which theory does not support. This concern,
while possibly also related to the shortage of data, is
clearly a very significant one and is sufficient to render
Smirlock and Marshall’s assertion that "the above results
provide strong support for the view that the firm’s dividend
and investment decisions are separable" insupportable.
Another study conducted around the same time with
similar intent but different methodology is Partington
[1985]. This study examined the question of potential

dividend-investment causality by surveying senior managers

34

of 152 large Australian firms representing a cross-section
of the largest 300 firms on the Sydney Stock Exchange
Industrial list; 93 responses were obtained. The survey was
structured to elicit information regarding perceived
dividend policies. As with other survey based
investigations there are behavioral factors present in this
study which make interpretation of the results somewhat
difficult at times. In an effort to clarify matters, an
attempt is made to gather data relating not only to the
frequency and circumstances of different dividend,
investment and financing policies, but also the motivations
behind them. Partington uses this data to test the null
hypothesis that dividends are not determined as a residual.
The survey is segmented according to whether or not external
financing is seen to be a viable alternative in the case
under consideration. In the cases where external financing
was raised 39 percent of the executives responding said that
there were times when dividends were still given priority
and some restrictions were applied to investment spending.
In cases where no external financing was raised 39.1 percent
responded in this way. Thus, although for the most part
Partington’s findings support those of Smirlock and
Marshall, he finds that for a significant minority of firms
there are at times perceived conflicts between dividend and

investment policy. He sums up his findings as follows:

"The evidence suggests that independence between

35

dividend and investment policies is usual, but not
universal. It appears that there are occasions when
firms adopt simultaneous dividend and investment
policies, or even give dividends priority over
investments....Perhaps more surprising, in the light of
Miller and Modigliani’s [1961] arguments for the
primacy of the investment decision, is the evidence
that, when a conflict occurs, the dividend decision is
more likely to dominate the investment decision."
(Partington [1985], pp. 540-541.)

Partington points out that theoretically conflicts of this
sort should be resolved by resorting to external financing.
The fact that managers apparently do not universally
perceive external financing to be an alternative that is
available to them at all times is surmised to be due to the
presence of market imperfections such as transactions costs
and informational asymmetries.

Although Partington’s study suggests that dividend-
investment independence may not be universal among firms,
the small number of observations in the data set and the
subjectivity of the survey data make these results far from
conclusive. Nevertheless, it is troubling to note that
Smirlock and Marshall do not find evidence of the same
minority of firms giving dividends priority over investment.
In an attempt to resolve this discrepancy we return to a
consideration of the previous work of Smirlock and Marshall.

In addition to the problems mentioned earlier, there is
another serious obstacle to the interpretation of the work
of Smirlock and Marshall; that is, the possibility of
dividend-investment dependency in a dividend generating

36

process that is strictly contemporaneous within the context
of the temporal screen. As pointed out by Smirlock and
Marshall Granger causality methodology is incapable of
detecting such dependencies. The current study seeks to
demonstrate through a series of simulations that a wholly
dependent dividend generating process of the kind proposed
by Lintner [1956], and given empirical support in Fama and
Babiak [1968], can produce causality test results of a sort
indistinguishable from those obtained by Smirlock and
Marshall. This is followed up with an empirical test using

the longer data series now available.

a ed iv ds a ves ‘ :

There are numerous alternative approaches which could
be taken to simulating dividends and investment while still
allowing for the kind of explicit contemporaneous dependence
which we wish to model. The objective of the simulation
segment of this study is to determine whether it is possible
to identify a causal relationship between dividends and
investment in a series consisting of only 20 observations.
In this context the Lintner model of dividend policy has
some attractive features. Specifically, since dividends are
always chosen first, with investment determined as the
residual, this constitutes the most extreme case of a causal
relationship running from dividends to investment. The

implication is that if Granger causality methods cannot

37

consistently detect a causal relationship in series of
length 20 specifically constructed to conform to the Lintner
model, their usefulness in detecting weaker relationships
between series of this length is suspect.

Apart from the rather implausible Lintner relationship
to be imposed between the simulated dividend and investment
series, it is important that the series themselves be
simulated along very plausible lines. That is to say, the
behavior of the simulated series should have some empirical
support. One very straightforward model which meets this
description was suggested by Fama and Babiak [1968]. Fama

and Babiak began with the following model:

D, - D,,1 = a + fi,D,,1 + 82E, + 83A, + u, (8)
II : dividends per share during year t
EH : earnings per share during year t
A, : depreciation per share during year t
u. : a random disturbance term

After some empirical testing they conclude that the
coefficient of the A, series is insignificant and they
estimate the values of the other coefficients in the model

as follows:

D - D- = -0.45D,_1 + 0.1513, + u, (9)

u = 0.2u,_1 + v (10)

t

38

While Fama and Babiak simulate earnings as an AR(1) series,
a more fundamental approach is taken here. Instead,

earnings, E (are generated from the following

t!

relationships:
E, = r,1<,_1 (11)
I, = E, - D, (12)
K, = K,_1(1-6) + I, (13)
where: K, : Capital at time t: K0 = 20

I : Investment at time t
r' : ROA at time t: distributed N(10%,25%)

6 : Depreciation at time t; 6 = 5%

The key relationship here is equation (12) which specifies
that in each period investment is determined as the residual
of earnings after dividends have been determined. Equations
(11) and (13) provide the dynamic link between observations
in the simulated time series. The objective here is to
provide a set of relationships which allow for a credible
simulation of the dividend and investment series, while
avoiding complexity on the grounds that it could introduce
confounding factors. Note also that Do== 0.05, and minimum
dividends are constrained to be 0.05. The attractions of
this parameterization of the simulation model are:

i) Since investment is determined as a residual

item only, this is a very clear violation of the

39

separation principle. However, since this
relationship is contemporaneous we can demonstrate
that it will not be detected in a test for
causality.
ii) There is a secondary relationship which is
clearly evident in the above equations. This
period’s dividends affect investment which in turn
affects next year’s capital. Next year’s capital
affects next year’s earnings which affects next
year’s dividends. Thus, the Lintner model does
imply an indirect underlying causal relationship.
Since this relationship via earnings is non-
contemporaneous we can hope to identify it by
means of a causality test if it is strong enough.
Hence, the simulation, as outlined above, constitutes a test
of the ability of the methodology employed by Smirlock and
Marshall [1983] to detect a violation of the separation
principle of the sort implied by the Lintner model of
dividend policy. Since managers are widely believed to
violate this principle, this represents a critique of the
efficacy of the Smirlock and Marshall methodology in

identifying this behavior.

esu :
The above simulation was run with the series length set

equal to 20 to match Smirlock and Marshall, and n=10,000.

40

Initially nine simulations were run, using three values for
02(v,) (0.001, 0.010, 0.100), and three values for the
coefficient of earnings (0.10, 0.15, 0.20). A listing of
the code used to generate the simulations is provided in
Appendix IVA. Figures IV.1 and IV.2 provide a visual
comparison of simulated and actual dividends. In order to
achieve stationarity it was necessary to take log first
differences of the dividend series, and first differences of
the investment seriesz. Selected percentiles of the
Dickey-Fuller test statistics on the transformed series are
presented in Tables IV.1-IV.3. Results significant at the
a=0.05 level are designated by an asterisk. In all cases
the series are shown to be statiOnary to within a small
margin of random error.

Causality tests were conducted as described in Chapter
III above. The regression equations involved in the test
were identical to equations (6) and (7) above with n and m,
the number of lags, set equal to 2. For series of length 20
this resulted in causality test F-statistics with 2 degrees
of freedom in the numerator and 12 degrees of freedom in the
denominator. Selected percentiles of these statistics are
presented in Tables IV.4-IV.6.

These results demonstrate very clearly that for all
values of the earnings coefficient and can“) covered by the
simulation, a causal relationship of the Lintner type cannot

be unambiguously identified in a series of length T=20. It

41

is clear that the discriminatory power of the test is
positively related to both the earnings coefficient and the
c3(v,) over the range of values covered in the simulations.
This effect is consistent with intuition in the sense that
we expect the lagged effects of the built-in contemporaneous
dependencies to be more easily identifiable when the signal
is stronger. Increases in both the coefficient of earnings
and the 020“) contribute to the strength of the lagged
signal in the simulation model.

Further simulation runs included a range of values of
the autocorrelation coefficient (-0.2 and 0.0 as well as the
original value of 0.2) in equation (10). Selected
percentiles of the resulting F-statistics are shown in
Tables IV.7-IV.9. We conclude that the results shown
earlier are robust to these changed assumptions. That is,
even with a strong non-contemporaneous secondary element
causality cannot be unambiguously detected in a series of

length 20.

mm:

The evidence from the first series of simulations shows
that the variance of the error term, and to some extent also
the magnitude of the coefficients have an impact on the
discriminatory power of the causality test. Because of this
an attempt was made to empirically verify the results of

Fama and Babiak [1968].

42

The current study significantly updates the data set:
254 firms are included for which both dividends and net
income were reported for every year during the interval 1952
- 1989. Screens were implemented to exclude banks,
utilities, insurance companies, ADR’s, limited partnerships
and real estate investment trusts; in short, firms for which
the regulatory environment would tend to make dividends
particularly sticky. The results of estimating equations
(9) and (10) on a firm by firm basis are presented in Table
IV.10. Histograms are provided in Figures IV.3 - IV.14.
Although there are a wide range of values for each
coefficient, it is worth noting that the median values of d
and B are smaller than those found by Fama and Babiak, and
the median value of 6 is larger than expected.

In an effort to resolve this discrepancy the sample
period was split into two subperiods, 1952 - 1970 and 1971 -
1989, and the model estimated for each subperiod. These
results are presented in Table IV.11. Applying the same
screens as before results in somewhat larger samples in both
subperiods; 263 firms for 1952 - 1970 and 864 firms for 1971
- 1989. Although the median of d and B in the first
subperiod do have the same sign as those provided by Fama
and Babiak they are much smaller in magnitude. For the
second subperiod the d and 3 do not appear to be
significantly different from zero. However, for both

subperiods d is many times smaller than it was when

43

estimated for the entire sample period. This suggests the
presence of non-linearities and/or non-stationarity in the
data. Because the objective of this part of the study is to
generate a plausible simulated dividend series rather than
to predict actual dividends, these results are accepted with
the acknowledgement that although adequate for the purpose
used here, it would not be appropriate to use the Fama-
Babiak model to predict future dividends. While the
estimated parameters allow us to generate a simulated
dividend vector that could be drawn from the same
distribution as actual dividend realizations, it is unlikely
that the values taken by the simulated series will closely

parallel the realized values for any one particular firm.

Pu im tio e ults:

The fact that the empirically estimated parameters of
the dividend generating equation differ so markedly from
those reported by Fama and Babiak may cast some suspicion on
the validity of the results drawn from the earlier
simulation. In order to address this concern several
additional simulations were run using, respectively, the
median, mode and mean of the estimated 6, 3, 0 and 6. These
simulations were conducted for the entire 1952 - 1989 sample
period, and for both of the subperiods (1952 - 1970 and 1971
- 1989). Selected percentiles of the results are shown in

Tables IV.12 - IV.17. Histogram representations of these

44

results are presented in Figures IV.15 - IV.32. An
examination of these findings reveals that given the
empirical relationship between dividends, lagged dividends
and contemporaneous earnings, the secondary effects of a
contemporaneous causal relationship between dividends and
investment (a la Lintner) are no easier to detect than they
were under the parameters estimated by Fama and Babiak. In
fact a careful comparison of these simulation results with
those from the original simulation suggest that even in
cases where d is quite large there is no discernable
increase in discriminatory power. Given the findings from
the earlier simulation it seems clear that this phenomenon
is due to the much lower coefficient of the earnings term in
all cases covered in the second series of simulations.

The only conclusion to be drawn here is that if in fact
the empirical relationship between dividends and investment
is purely contemporaneous in the Lintner sense, given the
nature of the empirical relationship between dividends and
earnings (described in the previous sections) we truly
cannot expect to detect any signs of this relationship in a

test for Granger causality.

at v d - ves e us :
The sample used in testing for dividend-investment
causality includes all firms on the Compustat Annual tape

for which both dividends and the ending balance of the

45

property, plant and equipment account were reported for
every year during the interval 1952 - 1989. Screens were
implemented to exclude banks, utilities, insurance
companies, ADR’s, limited partnerships and real estate
investment trusts: again, firms for which the regulatory
environment would tend to make dividends particularly
sticky. The dividend series used consists of the amount of
common stock dividends paid in each year. Since several
significant changes in the format and content of sources and
uses of funds disclosures required by the Financial
Accounting Standards Board occurred during the sample
period, consistent investment data was not readily
available. In order to avoid the possibility of obtaining
test results driven by the method of disaggregating the
accounting data for the years in which full information was
not disclosed, a simple proxy for net investment was
constructed by first differencing the property, plant and
equipment account. This had the effect of reducing the
length of the series to the 37 years covering 1953 - 1989.
The first attempt to test the hypothesis that dividends
and investment are causally related was conducted in the
spirit of a replication and extension of the work of
Smirlock and Marshall to the significantly longer data
series now available. Since Smirlock and Marshall used a
log differencing transformation on both the dividend and

investment series it was necessary to screen for firms which

46

had strictly positive dividends and investment in all years
from 1953 - 1989. However, no firms met these criteria for
the period 1953 - 1989. In fact no firms met these criteria
for any sample period starting between 1953 and 1974 and
ending in 1989. Only one firm passed the screen for sample
periods starting between 1975 and 1980 and ending in 1989.
Clearly, generalizable results cannot be obtained from a
sample consisting of only one firm and a time series of
length 15. Thus this particular approach to the problem had
to be abandoned3.

The second approach adopted involved relaxing the
screening restrictions to allow firms that had negative or
zero investment and zero dividends in some years. This
resulted in a sample of 220 firms for which there were no
missing observations between 1953 and 1989.

Initially, causality tests were performed on the raw
series (levels). Although some indications of a causal
relationship were found they were deemed to be inconclusive
due to the very weak stationarity test results. Table IV.18
presents selected percentiles of both Dickey-Fuller and F-
statistics for the raw series. Histograms of these results
are presented in Figures IV.33 - IV.36.

The first differences of these series were found to be
stationary in most cases. Table IV.19 presents stationarity
test and causality test statistics for the differenced

series. It can be seen by examining these results that the

47

F-statistics for the significance of lagged dividends in
predicting investment, i.e. in equation (6), meet the
critical value for significance at the a=0.05 level all the
way down to the 75th percentile. In fact 61 of the 220
firms in the sample exhibit F-statistics greater than the
critical value at the a=0.05 level. Under the null
hypothesis of no causal relationship between dividends and
investment we should observe such F-statistics only at the
95th percentile and above. This could be viewed as sampling
from a binomial distribution with p=0.05. We can obtain
some insight regarding the overall significance of the test
results by evaluating the complement of the cumulative
binomial probability, P{N>k}, for the number of significant
observations of the F-statistic found. This is the
probability, under the null hypothesis, of finding a higher
frequency of significant F-statistics than that actually
observed in the sample of firms studied. Thus, it could be
viewed as a measure of the significance level of the
aggregate test results, with a lower probability
corresponding to greater significance.

The table below shows the frequency count of F-
statistics significant at the a=0.05 level for the 220 firms
in the sample. These F-statistics are for block exclusion
tests of all lags of the variable named. Thus, the F-
statistics for dividends relate to tests of the hypothesis

that lagged dividends are statistically significant in

48

explaining current investment. The corresponding cumulative
binomial probabilities, shown in the column to the right,
indicate that the distribution of F-statistics is
significantly different from what one would expect under the

null hypothesis.

e B - 9
niII2ranged_ssrissl_zzg_21rms
rfimuzz, = 3.33
Izgtatist__s 1:232:22! Bisenisl_£lNle
Dividends 0.0000
Investment 78 0.0000

An alternative, and potentially more efficient, means
of aggregating the statistics derived from the block F tests
performed on the individual firms is the xzigoodness-of-fit
test. In this test a frequency table of the sample F-
statistics, rather than a simple proportion, is used to test
the hypothesis that the distribution conforms to the F
distribution under the null. A,x? statistic greater than

the critical value indicates rejection of this hypothesis.

Z2 Goodness-of-git Tests
Sample Period 1953-1989

Ditterenced Bertes. ggg zirms

1 1-¢=0.95,df=19 = 30'“

F-stattgticg 5i
Dividends 276.9091 *
Investment 468.1818 *

49

Although the xF'test shows only that the distribution of
test statistics is significantly different from what it
would be under the null hypothesis, the direction of this
relationship is clear from the results shown in Table IV.19
and from the binomial test shown above. That is, the test
statistics are generally greater than those from the actual
F distribution. Thus, although we are not justified in
concluding that all firms exhibit Granger causality in the
dividend-investment relationship, the test results clearly
support the inference that a substantially greater than
random proportion of the firms tested do exhibit this
behavior. Figures IV.37 - IV.40 provide a visual
representation of these results in the form of histograms.
Note also that the goodness-of-fit test and Table IV.19
reveal evidence of even stronger causality going from
investment to dividends. However, as explained in the
introductory section, this is a less interesting result
since it is completely in accord with what theory would
suggest, and implies no suboptimality in management policy.
One potential concern with the above results is the
possibility that the findings could be driven by the firms
in the sample which did not exhibit stationarity even in the
differenced series. In order to address this issue the
sample was segmented according to whether or not firms met
the criterion for stationarity. The first group consists of

103 firms which passed the test for stationarity at the

50

a=0.05 level for both the dividend and investment series.
The second group consists of 117 firms for which either
dividends or investment failed to pass the test for
stationarity. The distribution of the causality test F-
statistics was then examined separately for each subgroup.
Selected percentiles of these distributions are presented in
Table IV.20. Figures IV.41 - IV.44 provide histograms
showing the same results visually. An examination of Table
IV.20 makes it clear that the causality test results
presented earlier are not driven by non-stationarity. In
fact, the F-statistics from the two subgroups are virtually
indistinguishable. Thus, the conclusion that dividends
Granger cause investment does appear to be very clearly
supported by the data, for a significant proportion of firms
in the sample.

At this point it may be of interest to examine the
characteristics of firms exhibiting Granger causality in the
relationship between dividends and investment. Table IV.21
provides a listing in order from highest to lowest F-
statistic of the 61 firms that met or exceeded the critical
value for dividend-investment causality at the a=0.05 level
of significance. These firms do not appear to exhibit any
immediately identifiable common characteristics apart from
the fact that they are predominantly large manufacturing
firms. Given the screening process, they are fairly typical

within the sample. It does not appear that there is any

51

significant clustering within industry groups. Perhaps the
most remarkable observation to be drawn from Table IV.21 is
the evident success of the firms listed: most are household
names. Clearly, requiring that firms in the sample release
financial statements for all years from 1952 - 1989 does
induce some bias toward successful firms. Repeating the
study using data from the Compustat Research tape is not a
viable alternative since for time series work the series
length used in this study, T=37, is already approaching the
minimum necessary for reliable inference. Thus, data from
firms which were in operation for only a part of the sample
period would not be useable. For this reason, we are
effectively limited to the conclusions that can be drawn
from the current data set. However, even taking into
account the survivorship issue it is remarkable that the
firms which exhibit the strongest dividend-investment
causality are such an entrenched part of the economy. While
there are several possible regulatory and/or agency
explanations for this phenomenon which could be fruitful
directions for future work, they are beyond the scope of

this study and are therefore not investigated here.

Con o :
While Granger causality techniques can be appropriately
used to demonstrate the existence of a causal relationship

between two or more time series, it is difficult to prove

52

conclusively that such a relationship does not exist.
Pierce and Haugh [1977] have shown that in order to achieve
this it is necessary to show that the cross correlations at
all lags are equal to zero". This result is in keeping
with what intuition would suggest.

The current study uses simulations in the initial phase
to explore the limitations of the relationships which one
can reasonably expect to identify in the context of Granger
causality methodology. The conclusion from this part of the
study is clear: given the empirical relationship between
dividends, lagged dividends and earnings, the methodology
employed in this study and the earlier study conducted by
Smirlock and Marshall cannot be used to rule out the
possibility of a contemporaneous causal relationship.
Furthermore, when a series of only 20 observations is used
the discriminatory power of the test is very weak. Having
established this fundamental limitation the current study
proceeds to an empirical test of the potential causal
relationship between dividends and investment. Granger
causality methodology is employed here as it is in the
earlier study by Smirlock and Marshall. However, the
availability of additional data makes it possible to
significantly update the data set. Using a series of 37
annual observations for each firm (i.e. after differencing
property, plant and equipment once), statistically

significant evidence of Granger causality from dividends to

53

investment is found in approximately 28 percent of the firms
in the sample. These firms do not appear to be clustered in
any particular industry group. The results of this study
are consistent with the survey results found by Partington
in studying 93 Australian firms. Because the current study
employs a much larger sample of firms and a more objective
methodology the results contribute significantly to the
credibility of Partington’s conclusions.

In the present study, screens were implemented to
exclude banks, utilities, insurance companies, ADR’s,
limited partnerships and real estate investment trusts; that
is, firms for which the regulatory or tax environment would
tend to make dividends and/or investment behave in ways
other than what one would expect under perfect or close to
perfect market assumptions. Given the screens applied to
the sample, it is difficult to imagine a particular set of
market imperfections which would make it optimal to allow
dividends to influence investment for any of the firms
included in the sample. If this assessment is accurate the
implication is that many of the largest domestic firms have
been managed in a way that is directly opposed to accepted
theory within the field of corporate finance. Although it
would be impossible to accurately assess the opportunity
cost of such suboptimal decision making, the magnitude of
the variables involved suggests that it would be

substantial.

54

We

This appendix provides a sample listing of the code
used to generate the simulations reported in the first part
of this study. All simulations were performed using RATS
(Regression Analysis of Time Series) software. On this page
a sample of the calling routine is provided. The following
pages provide a listing of the steps in the simulation
procedure itself.

Sgpp;g Qalting Bputipe:

* Program to Simulate Dividend-Investment Relationship with
* Contemporaneous Dependence

* SMIRLOCK AND MARSHALL’S APPROACH: MODEL: 1952 - 1989

*

environment noundefinederrors

bma(series=partial)

ieval runs=10000 :* set desired number of
iterations

ieval n=38 :* set desired series
length**

if n .ge. runs

ieval length = n
else

ieval length = runs+1
end if

all 0 length

output noecho

source dfunit.ext

source hist200.ext

source smr.ext

output echo

declare vector frc(7)

*

*Run #1: Median Values

clear frcdiv frcinv frcdfdiv frcdfinv bf_div hf_div bf_inv $
hf_inv bdf_div bdf_div bdf_inv hdf_inv

@smr n runs 63.617 0.0193 0.0035 0.272 frcdiv frcinv $

frcdfdiv frcdfinv bf_div hf_div bf_inv hf_inv $
bdf_div bdf_div bdf_inv hdf_inv frc

open copy f_a_med.f38

copy(org=obs,format=’(2f12.4)’) 1 7 frcdiv frcinv

open copy df_a_med.f38

copy(org=obs,format=’(2f12.4)’) 1 7 frcdfdiv frcdfinv

open copy a_med.h38

copy(org=obs,format=’(8f9.3)’) 1 200 bf_div hf_div bf_inv $
hf_inv bdf_div bdf_div bdf_inv hdf_inv

55

W:

* Procedure to Simulate Dividend-Investment Relationship
* with Contemporaneous Dependence

* SMIRLOCK AND MARSHALL’S APPROACH

*

*

PROCEDURE SMR n runs var_ dshk coef _d coef_ e a_ corr $
frcdiv frcinv frcdfdiv frcdfinv bf_ —div hf_ “div bf_ inv $
hf_ inv bdf _div hdf_ div bdf_ inv hdf_ inv frc

TYPE PARAM- n runs

TYPE REAL var_dshk coef_d coef_e a_corr

TYPE SERIES frcdiv frcinv frcdfdiv frcdfinv bf_div $
hf_div bf_inv hf_inv bdf_div bdf_div bdf_inv hdf_inv
TYPE VECTOR frc

LOCAL SERIES roa div inv earn capital dshock f_div $
f_inv df_div df_inv

*

* Define Remaining Simulation Parameters

output noecho

eval mroa = 0.15

eval var_roa = 0.00025

eval dep = 0.05

eval d1 = 0.05

eval initcap = 20

eval mindiv = 0.15

eval minratio = 0.5

*

* Set Up Simulation Equations for Random Draw

clear roa div inv earn capital dshock f_div f_inv $
df_div df_inv

set roa = 0.0

set dshock = 0.0

equation simr roa

# constant

associate simr 0 0 var_roa

# mroa

equation(noconstant) simd dshock

# dshock{1)

associate simd 0 0 var_dshk

# a_corr

simulate(setup) 2 n 1

# simr roa

# simd dshock

*

* Run Iterations of Simulation

do loop=1,runs

simulate

do t=l,n

I
if t==

56

eval earn(t)=initcap*roa(t)
eval div(t)=d1+dshock(t)
eval inv(t)=earn(t)-div(t)
eval capital(t)=initcap*(1-dep)+inv(t)
}
else
I
eval earn(t)=capital(t-1)*roa(t)
eval div(t)=coef_d*div(t-1)+coef_e*earn(t-1) $
+dshock(t)
eval inv(t)=earn(t)-div(t)
eval capital(t)=capital(t-1)*(1-dep)+inv(t)

}
if div(t) .1e. mindiv .or. capital(t) .1e. 3
initcap*minratio
{
eval div(t)=mindiv+abs(dshock(t))
eval inv(t)=earn(t)-div(t)
if t==
eval capital(t)=initcap*(1-dep)+inv(t)
else
}
}
end do t
*
* Transformation of Series and Dickey-Fuller Tests
set div = log(div(t))
smpl 2 n
diff div
diff inv
@dfunit(lags=1,ttest) div
eval df_div(loop) = dfstat
@dfunit(lags=1,ttest) inv
eval df_inv(loop) = dfstat
*
* Granger Causality Tests Performed on Transformed Series
output noregress
smpl 4 n
linreg(noprint) div
# constant div{1 to 2} inv{1 to 2)
exclude(noprint)
# inv{1 to 2}
fetch f_inv(loop) = cdstat
linreg(noprint) inv
# constant div{1 to 2} inv{1 to 2)
exclude(noprint)
# div{1 to 2}
fetch f_div(loop) = cdstat
display(unit=output) loop runs
end do loop

eval capital(t)=capital(t-1)*(1-dep)+inv(t)

57

i

* Sort and Save Selected Fractiles of Simulation Results
smpl 1 runs

order f_div

order f_inv

order df_div

order df_inv

eval frc(1)=0.05

eval frc(2)=0.10

eval frc(3)=0.25

eval frc(4)=0.50

eval frc(5)=0.75

eval frc(6)=0.90

eval frc(7)=0.95

do i=1,7

eval frcdiv(i)=f_div(fix(runs*frc(i)))

eval frcinv(i)=f_inv(fix(runs*frc(i)))

eval frcdfdiv(i)=df_div(fix(runs*frc(8-i)))
eval frcdfinv(i)=df_inv(fix(runs*frc(8-i)))
end do i

*

* Save Data for Histogram of Simulation Output
@hist bf_div hf_div f_div 1 runs

@hist bf_inv hf_inv f_inv 1 runs

@hist bdf_div hdf_div df_div 1 runs

@hist bdf_inv hdf_inv df_inv 1 runs

*

end

58

Table IV.1

stationarity of simulated Dividends and Investment, T=20
Smirlock and Marshall Approach

Dickey-Fuller statistics

Coefficient of Earnings = 0.10

 

Critical Value of DEW“,5 ":19 = -3.05
DF¢=0JO,n=19 = “2'67
g2(y,) = 0.901
Dixidends _n___I vestment
5 -3.2758* -2.5181
10 -3.3800* -2.8807
25 -3.5494* -3.4647*
Percentile 50 -3.7523* -4.1997*
75 -3.9602* -5.0835*
90 -4.1519* -6.0159*
95 -4.2726* -6.6599*
g2(v,) = 0.010
11111532an Manse);
5 -2.8118 -2.4661
10 -3.0006 -2.8249
25 -3.3171* -3.4337*
Percentile 50 -3.6834* -4.l786*
75 -4.0717* -5.0449*
90 -4.4122* -6.0060*
95 -4.6480* -6.7157*
02(v,) = 0.;90
Dividends Investment
5 -2.4894 -2.4368
10 -2.7224 -2.7726
25 -3.1421* -3.3324*
Percentile 50 -3.6709* -4.0018*
75 -4.2770* -4.8196*
90 -4.8856* -5.6888*
95 -5.2727* -6.3383*

59

Table IV.2

Stationarity of simulated Dividends and Investment, T=20
Smirlock and Marshall Approach

Dickey-Fuller statistics

Coefficient of Earnings = 0.15

 

Critical Value of DF,,,0.05',,,19 :- -3.05

60

Dcho.1o,n-:19 '2 ° 67
Q20“) = Q 991
Digiggpgs Investment
5 -4.4910* -2.8225
10 -4.6551* -3.1502*
25 -4.9525* -3.7367*
Percentile 50 -5.3114* -4.4540*
75 -5.6912* -5.2970*
90 -6.0656* -6.2203*
95 -6.2883* -6.8891*
9311, = 0.0
Dixidends Eminent
5 -3.8021* -2.8160
10 -4.0453* -3.1426*
25 -4.4888* -3.7187*
Percentile 50 -5.0074* -4.4234*
75 -5.5959* -5.2819*
90 -6.1466* -6.1476*
95 -6.5228* -6.7921*
92(2, = 0.
Diyidends I..__tme__nves nt
5 -2.6852 -2.6260
10 -2.9433 -2.9405
25 -3.4699* -3.4842*
Percentile 50 -4.1260* -4.1732*
75 -4.8814* -4.9822*
90 -5.6650* -5.8372*
95 -6.2063* -6.4719*

Table IV.3

stationarity of simulated Dividends and Investment, T=20
Smirlock and Marshall Approach

Dickey-Fuller statistics

Coefficient of Earnings = 0.20

 

61

Critical Value of DFMJS'M,’ = -3.05
DFa-o.1o,n=19 = “2'67
2101:9101].
t
Ipxestpent
5 -6.2807* -2.9948
10 -6.5272* -3.3125*
25 -6.9947* -3.8881*
Percentile 50 -7.5773* -4.5957*
75 -8.2240* -5.4056*
90 -8.8733* -6.2976*
95 -9.2543* -6.9286*
93.1,
Dixidends WW 8 men
5 -5.1451* -3.0338
10 -5.5128* -3.3157*
25 -6.1411* -3.8456*
Percentile 50 -6.8978* -4.5336*
75 -7.7463* -5.3382*
90 -8.6599* -6.2119*
95 -9.2219* -6.8509*
0201,) = 0,;99
01.11%an WV 8 nt
5 ~3.0695* -2.7035
10 -3.4000* -3.0053
25 -4.0463* -3.5143*
Percentile 50 -4.8566* -4.1515*
75 -5.8565* -4.9034*
90 -6.8788* -5.7544*
95 -7.5605* -6.3213*

Table IV.4

simulated Dividends and Investment, T=20
Smirlock and Marshall Approach
F-statistics from Granger Causality Tests
Coefficient of Earnings = 0.10

 

Critical Value of Fa=0.05,2,12 f 3.81

a=0.10,2,12 2 ' 75
9314.11.20;
Qigidppgs Investment
5 0.0182 0.1476
10 0.0384 0.2317
25 0.1083 0.4401
Percentile 50 0.2694 0.7396
75 0.5886 1.1631
90 1.0494 1.7012
95 1.4396 2.1293
g2(v,) = 0.010
Dividends anestment
5 0.0231 0.0838
10 0.0457 0.1557
25 0.1228 0.3478
Percentile 50 0.3007 0.6845
75 0.6382 1.1764
90 1.1581 1.8590
95 1.5802 2.3785
g2(v, = 00
massage mm nt
5 0.0372 0.0506
10 0.0730 0.1042
25 0.1963 0.2771
Percentile 50 0.4887 0.6645
75 1.0186 1.3835
90 1.7958 2.4192
95 2.4783 3.2766

62

Table IV.5

simulated Dividends and Investment, T=20
Smirlock and Marshall Approach
r-statistics from Granger Causality Tests
Coefficient of Earnings = 0.15

 

Critical Value of Faso.os,2,12 = 3.81
mflJm2J2:= 2'76
9313:9991
012199898 Ingestnent
5 0.0247 0.1894
10 0.0501 0.2979
25 0.1371 0.5542
Percentile 50 0.3428 0.9449
75 0.7049 1.4979
90 1.2575 2.1801
95 1.7282 2.7201
22““ = 0
Inxestment
5 0.0252 0.0986
10 0.0520 0.1888
25 0.1421 0.4182
Percentile 50 0.3676 0.8234
75 0.7645 1.4133
90 1.3515 2.2036
95 1.9119 2.8237
,Zzn,t = 0
012192808 Inxestment
5 0.0462 0.0476
10 0.0944 0.0967
25 0.2569 0.2687
Percentile 50 0.6305 0.6500
75 1.2896 1.3609
90 2.2617 2.3563
95 3.0143 3.1988

63

Table IV. 6

simulated Dividends and Investment, T=20
Smirlock and Marshall Approach
F-statistics from Granger Causality Tests
Coefficient of Earnings = 0.20

 

Critical Value of Fir-0.05 2,12 = 3.81
Fe-0.10,2,12 = 2'75
22”,) = 0,001
Dixidends Ingestment
5 0.0344 0.2249
10 0.0719 0.3754
25 0.1897 0.7138
Percentile 50 0.4598 1.2368
75 0.9875 1.9587
90 1.7473 2.8500
95 2.3981 3.5431
gfi(g, = 0.
Dixidends Inxestment
5 0.0373 0.1197
10 0.0734 0.2199
25 0.2094 0.5030
Percentile 50 0.5114 1.0134
75 1.0640 1.7568
90 1.8750 2.7071
95 2.6018 3.4761
2205) = Q 199
Dixidends Ingestment
5 0.0572 0.0472
10 0.1201 0.0939
25 0.3166 0.2585
Percentile 50 0.7639 0.6199
75 1.5742 1.3043
90 2.7368 2.3339
95 3.7472 3.1982

64

Table IV.7

simulated Dividends and Investment, T=20
Smirlock and Marshall Approach

F-Btatistics from Granger Causality Tests
Coefficient of Earnings = 0.15, 02“,) = 0.001

 

Critical Value of Fno.05,z,12 :
F60Am2n2" 2'75

Aut222rrelatien_geefficient_s_2212

Dixidends Inxestnent
5 0.0264 0.1919
10 0.0508 0.3045
25 0.1384 0.5669
Percentile 50 0.3417 0.9582
75 0.7285 1.4801
90 1.2799 2.1615
95 1.7321 2.7034
Dixidends Inxestnent
5 0.0240 0.1933
10 0.0497 0.3056
25 0.1371 0.5599
Percentile 50 0.3439 0.9535
75 0.7333 1.4925
90 1.3263 2.1801
95 1.7933 2.6960
t=
Dixidends Inxestment
5 0.0247 0.1893
10 0.0501 0.2979
25 0.1370 0.5541
Percentile 50 0.3427 0.9449
75 0.7048 1.4978
90 1.2575 2.1801
95 1.7282 2.7201

65

Table IV. 8

Simulated Dividends and Investment, T=20
Smirlock and Marshall Approach

F-statistics from Granger Causality Tests
Coefficient of Earnings = 0.15, 02”,) = 0.010

 

 

Critical Value of Fa=0.05,2,12 = 3.81
Fmenm2n2:= 2'75
Auteserrelatien_£99ffisient = ~01;
012199895 Inxsstnent
5 0.0265 0.1343
10 0.0548 0.2275
25 0.1490 0.4925
Percentile 50 0.3676 0.9255
75 0.7634 1.5350
90 1.3716 2.3179
95 1.8770 2.9420
A t =
Dixidends Ingestment
5 0.0268 0.1233
10 0.0542 0.2220
25 0.1482 0.4591
Percentile 50 0.3719 0.8698
75 0.7684 1.4565
90 1.3608 2.2226
95 1.8278 2.8085
= 0.
Dixidends Ingestment
5 0.0260 0.1101
10 0.0540 0.1942
25 0.1520 0.4274
Percentile 50 0.3701 0.8206
75 0.7838 1.4054
90 1.3679 2.1434
95 1.8870 2.7490

66

 

Table IV.9

simulated Dividends and Investment, T=20
Smirlock and Marshall Approach

F-statistics from Granger Causality Tests
Coefficient of Earnings = 0.15, 02“,) = 0.100

 

Critical Value of memzznz
«0.10.2,12 2 ' 76

II II
N
O
00
H

 

Autesgrrelatign_seefficient = -0.2
Dixidends Ingestment
5 0.0377 0.0662
10 0.0754 0.1391
25 0.2082 0.3561
Percentile 50 0.5231 0.8308
75 1.1124 1.6664
90 1.9479 2.8838
95 2.6655 3.8445*
A e a o ffic' n = 0.0
Dixidends Inxestment
5 0.0387 0.0582
10 0.0787 0.1200
25 0.2233 0.3098
Percentile 50 0.5495 0.7300
75 1.1692 1.4972
90 2.0479 2.5508
95 2.8200 3.5224

All 0 re

pividgngs

5 0.0462

10 0.0944

25 0.2569

Percentile 50 0.6305
75 1.2896

90 2.2616

95 3.0142

67

ic' n =

Investment

0.0475
0.0967
0.2687
0.6500
1.3609
2.3563
3.1987

Table IV.10

Fama and Babiak : Dividend Prediction Model
254 firms with data spanning the years 1952-1989

 

Fama and Babiak [1968] find evidence supporting a dividend
generating model of the form:

I) - D

, aD

, + SE, + u, (9)

t-1 t-

1: = pu,._1 + v (10)

t I

They estimate d=-0.45, B=0.15 and 0 between -0.2 and 0.2

The current study significantly updates the data set: 254
firms are included for which both dividends and net income
were reported for every year during the interval 1952 -
1989. Screens were implemented to exclude banks, utilities,
insurance companies, ADR’s, limited partnerships and real
estate investment trusts.

The results are as follows:

 

95 - 89

a B p 6

5 -.4833 -.0295 -.2455 .0826

10 -.2829 -.0104 -.1070 .1598

25 -.0789 -.0012 .0781 1.0004
Percentile 50 .0193 .0035 .2720 7.9760
75 .1083 .0119 .4050 66.4139

90 .1800 .0359 .5261 414.7019
95 .2354 .0627 .5876 1644.3631
Mean .0437 .0308 .2310 3881.2000

* Mode .0198 .0011 .3338 384.0240
Number 35 104 4 234

* Note: Estimates of the mode given here are obtained by
dividing the range of the distribution into 500 bins of
equal size. The mode is then given as the mid-point of the
bin containing the most observations. That this method is
particularly susceptible to the presence of outliers is
obvious by comparing the mode of 6 to the selected
percentiles shown. Examination of the entire series reveals
that 132 of the estimates of d are less than 10.

68

 

 

 

Table IV. 11

Fama and Babiak : Dividend Prediction Model
Subperiod 1: 263 firms with data spanning the years 1952-1970
Subperiod 2: 864 firms with data spanning the years 1971-1989

 

 

 

1222:1212

d B 0 d

5 -.5490 -.0297 -.3934 .0055

10 -.4094 -.0115 -.3205 .0126

25 -.2328 .0016 -.1266 .0776
Percentile 50 -.0907 .0144 .0702 .5500
75 .0301 .0415 .2592 3.8581

90 .0939 .0855 .4126 19.3523

95 .1483 .1340 .4623 46.2273
Mean -.1241 .0290 .0632 16.3529

* Mode .0287 .0112 .3707 1.4673
Number 8 21 4 187

1211:1222

d 8 p d
5 -.7766 -.0155 -.2766 .0000

10 -.5118 -.0063 -.1479 .0013
25 -.2260 .0000 .0000 .0306
Percentile 50 .0000 .0039 .1792 .5449
75 .0885 .0128 .3570 11.2811

90 .1869 .0331 .5129 196.0823

95 .2554 .0590 .5907 768.1339
Mean .1120 .0228 .1713 6174.6181
* Mode .0627 .0109 .0013 1554.0890
Number 309 657 70 841

* For the first subperiod 227 of the estimates of 6 are below 10.
In the second subperiod 642 of the estimates of d are below 10.

69

Table IV.12

stationarity of simulated Dividends and Investment, T=30
Smirlock and Marshall Approach

Estimated Parameters from 1952-1909 as shown in Table IV.10
Dickey-Fuller statistics

 

Critical Value of DFe-O.OS,nI37 = -2.95
DFeaOJOm-ST = '2'”

02182_M22128_2f_222182222_2222822222

012122822 1822228282
5 -4.5669* -1.7478
10 -5.0506* -2.2351
25 -5.9422* -2.9442
Percentile 50 -6.9621* —3.7121*
75 -8.17l4* -4.4917*
90 -9.5295* -5.3032*
95 ~10.4544* -5.8097*
02182_E222_2f.222182t22.£28282t282__
012122822 1822228282
5 -4.3620* -1.6776
10 -4.8904* -2.1445
25 -5.8416* -2.8571
Percentile 50 -7.0090* -3.6464*
75 -8.4439* -4.4368*
90 -10.0154* -5.2050*
95 -11.0900* -5.7403*
s o sti
012122822 1822228282
5 -3.1038* -1.4304
10 —3.5950* -1.9432
25 -5.7589* -2.7088
Percentile 50 -9.1688* -3.5302*
75 -21.0546* -4.3311*
90 -418.5514* -5.1701*
95 -1239.9369* -5.6840*

70

Table IV.13

Stationarity of simulated Dividends and Investment, T=19
Smirlock and Marshall Approach

Estimated Parameters from 1952-1970 as shown in Table IV.11
Dickey-Fuller statistics

 

Critical Value of DFa-o.os,n-18 = -3.05
DFe-O.10,m18 = "2'67

22182_822128_22_E22182222_22228222r2

012122822 1822228282
5 -2.7880 -1.8402
10 -3.0187 -2.1973
25 -3.4530* -2.8079
Percentile 50 -4.0140* -3.4820*
75 -4.6830* -4.2608*
90 -5.3830* -5.08l9*
95 -5.9l98* -5.6530*
02182_8222_22_E22182222_2222822222
012122822 1822228282
5 -2.8408 -2.7724
10 -3.1149* -3.0535*
25 -3.5937* -3.5875*
Percentile 50 -4.2277* -4.2302*
75 -4.9872* -5.0106*
90 -5.8221* -5.8859*
95 -6.3916* -6.4388*
Me a
012122822 1822228282
5 -2.3473 —2.6032
10 -2.7809 -2.9487
25 -3.8092* -3.5199*
Percentile 50 -5.3204* -4.1514*
75 -6.9720* -4.9017*
90 -8.7590* -5.6812*
95 -10.0393* -6.2508*

71

Table IV.14

stationarity of simulated Dividends and Investment, T=19
Smirlock and Marshall Approach

Estimated Parameters from 1971-1980 as shown in Table IV.11
Dickey-Fuller Statistics

 

Critical Value of DF¢=0.05,n=18 : -3.05
DFe-O.10,n-18 '-

flsing nsgign pt Estinstsg Espsnstsps

012122822 M282
5 -2.7061 -1.8098
10 -2.9625 -2.1816
25 -3.4010* -2.7961
Percentile 50 -3.9728* -3.4854*
75 -4.6312* -4.2495*
90 -5.3290* -5.0858*
95 -5.8274* -5.6454*
s' s a rs
Dividends tnvsstnent
5 -2.5184 -2.6809
10 -2.9159 -3.0108
25 -3.7347* -3.5861*
Percentile 50 -4.8799* -4.2178*
75 -6.2477* -4.9731*
90 -7.6627* -5.7677*
95 -8.5754* -6.3148*
Using Mean 0: Estimatsd Estsnstsps
Dividends Inysstment
5 -1.9416 -2.4621
10 -2.2879 -2.8052
25 -3.7357* -3.3660*
Percentile 50 -6.0516* -4.0049*
75 -11.8095* -4.7605*
90 -231.3182* -5.5144*
95 -1256.8081* -6.0646*

72

Table IV. 15

Simulated Dividends and Investment, T=38

Smirlock and Marshall Approach

Estimated Parameters from 1952-1989 as shown in Table IV.10
P-statistics from Granger Causality Tests

 

Critical Value of Feta-05,2,”
Fmenm239

IIIi
mu
use:
1002

02182_822128_22_222182222_2222822222

012122822 1822228282
5 0.0375 0.0372
10 0.0772 0.0766
25 0.2131 0.2121
Percentile 50 0.5389 0.5139
75 1.1852 1.0961
90 2.1874 1.9658
95 3.0217 2.7646
22182_E222_22.822182222_£2228222r2__
012122822 1822228282
5 0.0283 0.0372
10 0.0621 0.0755
25 0.1705 0.2052
Percentile 50 0.4288 0.4960
75 0.9306 1.0853
90 1.7717 2.0248
95 2.5223 2.8740
22182_E228_22_222182222_£2r2822222
012122822 1822228282
5 0.0220 0.0205
10 0.0447 0.0426
25 0.1131 0.1139
Percentile 50 0.2295 0.2351
75 0.3945 0.3849
90 0.5845 0.6161
95 0.7375 1.0379

73

Table IV.16

simulated Dividends and Investment, T=19

Smirlock and Marshall Approach

Estimated Parameters from 1952-1970 as shown in Table IV.11
P-statistics from Granger Causality Tests

 

Critical Value of F«0.05,2,1o
aao.1o,2,10 2 ‘ 93

Using Medisn pf Estinsted Eatsnsters
012122822 1822228282
5 0.0553 0.0546
10 0.1105 0.1130
25 0.3101 0.3204
Percentile 50 0.7824 0.7781
75 1.6599 1.6207
90 2.9919 2.9717
95 4.1889* 4.0680
d a 5
012122822 182_28_8_vset
5 0.0501 0.0561
10 0.1063 0.1221
25 0.2943 0.3252
Percentile 50 0.7185 0.8133
75 1.5274 1.7579
90 2.6967 3.2203
95 3.8389 4.4686*
n s 'm a te 5
012122822 th t
5 0.0519 0.0237
10 0.1030 0.0507
25 0.2737 0.1739
Percentile 50 0.6699 0.6516
75 1.3702 2.0747
90 2.3937 4.3541*
95 3.3116 6.4463*

74

Table IV. 17

Simulated Dividends and Investment, T=19

Smirlock and Marshall Approach

Estimated Parameters from 1971-1989 as shown in Table IV.11
r-statistics from Granger Causality Tests

 

Critical Value of Fac0.05,2,10 = 4.10
F030.10,2,10 = 2'93
d' 0 st' e ters
inidengs I v s e
5 0.0536 0.0521
10 0.1054 0.1097
25 0.3039 0.3049
Percentile 50 0.7442 0.7703
75 1.6212 1.6245
90 2.9541 2.9212
95 4.1061* 4.0601
M o s ' ed a ameters
inigsnds investment
5 0.0523 0.0375
10 0.1055 0.0767
25 0.2879 0.2390
Percentile 50 0.6908 0.7906
75 1.4006 2.1397
90 2.4884 4.3031*
95 3.3898 6.3578*
Qsing Mean 0; Estimsted Parametets
0121228d_s W
5 0.0489 0.0118
10 0.1019 0.0251
25 0.2689 0.0690
Percentile 50 0.6211 0.1974
75 1.2686 0.6212
90 2.2050 1.6635
95 3.0245 2.8453

75

Table IV.18

Empirical Test for Dividend-Investment Causality, T=37
Levels of Variables, 220 Firms

Sample Period 1953-1989

 

Percentile

Percentile

Critical Value of DFF0.05'M37

10
25
50
75
90
95

Critical

10
25
50
75
90
95

4.3022
3.5041
2.0110
0.2742
-1.4732
-2.3038

-2.9957*

.012122822

0.1342
0.2880
0.7412
2.0937

012822:Enll2r.§222122122

-2.95
-2.62

DF¢=0.1O,n=37

1822228282
-2.1104

-3.0036*
-3.8117*
-4.9418*
-6.1566*
-7.2188*
-7.4573*

Value of F¢=0.05,2,30 : 3.33

menmzso

IILVQS tnen E
0.0836

0.2201
0.6304
1.9333
4.7497*

4.7375*
9.0015*

12.3020*

76

12.7004*
17.6219*

Table IV.19

Empirical Test for Dividend-Investment Causality, T=37
Differenced Variables, 220 Firms
Sample Period 1953-1989

 

e - t'cs

Critical Value of DFe80.05,n=36 = -2.95
DFaao.1o,n-36 = ’2'62
012122822 18_2__m_8_v st e t
5 1.4755 -4.2513*
10 0.1732 -4.8103*
25 -1.2583 -6.0326*
Percentile 50 -2.9255 -7.0639*
75 -3.9531* -8.6787*
90 -5.1261* -10.1299*
95 -6.6050* -11.1540*
22222122122

Critical Value of F¢=0.05,2,29 f 3.33
menng9"

Dividends Inves ment
5 0.1209 0.0538
10 0.2220 0.1785
25 0.6941 0.6962
Percentile 50 1.7463 2.1340
75 3.5787* 4.9604*
90 6.8876* 13.2539*
95 11.3105* 18.0144*

77

 

Table IV.20

Empirical Test for Dividend-Investment Causality, T=37
Differenced Variables, Total of 220 Firms
Sample Period 1953-1989, Firms Segmented by Stationarity

 

-2.95

Critical Value of DFa=0.05,n=36 2 62

DFe=0.10,n=36

Critical Value of ago-05.2.29 : 3.33
menngv" 2'49

s < - o t Series
- 'st'
Dividengs invsstmsnt
5 0.1218 0.0538
10 0.2220 0.1686
25 0.5138 0.6962
Percentile 50 1.5342 2.4811
75 3.6759* 5.1046*
90 6.4768* 13.5594*
95 9.4618* 27.9175*

Finns with DF > -z.95 to; Either Series

 

E-Statistics

Dividengs inysstnent

5 0.1111 0.0451

10 0.2013 0.2001

25 0.8818 0.6271

Percentile 50 1.8486 1.8833
75 3.3448* 4.2910*
90 6.8017* 12.4258*
95 11.3105* 15.2892*

78

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Figure IV.1

simulated Dividend Series, T=2o

 

 

30

25-

 

ZO-

 

 

 

 

Years

82

Figure Iv. 2

Actual Dividend Series, T=20

Exxon C’mvflm 15629-15w

 

27501

22504
2000-1
1750‘
lSOOfi
1250‘
1000‘

 

Actual Dividends

 

 

 

750 I I I I j I I I r I I I r W I I I I T T

6870 72 74 767880828486
Year‘s

Vestiy‘use £7be l.%:9-l%

 

2'50“

200‘

150-

Actual Dividends

100‘

 

 

 

 

Figure IV. 3

Estimation or rule and Babiak Dividend Prediction nodal
Prequenoy Histogram of d for 1952 - 1989

D-D =aD

t H + HEt + ut (9)

t-1

ut = put.1 + vt (10)

1952-19892541111113

 

14

128

 

L mmmsmmum 1

 

 

 

Number 01 Occumnoee
on
I

 

 

 

 

 

 

 

 

 

 

 

 

4+ I
I I
II ,
o- Illll IiIIIiIIiIi II Ill I I i I’iIIIII
0.183 8.188 0.097
-0.411 «0.120 0.025 0.170
momammm

84

 

Figure 117. 4

Estimation of Fama and Babiak Dividend Prediction Model
Frequency Histogram of 5 for 1952 - 1989

 

Number of Occurrences

 

- D_ = an)”1 + fiEt + ut (9)

t = pub.l + vt (10)

1952-19892541111118

l-0.|011

 

 

 

 

 

 

 

 

 

 

0.017 0.015 (1054
Coefficient of Eurhgs

85

Figure 117. 5

Estimation of Fama and

Frequency Histogram or 5 for 1952 - 1989

Babiak Dividend Prediction Model

 

Number of Occurrences

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Dt - Dt_1 = (:0H + fiEt + ut (9)
ut — pub1 + \It (10)
1952-1989225411mis
3 I
7- i
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-0.161 0.1!)? 0.175 0.344 0.512
AR(1)coefnd8nt

86

Figure IV. 6

Estimation of Fama and Babiak Dividend Prediction Model

Frequency Histogram of d for 1952 - 1989

 

 

 

 

 

Dt - Dt,1 = “Dz-1 + pi:t + nt (9)
tn = pub1-+ vt (10)
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87

 

Figure IV.7

Estimation of Fama and Babiak Dividend Prediction Model
Frequency Histogram of 6 for 1952 - 1970

humewctOcamnumae

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0
I
D
II

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Figure IV.8

Estimation of Fama and Babiak Dividend Prediction Model
Frequency Histogram of 3 for 1952 - 1970

 

I) - D = an

t t-1 + fiEt + llt (9)

t-‘I

11 = put“1 + v (10)

t t

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14

12‘

 

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a:
l

 

i l
H
Ii

: I I IIIIIII IIIII I III

-an 0am nun
0.013 0.120 0.0% 0.119
(xemxmuanflmp

 

 

 

 

 

 

 

89

 

 

Figure IV.9

Estimation of Fama and Babiak Dividend Prediction Model
Frequency Histogram of 0 for 1952 - 1970

 

I) - D = no

t M + 5E1: + nt (9)

t-‘I

u = put.1 + v (10)

t t

18$b1mmzznmmn

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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I . . I
0.. I .I I II II I I III
(M38 {H21 -008 Qflfi man
W 0.134 0.“ 0.212 0.385
NMOCUMUHH

90

Figure IV.10

Estimation of Fama and Babiak Dividend Prediction Model
Frequency Histogram of a for 1952 - 1970

D-D =aD

t t-1 1 'I’ 5E: + “t (9)

t.

1% = pu + v (10)

P1 t

1952-1970:2631?“

 

126

 

Number 0! Occurrences
$

 

 

 

II||.III..II . .l .. . .. l I . I . . . ..
QM 9.343 18.681 28.019 37 .356
4.674 14.012 2&350 32.688 42‘

sums

d

 

91

Figure IV.11

Estimation of Fame and Babiak Dividend Prediction Model
Frequency Histogram of 6 for 1971 - 1989

I) - D = a0

t M + 5Et + nt (9)

M + vt (10)

P1

ti = pu

t

1971-1-:8641'1118

 

 

 

 

 

 

 

 

 

 

 

 

90
001
70-
E w Top-umsmmuduy
g «r
E 40-
B
E
3 30-
I
20« I I
II I I
10- II I
I ~ I IIII I III II
0- I .I.I.II.III III III.I.I.IIH IIIIIII.I|IIIIIIIIIIIII IIIIIIIIIII I. II .I II II“ I I
0.777 0500 0360 0.151 0.057 '
0.672 0464 0255 0.047 0.102
coemdamamgedwdem

¢

92

Figure IV.12

Estimation of Fama and Babiak Dividend Prediction Model

Frequency Histogram of fi for 1971 - 1989

 

 

 

 

 

 

Dt - Db1 = cIDt_1 + 3Et + nt (9)
ut = pub1 + vt (10)
19fl-1§9:&Mflw3
um
13%
meuuummnnumumumuhnuy ‘]
un« ‘
é IR?
8
g «r
E
s
2
ah
ah H I
o_ lHlllllllllllllllIl I III“ ”I” |lilIlll'lIlhll‘llllilllII Mm II...| .l. I.I.I.. |.::|..l=n.
«0.016 0000 0.015 0000 0.045
-0un man man may GEE
Cumuuudfsflmp

93

 

 

Figure IV.13

Estimation of Fama and

Frequency Histogram of b for 1971 - 1989

Babiak Dividend Prediction Model

 

D-

t D

M = an1 + 31E:t + ut

ut = put-1 + Vt

1971-1989:864flms

(9)
(10)

 

 

 

 

 

 

 

 

 

 

 

90
ao-
70-
g ”'1 TQNMSMMHM
550-
E“ ‘
5..
20"
"’ II I III
I ~ I . "II IIIIIII I I
....II....I..,I.I.IIII III III IIIIII III III I II III II. IIIIIIIIIIIII.
0277

0.101
0.014

0.074 0.249

0.1% 0.181

AR(1) comm

0.337

94

 

 

 

0.424

0.512

Figure IV.14

Estimation of Fama and Babiak Dividend Prediction Model
Frequency Histogram of 6 for 1971 - 1989

D -I) = on

t M + 3Et + ut (9)

t-1

ut = put.1 + vt (10)

1971-1900:0640113

 

g $

3

 

 

III.- I .. ... . .
0.1K” 155.179 310.357 465.5% “.714
715” ZQJHB 3W3“; {Maflfi (QQKH

Sbma

95

 

 

Figure IV.15

significance of Dividends in Explaining Investment
simulation Using Median of Estimated Parameters from 1952-1989
Differenced Series, T=37

Block F Test for Exclusion of Dividends

 

 

2 2
INVt = a0 +.z: aiINVt-i + .2 fijDIVM. + at (6)
i=1 3=1
Mamm1mm4aEPsmmmm:
1am
1am-

 

 

WVMEWIQOSMdW

 

 

 

Number of Occurrences
é

 

 

 

 

c “I‘.II‘II‘II-' I|'li ‘HI‘IHH‘IHLIIIHI WM)”
0 1.75 3.51 5.26 7.02 8.77 10.53 12.279 14.“ 15.788

0.88 2% 4.39 6.14 1% 9.65 11.40213156 14.91 1&fl5
FSHBMS

96

Figure IV.16

significance of Investment in Explaining Dividends
simulation Using Median of. Estimated Parameters from 1952-1909

Differenced series, T=37
Block F Test for Exclusion of Investment

2 2
DIVt = r0 + z erva. + z: .simvH + pt (7)
j=1 i=1

Makm1§n4mnPammmms

 

$§$§

0

Number of Occurrences

 

 

7.5a 0.7051004 11295
000 100 014 4.00 5.05 0.002 0.157 0.412 1000711322
Fsumm:

97

 

 

Figure IV.17

significance of Dividends in Explaining Investment
simulation Using Mode of Estimated Parameters from 1952-1989
Differenced Series, T=37

Block F Test for Exclusion of Dividends

 

2 2
INVt = a0 + z: aiINVH + .2 1910va1 + at (0)
i=1 j=1
Ikued1mndmanummm1
1am
1am-

 

 

mvmuwnaosmuw

 

 

 

Number or Occurrences

 

 

 

 

200 0.00 5.13 ' 004’ 7.07 0205 10..
0.00 1.00 032 4.05 500 7.30 0.001 0.050 1120712015
Fm

98

Figure IV.18

significance of Investment in Explaining Dividends
simulation Using Mode of Estimated Parameters from 1952-1989
Differenced series, T=37

Block F Test for Exclusion of Investment

 

2 2
DIVt = to + z PMDIV . + z 5.1mH + pt (7)
j=1 i=1
lwn0m1§24anPsmmmms
1000
900-
an-

Number or Occurrences

 

 

I
1
II
I
. 1..
400 ‘
-
I.
I.
‘I.
LII. ‘1
‘3 . .I
aoo~ . ~ ,
..... :II
..I‘.
‘.II; 1‘“
.1 I ‘-
1ft! III."
:1I.'I I.
.,11.’l';‘-'
II V I ‘III
;.I .h”.
I
a: ‘ I
I '1 "f
III ‘1111 1
‘1
1. l, . .‘
. 1'1
100- I . 1
lb
.‘ 1.
.1.? i
, 1,
. 1'
. '1
:11 IV
.1
II . :I‘
J i,
o ' l' " ' 'llll ,:I "II II‘ ' l"'|l.="
0 1. 2.80 4.19 5% 6.99 8.388 9.784 11.1& 12.579

0.70 2.10 3.49 4m 63 7.687 9.135 10.483 11.08 13.270
Fsumus

99

 

Figure IV.19

Significance of Dividends in Explaining Investment
Simulation Using Mean of Estimated Parameters from 1952-1989
Differenced Series, T=37

Block F Test for Exclusion of Dividends

 

 

 

 

 

 

2 2
INVt = a0 + 2: aziINVt,i + E EJDIVH + ‘1 (6)
i=1 j=1
annd1mn4manammns
400
am.
301 IHVI
IIIIII
‘IIIIIE
E 25% iIIlII mvuuaaasomwum
I IN
§ II 'II'II
3 and .IIIMI
E III II II:
0150- ;I II III
3 ;‘I ’I I, «I:
2 If. II
"n“ IIIII III.
II :II; ’5“
II II III
50" I :‘ III“:
II II IIIHI
I: 'III IIIIIII.
III II. II 'zIIIII, I
0.1 -‘ IIIII II :IIHI-III 'f"I1,I‘ ., I _ ‘ ' '1‘ ‘ L H} i"
0 0.30 0.60 0.90 1.19 1.49 1.79 2.188 2000 2.684

015 045 015 104 134 154 LEE ZZH' 2&5. ZED
Pasha:

100

 

 

Figure IV.20

significance of Investment in Explaining Dividends
simulation Using Kean of Estimated Parameters from 1952-1989
Differenced Series, T=37

Block E Test for Exclusion of Investment

 

 

2 2
DIVt = r0 +.2 PJDIVH + .2 csimvpi + pt (7)
3=l l=1
lwnnd1m24mnfisummn:
z:
18~
NF
5%

 

 

 

 

Number of Occurrences
?'

 

 

I»

I .1 I 1L11 “9.1.4 .i1-' ,1. I.
I . . .. .Ii
1. 1:: mm“! ‘IIIIIIIIII, IIIII; . I
I .II.I.; I11~II:'I.I III vl II
I'II“ |‘l:|,!I1I h Ii 0 I III U- H
. .u 1‘“ I yr 1H,... m‘. I

 

 

 

o" 1.53 3.06 4.56 6.11 7.64 9.164 19.691 19.219 13.746
0.78 2.29 3.82 595 667 64 9.928 11.455 12.962 14.51
Fsumu:

101

 

 

Figure IV.21

Significance of Dividends in Explaining Investment
Simulation Using Median of Estimated Parameters from 1952-1970
Differenced Series, T=37

Block F Test for Exclusion of Dividends

 

 

2 2
INVt = 00 + 2: azilet,i + z ijIVH. + et (6)
i=1 j=1
Matn1flflH9flH¥nmubm
1am
1am-
1am-

 

 

WMIGNMdeMO

 

 

 

Number or Occurrences
§

2001 Is:

I
I .
I

 

 

I I

 

290 569 3701199 14.49 17 29266 231
1.45 495 725 19.14 1304 1594 13699 21.737 24.695 27999
Fame

102

Figure Iv. 22

significance of Investment in Explaining Dividends
simulation Using Median of Estimated Parameters from 1952-1970
Differenced series, T=37

Block I Test for Exclusion of Investment

 

2 2
DIVt = ra + r. rjmvw. + .2 6iINVH + 0. (7)
j=1 l=1
Mafin1mfl4mMPsammms
000
700:
0001

9"; 4"?”

$

 

 

i

 

. V 4.70 020 709 0991 10.950 12.521 '1007.
0.70 295 391 5.40 7.04 3000 10.174 11.799 13904 14900
Fsmmuz

103

 

Figure IV. 29

Significance of Dividends in Explaining Investment
Simulation Using node of Estimated Parameters from 1952-1970
Differenced Series, T=37

Block P Test for Exclusion of Dividends

 

 

 

 

 

 

2 2
INVt = 010 + E 0:,leH + E ijIVt,j + et (6)
i=1 j=1
meuxflfizflNOHmmnmm
140
1305
1301
g “-1
g mmsnmwddgmbuo
8
z 100-
E
3
z
an~
200- W ;
111i; 1
,E(
04 . “

 

0 290 500 3711011. 115174120911 2921 9 23114
1.45 4.95 795 10.10 1300 15.90 1000 21.702 24.004 27.505
Penman

104

 

Pigure IV.24

Significance of Investment in Explaining Dividends
Simulation Using node of Estimated Parameters from 1952-1970
Differenced Series, T=37

Block P Test for Exclusion of Investment

2 2
DIVt = Fe + 2: erIvM. + 2 S‘INVH + 0t (7)
j=1 i=1
Iku0d1mm4mmflmammms

 

$§§§

3

Number of Occurrences
g

 

 

m E’ Zl‘:

001g

, I . 1

:NEHH
1m“ 11:... ‘1 ."

- 1. . 1 _

‘ ‘ . 91:3.
0- .manin:=310m .

0 210 ’49s 0.54 ' 371 "100913071 1525‘ 17.429 19007 '
1.09 327 545 7.09 9.00 11.902 14.101 13990 10510 mags
00000:

105

 

 

Pigure IV.25

Significance of Dividends in Explaining Investment
Simulation Using nean of Estimated Parameters from 1952-1970
Differenced Series, T=37

Block P Test for Exclusion of Dividends

 

 

2 2
INVt = a0 + z aiINVH + 2 fijDIVH. + at (6)
i=1 j=1
Nbaum1unH9nnhnnsmm
1am
1am-

 

 

wmdnmbvadugmhuo

 

 

 

Number or Occurrences

 

240 4.92 7.90 ' 9.04 " 4.70 12297 10049. a1"
129 309 0.15 301 11.07 1359 15999 10.454 20.914 29975
0919119000

106

 

Pigure IV.26

Significance of Investment in Explaining Dividends
Simulation Using Mean of Estimated Parameters from 1952-1970
Differenced Series, T=37 ‘
Block P Test for Exclusion of Investment

 

2 2
DIVt = to + 2 PJDIVH. + z 5,INVH + 0: (7)
j=1 i=1
annd1RfldWMPaammms
9000
25004

3

 

Number or Occurrences

é

 

' 300' '720 10.00 “14.40 10.01 21.007 25200 20.009 92.41
1.00 5.40 9.00 12.00 1021 19.000 23407 27.000 90009 94211
Esme:

01

 

107

 

Pigure IV.2?

Significance of Dividends in Explaining Investment
Simulation Using Hedian of Estimated Parameters from 1971-1989
Differenced Series, T=37

Block P Test for Exclusion of Dividends

Number 01 Occurrences

 

 

 

 

 

 

 

2 2
INV = a0 + z aiINVM + 2 0})va + at (6)
i=1 j=1
M069111971-1989Paramet019
1a»
900-
30-
un«
30‘
50% wmeamwdwbuo
KD- '
«Dd
2MP ..
000
‘HWE,
wo- mm,
0 2.00 4.01 6.01 302 10.02 12.12 11.10.11? 10.03
1.1!) 3.01 5.01 7.01 9.02 11.02 13.026 15.13 17.034 19.138

Fsumnx

108

 

Figure IV.2S

Significance of Investment in Explaining Dividends
Simulation Using Median of Estimated Parameters from 1971-1989
Differenced Series, T=37

Block F Test for Exclusion of Investment

2 2
DIVt = 20 +2 erIvm. + 2 6‘10!th + 0t (7)
3=1 i=1

Median1971-1989 P39010191:

 

1400

1200-

§

3;

Number of Occurrences

3

    

 

0 294 507 301 11.74 14.00 17.015 20.551 23407
1.47 4.40 7.94 1020 1321 13147 13000 22.019 24.955 27.091
Fsmstlcs

109

 

Figure IV.29

Significance of Dividends in Explaining Investment
Simulation Using Mode of Estimated Parameters from 1971-1989
Differenced Series, T=37

Block F Test for Exclusion of Dividends

2 2
INV = on + 2 41in . + 2 0.01v
= 1

_.+6 (6)
11 j=’ " t

0100001197149um

 

 

 

5m- WWIQQWdWBMO

 

 

 

Number of Occurrences

 

‘ 2.00 4.11 310 022 12.99 14. 10.497
1.09 300 514 7.19 925 11.90 13955 15.41 17.404 19.519
Fsmstlcs

110

 

Figure IV. 30

Significance of Investment in Explaining Dividends
Simulation Using Mode of Estimated Parameters from 1971-1989
Differenced Series, T=37

Block F Test for Exclusion of Investment

2 2
DIVt = r0 +.2 erIvm. + .2 5.101th + pt (7)
3=1 l=l

M000011971-1989Pm0m

 

 

Number 01 Occurrences

§

 

 

‘. 1. EMEMWNL... 1 ,, _ 1 -~1
0 3.52 715 10.57 14.10 17.62 21.148 24.671 28.195 31.719
1.78 529 8.81 12.34 15.3 19.384 22.” 28.433 3.957 33.481

Fsmnmas

111

 

Figure IV.31

Significance of Dividends in Explaining Investment .
Simulation Using Mean of Estimated Parameters from 1971-1989
Differenced Series, T=37

Block F Test for Exclusion of Dividends

Number 01 Occurrences

INV

2 2
“0 +15 aiINVH +j2 lfiiDIVt-i + ‘1 (6)

Mam 011971-1989 P30109101:

 

1mm

9

§

 

 

cumnnosmuaugmuno

 

 

 

'401“ 301“ ‘ 302 10994.

LN 3.01 5.01 712 9.12 11.03 13.03 15.” 17.04 19.044

FSHHMS

112

 

Figure IV.32

Significance of Investment in Explaining Dividends
Simulation Using Mean of Estimated Parameters from 1971-1989
Differenced Series, T=37

Block F Test for Exclusion of Investment

- _
- -

. 2 2
DIVt = to +2 erIvm. + .2 63va + 0t (7)
3=1 l=1

M0m011971-1909Pm1010

 

 

 

!

.1 :1.

0‘ 200 '571 0.57 11.49 1420 17.199 19.990 2052 25.709
1.49 429 7.14 10.00 1205 15711 13507 21.424 2420 27.197
annwas

113

 

Figure Iv. 39

Dickey-Fuller Test for Stationarity of Dividends
Levels of Variables, T=37

The hypothesis that one of the p+l roots of the characteristic
equation is unity can be tested by computing a 't-like’
statistic consisting of fi/SE(B) from the following regression:

 

 

 

 

 

 

 

P
(l-L)Yt = a + 03!” + )3 Pin-LN“.i + 6t (4)
i=1
22011111019591909
25
20~
g 154 crumb-29511005de
'5
B 10-
E a
a
Z
5. E
1 i
45.737 -5.74 4.26 14.26 24.26
-1 0.74 -0.74 9.26 19.26 29.26
MMTSWG

114

 

 

Figure IV. 34

Dickey-Fuller Test for Stationarity of Investment
Levels of Variables, T=37

The hypothesis that one of the p+1 roots of the characteristic
equation is unity can be tested by computing a 't-like’
statistic consisting of B/SE(B) from the following regression:

P
2 I‘i(1-L)YH + et (4)

(1-L)Yt = a + 02M 4-
i=1

220111111019591909

 

 

 

PE

 

 

mmu-zouamwddgmu

 

 

 

 

Number or Occurrences
EL

‘9‘

__ _ . _..__—__ ___.___....____..

WWWWW*WMM” ____...._

“E

E. 1

o_ l I 1 l Ilzlil I
-1 2.3% -2.34 7.87 17.67 27.87

-7.94 207 1207 2207 9207
01949175109: 1' sumac

 

115

 

 

Figure IV.35

Significance of Dividends in Explaining Investment
Levels of Variables, T=37
Block F Test for Exclusion of Dividends

2 2
INVt = 020 + )3 ailNVH + 2 fijDIVH + 5: (6)
i=1 j=1

:200m31mn1un

 

 

12— mvmnauawwuw

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

:‘ I “III I Illllllll l IIIII

 

 

H IIIII IIIFTIIIIIII lllllllllllllllillll IIIIW1IIUIIIUIIIIII

0 500 1. 15. 20
251 75) 125) 175) zum

-
q
d
.1
C
—
-
-
-

116

Figure IV.36

significance of Investment in Explaining Dividends
Levels of Variables, T=37
Block r Test for Exclusion of Investment

 

 

 

 

 

 

 

2 2
DIVt = r0 43:1ervaj +1116;va + pt (7)
iflflhma1§§4fl9
a;
2?
g 20-
§.5. i
B I
2 I “
§ I“
z 10‘
5‘ l
' l
m I II‘HII'HIII III I II III IIIIII I IIIII I I I II
0 500 1Q“) 15a) 2&“)
25) 15) 125) 115) zum

Fsmmns

117

 

Figure IV.37

Dickey-Fuller Test for Stationarity of Dividends
Differenced Series, T=36

j
-

The'hypothesis that one of the p+l roots of the characteristic
equation is unity can be tested by computing a ’t-like'
statistic consisting of B/SE (B) from the following regression:

P
(1-L)1It = a + gym +131 rim-1.)}!M + at (4)

Innmm91mn4mn

 

at:

Q3

 

--.

mmb-msammdw

-1 3.411 41.41 19.59 29.59
441 1.59 1159 2159 31.59
Dickey-Eula! 1' sum:

 

 

 

Number 01 Occurrences
3'

‘

 

 

118

 

Eigure IV. 38

Dickey-Puller Test for Stationarity of Investment
Differenced Series, T=36

The hypothesis that one of the p+l roots of the characteristic
equation is unity can be tested by computing a ’t-like'
statistic consisting of fi/SE(B) from the following regression:

P
(1-L)Yt = a + BYt,1 +. 211"i(1-L)¥t_i + at (4)
1:

220m,1953-1999

 

F

 

 

#3

 

 

 

 

II
1|
'!
‘i mmbozouaosmaw
I!
‘1

 

Number of Occurrences
‘? ‘I'

 

 

 

I
o- I I I Illl I I
99122 45.12 912 4.99 14.99
99.12 -1912 9.12 9.99 19.99
mamas: r Statistic

119

 

“.- ..--ee ...—..- - . n-.

u ...-..-... 0.. u*.*.-.

 

rigure IV.39

Significance of Dividends in Explaining Investment
Differenced Series, T=36
Block r Test for Exclusion of Dividends

2 2
INVt = a0 +.z: aiINVH + 2 3,43va + at (6)
l=1 j=1

zmmmmIanmn

 

§

 

wvubaaamoswdw

 

 

 

NumberotOccurrencee
#3 ‘13 § $$ $ § $

 

 

 

 

 

I 7 3..
'315 II ..
1“ ‘

0 5.00 10.00 1500 20.00
as) 750 125) 115) zuw
Fsmmu:

 

 

120

 

Figure IV.40

Significance of Investment in Explaining Dividends

Differenced Series, T=36
Block F Test for Exclusion of Investment

 

 

 

 

 

 

2 2
DIVt = r0 + z: erIvm. + 2 6.119th + pt (7)
j=1 i=1
ZNflmm1fiBdfiE
30
F
25-
g 20-
39 i
B I
2 II
E I
5 1“ 3
II’ I
g I
m I II II I II . ..I. I . I .I ....I .II. .. . I.
0 5d) 10m) 15m) ZN”
2.50 7.50 12.50 17.50 £50

Panama

121

 

Figure IV.4l

Significance of Dividends in Explaining Investment
Subsample Exhibiting stationarity at a=o.os Level
Differenced Series, T=36

Block F Test for Exclusion of Dividends

Number of Occurrences

2 2
=ao+2aiINV.+EfijDIV +6
-I t

=1 j=l

1091111119. DF < -2.95,1953-1989

(6)

 

14

12A

10-

 

mvubaaamoswdw

 

 

 

2J I" ll

 

 

 

 

 

 

 

 

 

 

 

 

 

"_

II I

I

 

llllllIllI UITTTIFTIII l

2.50 750 12.50 17.50
Fsmmus

122

III llllllllIllllllllllII1IIFIIIIIIIIIIIIIII

0 W0 1500 20.

IIIIIITIIIIIIII

zum

 

Figure IV.42

Significance of Investment in Explaining Dividends
Subsample Exhibiting stationarity at a=0.05 Level
Differenced Series, T=36

Block F Test for Exclusion of Investment

r0 + 2 erIv

PI

2
+ 2 CiINVt_i + u.

i=1 t

109wm9cw<92951234mm

(7)

 

”h

“H

Nmmbmnflthmmuwas
a
l

4.4

21

 

 

 

 

 

 

 

 

am)

10.00 15.00 20.00
750 128) 115)
Fsumus

123

 

 

Figure IV.43

Significance of Dividends in Explaining Investment
Subsample Failing to Exhibit stationarity at a=0.05 Level

Differenced Series, T=36
Block F Test for Exclusion of Dividends

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2 2
INVW=ao+2aINV +2IIsjt>Ivj+Ist (6)
i=1 j=l
1171111119. DF > -295,19531909
14
12-
10—
g 9 ouvubaauonsmaugrm
‘5
i 5'
E
3
z
4-
2- III I]
G I III |IIJIIIIIIIIIITII|IIII IIIIIIIIIIIII HIIIlJIJIIIIIIIlIIIIIFIIIIIIIIIIIIIIIIIIIIIIIIIIIIIT
0 1.
2.50 750 12.50 1750 22.50

Penman

124

Figure IV.44

Significance of Investment in Explaining Dividends
Subsample Failing to Exhibit Stationarity at c=0.05 Level

Differenced Series, T=36
Block F Test for Exclusion of Investment

2 2
DIVt = r0 + z erIvm. + 2 6.1vai + pt (7)
j=l i=1

117M118, DF > 2.95. 1953-1999

 

16

14*

12‘

§

 

 

a
I
1
I

Number or Occurrences
on
1

 

 

 

 

 

 

 

 

 

6. I
‘G
2-1
0 II II IIII I III III II III
0 5G3 100) 15
250 15) 125) 1750 ZU”
FSMMKS

125

‘HIII I | I I- IF

126

;u:;- ‘ -t- ° 1 3‘ ; °252-° 3 --2 Pl’° ltd RiSk

W:
Kalay [1981] was the first to conduct a specific

empirical test of the hypothesis that dividend payout and
earnings uncertainty are negatively correlated. Since
earnings is an accounting variable, and price is not a
function of earnings alone, measures of earnings uncertainty
are far removed from measures of price risk. Nevertheless,
this study is relevant to the investigation at hand because
the strong correlation believed to exist between earnings
and price suggests that the relationship between dividend
payout and price risk may be similar to that observed
between dividend payout and earnings uncertainty.

As a measure of risk, Kalay [1981] uses the "size
adjusted average squared deviation from the best prediction
of next period earnings (given past and current earnings)"
(see Kalay [1981], p.440). Such a measure of risk has
several advantages: i) they are scale free and thus
comparable to payout: and ii) by taking the squared
deviation from predicted earnings, negative earnings can be
dealt with in a natural way. Predicted earnings are drawn
from two alternative models. The first is a random walk
with an additive drift parameter: the second is a first
order moving average process in the first differences.

Kalay derives an earnings uncertainty measure for each of

127

 

these processes, however, the only difference between them
is the method of obtaining predicted earnings. He calls
these risk measures U1 and U2 respectively.

Payout ratio is estimated as an earnings weighted
average of past payout ratios. Kalay contends that this is
an appropriate way of reducing bias due to observations with
very small earnings per share. Thus, an implicit assumption
in this study is that over time individual firms try to
maintain some target dividend payout ratio.

Kalay's sample consists of 474 firms from the Compustat
Industrial File screened such that each firm reported annual
earnings per share and annual dividends per share in every
year from 1949 through 1972. Kalay conducts both cross-
sectional and time series tests using differenced series.
Cross-sectional tests, in this case, consist of computing
Spearman rank correlation coefficients between payout and

each measure of earnings uncertainty used.

Spearman Bank Correlation
Earnings uncertainty and Baggy; Batig. 471 Firms

Enssrteinsx_§sesure Sans_£2rrslatisn
U1 -0.1238
U2 -o.204o
(Kalay [1991], p.441, Table 1)
In both cases the sample rank correlation is negative and
significantly different from zero: U1 is significant at the

0.05 level and U2 is significant at the 0.01 level. These

results suggest that firms with higher earnings uncertainty

128

 

have lower payout ratios.

Chi-squared tests of the independence of changes in
uncertainty and changes in payout at the individual firm
level were conducted using the time series of payout and

uncertainty for each firm.

a
s nt o t o 47 F
c t as 1:
U1 -o.1239
U2 -o.204o

Critical values 0.05 and 0.10 levels of
significance are 3.84 and 2.71 respectively.
(Kalay [1981], p.442, Table 2)

These tests suggest that dividend payout and earnings
uncertainty are unrelated. Kalay speculates that this
discrepancy between time series and cross-sectional results
may reflect a failure in the cross-sectional tests to
control for other variables which are potentially correlated
with earnings uncertainty, in particular, leverage.

Rozeff [1982] found similar results in a cross-
sectional regression. The objective of this study was to
identify possible links between dividend policy and various
proxies for agency costs. Since the study was not directed
at the relationship between dividend payout and risk this
issue is dealt with only in passing. In order to control
for risk a measure of 3 was included in the regression. The

sample used by Rozeff consists of 1000 firms listed in the

129

 

Value Line Investment Survey of June 5th, 1981 and spanning
the years 1974—1980. Firms in the following industry
categories are excluded: regulated firms (gas, telephone,
electrical utilities, air transport, railroad, banking,
insurance, savings and loan, and investment companies),
foreign firms, and firms involved in petroleum exploration.
Rozeff employs a smoothing process to estimate each firm's
'target' payout ratio as an arithmetic average of the actual
payout ratios recorded during the period of the study. This
variable is then regressed on several growth variables,
Value Line beta, measures of inside ownership, and total
number of stockholders. Regression results are as follows

(see Rozeff [1982], p.256):

variable WW L_LL_-sta ’stic
Constant . 47.810 12.83
Percent Inside Ownership -0.090 -4.10
Average Revenue Growth -0.321 -6.38
Value Line Forecast Growth -0.526 -6.43
Value Line Beta -26.543 -l7.05
ln(number of stockholders) 2.584 7.73
Regression R2== 0.48 F-statistic = 185.47

One of the more striking results of this study is the large,
strongly significant, negative coefficient of Value Line

beta. Rozeff’s view of this is as follows:

"There are many reports in the literature that
beta is negatively related to dividend payout, but
explanations of this phenomenon are in short
supply. The author’s view is that high beta firms
are more likely to require costly external
financing, other things equal. Hence, they

130

 

intentionally choose lower dividend payout
policies. This explanation relies on the fact
that beta incorporates operating and financial
leverage."

(Rozeff [1982], p. 257)

An alternative explanation, consistent with the signalling
and clientele literature, would be that changes in dividend
policy affect the frequency and magnitude of price changes
and therefore contribute to risk. Although Rozeff's study
did not address the possibility of an omitted leverage I
variable, and the use of a ’target' payout ratio may to some

extent obscure the true relationship between payout and

 

risk, the presence of strong statistical significance in the
context of a smoothed dependent variable may suggest the
existence of a causal underlying relationship. That is, the
smoothing process may proxy for the explicit use of lags.

The current study seeks to investigate this possibility.

Di Fa o t nd sk:

The hypothesis that dividend payout causally precedes
risk is tested via Granger [1969,1980] causality
methodology. Leverage concerns of the sort raised by Kalay
are not an issue here since only firm specific time series
tests are performed and thus the potential problem of
leverage differences inducing bias in cross-sectional
results does not arise. However, as discussed below,

leverage may pose problems in the sense that if we find a

131

causal relationship between risk and payout, but a leverage
variable is not included in the test, we cannot preclude the
possibility that leverage rather than risk is the true
causal factor.
Two risk variables, OLS beta and standard deviation of
returns, are used in the initial work. The possible
outcomes can be summarized as follows: .
i) a) payout causes OLS beta: since systematic risk a
has been demonstrated to be a determinant of
value, this finding would imply that dividend
policy is a relevant concern. I
b) payout causes standard deviation of returns:
this finding may indicate that a potential for
agency problems (as in Jensen and Meckling [1976])
exists, particularly if a) above is found not to
be true, since managers are likely to be more
concerned about a firm's total risk than are
shareholders.
ii) a) OLS beta causes payout: this would support the
costly external financing explanation put forward
by Rozeff and cited above.
b) standard deviation of returns causes payout:
once again this raises potential agency concerns,
although by itself it is not conclusive.
iii) no causal relationship: this does not rule out the

possibility of a strictly contemporaneous causal

132

 

relationship.
Furthermore, it should be noted that sections i.) and ii.)
above are not mutually exclusive since causality can be bi-

directional.

M:

Tests for the presence of a causal relationship between
risk and payout were carried out using the methodology
proposed by Granger [1969,1980] and discussed in section
III. In the bivariate case with symmetric lags this reduces

to two regression equations of the form:

n n
RISKt = a0 +.2 aiRISKH + .2 fijPAYOUTM. + at (14)
l=1 j=1
n n
PAYOUTt = F0 + 2 PIPAYOUTH. + 2 6iRISKH + “t (15)
j=1 i=1

As discussed in section III the operational definition of
this methodology requires that the dataset used approximates
the universe of information available at time t that could
have a bearing on the variables involved. Obviously, if a
much longer series were available it would be theoretically
preferable to conduct this test with many more explanatory
variables, and more lags, included in the equations. Data
limitations and power considerations prohibit this in the
current study. However, the results of Rozeff [1982] lend
some support to the choice of the bivariate model. In

133

 

Rozeff’s cross-sectional regression of target payout on a
variety of explanatory variables, OLS beta emerged with a t
statistic nearly three times that of any other variable in
the equation. One remaining issue is that Rozeff did not
include a measure of leverage in his study. Since leverage
is known to be strongly correlated with OLS beta any
findings showing significance of this variable would be
confounded by the fact that it could be proxying for
leverage. On the other hand, the results of a test using a
trivariate model, with both risk and leverage measures
included, are not likely to prove illuminating due to the
multicollinearity problems which would arise. As in most
cases where potential explanatory variables are known to be
correlated, the order of precedence must be established on
theoretical grounds. Since it appears to be more plausible
that changes in leverage precede changes in risk measures
than that changes in risk measures precede changes in
leverage, risk variables rather than leverage variables are

used in the current study. Thus, the specification of the

model in the current study seeks to strike a balance between

theoretical and practical considerations by including a
limited number of the most relevant variables.

In the context of equations (14) and (15), testing the
hypothesis that PAYOUT causally precedes RISK amounts to a
test of the significance of the B and 6 coefficients in

these equations. If 8 proves to be statistically

134

‘=W'_' ; " -....-

 

significant while 6 does not, we would reject the null
hypothesis in favor of the alternative hypothesis that
PAYOUT ’Granger causes’ RISK.

There is, however, an important underlying assumption
in the development of this model which constitutes a
precondition for its application: that is, the series must
be stationary. Stationarity and techniques for testing for

its presence are discussed in section III above.

W:

The sample used for the initial tests included all
firms that met the following criteria:
a) listed on both the Annual Compustat tape and
the CRSP Daily tape for the period 1969
through 1988;
b) fiscal year-end in December throughout the

sample period;

c) no firms with more than one class of common
stock:
d) no missing payout observations.

This screening process resulted in a sample of 506 firms.
Imposing the non-singularity requirement necessary in order
to make estimation of the test equations feasible further
reduced the sample to 483 firms. Of the cases of
singularity, 21 were attributable to firms with zero payout

over the entire sample period and 2 were attributable to

135

 

firms with zero payout over all but one year of the sample
period. For purposes of this study the payout variable is

defined as:

COMMON DIVIDENDS
PAYOUT =

 

(NET INCOME - PREFERRED DIVIDENDS)

The items on the right hand side of the above equation
correspond to the following Compustat item numbers:

18 Income Before Extraordinary Items

19 Preferred Dividends

21 Common Dividends
Risk variables used are OLS beta and standard deviation of
returns. These were computed from returns series on the
CRSP Daily Tape using non-overlapping daily series for each
calendar year. Firms for which data were not available for

the full year were excluded from the sample.

I as es lt : First, in order to address the
stationarity issue discussed above, Dickey-Fuller [1979]
test statistics were computed for each of the series
involved in the study. The following results were obtained
by comparing these test statistics to the appropriate

critical valuess:

136

g: I'll-1 73:1,,

 

O- O 8 t6

 

ve
(Percent of Sample Firms Significant)
W
Series L91 1.9.2.5 0.05
PAYOUT 36.36% 47.43% 60.28%
STD DEV 76.68 86.36 91.70
OLS BETA 49.41 66.80 77.27

In an effort to a achieve a higher proportion of sample
firms exhibiting stationarity at a significant level, the

series were first differenced.

c -Fu e s St t tics

W
(Percent of Sample Firms Significant)

v ~ c n

Series 9&2; 2‘03; 9.05
PAYOUT 61.07% 72.92% 80.04%
STD DEV 69.96 86.17 93.48
OLS BETA 56.92 74.31 89.53

frable v.1 gives selected percentiles of these test
statistics. Significant test statistics are denoted by an
Easterisk. Histograms showing these results are provided in
IFigures V.1 — V.3. Note that for some firms this
transformation appears to have induced a unit root where
there was none before. Thus, for the STD DEV series, a
Lower percentage of firms exhibit stationarity at the 0.01
level of significance after the transformation than before
the transformation. Nevertheless, at the 0.05 level, the
transformation helps more than it hurts. Indeed, since a
substantial majority of firms appear to exhibit stationarity

137

 

 

in all three series with the differencing transformation, it
is the transformed rather than the raw series which are used
in the subsequent causality tests.
Selected percentiles of the F-statistics resulting from
the causality tests performed on these series are provided
in Table v.1. These tests were performed as described above
with two lags on both the payout and risk variables. Thus, 1.
the degrees of freedom for the F-tests involved are 2 in the g
numerator and 12 in the denominator. '
Although the results are slightly slanted towards
significance of lagged PAYOUT in the second test, they are é
not grounds for acceptance of the hypothesis that dividend
payout Granger causes risk at a statistically significant
level. In fact if we apply the critical value of 3.81 for
significance at the c=0.05 level with 2 degrees of freedom
in the numerator and 12 degrees of freedom in the
denominator, under the null hypothesis of no causal
relationship, we can view this as repeated sampling from the
binomial distribution with p=0.05. This can be used to
obtain some insight regarding the overall significance of
the test results by evaluating the complement of the
cumulative binomial probability, P{N>k}, for the number of
significant observations of the F-statistic found.
The table below shows the frequency count of F-
statistics significant at the a=0.05 level for the 483 firms

in the sample. These F-statistics are for block exclusion

138

tests of all lags of the variable named. Thus, the F-
statistics for OLS beta relate to tests of the hypothesis
that lagged OLS beta is statistically significant in
explaining current dividend payout. The resulting

cumulative binomial probabilities are as follows:

W
enc e i s
Pumas, z, 12 = 3'31
heuristics 2331212021 ELLA—inc 1:1 P 11>):
Payout(Beta) 0.6242
OLS Beta 28 0.1802
Payout(SDev) 46 0.0000
Std. Dev. 31 0.0670

These are the probabilities, under the null hypothesis, of
finding a higher frequency of significant F-statistics than
that actually observed in the sample of firms studied. They
could therefore be viewed as measures of the significance
levels of the aggregate test results. A lower cumulative
binomial probability would correspond to greater
significance in the test results.

Alternatively, the x2 goodness-of-fit test provides a
useful means of measuring the aggregate significance of the
sample F-statistics. In this test a frequency table of the
sample F-statistics, rather than a simple proportion, is
used to test the hypothesis that the distribution of the
sample statistics conforms to the F distribution under the

null. A x? statistic greater than the critical value

139

 

 

indicates rejection of this hypothesis.

2
W
Sample Period 1969-1288

1 1-e=0.95,df=19 = 30'1‘

2mm; 5:
Payout 26.8551
OLS Beta 10.6232
Payout 46.3168 *
Std. Dev. 22.8799

The direction of the relationship between the test
statistics and the F distribution under the null hypothesis
is clear from Table V.1 and from the binomial test shown
above. It is evident from these results that when standard
deviation of returns is used as the risk variable the null
hypothesis is rejected in a significant proportion of sample
firms. It appears that in these firms changes in dividend
payout precede changes in price risk, but do not necessarily
precede changes in market risk. As noted earlier, findings
of this sort could be construed as evidence supporting
signalling and/or clientele effects.

Segmenting the results of both tests further by means
of histograms (see Figures v.4 through V.7), this
observation comes through even more clearly. There is
evidence of the originally hypothesized relationship between

the PAYOUT and STD DEV series but none between the PAYOUT

140

 

 

 

and OLS BETA series.

At this stage it may be helpful to examine the various
factors which may contribute to the lack of clearly
interpretable results:

i) The temporal screen may be too coarse. That

is, the observations may be spaced too far apart.

Even in the presence of a clear uni-directional

causal relationship this could lead to findings of

bi-directional causality, or, if the underlying
relationship is contemporaneous within the context
of the temporal screen, no causality. While
quarterly data is available, its information content
is suspect due to the common practice of paying
dividends quarterly while only making changes in
dividends annually. Thus, with existing data one
may establish a prima facie case supporting
causality. However, one cannot establish a case for
its rejection.

ii) The series may be too short. Since the current

Compustat tape includes only 20 annual observations

per firm, the payout series is necessarily limited.

After first differencing, and including an

intercept, the degrees of freedom for the

unrestricted model are reduced to 12. This raises
concerns regarding the power of the test. As

evidenced by the simulation results in the earlier

141

 

section, a moderately strong non-contemporaneous
causal relationship can be consistently detected
with series of this length. However, with a
stronger contemporaneous element to the
relationship, and more noise, the discriminatory
power of the test drops precipitously. This concern
is addressed later in the current study through the E
use of a back-dated Compustat tape which provides 18 1
additional observations for firms in operation for

the entire 38 years covered by both tapes.

 

iii) Stationarity conditions may not have been 6
adequately net. It is noteworthy that a weak causal
relationship between PAYOUT and STD DEV is hinted at
while the same did not hold true when OLS BETA was
used as the risk variable. It is possible that this
phenomenon is attributable at least in part to the
weaker stationarity of the OLS BETA series. If this
does not provide a satisfactory explanation for the
discrepancy, then this would suggest that the agency
dimension of this problem could be a fruitful area
for further investigation.

iv) Results may be obscured by firms with 'sticky'
dividends. Specifically, highly regulated firms
.such as utilities, banks, and insurance companies
for which market imperfections may be viewed as

particularly pronounced may exhibit behavior which

142

is not representative of other less regulated firms.
v) An alternative specification of the PAYOUT
variable may be more appropriate. That is, changes
in the dividend payout ratio may not be an
appropriate proxy for changes in dividend policy.
Specifically, since PAYOUT incorporates two sources
of variance, dividend policy effects may be
confounded with earnings effects or totally

obscured.

Tests t d D :

Although all of the concerns listed above may bear further
consideration, augmentation of the data series to improve
the power of the test appeared to hold the most promise.
Using the Compustat Backdata tape in conjunction with the
current tape series of 38 annual observations covering the
period 1952-1989 were constructed. Since the CRSP Daily
tape only contains data going back as far as 1962, risk
series were constructed using monthly return observations
from within each year. These data were obtained from the
CRSP monthly tape. Although this approach may result in
less accurate risk observations than those obtainable from
daily data, the greater degrees of freedom available with
the longer series should improve estimational efficiency.
It is not clear which effect predominates.

In addition screens were implemented to exclude banks,

143

 

utilities, insurance companies, ADR’s, limited partnerships
and real estate investment trusts: that is, firms for which
the regulatory environment would tend to make dividends
particularly sticky. Also, firms with zero dividend payout
over the entire sample period were excluded in order to
avoid cases of singularity. This resulted in a data set

consisting of 115 firms for which payout and risk data were

_-:F'

available for the entire 38 year sample period. I
Initially, stationarity tests were performed on the
series. Since a large proportion of the firms in the sample
exhibit stationarity in the raw series, the results of these
tests and the related causality tests using the raw series

are presented in Table v.2. Although the results are
consistent with those for the larger sample shown in Table
v.1, they are still far from conclusive.

Since stationarity is accepted in a far greater
proportion of cases when the differenced series are used,
the causality tests performed on these series would appear
to be more relevant. The results of these tests are
presented in Table v.3 and the accompanying histograms in
Figures v.8 - v.14. Although the results are still far from
conclusive, if we return to the application of the binomial
distribution presented earlier, it is clear that the
relationship between dividend payout and standard deviation
of returns observed earlier is still present in a

significant proportion of firms.

144

838212_£2£12§_12§2:12§2
ced s
Fd_05.2.a = 3 . 33

123.951.9119.: frames! Maill’wk
Payout(Beta) 6 0.3525
OLS Beta 3 0.8321
Payout(SDev) 12 0.0050
Std. Dev. 8 0.1126

Once again, the 12 goodness-of-fit test provides a
convenient means of comparing the distribution of these F
statistics with the distribution of the F statistics under
the null hypothesis of no causal relationship between the

variables.

12 Goodnggs-of-zir Trgrr
grmple Period 1953-1982

fferenced Serie 5 s
X 1-e=0.95,df-19 = 30'1‘
z-srarigricg l:
Payout 27.7826
OLS Beta 20.4783
Payout 18.7391
Std. Dev. 14.5652

These results, although statistically insignificant,
represent a reversal of the results obtained over the
shorter 1969-1988 sample period in the sense that dividend
payout appears to have stronger significance in explaining
OLS Beta than in explaining standard deviation. This

suggests that the unusually high frequency count on the

145

- ==mflrpf

PAYOUT F-statistics in the second section of the first of
the two tables on the previous page is an aberration, and
the distribution of the test statistics overall closely
matches the F distribution under the null hypothesis. Thus,
over the longer sample period, the test results do not
support the hypothesis that dividend payout Granger causes
risk.

929211321211:
Although the results of the tests performed do not lead to
an unambiguous acceptance of the hypothesis that dividend
payout Granger causes risk, the available data does not
allow for unambiguous rejection. Perhaps the most notable
result in this study is the evident reversal of the
relationship between dividend payout and OLS beta and
dividend payout and standard deviation of returns. It
should be noted that although the x? statistic for dividend
payout in the causality test of dividend payout and OLS beta
is not significant at the a=0.05 level it is significant at
the a=0.10 level. Thus, there is evidence in support of an
empirical relationship between dividend payout and risk.
Specifically, at the a=0.10 level we would reject the null
hypothesis in favor of the hypothesis that dividend payout
Granger causes OLS beta.

The results obtained with shorter time series suggested

that changes in dividend payout precede changes in

146

g"

volatility more often than changes in systematic risk. Such
findings would imply that changes in dividend payout
contribute (at least in some firms) to increased non-
systematic risk. This interpretation is consistent with the
signalling and clientele effect literature but does not
necessarily have any immediate implication for firm value.
However, the results obtained with the longer data series
have more serious implications. If in fact dividend payout
Granger causes systematic risk, even in a minority of firms,
then dividend policy does affect firm value, at least for
these firms.

In order to confirm and possibly further illuminate
this phenomenon a thorough attempt should be made to
identify the unique characteristics of the current
statistically significant subset of the sample, i.e. in
terms of dividend policy, leverage, market capitalization,
etc. In particular it may be helpful to compare these
results to those obtained from causality tests for a
relationship between dividend policy and leverage. Although
it is possible that the results observed in this study are
driven by disparities in leverage it appears unlikely since

leverage differences should be closely related to beta.

147

 

Table V.l

Empirical Test for Causality between Payout and Risk, T=19
Differenced Variables, 483 Firms
Samplc Puriod 1969-1988

 

Percentile

Percentile

Percentile

I' 1 “E 11 E! !i !'
Critical Value of DFagoJr‘Mfl19 = -3.05
DF¢=0.10,n=19 = '2'57
281991 QLE_§§L§ 5:91.292; ;
5 -1.4184 -2.7075 -2.8470 m
10 -2.4508 -2.9971 -3.0760*
25 -3.3324* -3.3224* -3.5610*
50 -4.1846* -3.9311* -4.0282* .‘
75 -4.9337* -4.5831* -4.5505* ‘
90 -5.8435* -5.4442* -5.0939*
95 -7.0387* -5.8287* -5.4398*
mm
Critical Value of Fc-0.05,2,12 : 3.81
F111:0.1o,2,12 " 2°76

W
QL§.B§§Q

10
25
50
75
90
95

US

10
25
50
75
90
95

222923
0.0459

0.0931
0.2759
0.6344
1.5962
2.7530
3.5122

EEIQQL
0.0425

0.0769
0.3307
0.8975
1.9622
3.3737

5.3519*

148

0.0504
0.1040
0.2788
0.6804
1.4606
2.8473
3.9760

g Lg . Dev

0.0412
0.0812
0.2508
0.6613
1.4868
2.9178
4.1002

*

d

*

 

Table v.2

Empirical Test for Causality between Payout and Risk, T=38

Levels of Variables, 115 Firms

Sample Period 1953-1989

 

WM
Critical Value of DFaao.os,n-:39 : -2.95
DFa-o.1o,n-39 " ’2'”
282291 QL£_B§§§ §§Q1_D§!1
5 0.6868 -2.9437* -2.1006
10 -1.0129 -3.1155* -2.3502
25 -2.1350 -3.3843* -2.8287
Percentile 50 -2.8931 -4.0455* -3.7241*
75 -4.0271* -4.8744* -4.3042*
90 -4.7311* -5.5325* -4.7671*
95 -5.1224* -5.7530* -5.2189*
- s 5
Critical Value of Fa-0.05,2,31 : 3.33
«mnmzs1" 2'49
Can a t s o n 0 Beta
Bayou; OLS Beta
5 0.0425 0.0485
10 0.1012 0.0911
25 0.3602 0.2323
Percentile 50 0.7630 0.5428
75 1.7098 1.1065
90 2.4885 1.8500
95 3.3644* 2.4814

Causality Tesr of Payout and Std. Dev.

Percentile

5
10
25
50
75
90
95

Euyuuu Std,Dev,
0.1037 0.1010
0.2373 0.1326
0.5924 0.4389
1.2964 0.8697
2.3795 1.7325
3.7173* 3.3222
4.6893* 4.9369*

149

 

Ii

Table V.3

Empirical Test for Causality between Payout and Risk, T=37
Differenced Variables, 115 Firms
Sample Period 1953-1989

 

-F ta istics
Critical Value of DFaIO.05,n=37 : -2.95
DFaso.1o,na37 "' "2'62
281991 §£Q1_D§XI
5 -3.4821* -5.2902* -4.9601*
10 -4.1742* -5.6527* -5.3364*
25 -5.0150* -6.3314* -5.6848*
Percentile 50 -6.1568* -7.1034* -6.2449*
75 -6.9773* -8.0589* -7.l372*
90 -8.3398* -9.0011* -7.7847*
95 -9.6348* -9.6435* -8.2933*
mm
Critical Value of Fa=0.05,2,30 : 3.33
azo.1o,2,30 " 2'49
Causulity Tear g: Bayou; and OLS Beta
£52225 QL§_§§£Q
5 0.0263 0.0264
10 0.0910 0.0769
25 0.3081 0.2552
Percentile 50 0.7488 0.6242
75 1.6695 1.2752
90 2.6629 2.0306
95 3.0172 2.5481
Causal' T st a on nd Std. Dev.
a t . D .
5 0.0383 0.0285
10 0.0795 0.0906
25 0.3505 0.2817
Percentile 50 0.8190 0.6906
75 1.6625 1.4749
90 3.1456 2.7328
95 5.9608* 3.7035*

150

 

 

Figure V. l

Dickey-Fuller Test for Stationarity of Dividend Payout
Differenced Series, T=19

The hypothesis that one of the p+1 roots of the characteristic
equation is unity can be tested by computing a ’t-like’
statistic consisting of B/SE (B) from the following regression:

p
(1-L)Irt = a + gym +1E1ri(1-L)Yt'i + at (4)

 

E

1?

 

[ cumbeosunonsww

 

Number of Occurrences
1? §

1‘

 

 

95.39 <11.’ 1.! ..- -19 115’. .1... - 9.
mm

151

 

 

 

Figure V. 2

Dickey-Fuller Test for Stationarity of OLS Beta
Differenced Series, T=19

The hypothesis that one of the p+1 roots of the characteristic
equation is unity can be tested by computing a ’t-like'
statistic consisting of B/SE(3) from the following regression:

p
(l-L)Yt = a + 911?1 +1311 I‘.(:I-L)1:H + et (4)

uthm:

 

 

 

 

 

 

‘P

Number of Occurrences

 

 

 

 

 

 

 

 

 

 

 

 

 

.. WWW I I
? I
H .I I I I I' I WIIIII

5%M”Hm ab e&”'5m em 4% a:
quruusdwa

152

Figure V.3

Dickey-Fuller Test for Stationarity of Standard Deviation
Differenced Series, T=19

The hypothesis that one of the p+l roots of the characteristic
equation is unity can be tested by computing a ’t—like'
statistic consisting of B/SE (B) from the following regression:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(1-L)IIt = a + 92” +82 Pi(l-L)YH + at (4)
i=1
409nmn
E
I'
20" .
I mmuaosemonsww I
£19 I
= I
§ I
' I
£10. ”I I
2 I I
. I 1,
5— II
. I I..IIIIIII|I II I ..
6.05 '-X 5.4 {.18 '4.” 4.07 1 -1
WM

153

 

 

Figure v.4

Significance of Dividend Payout in Explaining OLS Beta

Differenced Series, T=19
Block 2 Test for Exclusion of Dividend Payout

 

 

 

 

 

 

 

2 2
BETAt = a0 +.2 aiBETAH + .2 pijyou'rt_j + at (14)
1=1 3=1
CmBSMHmenawEbmuwaflmm
70
a»
ar
ééur
‘5
.230" I wmhamehawwm
3
a}
IN I
m I“IJ””JHMH..JII III . . . .. . . .
-.1 e; n 7a a: #3 mun

 

1.17 2.34
PM

154

 

Figure v.5

Significance of ODS Beta in Explaining Dividend Payout
Differenced Series, T=19
Block F Test for Exclusion of ODS Beta

 

 

 

 

 

 

 

2 2
PAYOUTt = r0 + 2 I‘jpmrou'rt,j + z: SiBE'l‘AH + at (15)
j=1 i=1
CandefiwunamHhmdwafimu
no
1«»
E ar
g ..
3 I mmuamemmmm
E
5
«r
I
2. I
& IIIIIIIIIII.I..I... .
moo 2. ass 11.1 1am 1a. 1a 2234 1a

 

PM

155

 

 

 

Figure v.6

Significance of Dividend Payout in Explaining Std. Deviation

Differenced Series, T=19
Block F Test for Exclusion of Dividend Payout

2 2
smavt = a0 +.§1aiSDEVt_i +jzz-lfijPAYOUTt-j + at (14)

CausalitszaywtandSDav..483FIms

 

§

‘5

 

”Wham INQNWM

 

 

‘3

Number 0! Occurrencee
§

#3

 

1

Q 1

 

 

III

 

 

 

10~
0

.Il ..lIIIIE. I... IiI .. ..... .. . ..
4. 9 : ' I 1*" 154 111
sedan

156

 

 

Figure v.7

Significance of Std. Deviation in Explaining Dividend Payout

Differenced Series, T=19
Block F Test for Exclusion of Std. Deviation

2 2
PAYOUTt = to + z: FJPAYOUTt_j + z 6iSDEVM. + fit (15)
j=1 i=1

(xmamthwmumdSuw.«thms

 

9

 

 

$

 

GIMMDSM INQNWM

 

Number of Occurrences
$

  

#3

 

#5

I I I I I
I! : -" n42 1.1
Feeds

munhhdflhuuhlluhl.
139 2.73 41 .55.-

157

 

 

fir... ’

Figure v. S

Dickey-Fuller Test for Stationarity of Dividend Payout
Differenced Series, T=37

The hypothesis that one of the p+1 roots of the characteristic
equation is unity can be tested by computing a 't-like’
statistic consisting of fi/SE (B) from the following regression:

p
(1-L)Irt = a + 3y“ +1331 Pi(1-L)YH + at (4)

115Flrms

 

 

 

 

 

 

 

 

 

 

 

10-
G-
g mme-zesemaosmm
5.
3 .
E I
2 l
4-
2¢ : ;
6 ll. ,HIIIIIII l
H l
40.11 £13 £15 4.1 '2. : . 1. . 4
WWW

158

 

 

 

Figure v. 9

Dickey-Fuller Test for Stationarity of OLS Beta
Differenced Series, T=37

The hypothesis that one of the p+1 roots of the characteristic
equation is unity can be tested by computing a ’t-like’
statistic consisting of B/SE (B) from the following regression:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

P
(1-L)Yt== a + )9th1 + 2 Pia-Lug,i + at (4)
i=1
115kas
«e
4-
as
cumeeesehaosmuw
g} 1 I
525-
a
§2~ M
3 .
z I .I
15- I I
'- ” ’ I * i” I II
I I: I I I
G II T IIIIII I I; L
4zd3”3fr"1mb‘ £31 emr em: Imus an 4n:

 

 

 

 

 

 

 

mm

159

 

Figure v. 10

Dickey-Fuller Test for Stationarity of Standard Deviation
Differenced Series, T=37

The hypothesis that one of the p+l roots of the characteristic
equation is unity can be tested by computing a 't-like’
statistic consisting of B/SE (B) from the following regression:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

P
(1-L)I{t = a + mm + z Pia-Ln!H + e:t (4)
i=1
H5Hmm

4.5+

4. animus-macaw“

as I
g .
’ I
32.5. I
s i
E . I
3
z I I

t& II * I

1. I I I ; II ..-- g I I

ay I' '

. 'I' I
4.1 ”"33“” "1 -os -I 4.75 w 432 .* . "'1
warm:-

160

 

 

Figure v.11

Significance of Dividend Payout in Explaining OLS Beta
Differenced Series, T=37
Block F Test for Exclusion of Dividend Payout

2 2
BETAt --- a0 + z aiBETAt_i + .3 BJPAYOUTH + et (14)
i=1 j=1
CamdMnmenaUBMa1flHWms

 

12—

10*

 

T

WWbSQIhOBSMdW

 

 

 

Number of Occurrences

 

 

Y f 4;?

 

 

 

0.” 1.1102.»

0.1‘1
PM

161

 

 

 

Figure v.12

Significance of OLS Beta in Explaining Dividend Payout
Differenced Series, T=37
Block F Test for Exclusion of OLS Beta

 

 

 

 

 

 

 

 

2 2
PAYOUTt = to + z PJPAYOUTt.j + z 1593311pri + pt (15)
j=1 i=1
(humMnchnsuBmaIflflwms
12
10
g e 1
g Lcumbwsmaosmuugm
S
g o-
E
3
z I
4— .
s ' . i
IIIII IIIIIIII II | I I |
. I5
o- 1 II I
0.1'1 1' 1.13 1. 9» :1 3.33 V « 5.1
PM

162

 

 

 

Figure v.13

Significance of Dividend Payout in Explaining Std. Deviation
Differenced Series, T=37
Block F Test for Exclusion of Dividend Payout

Number of Occurrences

2 2
SDEVt = a0 +i_2.1az,sr)1::vt_i +j§1fi5PAYOUTM + at

mumpayaamdsoev..1151=m

(14)

 

 

 

 

 

 

1c
8‘ I I cumhmenaoswdw
. I -
I
‘ I
" i
s
I ? II III I
. I 1| III I I II II III
PM

163

I
11.1

 

 

 

 

 

Figure v.14

Significance of Std. Deviation in Explaining Dividend Payout
Differenced Series, T=37 .
Block F Test for Exclusion of Std. Deviation

2 2
qurou'rt = I‘0 + z: I‘jPAYOUTt_j + 2: SISDEVH + pt (15)
j=l i=1

CadeKkunauSDmQIEHTms

 

 

 

+

Number of Occurrences
‘f‘

 

 

 

 

 

 

II I [ mmuwuummam
I
I

I
I
I
I
IIII

II I II

II
II II IIIII

1:10 15! I» w. .1 .111.
Pm

 

 

 

 

 

 

164

 

 

£229.22!

This is essentially the test suggested by Dickey and
Fuller [1979], p.431, but without the time trend term.

The 'augmented' Dickey-Fuller test used in much of the
empirical literature was used to confirm the stationarity
of the series” This is essentially the test suggested by
Dickey and Fuller [1979], p. 431, but without the time
trend term. The tables in Fuller [1976], and Schmidt
[1990] only provide critical values for selected sample
sizes. However, the changes in critical value from
sample size T to T-1 become more pronounced as T
declines, making interpolation difficult. Fortunately,
Peter Schmidt was willing to provide a Monte Carlo
simulation routine capable of producing critical values
for any sample size, thus resolving the difficulty.

It is interesting to note that Smirlock and Marshall
report 194 firms which pass this screen over the sample
period 1958 - 1977. This suggests that the investment
variable used in their study was constructed with the
intention of obtaining a proxy for gross rather than net
investment. Unfortunately, the published version of
Smirlock and Marshall’s study is vague on this point and
repeated attempts to obtain clarification from the
authors have been unsuccessful. Had information
specifying the exact construction of their investment
variable been available, it would have been interesting
and perhaps instructive to follow up on the attempt to
replicate their study with the data currently available.

Pierce and.Haugh [1977] p. 274, Theorem.4.2, derive seven
equivalent conditions, any one of which could be used to
demonstrate the absence of a causal relationship if
sufficient data are available to apply it in a practical
context.

See note 2.

165

 

 

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169