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Federal Reserve Bank of Chicago
An Empirical Examination of the PriceDividend Relation with Dividend
Management
By: Lucy F. Ackert and William C.
Hunter
WP 2000-22
Lucy F. Ackert, PhD
Department of Economics and Finance
Michael J. Coles College of Business
Kennesaw State University
1000 Chastain Road
Kennesaw, GA 31044
(770) 423-6111
and
Research Department
Federal Reserve Bank of Atlanta
104 Marietta Street NW
Atlanta, GA 30303
William C. Hunter, PhD
Research Department
Federal Reserve Bank of Chicago
230 South La Salle Street
Chicago, IL 60604
(312) 322-5800
chunter@frbchi.org
December 2000
The views expressed here are those of the authors and not necessarily those of the Federal Reserve
Banks of Atlanta or Chicago or the Federal Reserve System. The authors thank Roberto Chang,
Paul Childs, Bryan Church, Brian Smith, Mary Beth Walker, Olivier de Bandt, Gerald Dwyer, and
workshop participants at Universite Laval, the University of Waterloo, Auburn University, Wake
Forest University, and the University of Oklahoma for helpful comments. All errors are the authors'
responsibility.
Some recent empirical evidence suggests that stock prices are not properly modelled as the
present discounted value of expected dividends. In this paper we estimate a present value model of
stock price that is capable of explaining the observed long-term trends in stock prices. The model
recognizes that firm managers control cash dividend payments. The model estimates indicate that
stock price movements may be explained by managerial behavior.
-2-
This paper empirically examines the relationship between stock price and cash dividends.
Despite much research into the determinants of stock price fluctuations, economists continue to
debate whether changes in stock prices reflect rational responses to changes in fundamentals. We
show that the observed relationship between aggregate stock price and dividends may be explained
by how managers choose dividend payout.
Early research on the speculative behavior of stock prices strongly supports the efficient
markets hypothesis.1 The economic rationale for such behavior is that, in competitive markets, the
actions of well-informed participants are reflected asset prices. Since the influential paper by Lucas
(1978), who constructed an equilibrium model that linked asset prices to their underlying dividend
processes, the efficiency of the stock market has generally been equated with the notion that the price
of a stock is equal to the present discounted value of its dividends.2 The view that stock prices are
determined by so-called fundamentals like earnings and dividends has its origins in the early works
of Graham and Dodd (1934) and Williams (1938).
More recently, compelling empirical evidence suggests that the view that a stock's value is
intrinsically equal to the present value of its dividends is incomplete. Perhaps the strongest evidence
against the present value model is the apparent excess volatility of stock prices. 3 LeRoy and Porter
(1981), Shiller (1981), and West (1988a), among others, reject the simple present value model based
on the results of variance-bound inequality tests. Their tests indicate that stock prices are too volatile
to be determined by the present value of dividends.
improvements to the present value model resulted.
Numerous attempts at parsimonious
Although the observed deviations in stock prices from prices predicted by the simple present
value model are large, no simple alternative to the present value model has received wide-spread
support. Proposed alternatives include models of rational bubbles.4 For example, Froot and Obstfeld
(1991a) use a rational ‘intrinsic’ bubble to model stock price. Their model is appealing because
deviations from present-value prices are driven by changes in fundamental value. Although rational
bubbles models have the potential to explain observed patterns in stock prices, they soon fell into
disfavor for various theoretical and empirical reasons. 5
In response to the evidence of excess volatility in stock prices, other studies focus on the
specification of variance-bound tests. Some dispute the validity of the tests and their assumptions
(e.g., Flavin, 1983; Kleidon, 1986a; Marsh and Merton, 1986; Mattey and Meese, 1986).6 For
example, Fama (1991) argues that because variance-bound tests assume constant expected returns,
they provide no information concerning market efficiency. Instead, violations of variance-bound
inequalities simply provide evidence of time-varying expected returns. In contrast, Ackert and Smith
(1993) point out that previous volatility tests use dividends narrowly defined to include only those
cash flows distributed to shareholders as ordinary dividends. Yet, the finance literature recognizes
that firms distribute cash through other methods (Miller and Modigliani, 1961; Shoven, 1986;
Bagwell and Shoven, 1989). Ackert and Smith show that West's (1988a) variance-bound test results
reverse if cash distributions to shareholders are defined to include other distributions such as those
made through share repurchases and takeovers. Thus, the level of stock price volatility is not
excessive when the present value relation is tested using a better cash flow measure. 7
Managers have almost complete discretion and control over the choice of dividend policy
because there are few, if any, legal and accounting constraints on the firm's policy (Marsh and
-4-
Merton, 1986).8,9 No theory of dividend policy fully describes managerial behavior though Lintner’s
(1956) classic study provides a foundation. His empirical documentation of the tendency of
managers to engage in dividend smoothing is supported by others (Fama and Babiak, 1968; Marsh
and Merton, 1986, 1987; Kleidon, 1986a, 1986b; and Lee, 1996). Nevertheless, researchers have
only recently proposed models of economic behavior that predict smoothing of cash dividends by
managers (Warther, 1994; Fudenberg and Tirole, 1995). In addition to ordinary cash dividends, the
importance of other cash flows to shareholders has been documented (Shoven, 1986; Bagwell and
Shoven, 1989; Ackert and Smith, 1993). Although management has sole responsibility for and
control over the dividends paid by the firm and can influence the intrinsic value of the firm by its
investment decisions, management has little, if any, control over stochastic or unanticipated changes
in the intrinsic value of the firm's shares.
The extant literature provides an incomplete explanation of the relationship between
dividends, fundamentals, and stock prices. As Marsh and Merton argue "(s)ince management's
choice of dividend policy clearly affects the time-series variation in observed dividends, the
development of the relation between the volatility of dividends and rational stock prices requires
analysis of the linkage between the largely controllable dividend process and the largely
uncontrollable process for intrinsic value" (1986, p. 488).10 Ackert and Hunter (1999) propose a
model of dividend control as an alternative to the standard dividend smoothing model which
recognizes that the cash dividends paid by a firm are not necessarily equal to the firm’s intrinsic
value. In their model stock price is a function of unobservable fundamental value and observed,
ordinary cash dividends are managed by the firm.
In this paper, we further examine whether the empirical measure of dividends can explain
-5-
why we observe large and persistent deviations in stock prices from the prices predicted by the
present value model. To do so, we estimate Ackert and Hunter’s present value model of stock price
that, in line with the empirical evidence, takes as given managers’ ability to control ordinary cash
dividend payments. In examining the responsiveness of stock prices to changes in intrinsic value
or fundamentals, it is important to recognize that unanticipated changes in fundamentals are not
necessarily identical to unanticipated changes in ordinary cash dividends because these dividends
are controlled by managers. Thus, what appears to be evidence against the present value model may
be a result of improper empirical measurement of fundamentals.
The paper is structured as follows. In section 1, we describe the discounted present value
model of stock price. In section 2, we discuss the empirical methods employed, describe the data
used in the analysis, and report the estimates. Section 3 offers a conclusion and interpretation of the
results.
The intrinsic value of the firm's shares under the present-value model is obtained by
discounting the expected future dividend stream, i.e.,
t
=
∞
∫
t+s e
− ks
(1)
0
where Pt is the time t real stock price, Dt is the true real dividend or fundamental per share paid over
time t, E is the expectations operator, and k is the discount rate. With constant growth in dividends
(µ) and in the absence of dividend management, equation (1) has the familiar simple solution
-6-
t
t
=
(2)
−µ
where k > µ.
Deviations in actual stock prices from those predicted by the simple present value model are
large and persistent. Froot and Obstfeld (1991a) propose an intrinsic bubbles model that provides
"a more plausible empirical account of deviations from present-value pricing than do the traditional
examples of rational bubbles" (page 1189). Froot and Obstfeld model stock price using a rational
‘intrinsic’ bubble which depends exclusively on economic fundamentals, i.e., aggregate dividends,
and not on the extraneous or extrinsic factors which often underlie bubble terms. The Froot and
Obstfeld model is
t
=
t
−µ
+α
β1
t
(3)
Intrinsic bubbles are appealing because they are able to generate persistent deviations from presentvalue prices, but the deviations are driven exclusively by changes to fundamental value. Despite this
appeal, the intrinsic bubbles model has not ended the search for alternatives to the simple present
value model. These bubbles are arbitrary and problematic in that their existence depends on rather
stringent assumptions about investor behavior and the dynamic inefficiency of the economy. Froot
and Obstfeld assert that "(e)ven if one is reluctant to accept the bubble interpretation, the apparent
nonlinearity of the price:dividend relation requires attention" (1991a, p. 1208).
Using a model of regulated Brownian motion, Ackert and Hunter (1999) show that dividend
-7-
control gives a present value model that is observationally equivalent to the intrinsic bubbles model
proposed by Froot and Obstfeld given in (3) above. 11 In the case of dividend management, a problem
arises when empirically evaluating the present value relation in equation (1) because the true
dividend or fundamental (D t) is unobservable. Instead, we observe the managed dividend process
(dt). As shown by Ackert and Smith (1993) (see also Shoven (1986) and Bagwell and Shoven
(1989)) the observed dividend stream (dt) is much less volatile than the cash flows received by
shareholders. In addition, stock prices are underpredicted by ordinary cash dividends alone. Ackert
and Hunter show that the stock price equation
t
=
t
−µ
+α
β1
t
+γ
β2
t
(4)
results after specifying the relationship between observed dividends (dt) and intrinsic value (Dt ),
where β1 and β2 are the positive and negative roots of the quadratic equation
1
2
σ 2β β −
+
−µ β−
=
(5)
(Harrison (1985), Bentolila and Bertola (1990)). Although (4) is observationally equivalent to the
intrinsic bubbles model proposed by Froot and Obstfeld given in (3), this model of stock price is
based on observables. Furthermore, the nonlinearities in the model arise from a documented
managerial behavior rather than from arbitrary bubbles.12
Equation (4) implies that dPt /ddt > 1/(k-µ) so that the responsiveness of price to changes in
ordinary smoothed dividends is greater than that predicted by the simple present value model when
dividend control is ignored. The long term trends implied by the model in (4) do not depend on
bubbles but instead result from the control of dividend payments by managers.
-8-
In this section we report estimates of (4) using Standard and Poor's stock price and dividend
index series. In order to test (4) we first generalize the specification following Froot and Obstfeld
(1991a) by allowing error in the present value relation. The estimable model is
t
t
=
−µ
+α
β1
t
+γ
β2
t
+
t
(6)
where et is the present value of the errors in the present value relation. Due to collinearity in the right
hand side variables in equation (5) we estimate
t
t
=
0
+
1
β 1 −1
t
+
2
β2 −1
t
+ ηt
(7)
The model of dividend management and the simple present value model suggest that the constant
term (c0) equals 1/(k-µ). The dividend management model also implies that c1 is positive and c is
2
negative, whereas the simple present value model suggests that both c 1 and c 2 equal zero. The
validity of the null hypothesis of no dividend management is examined using a joint test of
restrictions on the coefficients, i.e., H0: c0 = 1/(k-µ), c1 = 0, c2 = 0.
We estimate equation (7) using Standard and Poor's stock price and dividend index series
from the
as extended by Alfred Cowles and Associates (1939) and
reported in Shiller (1989). The full length of the series runs from 1872 through 1987. We extended
the series to 1998 with additional data obtained from Standard and Poor's and the Bureau of Labor
Statistics. Following Froot and Obstfeld (1991a), we deflated January stock prices by the January
-9-
producer price index (PPI) and annual dividends by the average PPI for the year. We report
estimates for three sample periods. Although the series run from 1872 through 1998, we report
results based on the 1900-1998 sample period. The number of stocks included in the index was
limited in the early sample years so these years are excluded from the analysis (Froot and Obstfeld,
1991a, footnote 17).13 We also report estimates for two subperiods of this sample: 1900-1949 and
1950-1998. As pointed out by Kleidon (1986b), the importance of dividend smoothing appears to
have increased around 1950. We examine whether the model fit is substantially different for the two
subperiods.
Table 1 reports point estimates of the growth rate (µ) and variance of real dividends (σ2), the
real return on stock (k), and the roots of the quadratic equation (5) for each sample period. The point
estimates of the roots of the quadratic equation, β 1 and β 2, were obtained using the point estimates
of k and the parameters of the dividend process, µ and σ2.
In order to test the dividend management model, we estimated equation (7) using ordinary
least squares (OLS) techniques.14
We used Newey and West's (1987) autocorrelation and
heteroskedasticity consistent covariance matrix estimation to correct the estimates for
autocorrelation.15,16 We did not estimate the parameters simultaneously using an unrestricted
estimation technique such as nonlinear least squares. Equation (7) is likely to be a poorly identified
regression function whatever the true parameters values may be, but particularly so when the true
value of one of the parameters c0, c1, β1 - 1, or β2 - 1 is close to zero (Davidson and MacKinnon,
1993). It is very difficult to estimate the parameters of such a regression function with precision.17
Instead, we estimated equation (7) using OLS with β 1 and β2 constrained to equal the point estimates
reported in Table 1. We then used a Gauss-Newton regression (GNR) in order to gauge the accuracy
-10-
of our estimates.
Express the nonlinear regression model as
δ +
=
(8)
where δ is a k-vector of unknown parameters and x(δ) is a nonlinear regression function. Then the
GNR is
−
*
*
=
+
(9)
where X L Dx(δ) is a matrix of the derivatives of x(δ) with respect to δ, b is a k-vector of
coefficients, and the asterisks denote estimates. Whether the OLS estimates of δ are sufficiently
accurate can be gauged by estimating the GNR and testing whether each element of b differs
significantly from zero. The GNR for equation (7) is
t
0
t
+
−
*
0
−
*
β1 −1
1 t
+
β 1 −1
t
*
1
2
*
1
−
β2 −1
t
*
2
t
=
*
β1 −1
t
+
3
*
β2 −1
t
+
4
*
2
t
*
β2 −1
t
+
(10)
If b0, b1, b2, b3, and b4 do not differ significantly from zero, the parameter estimates are close the
nonlinear least squares estimates (Davidson and MacKinnon, 1993).
Table 2 reports the OLS estimates of equation (7) with t-statistics for tests of the null
hypothesis that each coefficient equals zero in parentheses. The second column of Table 2 reports
the estimate of the constant term in equation (7) for each sample period. We also report a t test of
the null hypothesis that c0 = 1/(k-µ). As the results of this test in the fifth column show, the null is
rejected in all three sample periods. In all three cases the estimated constant exceeds the
-11-
hypothesized value. The third and fourth columns of Table 2 report the estimates of the coefficients
of the nonlinear terms involving the positive and negative roots, β1 and β2 . Five out of six estimates
differ significantly from zero. Although the coefficients are not always significant, the estimated
signs are consistent with the model's predictions (c 1 > 0, c2 < 0) when the coefficient estimates differ
significantly from zero.
Additional analysis provides insight into the fit of the model of dividend management. Table
2 reports the results of three F-tests. The first is an F test (F test: No) of the null hypothesis of no
dividend management (c0 = 1/(k-µ), c1 = 0, c2 = 0). The null is rejected for all three sample periods
at the one-percent significance level. The seventh column reports a test (F test: No Slope) of the null
hypothesis that the slope coefficients are zero (c 1 = 0, c2 = 0). This hypothesis is rejected at the fivepercent significance level for all sample periods. The final F-test (F test: Model) compares the mean
squared error of the model of dividend management to that of the simple present value model.
Rejection of the null hypothesis favors the model of dividend management. For the 1900-1998 and
1950-1998 sample periods the model of dividend management provides superior fit, but for the
earlier time period, the simple present value model is favored. Additional tests indicated that the
coefficients are significantly different across the various sample periods.
We next gauged the accuracy of the OLS estimates of the nonlinear model of dividend
management. As discussed above, when any of the parameters are close to zero (as the estimates
in Table 2 indicate), nonlinear least squares estimation is extremely imprecise. Table 3 reports OLS
estimates of the GNR given in equation (10). Reported below each estimated coefficient is the tstatistic for a test of the null that the coefficient equals zero. We used standard errors that are
corrected for first-order autocorrelation following Newey and West (1987). 18 If the coefficients do
-12-
not differ significantly from zero, we can have confidence in the accuracy of the restricted OLS
estimates for equation (7), as reported in Table 2. For the 1900-1998 and 1950-1998 sample periods
the GNR regression results indicate that the estimates are sufficiently accurate. However, all
estimated coefficients are significantly different from zero for the 1900-1949 period which indicates
that the restricted OLS regression may not be properly specified for this sample period.
Figures 1 through 3 lend further insight into the relationships between actual stock price and
predicted stock prices under the model of fundamentals with managed dividends and the simple
present value model. These figures plot the actual real stock price, the stock price predicted by the
dividend management model estimates reported in Table 2 (managed price), and the stock price
predicted by the simple present value model in the absence of dividend control (PV price). Figures
1, 2, and 3 show the time paths of each price series for the 1900-1998, 1900-1949, and 1950-1998
periods, respectively. Overall, the predictions of the dividend control model (managed price) better
reflect actual stock price movements than the price predictions based on the simple present value
model (PV price). What is also apparent from these figures is that both models performed equally
poorly prior to 1950. However, since 1950 the dividend management model is superior to the simple
present value model at reflecting movements in real stock prices. This is consistent with our results
reported in Tables 2 and 3 and earlier studies of the relationship between dividends and stock prices.
Prior research has recognized that prices and dividends moved together prior to 1950 (Froot and
Obstfeld, 1991a) and changes in dividends are much smoother than changes in prices since around
1950 (Kleidon, 1986b). In addition, Brittain (1968), Miller (1985), Marsh and Merton (1987), and
Lee (1996) report a shift in dividend policy though they suggest that the change occurred somewhat
earlier in the 1930's and 1940's.
-13-
Taken together, the results suggest that the nonlinearities in stock price behavior and the
break-down in the relationship between prices and ordinary cash dividends that occurred around
1950 may be a direct result of dividend management by firms. Stock price moves more than
predicted by a present value model that ignores dividend management because ordinary cash
dividends are controlled and fundamentals are not.
The nonlinearity in the relationship between prices and dividends may arise from how
managers choose dividend payout. In this paper we examined a model of dividend management
which can explain observed long-term trends in stock prices but does not depend on the existence
of intrinsic or extrinsic bubbles. We estimated the model using Standard and Poor's stock price and
dividend index series for the 1900-1998 time period. The model recognizes that ordinary cash
dividends may not properly represent intrinsic value yet estimation of the model does not require
measurement of (possibly unobservable) fundamentals. The estimates provide support for the
dividend management model and indicate that the nonlinear relationship between prices and
dividends may be explained by managerial behavior.
We also showed that the simple present value model seems to track movements in actual
stock price prior to 1950 as well as the model of dividend control. However, since 1950 the
importance of dividend management has increased. A missing piece to the puzzle is an explanation
of why managerial control of ordinary cash dividends became more prevalent around 1950.
-14-
1. See Fama (1970) and Samuelson (1973) for reviews of the early literature.
2. In the Lucas model, economic agents maximize the expected utility of lifetime consumption in
a one good pure exchange economy. Within this framework, a current period asset price is equal to
the conditional expectation of the asset's next period price
dividend payment weighted by the
marginal rate of substitution between current and next period consumption.
3. Other stock price behavior casts additional doubt on the present value model. For example, Mehra
and Prescott (1985), using calibration techniques, demonstrate that the expected utility maximization
framework does not explain the ‘equity premium’ which is defined to be the difference between the
real return to equity and the real risk-free interest rate. Fama and French (1988), Lo and Mackinlay
(1988), and Poterba and Summers (1988) all report evidence consistent with the presence of mean
reversion in asset prices. See also the papers by Cecchetti, Lam, and Mark (1990) and Lehmann
(1990).
4. See, for example, the symposium on bubbles in the
which
included papers by Flood and Hodrick (1990) and White (1990).
5. See, for example, the review articles by West (1988b), Camerer (1989), and Flood and Hodrick
(1990).
6. See also the reviews by West (1988b) and Cochrane (1991).
7. Donaldson and Kamstra (1996a, 1996b) develop a procedure to forecast future cash flows which
are in turn used to construct present value prices. The model uses a nonlinear ARMA-ARCH
artificial neural network. Based on the results of excess volatility tests, Donaldson and Kamstra also
reject bubbles in stock prices.
-15-
8. In selecting a dividend policy, managers do face a cash flow accounting identity which applies to
dividends paid net of any purchases of its outstanding securities, i.e., the dividend policy must be
consistent with providing a current intrinsic value per share equal to the discounted present value
of expected future real cash flows of the firm that will be available for distribution to each of the
shares currently outstanding. Clearly, for any given intrinsic value, there are an uncountable number
of dividend policies which will satisfy this constraint (see Marsh and Merton, 1986, p. 487).
9. The variety of dividend policies observed among U.S. corporations attests to the discretion
available to managers and is consistent with the fact that unlike consumer choice theory, there is no
generally accepted theory of optimal dividend policy.
10. Marsh and Merton (1986) showed that if dividend policy can be described by their model of
dividend smoothing, nonstationarity of the stock price process results. Under nonstationarity,
Shiller's (1981) variance-bound test is invalid. Marsh and Merton do not empirically examine
whether dividend smoothing can explain the time path of stock prices. See also Mattey and Meese
(1986) who examine the affect of dividend smoothing on tests of present value relations.
11. The derivation of equation (4) which follows, where the true dividend or fundamental per share
paid over time, {Dt}, is assumed to follow a continuous time geometric Brownian motion process
with a constant drift or mean growth rate, i.e., a standard Ito process, is extremely complicated and
lengthy. As noted in Ackert and Hunter (1999), the solution can be derived derived using the
methods outlined by Harrison (1985, Chapters 2 and 5)). Bentolila and Bertola (1990, page 386)
using the methods outlined in Harrison, provide a comprehensive derivation of the discounted
present value of a generalized regulated Brownian motion process of the type we use to represent
true cash dividends in this paper. The derivation of our equation (4) follows directly from the
-16-
derivation given by Bentolila and Bertola. Froot and Obstfeld (1991b) propose a similar
representation to express the relationship between exchange rates and fundamentals in the presence
of target zones.
12. The second nonlinear term in (4) is included in the general solution to the Froot and Obstfeld
model.
13. Including these observations in the analysis does not affect the results.
14. Under complete markets the discount rate and the risk-free interest rate are equal. Clearly,
however, this assumption does not strictly hold. We used the average real return as our discount
rate to obtain the estimates of equation (7) reported subsequently because the real return is a better
reflection of individuals' subjective discount rate. We also performed the analysis using the real
commercial paper rate as the discount rate and inferences are unaffected.
15. Statistical inferences may be invalid in the presence of autocorrelation. As autocorrelation is not
ruled out by the model, its possible presence must be taken into consideration in estimation.
16. The reported standard errors are corrected for first-order autocorrelation. An examination of the
residuals indicated the presence of significant first-order autocorrelation but no significant higherorder autocorrelation. We also estimated (7) allowing for up to fourth-order autocorrelation and
statistical inferences were not affected.
17. In their footnote 28, Froot and Obstfeld reported that they estimated an extended version of their
model (13) which is our (7). They found that the coefficient of the second nonlinear term was
estimated imprecisely and that there was no evidence that this second term explained movements
in stock prices. We found that all coefficients were imprecisely estimated using unrestricted
estimation techniques, regardless of whether the second term was included in the model.
-17-
18. We also estimated (10) allowing for up to fourth-order autocorrelation with no change in the
results.
-18-
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60 (1987), 1-40.
Mattey, Joe and Richard Meese. "Empirical Assessment of Present Value Relations",
5(2) (1986), 171-234.
Mehra, Rajnesh and Edward C. Prescott. "The Equity Premium: A Puzzle",
15 (1985), 145-161.
Miller, Merton H. "Behavioral Rationality in Finance: The Case of Dividends",
59(4) (1986), S451-S468.
Miller, Merton H. and Franco Modigliani. "Dividend Policy, Growth, and the Valuation of Shares",
34 (1961), 411-433.
Newey, Whitney K. and Kenneth D. West. "A Simple Positive Definite Heteroskedasticity and
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55(3) (May 1987), 703-708.
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27(5) (1972), 993-1007.
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22 (1988), 27-59.
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. Cambridge, MA: MIT Press, 1989.
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1.
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-23-
Time Period
µ
σ2
k
β1
β2
1900-1998
0.0170
0.0142
0.0901
3.4670
-3.6705
1900-1949
0.0107
0.0246
0.0708
2.6974
-2.1298
1950-1998
0.0235
0.0037
0.1097
5.4933
-10.9423
Notes: The table reports the mean growth rate (µ) and variance (σ2) of real dividends and the mean
real return on stocks (k) over each time period. Also reported are estimates of the positive (β 1) and
negative (β2) roots of the quadratic equation (5) using these point estimates.
-24-
t test
F test:
No
F test:
No slope
F test:
Model
R2
0.000
DW
prob
96
df
c2
0.67
c1
63.41***
c0
75.00***
Time
Period
128.97***
-0.690
(-1.78)*
5.31***
0.748
(10.73)***
47
17.960
(22.36)***
0.000
19001998
0.08
1.79*
1.32
-2.034
(-2.33)**
4.72**
-0.135
(-0.17)
9.26***
20.410
(9.65)***
46
19001949
0.000
10.05***
0.65
-2112.90
(4.85)***
28.21***
0.031
(8.70)***
97.14***
24.063
(19.43)***
218.87***
19501998
Notes: The table reports OLS estimates of the parameters of equation (7), with t-statistics reported below in parentheses. These t-statistics
use standard errors that are corrected for first-order serial correlation following Newey and West (1987). The fifth column reports the
results of a t test of whether the constant term is indistinguishable from the value predicted by the simple present value model. Three F-
statistics are reported in the following columns. The sixth column reports the results of an F test of the null hypothesis of no dividen
management(c0 = 1/(k-µ), c1 = 0, c2 = 0) and the seventh column reports a test of the null hypothesis that the slope coefficients are zero
(c1 = 0, c2 = 0). The final F-test compares the mean squared error of the model of dividend management to that of the simple present value
model. The DW prob is the probability of rejecting the null hypothesis of no positive autocorrelation when autocorrelation is present. The
final column reports the degrees of freedom.
***, **, * Significant at the 1%, 5%, and 10% levels, respectively.
-25-
b3
R2
df
0.25
0.00
94
33.715
(2.89)***
5.83**
*
0.08
45
13.249
(1.34)
1.53
0.04
44
Time
Period
b0
b1
b2
19001994
1.408
(0.49)
-0.313
(-0.38)
0.255
(0.35)
-1.752
(-0.60)
6.690
(0.65)
19001949
100.090
(2.60)**
-57.444
(-2.53)**
-314.860
(-2.51)**
-43.857
(-2.75)***
19501994
1.806
(0.61)
-0.036
(-0.54)
0.718
(0.53)
12456.000
(1.40)
b4
F test
Notes: The table reports OLS estimates of the parameters of equation (10), with t-statistics reported
below in parentheses. These t-statistics use standard errors that are corrected for first-order serial
correlation following Newey and West (1987). The following column reports the results of an F test
of the null hypothesis that the coefficients jointly equal zero. The table also reports the regression
R2 and degrees of freedom.
***, **, * Significant at the 1%, 5%, and 10% levels, respectively.
-26-
Figure 1: Actual and Predicted Prices
1900-1998
300~----------------------------------------------~
2501-------------------------------------------~
Q)
200
>
...J
<1>
0
27
<1>
150
,_
·-
a. 100
.
50
~
, "'- -.. -,r
~~
-.L
1
'
0+-+-~~r-~~~~-+-+-+-+-r-r~~-r~,_~+-+-~
1900
1920
1940
1960
1- Actual Price ······Managed Price -
1980
PV-Pricef
Figure 2: Actual and Predicted Prices
1900-1949
60~--------------------------~------------------~
40T---------·------------------~~----~----------~
30
I
20
1~··::!
;-=--..
I
j
c
)
'
j
I
'I
"""'
"
I
'II
.
,_..,.. . . .' '~I
'
J,
I
I
28
~
C!l
..J
a>
(.)
~
.
.....
).
10
r'/
\
I
~''I
)..,d.
.'
0+-+-+-+-+-+-+-+-+-+-+-+-+-~~~~~r-r-r-r-r-r-~
1900
1910
1920
1930
1-- Actual Price ······Managed Price -
1940
PV Price J
1950
Figure 3: Actual and Predicted Prices
1950-1998
280
~--------------------------~·-·--····--·-···--·-··
~
...
~. -""-·"~~""
-
""'--~"'~,,..----~·-·-"-·~'-"'--- "~'~"··-··~·'
. "' ...
240+-----------------------------------------------~
~
~
~
160
£ 120
~
~
.'
1_------------------------------------------------------~--
1_--------------------------~~~-
80
4o
. -.- ..
1
·.
.,c---~-~-
=z7
-----
~
--
-
v
~/
--
/
~
0+-+-+-+-+-+-~~~~~~~~-r-r-r-r-+-+-+-+-+-+~
1950
1960
1970
1980
1-Actual Price ······Managed Price -
1990
PV Price
I
29
200
@FedFRASER