Regression Specification Issues for Stock Price
Equation
The issue discussed here is
how variations in regression model specifications impact estimated coefficients
and conclusions reached from a model
Question: A post on my finance blog considered share
price as a function of earnings per share, sales per share, and a dummy
variable set to one if the firm pays dividends.
Do Dividend Affect Firm
Value?
The estimates from this
regression model are presented below.
Regression Results for Share Price Equation


Earnings Per Share

10.5

2.36

Sales Per Share

0.2

3.63

Dividend Dummy

331.0

4.27

_cons

385.6

4.92

R2

0.66


N

67.0

The model suggests that dividend
paying firms have a lower stock price than firms that do not pay dividends.
Around half of the firms used
to estimate this model are growth firms and half of the firms are value firms. How did the dividend policy of growth firms
differ from the dividend policy of value firms in this sample?
After accounting for the
difference in dividend policy between growth and value firms what can we say
about whether the decision to pay dividends affects share price?
The Incidence of Dividend Payments for Growth and
Value Firms:
Dividend Policy Growth and Value Firms


Growth Firms

Value Firms


No Dividends

9

0

Dividends

25

33

Total

34

33

Observations:
All 33 firms in the value
firm sample pay some dividends. We
cannot estimate a model with the div dummy in the value firm sample because the
div dummy would be perfectly correlated with the constant term.
Estimated Coefficients from the Growth Model:
Share Price Equation for Growth Firms


Coef.

t


earnings per share

11.8

1.53

Sales Per share

0.17

2.14

Dividend Dummy

328.2

2.77

_cons

377.4

3.26

R2

0.64


N

34

Observation:
The estimated coefficients for the growthonly
sample are similar to the combined sample.
The earnings per share
coefficient is no longer significantly different from zero.
The dividend dummy is
negative.
Concluding Remark:
Growth firms that do not pay
dividends appear to have higher share prices than dividend paying growth firms.
We can’t conclude anything on
this issue about value firms from our sample because all 33 value firms in our
sample pay dividends
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