## Wednesday, September 19, 2018

### Regression Specification Issues for Stock Price Equation

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 growth-only 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