The data is a cross-section of 65 companies averages in the Standard & Poor 500

Question

The data is a cross-section of 65 companies averages in the Standard & Poor 500 over 1996-2000, consisting of price/earning ratio (PE), dividends paid (DIV), earning growth (EARN), and a measure of company riskiness (BETA). Run a regression of log of PE on EARN DIV and BETA employing a semi log (in Y) functional form (that is a function expressed in log of the dependent variable only.) What is the interpretation of the coefficient estimates? Do you think this functional form is appropriate for the relationship of PE to EARN, DIV and BETA? Try a double-log as an alternative model. Comment on the results. Which model seems more appropriate? Is there any evidence that EARN may be an irrelevant variable? Discuss.

Explanation / Answer

a. The overall model is statistically significant at the 5% level. However, the coefficients for the EARN and BETA are not significant at 5%. So, we can say that DIV is the only significant variable here.

b. The double log model shows that again the model is significant at 5% as the p value is less than 5%, but the F value is lesser here compared to model in (a). Again the EARN and BETA are insignificant and DIV is significant. Also, t values for log DIV and intercept are lesser in this case as compared to (a). So, we should go with the first model.

c. EARN is an irrelevant variable as it is not statistically significant in both the models. However we have used the complete model here with all independent variables. If we use only EARN or EARN and DIV only, we can get EARN as a significant variable.

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