Question

The impact of product differentation. To find out whether firms selling differentiated products (i.e. brand names) experience higher
rates of return on their equity. Simon and Jane obtained the regression result based on a sample of 23 firms.

Model 1
?? = 1.399 + 1.490?? + 0.246??
p value = (0.00) (0.1433) (0.065)
R2 = 0.26
Model 2
?? = 0.345 + 0.22?? + 0.211?? − 0.016????
p value = (0.01) (0.0004) (0.0002) (0.001)
R2 = 0.80
where Yi = the rate of return on equity (net profit in dollars per dollar of shareholders’
equity) for firm i
Di = 1 for firms with high or moderate product differentiation
Xi = the market shares for firm i

a) Do firms that product-differentiate earn a higher rate of return in model I and II? How
do you know? (level of significance 5%)
b) Interpret model 1 and 2
c) Between model 1 and 2 which would you prefer? Why?

Answer 1

Part a)

Model 1)

In this model we need to check whether the coefficient of D_i is significant or not. It is given that its p value is 0.1433 (14.33%) It is higher than the level of significance which is 5% and hence we conclude that it is insignificant and that firms that product differentiate earn a higher rate of return in model 1.

Model 2)

Similar to the previous model, here we check the p values for significance of both the coefficients of D_i and D_iX_i. They are 0.0004(0.04%) and 0.001(0.1%) respectively, which is lower than 5% for both. Hence we conclude that it is significant and that firms that product differentiate earn a higher rate of return in model 2.

Part b)

Model 1 tries to explain the rate of return on equity of firms using the independent variable of the market shares of the firms and the dummy variable which indicates whether the firm product differentiates or not.

Model 2 tries to do the same as model 1 but adds the product term (D_iX_i). Adding the term takes into account the interaction between the variables D_i and X_i and hence is a more suitable model.

Part c)

We would prefer model 2 as its R² (which determines the goodness of fit) is 0.80 which is much higher than the R² for model 1(0.26). Moreover, all the independent variables are significant in model 2 and not in model 1. Hence we can determine that model 2 is a better fit than model 1.