Question

Suppose you want to conduct an Exclusion Restriction Test. You estimate the Unrestricted Linear Regression with the number of homes for sale as the dependent variable and the population in the area, the population density of the area, unemployment rate, the fraction of the population over 65 years of age as independent variables. You estimate the Restricted Linear Regression with the number of homes for sale as the dependent variable and the population in the area and the population density of the area as independent variables. From the Exclusion Restriction Test, you get the F-statistic is 15.132 with a p-value of 0.001. At a Level of Significance of 5%, what does the Exclusion Restriction Test say about the Linear Regression?

Answer 1

The model fit of the unrestricted regression model is at least as good as the restricted model.

The p-value of the restricted regression model is 0.001 < level of significance (0.05), so the restricted model is significant.

Since, the independent variables: unemployment rate, the fraction of the population over 65 years of age are not present in the retricted set, these variables do not have significant explanatory power as the other two independent variables.

So, exclusion restriction test says that population in the area and the population density of the area have significant explanatory power in predicting the number of homes for sale.