Question

Suppose you run a regression of ln GDP per capita (the dependent variable) on a measure of institutional quality (the explanatory variable). You estimate the value of the coefficient (β1Institutions)on the institutions variable to be 0.54 with a standard error of 0.04. Your classmate suggests that institutional quality is positively correlated with having British legal origins. That is, countries with British legal origins have higher quality institutions. Your classmate also thinks that British legal origins has a direct positive effect on ln GDP per capita. You gather data on whether a country’s legal system originated from Britain and add this as a control variable to the regression. If your classmate is correct, then it is likely that in the new regression the coefficient estimate will:

A) be greater than 0.54

B) be less than 0.54

C) remain unchanged, but the R² will increase.

D) will remain unchanged and the R² will not change.

Answer 1

The answer is (b) be less than 0.54

In the initial regression, the variable British legal origins is an omitted variable as it is correlated to both the independent variable (measure of institutional quality) and the dependent variable (GDP per capita)

Thus, the estimated coefficient on the measure of institutional quality will be biased, The direction of bias = sign of correlation between omitted variable and independent variable * sign of correlation between omitted variable and dependent variable = positive*positive = positive

Thus, when the omitted variable is actually added to the regression, the estimated coefficient will decrease as the positive bias goes away