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
(*β1**Institutions)*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 R^{2} will increase.

D) will remain unchanged and the R^{2} 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

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