Your first candidate for a regression to identify the effect of X₁ on Y is: Y_i = β₀ + β₁X₁_i + β₂X₂_i + U_i, where X₂ is a control variable. Suppose a member of your consulting team suggests to you that another variable R_i should be a control that is also included in your regression, in order for you not to be worried about the endogeneity problem. What condition could you credibly test using data on Y, X₁, X₂, and R which could justify the inclusion of R_i as a control in your regression? A) R_i has no effect per se on Y_i. B) R_i has a strong correlation with X₂. C) R_i is exogenous. D) spcorr(R_i, Y_i (X_i₁, X_i₂)) ≠ 0

Question

Quizplus · Accepted Answer

In order to justify the inclusion of a control variable, it is important to ensure that it is not endogenous, meaning that it is not correlated with the error term in the regression. Testing for the correlation between the control variable and the dependent variable, as well as the other independent variables in the regression, can be a way to check for endogeneity. Therefore, the condition that could credibly test the inclusion of R_i as a control is spcorr(R_i, Y_i (X_i₁, X_i₂)) ≠ 0. This means that the partial correlation between R_i and Y, controlling for X_i₁ and X_i₂, is not equal to zero. If the partial correlation is zero, it suggests that R_i has no additional explanatory power beyond the other variables in the regression, and thus there may be no need to include it as a control.

Your First Candidate for a Regression to Identify the Effect