Introduction to Econometrics 3rd Edition by James Stock, James Stock

Exercise 21

A researcher studying the relationship between earnings and gender for a group of workers specifies the regression model, Y i = ß 0 + X₁ i ß 1 + X₂ i ß 2 + u i , where X₁ i is a binary variable that equals 1 if the i th person is a female and X₂i is a binary variable that equals 1 if the i th person is a male. Write the model in the matrix form of Equation (18.2) for a hypothetical set of n = 5 observations. Show that the columns of X are linearly dependent so that X does not have full rank. Explain how you would respecifiy the model to eliminate the perfect multicollinearity.