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

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A researcher studying the relationship between earnings and gender for a group of workers specifies the regression model, Y i = ß 0 + X 1 i ß 1 + X 2 i ß 2 + u i , where X 1 i is a binary variable that equals 1 if the i th person is a female and X 2i 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.