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

تمرين 1

Consider the binary variable version of the fixed effects model in Equation (10.11), except with an additional regressor, Dl i ; that is, let
a. Suppose that n = 3. Show that the binary regressors and the "constant" regressor are perfectly multicollinear; that is, express one of the variables D 1 i D2 i D 3 i and X 0,it as a perfect linear function of the others, where X 0,it , = 1 for all i, t.
b. Show the result in (a) for general n.
c. What will happen if you try to estimate the coefficients of the regression by OLS