(Requires Matrix Algebra)Consider the Time and Entity Fixed Effect Model

question 30

Essay

(Requires Matrix Algebra)Consider the time and entity fixed effect model with a single explanatory variable
Yit = β0 + β1Xit + D2i + ...+ Dni + δ2B2t + ...+ δTBTt + uit,
For the case of n = 4 and T = 3,write this model in the form Y = Xβ + U,where,in general,
Y = ,U = ,X = = ,and β = How would the X matrix change if you added two binary variables,D1 and B1? Demonstrate that in this case the columns of the X matrix are not independent.Finally show that elimination of one of the two variables is not sufficient to get rid of the multicollinearity problem.In terms of the OLS estimator, = ( X)-1 Y,why does perfect multicollinearity create a problem?

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