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2. Consider the binary variable version of the fixed effects model in the following equation, Yit=0+1Xit+2D2i+3D3i++nDni+uit, except with an additional regressor, D1i; that is, let Yit=0+1Xit+1D1i+2D2i++nDni+uit. (a) Suppose that n=3. Show that the binary regressor and the "constant" regressor are perfectly multicollinear; that is, express one of the variables D1i,D2i,D3i and X0,it as a perfect linear function of the others, where X0,it=1 for all i,t. (b) Show that the result in (a) for general n. (c) What will happen if you try to estimate the coefficients of the regression by OLS? 3. Using the following regression below: Yit=0+1Xit+2D2i+3D3i++nDni+uit, what is the slope and intercept for (a) Entity 1 in time period 1 ? (b) Entity 1 in time period 3 ? (c) Entity 3 in time period 1? (d) Entity 3 in time period 3 ? 2. Consider the binary variable version of the fixed effects model in the following equation, Yit=0+1Xit+2D2i+3D3i++nDni+uit, except with an additional regressor, D1i; that is, let Yit=0+1Xit+1D1i+2D2i++nDni+uit. (a) Suppose that n=3. Show that the binary regressor and the "constant" regressor are perfectly multicollinear; that is, express one of the variables D1i,D2i,D3i and X0,it as a perfect linear function of the others, where X0,it=1 for all i,t. (b) Show that the result in (a) for general n. (c) What will happen if you try to estimate the coefficients of the regression by OLS? 3. Using the following regression below: Yit=0+1Xit+2D2i+3D3i++nDni+uit, what is the slope and intercept for (a) Entity 1 in time period 1 ? (b) Entity 1 in time period 3 ? (c) Entity 3 in time period 1? (d) Entity 3 in time period 3

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