1. Consider the standard panel data model: Yit = Bo + B1Xit + Uit = Bo+...

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1. Consider the standard panel data model: Yit = Bo + B1Xit + Uit = Bo+ B1Xit + a; + vit, where i 1,2 ... , n, and t = 1,2. In addition, a; is the fixed effect correlated with the endogenous variable xit (a) Write down the first-differenced equation. (b) Derive the BLed- [Note that E(Avit) may not be zero. To estimate the first-differenced 1,FD• equation, we include an intercept a, in the first-differenced equation.] (c) State the assumptions required for an unbiased and consistent B.fd. Prove that under these assumptions B1,fd is indeed unbiased and consistent. '1,FI „FD (d) Is this B Fp the best linear unbiased estimator? Explain. 1. Consider the standard panel data model: Yit = Bo + B1Xit + Uit = Bo+ B1Xit + a; + vit, where i 1,2 ... , n, and t = 1,2. In addition, a; is the fixed effect correlated with the endogenous variable xit (a) Write down the first-differenced equation. (b) Derive the BLed- [Note that E(Avit) may not be zero. To estimate the first-differenced 1,FD• equation, we include an intercept a, in the first-differenced equation.] (c) State the assumptions required for an unbiased and consistent B.fd. Prove that under these assumptions B1,fd is indeed unbiased and consistent. '1,FI „FD (d) Is this B Fp the best linear unbiased estimator? Explain.