Lahore School of Economics MPHIL Econometrics I (Winter 2010) Problem Set 2-Solutions

# Lahore School of Economics MPHIL Econometrics I (Winter 2010) Problem Set 2-Solutions

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Lahore School of Economics MPHIL Advanced Econometrics Winter 2010 Solutions to Problem Set 2 1. E[y|x]= α + β x where β = Cov(x,y)/Var(x) = 3/5 and α = μ y - βμ x 1 – 2(3/5) = -1/5 E[y|x,z] = α + γ 1 x+ γ 2 z where ( γ 1 , γ 2 ) = [Var(x,z)] -1 Cov[(x,z),y] = 1 5 2 3 2 6 1 -     ÷    = 16/ 26 1/ 26 ÷ - and α = μ y - γ 1 μ x - γ 2 μ z = 1 – 2(16/26) – 4(-1/26) 2. Since log(S/Y) = log(S/N) – log(Y/N), it must be the case that log(S/Y) = 8.7851 + 1.1486log(Y/N) – 1 × log(Y/N) etc. But, that would mean that the coefficients in the first equation would be identical to those in the second equation, save for that on log(Y/N) which should be exactly one less than that in the second equation. Neither is true. The results are wrong. 3. The sum of squares must rise, since this is a linear restriction on β . What happens to R 2 depends on how it is computed. Usually, packages use 1-e e/y M 0 y, which must go down, and, in fact, can become negative.
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