2022 Assignment 3
Econometrics (CH05-06)
1. Consider the following simple regression model,
y=4+Bx+u, where E(x)<[infinity], E(ux)=0, Var(ux)=o, let ty,x,i=1,2,...,n}
be a random sample from the population, satisfies x>0.
(1) Please estimate the mode by OLS, and write down the expression of the OLS estimator of B
(2) Please derive the conditional variance of B, Var(Bxxx);
(3) Please give the expression of the standard error of B, se(B), and prove that plima(A)-0.
2. Suppose that log(y) = B+B,x,+u,, i=1,2,, satisfies Gauss-Markov assumptions, please answer the following questions.
(1) Please derive the OLS estimator of B, B (please write down the objective function, first order conditions, and OLS expression), and prove that is an unbiased estimator of B;
(2) Prove that the OLS estimator, is a consistent estimator of ẞ;
(3) Please derive the asymptotic distribution of the OLS estimator ;
(4) Please prove that will underestimate the conditional expectation of y
E(y x).