Advanced economics questions;

The questions are complete please;

Let y be scalar and a be k x 1 vector random variables. Observations (#, c, ) are drawn at random from the population of (y, x). You are told that E [y|x] = x'S and that V [y|x] = exp(x's to), with (8, a) unknown. You are asked to estimate B. 1. Propose an estimation method that is asymptotically equivalent to GLS that would be com- putable were V[ylx] fully known. 2. In what sense is the feasible GLS estimator of part 1 efficient? In which sense is it inefficient?In the standard linear mean regression model, one estimates k x 1 parameter / by where A > 0 is a fixed scalar, I, is a k x k identity matrix, A is n x k and ) is n x 1 matrices of data. 1. Find E[8 X]. Is 8 conditionally unbiased? Is it unbiased? 2. Find the probability limit of f as n - co. Is f consistent? 3. Find the asymptotic distribution of B. 4. From your viewpoint, why may one want to use 8 instead of the OLS estimator ? Give conditions under which 8 is preferable to / according to your criterion, and vice versa.Suppose that y= at Brtu. where u is distributed /(0,o') independently of z. The variable a is unobserved. Instead we observe z = c + v, where v is distributed /(0, ,') independently of a and u. Given a sample of size n, it is proposed to run the linear regression of y on z and use a conventional t-test to test the null hypothesis 8 =0. Critically evaluate this proposal.A researcher presents his research on returns to schooling at a lunchtime seminar. He runs OLS. using a random sample of individuals, on a Mincer-type linear regression, where the left side variable is a logarithm of hourly wage rate. The results are shown in the table. Regressor Point estimate Standard error t-statistic Constant -0.30 2.16 -0.14 Male (9) 0.39 0.07 5.54 Age (a) 0.14 0.12 1.16 Experience (e) 0.019 0.036 0.52 Completed schooling (s) 0.027 0.023 1.15 Ability (f) 0.081 0.124 0.65 Schooling-ability interaction (sf) -0.001 0.014 -0.06 1. The presenter says: "Our model yields a 2.7 percentage point return per additional year of schooling (I allow returns to schooling to vary by ability by introducing ability-schooling interaction, but the corresponding estimate is essentially zero). At the same time, the esti- mated coefficient on ability is 8.1 (although it is statistically insignificant). This implies that one would have to acquire three additional years of education to compensate for one standard deviation lower innate ability in terms of labor market returns." A person from the audience argues: "So you have just divided one insignificant estimate by another insignificant estimate. This is like dividing zero by zero. You can get any answer by dividing zero by zero, so your number '3' is as good as any other number." How would you professionally respond to this argument? 2. Another person from the audience argues: "Your dummy variable 'Male' enters the regression only as a separate variable, so the gender influences only the intercept. But the corresponding estimate is statistically very significant (in fact, it is the only significant variable in your regression). This makes me think that it must enter the regression also in interactions with the other variables. If I were you, I would run two regressions, one for males and one for females, and test for differences in coefficients across the two using a sup-Wald test. In any case, I would compute bootstrap standard errors to replace your asymptotic standard errors hoping that most of parameters would become statistically significant with more precise standard errors." How would you professionally respond to these arguments