Introduction to Econometrics 3rd Edition by James Stock, James Stock

Exercise 15

Consider the heterogeneous regression model where 0i and 1i are random variables that differ from one observation to the next. Suppose that are distributed independently of X i.
a. Let denote the OLS estimator of 1 given in Equation (17.2). Show that , where E ( 1 ) is the average value of 1 i in the population.
b. Suppose that , where 0 and 1 are known positive constants. Let denote the weighted least squares estimator. Does Explain.