Consider the regression model Y = XB + ε. Assume X is stochastic and ε is such that E(X'=)= 0. However, there is a matrix of variables Z such that E(Z'E) = 0 and E(Z'XY= 0. The dimension of the matrix X is T xk (T is the
number of observations and k is the number of regressors) whereas the dimension of the matrix Z is Txq
with q> k.
1.Is B^ from a regression of Yon X consistent for ß?
2.Regress the matrix X on the matrix Z (i. e., you want to regress each column of X on the matrix Z). Express
the fitted values compactly as a function of X and Z.
3.Regress the observations Y on the fitted values from the previous regression (a Txk matrix). Express
compactly the new estimator as a function of X, Z, and Y. (Note: you could use a very specific idempotent
matrix here).
4.Is the new estimator consistent for B?
5. Assume k = q. Does the form of the estimator simplify?
6.(Interpret all of your previous results from an applied stand-point. Why are they useful? NEED IT DONE
ON TIME ONLY ACCEPT IF YOU UNDERSTAND