Hey guys, this is my first post here. I was hoping you could help point out how I should go about tackling this proof:
Let ( , , , , )...,( , , , , ) be an i.i.d. sample from ( , , ) satisfying:
= + + +
where (1, , ) is not perfectly collinear, < and < (** - please note it should be in the above, not just , but my Latex-fu is weak).
Suppose a professor estimates the equation: = * + * + *
by OLS. Show that:
* p + Cov[ , ]/Var[ ].
Also, under what conditions will it be true that * is consistent for ? (Here I'm confused - it's obvious that (X'X)^-1 is well defined since they already explicitly stated that (1, , ) is not perfectly collinear and that < and < ).
Any advice to get me started?