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 ( Y_1, X_1, _1, X_1, _2)...,( Y_n, X_n, _1, X_n, _2) be an i.i.d. sample from ( Y, X_1, X_2) satisfying:

Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + U

where (1, X_1, X_2) is not perfectly collinear, E[Y^4] < \infty and E[X^4] <  \infty (** - please note it should be X_j in the above, not just X, but my Latex-fu is weak).

Suppose a professor estimates the equation: Y = \beta_0* + \beta_1* X_1 + U*

by OLS. Show that:

\hat\beta_1* p \to \beta_1 + \beta_2 Cov[ X_1 , X_2]/Var[ X_1].

Also, under what conditions will it be true that \hat\beta_1* is consistent for \beta_1? (Here I'm confused - it's obvious that (X'X)^-1 is well defined since they already explicitly stated that (1, X_1, X_2) is not perfectly collinear and that E[Y^4] < \infty and E[X^4] <  \infty).

Any advice to get me started?