Consider the regression model with a single regressor: Y1 = β0 + β1βi + ui,
Suppose that the assumption in key concept are satisfied.
a. Show that Xi is a valid instrument. That is, show that key concept 12.3 is satisfied with Zi = Xi.
b. Show that the IV regression assumptions in key concept 12.4 are satisfied with this choice of Zi.
c. Shows that the IV estimator constructed using Zi = Xi is identical to the OLS estimator.