Question: 12.2 Consider the regression model with a single regressor: Yi = b0 + b1Xi + ui. Suppose that the least squares assumptions in Key Concept

12.2 Consider the regression model with a single regressor: Yi = b0 + b1Xi + ui.

Suppose that the least squares assumptions in Key Concept 4.3 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. Show that the IV estimator constructed using Zi = Xi is identical to the OLS estimator.

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