Consider a univariate linear regression Yi = Bo + Bixi tei = where Xi is endogenous. Suppose there exists a valid instru

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Consider A Univariate Linear Regression Yi Bo Bixi Tei Where Xi Is Endogenous Suppose There Exists A Valid Instru 1 (120.24 KiB) Viewed 31 times

Consider a univariate linear regression Yi = Bo + Bixi tei = where Xi is endogenous. Suppose there exists a valid instrument for Xi, call it Zi. (a) [5 points) Show that the IV estimator of B1, BIV, is consistent. If you make any additional assumptions, state them explicitly. (b) [5 points) Derive the asymptotic distribution of ßIV. If you make any additional assumptions, state them explicitly. (c) [5 points) Compare the asymptotic variance of ŜIV with that of the OLS estimator BOLS in case zi is a weak instrument. (d) [5 points) Show that a non-zero correlation between zi and εi would lead to the inconsistency of the IV estimator.