4. A single endogenous explanatory variable Consider the following structural model: y1 = Bo + Biy2 + B2z1 + u1 Suppose now that there are two exogenous variables excluded from the model: 22 and z3. The assumptions that z2 and z3 do not appear in the model and are uncorrelated with the error uj are known as rank conditions The linear combination that is most highly correlated with y2 is given by the reduced form equation for y2: 2SLS overidentifying restrictions y2 = TO + TA121+ 722 + T323 + v2 exclusion restrictions E(v2) = 0, Cov(21, v2) = 0, Cov(22, v2) = 0, and Cov(z3, v2) = 0. Which of the following is the best IV for y2? O 5 = TO +T121 + T222 + T323 + v2 O y5 = TO + 7121 + 722 O vi = TO +7121 + T222 + v2 O 5 = TO +T121 + T222 + T323 What is the least restrictive assumption we need to impose on the T parameters in order for the instrument y5 to not be perfectly correlated with z1? O T2 +0 or 13 #0 O T1 +0 or T2 #0 and T3 # 0 O T1 = 0 and 72 +0 and T3 +0 O T2 +0 and 73 # 0

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