1. Consider the following regression model with a single endogenous variable, y: y = 3 +3x...

 

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1. Consider the following regression model with a single endogenous variable, y₂: y = 3₂ +3₁x + B₂²₁ + u and given the reduced from for : x = ₁₂ +₁ ²₁ +₂²₂ +₂ where exogenous variables in 72 the sense that cov(u, z) = cov(u,z₂) = 0 and cov(v, z) = cov(v, z)=0 (i.e., both z, and 2, are uncorrelated with u and y, and u is uncorrelated with v). (a) By substituting z into the equation for y, we obtain the reduce formed equation for y: and are y = a₁ + a₂²₂₁ + a₂²₂ +e Find the o, in terms of 3, and, for j = 0,1,2. What is the reduced form error e in terms of u and v? (10 points) (b) Discuss how you would obtain found in part (a). consistent estimation for 3, using what you (10 points) 1. Consider the following regression model with a single endogenous variable, y₂: y = 3₂ +3₁x + B₂²₁ + u and given the reduced from for : x = ₁₂ +₁ ²₁ +₂²₂ +₂ where exogenous variables in 72 the sense that cov(u, z) = cov(u,z₂) = 0 and cov(v, z) = cov(v, z)=0 (i.e., both z, and 2, are uncorrelated with u and y, and u is uncorrelated with v). (a) By substituting z into the equation for y, we obtain the reduce formed equation for y: and are y = a₁ + a₂²₂₁ + a₂²₂ +e Find the o, in terms of 3, and, for j = 0,1,2. What is the reduced form error e in terms of u and v? (10 points) (b) Discuss how you would obtain found in part (a). consistent estimation for 3, using what you (10 points)

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a By substituting the reduced form equation for x into the equation for y we obtain y beta0 beta1pi0 ... View the full answer