Question

1. Consider the following regression model with a single endogenous variable, ya : and given the reduced from for x: where z and are exogenous variables in the sense that cov(u,21) = cov(11,2 ) = 0 and cov(v,21) = cov(ng) = 0 (i.e., both zi and z2 are uncorrelated with u and v, and u is uncorrelated with v) (a) By substituting x into the equation for y, we obtain the reduce formed equation for y: Find the a in terms of 3 and π for 1-0.1.2. What is the reduced form error e in terms of u and v?(10 points) (b) Discuss how you would obtain consistent estimation for , using what you found in part (a) (10 points)

Answer 1

Given data: - y = beta_0 + beta_1 x + beta_2 z_1 + u_1 the reduce from for x x = pi_0 + pi_1 z_1 + pi_2 z_2 + u where z_1 & z_2 are exogenous variables con (u_1 z_1) = con (u_1 z_2) = 0 & cov (u_1 z_1) = cov (u_1 z_2) = 0 reduce formed equation For y y = alpha_0 + alpha_1z_1 + alpha_2z_2 + e v_1 = u_1 + beta_1 k_2 rightarrow reduced form error. Because y_2 is a exogenous variables estimates obtained For B_j are consistent For this reasons use introduce of the z_1 and 2 value cov (u_1, z_1) = 0 and cov (u_1 z_2) = 0 cov (u_2 z_1) = cov (u_2z_2) = 0 obtaing estimates of B_j using stage use square estimation technique use obtain consistent estimates of B_j let y_1 = beta_0 + beta_1y_2 + beta_2z_1 + v_1 = pi_0 + pi_1z_1 + pi_2z_2 + u y_1 = beta_0 + beta_1 (pi_0 + pi_1 z_1