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Consider the basic panel data set-up in which the population regression model is given by Yit = 1Xit i it (1) where i = 1,
Consider the basic panel data set-up in which the population regression model is given by Yit = 1Xit i it (1) where i = 1, ..., n is the location, t = {1, 2} is the time period, Yit is wage and Xit is employment and it is a structural error term in location i at time t. Assume, for simplicity that i1 = 0. The parameter of interest is 1. Employment growth at location i is given by a weighted average of industry-location growth rates Xi = Xi2 Xi1 = K k=1 ikgik where gik k ik is the growth rate in industry k and location i with k is random and independent across industries k = {1, ..., K}. ik is is random and independent across industries and locations. and ik are the industry k non-random shares in location i. (all parts have equal weight) 1. If Cov(, X) 6 = 0, would pooling the data and running OLS yield a consistent estimator of 1? A heuristic explanation will suffice
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