4. (25 points) Suppose you want to estimate the model: Yi = Bo+ BiXi+Ui where X,...

  

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4. (25 points) Suppose you want to estimate the model: Yi = Bo+ BiXi+Ui where X, is an endogenous variable and all our setup assumptions for instrumental variables hold. Assume Z, is a binary variable. Denote the reduced-form equation by: And the first-stage equation by: X To + 1 Z + V You collect an i.i.d. sample from the population in order to estimate and get access to the information in the following two tables: Y % +71Z + Ei Zi=0 Zi=1 Total Intercept Zi Figure 1: Sample statistics for the variables. Sample Mean of Y Observations 75 25 100 200 160 190 12 8 Sample Mean of X Figure 2: First stage regression results Estimate Std. Error t-value 60 5 20 2.5 60 80 65 Pr(t) 2.10E-05 0.012 (a) (8 points) Express the populational coefficient IV as a functional of other populational parame- ters. (b)(8 points) Using the information from the tables above, compute the estimate for $1 (c) (9 points) Test the relevance condition for the instrument. Is the instrument weak? 10 4. (25 points) Suppose you want to estimate the model: Yi = Bo+ BiXi+Ui where X, is an endogenous variable and all our setup assumptions for instrumental variables hold. Assume Z, is a binary variable. Denote the reduced-form equation by: And the first-stage equation by: X To + 1 Z + V You collect an i.i.d. sample from the population in order to estimate and get access to the information in the following two tables: Y % +71Z + Ei Zi=0 Zi=1 Total Intercept Zi Figure 1: Sample statistics for the variables. Sample Mean of Y Observations 75 25 100 200 160 190 12 8 Sample Mean of X Figure 2: First stage regression results Estimate Std. Error t-value 60 5 20 2.5 60 80 65 Pr(t) 2.10E-05 0.012 (a) (8 points) Express the populational coefficient IV as a functional of other populational parame- ters. (b)(8 points) Using the information from the tables above, compute the estimate for $1 (c) (9 points) Test the relevance condition for the instrument. Is the instrument weak? 10

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To estimate the model we have the following information Sample statistics for the variables Number o... View the full answer