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Use the data in CARD for this exercise.(i) In Table 15.1, the difference between the IV and OLS estimates of the return to educationis economically important. Obtain the reduced form residuals, $\hat{v}_{2},$ from the reduced formregression educ on nearc4, exper, exper2, black, smsa, south, smsa66, reg662, ..., reg669-see Table 15.1. Use these to test whether educ is exogenous; that is, determine if the differencebetween OLS and IV is statistically significant.(ii) Estimate the equation by 2SLS, adding nearc2 as an instrument. Does the coefficient on educchange much?(iii) Test the single overidentifying restriction from part (ii).

(i) The coefficient is 0.057 with the p-value 0.28, indicating the variable is not statistically significant at the 5$\%$ level. This also indicates that the difference between OLS and IV is not statistically significant.(ii) The coefficient of educ is $0.157$ (iii) not rejected

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Chapter 15

Instrumental Variables Estimation and Two Stage Least Squares

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part one. Okay, we at new sub to hat to the original equation. An estimated by old L s. The coefficient on new to hat is minus point Oh, 57 with 80 statistic of minus one point. Oh, eight. So what's the difference in the estimates of the return to education is large. It is not statistically significant. Part two. We now add near C two as an ivy along with near C four. The two stage least square estimate of beta one is now 0.157 with a standard error of point. Oh, 53 Okay, so the estimate is even larger. Yeah. Part three. Let you said I had to be the two stage least square residuals. Mm. We regret these on all exogenous variables, including near C two and near C four. The Choice square statistic, which is calculated by ticking and the number of observation multiply with our square from the regression is the product of 3000 and 10 observations and 0.4 which is the our square of the regression. You get 1.2. Yeah. The P value of this called square sta district is mhm 0.5 0.55 Yeah, so the over identifying restriction is not rejected. Mhm. Yeah,

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