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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 education is economically important. Obtain the reduced form residuals, v^ 2, from the reduced form regression 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 difference between OLS and IV is statistically significant.
(ii) Estimate the equation by 2SLS, adding nearc2 as an instrument. Does the coefficient on educ change much?
(iii) Test the single overidentifying restriction from part (ii)
What would be the command we need to run to test for the overidentifying restriction?