Use the data in CARD.RAW for this exercise.
(i) The equation we estimated in Example 15.4 can be written as
log(wage) = β0 + β1 educ + β2 exper + ... + u,
where the other explanatory variables are listed in Table 15.1. In order for IV to be consistent, the IV for educ, nearc4, must be uncorrelated with u. Could nearc4 be correlated with things in the error term, such as unobserved ability? Explain.
(ii) For a subsample of the men in the data set, an IQ score is available. Regress IQ on nearc4 to check whether average IQ scores vary by whether the man grew up near a four-year college. What do you conclude?
(iii) Now, regress IQ on nearc4, smsa66, and the 1966 regional dummy variables reg662 ,..., reg669. Are IQ and nearc4 related after the geographic dummy variables have been partialled out? Reconcile this with your findings from part (ii).
(iv) From parts (ii) and (iii), what do you conclude about the importance of controlling for smsa66 and the 1966 regional dummies in the log(wage) equation?