Introductory Econometrics 4th Edition by Jeffrey Wooldridge

Exercise 5

The purpose of this exercise is to compare the estimates and standard errors obtained by correctly using 2SLS with those obtained using inappropriate procedures. Use the
data file WAGE2.RAW.
(i) Use a 2SLS routine to estimate the equation
log(wage) = 0 + 1 educ + 2 exper + 3 tenure + 4 black + u,
where sibs is the IV for educ. Report the results in the usual form.
(ii) Now, manually carry out 2SLS. That is, first regress educ i on sibs i , exper i , tenure i , and black i and obtain the fitted values, educ i = 1, n. Then, run the second stage regression log(wage.) on educ t , exper i , tenure i , and black i = 1, n. Verify that the are identical to those obtained from part (i), but that the standard errors are somewhat different. The standard errors obtained from the second stage regression when manually carrying out 2SLS are generally inappropriate.
(iii) Now, use the following two-step procedure, which generally yields inconsistent parameter estimates of the j , and not just inconsistent standard errors. In step one, regress educ i on sibs i only and obtain the fitted values, say educ i. (Note that this is an incorrect first stage regression.) Then, in the second step, run the regression of log(wage) on educ i , exper i , tenure i , and black i , i = 1,...,n. How does the estimate from this incorrect, two-step procedure compare with the correct 2SLS estimate of the return to education