Use the data in CPS91.RAW for this exercise. These data are for married women, where we also have information on each husband's income and demographics.
(i) What fraction of the women report being in the labor force?
(ii) Using only the data for working women-you have no choice-estimate the wage equation
log(wage) = β0 + β1educ + β2exper + β3exper2 + β4plack + β5hispanic + u
by ordinary least squares. Report the results in the usual form. Do there appear to be significant wage differences by race and ethnicity?
(iii) Estimate a probit model for inlf that includes the explanatory variables in the wage equation from part (ii) as well as nwifeinc and kidlt6. Do these last two variables have coefficients of the expected sign? Are they statistically significant?
(iv) Explain why, for the purposes of testing and, possibly, correcting the wage equation for selection into the workforce, it is important for nwifeinc and kidlt6 to help explain inlf. What must you assume about nwifeinc and kidlt6 in the wage equation?(v) Compute the inverse Mills ratio (for each observation) and add it as an additional regressor to the wage equation from part (ii). What is its two-sided /7-value? Do you think this is particularly small with 3,286 observations?
(vi) Does adding the inverse Mills ratio change the coefficients in the wage regression in important ways? Explain.