4. We estimated the labor force participation of married women in Mroz data set by logit and probit. We also report the linear probability model estimates. The results, with robust standard errors in parentheses, are given in Table 2. The dependent variable is inlf (’’in the labor force’’). It is a binary variable indicating labor force participation by a married woman during 1975: inlf = 1 if the woman reports working for a wage outside the home at some point during the year, and zero otherwise. The regressors are nwifeinc is husband’s earning measured in thousands of dollars, years of education (educ), past years of labor market experience (exper), age, number of children less than six years old (kidslt6), and number of kids between 6 and 18 years of age (kidsge6).
Table 2 LPM, Logit, and Probit Estimates of Labor Force Participation
Dependent Variable: inlf
Independent Variables LPM (OLS) Logit (MLE) Probit (MLE)
nwifeinc -.0034 -.021 -.012
(.0015) (.008) (.005)
educ .038 .221 .131
(.007) (.043) (.025)
exper .039 .206 .123
(.006) (.032) (.019)
exper^2 -.00060 -.0032 -.0019
(.00019) (.0010) (.0006)
age -.016 -.088 -.053
(.002) (.015) (.008)
kidslt6 -.262 -1.443 -.868
(.032) (.204) (.119)
kidsge6 .013 .060 .036
(.014) (.075) (.043)
constant .586 .425 .270
(.152) (.860) (.509)
Percentage correctly predicted 73.4 73.6 73.4
Log-likelihood value -401.77 -401.30
Pseudo R-squared .264 .220 .221
The pseudo R-squared for the LPM is just the usual R-squared reported for OLS; for logit and probit, the pseudo R-squared is the measure based on the log-likelihoods.
Take a woman with nwifeinc = 20.13, educ = 12.3, exper = 10.6, and age = 42.5.
(a) Using LPM, logit and probit models, what is the estimated decrease in the probability of working in going from zero to one small child (less than 6 years old)?
(b) Repeat (a) for case that the number of small child goes form one to two.
(c) Compare your results in parts (a) and (b). What is the important difference between LPM model and logit and probit models? Explain.
(d) Interpret the estimated coefficient on nwifeinc using LPM. Is it statistically significant at 5%?
(e) Compute changes in the probability of working if years of education increase from 12 to 13 for a woman with nwifeinc = 20.13, exper = 10.6, and age = 42.5 and no children using logit model.