Endogenous sample selection: Unobserved variables cause correlation in outcome and participation
Outcome is ordinal
Robust, cluster–robust, and bootstrap standard errors optional
Extensive postestimation model analysis tools
Classic Heckman sample selection concerns a continuous outcome such as wages. Wages are observed only for those who work.
heckoprobit generalizes the Heckman selection model to ordered outcomes such as job satisfaction on a Likert scale, which is also observed only for those who work.
Say we have data on adult women, some of whom work.
We will fit a model in which job satisfaction, when it is observed, is a function of education and age. Whether a woman works is also determined by education and age as well as her marital status and number of children.
. webuse womensat
. heckoprobit satisfaction educ age, select(work=educ age i.married##c.children)
(output omitted)
Ordered probit model with sample selection Number of obs = 5,000
Selected = 3,480
Nonselected = 1,520
Wald chi2(2) = 842.42
Log likelihood = -6083.037 Prob > chi2 = 0.0000
| Coefficient Std. err. z P>|z| [95% conf. interval] | ||
| satisfaction | ||
| education | .1536381 .0068266 22.51 0.000 .1402583 .1670179 | |
| age | .0334463 .0024049 13.91 0.000 .0287329 .0381598 | |
| work | ||
| education | .0512494 .0068095 7.53 0.000 .037903 .0645958 | |
| age | .0288084 .0026528 10.86 0.000 .023609 .0340078 | |
| 1.married | .6120876 .0700055 8.74 0.000 .4748794 .7492958 | |
| children | .5140995 .0288529 17.82 0.000 .4575489 .5706501 | |
| married# | ||
| c.children | ||
| 1 | -.1337573 .035126 -3.81 0.000 -.202603 -.0649117 | |
| _cons | -2.203036 .125772 -17.52 0.000 -2.449545 -1.956528 | |
| /cut1 | 1.728757 .1232063 14.03 0.000 1.487277 1.970237 | |
| /cut2 | 2.64357 .116586 22.67 0.000 2.415066 2.872075 | |
| /cut3 | 3.642911 .1178174 30.92 0.000 3.411993 3.873829 | |
| /athrho | .7430919 .0780998 9.51 0.000 .5900191 .8961646 | |
| rho | .6310096 .0470026 .5299093 .7144252 | |
We find that job satisfaction and work-force participation are positively correlated (0.63) after accounting for the observed covariates. That correlation is typically attributed to unobserved components.
We find that increasing education raises the probability of working, and it increases job satisfaction.
See the Heckman sample selection for ordered probit manual entry. As with all Stata's estimation features, you can obtain predicted outcomes (in this case, predicted probabilities of levels of job satisfaction and of working) and perform hypothesis tests and more, including marginal effects; see the Heckman selection for ordered probit postestimation manual entry.
