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Sample selection for ordered probit


Highlights

  • 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

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Classic Heckman sample selection concerns a continuous outcome such as wages. Wages are observed only for those who work.

The 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.

. heckoprobit satisfaction educ age, select(work=educ age i.married##c.children) Ordered probit model with sample selection Number of obs = 5000 Censored obs = 1520 Uncensored obs = 3480 Wald chi2(2) = 842.42 Log likelihood = -6083.037 Prob > chi2 = 0.0000
  Coef. 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
LR test of indep. eqns. (rho = 0): chi2(1) = 88.10 Prob > chi2 = 0.0000

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.

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See the Heckman sample selection for ordered probit manual entry. As with all Stata estimation commands, 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.

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