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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

### Show me

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

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.

### Show me more

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.