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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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See New in Stata 18 to learn about what was added in Stata 18.