Heckman Sample Selection Model (Heckit / Tobit Type II)
Also known as: heckit, tobit type II, sample selection model, Heckman Seçim Modeli (Heckit / Tobit II)
The Heckman selection model, introduced by James J. Heckman in 1979, is a two-step model that corrects sample selection bias when the outcome is only observed for a non-random subset of cases. A probit selection equation models who is observed, and the outcome equation then corrects for the resulting bias using the inverse Mills ratio.
Key highlights
- Directly corrects sample selection bias when the outcome is only observed for a non-random subsample.
- The two-step Heckit estimator is transparent: the inverse Mills ratio term makes the selection correction explicit and testable.
- Applicable to classic non-random observation problems such as labour-force participation, credit approval, and survey non-response.
Intuition
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How it works
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When to use it
Use the Heckman model when the dependent variable is observed only for a self-selected subsample, such as wages for those who work or repayment behaviour for approved loan applicants, and you suspect the selection is correlated with the outcome. It needs a reasonable sample size (at least about 100 observations) and works for cross-sectional or panel data. Critically, the model relies on an exclusion restriction: at least one variable that affects selection but not the outcome, justified on theoretical or economic grounds. The errors are assumed to follow a bivariate normal distribution; under severe violations a semiparametric alternative is preferable.
Strengths & limitations
- Directly corrects sample selection bias when the outcome is only observed for a non-random subsample.
- The two-step Heckit estimator is transparent: the inverse Mills ratio term makes the selection correction explicit and testable.
- Applicable to classic non-random observation problems such as labour-force participation, credit approval, and survey non-response.
- Requires a credible exclusion restriction; without a variable that affects selection but not the outcome, identification rests fragilely on the model's functional form.
- Assumes bivariate normal errors, and the maximum-likelihood version is sensitive to this assumption.
- Needs a reasonably large sample (about 100 or more); the two-step estimator is less efficient than full maximum likelihood.
Common pitfalls
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Applications
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Frequently asked
What is the inverse Mills ratio in the Heckman model?
It is a correction term computed from the first-stage probit, equal to the standard normal density divided by the cumulative distribution function of the selection index. Adding it as a regressor in the outcome equation absorbs the selection effect; a significant coefficient on it indicates that selection bias was present.
What is an exclusion restriction and why do I need one?
An exclusion restriction is at least one variable that influences whether a case is observed but has no direct effect on the outcome. It anchors the identification of the selection correction; without it, the model is identified only through functional-form assumptions and the estimates become fragile.
Should I use the two-step Heckit or full maximum likelihood?
The two-step Heckit is transparent and robust, while full maximum likelihood is more efficient but more sensitive to the bivariate normality assumption. When normality is questionable, the two-step estimator or a semiparametric alternative is safer.
How is the Heckman model different from a Tobit model?
A standard (Type I) Tobit handles censoring where the same equation governs both the limit and the value. The Heckman model (Tobit Type II) uses two separate equations — one for selection and one for the outcome — so the process determining whether you observe a case can differ from the process determining its value.
Sources
- 1.Heckman, J. J. (1979). Sample Selection Bias as a Specification Error. Econometrica, 47(1), 153–161.
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ScholarGate. (2026, June 1). Heckman Selection Model. ScholarGate. https://scholargate.app/econometrics/heckman-selection