Heckman Two Stage Selection Model

The Heckman two-stage selection model corrects regression estimates for sample selection bias by first modeling the probability of being observed with a probit and then adding the inverse Mills ratio to the outcome equation.

Heckman 2단계 표본선택모형은 먼저 프로빗으로 관측될 확률을 모형화한 뒤 역밀스비를 결과식에 추가하여 표본선택 편의를 보정하는 회귀모형이다.

How do I correct for selection bias when the outcome is observed only for a non-random subset?

결과변수가 무작위가 아닌 일부에게만 관측될 때 선택편의는 어떻게 보정하나요?

The Heckman model estimates a probit selection equation for whether the outcome is observed, then includes the inverse Mills ratio from that equation as a regressor in the outcome regression. It fits cases such as wages observed only for people who work, where those observed differ systematically from those who are not.

When to use Heckman Two Stage Selection Model

• Outcome observed only for a self-selected subset, such as wages of employed people
• A variable affects selection but not the outcome (exclusion restriction) is available
• Testing whether selection bias is present via the inverse Mills ratio coefficient

When to use something else

• The outcome is observed for everyone but piles up at zero: use a Tobit model
• The goal is the effect of a binary treatment on observed outcomes under selection on observables: use propensity score matching

Assumptions and requirements

• At least one variable in the selection equation is excluded from the outcome equation
• Jointly normal errors in the selection and outcome equations
• The selection equation is correctly specified
• Corrected standard errors (two-step adjustment or full maximum likelihood)

What the analysis reports

• Probit selection equation coefficients
• Outcome equation coefficients corrected for selection
• Inverse Mills ratio coefficient (lambda) with test
• Rho (error correlation) and sigma

How to report it

The inverse Mills ratio was significant, λ = [value], SE = [value], p = [value], indicating selection bias; after correction, [predictor] was associated with [outcome], b = [value], p = [value].

Related methods

• Tobit Regression Model
• Propensity Score Matching
• Instrumental Variables Regression

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