Heckman Selection Model

Updated on April 11, 2024
Article byPriya Choubey
Edited byShreya Bansal
Reviewed byDheeraj Vaidya, CFA, FRM

What Is Heckman Selection Model?

The Heckman Selection Model, developed by James Heckman in 1979, is a two-step statistical estimation approach designed to rectify sample selection bias. Sample selection bias arises when the sample used in econometric analyses does not accurately mirror the entire population, leading to unfair estimates.

Heckman Selection Model

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This model’s innovative methodology, which involves simultaneously modeling the selection process and outcome variables, positions it as a vital tool in empirical research within social sciences and economics. Particularly valuable in scenarios where sample selection bias challenges accurate analysis, the Heckman model enhances the reliability of research outcomes.

Key Takeaways

  • The Heckman selection model is a statistical framework designed to identify, correct, and omit the sample selection bias in econometric analysis for acquiring accurate empirical research predictions.
  • It is a two-stage estimation method – selection equation where the researchers gauge the probability of a variable being selected as a sample and the outcome equation to determine the relation between the variables of interest.
  • It ensures the accuracy and reliability of empirical findings, especially when the data is susceptible to sample selection errors or missing variables. 
  • It helps researchers and economists to draw precise conclusions about variable relationships and make well-informed policy recommendations.

Heckman Selection Model Explained

The Heckman selection model in r is crucial in econometrics and statistics as it tackles the issue of sample selection bias, a common problem in empirical research. Sample selection bias arises when the sample used for analysis is representative of only some of the population due to specific selection criteria. If not adequately accounted for, this bias can result in distorted and inconsistent parameter estimates. 

Hence, this framework simultaneously estimates two equations:

  1. Selection equation, which predicts the probability of being selected into the sample; and
  2. The outcome equation that explores the relationship between the variables of interest.
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By analyzing both equations together, researchers can obtain reliable and unbiased parameter estimates. In the selection equation, the researcher can employ a probit or logit model to gauge the probability of sample selection based on observable characteristics. The outcome equation involves the inverse Mills ratio, derived from the selection equation, as a correction term, accounting for the sample selection bias. Interpreting the Heckman two-stage selection model involves analyzing both the selection and outcome equations:

Selection Equation: Coefficients indicate the factors influencing sample selection. Positive coefficients reflect a higher probability of being selected for the sample, while negative coefficients imply a lower probability. Significant coefficients are crucial to understanding which variables significantly affect sample selection.

Outcome Equation: The outcome equation, coefficients reveal the impact of predictors on the dependent variable for the selected sample, with significant coefficients indicating influential variables. Comparing outcomes between selected and non-selected groups provides insights into variable effects. The Inverse Mills Ratio (IMR) corrects sample selection bias, signaling potential outliers. Researchers assess model fit using measures like the likelihood ratio test, Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC), with lower AIC and BIC values suggesting a more fitting framework.


The Heckman selection model is used to predict unbiased sample inferences in econometric analysis. Here are the fundamental assumptions of this framework:

  1. Independence assumption: It states that the error terms in the selection and outcome equations should be independent.
  2. Non-Linearity: In this model, non-linearity is allowed, but functional forms must be correctly specified.
  3. No perfect prediction: The sample of selection variables cannot provide a perfect estimation of an individual’s inclusion.
  4. Exclusion restriction: This model requires at least one variable influencing sample selection but not the outcome directly.
  5. Sample variation in selection: The sample selection variables should be diverse across the population data to ensure the reliability of this framework.
  6. No measurement error in the selection variable: There should be no measurement error in the selection process to influence the accuracy of the research estimates.


Moving forward with the concept, let us have a look at the following implications of this framework in real-world and hypothetical scenario.

Example #1

Consider a study in labor economics focusing on the relationship between wages and job satisfaction. In this scenario, individuals may decide whether to be employed or not based on their wages, potentially leading to sample selection bias. The Heckman selection model can be employed to account for this bias by simultaneously modeling the factors affecting employment and the relationship between wages and job satisfaction. Researchers use the selection equation to obtain more accurate assessments of the consequence of wages on job satisfaction.

Example #2

The researchers employed Heckman’s two-stage selection model for gauging the impact of income on rice consumption in the households of Papua New Guinea in 2018. The COVID-19 pandemic led to trade restrictions and a substantial increase in rice prices from significant exporters like Thailand and Vietnam. Papua New Guinea (PNG) heavily depends on imported rice, making it vulnerable to these global price fluctuations.

The study utilized household survey data to analyze rice consumption patterns, focusing on both urban and rural households in PNG. Model simulations revealed that a 25% global rice price hike would result in a 14% drop in overall rice consumption in PNG. The research highlighted a 15% reduction in rice consumption among the impoverished segment of the population in PNG. Considering the pandemic’s impact on household incomes, the study projected a 20% decrease in rice consumption for urban poor households and a 17% reduction for rural poor households.

The importance of maintaining efficient domestic supply chains for staple goods was emphasized to counter the effects of surging global rice prices, enabling urban households to raise their consumption of locally grown staples.

Advantages And Disadvantages

The Heckman selection model in r is valuable for handling sample selection bias in regression analysis, a common issue in empirical studies. However, it has various limitations and assumptions that need to be carefully considered in its application. Let us discuss these pros and cons:


  • It provides consistent and efficient parameter estimates under appropriate assumptions in regression analysis, ensuring reliable results in the presence of selection bias.
  • Additionally, it can handle situations where the selection process and the outcome variable are jointly determined, making it applicable across various fields such as labor economics, health economics, and education research.
  • It provides more efficient and interpretable results compared to ordinary least squares regression by accounting for omitted variables and unobserved characteristics.
  • Employing a two-stage estimation process to interpret the probability of selection in the first stage and the regression of interest in the second stage enhances the efficiency of parameter predictions compared to other single-equation models.
  • Further, the foremost benefit of this model is its computational ease of estimation.


  • The model’s validity hinges on specific assumptions, such as the jointly regular error terms in the selection and outcome equations. Violating these assumptions can lead to misleading and inconsistent results.
  • It has inferior statistical properties when there are finite samples and asymptotic theory compared to modern models like the complete information maximum likelihood (FIML) estimator.
  • Incorrect specification of the selection equation can result in biased outcomes, making it crucial to specify the model accurately.
  • It requires gathering suitable data for both the selection process and the outcome variable, which can be challenging on practical grounds.
  • This model needs an exclusion restriction, such as ensuring that the selection equation has at least one variable coefficient of a non-zero value for providing valid inferences or correcting the sample selection.
  • It is not easy to interpret the outcome of this method due to its dual-equation nature, especially for a novice.

Frequently Asked Questions (FAQs)

1. When to use the Heckman selection model?

The Heckman model is adequate for correcting sample selection bias, especially when the sample is not fully representative. It’s suitable for non-random missing data, censoring, and situations involving self-selection or endogeneity, ensuring unbiased and reliable research outcomes.

2. How to run the Heckman selection model in Stata?

Following are the instructions for running the Heckman selection model in Stata:
– Put the relevant dataset into Stata.
– Use a probit model for binary selection or a tobit model for censored selection to estimate the selection equation.
– Generate the inverse Mills ratio (IMR) based on the predicted values from the selection equation.
– Use Ordinary Least Square (OLS) to estimate the outcome equation, including the IMR as an additional regressor.

3. Are there alternatives to the Heckman selection model?

Yes, there are alternatives to the Heckman selection model. One common alternative is the complete information maximum likelihood (FIML) estimator, which is a modern method used to address sample selection bias. The choice between models depends on the specific characteristics of the data and the research objectives.

This article has been a guide to what is Heckman Selection Model. Here, we explain the concept along with its examples, assumptions, advantages, and disadvantages. You may also find some useful articles here –

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