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A Heckman Selection- t Model


  • Yulia V. Marchenko
  • Marc G. Genton


Sample selection arises often in practice as a result of the partial observability of the outcome of interest in a study. In the presence of sample selection, the observed data do not represent a random sample from the population, even after controlling for explanatory variables. That is, data are missing not at random. Thus, standard analysis using only complete cases will lead to biased results. Heckman introduced a sample selection model to analyze such data and proposed a full maximum likelihood estimation method under the assumption of normality. The method was criticized in the literature because of its sensitivity to the normality assumption. In practice, data, such as income or expenditure data, often violate the normality assumption because of heavier tails. We first establish a new link between sample selection models and recently studied families of extended skew-elliptical distributions. Then, this allows us to introduce a selection- t (SLt) model, which models the error distribution using a Student's t distribution. We study its properties and investigate the finite-sample performance of the maximum likelihood estimators for this model. We compare the performance of the SLt model to the conventional Heckman selection-normal (SLN) model and apply it to analyze ambulatory expenditures. Unlike the SLN model, our analysis using the SLt model provides statistical evidence for the existence of sample selection bias in these data. We also investigate the performance of the test for sample selection bias based on the SLt model and compare it with the performances of several tests used with the SLN model. Our findings indicate that the latter tests can be misleading in the presence of heavy-tailed data.

Suggested Citation

  • Yulia V. Marchenko & Marc G. Genton, 2012. "A Heckman Selection- t Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 304-317, March.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:497:p:304-317
    DOI: 10.1080/01621459.2012.656011

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    Cited by:

    1. Jean-Francois Richard, 2016. "Finite Gaussian Mixture Approximations to Analytically Intractable Density Kerkels," Working Paper 5980, Department of Economics, University of Pittsburgh.
    2. Marra, Giampiero & Wyszynski, Karol, 2016. "Semi-parametric copula sample selection models for count responses," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 110-129.
    3. Marra, Giampiero & Radice, Rosalba, 2013. "Estimation of a regression spline sample selection model," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 158-173.
    4. repec:eee:jmvana:v:163:y:2018:i:c:p:1-14 is not listed on IDEAS
    5. Mikhail Zhelonkin & Marc G. Genton & Elvezio Ronchetti, 2016. "Robust inference in sample selection models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 805-827, September.
    6. Gustavo Rocha & Reinaldo Arellano-Valle & Rosangela Loschi, 2015. "Maximum likelihood methods in a robust censored errors-in-variables model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 857-877, December.
    7. repec:eee:jmvana:v:164:y:2018:i:c:p:65-82 is not listed on IDEAS
    8. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.
    9. Emmanuel O. Ogundimu & Jane L. Hutton, 2016. "A Sample Selection Model with Skew-normal Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 172-190, March.
    10. repec:jss:jstsof:v:071:i06 is not listed on IDEAS
    11. Wiredu, Alexander Nimo & Zeller, Manfred & Diagne, Aliou, 0. "What Determines Adoption of Fertilizers among Rice-Producing Households in Northern Ghana?," Quarterly Journal of International Agriculture, Humboldt-Universität zu Berlin, vol. 54.

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