IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v193y2023ics0047259x22000896.html
   My bibliography  Save this article

Bivariate symmetric Heckman models and their characterization

Author

Listed:
  • Saulo, Helton
  • Vila, Roberto
  • Cordeiro, Shayane S.
  • Leiva, Víctor

Abstract

A sample selection bias problem arises when a variable of interest or response is correlated with a latent variable. This problem is presented when the response variable has part of its observations censored. The Heckman sample selection model is based on the bivariate normality assumption and fits both response and latent variables. Recently, this assumption has been relaxed to more flexible models based on the Student-t distribution, which has appealing statistical properties. In this article, we introduce an extention of the Heckman sample selection model to the wide class of symmetric distributions. In the new class of sample selection models, covariates are used to describe its dispersion and correlation parameters explaining heteroscedasticity and sample selection bias, respectively. We derive mathematical and statistical properties of the introduced model, and estimate its parameters with the maximum likelihood method. The case of the bivariate Heckman-Student-t model, as a special member of the family of symmetric Heckman models, is analyzed. Monte Carlo simulations are performed to assess the statistical behavior of the estimation method. Two real data sets are analyzed to illustrate our results.

Suggested Citation

  • Saulo, Helton & Vila, Roberto & Cordeiro, Shayane S. & Leiva, Víctor, 2023. "Bivariate symmetric Heckman models and their characterization," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:jmvana:v:193:y:2023:i:c:s0047259x22000896
    DOI: 10.1016/j.jmva.2022.105097
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X22000896
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2022.105097?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Nelson, Forrest D., 1984. "Efficiency of the two-step estimator for models with endogenous sample selection," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 181-196.
    2. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492, National Bureau of Economic Research, Inc.
    3. Manning, W. G. & Duan, N. & Rogers, W. H., 1987. "Monte Carlo evidence on the choice between sample selection and two-part models," Journal of Econometrics, Elsevier, vol. 35(1), pages 59-82, May.
    4. Lachos, Victor H. & Prates, Marcos O. & Dey, Dipak K., 2021. "Heckman selection-t model: Parameter estimation via the EM-algorithm," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    5. Ding, Peng, 2014. "Bayesian robust inference of sample selection using selection-t models," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 451-464.
    6. Paarsch, Harry J., 1984. "A Monte Carlo comparison of estimators for censored regression models," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 197-213.
    7. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    8. von Rosen, Dietrich, 1989. "Maximum likelihood estimators in multivariate linear normal models," Journal of Multivariate Analysis, Elsevier, vol. 31(2), pages 187-200, November.
    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. Liu, Shuangzhe & Leiva, Víctor & Zhuang, Dan & Ma, Tiefeng & Figueroa-Zúñiga, Jorge I., 2022. "Matrix differential calculus with applications in the multivariate linear model and its diagnostics," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    11. Fernando de Souza Bastos & Wagner Barreto-Souza, 2021. "Birnbaum–Saunders sample selection model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(11), pages 1896-1916, August.
    12. Leung, Siu Fai & Yu, Shihti, 1996. "On the choice between sample selection and two-part models," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 197-229.
    13. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Danúbia R. Cunha & Jose Angelo Divino & Helton Saulo, 2024. "Zero-Adjusted Log-Symmetric Quantile Regression Models," Computational Economics, Springer;Society for Computational Economics, vol. 63(5), pages 2087-2111, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Helton Saulo & Roberto Vila & Shayane S. Cordeiro, 2022. "Symmetric generalized Heckman models," Papers 2206.10054, arXiv.org.
    2. Kossova, Elena & Potanin, Bogdan, 2018. "Heckman method and switching regression model multivariate generalization," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 50, pages 114-143.
    3. Patrick Puhani, 2000. "The Heckman Correction for Sample Selection and Its Critique," Journal of Economic Surveys, Wiley Blackwell, vol. 14(1), pages 53-68, February.
    4. Leung, Siu Fai & Yu, Shihti, 1996. "On the choice between sample selection and two-part models," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 197-229.
    5. 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.
    6. 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.
    7. Liu, Lei & Strawderman, Robert L. & Cowen, Mark E. & Shih, Ya-Chen T., 2010. "A flexible two-part random effects model for correlated medical costs," Journal of Health Economics, Elsevier, vol. 29(1), pages 110-123, January.
    8. Ross M. Stolzenberg & Daniel A. Relles, 1990. "Theory Testing in a World of Constrained Research Design," Sociological Methods & Research, , vol. 18(4), pages 395-415, May.
    9. Emmanuel O. Ogundimu, 2022. "Regularization and variable selection in Heckman selection model," Statistical Papers, Springer, vol. 63(2), pages 421-439, April.
    10. William Martin & Cong S. Pham, 2020. "Estimating the gravity model when zero trade flows are frequent and economically determined," Applied Economics, Taylor & Francis Journals, vol. 52(26), pages 2766-2779, May.
    11. Wojtyś, Małgorzata & Marra, Giampiero & Radice, Rosalba, 2018. "Copula based generalized additive models for location, scale and shape with non-random sample selection," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 1-14.
    12. Wiemann, Paul F.V. & Klein, Nadja & Kneib, Thomas, 2022. "Correcting for sample selection bias in Bayesian distributional regression models," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    13. Nawata, Kazumitsu, 1995. "Estimation of sample-selection models by the maximum likelihood method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 39(3), pages 299-303.
    14. Watanabe, Hajime & Maruyama, Takuya, 2024. "A Bayesian sample selection model with a binary outcome for handling residential self-selection in individual car ownership," Journal of choice modelling, Elsevier, vol. 51(C).
    15. Rémi Lardellier & Renaud Legal & Denis Raynaud & Guillaume Vidal, 2011. "Un outil pour l’étude des dépenses de santé et des « restes à charge » des ménages : le modèle Omar," Économie et Statistique, Programme National Persée, vol. 450(1), pages 47-77.
    16. Takashi Yamagata & Chris Orme, 2005. "On Testing Sample Selection Bias Under the Multicollinearity Problem," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 467-481.
    17. Lachos, Victor H. & Prates, Marcos O. & Dey, Dipak K., 2021. "Heckman selection-t model: Parameter estimation via the EM-algorithm," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    18. Kim, Sung Hoo & Mokhtarian, Patricia L., 2023. "Comparisons of observed and unobserved parameter heterogeneity in modeling vehicle-miles driven," Transportation Research Part A: Policy and Practice, Elsevier, vol. 172(C).
    19. Danúbia R. Cunha & Jose Angelo Divino & Helton Saulo, 2024. "Zero-Adjusted Log-Symmetric Quantile Regression Models," Computational Economics, Springer;Society for Computational Economics, vol. 63(5), pages 2087-2111, May.
    20. Goic, Marcel & Rojas, Andrea & Saavedra, Ignacio, 2021. "The Effectiveness of Triggered Email Marketing in Addressing Browse Abandonments," Journal of Interactive Marketing, Elsevier, vol. 55(C), pages 118-145.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:193:y:2023:i:c:s0047259x22000896. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.