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Bayesian inference in a sample selection model

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  • van Hasselt, Martijn

Abstract

This paper develops methods of Bayesian inference in a sample selection model. The main feature of this model is that the outcome variable is only partially observed. We first present a Gibbs sampling algorithm for a model in which the selection and outcome errors are normally distributed. The algorithm is then extended to analyze models that are characterized by nonnormality. Specifically, we use a Dirichlet process prior and model the distribution of the unobservables as a mixture of normal distributions with a random number of components. The posterior distribution in this model can simultaneously detect the presence of selection effects and departures from normality. Our methods are illustrated using some simulated data and an abstract from the RAND health insurance experiment.

Suggested Citation

  • van Hasselt, Martijn, 2011. "Bayesian inference in a sample selection model," Journal of Econometrics, Elsevier, vol. 165(2), pages 221-232.
    • Handle: RePEc:eee:econom:v:165:y:2011:i:2:p:221-232
    DOI: 10.1016/j.jeconom.2011.08.003
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    Cited by:

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    2. Anastasios Panagiotelis & Michael S. Smith & Peter J. Danaher, 2014. "From Amazon to Apple: Modeling Online Retail Sales, Purchase Incidence, and Visit Behavior," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(1), pages 14-29, January.
    3. 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).
    4. 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).
    5. Sizhong Sun, 2023. "Firm heterogeneity, worker training and labor productivity: the role of endogenous self-selection," Journal of Productivity Analysis, Springer, vol. 59(2), pages 121-133, April.
    6. Ignacio Abásolo & Miguel Negrín & Jaime Pinilla, 2014. "Utilización y tiempos de espera: dos vertientes inseparables del análisis de la equidad en el acceso al sistema sanitario público," Hacienda Pública Española / Review of Public Economics, IEF, vol. 208(1), pages 11-38, March.
    7. Watanabe, Hajime & Maruyama, Takuya, 2023. "A Bayesian instrumental variable model for multinomial choice with correlated alternatives," Journal of choice modelling, Elsevier, vol. 46(C).
    8. Zhao, Jun & Kim, Hea-Jung & Kim, Hyoung-Moon, 2020. "New EM-type algorithms for the Heckman selection model," Computational Statistics & Data Analysis, Elsevier, vol. 146(C).
    9. Rong Zhang & Brett A. Inder & Xibin Zhang, 2012. "Parameter estimation for a discrete-response model with double rules of sample selection: A Bayesian approach," Monash Econometrics and Business Statistics Working Papers 5/12, Monash University, Department of Econometrics and Business Statistics.
    10. Li, Phillip, 2011. "Estimation of sample selection models with two selection mechanisms," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1099-1108, February.
    11. Didier Nibbering, 2019. "A High-dimensional Multinomial Choice Model," Monash Econometrics and Business Statistics Working Papers 19/19, Monash University, Department of Econometrics and Business Statistics.
    12. Zhang, Rong & Inder, Brett A. & Zhang, Xibin, 2015. "Bayesian estimation of a discrete response model with double rules of sample selection," Computational Statistics & Data Analysis, Elsevier, vol. 86(C), pages 81-96.
    13. Ovielt Baltodano L'opez & Roberto Casarin, 2022. "A Dynamic Stochastic Block Model for Multi-Layer Networks," Papers 2209.09354, arXiv.org.
    14. Timothy J. Halliday & Bhashkar Mazumder & Ashley Wong, 2020. "The intergenerational transmission of health in the United States: A latent variables analysis," Health Economics, John Wiley & Sons, Ltd., vol. 29(3), pages 367-381, March.
    15. Dogan, Osman & Taspinar, Suleyman, 2016. "Bayesian Inference in Spatial Sample Selection Models," MPRA Paper 82829, University Library of Munich, Germany.
    16. Ding, Peng, 2014. "Bayesian robust inference of sample selection using selection-t models," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 451-464.
    17. Rong Zhang & Brett A. Inder & Xibin Zhang, 2013. "Bayesian estimation of a discrete response model with double rules of sample selection," Monash Econometrics and Business Statistics Working Papers 24/13, Monash University, Department of Econometrics and Business Statistics.

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    More about this item

    Keywords

    Sample selection; Gibbs sampling; Mixture distributions; Dirichlet process;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models

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