IDEAS home Printed from https://ideas.repec.org/p/sce/scecf5/241.html
   My bibliography  Save this paper

Bayesian Sampling Algorithms for the Sample Selection and Two-Part Models

Author

Listed:
  • Martijn van Hasselt

Abstract

This paper considers two models to deal with an outcome variable that contains a large fraction of zeros, such as individual expenditures on health care: a sample-selection model and a two-part model. The sample-selection model uses two possibly correlated processes to determine the outcome: a decision process and an outcome process; conditional on a favorable decision, the outcome is observed. The two-part model comprises uncorrelated decision and outcome processes. The paper addresses the issue of selecting between these two models. With a Gaussian specification of the likelihood, the models are nested and inference can focus on the correlation coefficient. Using a fully parametric Bayesian approach, I present sampling algorithms for the model parameters that are based on data augmentation. In addition to the sampler output of the correlation coefficient, a Bayes factor can be computed to distinguish between the models. The paper illustrates the methods and their potential pitfalls using simulated data sets

Suggested Citation

  • Martijn van Hasselt, 2005. "Bayesian Sampling Algorithms for the Sample Selection and Two-Part Models," Computing in Economics and Finance 2005 241, Society for Computational Economics.
    • Handle: RePEc:sce:scecf5:241
    as

    Download full text from publisher

    File URL: http://repec.org/sce2005/up.17210.1107127152.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hakon Tjelmeland & Bjorn Kare Hegstad, 2001. "Mode Jumping Proposals in MCMC," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(1), pages 205-223, March.
    2. 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.
    3. McCulloch, Robert E. & Polson, Nicholas G. & Rossi, Peter E., 2000. "A Bayesian analysis of the multinomial probit model with fully identified parameters," Journal of Econometrics, Elsevier, vol. 99(1), pages 173-193, November.
    4. Lee, Lung-Fei & Chesher, Andrew, 1986. "Specification testing when score test statistics are identically zero," Journal of Econometrics, Elsevier, vol. 31(2), pages 121-149, March.
    5. Cragg, John G, 1971. "Some Statistical Models for Limited Dependent Variables with Application to the Demand for Durable Goods," Econometrica, Econometric Society, vol. 39(5), pages 829-844, September.
    6. 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.
    7. Francis Vella, 1998. "Estimating Models with Sample Selection Bias: A Survey," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 127-169.
    8. Gronau, Reuben, 1974. "Wage Comparisons-A Selectivity Bias," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1119-1143, Nov.-Dec..
    9. Munkin, Murat K. & Trivedi, Pravin K., 2003. "Bayesian analysis of a self-selection model with multiple outcomes using simulation-based estimation: an application to the demand for healthcare," Journal of Econometrics, Elsevier, vol. 114(2), pages 197-220, June.
    10. Koop, Gary & Poirier, Dale J., 1997. "Learning about the across-regime correlation in switching regression models," Journal of Econometrics, Elsevier, vol. 78(2), pages 217-227, June.
    11. 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.
    12. Willard G. Manning Jr. & Charles E. Phelps, 1979. "The Demand for Dental Care," Bell Journal of Economics, The RAND Corporation, vol. 10(2), pages 503-525, Autumn.
    13. McCulloch, Robert & Rossi, Peter E., 1994. "An exact likelihood analysis of the multinomial probit model," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 207-240.
    14. Hay, Joel W & Olsen, Randall J, 1984. "Let Them Eat Cake: A Note on Comparing Alternative Models of the Demand for Medical Care," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(3), pages 279-282, July.
    15. Duan, Naihua, et al, 1983. "A Comparison of Alternative Models for the Demand for Medical Care," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(2), pages 115-126, April.
    16. Olsen, Randall J, 1982. "Distributional Tests for Selectivity Bias and a More Robust Likelihood Estimator," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(1), pages 223-240, February.
    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. Raphaële Préget, 2011. "What is the cost of low participation in French Timber auctions?," Post-Print hal-00670762, HAL.
    2. R. Pr駥t & P. Waelbroeck, 2012. "What is the cost of low participation in French timber auctions?," Applied Economics, Taylor & Francis Journals, vol. 44(11), pages 1337-1346, April.
    3. Dogan, Osman & Taspinar, Suleyman, 2016. "Bayesian Inference in Spatial Sample Selection Models," MPRA Paper 82829, University Library of Munich, Germany.

    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. Maksym, Obrizan, 2010. "A Bayesian Model of Sample Selection with a Discrete Outcome Variable," MPRA Paper 28577, University Library of Munich, Germany.
    2. 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.
    3. van Hasselt, Martijn, 2011. "Bayesian inference in a sample selection model," Journal of Econometrics, Elsevier, vol. 165(2), pages 221-232.
    4. Madden, David, 2008. "Sample selection versus two-part models revisited: The case of female smoking and drinking," Journal of Health Economics, Elsevier, vol. 27(2), pages 300-307, March.
    5. Kohei Enami & John Mullahy, 2009. "Tobit at fifty: a brief history of Tobin's remarkable estimator, of related empirical methods, and of limited dependent variable econometrics in health economics," Health Economics, John Wiley & Sons, Ltd., vol. 18(6), pages 619-628, June.
    6. 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.
    7. Valerie Albouy & Laurent Davezies & Thierry Debrand, 2009. "Dynamic Estimation of Health Expenditure: A new approach for simulating individual expenditure," Working Papers DT20, IRDES institut for research and information in health economics, revised Jan 2009.
    8. 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.
    9. Marjan Petreski & Nikica Blazevski & Blagica Petreski, 2014. "Gender Wage Gap when Women are Highly Inactive: Evidence from Repeated Imputations with Macedonian Data," Journal of Labor Research, Springer, vol. 35(4), pages 393-411, December.
    10. John Mullahy, 1998. "Much Ado About Two: Reconsidering Retransformation and the Two-Part Model in Health Economics," NBER Technical Working Papers 0228, National Bureau of Economic Research, Inc.
    11. Mullahy, John, 1998. "Much ado about two: reconsidering retransformation and the two-part model in health econometrics," Journal of Health Economics, Elsevier, vol. 17(3), pages 247-281, June.
    12. Kohei Enami & John Mullahy, 2008. "Tobit at Fifty: A Brief History of Tobin's Remarkable Estimator, of Related Empirical Methods, and of Limited Dependent Variable Econometrics in Health Economics," NBER Working Papers 14512, National Bureau of Economic Research, Inc.
    13. 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.
    14. 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.
    15. Kevin E. Staub, 2014. "A Causal Interpretation of Extensive and Intensive Margin Effects in Generalized Tobit Models," The Review of Economics and Statistics, MIT Press, vol. 96(2), pages 371-375, May.
    16. Shoshana Neuman & Ronald Oaxaca, 2004. "Wage Decompositions with Selectivity-Corrected Wage Equations: A Methodological Note," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 2(1), pages 3-10, April.
    17. Sirchenko Andrei, 2012. "A model for ordinal responses with an application to policy interest rate," EERC Working Paper Series 12/13e, EERC Research Network, Russia and CIS.
    18. Peter Egger & Mario Larch & Kevin E. Staub & Rainer Winkelmann, 2011. "The Trade Effects of Endogenous Preferential Trade Agreements," American Economic Journal: Economic Policy, American Economic Association, vol. 3(3), pages 113-143, August.
    19. 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.
    20. Alaitz Artabe & Waleska Sigüenza, 2019. "The effects of the economic recession on spending on private health insurance in Spain," International Journal of Health Economics and Management, Springer, vol. 19(2), pages 155-191, June.

    More about this item

    Keywords

    Sample Selection; Data Augmentation; Gibbs Sampling;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:sce:scecf5:241. 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: Christopher F. Baum (email available below). General contact details of provider: https://edirc.repec.org/data/sceeeea.html .

    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.