IDEAS home Printed from https://ideas.repec.org/a/eee/eejocm/v40y2021ics1755534521000348.html
   My bibliography  Save this article

A two recursive equation model to correct for endogeneity in latent class binary probit models

Author

Listed:
  • Sarrias, Mauricio

Abstract

This article proposes a two recursive equation model to correct for endogeneity in latent class Probit models. Concretely, it is assumed that there exists an endogenous and continuous variable defined as a predictor, while unobserved heterogeneity is conceptualized as a vector of parameters that varies across individuals following a discrete distribution. A Maximum Likelihood Estimator is provided to estimate the model parameters based on normally distributed random terms and a free code in R software is provided to carry out the estimation procedure. A small Monte Carlo experiment is carried out to analyze the properties of the estimator. Finally, the estimator is applied to analyze the heterogeneous effects of weight on mental well-being.

Suggested Citation

  • Sarrias, Mauricio, 2021. "A two recursive equation model to correct for endogeneity in latent class binary probit models," Journal of choice modelling, Elsevier, vol. 40(C).
    • Handle: RePEc:eee:eejocm:v:40:y:2021:i:c:s1755534521000348
    DOI: 10.1016/j.jocm.2021.100301
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1755534521000348
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jocm.2021.100301?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. J. P. Florens & J. J. Heckman & C. Meghir & E. Vytlacil, 2008. "Identification of Treatment Effects Using Control Functions in Models With Continuous, Endogenous Treatment and Heterogeneous Effects," Econometrica, Econometric Society, vol. 76(5), pages 1191-1206, September.
    2. Andrew Clark & Fabrice Etilé & Fabien Postel-Vinay & Claudia Senik & Karine Van der Straeten, 2005. "Heterogeneity in Reported Well-Being: Evidence from Twelve European Countries," Economic Journal, Royal Economic Society, vol. 115(502), pages 118-132, March.
    3. David Revelt and Kenneth Train., 2000. "Customer-Specific Taste Parameters and Mixed Logit: Households' Choice of Electricity Supplier," Economics Working Papers E00-274, University of California at Berkeley.
    4. Lee C. Adkins, 2008. "Small Sample Performance of Instrumental Variables Probit Estimators: A Monte Carlo Investigation," Economics Working Paper Series 0807, Oklahoma State University, Department of Economics and Legal Studies in Business.
    5. Vincenzo Atella & Francesco Brindisi & Partha Deb & Furio C. Rosati, 2004. "Determinants of access to physician services in Italy: a latent class seemingly unrelated probit approach," Health Economics, John Wiley & Sons, Ltd., vol. 13(7), pages 657-668, July.
    6. Joseph Sabia & Daniel Rees, 2015. "Body weight, mental health capital, and academic achievement," Review of Economics of the Household, Springer, vol. 13(3), pages 653-684, September.
    7. Guevara, C. Angelo, 2015. "Critical assessment of five methods to correct for endogeneity in discrete-choice models," Transportation Research Part A: Policy and Practice, Elsevier, vol. 82(C), pages 240-254.
    8. Smith, Richard J & Blundell, Richard W, 1986. "An Exogeneity Test for a Simultaneous Equation Tobit Model with an Application to Labor Supply," Econometrica, Econometric Society, vol. 54(3), pages 679-685, May.
    9. Marina Selini Katsaiti, 2012. "Obesity and happiness," Applied Economics, Taylor & Francis Journals, vol. 44(31), pages 4101-4114, November.
    10. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, April.
    11. William Greene, 2004. "Convenient estimators for the panel probit model: Further results," Empirical Economics, Springer, vol. 29(1), pages 21-47, January.
    12. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-959, July.
    13. Jackson, Christopher, 2011. "Multi-State Models for Panel Data: The msm Package for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 38(i08).
    14. Deb, Partha & Trivedi, Pravin K., 2002. "The structure of demand for health care: latent class versus two-part models," Journal of Health Economics, Elsevier, vol. 21(4), pages 601-625, July.
    15. Amemiya, Takeshi, 1978. "The Estimation of a Simultaneous Equation Generalized Probit Model," Econometrica, Econometric Society, vol. 46(5), pages 1193-1205, September.
    16. Willage, Barton, 2018. "The effect of weight on mental health: New evidence using genetic IVs," Journal of Health Economics, Elsevier, vol. 57(C), pages 113-130.
    17. Christopher L. Skeels & Larry W. Taylor, 2015. "Prediction in linear index models with endogenous regressors," Stata Journal, StataCorp LP, vol. 15(3), pages 627-644, September.
    18. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-529, October.
    19. James J. Heckman & Sergio Urzua & Edward Vytlacil, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 389-432, August.
    20. Peiming Wang & Iain Cockburn & Martin L. Puterman, "undated". "A Mixed Poisson Regression Model for Analysis of Patent Data," Computing in Economics and Finance 1996 _049, Society for Computational Economics.
    21. Junyi Shen, 2009. "Latent class model or mixed logit model? A comparison by transport mode choice data," Applied Economics, Taylor & Francis Journals, vol. 41(22), pages 2915-2924.
    22. Rivers, Douglas & Vuong, Quang H., 1988. "Limited information estimators and exogeneity tests for simultaneous probit models," Journal of Econometrics, Elsevier, vol. 39(3), pages 347-366, November.
    23. Guevara, C. Angelo, 2018. "Overidentification tests for the exogeneity of instruments in discrete choice models," Transportation Research Part B: Methodological, Elsevier, vol. 114(C), pages 241-253.
    24. Bago d'Uva, Teresa & Jones, Andrew M., 2009. "Health care utilisation in Europe: New evidence from the ECHP," Journal of Health Economics, Elsevier, vol. 28(2), pages 265-279, March.
    25. Greene,William H. & Hensher,David A., 2010. "Modeling Ordered Choices," Cambridge Books, Cambridge University Press, number 9780521194204, September.
    26. Greene, William H. & Hensher, David A., 2003. "A latent class model for discrete choice analysis: contrasts with mixed logit," Transportation Research Part B: Methodological, Elsevier, vol. 37(8), pages 681-698, September.
    27. Michel Wedel & Wayne DeSarbo, 1995. "A mixture likelihood approach for generalized linear models," Journal of Classification, Springer;The Classification Society, vol. 12(1), pages 21-55, March.
    28. repec:adr:anecst:y:2008:i:91-92:p:12 is not listed on IDEAS
    29. Juan Palomino & Mauricio Sarrias, 2019. "The monetary subjective health evaluation for commuting long distances in Chile: A latent class analysis," Papers in Regional Science, Wiley Blackwell, vol. 98(3), pages 1397-1417, June.
    30. Bhat, Chandra R., 2011. "The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models," Transportation Research Part B: Methodological, Elsevier, vol. 45(7), pages 923-939, August.
    31. Bhat, Chandra R. & Astroza, Sebastian & Sidharthan, Raghuprasad & Alam, Mohammad Jobair Bin & Khushefati, Waleed H., 2014. "A joint count-continuous model of travel behavior with selection based on a multinomial probit residential density choice model," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 31-51.
    32. Joan L. Walker & Moshe Ben-Akiva & Denis Bolduc, 2007. "Identification of parameters in normal error component logit-mixture (NECLM) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(6), pages 1095-1125.
    33. Stephane Hess, 2014. "Latent class structures: taste heterogeneity and beyond," Chapters, in: Stephane Hess & Andrew Daly (ed.), Handbook of Choice Modelling, chapter 14, pages 311-330, Edward Elgar Publishing.
    34. Johan Håkon Bjørngaard & David Carslake & Tom Ivar Lund Nilsen & Astrid C E Linthorst & George Davey Smith & David Gunnell & Pål Richard Romundstad, 2015. "Association of Body Mass Index with Depression, Anxiety and Suicide—An Instrumental Variable Analysis of the HUNT Study," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-15, July.
    35. Robert Moffitt, 2008. "Estimating Marginal Treatment Effects in Heterogeneous Populations," Annals of Economics and Statistics, GENES, issue 91-92, pages 239-261.
    36. Kamel Jedidi & Venkatram Ramaswamy & Wayne Desarbo, 1993. "A maximum likelihood method for latent class regression involving a censored dependent variable," Psychometrika, Springer;The Psychometric Society, vol. 58(3), pages 375-394, September.
    37. Amemiya, Takeshi, 1979. "The Estimation of a Simultaneous-Equation Tobit Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(1), pages 169-181, February.
    38. Arne Henningsen & Ott Toomet, 2011. "maxLik: A package for maximum likelihood estimation in R," Computational Statistics, Springer, vol. 26(3), pages 443-458, September.
    39. Elizabeth S. Garrett & Scott L. Zeger, 2000. "Latent Class Model Diagnosis," Biometrics, The International Biometric Society, vol. 56(4), pages 1055-1067, December.
    40. Sarrias, Mauricio & Daziano, Ricardo A., 2018. "Individual-specific point and interval conditional estimates of latent class logit parameters," Journal of choice modelling, Elsevier, vol. 27(C), pages 50-61.
    41. Guevara, C. Angelo & Hess, Stephane, 2019. "A control-function approach to correct for endogeneity in discrete choice models estimated on SP-off-RP data and contrasts with an earlier FIML approach by Train & Wilson," Transportation Research Part B: Methodological, Elsevier, vol. 123(C), pages 224-239.
    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. Sarrias, Mauricio & Blanco, Alejandra, 2022. "Bodyweight and human capital development: Assessing the impact of obesity on socioemotional skills during childhood in Chile," Economics & Human Biology, Elsevier, vol. 47(C).
    2. Wang, Shunchao & Song, Zhanguo, 2024. "Exploring the behavioral stage transition of traveler's adoption of carsharing: An integrated choice and latent variable model," Journal of choice modelling, Elsevier, vol. 51(C).

    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. Brown, Sarah & Greene, William H. & Harris, Mark N. & Taylor, Karl, 2015. "An inverse hyperbolic sine heteroskedastic latent class panel tobit model: An application to modelling charitable donations," Economic Modelling, Elsevier, vol. 50(C), pages 228-236.
    2. Maness, Michael & Cirillo, Cinzia, 2016. "An indirect latent informational conformity social influence choice model: Formulation and case study," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 75-101.
    3. Manuel Denzer, 2019. "Estimating Causal Effects in Binary Response Models with Binary Endogenous Explanatory Variables - A Comparison of Possible Estimators," Working Papers 1916, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    4. Bago d'Uva, Teresa & Jones, Andrew M. & van Doorslaer, Eddy, 2009. "Measurement of horizontal inequity in health care utilisation using European panel data," Journal of Health Economics, Elsevier, vol. 28(2), pages 280-289, March.
    5. Thomas E. Guerrero & C. Angelo Guevara & Elisabetta Cherchi & Juan de Dios Ortúzar, 2021. "Addressing endogeneity in strategic urban mode choice models," Transportation, Springer, vol. 48(4), pages 2081-2102, August.
    6. Guevara, C. Angelo, 2018. "Overidentification tests for the exogeneity of instruments in discrete choice models," Transportation Research Part B: Methodological, Elsevier, vol. 114(C), pages 241-253.
    7. Jacob N. Arendt, 2002. "Endogeneity and Heterogeneity in LDV Panel Data Models," 10th International Conference on Panel Data, Berlin, July 5-6, 2002 D6-1, International Conferences on Panel Data.
    8. Antecol, Heather & Bedard, Kelly & Helland, Eric, 2001. "Does Single Parenthood Increase the Probability of Teenage Promiscuity, Drug Use, and Crime? Evidence from Divorce Law Changes," University of California at Santa Barbara, Economics Working Paper Series qt3fc7n20b, Department of Economics, UC Santa Barbara.
    9. Hendrik Schmitz, 2012. "More health care utilization with more insurance coverage? Evidence from a latent class model with German data," Applied Economics, Taylor & Francis Journals, vol. 44(34), pages 4455-4468, December.
    10. Jörg Schwiebert, 2015. "Estimation and interpretation of a Heckman selection model with endogenous covariates," Empirical Economics, Springer, vol. 49(2), pages 675-703, September.
    11. Guevara, C. Angelo & Hess, Stephane, 2019. "A control-function approach to correct for endogeneity in discrete choice models estimated on SP-off-RP data and contrasts with an earlier FIML approach by Train & Wilson," Transportation Research Part B: Methodological, Elsevier, vol. 123(C), pages 224-239.
    12. Chesher, Andrew, 2013. "Semiparametric Structural Models Of Binary Response: Shape Restrictions And Partial Identification," Econometric Theory, Cambridge University Press, vol. 29(2), pages 231-266, April.
    13. Gopalakrishnan, Raja & Guevara, C. Angelo & Ben-Akiva, Moshe, 2020. "Combining multiple imputation and control function methods to deal with missing data and endogeneity in discrete-choice models," Transportation Research Part B: Methodological, Elsevier, vol. 142(C), pages 45-57.
    14. Watanabe, Hajime & Maruyama, Takuya, 2023. "A Bayesian instrumental variable model for multinomial choice with correlated alternatives," Journal of choice modelling, Elsevier, vol. 46(C).
    15. Guilhem Bascle, 2008. "Controlling for endogeneity with instrumental variables in strategic management research," Post-Print hal-00576795, HAL.
    16. Anna Piil Damm, 2009. "Ethnic Enclaves and Immigrant Labor Market Outcomes: Quasi-Experimental Evidence," Journal of Labor Economics, University of Chicago Press, vol. 27(2), pages 281-314, April.
    17. Sarah Brown & William Greene & Mark N. Harris, 2014. "A New Formulation for Latent Class Models," Working Papers 2014006, The University of Sheffield, Department of Economics.
    18. Julia Bredtmann, 2014. "The Intra-household Division of Labor: An Empirical Analysis of Spousal Influences on Individual Time Allocation," LABOUR, CEIS, vol. 28(1), pages 1-39, March.
    19. Vásquez Lavin, Felipe & Barrientos, Manuel & Castillo, Álvaro & Herrera, Iván & Ponce Oliva, Roberto D., 2020. "Firewood certification programs: Key attributes and policy implications," Energy Policy, Elsevier, vol. 137(C).
    20. Roy Cerqueti & Fabio Sabatini & Marco Ventura, 2019. "Civic capital and support for the welfare state," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(2), pages 313-336, August.

    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:eejocm:v:40:y:2021:i:c:s1755534521000348. 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.journals.elsevier.com/journal-of-choice-modelling .

    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.