IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1811.03329.html
   My bibliography  Save this paper

Nonparametric maximum likelihood methods for binary response models with random coefficients

Author

Listed:
  • Jiaying Gu
  • Roger Koenker

Abstract

Single index linear models for binary response with random coefficients have been extensively employed in many econometric settings under various parametric specifications of the distribution of the random coefficients. Nonparametric maximum likelihood estimation (NPMLE) as proposed by Cosslett (1983) and Ichimura and Thompson (1998), in contrast, has received less attention in applied work due primarily to computational difficulties. We propose a new approach to computation of NPMLEs for binary response models that significantly increase their computational tractability thereby facilitating greater flexibility in applications. Our approach, which relies on recent developments involving the geometry of hyperplane arrangements, is contrasted with the recently proposed deconvolution method of Gautier and Kitamura (2013). An application to modal choice for the journey to work in the Washington DC area illustrates the methods.

Suggested Citation

  • Jiaying Gu & Roger Koenker, 2018. "Nonparametric maximum likelihood methods for binary response models with random coefficients," Papers 1811.03329, arXiv.org, revised Jan 2020.
    • Handle: RePEc:arx:papers:1811.03329
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1811.03329
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Groeneboom,Piet & Jongbloed,Geurt, 2014. "Nonparametric Estimation under Shape Constraints," Cambridge Books, Cambridge University Press, number 9780521864015, January.
    2. Horowitz, Joel L., 1993. "Semiparametric estimation of a work-trip mode choice model," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 49-70, July.
    3. Jiaying Gu & Roger Koenker, 2016. "On a Problem of Robbins," International Statistical Review, International Statistical Institute, vol. 84(2), pages 224-244, August.
    4. Koenker, Roger & Mizera, Ivan, 2014. "Convex Optimization in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 60(i05).
    5. Eric Gautier & Yuichi Kitamura, 2013. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Econometrica, Econometric Society, vol. 81(2), pages 581-607, March.
    6. Jiaying Gu & Roger Koenker, 2017. "Rebayes: an R package for empirical bayes mixture methods," CeMMAP working papers CWP37/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    8. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
    9. Ichimura, Hidehiko & Thompson, T. Scott, 1998. "Maximum likelihood estimation of a binary choice model with random coefficients of unknown distribution," Journal of Econometrics, Elsevier, vol. 86(2), pages 269-295, June.
    10. Roger Koenker & Ivan Mizera, 2014. "Convex Optimization, Shape Constraints, Compound Decisions, and Empirical Bayes Rules," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 674-685, June.
    11. Cosslett, Stephen R, 1983. "Distribution-Free Maximum Likelihood Estimator of the Binary Choice Model," Econometrica, Econometric Society, vol. 51(3), pages 765-782, May.
    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. Gu, Jiaying & Russell, Thomas M., 2023. "Partial identification in nonseparable binary response models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 235(2), pages 528-562.
    2. Jiaying Gu & Thomas M. Russell, 2021. "Partial Identification in Nonseparable Binary Response Models with Endogenous Regressors," Papers 2101.01254, arXiv.org, revised Jul 2022.

    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. Jiaying Gu & Roger Koenker, 2018. "Nonparametric maximum likelihood methods for binary response models with random coefficients," CeMMAP working papers CWP65/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Matzkin, Rosa L., 2019. "Constructive identification in some nonseparable discrete choice models," Journal of Econometrics, Elsevier, vol. 211(1), pages 83-103.
    3. Amit Gandhi & Jeremy T. Fox, 2009. "Identifying Heterogeneity in Economic Choice and Selection Models Using Mixtures," 2009 Meeting Papers 165, Society for Economic Dynamics.
    4. Giovanni Compiani & Yuichi Kitamura, 2016. "Using mixtures in econometric models: a brief review and some new results," Econometrics Journal, Royal Economic Society, vol. 19(3), pages 95-127, October.
    5. Matzkin, Rosa L., 2012. "Identification in nonparametric limited dependent variable models with simultaneity and unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 166(1), pages 106-115.
    6. Feng, Long & Dicker, Lee H., 2018. "Approximate nonparametric maximum likelihood for mixture models: A convex optimization approach to fitting arbitrary multivariate mixing distributions," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 80-91.
    7. Hoderlein, Stefan & Sherman, Robert, 2015. "Identification and estimation in a correlated random coefficients binary response model," Journal of Econometrics, Elsevier, vol. 188(1), pages 135-149.
    8. Li Tan & Cory Koedel, 2019. "The Effects of Differential Income Replacement and Mortality on U.S. Social Security Redistribution," Southern Economic Journal, John Wiley & Sons, vol. 86(2), pages 613-637, October.
    9. Jiaying Gu & Roger Koenker, 2020. "Invidious Comparisons: Ranking and Selection as Compound Decisions," Papers 2012.12550, arXiv.org, revised Sep 2021.
    10. Taisuke Otsu & Mengshan Xu, 2022. "Isotonic propensity score matching," STICERD - Econometrics Paper Series 623, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    11. Arthur Lewbel, 2019. "The Identification Zoo: Meanings of Identification in Econometrics," Journal of Economic Literature, American Economic Association, vol. 57(4), pages 835-903, December.
    12. Fox, Jeremy T. & Kim, Kyoo il & Yang, Chenyu, 2016. "A simple nonparametric approach to estimating the distribution of random coefficients in structural models," Journal of Econometrics, Elsevier, vol. 195(2), pages 236-254.
    13. Tushar Kanti Nandi, 2006. "Parametric and Semiparametric Estimation of the Adoption of Work Teams," Department of Economics University of Siena 484, Department of Economics, University of Siena.
    14. Jeff Racine, 2002. "Generalized Semiparametric Binary Prediction," Annals of Economics and Finance, Society for AEF, vol. 3(1), pages 117-134, May.
    15. Jeremy T. Fox & Amit Gandhi, 2009. "Identifying Heterogeneity in Economic Choice Models," NBER Working Papers 15147, National Bureau of Economic Research, Inc.
    16. Mengshan Xu & Taisuke Otsu, 2022. "Isotonic propensity score matching," Papers 2207.08868, arXiv.org, revised Aug 2024.
    17. Liu, Ruixuan & Yu, Zhengfei, 2022. "Sample selection models with monotone control functions," Journal of Econometrics, Elsevier, vol. 226(2), pages 321-342.
    18. Ranjeeta Thomas, 2012. "Conditional Cash Transfers To Improve Education And Health: An Ex Ante Evaluation Of Red De Protección Social, Nicaragua," Health Economics, John Wiley & Sons, Ltd., vol. 21(10), pages 1136-1154, October.
    19. Ichimura, Hidehiko & Thompson, T. Scott, 1998. "Maximum likelihood estimation of a binary choice model with random coefficients of unknown distribution," Journal of Econometrics, Elsevier, vol. 86(2), pages 269-295, June.
    20. Fosgerau, Mogens & Bierlaire, Michel, 2007. "A practical test for the choice of mixing distribution in discrete choice models," Transportation Research Part B: Methodological, Elsevier, vol. 41(7), pages 784-794, August.

    More about this item

    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:arx:papers:1811.03329. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.