IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/15210.html
   My bibliography  Save this paper

A Simple Nonparametric Estimator for the Distribution of Random Coefficients

Author

Listed:
  • Patrick Bajari
  • Jeremy T. Fox
  • Kyoo il Kim
  • Stephen P. Ryan

Abstract

We propose a simple nonparametric mixtures estimator for recovering the joint distribution of parameter heterogeneity in economic models, such as the random coefficients logit. The estimator is based on linear regression subject to linear inequality constraints, and is robust, easy to program and computationally attractive compared to alternative estimators for random coefficient models. We prove consistency and provide the rate of convergence under deterministic and stochastic choices for the sieve approximating space. We present a Monte Carlo study and an empirical application to dynamic programming discrete choice with a serially-correlated unobserved state variable.

Suggested Citation

  • Patrick Bajari & Jeremy T. Fox & Kyoo il Kim & Stephen P. Ryan, 2009. "A Simple Nonparametric Estimator for the Distribution of Random Coefficients," NBER Working Papers 15210, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:15210
    Note: ED IO LS PR TWP
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w15210.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
    2. Fox, Jeremy T. & Kim, Kyoo il & Ryan, Stephen P. & Bajari, Patrick, 2012. "The random coefficients logit model is identified," Journal of Econometrics, Elsevier, vol. 166(2), pages 204-212.
    3. Wilfried Seidel & Karl Mosler & Manfred Alker, 2000. "A Cautionary Note on Likelihood Ratio Tests in Mixture Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 481-487, September.
    4. Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July.
    5. repec:cdl:compol:217 is not listed on IDEAS
    6. 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.
    7. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
    8. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    9. Briesch, Richard A. & Chintagunta, Pradeep K. & Matzkin, Rosa L., 2010. "Nonparametric Discrete Choice Models With Unobserved Heterogeneity," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 291-307.
    10. Wolak, Frank A., 1989. "Testing inequality constraints in linear econometric models," Journal of Econometrics, Elsevier, vol. 41(2), pages 205-235, June.
    11. Geweke, John, 1986. "Exact Inference in the Inequality Constrained Normal Linear Regression Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 1(2), pages 127-141, April.
    12. Daniel Ackerberg, 2009. "A new use of importance sampling to reduce computational burden in simulation estimation," Quantitative Marketing and Economics (QME), Springer, vol. 7(4), pages 343-376, December.
    13. Burda, Martin & Harding, Matthew & Hausman, Jerry, 2008. "A Bayesian mixed logit-probit model for multinomial choice," Journal of Econometrics, Elsevier, vol. 147(2), pages 232-246, December.
    14. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard, 2003. "Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 561-575, January.
    15. John Rust, 1997. "Using Randomization to Break the Curse of Dimensionality," Econometrica, Econometric Society, vol. 65(3), pages 487-516, May.
    16. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    17. Karlis, Dimitris & Xekalaki, Evdokia, 2003. "Choosing initial values for the EM algorithm for finite mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 577-590, January.
    18. Eric Gautier & Yuichi Kitamura, 2013. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Econometrica, Econometric Society, vol. 81(2), pages 581-607, March.
    19. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
    20. Wagner Kamakura, 1991. "Estimating flexible distributions of ideal-points with external analysis of preferences," Psychometrika, Springer;The Psychometric Society, vol. 56(3), pages 419-431, September.
    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. Fox, Jeremy T. & Kim, Kyoo il & Ryan, Stephen P. & Bajari, Patrick, 2012. "The random coefficients logit model is identified," Journal of Econometrics, Elsevier, vol. 166(2), pages 204-212.
    2. Moon, Hyungsik Roger & Shum, Matthew & Weidner, Martin, 2018. "Estimation of random coefficients logit demand models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 206(2), pages 613-644.
    3. Christopher T. Conlon & Julie Holland Mortimer, 2013. "Demand Estimation under Incomplete Product Availability," American Economic Journal: Microeconomics, American Economic Association, vol. 5(4), pages 1-30, November.
    4. Joao Macieira, 2010. "Oblivious Equilibrium in Dynamic Discrete Games," 2010 Meeting Papers 680, Society for Economic Dynamics.
    5. Yu Zheng & Juan Pantano, 2012. "Using Subjective Expectations Data to Allow for Unobserved Heterogeneity in Hotz-Miller Estimation Strategies," 2012 Meeting Papers 940, Society for Economic Dynamics.
    6. Christopher T. Conlon & Julie Holland Mortimer, 2010. "Effects of Product Availability: Experimental Evidence," Boston College Working Papers in Economics 798, Boston College Department of Economics.
    7. Cerquera Dussán, Daniel & Ullrich, Hannes, 2010. "Consumer welfare and unobserved heterogeneity in discrete choice models: The value of alpine road tunnels," ZEW Discussion Papers 10-095, ZEW - Leibniz Centre for European Economic Research.

    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. 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.
    2. Matzkin, Rosa L., 2019. "Constructive identification in some nonseparable discrete choice models," Journal of Econometrics, Elsevier, vol. 211(1), pages 83-103.
    3. 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.
    4. Christoph Breunig & Stefan Hoderlein, 2016. "Nonparametric Specification Testing in Random Parameter Models," Boston College Working Papers in Economics 897, Boston College Department of Economics.
    5. Christoph Breunig & Stefan Hoderlein, 2018. "Specification testing in random coefficient models," Quantitative Economics, Econometric Society, vol. 9(3), pages 1371-1417, November.
    6. Steven T. Berry & Philip A. Haile, 2009. "Nonparametric Identification of Multinomial Choice Demand Models with Heterogeneous Consumers," NBER Working Papers 15276, National Bureau of Economic Research, Inc.
    7. Steven T. Berry & Philip A. Haile, 2014. "Identification in Differentiated Products Markets Using Market Level Data," Econometrica, Econometric Society, vol. 82, pages 1749-1797, September.
    8. Kyoo il Kim, 2014. "Identification of the Distribution of Random Coefficients in Static and Dynamic Discrete Choice Models," Korean Economic Review, Korean Economic Association, vol. 30, pages 191-216.
    9. Fox, Jeremy T. & Kim, Kyoo il & Ryan, Stephen P. & Bajari, Patrick, 2012. "The random coefficients logit model is identified," Journal of Econometrics, Elsevier, vol. 166(2), pages 204-212.
    10. Roy Allen & John Rehbeck, 2020. "Identification of Random Coefficient Latent Utility Models," Papers 2003.00276, arXiv.org.
    11. Arthur Lewbel & Krishna Pendakur, 2017. "Unobserved Preference Heterogeneity in Demand Using Generalized Random Coefficients," Journal of Political Economy, University of Chicago Press, vol. 125(4), pages 1100-1148.
    12. Andrew Chesher & Adam M. Rosen, 2014. "An instrumental variable random‐coefficients model for binary outcomes," Econometrics Journal, Royal Economic Society, vol. 17(2), pages 1-19, June.
    13. Steven T. Berry & Philip A. Haile, 2009. "Identification of a Heterogeneous Generalized Regression Model with Group Effects," Cowles Foundation Discussion Papers 1732, Cowles Foundation for Research in Economics, Yale University.
    14. Victor H. Aguiar & Nail Kashaev, 2019. "Discrete Choice and Welfare Analysis with Unobserved Choice Sets," Papers 1907.04853, arXiv.org, revised Jul 2019.
    15. 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.
    16. Levon Barseghyan & Francesca Molinari & Matthew Thirkettle, 2019. "Discrete choice under risk with limited consideration," CeMMAP working papers CWP08/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    17. Lombardi, Stefano & van den Berg, Gerard J. & Vikström, Johan, 2020. "Empirical Monte Carlo evidence on estimation of Timing-of-Events models," Working Paper Series 2020:26, IFAU - Institute for Evaluation of Labour Market and Education Policy, revised 05 Jan 2021.
    18. 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.
    19. Pietro Tebaldi & Alexander Torgovitsky & Hanbin Yang, 2019. "Nonparametric Estimates of Demand in the California Health Insurance Exchange," NBER Working Papers 25827, National Bureau of Economic Research, Inc.
    20. Dunker, Fabian & Hoderlein, Stefan & Kaido, Hiroaki & Sherman, Robert, 2018. "Nonparametric identification of the distribution of random coefficients in binary response static games of complete information," Journal of Econometrics, Elsevier, vol. 206(1), pages 83-102.

    More about this item

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education
    • I28 - Health, Education, and Welfare - - Education - - - Government Policy
    • L0 - Industrial Organization - - General
    • O1 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development
    • O15 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Economic Development: Human Resources; Human Development; Income Distribution; Migration

    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:nbr:nberwo:15210. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: https://edirc.repec.org/data/nberrus.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.