IDEAS home Printed from https://ideas.repec.org/p/uwo/uwowop/20224.html
   My bibliography  Save this paper

Identification and Estimation of Multinomial Choice Models with Latent Special Covariates

Author

Abstract

Identification of multinomial choice models is often established by using special covariates that have full support. This paper shows how these identification results can be extended to a large class of multinomial choice models when all covariates are bounded. I also provide a new √n-consistent asymptotically normal estimator of the finite-dimensional parameters of the model.

Suggested Citation

  • Nail Kashaev, 2022. "Identification and Estimation of Multinomial Choice Models with Latent Special Covariates," University of Western Ontario, Departmental Research Report Series 20224, University of Western Ontario, Department of Economics.
    • Handle: RePEc:uwo:uwowop:20224
    as

    Download full text from publisher

    File URL: https://ir.lib.uwo.ca/cgi/viewcontent.cgi?article=1846&context=economicsresrpt
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Hoderlein, Stefan & Holzmann, Hajo & Meister, Alexander, 2017. "The triangular model with random coefficients," Journal of Econometrics, Elsevier, vol. 201(1), pages 144-169.
    2. Gautier, Eric & Hoderlein, Stefan, 2011. "A triangular treatment effect model with random coefficients in the selection equation," TSE Working Papers 15-598, Toulouse School of Economics (TSE), revised 25 Aug 2015.
    3. Chen, Xiaohong & Liao, Zhipeng, 2014. "Sieve M inference on irregular parameters," Journal of Econometrics, Elsevier, vol. 182(1), pages 70-86.
    4. Jeremy T. Fox & Chenyu Yang & David H. Hsu, 2018. "Unobserved Heterogeneity in Matching Games," Journal of Political Economy, University of Chicago Press, vol. 126(4), pages 1339-1373.
    5. Steven T. Berry & Philip A. Haile, 2020. "Nonparametric Identification of Differentiated Products Demand Using Micro Data," NBER Working Papers 27704, National Bureau of Economic Research, Inc.
    6. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
    7. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
    8. 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.
    9. Steven T. Berry & Philip A. Haile, 2014. "Identification in Differentiated Products Markets Using Market Level Data," Econometrica, Econometric Society, vol. 82(5), pages 1749-1797, September.
    10. Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 655-679.
    11. Greg M. Allenby & Peter E. Rossi, 1991. "Quality Perceptions and Asymmetric Switching Between Brands," Marketing Science, INFORMS, vol. 10(3), pages 185-204.
    12. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    13. Nevo, Aviv, 2001. "Measuring Market Power in the Ready-to-Eat Cereal Industry," Econometrica, Econometric Society, vol. 69(2), pages 307-342, March.
    14. Magnac, Thierry & Maurin, Eric, 2007. "Identification and information in monotone binary models," Journal of Econometrics, Elsevier, vol. 139(1), pages 76-104, July.
    15. Steven Berry & James Levinsohn & Ariel Pakes, 2004. "Differentiated Products Demand Systems from a Combination of Micro and Macro Data: The New Car Market," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 68-105, February.
    16. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    17. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2017. "Nonparametric identification of random coefficients in endogenous and heterogeneous aggregate demand models," CeMMAP working papers 11/17, Institute for Fiscal Studies.
    18. 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.
    19. Patrick Bajari & Han Hong & Stephen P. Ryan, 2010. "Identification and Estimation of a Discrete Game of Complete Information," Econometrica, Econometric Society, vol. 78(5), pages 1529-1568, September.
    20. Ivan A. Canay & Andres Santos & Azeem M. Shaikh, 2013. "On the Testability of Identification in Some Nonparametric Models With Endogeneity," Econometrica, Econometric Society, vol. 81(6), pages 2535-2559, November.
    21. Rachel Griffith & Lars Nesheim & Martin O'Connell, 2018. "Income effects and the welfare consequences of tax in differentiated product oligopoly," Quantitative Economics, Econometric Society, vol. 9(1), pages 305-341, March.
    22. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November.
    23. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
    24. Heckman, James J, 1990. "Varieties of Selection Bias," American Economic Review, American Economic Association, vol. 80(2), pages 313-318, May.
    25. 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.
    26. Matthew Gentzkow, 2007. "Valuing New Goods in a Model with Complementarity: Online Newspapers," American Economic Review, American Economic Association, vol. 97(3), pages 713-744, June.
    27. Kleiber, Christian & Stoyanov, Jordan, 2013. "Multivariate distributions and the moment problem," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 7-18.
    28. Steven T. Berry, 1994. "Estimating Discrete-Choice Models of Product Differentiation," RAND Journal of Economics, The RAND Corporation, vol. 25(2), pages 242-262, Summer.
    29. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    30. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    31. Xiaohong Chen & Elie Tamer & Alexander Torgovitsky, 2011. "Sensitivity Analysis in Semiparametric Likelihood Models," Cowles Foundation Discussion Papers 1836, Cowles Foundation for Research in Economics, Yale University.
    32. Thompson, T.S., 1989. "Identification Of Semiparametric Discrete Choice Models," Papers 249, Minnesota - Center for Economic Research.
    33. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(1), pages 147-165.
    34. Andrews, Donald W.K., 2017. "Examples of L2-complete and boundedly-complete distributions," Journal of Econometrics, Elsevier, vol. 199(2), pages 213-220.
    35. Arthur Lewbel & Jin Yan & Yu Zhou, 2021. "Semiparametric Identification and Estimation of Multinomial Discrete Choice Models using Error Symmetry," Boston College Working Papers in Economics 1028, Boston College Department of Economics, revised 15 Dec 2021.
    36. Matzkin, Rosa L, 1992. "Nonparametric and Distribution-Free Estimation of the Binary Threshold Crossing and the Binary Choice Models," Econometrica, Econometric Society, vol. 60(2), pages 239-270, March.
    37. Steven T. Berry & Philip A. Haile, 2009. "Nonparametric Identification of Multinomial Choice Demand Models with Heterogeneous Consumers," Cowles Foundation Discussion Papers 1718, Cowles Foundation for Research in Economics, Yale University, revised Mar 2010.
    38. Dries F. Benoit & Stefan Van Aelst & Dirk Van den Poel, 2016. "Outlier‐Robust Bayesian Multinomial Choice Modeling," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(7), pages 1445-1466, November.
    39. Chen, Songnian & Khan, Shakeeb & Tang, Xun, 2016. "Informational content of special regressors in heteroskedastic binary response models," Journal of Econometrics, Elsevier, vol. 193(1), pages 162-182.
    40. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    41. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    42. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    43. Nail Kashaev & Bruno Salcedo, 2021. "Discerning Solution Concepts for Discrete Games," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(4), pages 1001-1014, October.
    44. Eric Gautier & Yuichi Kitamura, 2013. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Econometrica, Econometric Society, vol. 81(2), pages 581-607, March.
    45. Jeremy T. Fox & Natalia Lazzati, 2017. "A note on identification of discrete choice models for bundles and binary games," Quantitative Economics, Econometric Society, vol. 8(3), pages 1021-1036, November.
    46. Jeremy T. Fox & Amit Gandhi, 2016. "Nonparametric identification and estimation of random coefficients in multinomial choice models," RAND Journal of Economics, RAND Corporation, vol. 47(1), pages 118-139, February.
    47. Brendan Kline, 2016. "The empirical content of games with bounded regressors," Quantitative Economics, Econometric Society, vol. 7(1), pages 37-81, March.
    48. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    49. Chernozhukov, Victor & Imbens, Guido W. & Newey, Whitney K., 2007. "Instrumental variable estimation of nonseparable models," Journal of Econometrics, Elsevier, vol. 139(1), pages 4-14, July.
    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. Roy Allen & John Rehbeck, 2020. "Identification of Random Coefficient Latent Utility Models," Papers 2003.00276, arXiv.org.

    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. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2023. "Nonparametric identification of random coefficients in aggregate demand models for differentiated products," The Econometrics Journal, Royal Economic Society, vol. 26(2), pages 279-306.
    2. 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.
    3. 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.
    4. 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.
    5. Pietro Tebaldi & Alexander Torgovitsky & Hanbin Yang, 2023. "Nonparametric Estimates of Demand in the California Health Insurance Exchange," Econometrica, Econometric Society, vol. 91(1), pages 107-146, January.
    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. Wang, Ao, 2023. "Sieve BLP: A semi-nonparametric model of demand for differentiated products," Journal of Econometrics, Elsevier, vol. 235(2), pages 325-351.
    8. Matzkin, Rosa L., 2019. "Constructive identification in some nonseparable discrete choice models," Journal of Econometrics, Elsevier, vol. 211(1), pages 83-103.
    9. Roy Allen & John Rehbeck, 2020. "Identification of Random Coefficient Latent Utility Models," Papers 2003.00276, arXiv.org.
    10. 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.
    11. Wang, Ao, 2020. "Identifying the Distribution of Random Coefficients in BLP Demand Models Using One Single Variation in Product Characteristics," The Warwick Economics Research Paper Series (TWERPS) 1304, University of Warwick, Department of Economics.
    12. Wang, Ao, 2021. "A BLP Demand Model of Product-Level Market Shares with Complementarity," The Warwick Economics Research Paper Series (TWERPS) 1351, University of Warwick, Department of Economics.
    13. 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.
    14. Arthur Lewbel, 2012. "An Overview of the Special Regressor Method," Boston College Working Papers in Economics 810, Boston College Department of Economics.
    15. Xiaohong Chen & Andres Santos, 2018. "Overidentification in Regular Models," Econometrica, Econometric Society, vol. 86(5), pages 1771-1817, September.
    16. Yingying Dong & Arthur Lewbel, 2015. "A Simple Estimator for Binary Choice Models with Endogenous Regressors," Econometric Reviews, Taylor & Francis Journals, vol. 34(1-2), pages 82-105, February.
    17. Andrews, Donald W.K., 2017. "Examples of L2-complete and boundedly-complete distributions," Journal of Econometrics, Elsevier, vol. 199(2), pages 213-220.
    18. Escanciano, Juan Carlos, 2023. "Irregular identification of structural models with nonparametric unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 234(1), pages 106-127.
    19. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    20. Hidehiko Ichimura & Whitney K. Newey, 2022. "The influence function of semiparametric estimators," Quantitative Economics, Econometric Society, vol. 13(1), pages 29-61, January.

    More about this item

    Keywords

    Multinomial Choice; Random Coefficients; Special Covariate; Identification at Infinity; Bundles;
    All these keywords.

    JEL classification:

    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • C57 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Econometrics of Games and Auctions

    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:uwo:uwowop:20224. 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: the person in charge (email available below). General contact details of provider: https://economics.uwo.ca/research/research_papers/department_working_papers.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.