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Semiparametric Discrete Choice Models for Bundles

Author

Listed:
  • Fu Ouyang

    () (School of Economics, University of Queensland)

  • Thomas Tao Yang

    () (Australian National University)

Abstract

We propose new identi cation and estimation approaches to semiparametric discrete choice models for bundles in both cross-sectional and panel data settings. The random utility functions of these models take the usual parametric form, while no distributional assumption is imposed on the stochastic disturbances. Our proposed methods permit certain forms of heteroskedasticity and arbitrary correlation in the disturbances across choices. Our identi cation approach is matching-based; it matches observed covariates across agents for the cross-sectional case, and over time for the panel data case. For the cross-sectional model, we propose a kernel-weighted rank procedure and establish N-asymptotic normality of the resulting estimators. We show the validity of the nonparametric bootstrap for the inference. For the panel data model, we propose localized maximum score type estimators which have a non-standard asymptotic distribution. We show that the numerical bootstrap developed by Hong and Li (2020) is a valid inference method for our panel data estimators. Monte Carlo experiments demonstrate that our proposed estimation and inference procedures perform adequately in nite samples.

Suggested Citation

  • Fu Ouyang & Thomas Tao Yang, 2020. "Semiparametric Discrete Choice Models for Bundles," Discussion Papers Series 625, School of Economics, University of Queensland, Australia.
  • Handle: RePEc:qld:uq2004:625
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    File URL: http://www.uq.edu.au/economics/abstract/625.pdf
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    References listed on IDEAS

    as
    1. Jeremy T. Fox, 2007. "Semiparametric estimation of multinomial discrete-choice models using a subset of choices," RAND Journal of Economics, RAND Corporation, vol. 38(4), pages 1002-1019, December.
    2. Jason Abrevaya & Jerry A. Hausman & Shakeeb Khan, 2010. "Testing for Causal Effects in a Generalized Regression Model With Endogenous Regressors," Econometrica, Econometric Society, vol. 78(6), pages 2043-2061, November.
    3. 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.
    4. 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.
    5. 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.
    6. Matthew Gentzkow & Jesse M. Shapiro & Michael Sinkinson, 2014. "Competition and Ideological Diversity: Historical Evidence from US Newspapers," American Economic Review, American Economic Association, vol. 104(10), pages 3073-3114, October.
    7. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2017. "Nonparametric Identification of Random Coefficients in Endogenous and Heterogeneous Aggregate Demand," Courant Research Centre: Poverty, Equity and Growth - Discussion Papers 224, Courant Research Centre PEG.
    8. 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.
    9. Shakeeb Khan & Fu Ouyang & Elie Tamer, 2019. "Inference on Semiparametric Multinomial Response Models," Boston College Working Papers in Economics 980, Boston College Department of Economics.
    10. Aviv Nevo & Daniel L. Rubinfeld & Mark McCabe, 2005. "Academic Journal Pricing and the Demand of Libraries," American Economic Review, American Economic Association, vol. 95(2), pages 447-452, May.
    11. Steve Berry & Ahmed Khwaja & Vineet Kumar & Andres Musalem & Kenneth Wilbur & Greg Allenby & Bharat Anand & Pradeep Chintagunta & W. Hanemann & Przemek Jeziorski & Angelo Mele, 2014. "Structural models of complementary choices," Marketing Letters, Springer, vol. 25(3), pages 245-256, September.
    12. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
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    More about this item

    Keywords

    Bundle choices; rank estimation; panel data; bootstrap.;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

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