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Partial Identification of Heterogeneity in Preference Orderings Over Discrete Choices

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  • Itai Sher
  • Jeremy T. Fox
  • Kyoo il Kim
  • Patrick Bajari

Abstract

We study a variant of a random utility model that takes a probability distribution over preference relations as its primitive. We do not model products using a space of observed characteristics. The distribution of preferences is only partially identified using cross-sectional data on varying budget sets. Imposing monotonicity in product characteristics does not restore full identification. Using a linear programming approach to partial identification, we show how to obtain bounds on probabilities of any ordering relation. We also do constructively point identify the proportion of consumers who prefer one budget set over one or two others. This result is useful for welfare. Panel data and special regressors are two ways to gain full point identification.

Suggested Citation

  • Itai Sher & Jeremy T. Fox & Kyoo il Kim & Patrick Bajari, 2011. "Partial Identification of Heterogeneity in Preference Orderings Over Discrete Choices," NBER Working Papers 17346, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:17346 Note: IO TWP
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    References listed on IDEAS

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    1. Goettler, R., 1999. "Advertising Rates, Audience Composition, and Competition in the Network Television Industry," GSIA Working Papers 1999-28, Carnegie Mellon University, Tepper School of Business.
    2. 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.
    3. Barbera, Salvador & Pattanaik, Prasanta K, 1986. "Falmagne and the Rationalizability of Stochastic Choices in Terms of Random Orderings," Econometrica, Econometric Society, vol. 54(3), pages 707-715, May.
    4. Matzkin, Rosa L., 1993. "Nonparametric identification and estimation of polychotomous choice models," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 137-168, July.
    5. 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.
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    Cited by:

    1. Sam Cosaert & Thomas Demuynck, "undated". "Nonparametric welfare and demand analysis with unobserved individual heterogeneity," ULB Institutional Repository 2013/251988, ULB -- Universite Libre de Bruxelles.
    2. Yuichi Kitamura & Jorg Stoye, 2013. "Nonparametric Analysis of Random Utility Models: Testing," Cowles Foundation Discussion Papers 1902, Cowles Foundation for Research in Economics, Yale University.

    More about this item

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • L0 - Industrial Organization - - General

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