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A discrete choice model for partially ordered alternatives

Publication ,  Journal Article
Aristodemou, E; Rosen, AM
Published in: Quantitative Economics
July 1, 2022

In this paper, we analyze a discrete choice model for partially ordered alternatives. The alternatives are differentiated along two dimensions: the first an unordered “horizontal” dimension, and the second an ordered “vertical” dimension. The model can be used in circumstances in which individuals choose among products of different brands, wherein each brand offers an ordered choice menu, for example, by offering products of varying quality. The unordered–ordered nature of the discrete choice problem is used to characterize the identified set of model parameters. Following an initial nonparametric analysis that relies on shape restrictions inherent in the ordered dimension of the problem, we then provide a specialized analysis for parametric specifications that generalize common ordered choice models. We characterize conditional choice probabilities as a function of model primitives with particular analysis focusing on cases in which unobservable taste for quality of each brand offering is multivariate normally distributed. We provide explicit formulae used for estimation and inference via maximum likelihood, and we consider inference based on Wald and quasi-likelihood ratio statistics, the latter of which can be robust to a possible lack of point identification. An empirical illustration is conducted using data on razor blade purchases in which each brand has product offerings vertically differentiated by quality.

Duke Scholars

Published In

Quantitative Economics

DOI

EISSN

1759-7331

ISSN

1759-7323

Publication Date

July 1, 2022

Volume

13

Issue

3

Start / End Page

863 / 906

Related Subject Headings

  • 3802 Econometrics
  • 3801 Applied economics
  • 1403 Econometrics
 

Citation

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Aristodemou, E., & Rosen, A. M. (2022). A discrete choice model for partially ordered alternatives. Quantitative Economics, 13(3), 863–906. https://doi.org/10.3982/QE1497
Aristodemou, E., and A. M. Rosen. “A discrete choice model for partially ordered alternatives.” Quantitative Economics 13, no. 3 (July 1, 2022): 863–906. https://doi.org/10.3982/QE1497.
Aristodemou E, Rosen AM. A discrete choice model for partially ordered alternatives. Quantitative Economics. 2022 Jul 1;13(3):863–906.
Aristodemou, E., and A. M. Rosen. “A discrete choice model for partially ordered alternatives.” Quantitative Economics, vol. 13, no. 3, July 2022, pp. 863–906. Scopus, doi:10.3982/QE1497.
Aristodemou E, Rosen AM. A discrete choice model for partially ordered alternatives. Quantitative Economics. 2022 Jul 1;13(3):863–906.
Journal cover image

Published In

Quantitative Economics

DOI

EISSN

1759-7331

ISSN

1759-7323

Publication Date

July 1, 2022

Volume

13

Issue

3

Start / End Page

863 / 906

Related Subject Headings

  • 3802 Econometrics
  • 3801 Applied economics
  • 1403 Econometrics