A discrete choice model for partially ordered alternatives

Eleni Aristodemou ()
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Eleni Aristodemou: Institute for Fiscal Studies and University College London

No CWP35/21, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: In this paper we analyze a discrete choice model for partially ordered alternatives. The alternatives are differentiated along two dimensions, the ?rst an unordered “horizontal” dimension, and the second an ordered “vertical” dimension. The model can be used in circumstances in which individuals choose amongst 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 identi?ed 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 speci?cations 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 identi?cation. An empirical illustration is conducted using consumer purchase data in the UK to study consumers’ choice of razor blades in which each brand has product o?erings vertically di?erentiated by quality.

Date: 2021-08-05
New Economics Papers: this item is included in nep-dcm
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