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An instrumental variable model of multiple discrete choice

Chesher, AD; Rosen, A; Smolinski, K; (2013) An instrumental variable model of multiple discrete choice. Quantitative Economics , 4 (2) pp. 157-196. 10.1920/wp.cem.2011.3911. Green open access

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Abstract

This paper studies identification of latent utility functions in multiple discrete choice models in which there may be endogenous explanatory variables, that is explanatory variables that are not restricted to be distributed independently of the unobserved determinants of latent utilities. The model does not employ large support, special regressor or control function restrictions, indeed it is silent about the process delivering values of endogenous explanatory variables and in this respect it is incomplete. Instead the model employs instrumental variable restrictions requiring the existence of instrumental variables which are excluded from latent utilities and distributed independently of the unobserved components of utilities. We show that the model delivers set identification of the latent utility functions and we characterize sharp bounds on those functions. We develop easy-to-compute outer regions which in parametric models require little more calculation than what is involved in a conventional maximum likelihood analysis. The results are illustrated using a model which is essentially the parametric conditional logit model of McFadden (1974) but with potentially endogenous explanatory variables and instrumental variable restrictions. The method employed has wide applicability and for the first time brings instrumental variable methods to bear on structural models in which there are multiple unobservables in a structural equation.

Type: Article
Title: An instrumental variable model of multiple discrete choice
Open access status: An open access version is available from UCL Discovery
DOI: 10.1920/wp.cem.2011.3911
Publisher version: http://dx.doi.org/10.1920/wp.cem.2011.3911
Language: English
Additional information: © 2013 Andrew Chesher, Adam M. Rosen, and Konrad Smolinski. Licensed under the Creative Commons Attribution-NonCommercial License 3.0. Available at http://www.qeconomics.org. DOI: 10.3982/QE240 doi refers to the CeMMAP working paper version of this paper.
Keywords: Partial identification, Random sets, Multiple discrete choice, Endogeneity, Instrumental variables, Incomplete models
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS > Dept of Economics
URI: https://discovery.ucl.ac.uk/id/eprint/1362037
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