Inference on semiparametric multinomial response models

We explore inference on regression coefficients in semiparametric multinomial response models. We consider cross-sectional, and both static and dynamic panel settings where we focus throughout on inference under sufficient conditions for point identification. The approach to identification uses a ma...

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Bibliographic Details
Published in:Quantitative economics 2021-07, Vol.12 (3), p.743-777
Main Authors: Khan, Shakeeb, Ouyang, Fu, Tamer, Elie T
Format: Article
Language:English
Subjects:
Alternatives
C14
C23
C35
Convergence
Data models
dynamic panel data
Econometrics
Identification
Inference
Insight
Longitudinal studies
Multinomial response
Panel data
Preferences
Probability
Random variables
rank estimation
Simulation
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Summary:We explore inference on regression coefficients in semiparametric multinomial response models. We consider cross-sectional, and both static and dynamic panel settings where we focus throughout on inference under sufficient conditions for point identification. The approach to identification uses a matching insight throughout all three models coupled with variation in regressors: with cross-section data, we match across individuals while with panel data, we match within individuals over time. Across models, we relax the Indpendence of Irrelevant Alternatives (or IIA assumption, see McFadden (1974)) and allow for arbitrary correlation in the unobservables that determine utility of various alternatives. For the cross-sectional model, estimation is based on a localized rank objective function, analogous to that used in Abrevaya, Hausman, and Khan (2010), and presents a generalization of existing approaches. In panel data settings, rates of convergence are shown to exhibit a curse of dimensionality in the number of alternatives. The results for the dynamic panel data model generalize the work of Honoré and Kyriazidou (2000) to cover the semiparametric multinomial case. A simulation study establishes adequate finite sample properties of our new procedures. We apply our estimators to a scanner panel data set.
ISSN:1759-7331
1759-7323
1759-7331
DOI:10.3982/QE1315