Identification of Semiparametric Discrete Choice Models

Abstract

The question of model identification is analyzed for the
\nsemiparametric random utility model of discrete choice. Attention is focused
\non settings where agents face a common choice between a set of J+l
\nalternatives, but where actual choices are only partially observed.
\nNecessary conditions are derived for the setting where the only data on
\nactual choices consists of a binary indicator for one of the alternatives.
\nSufficient conditions are developed in this setting for a linear in
\nparameters specification of indirect utility. It is found that relative to
\nthe parametric case, only a mild continuity restriction on the distribution
\nof regressors is needed in the semiparametric model. Under these
\ncircumstances all of the choice probabilities are identified, even though
\nactual choices are only partially observed. It is shown that estimators that
\nrely only on the index structure of the model require substantially stronger
\nprior restrictions on the parameters for identification when the number of
\nalternatives is large. Finally, results on the model with partial
\nobservability of choices are used to analyze the special case of full
\nobservability.