Semiparametric Identification and Estimation of Multinomial Discrete Choice Models using Error Symmetry

Assistant Professor, Chinese University of Hong Kong

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Individual heterogeneity is prevalent in economic studies of choice behavior. A single type of error structure may not represent all the individuals in the population and the preference or taste for each attribute of an alternative could vary across individuals. To capture heterogeneous choice behavior we provide an identification strategy for multinomial discrete choice models utilizing error symmetry. Our identification method allows for interpersonal heteroskedasticity on a subset of covariates. In the presence of random coefficients, our semiparametric method does not require numerical integration or the knowledge of the number of random coefficients, which are the two main challenges of implementing a random coefficient parametric method. Flexible correlation and heteroskedasticity among alternatives are also permitted. Based on the identification strategy, we propose an M-estimator by minimizing the squared difference of the volumes of two symmetric hyper-rectangles under the joint probability measure of the error terms. We show that the M-estimator is root-N-consistent and admits a normal limiting distribution. Monte Carlo experiments demonstrate finite-sample performance of the estimator under various data generating processes. We compare the estimates of the proposed method with those of a flexible conditional probit model and find prominent gaps between those estimates in the presence of interpersonal heteroskedasticity and heterogeneous preferences.