Essays on Multinomial Choice Models

Abstract

My dissertation contains three chapters which develop new identification and estimation methods for multinomial choice models in both cross-sectional and paneldata settings. In the first chapter, I propose a new semiparametric identification andestimation approach to multinomial choice models using cross-sectional data. The approach relies on the rank-order property proposed by Manski (1975) and employedby recent studies such as Fox (2007) and Yan (2013), which is a distribution-free restrictionon the random utility framework underlying a multinomial choice model.From the rank-order property, a novel reparameterization provides a multivariatenonlinear least squares (population) criterion identifying the structural parameters.This identification result then motivates a sieve-based estimation procedure, whichis the first in the semiparametric literature to allow joint estimation of regressioncoefficients and reduced-form parameters such as choice probabilities and marginaleffects. Asymptotic properties of two functional estimators are developed. A MonteCarlo study indicates that these functional estimators perform well in finite samples.I illustrate the implementation of the estimation procedure via estimating a modelof college major choice using UCOP data of 1998-2003. As extensions, I also proposeestimators for the model using a choice-based sample and the model with rankinginformation.The estimation problem in the second chapter is motivated by the local nonlinearleast squares (LNLS) estimation of preference parameters (regression coefficients) in the multinomial choice model under uncertainty in which the decision rule is affectedby conditional expectations. I propose a two-stage LNLS estimation procedure forthe preference parameters. In the first stage, conditional expectations are estimatednonparametrically. Then, in the second stage, the preference parameters are estimatedby the LNLS estimator of multinomial choice model, using the choice dataand first-stage estimates. The two-stage estimator has the advantage of being easilyimplementable using standard software packages. In this chapter, I establish consistencyof the two-stage LNLS estimator. Monte Carlo simulation results illustratethat the proposed two-stage LNLS estimator performs well in finite sample.The third chapter is a part of a co-authored project with Shakeeb Khan and ElieTamer. In this work, we consider identification, estimation, and inference on regressioncoefficients in semiparametric multinomial response models. Our identification result is constructive and estimation is based on a localized rank objective function,loosely analogous to that used in Abrevaya et al. (2010). We show this achieves sharpidentification which is in contrast to existing procedures in the literature such as, forexample, Ahn et al. (2015). In that sense, our procedure is adaptive (Khan andTamer (2009)) in the sense that it provides an estimator of the sharp set when point identification does not hold, and a consistent point estimator when it does. Furthermore,our rank procedure extends to panel data settings for inference in modelswith fixed effects, including dynamic panel models with lagged dependent variablesas covariates. A simulation study establishes adequate nite sample properties ofour new procedures.