Estimate of Panel Data Models of Discrete Choice and Sample Selection and Application to Household Brand and Purchase Quantity Decisions

本项目开发了离散选择模型和使用纵向（面板）数据的样本选择模型的估计方法。所研究的模型用于各种经济、医学和社会研究。大量的研究集中在开发估计面板数据模型的方法上，特别是在短固定长度模型的情况下，这种模型严重依赖于不可观测变量的统计分布的参数说明，无论是永久的个体变量还是时变的特殊冲击或干扰。该项目解决了这种方法固有的局限性：对感兴趣的参数的有偏差和不一致的估计，以及由于对不可观测值的分布及其与观察到的解释变量的统计关系的错误说明而导致的不正确推断，对参数值的限制不能被经济理论证明，以及非常苛刻的计算要求。更具体地说，该项目构造了一类m估计量，其中包括最小绝对偏差型（LAD）估计量，并检验了它们的渐近性质。该项目研究了这些依赖于严格外生解释变量假设的估计器如何被修改，以允许滞后选择和结果变量对当前选择和结果的动态反馈。第二部分考虑了面板数据离散选择模型的估计，其中解释变量集包括严格的外生变量以及滞后的内生变量和不可观察的个体特定（“固定”）效应，这些效应可以以任意方式与其他解释变量相关。目前还不知道如何估计这种类型的模型，也不知道估计是否可能。该项目的贡献将是给出可以估计这些模型的条件，提出估计量并推导其渐近性质。?？

9729430 Kyriazidou This project develops estimation methods for models of discrete choice and sample selection using longitudinal (panel) data. The models studied are used in a variety of economic, medical and social studies. A large amount of research has focused on developing methods for estimating panel data models, especially in the case of short fixed-length models, that rely heavily on the parametric specification of the statistical distribution of unobservable variables, both of the permanent individual ones as well as the time-varying idiosyncratic shocks or disturbances. This project addresses the limitations inherent in this approach: biased and inconsistent estimation of the parameters of interest and incorrect inference due to mis-specifications of the distribution of unobservables and their statistical relationship with observed explanatory variables, restrictions on parameter values that can not be justified by economic theory, and very demanding computational requirements. More specifically, the project constructs a class of M-estimators, that includes Least-Absolute-Deviations-type (LAD) estimators, and examines their asymptotic properties. The project examines how these estimators, which rely on the assumption of strictly exogenous explanatory variables, can be modified to allow for dynamic feedback from the lagged choice and outcome variables on the current choice and outcome. The second part considers estimation of panel data discrete choice models where the explanatory variable set includes strictly exogenous as well as lagged endogenous variables and unobservable individual-specific ('fixed") effects that can be correlated with the other explanatory variables in an arbitrary way. It is currently not known how to estimate this type of models or whether estimation is even possible. The contribution of the project will be to give conditions under which such models can be estimated, propose estimators and derive their asymptotic properties. ??