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

小行星9729430 本计画利用纵向（面板）资料，发展离散选择与样本选择模型之估计方法。 所研究的模型被用于各种经济，医学和社会研究。 大量的研究都集中在发展方法来估计面板数据模型，特别是在短的固定长度的模型，这在很大程度上依赖于不可观察变量的统计分布的参数规格，无论是永久的个人以及随时间变化的特质冲击或干扰。 该项目解决了这种方法固有的局限性：由于对不可观察变量的分布及其与观察到的解释变量的统计关系的错误指定，对参数值的限制不能被经济理论证明是合理的，以及非常苛刻的计算要求，对感兴趣的参数和不正确的推断的有偏见和不一致的估计。 更具体地说，该项目构造了一类M估计，其中包括最小绝对偏差型（LAD）估计，并检查其渐近性质。 该项目研究如何这些估计，依赖于严格的外生解释变量的假设，可以修改，以允许动态反馈滞后的选择和结果变量对当前的选择和结果。 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和滞后的内生变量，以及不可观察的个人特定（“固定”）的影响，可以与其他解释变量以任意的方式。 目前还不知道如何估计这种类型的模型或估计是否可能。 该项目的贡献将是给条件下，这些模型可以估计，提出估计，并得出其渐近性质。 ??

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. ??