Semiparametric Estimation of Multivariate Latent Variable Models

本研究的主要目的是研究一种创新技术，用于估计一类广泛应用于经济学和其他社会科学的统计模型。一般的模型，其中的工作线是一个因变量是不连续的。这样的模型包括那些数据筛选或聚合导致因变量是一个潜在的但未观察到的连续变量的离散分组或排序的模型。另一个这样的模型是所谓的离散选择模型，它被用来分析许多经济决策，如住房使用权的选择、交通方式和耐用消费品的购买。在这些模型中，观察到的数据通常只是关于是否做出了特定选择的观察。所有这些类型的模型基本上都是基于这样一个想法，即一个潜在的连续变量，通常被称为潜在变量，它是人们做出特定决定的关键因素，但这个变量本身并没有被观察到。所观察到的是一个指数或指标，它仅仅显示了经济主体所做的选择。在进行这种分析时，人们必须对潜在变量，特别是其分布形式做出假设，而过去的工作表明，研究结果很大程度上依赖于分布假设。鲍威尔教授是计量经济学研究领域的领军人物，他的研究开发了对分布假设稳健的估计技术。从技术上讲，鲍威尔教授在这个项目中推导了半参数估计来分析潜在变量模型。这个过程包括两个步骤。首先，根据模型外部的一组变量推导出一个指数。然后，对于数据中的每个观测值，隐变量的条件分布以该指标为中心。第二步使用新创建的索引数据集来估计研究人员感兴趣的参数。

The primary object of this research is the investigation of an innovative technique for estimating a class of statistical models widely used in economics and other social sciences. The general model with which the line of work is concerned is one where the dependent variable is not continuous. Such models include those in which data censoring or aggregation results in the dependent variable being a discrete grouping or ordering of an underlying but unobserved continuous variable. Another such model is the so-called discrete choice model, which is used to analyze many economic decisions, such as housing tenure choice, mode of transportation, and the purchase of consumer durables. In these models the observed data usually consists simply of an observation as to whether a particular choice was made or not. All these types of models are fundamentally based on the idea that an underlying continuous variable, often called a latent variable, is really the crucial factor in the person's making a particular decision, but that variable is not itself observed. What is observed is an index or indicator which merely shows the choice made by the economic agent. In doing such analysis one must make assumptions about the underlying variable, and in particular about its distributional form, and past work has shown research results to be quite dependent on the distributional assumptions. Professor Powell is a leader in a line of econometric research which develops estimation techniques robust to distributional assumptions. Technically, Professor Powell in this project derives semiparametric estimators for analyzing latent variable models. The procedure consists of two steps. First, an index is derived based on a group of variables exogenous to the model. Then for each observation in the data the conditional distribution of the latent variable is centered on this index. The second step uses the newly created data set of indices to estimate the parameters in which the researcher is interested.