Semiparametric Estimation of Multivariate Latent Variable Models

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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.