Some Issue on Modelling Unobservable Variables

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Models based on variables which are inherently unobservable are found very often in economics, psychology, and other social sciences. They might arise from errors in the data being analyzed, or because the behavioral responses of agents are in part determined by characteristics which cannot be observed or measured. Obtaining meaningful insight from models in which unobservable variables play a role requires either expanding the data set with more precise measurement or developing an analytical framework to extract the relevant information on the unobserved variables from the existing data. The former is often too costly or even impossible, particularly when large Federal statistical data sets are being studied. The project examines two analytical models widely used in econometric studies using Federal data, namely the errors-in-variables model and the hedonic model. The errors-in-variables model is studied from the standpoint of various assumptions regarding the structure of the errors, and model identification, and statistical inference. Using the hedonic model this project establishes correspondences between the underlying characteristics and the observed variables. It also derives conditions regarding identification, estimation, and interpretation of the coefficients. %%% Models based on variables which are inherently unobservable are found very often in economics, psychology, and other social sciences. They might arise from errors in the data being analyzed, or because the behavioral responses of agents are in part determined by characteristics which cannot be observed or measured. Large Federal data sets, such as those collected by the Bureau of the Census or the Bureau of Labor Statistics, often contain grouped data. For reasons of confidentiality or ease of collection, a household might be asked to list its income range, for instance between $15,000 and $25,000, rather than its exact income. If an econometric analysis uses these data on the assumption that they are precise measurements, the results can be misleading or erroneous. Obtaining meaningful insight from models in which unobservable variables play a role requires either expanding the data set with more precise measurement or developing an analytical framework to extract the relevant information on the unobserved variables from the existing data. The former approach is more desirable, but often too costly, particularly when a researcher is using large Federal statistical data sets. This project focuses on the latter, more analytical strategy. It develops an econometric framework to enhance the reliablity and usefulness of research based on Federal data where latent variable models are appropriate.