Statistical data are often measured with errors. Many of the theoretical constructions of economic, psychological, and sociological models also depend on conceptual variables that are unobservable (e.g., permanent income, rational expectation). To obtain meaningful statistical inference for models containing unobservable variables requires either the expansion of existing data bases with more precise measurements of variables of interest, or the development of analytical frameworks to extract relevant information from currently available data sources. Through the support of previous NSF grants, it has been demonstrated that a structural approach, while often imposing hypothetical assumptions, can yield useful information if properly conducted, and hence not only provides a means to take advantage of information that otherwise might be misused or totally ignored, but is also more economical. This award further investigates the identification, estimation, and statistical inference of (i) nonstationary time series or nonlinear models when variables are subject to random measurement errors; (ii) systematic measurement errors in sample surveys; (iii) the implicit market of attributes which forms the basis of new measurement of inflation rate and other complicated market analysis and; (iv) unobserved heterogeneity in panel data analysis. Classical parametric and nonparametric methods and Bayesian inference via Monte Carlo (Gibbs Sampling) methods will be explored. It is hoped that a successful completion of the project will provide additional repertoire of tools to enhance the reliability and validity of the research usefulness of federal or private statistical data.
