This project focuses on three important topics in econometric analysis, namely 1) the estimation of long run economic equilibrium, 2) the dynamics of models which are not fully identified, and 3) the unification of econometric distribution theory. The first topic involves examining the properties of economic time series data, in particular joint dependency of time series data sets, and nonstationarity. This project serves to link the econometric methodologies of cointegration models, vector-autoregression techniques, and error correction models into a unified framework. In doing so it derives an important relationship between correlation among time series variables and economic equilibrium. The work on partially identified models concentrates on two models in which identification is particularly important, namely simultaneous equations models, and spurious regressions in time series. Simultaneous equations models are analyzed in detail via systems methods of estimation. The project will produce a complete theory for estimation systems in which some equations are not fully identified or in which components of equations are not identified. The third part of the project applies operational algebra, a recently developed matrix calculus, to distributional problems in econometrics and statistics. This approach avoids much of the complex polynomial algebra that accompanies analysis of multivariate distribution theory. In particular, it obviates the need for expansion series representation of probability densities, and in turn greatly facilitates the derivation of both asymptotic properties and finite sample properties of estimators. %%% This research project is an analysis of the relationship between the statistical properties exhibited by many sets of economic time series data and the concept of econommic equilibrium. At the heart of most economic theory is the notion that systems tend to move toward a point of stability, rather than fluctuating randomly. From an empirical standpoint, however, the isolation of equilibrium points in actual data has proven to be very difficult. This is particularly true for time series data. When more than one series of data enter a model, for instance income data and price data, deriving an economic interpretation to the results of econometric analysis becomes problematic, since the values in both set of data exhibit the same tendency to grow over time. By applying recently developed statistical techniques this research isolates long run equilibrium in economic time series data. Tests are developed for the stability of such equilibruim points. Other econometric issues such as the identification of models consisting of simultaneous equations and the derivation of asymptotic properties of estimators are also addressed.
