Stochastic Economic Variables Having Equilibria as Simple Attractors

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This project makes an important contribution to the statistical theory concerning the analysis of economic time series data. Traditionally, models considered by time series analysts have concentrated on a few important economic variables and incorporated complicated lag structures of those variables. Structure of the economy was inferred from the data by examining the way the economy evolved and changed through time. This is in contrast to another form of economic modelling, which includes many variables in a sharply specified mathematical structure consisting of many equations. Both techniques have their advantages and disadvantages, and this project is part of an ongoing attempt to meld the two modelling strategies into a single coherent, and statistically consistent framework. Much empirical research in macroeconomics has shown that economic time series data typically include non-stationary processes such as trends. Different data series, for example national income data, GNP data, and price series, might include a common trend or tendency to grow over time. Thus these data are statistically linked with each other in the long run. To gain any meaningful insight into the actual movements of the variables in the economy, one must purge the data of the influence of non-stationary processes. In the past, achieving stationarity has been especially difficult if an analytical model included several data series each containing similar growth tendencies. Professor Granger has developed a statistical characterization of time series known as co-integration in which a linear combination of data series is itself stationary. This project makes a significant contribution to the existing literature in that it extends the idea of co-integration of time series to allow for nonlinear common trends, and offers an economic interpretation of data fluctuations as movements away from economic equilibrium. For example the price of an agricultural product such as tomatoes will vary from one section of the country to another, but will not vary a great deal, at least not in the long run. If the price of a product differs greatly from one location to another, market forces will act to eliminate the price disparities and reach an equilibrium. Professor Granger empirically identifies the equilibrium concept as a point to which the data in the series seem to gravitate. This point is known as an attractor, and the task of the econometrician is to isolate possible attractors in a group of data sets that the economic theory has suggested should be considered in the analysis and to confirm their importance. This work significantly increases the strength of the bond between economic theory and empirical analysis.