Stochastic Economic Variables Having Equilibria as Simple Attractors

该项目对经济时间序列数据分析的统计理论做出了重要贡献。传统上，时间序列分析师考虑的模型集中在几个重要的经济变量上，并包含了这些变量的复杂滞后结构。通过考察经济随时间演变和变化的方式，从数据中推断出经济结构。这与另一种形式的经济建模形成对比，后者包括由许多方程组成的严格指定的数学结构中的许多变量。这两种技术各有优缺点，该项目是将这两种建模策略合并为一个连贯的、统计上一致的框架的持续尝试的一部分。许多宏观经济学的实证研究表明，经济时间序列数据通常包括非平稳过程，如趋势。不同的数据系列，例如国民收入数据、国民生产总值数据和物价系列，可能包括一个共同的趋势或随着时间的推移而增长的趋势。因此，从长远来看，这些数据在统计上是相互关联的。要对经济中变量的实际变动有任何有意义的洞察，就必须清除非平稳过程对数据的影响。在过去，如果一个分析模型包括几个数据系列，每个数据系列都包含类似的增长趋势，那么实现平稳性就特别困难。格兰杰教授开发了一种称为协整的时间序列的统计特征，其中数据序列的线性组合本身是平稳的。这个项目对现有文献做出了重大贡献，因为它扩展了时间序列的协整概念，以允许非线性共同趋势，并提供了数据波动的经济学解释，即远离经济均衡的运动。例如，番茄等农产品的价格会因国家不同地区而有所不同，但不会有太大差异，至少从长远来看不会有太大差异。如果一种产品的价格从一个地区到另一个地区差异很大，市场力量就会采取行动消除价格差异，达到均衡。格兰杰教授经验性地将均衡概念定义为序列中的数据似乎被吸引到的点。这一点被称为吸引子，计量经济学家的任务是从一组数据集中分离出可能的吸引子，经济学理论建议在分析中应考虑这些吸引子，并确认它们的重要性。这项工作大大加强了经济理论和实证分析之间的纽带。

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.