Estimating Long Run Economic Equilibrium

本项目重点研究计量经济学分析中的三个重要课题，即1)长期经济均衡的估计，2)未完全确定的模型的动力学，以及3)计量经济学分配理论的统一。第一个主题涉及检查经济时间序列数据的属性，特别是时间序列数据集的联合依赖性和非平稳性。本项目旨在将协整模型、向量自回归技术和误差修正模型的计量经济学方法联系到一个统一的框架中。在此过程中，它推导出时间序列变量之间的相关性与经济均衡之间的重要关系。部分识别模型的工作集中在两个模型上，其中识别特别重要，即联立方程模型和时间序列中的伪回归。通过系统估计方法对联立方程组模型进行了详细的分析。该项目将为某些方程没有完全确定或方程的组成部分没有确定的估计系统提供一个完整的理论。该项目的第三部分应用运算代数，一个最近发展的矩阵演算，分布问题的计量经济学和统计学。这种方法避免了多变量分布理论分析所伴随的复杂多项式代数。特别是，它避免了对概率密度展开级数表示的需要，从而极大地方便了估计量的渐近性质和有限样本性质的推导。这个研究项目是分析许多组经济时间序列数据所显示的统计特性与经济均衡概念之间的关系。大多数经济理论的核心是这样一个概念，即系统倾向于走向一个稳定点，而不是随机波动。然而，从经验的角度来看，在实际数据中分离平衡点已被证明是非常困难的。对于时间序列数据尤其如此。当超过一个系列的数据进入一个模型时，例如收入数据和价格数据，对计量经济学分析的结果进行经济解释就会出现问题，因为这两组数据中的值随着时间的推移表现出相同的增长趋势。通过应用最新发展的统计技术，本研究分离了经济时间序列数据中的长期均衡。对这种平衡点的稳定性进行了试验。其他计量经济学问题，如由联立方程组成的模型的识别和估计量的渐近性质的推导也被解决。

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.