Macro Models Based on Aggregation of Micro Behavior Using Models of Changes in the Distribution of Individuals

大量的应用计量经济学分析使用聚合数据(来自人口普查、劳工统计局等)来测试和应用有关个人在经济中的行为的理论。例如，许多类型消费品的需求方程估计系统的研究基于描述个人优化行为的微观经济理论，但使用整个国家的消费者支出数据，从而隐含地将聚合数据视为由单个人生成。在类似的情况下，根据利润最大化原则从理论上推导出企业的产量。然而，对公司生产函数的估计通常是使用基于整个行业或国家的数据进行的。单个消费者或企业代表整个经济的假设是一个方便的假设，因为它允许使用现有的汇总数据应用和测试微观经济理论，并避免了聚合和集体选择的棘手问题。不幸的是，从经济学理论中没有理由假设，将数百万不同个体的经济活动相加后的国家总数据，将类似于单一公司或消费者的经济活动。因此，研究人员必须假设聚合数据的一些通用参数，以揭示潜在的优化行为。过去的理论工作表明，需要对聚集数据假定很少的结构来推断总需求或供给函数的存在，并且这些限制只需要对聚集数据的统计分布施加。因此，人们可以有效地限制消费者支出的分配，使其在一段时间内保持不变，或以一般指定的方式改变。这样的分布假设也可以应用于生产。路贝尔教授通过考虑总支出在人口中的分布随时间变化的限制，并将其与特定的个人需求行为相结合，得出了经济的总需求方程。这些总需求方程满足个体需求方程所基于的效用最大化的所有条件。从技术上讲，他构建了宏观经济数据的非线性模型，其基础既有异质微观经济行为的显式模型，也有经济中个体代理人分布随时间演变的显式模型。这允许构建与聚集理论兼容的分布随时间变化的模型。卢贝尔教授通过使用横截面或面板数据进行估计，并通过研究几个时间段的分布数据来检验聚合模型的理论有效性。这些方法适用于各种国家数据集，如国民收入和产品账户、消费者支出调查和美国当前人口报告。

A great deal of applied econometric analysis uses aggregated data (from Census, the Bureau of Labor Statistics and so on) to test and apply theories about the behavior of individuals in the economy. For instance, studies estimating systems of demand equations for many types of consumer goods are based on the microeconomic theory describing individual optimizing behavior, but use consumer expenditure data of the entire country, thereby implicitly treating the aggregated data as if they were generated by a single person. In a similar circumstance the output of a firm is theoretically derived based on the principle of profit maximization. Estimation of production functions of firms, however, is often done using data based on an entire industry or country. The assumption of a single consumer or firm being a representative of the entire economy is a convenient one, in that it allows application and testing of microeconomic theories with available aggregate data, and it avoids intractable problems of aggregation and collective choice. Unfortunately, there is no reason deriving from economic theory to assume that national aggregate data, which is the result of adding the economic activities of millions of diverse individuals, will resemble the economic activity of a single firm or consumer. The researcher must thus assume some general parameters for the aggregated data in order to uncover the underlying optimizing behavior. Past theoretical work has shown that very little structure need be assumed on the aggregated data to infer the existence of aggregate demand or supply functions, and that those restrictions need be placed only on the statistical distribution of the aggregate data. Thus one can validly restrict the distribution of consumer expenditures to remain unchanged through time or to change in general specified ways. Such distributional assumptions can also be applied to production. Professor Lewbel derives aggregate demand equations for the economy by considering the restrictions on the changes over time in the distribution of total expenditures in the population, and combining them with specific individual demand behavior. These aggregate demand equations satisfy all the conditions of utility maximization on which individual demand equations are based. Technically, he constructs nonlinear models of macroeconomic data based on explicit models of both heterogeneous microeconomic behavior and of the evolution over time of the distribution of individual agents in the economy. This allows for the construction of models of shifts in the distributions through time that are compatible with aggregation theory. Professor Lewbel tests the theoretical validity of aggregate models by estimation using cross sectional or panel data, and by studying the distribution data in several time periods. These methods are applied to various national data sets like the National Income and Product Accounts, the Consumer Expenditure Survey, and the U. S. Current Population Reports.