Collaborative Research on Applied Equilibrium with Increasing Returns: A Non Parametric Approach

应用一般均衡模型正在成为分析家庭、企业、政府政策和国际经济之间相互关系的主要方法。目前主要有两种方法在计算均衡值之前确定一般均衡模型。这些是计量规范和校准。这两种方法都有一定的缺点，特别是在经验应用中，测量中存在误差。本项目所做的工作将通过使用非参数方法来指定一般均衡模型来克服这些困难。该项目避免了与计量经济学和校准方法相关的困难，没有对误差的分布或精确值的形式做出假设。相反，我们推导出一组必要条件，用于检验一组给定的数据是否可以由市场参与者在通常的行为假设下产生。也就是说，企业利润最大化，消费者效用最大化。推导了效用函数存在性的检验，并应用于经验数据。这个项目是与耶鲁大学的Rosa Matzkin教授合作完成的。在过去的几十年里，人们发展了各种分析经济整体的方法。投入产出分析、线性规划和活动分析一直是经济中所有相互关系（企业、消费者和政府）建模和估计经济将达到平衡的价值的支柱。这些方法逐渐让位于一种更基本的方法，这种方法积极地纳入了作为市场个体参与者活动基础的行为假设。也就是说，假定消费者根据具有已知性质的数学函数的参数规范来实现效用最大化。同样，假定企业根据数学函数实现利润最大化。这种参数化方法的困难在于，必须对经验数据中出现的误差的值或分布做出非常强的假设。本项目通过推导一组必要条件来应用于一组观察到的经验数据，以测试这些数据是否可以由具有假设行为属性的模型生成，从而克服了这一困难。因此，这种非参数方法避免了对市场参与者行为进行参数规范的假设。这些非参数试验为进一步的参数分析提供了基本的理论依据。这个项目是与耶鲁大学的Rosa Matzkin教授合作完成的。

Applied general equilibrium models are becoming the primary method for analyzing the interrelations among households, firms, governmental policy, and the international economy. At present there exist two main methods of specifying general equilibrium models before equilibrium values are computed. These are econometric specification and calibration. Both methods have certain shortcomings, particularly in empirical application where there are errors in measurement. The work done in this project will overcome those difficulties by using a non-parametric approach in specifying the general equilibrium model. This project avoids the difficulties associated with the econometric and calibration methods by making no assumptions about the form, either distributional or exact value, of the errors. Rather, a set of necessary conditions is derived for testing whether a given set of data could have been generated by market participants acting under the usual behavioral assumptions. That is, the firms maximize profit, and the consumers maximize utility. Tests for the existence of utility functions are derived, and applied to the empirical data. This project is done in collaboration with Professor Rosa Matzkin of Yale University. %%% During the past several decades various methods for analyzing the economy in its entirety have been developed. Input-output analysis, linear programming, and activity analysis have been the mainstays for modeling all the interrelationships (firms, consumers, and government) in an economy, and estimating values at which the economy will reach equilibrium. These methods have increasingly given way to a more fundamental methodology which actively incorporates the behavioral assumptions underlying the activities of the individual market participants. That is, the consumers are assumed to maximize utility according to a parametric specification of a mathematical function with known properties. Likewise, firms are assumed to maximize profit according to a mathematical function. The difficulty with this parametric approach is that very strong assumptions must be made about the values or distribution of errors occuring in empirical data. This project overcomes that difficulty by deriving a set of necessary conditions to be applied to a set of observed empirical data to test whether those data could have been generated by a model with the assumed behavioral properties. Therefore, this non-parametric approach avoids the maintained hypothesis of parametric specification for the behavior of the market participants. These non-parametric tests provide a fundamental theoretical basis for further parametric analysis. This project is done in collaboration with Professor Rosa Matzkin of Yale University.