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

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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.