Approximate Generalizations and Computational Experiments

Felix Kubler

A chapter in Computational Aspects of General Equilibrium Theory, 2008, pp 109-133 from Springer

Abstract: Abstract In this paper I demonstrate how one can generalize finitely many examples to statements about (infinite) classes of economic models. If there exist upper bounds on the number of connected components of one-dimensional linear subsets of the set of parameters for which a conjecture is true, one can conclude that it is correct for all parameter values in the class considered, except for a small residual set, once one has verified the conjecture for a predetermined finite set of points. I show how to apply this insight to computational experiments and spell out assumptions on the economic fundamentals that ensure that the necessary bounds on the number of connected components exist. I argue that these methods can be fruitfully utilized in applied general equilibrium analysis. I provide general assumptions on preferences and production sets that ensure that economic conjectures define sets with a bounded number of connected components. Using the theoretical results, I give an example of how one can explore qualitative and quantitative implications of general equilibrium models using computational experiments. Finally, I show how random algorithms can be used for generalizing examples in high-dimensional problems.

Keywords: Computational economics; General equilibrium; o-minimal structures (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/978-3-540-76591-2_9

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