Approximate Generalizations and Applied Equilibrium Analysis
22 Pages Posted: 9 May 2005
Date Written: 4/30/2005
Abstract
In this paper I derive conditions on the fundamentals of general equilibrium models that allow for a generalization of finitely many examples to statements about (infinite) classes of economies and I show how these approximate generalizations can be applied in computational experiments.
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 it for a predetermined finite set of points. I spell out assumptions on economic fundamentals which ensure that these bounds on the number of connected components exist, and that the residual set can be bounded from above.
I argue that utility- and production functions used in applied equilibrium analysis satisfy these conditions. Using the theoretical results, I show how computational experiments can be used to explore qualitative and quantitative implications of economic models. I give examples for actual upper bounds in realistically calibrated economies and discuss both deterministic and random algorithms for generalizing examples in these economies.
Keywords: o-minimal economies, computational general equilibrium
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