Approximate generalizations and computational experiments

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. DOI: https://doi.org/10.1111/j.1468-0262.2007.00779.x Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-95953 Published Version Originally published at: Kübler, Felix (2007). Approximate generalizations and computational experiments. Econometrica, 75(4):967-992. DOI: https://doi.org/10.1111/j.1468-0262.2007.00779.x Econometrica, Vol. 75, No. 4 (July, 2007), 967–992 APPROXIMATE GENERALIZATIONS AND COMPUTATIONAL EXPERIMENTS