Knowledge that Transforms

The purpose of this paper is to analyze the accuracy of the Simon-Ando approximation for stochastic nearly-completely decomposable systems. Relations are established defining this accuracy as a function of the maximum degree of coupling (e) between aggregates, the conditioning and the indecomposability of these aggregates. A procedure is derived by which estimates in c2 may be computed from aggregate eigencharacteristics. Finally, the Simon-Ando approximation is shown to be optimal in block-stochastic matrices, and the accuracy achievable by higher-order aggregation is examined.

Direct or indirect additivity of production or utility functions implies dependence of substitution effects on income effects. This dependence is eliminated by implicit additivity, or strong separability along isoquants or indifference surfaces. The present study proposes and analyzes two models, with direct and indirect implicit additivity, respectively, which are generally non-homothetic, non-CES, and include less than 3n parameters for n goods. They give rise to log-linear systems of estimable demand relations. Many other models, such as Cobb-Douglas, CES, Direct and Indirect Addilog, CRESH, CDE, and Non-homothetic CES, are simple, testable special cases of either or both of these models.

It is shown that in markets with a continuum of traders, the allocations associated with the Shapley value are the same as the competitive allocations.