Econometrica: Jul, 1975, Volume 43, Issue 4

Error Analysis in Nearly-Completely Decomposable Stochastic Systems

https://doi.org/0012-9682(197507)43:4<691:EAINDS>2.0.CO;2-I
p. 691-709

P. J. Courtois

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 @e^2 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.