A Stochastic Analysis of an Input-Output Model

Abstract

accuracy or precision of the results. Input-output analysis is no different. The results of input-output studies are almost always expressed as point estimates, and an assessment of the reliability of these estimates is left the reader. The stochastic analysis of errors is difficult undertake because of the lack of hard data of a probabilistic nature validate or refute empirically any conclusions drawn from such a study. This fact, combined with the complex interrelationships involved, has resulted in few applied input-output studies within a stochastic framework. Early contributors in this research area were Evans and Quandt. Evans [5] developed a formula for the coefficient of variation of the estimated output vector, under the assumption that all elements of the A matrix are fixed except for one row where the coefficient of variation is constant. Quandt [ 16] derived approximations of the variances and covariances of the elements in the Leontief inverse, and thus approximations of the variances of the estimated sector outputs. Using simulation techniques on a 3 x 3 hypothetical matrix, he proposed that the lognormal distribution can be used to establish approximate confidence limits for the

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