A Stochastic Analysis of an Input-Output Model

A Generalized Input-Output Multiplier Calculus for Australia

“…Based on early work by Sherman and Morrison (1950), Bullard and Sebald develop a technique for estimating uncertainties by identifying important parameters. Examining work by West (1986), ten Raa & Steel (1994) conclude that standard errors of multipliers in large input± output systems defy exact analytical treatment, and suggest stochastic analysis. Therefore, in this work, Monte Carlo simulations will be applied to estimate uncertainties of multipliers.…”

The elucidation of multipliers and their moments in fuzzy closed Leontief input–output systems

“…Following [4], a non-exhaustive criterion for this certainty is that the column sums of the upper boundary matrix (A U, , ) should each be less than or equal to one. This concern exists in the concomitant non-fuzzy analysis, including in stochastic modelling (see [17]). In [2], the inclusion of the parameter in A U, , confers the largest value allowed to be used, defined max , is given by (using = 0) max = min 1,…”

“…A further development demonstrated here is a definition of a number of moments associated with the fuzzy multipliers. These include mean and standard deviation values originally identified in non-fuzzy stochastic input-output systems (see [10,15,17]). Their evaluation is a consequence of the non-linearity of the Leontief inversion (see later).…”

Qualitative data and error measurement in input-output analysis

“…Their main purpose is to provide an indication of the confidence intervals of the deterministic estimates (cf. Lahiri and Satchell 1986;West 1986). …”