Regional input-output analysis is strongly emerging as a useful tool in, and a vital part of, government planning. It now fulfills a role as both an assessable disaggregated form of regional accounts, and an economic impact measuring device for governments and industry. However, although published tables tend, by default, to assume an aura of authenticity, they are, like all empirical economic analysis, inevitably accompanied by limitations on the precision of the results.
The aim of this study is to investigate the analytical and probabilistic relationship between input-output coefficient "errors" or "changes" and the resultant multiplier values. It is not intended to be an exhaustive analysis of errors in input-output models. Rather it considers one aspect of additive coefficient errors in the static model; variations such as price changes, non-linear production functions, etc., are not considered. Furthermore, the intention is not simply to provide a set of formulae, but to provide a procedure and framework for coefficient-multiplier error analysis in input-output models.
A review of the literature in input-output economics reveals that sources of errors in regional models are wide and varied. This study discusses some of the possible sources of error, and considers various concepts of accuracy and some proposals regarding accuracy assessment. It is argued that cell-by-cell accuracy is an inappropriate criterion for regional input-output, and that the accuracy of a regional model should be assessed by its ability to predict the output projections of individual sectors within the economy. The emphasis in this study is therefore not on the accuracy of the table per se, but on the factors which influence the stability of the model in an operational sense.
A general (simplified) theoretical relationship between multiple input coefficient change and multiplier values is derived, which, to the author's knowledge, has not been achieved previously. A number of special cases of this general model are also considered because of their special characteristics, including the case where only one coefficient is allowed to change, and where coefficients in one sector only are allowed to vary. A number of empirical applications of the model are suggested and demonstrated, including (a) a static mathematical optimization model which determines which input coefficients in a prototype table should be updated, such that total cost (as a function of estimation cost and error) is minimized, and (b) a model for the identification of key sectors and linkages in a sensitivity analysis framework of an existing economy. The improvement in accuracy and reduction in operational cost results in this sensitivity model being far superior to the traditional simulation approach.
The general model derived above is further extended to incorporate probabilistic properties of the input coefficients. Under the assumption of normally distributed input coefficients, the theoretical multiplier probability distributions are derived together with their moments (mean and variance). This allows, for the first time, the computation of "exact" confidence intervals for the multipliers instead of highly imprecise interval estimates calculated using Chebyshev's inequality. Sensitivity analysis of the results indicate that the theoretical multiplier distributions are relatively insensitve to input misspecification, and that the procedure is superior to any previous model in both a theoretical and operational context.
It is asserted that models such as the ones derived in this study are not simply useful, but are necessary for the future development of regional input-output economics. There is no current measure of reliability in use that can be placed on input-output multipliers and projections. As regional input-output analysis becomes more widespread and sophisticated, there is going to be increased pressure on the analyst to provide some quantitative measure relating to the precision of the estimates that he produces, as is now the case with econometric and other decision modelling techniques.