On the Statistical Properties of RAS method for Measurement Error

Abstract

Input-output analysis is an important analytical tool for spatial interactions and allocations in the field of commodity flows, not only at a national but also at a regional scale. The heart of input-output analysis is the table of input-output coefficient, and a major drawback of the analysis is its heavy input requirements in terms of both money and time necessary to construct it by the fill-survey method. For the last two decades, so many studies have been focussed on the development of methods for constructing complete tables, using scarce and often incomplete data. These so-called non-survey methods attempt, in general, to adjust older tables to reflect more recent industrial structures or to borrow information in a table of national economy to use for a regional economy. We must select a method among them, in practice. In prior to make it, it is necessary to evaluate their estimation powers and to have informations about its properties. A large number of researches have been proceeded to test these techniques by the way of evaluating the goodness-of-fits, using full-surveyed input-output tables. However, we have no conclusive result which is accepted commonly, because there is a lack of measures of goodness-of-fit, that is commonly acceptable and directly comparative among various non-survey methods.The RAS method is considered to be one of the most widely used techinique in the applied fields. This is a techinique, in which an input-output table at base year or area is adjusted sequentially for rows and columns in order to generate a table at target one. There are so many articles to examining its efficiency as an estimation method by various types of error analysis. Almost all of them have analysed the error from its computational properties, for evaluating the accuracy of estimated results, and have studied the relationships between errors and informations.To estimate an input-output table by the RAS method, we are necessary to have an input-output table as a base, and to observe or predict gross outputs, total of intermediate inputs and sales by each sector. It is used or treated as if these informations are free from some kinds of error. However, in the view-points of a sampling and estimation theory, it is natural and reasonable to consider that these informations are subject to certain kinds of stochastic errors. In this paper, we have examined how the RAS method behaves against these errors. Our analysis is executed by experiments with Monte Carlo simulation. At a preliminary stage of this analysis, we have examined the shapes of distribution for each element of estimated results, without rigorous quantitative analysis. From these analyses, it was found out the facts that the fabrication change multipliers and substitution change multipliers have biased distributions in many cases and that there are several cases, where their distributions are skewed and have two modal values. And, it was shown that input-output coefficients have unbiased normal distributions as a whole.