# The appropriateness of using production coefficients from a national input-output model in a regional input-output model

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## Abstract

In regional economic studies, the input-output table has been one of the most widely used analytical tools. However, the construction of the regional input-output table has often resorted to a popular approach of using the national production coefficients as substitutes for the regional ones. This approach implicitly assumes a uniform technology among regions, and accordingly, the validity of the approach depends upon that of the assumption. Theoretically, the validity of the assumption requires, first of all, the existence of a national production function which can explain the regional differences of input ratios; and secondly, it requires that the elasticities of substitution between materials and the other inputs have zero or very small values. This study has provided some empirical evidences which cast doubt upon the validity of the assumption. The model developed in this study is a two-level, three-input constant-elasticity-of-substitution production function. Applying the ordinary least square method to the marginal productivity condition equation, the magnitudes of the elasticities of substitution between any pair of the three inputs can be estimated. The verification of a valid national production function is based upon the results of two tests. The first is a test of the equality between the two estimates of the elasticity of substitution from a national production function and from a substitution function. The second is a direct test of the equality of the input ratios predicted by national production function and the actually observed values of the input ratios. Based upon the time series data of the U. S. total manufacturing during the period of 1954 through 1969, this study has found that the elasticity of substitution between capital and material is significantly less than unity, while that of substitution between labor and material is statistically not different from unity. Based upon cross-section data for states from the 1967 Census of Manufactures of 36 selected 4-digit SIC manufacturing industry groups, this study has found that only seven industry groups probably have a national production function which can explain the regional differences of input ratios. These results seem to indicate that to use national production coefficients in the construction of a regional input-output table is subject to serious limitation.