Input-Output as a Simple Econometric Model: A Comment - Brown, Douglas M.; Giarratani, Frank (The Review of Economics and Statistics, 1979)
A substantial portion of the research in input-output analysis has been concerned with attempts to estimate more efficiently the structural parameters. As the coefficients have generally been estimated by nonstochastic techniques, efficiency in this context has implied acceptable estimates at reduced cost. It is possible to distinguish at least two directions of effort. One group of analysts has sought to develop and standardize sampling techniques that would bring the cost of estimating these models within reasonable limits (cf. Miernyk, 1970; Isard and Langford, 1971). Another group has concentrated their effort on non-survey and partial survey techniques-the most widely discussed in recent years being the RAS method developed in the Department of Applied Economics at Cambridge (cf. Bacharach, 1970) and applied for the first time at the regional level by Czamanski and Malizia (1969). In an article in this REVIEW, Gerking (1976a) has argued that acceptable coefficients can be estimated using standard regression techniques. Gerking recognizes the stochastic nature of sample estimates required for the construction of input-output models, and it is argued that a rigorous examination of the value of input-output coefficients is only possible in this context. Elsewhere (Gerking, 1976b; 1976c), he has applied similar methods to the problem of sample size selection and the problem of reconciling row and column coefficients in an input-output context. It is the purpose of this note to demonstrate that the application of stochastic techniques to the estimation of regional input-output coefficients encounters difficulties that must be recognized before more serious work is done in this area. Specifically, we will argue that (1) the nature of the distribution of stochastic disturbances has not been adequately explored, (2) the unique nature of regional input-output models makes application of stochastic techniques particularly difficult, if not impossible, (3) the estimator of major interest in Gerking's article produces parameter values that are not constrained to satisfy both input-output identities, and further, that empirical application of this estimator fails because the associated finitesample distribution does not possess moments.