SxieEcon. Plan. Sci. Vol. 18, No. 5, pp. 319-336, 1984 Printed in the U.S.A. 0038-0121/84 $3.00 + .@I Pergamon Press Ltd. zyxwvut THE ROLE OF PRIOR INFORMATION IN UPDATING REGIONAL INPUT-OUTPUT MODELS? GEOFFREY J. D. HEWINGS Department of Geography and Regional Science Program, 107- 109 Observatory, University of Illinois, 901 S. Mathews, Urbana, IL 61801 zyxwvutsrqponmlkjihgfedcbaZY U.S.A. Abstract-The research reported here focuses on several issues: (1) the specification and measurement of errors in single region input-output models and their impacts on the construction of new models from survey and nonsurvey sources and the updating of existing models; (2) the problems of errors in input-output models when the latter are incorporated into more extensive social accounting systems and (3) linkages between the aggregation issue, error analysis and micro-to-macro modelling within an input-output framework. Empirical analysis is conducted on many of these issues by reference to the State of Washington input-output models for 1963, 1967 and 1972. 1. INTRODUCI’ION While the use of input-output models has become an important component of analysis at the regional level in a large number of countries, there has been less agreement on the methods used for the construction of regional input-output models. More recent re- search has focused on the interaction between meth- ods of construction and error generation in the resulting tables. While the problems raised in the context of this research are not new (see, e.g. Evans’[ 151study of interindustry error propagation), they have become the source of a great deal of debate in recent years. The debate centers on what Jensen[28] has referred to as the concept of holistic versus partitive accuracy in input-output analysis. In the former case, the analyst would be concerned with the model’s ability to replicate or forecast some aggregate measures- such as a set of vectors detailing sectoral multipliers, gross outputs, employment or energy consumption. In contrast, partitive accuracy requirements focus attention on more specific aspects of the model, e.g. the accuracy of all the input coefficients for a set of industries. Since input-output models are often used at both levels, there would appear to be some interest in evaluating the possibilities for the development of models which will perform within acceptable margins of error at both holistic and partitive levels. Since funds for the construction of new, full survey-based regional input-output models are not likely to be forthcoming, the issues of error analysis in the con- struction and updating of regional models from other than full survey data will assume far more im- portance. The research reported here focuses on several issues some of which will be supported by empirical r: evidence: (1) The specification and measurement of errors in single region input-output models and their impacts on the construction of models from survey and nonsurvey sources and the updating of existing models. t The comments of Rodney Jensen, Richard Conway, William Beyers and Douglas Brown and the financial support of NSF grant SES-82-0596 1 are gratefully appreciated. (2) The problems of errors in input-output models when the latter are incorporated into more extensive social accounting systems. (3) Some thoughts on linkages between the aggre- gation issue, error analysis and micro-to-macro mod- elling within the input-output framework. In the next section of the paper, results of some work undertaken with reference to the Washington state table for 1963, 1967, and 1972 are reported. The analysis is extended to the role of error in an input-output model nested within a social accounting framework, drawing on the social accounts for Sri Lanka. Finally, the discussion focuses on some con- ceptual issues, which draw upon the earlier analysis: in particular, attention is directed towards the prob- lems of error associated with aggregation and uncer- tainty as well as the problem of error arising from the inability of the input-output model to handle economies of scale. 2. PRIOR INFORMATION AND ERROR ANALYSIS IN SINGLE REGION INPUT-OUTPUT MODELS In an earlier paper [25], some results were reported of attempts to use a modified bi-proportional tech- nique to update regional input&output matrices. The idea has been explored by Allen [ l] and Thuman and Morrison[38]: in essence, the concerns here are di- rected towards the possibilities for improving the accuracy of estimation by using prior information for a relatively small number of non-zero cells in con- junction with the usual marginal vectors necessary to implement the bi-proportional technique in updating an input-output structure. Several problems arise: first, how are the specific cells for which survey information is required to be identified and how many such cells should we expect to identify in an n x n system? Secondly, are the same cells likely to remain important over time? Thirdly, what criteria should be used to measure the effect of prior informa- tion about specific cells on the accuracy of the model estimates/forecasts? Fourthly, how does this tech- nique compare with the procedures developed by Matuszewski et a/.[351 and tested more extensively by Davis et al. [ 12]? Previous work on the application of bi-pro- portional techniques has focused on their application in a number of different contexts: (1) the estimation 319