An Empirical Test of Interregional Input-Output Models: Estimation of 1963 Japanese Production

As an economy develops, products sold in one region often are produced in another region of the country. This is one form of regional interdependence that can be analyzed within the framework of a spatially differentiated, general equilibrium trade model. For an analysis of regions within the American economy, one version of a large-scale multiregional input-output trade model will be implemented by the fall of 1970 at the Harvard Economic Research Project. The American economy will be separated into more than 30 regions and 60 industries. This will be the first time that a multiregional input-output model of this magnitude has been implemented for the United States. Many theoretical and empirical problems, however, must be solved before the model can be used for regional economic analyses on a routine basis. The American model will incorporate a gravity trade model. The author implemented a smallscale version of the multiregional gravity trade model two years ago using interregional data from Japan [10]. Since the American data are still being assembled, the Japanese data are again used in this paper to compare the gravity trade model with two other spatially differentiated, general equilibrium trade models: a fixed column coefficient model and a fixed row coefficient model. Wassily Leontief, in collaboration with Alan Strout, tested a gravity trade model for individual commodity shipments [5]. Gravity trade models have also been incorporated within a general equilibrium framework to analyze transportation investment in underdeveloped countries [4] [11] to analyze regional production in Argentina [1] and Japan [10], and to study transportation requirements in what is called the "Northeast corridor" of the United States. ' Chenery [2] and Moses [8] used the column coefficient trade model in their separate efforts to test empirically a multiregional input-output model. This author previously tested the row coefficient trade model using fresh fruit and vegetable shipments [9], but this paper presents the first results of testing the row coefficient model within the overall inputoutput framework. The three models tested are fixed trade coefficient models. A linear programming model, such as the one tested by Moses for the United States [7], would be an obvious alternative. Crosshauling of commodities,2 however, cannot occur in linear programming models, and actual data on transportation costs are required. Since the aggregate nature of the interregional shipment data does produce crosshauls in the actual data and because consistent sets of transportation cost data are extremely difficult to obtain, a linear programming model was not included in the present study. In comparison with the extensive data on transportation costs and other regional data required for a multiregional linear programming model, only a limited amount of actual regional data is needed to implement any of the fixed coefficient models. The required sets of regional data are: base-year technical coefficients, base-year trade coefficients, and a set of final demands for the given year. The technical and trade coefficients are assumed to remain fixed from year to year.