THE FULL-DISTRIBUTION APPROACH TO AGGREGATE REPRESENTATION IN THE INPUT-OUTPUT MODELING FRAMEWORK*

ABSTRACT. This paper presents a probabilistic specification of coefficients in the input- output modeling framework. Although previous works on probabilistic input-output models attribute uncertainty to measurement and sampling errors, this specification derives from systematic variation directly attributable to industrial, institutional, and location factors. Experiments with national input-output data support the existence of such variation. Employing the specification not only yields a more flexible aggregate modeling framework capable of producing interval impact estimates, but also an alternative perspective on such issues as interregional differentiation and structural comparison, the identification of key industrial sectors, aggregation, and spatial variation in production.     

UPPER BOUNDS ON THE SIZES OF INTERREGIONAL FEEDBACKS IN MULTIREGIONAL INPUT-OUTPUT MODELS*

ABSTRACT. Upper bounds are presented for a measure of the overall percentage error caused in a multiregional input-output model when interregional feedback effects are ignored. This error figure is thus a measure of the magnitude of interregional linkages. The upper bounds are expressed as a function of the levels of self-sufficiency in the regions in the model and of the norms of the regional technical coefficients matrices. Experimental results are presented for a variety of examples that are thought to reflect real-world situations, and it is clear that in many cases the upper bound (and hence the error) is extremely small. The implication is that single-region input-output models may be adequate for a variety of questions.     

INTERREGIONAL FEEDBACKS IN INPUT-OUTPUT MODELS: THE LEAST UPPER BOUND*

ABSTRACT. The least upper bound to the overall percentage error resulting from the omission of interregional feedbacks in input-output analysis is defined. This limiting value is the most informative of all upper bounds. A procedure for its computation is outlined and a number of experiments, using U.S. data, are discussed.     

NONSURVEY INPUT-OUTPUT ESTIMATION TECHNIQUES: EVIDENCE ON THE STRUCTURE OF ERRORS

ABSTRACT This paper concerns the nature and extent of error introduced to regional input-output multipliers by errors associated with the estimation of regional purchase coefficients (rpc's). Using the Washington State input-output model and computer simulations, estimates of multiplier error are generated for two distinct sources of rpc error. The results indicate that multiplier error from both rpc sources may be significant and support the findings of previous studies which highlight the importance of error introduced to the household purchases column for multiplier accuracy.     

AN EMPIRICAL ANALYSIS OF INTERREGIONAL PRICE LINKAGES*

ABSTRACT Vector autoregression models are used to analyze the relationships between Texas and Illinois corn prices, and the New Orleans export price. Decomposition of error variances suggests an increasing exogeneity in the recent years between the export market and the two U.S. markets. Impulse response functions indicate that the export price influences both the Illinois and Texas prices.     

THE SENSITIVITY OF INPUT-OUTPUT MULTIPLIERS*

The present paper derives analytical expressions for the sensitivity of input-output multipliers to errors in the data. The effects on the simple output multipliers are investigated for additive errors, multiplicative errors in the columns, multiplicative errors in the rows, error rectangles, the error couple and the single error, and price changes. In contrast to earlier investigations, the results are not obtained from the Leontief inverse. The present approach focusses on the effects of errors on the eigenvector corresponding to the dominant eigenvalue. It is indicated how similar expressions may be derived for several other multipliers.     

ARTIFICIAL NEURAL NETWORKS: A NEW APPROACH TO MODELING INTERREGIONAL TELECOMMUNICATION FLOWS*

ABSTRACT. During the last thirty years there has been much research effort in regional science devoted to modeling interactions over geographic space. Theoretical approaches for studying these phenomena have been modified considerably. This paper suggests a new modeling approach, based upon a general nested sigmoid neural network model. Its feasibility is illustrated in the context of modeling interregional telecommunication traffic in Austria, and its performance is evaluated in comparison with the classical regression approach of the gravity type. The application of this neural network approach may be viewed as a three-stage process. The first stage refers to the identification of an appropriate network from the family of two-layered feedforward networks with 3 input nodes, one layer of (sigmoidal) intermediate nodes and one (sigmoidal) output node (logistic activation function). There is no general procedure to address this problem. We solved this issue experimentally. The input-output dimensions have been chosen in order to make the comparison with the gravity model as close as possible. The second stage involves the estimation of the network parameters of the selected neural network model. This is performed via the adaptive setting of the network parameters (training, estimation) by means of the application of a least mean squared error goal and the error back propagating technique, a recursive learning procedure using a gradient search to minimize the error goal. Particular emphasis is laid on the sensitivity of the network performance to the choice of the initial network parameters, as well as on the problem of overfitting. The final stage of applying the neural network approach refers to the testing of the interregional teletraffic flows predicted. Prediction quality is analyzed by means of two performance measures, average relative variance and the coefficient of determination, as well as by the use of residual analysis. The analysis shows that the neural network model approach outperforms the classical regression approach to modeling telecommunication traffic in Austria.     

THE PURE THEORY OF HOUSEHOLD LOCATION AN AXIOMATIC APPROACH*

In this paper, I present an axiomatic basis for the neoclassical model of household location in a monocentric urban area. I generalize the existing framework and demonstrate that many of the conclusions derived using parametric models continue to hold even without the popularly assumed well-behaved utility and transportation cost functions.