ON THE PLAUSIBILITY OF THE SUPPLY-DRIVEN INPUT-OUTPUT MODEL: EMPIRICAL EVIDENCE ON JOINT STABILITY*

ABSTRACT. This paper addresses the issue of the plausibility of the supply-driven input-output model from an empirical standpoint. We suggest that requiring production coefficients to remain perfectly fixed during an application of the supply-driven input-output model is unnecessarily restrictive given the extensive use of approximation methods in mathematics, economics and regional science. Simulations with the supply-driven version of an input-output table for a representative region are shown to result in changes in the corresponding production coefficients well within conventional tolerance levels.     

THE SUPPLY-DRIVEN INPUT-OUTPUT MODEL: A NEW INTERPRETATION BUT STILL IMPLAUSIBLE

ABSTRACT. In this reply, I argue that the production function proposed by Gruver provides a theoretical foundation for the supply model only in a most trivial case. He proposes a more general alternative which is, however, still very implausible. Furthermore, against Rose and Allison, I argue that small input-coefficient changes provide an insufficient excuse for using the supply model for impact studies, and I show that employment estimates may be quite different depending on the approach used.     

ON THE PLAUSIBILITY OF THE SUPPLY—DRIVEN INPUT-OUTPUT MODEL: A THEORETICAL BASIS FOR INPUT-COEFFICIENT CHANGE*

ABSTRACT. Oosterhaven (1988) labels the supply-driven input-output model “theoretically implausible” and criticizes the straightforward use of the model for impact studies. This comment extends and corrects some of the issues addressed by Oosterhaven. We derive the characteristics which industry production relations must possess to be consistent with the implied changes in industry inputs and outputs when supply-side input-output models are employed for impact analysis. First, it is shown that an implicit assumption is the characteristic of perfect substitutability among all inputs in each industry production function. This is the polar opposite of the Leontief assumption of zero elasticity of factor substitution among all inputs, and is very unrealistic for large changes from the initially observed solution since it implies that all inputs are non-essential in the production process and that any input can be substituted for all others simultaneously. Second, it is shown that the model may still be reasonable for approximating the effect of small changes since the implied production relation may be interpreted as a cost minimizing choice for a standard constant-returns-to-scale production function linearized around the initial solution under the assumption that relative prices are unchanged. Under this alternative interpretation, the supply-side model may be expected to provide a reasonable approximation, useful for analyzing changes in the neighborhood of the initial solution, but would appear to be inappropriate for analyzing large changes.     

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.     

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.     

THE ROLE OF ERROR STRUCTURE IN SIMULATIONS ON REGIONAL INPUT-OUTPUT ANALYSIS*

Previous simulation experiments on regional input-output analysis have concluded that regional purchase coefficients are more important than technical coefficients in contributing to multiplier accuracy. This paper shows that the multiplicative error structure used in those experiments may have biased the results. A new error structure, combining a multiplicative and an additive component is introduced, and simulations are conducted on randomly generated models. The analysis shows that the results are sensitive to the relative magnitudes of the two error components, as well as to the closure of the model.     

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.     

ON THE SENSITIVITY OF GRAVITY MODEL FORECASTS*

In this paper we present a procedure for estimating small changes in gravity model forecasts in response to small changes in input values (trip end totals and/or parameter values). The procedure can be used to derive covariance matrices from which confidence intervals may be obtained and which may be used for tests of hypotheses. While this type of problem has been addressed by others, our approach is the only one that is conveniently applicable to the doubly constrained model and can accommodate the large numbers of origin and destination zones one typically encounters.     

A NOTE ON THE FORMULATION OF A FULL-ANALOGUE REGRESSION MODEL OF THE SHIFT-SHARE METHOD

ABSTRACT. This paper presents a full-analogue regression model of the deterministic shift-share method, for analyzing the components of regional employment change. The model is formulated as a constrained least squares regression problem. This leads to a direct determination of estimates for the national, industrial, and regional growth coefficients. The statistical significance of these coefficients and the overall model can then be tested by using standard regression test statistics.     

A DOUBLE-ENTRY METHOD FOR THE CONSTRUCTION OF BI-REGIONAL INPUT-OUTPUT TABLES*

ABSTRACT. In The Netherlands, a strong tradition in the construction and updating of (inter)regional input-output tables has been built up. The paper gives a brief overview of this Dutch experience and discusses the features of the by now more or less standardized double-entry bi-regional construction method (DEBRIOT). This method systematically adds sales and export coefficients to the usual construction procedures. Thus, it introduces consistency checks at the cell level of the input-output table. Moreover, it offers a non-survey technique to estimate a regional domestic sales table that is crucial to the double-entry character of the method.     

A NOTE ON THE GENERAL MATHEMATICAL EQUIVALENCY OF ECONOMIC BASE AND AGGREGATE INPUT-OUTPUT MULTIPLIERS: FACT OR FICTION*

ABSTRACT A longstanding inconsistency in the definition of basic and nonbasic economic activity is resolved. When indirect exports are included in the basic, rather than the nonbasic sector, and the model is closed with respect to households, economic base and aggregate input-output mulitpliers constructed with the same data and definitions will be mathematically identical.