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.     

IS THE GHOSH MODEL INTERESTING?*

ABSTRACT The overall value of the Ghosh model is appraised. Its treatment of quantities and prices is scrutinized by examining the variant with data in quantities and prices, and the variant with data in value and price indexes. The methodology involves returning to the accounting equations and shows that: (i) the Ghosh model offers solutions of limited interest, being incapable of providing prices or price indexes separately from quantities; (ii) what is taken to be the equation of Ghosh's value model is actually that of Ghosh's physical model; (iii) the Ghosh model may serve for cost‐push exercises, but the dual of the Leontief model performs the same task in a much simpler and more natural way; and (iv) Cronin's mixed models do not actually mix Leontief and Ghosh hypotheses.     

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 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.     

Supply-Side Urbanization? A Pooled Time Series Analysis

Tests of Tolley's supply-driven urban growth model for expanding sets of countries for time periods varying from 1831–1980 to 1951–1980 lead to its rejection in most contexts. The exception is for higher-income market economies, where supply-driven and demand-driven determinants of urban growth are shown to alternate with long-wave periodicity: During epochs of structural transformation following stagflation crises, supply-driven determinants dominate; during periods of technological diffusion following deflationary depressions, demand factors come to the fore. But for middle- and low-income nations, whatever the cross-section and timespan, Tolley's hypothesis is not supported: Coefficients have the wrong sign, suggesting that urban growth is greatest when there are the greatest relative gains in rural productivity, but are statistically insignificant. The need is demonstrated for an urban growth theory that is substantially broader than normally has been modeled, with dynamics that are firmly grounded in an understanding of the periodic structure of economic macrohistory.     

Leontief's “Environmental Repercussions and the Economic Structure…” Revisited: A General Equilibrium Formulation

A 1972 paper by Leontief on an input-output model with pollution removal activity as an explicit sector is reformulated as a computable general equilibrium model. The advantage of this reformulation is that substitution and rational behavior by producers and consumers can be modeled and prices are rendered endogenous. The two approaches are contrasted regarding the consequences of policy changes about taxation and technological improvements.     

Contributions to Change in the Input-Output Model: The Search for Inverse Important Coefficients

The relationship between changes in input-output structural coefficients and changes in the coefficients of the Leontief inverse is explained in a calculus-based framework. Knowledge of this relationship is essential for understanding how structural changes in one sector are transmitted across the economy, and is useful in forming updates to I-O tables given limited information. Empirically, we identify those coefficients likely to be the most important in causing inverse changes. We find that a selective and systematic updating procedure can lead to accurate updates without the need for complete data.     

PRODUCT-MIX AND TECHNOLOGICAL CHANGE WITHIN THE LEONTIEF INVERSE

ABSTRACT. Intertemporal differences in input-output coefficients can be attributed to technological change and to changes in the mix of products composing the aggregate sectors of input-output models. In this work, we develop the theoretical foundation necessary to separate these changes for both the structural and Leontief inverse matrices. Using this foundation, we examine the relative empirical importance of technological and product-mix change. The product-mix effect is then combined with RAS estimates of the technological effect to form updated estimates of the inverse. Results show that the accuracy of updated input-output coefficients can be improved in this manner.     

EMPIRICAL TESTS OF SOME SEMI-SURVEY UPDATE PROCEDURES APPLIED TO RECTANGULAR INPUT-OUTPUT TABLES*

ABSTRACT. This paper examines the RAS, Mc Menamin and Haring, and Lagrange-multiplier update methods in the context of the dual accounting system of the rectangular input-output model. The motivation was to determine if the additional information contained in the dual system is exploitable, while maintaining the integrity of the rectangular structure with all its advantages. Tests were conducted on the performance of the various algorithms for a derivative Leontief model relative to their performance on the rectangular structure. The results obtained for rectangular tables were generally better than those obtained for the more conventional Leontief ones.     

TRANSPORTATION RATES AND LOCATION OF THE FIRM: A COMPARATIVE STATIC ANALYSIS*

ABSTRACT This paper examines the role of the structure of transportation rates in the Weber-Moses triangle model. It shows that, in Zeigler's analysis, the appearance of the price elasticities of demand for inputs actually vanish by a simple application of the envelope theorem. Applying comparative statics analysis, we show when transportation rates are a function of quantity and distance, the assumptions that the production function is homogeneous of degree one and the transportation rates elasticities with respect to quantity and distance are constant are not sufficient to insure that the optimum location is independent of the level of output. This result is significantly different from that obtained by either Miller and Jensen or Zeigler.     

LOCATION,THEORY OF PRODUCTION,AND VARIABLE TRANSPORTATION RATES*

ABSTRACT. The question of what conditions insure independence between location and output decisions is investigated within the context of triangle space. Assuming that transportation rates vary with quantity and distance, it is shown that this independence is insured if the production function generates a linear expansion path and the following are all constant: transportation rate elasticities with respect to distance and quantity, and the price elasticity of demand for inputs.     

ON THE INTERPRETATION OF FIXED INPUT COEFFICIENTS UNDER AGGREGATION*

ABSTRACT A fixed input coefficient is traditionally interpreted as the additional input from one sector that is required for an additional unit of output in another sector. It is shown that this ratio of increments is, in general, not fixed under aggregation. A tight upper and lower bound for its variation are derived. A necessary and sufficient condition for the ratio to be fixed is obtained. As a consequence, adopting the common assumption of fixed input coefficients implies that additional assumptions at any subaggregate level are required. Similar results are given for the Leontief inverse, whose typical element is usually interpreted as the additional output in one sector that is required for an additional unit of final demand in another sector.     

Discovering the Language of Data: Personal Pattern Languages and the Social Construction of Meaning from Big Data

Abstract

This paper attempts to address two issues relevant to the sense-making of Big Data. First, it presents a case study for how a large dataset can be transformed into both a visual language and, in effect, a ‘text’ that can be read and interpreted by human beings. The case study comes from direct observation of graduate students at the IIT Institute of Design who investigated task-switching behaviours, as documented by productivity software on a single user’s laptop and a smart phone. Through a series of experiments with the resulting dataset, the team effects a transformation of that data into a catalogue of visual primitives — a kind of iconic alphabet — that allow others to ‘read’ the data as a corpus and, more provocatively, suggest the formation of a personal pattern language. Second, this paper offers a model for human-technical collaboration in the sense-making of data, as demonstrated by this and other teams in the class. Current sense-making models tend to be data- and technology-centric, and increasingly presume data visualization as a primary point of entry of humans into Big Data systems. This alternative model proposes that meaningful interpretation of data emerges from a more elaborate interplay between algorithms, data and human beings.     

NoteAbout the Concept of "Net Multipliers"

Net multipliers, as introduced by Oosterhaven and Stelder (2002) accept outputs as entries instead of final demand. They are found by multiplying ordinary multipliers by the final demand ratio over the sector's output. This pragmatic solution suffers from ratio instability over time. The alternative net multipliers proposed here are based on the interpretation of the Leontief inverse matrix for the effects generated at each round. The new solution is not sensitive to the size of impacts. Now net multiplier is equal to the corresponding ordinary multiplier minus one, and the ordering of multipliers is unchanged.     

The direction of migration: a dynamic general equilibrium model

A two-sector dynamic general equilibrium model is developed "to investigate the direction of migration in response to differing demographic and consumption demand behavior, as well as variations in production conditions." The model, which involves a rural sector and an urban sector, incorporates "returns to scale and the natural rate of sectoral population growth as important determinants of the direction of migration, in addition to price and income elasticities, and the sectoral technical change rate with which...previous studies dealt."     

LEONTIEF TECHNOLOGY AND THE LOCATION OF THE FIRM IN A WEBER TRIANGLE–SPECIFIC LOCALIZATION THEOREMS*

In special cases of the Leontief technology's constant input-output coefficients, the general localization theorem that an interior location is a global optimum if every input or market vertex is not a local optimum [Kusumoto (1984)] is confirmed and strengthened. Sufficient conditions are proposed for the portion of a triangular space in which the firm will locate. Finally, it is shown that, if input substitution is permitted and its effects dominate spatial effects, the firm's total cost function will be monotone, as well as concave, hence the vertex is a global optimum if it is a local optimum.     

Interpreting Spatial Economic Structure and Spatial Multipliers: Three Perspectives

The measurement and interpretation of spatial economic structure have presented many problems for analysts. The notion of a spatial multiplier has received even less formal attention; part of the motivation for this paper is the examination of the degree to which sectoral decomposition analysis might prove useful in illuminating the paths of interaction across space that are associated with changes in exogenous activity levels. In this paper, we present three perspectives that examine spatial structure in the context of an aggregated interregional social accounting matrix for Bangladesh. These perspectives examine structure at the micro-, meso-, and macrolevels and are interpreted with the assistance of several alternative methods, including structural path analysis, the field of influence, the superposition principle, multiregional feedback loop analysis, and the Matrioshka Principle; the results are interpreted analytically and cartographically. Some attention is also devoted to the formulation of a general approach to spatial multipliers. It is shown that the structure of flows and the structure of influence reveal patterns that, taken together, provide important insights into an understanding of structure and may prove to form the basis for the eventual formal presentation of the spatial multiplier.     

Silencing the laws to save the fatherland: Rousseau’s theory of dictatorship between Bodin and Schmitt

ABSTRACT

Jean-Jacques Rousseau devoted an important chapter of his Social Contract to the dictatorship. Carl Schmitt interpreted Rousseau’s chapter as marking the transition from ‘commissarial’ to ‘sovereign dictatorship’. This article argues that Schmitt’s interpretation is historically and conceptually inaccurate. Instead of paving the way for sovereign dictatorship, Rousseau carefully distinguished the dictatorship from the people’s sovereign authority. Taking position in the ‘debate’ between Bodin and Grotius on the relation between dictatorship and sovereignty, he argued that the dictator could provisionally suspend the people’s sovereign authority, but not abolish it. More particularly, the dictator did not possess the power to make generally binding laws, which had to remain the exclusive authority of the popular assembly. However, this did not prevent Rousseau from recognizing the dictatorship as a means for democratic reform. Rousseau thus conceived of the dictatorship as a time-limited and revocable commission to protect the constitution and to provide for a more stable and effective state organization based on the principle of popular sovereignty.