ECONOMETRIC ANALYSIS OF EUROPEAN CARBON DIOXIDE EMISSIONS BASED ON RECTANGULAR SUPPLY-USE TABLES

This paper formalises the so-called Supply-Use Based Econometric (SUBE) approach that allows for the introduction of econometric analysis in the calculation of backward input–output multipliers of the Leontief-type quantity model, using rectangular supply and use tables. The SUBE approach does not require any kind of inverse matrix and incorporates the traditional approach (with square supply-use tables) as a particular case. The empirical analysis shows that the SUBE carbon dioxide multipliers for the EU27 are considerably lower than those obtained by the traditional Leontief inverse. In an application of the SUBE approach, the European economy appears to emit about 10% less carbon dioxide than in a situation in which it would not import any intermediate inputs from outside the EU27.     

DISAGGREGATING INPUT–OUTPUT MODELS WITH INCOMPLETE INFORMATION

Disaggregating a sector within the Leontief input–output (IO) framework is not a straightforward task since there is more than one possibility for the unknown technical coefficients of the disaggregated IO table, and more information than what is embodied in the aggregated IO table is thus required. This paper presents a methodology for disaggregating sectors into an arbitrary number of new sectors when the only available information about the newly formed sectors is their output weights. A random walk algorithm is used to explore the polytope containing the admissible combinations for the unknown technical coefficients of the disaggregated IO table. These combinations are then used to construct the probability distribution of the coefficients of the inverse Leontief matrix. The methodology is illustrated by disaggregating the electricity production sector of China's 2007 IO table and by looking at the probability distribution of the CO₂ emission intensity factors of the sectors of the economy.     

THE ROLE OF SUPPLY CONSTRAINTS IN MULTIPLIER ANALYSIS

Multiplier analysis based upon the information contained in Leontief's inverse is undoubtedly part of the core of the input–output methodology and numerous applications and extensions have been developed that exploit its informational content, both at the national and regional levels. Nonetheless there are some implicit theoretical assumptions whose policy implications need to be assessed. This is the case for the ‘excess capacity’ assumption, which implies that resources are available as needed to adjust production to new equilibrium states. In an actual economy, however, new resources are often scarce and always costly. When supply constraints intervene, the assessment of the effects of government demand policies may be substantially different from that of the standard Leontief multiplier matrix. Using a closed general equilibrium model that incorporates supply constraints, we perform some simple numerical exercises and proceed to derive two ‘constrained’ multiplier matrices, based upon the implicit Jacobian matrix, that can be compared with the standard ‘unconstrained’ Leontief matrix.     

A global robustness measure for input–output projections from ESA and SNA tables

Input–output (interindustry) data are in wide use in empirical research and constitute an integral part of the European System of Accounts (ESA) and of the System of National Accounts (SNA). In a strict sense, however, these data are merely estimates of the true economic relationships. Therefore, we suggest a measure of robustness of input–output projections with respect to errors or changes in the underlying Leontief matrix. Our measure is based on the mathematical theory of norms and characterizes a complete Leontief matrix. Thereby, no assumptions are required on the distribution of the matrix elements. We discuss alternative numerical-computing algorithms and provide useful bounds and approximation formulas. The paper concludes with a large set of empirical sample applications.     

A STRUCTURAL DECOMPOSITION APPROACH TO COMPARING MRIO DATABASES

The construction of multi-regional input–output tables is complex, and databases produced using different approaches lead to different analytical outcomes. We outline a decomposition methodology for investigating the variations that exist when using different multiregional input–output (MRIO) systems to calculate a region's consumption-based account. Structural decomposition analysis attributes the change in emissions to a set of dependent determinants, such as technical coefficients, the Leontief inverse and final demands. We apply our methodology to three MRIO databases – Eora, GTAP and WIOD. Findings reveal that the variation between Eora and GTAP can be attributed to differences in the Leontief inverse and emissions’ data, whereas the variation between Eora and WIOD is due to differences in final demand and the Leontief inverse. For the majority of regions, GTAP and WIOD produce similar results. The approach in this study could help move MRIO databases from the academic arena to a useful policy instrument.     

Reconsidering Import Dependency in Turkey: The Breakdown of Sectoral Demands with Respect to Suppliers

The common practice for finding direct and indirect import requirements in response to domestic final demand changes involves multiplication of the direct imports coefficients matrix by the Leontief inverse matrix of domestic coefficients. The outcome is usually referred to as the import dependency matrix, a typical element of which gives intermediate import demand, induced by the domestic final demand (policy) sector (column), from the foreign (origin) sector (row). We propose an alternative methodology to capture all three dimensions of import dependency, i.e. origin, destination and policy. The information content of the import dependency matrix is expanded by information on domestic sectors (destination) which demand intermediate imports. Calculations reveal some interesting features of import dependency in Turkey, namely that policy sectors mostly coincide with destination sectors, that oil refinery emerges as a leading destination sector for all, and that raw petroleum is a leading origin sector.     

ENDOGENIZING CONSUMPTION IN THE INPUT‐OUTPUT MODEL: THEORY AND APPLICATION

Since the basic model of input‐output analysis does not take into consideration the income effect on consumption expenditure, we constructed a model which endogenizes consumption and breaks down integrated production inducement into Leontief and Keynesian effects in a generalized context and in two solution approaches. Using short‐term marginal consumption propensities, we estimated that Keynesian effects make up about 14% of the integrated inducement effects for Japan. The public services sector, which is not influential in the basic model, becomes very influential in consideration of Keynesian effects. Manufacturing and service sector products are the main targets of the expanded consumption. The impact of a change in exogenous final demand can be easily simulated by applying the suggested apparent input coefficient matrix to the integrated inverse matrix.     

An Alternative Factor-analytic Approach to Aggregation of Input–Output Tables

This paper is concerned with the question of finding sets of similar micro-level industries that can be grouped to obtain a smaller set of macro-level industries. We argue that factor analysis based on the Leontief inverse is a promising approach when multiple objectives of classification must be taken into account, provided that the cosine, rather than the correlation coefficient, is adopted as the measure of similarity. We apply this approach to the 1967 US input–output table because that table has been used by researchers experimenting with alternative classification methods.     

Income Distributive Effects in the Brazilian Economy

Studies aiming to evaluate the structural distribution of economic impacts usually treat consumption demand as an exogenous variable. In this case, the Leontief matrix multiplier lacks the multiplier process via the consumption function that one customarily finds in a Keynesian model. To regard the consumption as a fictitious production activity is not the appropriate procedure. Instead, the Keynesian consumption function is introduced at a disaggregated level. For that, a matrix multiplier was formulated in order to combine Leontief's propagation process with the Keynesian propagation process. This matrix includes the effects of endogenous changes in consumption demand. Based on the present production structure in Brazil, the results show how the propagation effect directs the induced income towards capitalists, depriving wage earners. The model also allows for evaluation of diverse effects of the propagation process according to income and consumption coefficients by sector.     

Georg Charasoff: A Pioneer in the Theory of Linear Production Systems

This paper exposes mathematically Charasoff s results on linear production systems. Charasoff developed an algorithm for the iterative calculation of the Leontief inverse, the concepts of basic and non-basic commodities, as well as the Srajfian standard system. This allowed him, given the real wage rate, to calculate the profit rate independently of prices as the ratio of two physically homogeneous magnitudes, and then the prices for an already given profit rate. Therefore, as early as 1910, Charasoff had developed significant concepts of the theory of linear production systems, which long afterwards became more broadly known through the works of Leontief and Sraffa.     

A Turnpike Theorem in the Closed Dynamic Leontief Model with a Singular Matrix of Capital Coefficients

The paper refers to the well-known Tsukui turnpike theorem on convergence of optimal growth trajectories in the closed dynamic Leontief model to the maximum balanced growth trajectory, called turnpike. In the original proof of this theorem, the assumption that the matrix B of capital coefficients is non-singular plays an essential role. For many reasons this assumption, very convenient for theoretical analysis, is not always satisfied in input-output systems built for empirical purposes. This paper fills the gap between theory and empirical studies, presenting a proof that convergence of optimal trajectories towards the turnpike is also a characteristic feature of the closed Leontief model in the case when matrix B is singular. The general idea of the proof is based on the approximation of a singular matrix B by an infinite sequence of non-singular matrices.     

Introduction of New Technology with a Sound Transition of the Input-Output Structure

We examine the general equilibrium repercussions associated with the introduction of new technologies, using the generalized Leontief system that allows technological substitutions. We show that an untested introduction of cost-increasing technologies in any industry may result in creating a non-productive technological structure that does not satisfy the Hawkins-Simon condition, following the autonomous dynamic adjustment process with structural transitions in the economic system. Therefore, we propose a practicable control scheme of introducing cost-increasing technologies that strictly avoids the creation of non-productive structures in all periods of structural transition, using the available information on the ex ante technological structure.     

A note on distortions from estimating the regional impacts of exogenous changes in output

This paper demonstrates both theoretically and empirically that when outputs instead of final demands are exogenously predetermined, the traditional Leontief final demand model overestimates economic impact, and even more so in a multiregional context. We assess this premise vis-à-vis the Leontief output model using the 2013 interregional input–output table of the Republic of Korea. We find that from a multiregional perspective the standard Leontief final demand model yields substantially biased output multipliers for Chungbuk Province.     

广东省现代物流业的波及效果分析

通过广东省2000年的6部门投入产出表，计算出各部门的直接前向关联指数和直接后的关联指数，直接消耗系数表，列昂惕夫逆阵，生产诱发系数表，影响力和感应度系数表，最后从各方面分析了广东省物流业与其他产业的关联关系。     

An Overview of Input-Output Analysis Applied to Production-Inventory Systems

Input-Output Analysis, together with the Laplace transform, have been applied to multi-level, multi-period production-inventory systems in a number of papers. This article gives a historical overview of the areas involved in these studies. It is shown that the input and output matrices as well as the Leontief inverse can be generalised to include timing properties for the inputs by means of the Laplace transform. The consequent advantages are exemplified in different production models, treating, for instance, capacity requirements and safety stock problems. The main literature in this field concerns assembly systems, but the approach is easily applicable to process industries with a divergent material flow or when feedback is essential.     

A New Method for the Identification of Patterns in Input–Output Matrices

This paper suggests a new algorithm for selecting the input–output (IO) coefficients of a Leontief matrix in order of importance, so providing an analytical method for decomposing an IO matrix. It avoids the choice of arbitrary thresholds for eliminating flows or coefficients, and allows for circular relationships. For this purpose, a simple inverse-important criterion has been chosen, which is consistent with the logic of the Leontief model. A procedure that greatly reduces the computational burden is then devised. This method permits new comparisons of IO structures of different countries or regions, for identifying their different degree of internal integration and their reciprocal influence through the exchange of intermediate goods. An application to an IO model for seven European Community countries for 1980 is then presented.     

The ECA-method for Identifying Sensitive Reactions within an IO Context

The paper introduces an alternative method to determine "sensitivity' within an input–output-context and makes the most sensitive connections visible in an overall graph. The method called ECA (Elasticity Coefficient Analysis) tries—like the Important Coefficient Analysis (ICA)—to derive structures from a certain property of the Leontief inverse. As the core of the method is elasticity—i.e. taking the relative reaction of the element bij of the inverse as a measure of response to a 1% change of the input coefficient aij—it describes the dynamic potential of certain sectors on possible changes of technical coefficients. In the second part of the paper, comparisons are made between the results of MFA (Minimal Flow Analysis), ICA and ECA upon using the same table for analysis. ICA and ECA to some extent show similarities but also some differences. Both contrast with MFA with respect to the very basis of the approach that enforces different interpretations of the results. Finally, some hypotheses on the differences and similarities are set up that could give a perspective for the further use of the different methods.     

A Property of the Leontief Inverse and its Applications to Comparative Static Analysis

We arbitrarily choose a submatrix of order 2 in the Leontief inverse matrix B . If a main diagonal element in the submatrix is a main diagonal element in B , then the determinant of the submatrix is non-negative; in particular, if the two main diagonal elements in the submatrix are all the main diagonal elements in B , then the determinant of the submatrix is greater than or equal to 1. This property can be used in the comparative static analysis for the input-output model. For example, when the change only occurs in one sectoral final demand or one corresponding row of the input coefficient matrix, which leads to a change of this sectoral gross output, the equivalent conditions that the absolute value of the rate of change of this sectoral gross output is larger than or equal to all other sectoral change rates and larger than at least one sectoral rate of change are shown. It is impossible to derive the exact results for the comparative static analysis if the property is not applied. A previous fault confirms this point.     

Technology Flows Matrix Estimation Revisited

This paper revisits the methodological problems of estimating matrices showing how technological advances--measured by industry research and development outlays--flow from industries of origin to using industries. An early effort relied upon the analysis of 15 112 US patents. Several alternative methods are explored to address methodological questions concerning the choice of carrier matrices, the handling of diagonal elements, and the treatment of capital goods flows. Technology flow matrices estimated using diverse combinations of assumptions are tested for goodness-of-fit relative to the original patent-based matrix and for their ability to "predict' productivity growth in Solowian regression equations. Although some anomalies emerge, the best results are obtained using combined first-order transactions and capital flows matrices with diagonal elements adjusted to reflect the ratio of internal process to all R&D spending. However, flow data compiled using the Leontief inverse matrix add explanatory power in productivity growth regressions.     

The approximation capabilities of the minflex-Laurents,translog, and generalized Leontief forms

This paper compares the approximation capabilities of the minflex-Laurents translog and minflex generalized Leontief cost functions with their translog and generalized Leontief counterparts in Monte Carlo experiments. The minflex Laurent specifications generally provided closer approximations to underlying technical and economic parameters. Imposition of nonlinear restrictions on some of the parameters of the minflex Laurent models yielded measurable improvement in estimated elasticities of substitutions, returns to scale, and rates of technical change.The refereeing process of this paper was handled through E. Appelbaum.