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Yasuhide Okuyama

In dynamic input-output analysis investment meets the capital requirements of output growth. The model is linear and the proportionality between type i capital requirements and output j is represented by a capital coefficient. This chapter presents the dynamic input-output model, its solution, and two main issues, namely singularity of the matrix of capital coefficients and causal indeterminacy. Singularity is a mathematical problem that has been solved. Causal indeterminacy is the incompatibility between non-negative output solutions and arbitrary initial conditions, an issue related to the instability of the model. Alternative modifications of the model address the issue. The dynamic input-output model revives in three areas. Human capital formation is modeled to explain endogenous growth. Environmental accounts are added to analyze the depletion of nonrenewable resources. And lagged production and expenditure models are employed in disaster impact analysis.

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Douglas S. Meade

Input-output analysis was invented by Wassily Leontief, who continued to be closely involved with its development, mostly in the United States. This chapter organizes the history in a nice, concrete way, by tracing the input-output tables of the USA from 1939 until 2007, released in 2014. The history is peppered by observations of Leontief's close collaborators Anne Carter and Clopper Almon, shared with the author. The chapter concludes with a clear discussion of the myths of input-output tables, such as consistency and purity.

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Kim Swales and Karen Turner

The basic input-output model is first extended by differentiating industry outputs by region. The consequent interregional input-output matrix accounts for pollution footprints of final consumption, possibly even including household income effects, which further boost output and pollution. Another extension is the internalization of cleansing activities, to account for the social cost of emissions. Attempts at full integration of production and environmental accounting, following the "materials balance principle," are critically examined. Other environmental analyses follow. Water satellite accounts facilitate the analysis of water trade. Waste input-output models integrate waste creation and management options so that waste can be tracked. Energy efficiency improvements reduce costs, which in turn boosts demand for energy: the rebound effect. The rebound effect is related to the input-output multipliers that include the household consumption effects. The extension to general equilibrium analysis is introduced.

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Richard Wood

Direct input-output coefficients reflect the effects of the delivery of goods and services in terms of produced and non-produced inputs and environmental impacts (emissions). Evaluation of the further effects of the produced inputs yields the total input-output coefficients, which thus incorporate the multiplier effects of the final delivery of goods and services. The most concrete examples of these are footprints, which trace the environmental impacts of final consumption through the direct and indirect production requirements. After presenting a short history of environmental accounting in input-output analysis, this chapter discusses five types of footprints: ecological, carbon, material, water and land footprints. The methodology of footprint analysis is Leontief inversion of the matrix of input-output coefficients, where products are differentiated by their locations. The dimension of such a matrix is the number of products times the number of regions and this analysis is called multiregional input-output analysis. Multiregional input-output analysis traces the indirect requirements of final consumption in terms of national and international outputs. Application of environmental pressure coefficients yields the footprints. This combination of multiregional input-output and environmental analyses is also called life-cycle assessment and accounts for the environmental impacts embodied in trade.

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Kurt Kratena

The supply-use system of production is extended to a social accounting matrix by and enriched with alternative model specifications in the blocks of final demand, production, and factor markets. Domestic, import and export prices are accommodated and different composite prices face industries, households, government and the Rest of the World, accounting for taxes and other margins. These price equations second the quantity equations. Alternative macroeconomic closure rules enable the determination of equilibrium values of output and prices, either by Leontief inversion or iteration. The demand function for private consumption nests different forms, including Cobb-Douglas, translog and the Almost Ideal Demand System. Production and trade are also generalized, using constant elasticity of substitution or translog functions, including for labor and capital demand and supply. Household consumption can be extended to a dynamic framework, to explain savings. The models, from static input-output to full-fledged computable general equilibrium are presented explicitly, in a unified manner.

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Edited by Thijs ten Raa

In this authoritative Handbook, leading experts from international statistical offices and universities explain in detail the treatment and role of input-output statistics in the System of National Accounts. Furthermore, they address the derivation of input-output coefficients for the purpose of economic and environmental modeling, the building of applied general equilibrium models, the use of these models for efficiency analysis, and the extensions to stochastic and dynamic input-output analysis. As well as revealing and exploring the theoretical foundations, the Handbook also acts as a useful guide for practitioners.
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Bart Los

The traditional view of trade - in final products that are considered packages of domestic factor inputs - has been upset by the emergence of trade in intermediate inputs. The labeling of products as "made in China" (or whichever country) is little informative when the assembled parts have been produced elsewhere. Only this century three sets of indicators have been launched to measure the international fragmentation of products - following the vertical specialization approach, the global value chain approach and the value-added exports approach. The differences are introduced using a stylized global production network of five countries, the respective policy measures are identified and the input-output-based formulas are presented. Next the testing of trade theories is discussed, starting with the Leontief paradox: the classic rejection of the neoclassical Heckscher-Ohlin theory. Various refinements in the literature, accounting for technology differences, international fragmentation and other variations, are reviewed. The author makes tantalizing suggestions for further research, including the modeling of international production networks and the decoupling of primary inputs (e.g., greenhouse gas emissions) from gross outputs.

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Victoria Shestalova

Under constant returns to scale, price-taking behavior and no external effects the general equilibrium allocation is efficient. Input-output analysis need not make these assumptions and has the capacity to measure the inefficiency of an observed economic allocation. The objective of a national economy is to fulfill domestic final demand. In this chapter the level of domestic final demand is maximized subject to material balance constraints on products and production factors. The gap between the maximum and the observed levels measures the inefficiency in the economy. The linear program that finds the frontier of the economy features complementary slackness: binding constraints are signaled by positive prices and non-binding constraints by zero prices. The frontier program is translated into a complementarity problem, which is easy to solve. The consequent efficiency is decomposed in trade efficiency, Leibenstein's X-efficiency and allocative efficiency. Moreover, Solow's total factor productivity growth measure is decomposed in technical change, efficiency change and a terms-of-trade effect. The analysis encompasses environmental policy analysis.

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Giovanni Russo and Laura Chies

The service industries have grown to absorb between two-thirds and three-quarters of total employment in advanced economies. The service industries combine great employment growth with limited productivity growth, prompting a policy dilemma, the affordability of services. After reviewing the recent literature on the shift towards the services, in spite of unfavorable relative price changes, and the role of rising income effects, this chapter presents the input-output framework for service productivity analysis and uses it to analyze the externalizations of in-house services to the market place by firms and households, which are called outsourcing and tertiarization, respectively. The chapter also discusses service growth factors other than demand and supply forces, namely institutional factors, offshoring and trade.

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Thijs ten Raa

The core instrument of input-output analysis is a matrix of technical coefficients. This input-output matrix orders national accounts by interconnecting the use and make statistics of the different sectors, traces indirect economic effects or multipliers, and is used to map environmental impacts or footprints. At all levels there are issues of its dimension, not only size but also type - commodities or industries - and resolution of these issues requires that statisticians, economists (applied and theoretical), and policy analysts (including environmental) familiarize themselves with each other's work. All contribute various chapters of the handbook and these are interrelated in this introductory chapter.