An input-output coefficient may vary between observations because of objective or subjective differences, such as spatial differentiation and measurement errors, respectively. The literature is organized by methodology. The first methodology is deterministic error analysis. Upper and lower bounds on exogenous variables (input-output coefficients and final demand) transmit into upper and lower bounds on endogenous variables (output). The analysis is not straightforward because Leontief inversion is a non-linear operation. The second methodology is the econometric estimation of input-output coefficients using establishment data. The third methodology returns to the transmission of errors but now takes into account the canceling out of random errors, yielding sharper results. The expected value of the Leontief inverse is compared to the standard Leontief inverse of the expected input-output coefficients matrix. Systematic establishment differences are the subject of the fourth methodology, the full probability density function approach, which is essentially an aggregation procedure. The next two methodologies are new and promising. Monte Carlo simulations are extended to equilibrium analysis and Bayesian and entropy approaches address data treatment such as balancing.
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This chapter explains in painstaking detail the compilation of input, output, and input-output tables in the modern System of National Accounts framework. The treatments of valuation and margin issues are presented and the presentation is elucidated using the example of the Belgium accounts. At long last there is a detailed, accessible exposition of input-output compilation, authored by an eminent contributor to national accounting and input-output analysis.
Thijs ten Raa
Thijs ten Raa
The theory underlying indirect, multiplier effects of final consumption is detailed in this chapter. The classical example is the computation of the factors of production, first and foremost labor, embodied in final products. These embodiments are determined by taking the Leontief inverse of the matrix of direct input-output coefficients. Conditions on the input-output matrix which are both necessary and sufficient for the convergence of the multiplier effects are presented. Further multiplier effects due to household consumption are incorporated. The less labor is embodied in a product of an economy, the more productive the economy is in making that product. The relationship between input-output analysis and productivity measurement is detailed. The neoclassical approach of measuring total factor productivity by measuring input reductions using fixed prices has been criticized and alternative "effective" industry productivity growth rates have been presented in the input-output literature, but the two approaches will be demonstrated to be perfectly consistent. The analysis is also shown to encompass inefficiency measures and service productivity measures.
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.
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.
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.
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.
Edited by Thijs ten Raa
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.