Input–Output Economics: Theory and Applications

The following sections are included:

• Contents

• Acknowledgments

• Introduction

Input–output analysis is the study of quantitative relations between the output levels of the various sectors of an economy, a practical tool for national accounting and planning. Neoclassical economics focusses on the pure theory of the price mechanism, equilibrating supply and demand in free market economies. This paper consolidates the two approaches. The mathematical theory of linear programming is used to establish price relations in an input–output model which match neoclassical results.

The following sections are included:

• Introduction

• The Measurement of Sectoral Productivity Rates

• The Location of Comparative Advantages

• Conclusion

• References

The following sections are included:

• The SUT Framework of the 1993 SNA

• SUT Features Determined by Analytical Uses
  • Input and Output Matrices
  • Impact Analysis
  • Imports and Impact Analysis
  • Household Consumption and Impact Analysis

• Requirements of Detail and Compilation
  • ISIC and CPC Classifications
  • Reliability of Data and Coefficients

• Theoretical and Practical Considerations for Future I–O Work
  • Theoretical Considerations
  • Practical Considerations

The construction of input–output coefficients on the basis of flow data is complicated by the presence of secondary outputs. Seven methods to deal with this problem coexist. For example, U.S. input–output requirement tables are based on the so-called industry technology model; Japan adopts the so-called Stone method, while West German tables are based on the so-called commodity technology model. This paper settles the issue on the ground of theory.

It postulates invariance and balance axioms, and proceeds to characterize one of the methods to construct input–output coefficients. The commodity technology model is singled out.

ten Raa, Chakraborty and Small (1984) rule out industry technology based input–output coefficients in favor of a construct based on the commodity technology model. The latter, however, produces negative coefficients. This note shows that the negatives cannot be ascribed to errors of measurement. The very framework of deriving unique technical coefficients matrices from the black-box of a single pair of input and output flows must be abandoned.

Kop Jansen and ten Raa (1990) established a purely theoretical solution to the problem of selecting a model for the construction of coefficients on the basis of make and use tables. In an axiomatic context, they singled out the so-called commodity technology model as the best one according to some desirable properties. The aim of this paper is to delineate the restrictions on the relevant data sets that ensure the fulfillment of the desirable properties by other models used by statistical offices.

Technical coefficients are usually constructed from commodity or industry technology models. Although these models are considered as competing, there is an encompassing framework which admits a clear comparison.

Presumably, input–output coefficients reflect technology, and these coefficients measure the input requirements per unit of product. The concept has been extended to consumption theory, where it models expenditure shares. Input–output coefficients are extracted from the national accounts of an economy, by taking average proportions between inputs and outputs. Since the latter represent all sorts of inefficiencies, this practice blurs the measurement of technology. Input requirements are better measured by minimal proportions between inputs and outputs. This approach separates the measurement of technology from that of productive efficiency.

The basic elements of input–output analysis, notably technical coefficients, quantity and value equations, and a total factor productivity growth measure, are derived as intermediate constructs when the problem of national income or product determination is directly related to input and output flow data. By embedding input–output concepts in a neoclassical framework, specification issues are resolved, notably the problems of construction of coefficients and of determination of value. Conversely, neoclassical concepts of marginal productivities can be related to a consistent input–output framework of data. Sources of substitution are identified.

The Canadian comparative advantage is determined by the maximization of foreign earnings, subject to 10 input–output relations between 29 industries and 92 commodities. Free trade would boost the mining, quarrying & oil wells, tobacco, and machinery sectors. The structure of the economy is not self-sufficient, as a necessary and sufficient price condition shows. When commodities are aggregated into the 29 sectors, the shadow prices of the programs fulfill the value equations of the input–output analysis and admit a decomposition of Canadian inefficiency in 5% X-inefficiency, 15% allocative inefficiency, and 80% international specialization mismatch.

The substitution theorem states that an economy with many commodities, but only one factor input (say labor), will not substitute inputs (commodities or labor) when final demand changes. This Note drops the assumption that all activities require some labor input and constructs the dominant technology.

The following sections are included:

• Introduction

• The Structure of an Economy

• The Material Balance

• The Subsumption of Dynamic Input–Output

• Conclusion

• References

This paper offers a new approach to economic models in which activities take time. Departing from a standard economic model (Leontief's dynamic input–output model), we recast the activities from ordinary vectors into temporal distributions. In doing so, we preserve the formal structure and simplicity of the standard model. This is the secret of the power of our approach which asserts itself in the resolution of some open dynamic input–output problems. In particular, we are able to solve models with singular capital structures (i.e. singular derivatives coefficients matrices), unbalanced growth and different time profiles of investment or other production activities.

This paper implements dynamic input–output analysis with distributed activities. For this purpose, the input–output equation is formulated and solved in discrete time. Existing dynamic input–output models are shown to be instances. The fully distributed input–output model is applied to analyze the dynamic structure of the Polish economy. The effects of investment distributions are expressed by a comparison with conventional, non-distributed input–output results.

Working capital is capital in the pipeline of the production process. Little has been done to formalize the concept of working capital in an input–output framework. The objective of the paper is to provide an input–output model of working capital and to assess its empirical value. In Section 1, a brief discussion on capital is presented. In Section 2, we develop the theoretical framework of the analysis. Section 3 deals with the empirical work, and Section 4 concludes the paper.

In this paper, we analyze the determinants of material inputs into individual production activities as a function of their outputs. We use observations on a large cross-section of U.S. manufacturing plants from the Census of Manufactures, including those that make goods primary to other industries, to study differences in production techniques. We find that in most cases, material requirements do not depend on whether goods are made as primary products or as secondary products. We thus elucidate support for the commodity technology model as a useful working hypothesis.

Although technical coefficients are estimated on the basis of flow data (use and make matrices), they are rarely treated as random variables. If this is done, an error term is added to the coefficients, rather than derived from the distribution of the data. Even so, the calculation of multipliers, by means of the Leontief inverse, is difficult. Due to the nonlinearity of this operation, the multiplier estimates are biased. By going back to the flow data, this paper provides unbiased and consistent employment and output multipliers estimates for the Andalusian economy. Rectangular use and make matrices are accommodated, and problems associated with the construction and estimation of technical coefficients and the Leontief inverse are circumvented.

Input–output analysis and neoclassical economics do not seem to mix. Neoclassical economists consider input–output analysis a futile exercise in central planning or at least resent the separation between the quantity and value systems. Conversely, input–output economists resent marginal analysis without an understanding of the underlying structure of the economy. In this paper, I turn the perceptions upside down by analyzing productivity. I ground the concept in the orthodox neoclassical general equilibrium framework. Then I introduce a linear specification and use input–output analysis to derive a measure of total factor productivity without using value shares of factor inputs. In other words, input–output analysis has the potential to explain prices which neoclassical growth accountants take at face value.

The standard measure of productivity growth is the Solow residual. Its evaluation requires data on factor input shares or prices. Since these prices are presumed to match factor productivities, the standard procedure amounts to accepting at face value what is supposed to be measured. In this paper, we determine total factor productivity growth without recourse to data on factor input prices. Factor productivities are defined as Lagrange multipliers to the program that maximizes the level of domestic final demand. The consequent measure of total factor productivity is shown to encompass not only the Solow residual, but also the efficiency change of the frontier analysis and the hitherto slippery terms of-trade effect. Using input–output tables from 1962 to 1991, we show that the source of Canadian productivity growth has shifted from technical change to terms-of-trade effects.

Neoclassical economists argue that competition promotes efficiency, but Schumpeter argues that it is monopoly rents that help entrepreneurs to invest in R&D. We investigate the overall effect of competition on TFP-growth. We use rent, defined as the factor reward above its perfectly competitive value, as a negative measure of competition. Our main finding is that performance is positively associated with rents on capital, but not with rents on labor. Neoclassical economists and Schumpeter may both be right, but the mechanisms differ.

Can the slowdown in total factor productivity that we have experienced since the mid-seventies be ascribed to the increasing importance of services, or do we instead observe an improvement of productivity in the service sectors by way of learning-by-doing or specialization? We feel that such questions are best answered within a general equilibrium analysis of the whole economy, i.e. a structural view of the whole economy. We maximize the level of domestic consumption subject to commodity balances and endowment constraints. The Lagrange multipliers associated with the endowment constraints measure the marginal productivities of labor and capital. We declare these shadow prices to be the factor productivities. The main empirical contribution of this paper is a reexamination of the services paradox. In Canada, the sluggish productivity in services is limited to finance, insurance and real estate, and to business and personal services. Any attempt to resolve the services paradox may focus on these two sectors. Transportation, trade, and to a lesser extent communication, are progressive sectors.

The following sections are included:

• Introduction

• Labor Employment and Productivity

• Value Added Versus Final Demand

• A Shift in Comparative Advantage?

• Technological Change

• Conclusion

• Acknowledgements

• References

We propose a new way to locate the comparative advantages of two economies linked by international trade. We construct a competitive benchmark based only on the fundamentals of the two economies: endowments, preferences and technologies. The direction of trade is endogenously determined by a linear program with an input–output core. The factor contents of that trade are compared with factor endowments to test the Heckscher–Ohlin model in the presence of different technologies and preferences. We can also evaluate the gains of free bilateral trade. The model is applied to a customs union between Europe and Canada. The Heckscher–Ohlin factor abundance specialization hypothesis is supported by the data.

How would perfect competition affect the distribution of income in China? To answer this question, we integrate the two main streams of income distribution theory, namely the functional and the personal income approaches. First, using a general equilibrium model of China comprising 30 sectors and 27 provinces, marginal productivities are used as competitive commodity prices and factor rewards. Second, the rewards are imputed to households using their compositions in terms of persons and factor endowment entitlements. The ensuing distribution is contrasted with the status quo. Less skilled labor would stand to lose and, therefore, inequality would mount. Skilled workers, managers and technicians would move from Western and Central China to Eastern China. These flows would be more than offset by a flow of unskilled labor from Eastern China to Central China. Our finding that Eastern China has too many unskilled workers, relative to the competitive benchmark, suggests that the Harris-Todaro mechanism operates in China. Competition would change the predominant nature of inequality from the rural-urban divide to differences between the social classes. Moreover, the existing negative relationship between development and inequality would evaporate.

India and Bangladesh pursued policies of trade liberalization since the early 1990s. However, due to the differential speeds of opening up, Bangladesh's bilateral trade deficit with India widened substantially over the years. This aggravated the economic and the political tensions between the economies. It has been held that the promotion of free trade between the two economies may enhance trade and hence economic cooperation between them. Against this backdrop, the present chapter proposes a theoretical framework which provides a general equilibrium determination of the commodity pattern of trade and hence locates the comparative advantages of the economies. The empirical implementation of the model considers trade in 25 sectors comparable in the input–output tables of the economies. The study isolates the gains from free trade accruing to either economy. The chapter also explores the pattern of bilateral trade when each economy produces goods by utilizing their own, as well as the other country's technology. The gains from this trading arrangement are also isolated.

How would competitive pressure impact upon the income distribution and the poverty of household groups? We analyze the gains in efficiency and productivity due to competitive pressure, and its distributional effects using a general equilibrium input–output framework. The efficient utilization of the available resources, technical progress and free trade constitute our sources of growth. Welfare would increase under competition, but the income distribution would become more skewed. Rural household groups would stand to lose relative to the urban ones. Urban poverty would be reduced significantly more than rural. In fact, the agricultural worker would even suffer from an increase in poverty. The study shows that competitive pressure has a positive effect on efficiency, productivity and poverty, but an adverse effect on the income distribution in the Indian economy.

The following sections are included:

• Index