Abstract
In this chapter, a new temporal approach to the classical Leontief input–output analysis is elaborated that avoids the assumption of the constant direct input coefficients. The presentation builds on earlier work (Sonis & Hewings, 1989, 1991, 1992) that examined a variety of issues surrounding error and sensitivity analysis, decomposition and inverse important parameter estimation. These ideas are now brought into a general form as a basis for a more complete, general fields of influence approach that is the main vehicle for describing the overall changes in economic relationships between industries created by combinations of changes in technological coefficients caused by diffusion of technological, organizational and administrative innovations. The most important new concept based of the notion of the direct fields of influence is the multiplier product matrix and the corresponding artificial economic landscape which represents the classical key sector analysis and hierarchies of sectoral backward and forward linkages. The multi plier product matrix is the main part of the fundamental minimal information decomposition of Leontief inverse in the form of the difference between the global presentation of direct effects of the changes in inputs coefficients and the syner getic effects of the overall interaction of the changes. The new Temporal Leontief inverse is constructed such that it can serve as the basis for the temporal analysis of an evolving input–output system; the inverse depends on an evolutionary tail of changes in a highly non-linear manner. The detailed analytical structure of the Temporal Leontief inverse addresses the possibilities of tracing the impact of each change in the individual direct inputs in each time period through to the final state of the economy. This dynamic approach provides the basis for a new perturbation theory for matrix inversion.
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References
Bacharach, M. (1970). Biproportional matrices and input–output change. Cambridge: Cambridge University Press,.
Bullard, C. W., & Sebald, A. V. (1977). Effects of parametric uncertainty and technological change in input–output models. Review of Economics and Statistics, 59, 75–81.
Bullard, C. W., & Sebald, A. V. (1988). Monte Carlo sensitivity analysis of input–output models. Review of Economics and Statistics, 70, 705–712.
Carter, A. P. (1970). Structural change in American economy. Cambridge: Harvard University Press.
Defourny, J., & Thorbecke, E. (1984). Structural path analysis and multiplier decomposition within a social accounting matrix framework. Economic Journal, 94, 111–136.
Dietzenbacher, E. (1988). Estimation of the leontief inverse from the practitioner's point of view. Mathematical Social Sciences, 16, 181–187.
Dietzenbacher, E. (1990). Seton's eigenprices: Further evidence. Economic Systems Research, 2, 103–123.
Dietzenbacher, E. (1991). Perturbations and eigenvectors, essays. Rijksuniversiteit Groningen.
Drud, A. Grais, W., & Pyatt, G. (1985). An approach to macroeconomic model building based on social accounting principles. Report No. DRDISO, Washington D C, World Bank.
Eliasson, G. (Ed). (1978). A macro-to-macro model of Swedish economy. Stockholm: Almqvist and Wicksell.
Evans, W. D. (1954). The effect of structural matrix errors in interindustry relations estimates. Econometrica, 22, 461–480.
Gillen, W. J., & Guccione, A. (1980). Interregional feedbacks in input–output models: some formal results. Journal of Regional Science, 20, 477–482.
Giarratani, F., & Garhart, R. E. (1991). Simulation techniques in the evaluation of regional Input–Output models: a Survey. In J. J. L. I. Dewhurst, G. J. D. Hewings & R. C. Jensen (Eds), Regional input–output modeling: New developments and interpretations (pp. 14–50). Aldershot: Avebury.
Henderson, H. V., & Searle, S. R. (1981). On deriving the inverse of a sum of matrices. SIAM Review, 23, 53–60.
Hewings, G. J. D. (1982). The empirical identification of key-sectors in an economy: A regional perspective. The Developing Economies, 20, 173–195.
Hewings, G. J. D. (1984). The role of prior information in updating regional input–output models. Socio-Economic Planning Sciences, 18, 319–336.
Hewings, G. J. D. (1985). Regional input–output analysis. Beverly Hills: Sage Publications.
Hewings, G. J. D., & Syversen, W. M. (1982). A modified bi-proportional method for updating regional input–output matrices; holistic accuracy evaluation. Modeling and Simulation, 13, 1115–1120.
Hirschman, A. (1958). The strategy of economic development. New Haven: Yale University Press.
Israilevich, P. R., Hewings, G. J. D. (1991). Regional trade and regional structure: Implications for the construction of regional input–output models Unpublished manuscript. Regional Economic Application Laboratory (REAL), Urbana, Illinois.
Jackson, R. W. (1986). The ‘full-distribution’ approach to aggregate representation in the input–output modeling framework. Journal of Regional Science, 26, 515–532.
Jackson, R. W., & Hewings, G. J. D. (1984). Structural change in regional economy: An entropy decomposition approach. Modeling and Simulation, 15, 451–455.
Jackson, R., Hewings, G. J. D., & Sonis, M. (1990). Economic structure and coefficient change: a comparative analysis of alternative approaches, Economic Geography, 66, 216–231.
Jackson, R. W., & West, G. R. (1989). Perspectives on probabilistic input–output analysis. In R. Miller, K. Polenske, & A. Rose (Eds.), Frontiers of input–output analysis. London: Oxford University Press.
Jensen, R. C. & West, G. R. (1980). The effect of relative coefficient size in input–output multipliers, Environment and Planning, A 12, 659–670.
Kymm, K. O. (1990). Aggregation in input–output models: A comprehensive review, 1946–71. Economic Systems Research, 2, 65–93.
Lahiri, S. (1976). Input–output analysis with scale-dependent coefficients. Econometrica, 44, 947–962.
Lahiri, S., & Satchell, S. (1986). Properties of the expected value of the leontief inverse: Some further results. Mathematical Social Science, 11, 69–82.
Lawson, T. (1980). A ‘rational modeling’ procedure. Economics of Planning, 16, 105–117.
Leontief, W. (1951). The structure of American economy, 1919–1939, An empirical application of equilibrium analysis. New York: Oxford University Press.
Matuszewski, T. I., Pitts, P. R., & Sawyer, J. A. (1964). Linear programming estimates of changes in input coefficients. Canadian Journal of Economics and Political Science, 30, 203–210.
Miller, R. E., & Blair, P. D. (1985). Input–output analysis: Foundations and extensions. Englewood Hills, N.J: Prentice-Hall.
Morrison, W. I., & Thumann, R. G. (1980). A lagrangian multiplier approach to the solution of a special constrained matrix problem. Journal of Regional Science, 20, 279–292.
Rasmussen, P. (1956). Studies in inter-sectoral relations. Copenhagen: Einar Harks.
Romanoff, E., & Levine, S. H. (1977). Interregional sequential interindustry modeling: A preliminary analysis of regional growth and decline in a two region case. Northeast Regional Science Review, 7, 87–101.
Romanoff, E., & Levine, S. H. (1991). Technical change and regional development: Some further developments with the sequential interindustry Model. In D. E. Boyce, P. Nijkamp, & D. Shefer (Eds.), Regional science: Retrospect and prospect (pp. 251–275). Berlin: Springer.
Sevaldson, P. (1970). The stability of input–output coefficients. In A. P. Carter, & A. Brody (Eds.), Applications of input–output analysis (pp. 207–307). Amsterdam: North Holland.
Shannon, C. E., & Weaver, W. (1964). The mathematical theory of communications urbana, IL: University of Illinois Press.
Sherman, J., & Morrison, W. J. (1949). Adjustment of an inverse matrix corresponding to change in the elements of a given column or a given row of the original matrix. Annals of Mathematical Statistics, 20, 621.
Sherman, J., & Morrison, W. J. (1950). Adjustment of an inverse matrix corresponding to a change in an element of a given matrix. Annals of Mathematical Statistics, 21, 124–127.
Simonovits, A. (1975). A note on the underestimation and overestimation of the leontief inverse, Econometrica, 43, 493–498.
Snower, D. J. (1990). New Methods of updating Input–Output matrices. Economic Systems Research, 2, 27–38.
Sonis, M. (1968). Significance of Entropy measures of homogeneity for the analysis of population redistributions. Geographical Problems. Mathematics in Human Geography, 77, 44–63, (in Russian).
Sonis, M., & Hewings, G. J. D. (1989). Error and sensitivity input–output analysis: A new approach. In R. Miller, K. Polenske, & A. Rose (Eds.), Frontiers in input–output analysis (pp. 232–244). New York: Oxford University Press.
Sonis, M., & Hewings, G. J. D. (1991). Fields of influence and extended input–output analysis: a theoretical account. In J. J. L. I. Dewhurst, G. J. D. Hewings, & R. C. Jensen (Eds.), Regional input–output modeling: New developments and interpretations (pp. 141–158). Aldershot: Avebury.
Sonis, M., & Hewings, G. J. D. (1992). Coefficient change in input–output models: theory and applications. Economic Systems Research, 4, 143–157.
Sonis, M., & Hewings, G. J. D. (1995). Matrix sensitivity, error analysis and internal/external multiregional multipliers. Hitotsubashi Journal of Economics, 36, 61–70.
Sonis, M., & Hewings, G. J. D. (1998a). Theoretical and applied input–output analysis: A new synthesis. Part I: Structure and structural changes in input–output systems. Studies in Regional Science, 27, 233–256.
Sonis, M., Hewings, G. J. D. (1998b). The temporal leontief inverse. Macroeconomic Dynamics, 2, 89–114.
Sonis, M., Hewings, G. J. D., & Guo, J -M. (1997). Comparative analysis of China's metropolitan economies: an input–output perspective. In M. Chatterji, & Y. Kaizhong (Eds.), Regional science in developing countries (pp. 147–162), Basingstoke, England: Macmillan.
Sonis, M., Hewings, G. J. D., & Guo, J -M. (2000). A new image of classical key sector analysis: minimum information decomposition of the leontief inverse. Economic Systems Research, 12, 401–423.
Stevens, B. H., & Trainer, G. A. (1976). The generation of errors in regional input–output impact models. Working Paper, Peace Dale, Rhode Island, Regional Science Institute.
Theil, H. (1957). Economics and information theory. Amsterdam: North Holland.
Theil, H. (1972). Statistical decomposition analysis. Amsterdam: North Holland.
Tilanus, C. B. (1966). Input–output analysis experiments: The Netherlands, 1948–61. Rotterdam: Rotterdam University Press.
West, G. R. (1981). An efficient approach to the estimation of input–output multipliers. Environment and Planning, A, 13, 857–876.
West, G. R. (1982). Sensitivity and key sector analysis in input–output models. Australian Economic Papers, 21, 365–378.
Wibe, S. (1982). The distribution of input coefficients. Economics of Planning, 18, 65–70.
Xu, S., & Madden, M. (1991). The concept of important coefficients in Input–Output models. In J. J. L. I. Dewhurst, G. J. D. Hewings, & R. C. Jensen (Eds.), Regional input–output modeling: New developments and interpretations. Aldershot: Avebury.
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Sonis, M., Hewings, G.J.D. (2009). New Developments in Input-Output Analysis. In: Sonis, M., Hewings, G. (eds) Tool Kits in Regional Science. Advances in Spatial Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00627-2_3
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