Revisiting Miyazawa on Multisectoral Multipliers

  • Yoshio Kimura
  • Hitoshi Kondo
Part of the Advances in Spatial Science book series (ADVSPATIAL)


It was slightly more than thirty years ago that Miyazawa published his pioneering article on the theoretical and empirical analysis of the interindustry multipliers in an open Leontief model involving a foreign trade sector (Miyazawa, 1960). Notwithstanding the time that has elapsed since then, theoretical and empirical papers on multisectoral- and/or interindustry- multipliers, are still growing in various fields of economics and particularly, in regional science, studies focused on matrix multipliers in connection with multiregional input-output models are still prominent. This evidence suggests that Miyazawa, through a series of his papers on multisectoral multiplier analysis1 has not only exerted a wide and strong intellectual influence on the direction of research thereafter, but also laid a firm foundation of our present studies concerning matrix multipliers. Therefore, a revisitation of Miyazawa’s numerous contributions, in particular, that of Miyazawa (1976), which is undoubtedly the most prominent of his publications, is of some value at least as way of reminding ourselves just how far the research has progressed from such an important base.


Multiplier Decomposition Input Coefficient Convergent Speed Matrix Multiplier Nonempty Proper Subset 
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  1. Batey, P.W.J. 1985. “Input-output models for regional demographic-economic analysis: some structural comparisons.” Environment and Planning A, 17, 73–99.CrossRefGoogle Scholar
  2. Hewings, G.J.D., J. Merrifield and J. Schneider. 1984. “A regional test of the linkage hypothesis.” Revue d’economie Regional et Urbaine, 25, 275–290.Google Scholar
  3. Kemp, M.C., and Y. Kimura, 1978. Introduction to Mathematical Economics, Berlin, Springer-Verlag.CrossRefGoogle Scholar
  4. Kimura, Y., and H. Kondo, 1990. “Multiplier decomposition and nonnegativity of Leontief inverse.” Studies in Regional Science, 20, 62–71.CrossRefGoogle Scholar
  5. Lancaster, P. 1969. Theory of Matrices, N.Y., Academic Press.Google Scholar
  6. Miyazawa, K. 1960. “Foreign trade multiplier, input-output analysis and the consumption function.” Quarterly Journal of Economics, 74, 53–64.CrossRefGoogle Scholar
  7. Miyazawa, K. 1966. “Internal and external matrix multipliers in the input-output model.” Hitotsubashi Journal of Economics, 7, 38–55.Google Scholar
  8. Miyazawa, K. 1968. “Input-output analysis and interregional income multiplier as a matrix.” Hitotsubashi Journal of Economics, 8, 39–58.Google Scholar
  9. Miyazawa, K. 1971. “An analysis of interdependence between service and goods-producing sectors.” Hitotsubashi Journal of Economics, 12, 10–21.Google Scholar
  10. Miyazawa, K. 1976. Input-Output Analysis and the Structure of Income Distribution. Lecture Notes in Economics and Mathematical Systems 116, Berlin, Springer-Verlag.Google Scholar
  11. Miyazawa, K., and S. Masegi. 1963. “Interindustry analysis and the structure of income distribution.” Metroeconomica, 15, 89–103.CrossRefGoogle Scholar
  12. Morishima, M., and Y. Kaneko. 1962. “On the speed of establishing multisectoral equilibrium.” Econometrica, 30, 818–823.CrossRefGoogle Scholar
  13. Robinson, S., and A. Markandya. 1973. “Complexity and adjustment in input-output systems.” Oxford Bulletin of Economics and Statistics, 35, 119–134.CrossRefGoogle Scholar
  14. Shinohara, M., K. Miyazawa, and M. Mizuno. 1959. An Extension of the Theory of Income Multiplier (in Japanese). Tokyo, Yuhikaku.Google Scholar
  15. Sonis, M., and G.J.D. Hewings, 1993. “Hierarchies of regional sub-structures and their multipliers within input-output systems: Miyazawa revisited.” Hitotsubashi Journal of Economics, 34, 33–44.Google Scholar
  16. Sonis, M., and G.J.D. Hewings. 1995. “Matrix sensitivity, error analysis and internal/external multiregional multipliers.” Hitotsubashi Journal of Economics, 36, 6170.Google Scholar
  17. Trigg, A., and M. Madden. 1990. “The partition and decomposition of extended inputoutput multipliers.” in L. Ansclin and M. Madden eds. New Directions in Regional Analysis: Integrated and Multi-regional Approach. London, Belhaven Press.Google Scholar
  18. Waugh, F.V. 1950. “Inversion of the Leontief matrix by power series.” Econometrica, 18, 142–154.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Yoshio Kimura
    • 1
  • Hitoshi Kondo
    • 2
  1. 1.Faculty of EconomicsChukyo UniversityNagoyaJapan
  2. 2.Faculty of EconomicsNanzan UniversityNagoyaJapan

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