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A continuous Leontief dynamic input-output model

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Papers of the Regional Science Association

Abstract

This paper extends the Leontief dynamic input-output model by incorporating continuous lags, capacity constraints, excess capacity and limits on disinvestment in each sector. These extensions result in “phase changes”, where sectors discretely change from one set of conditions to another. The resulting system of equations is “solved” by numerical methods and applied to the U.S. economy. Projections for the 1952 to 1962 period are compared with actual levels.

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References

  • Allen, R. G. D. 1957.Mathematical economics. London: MacMillan and Company.

    Google Scholar 

  • Allen, R. G. D. 1967.Macro-economic theory: a methematical treatment. London: MacMillan and company.

    Google Scholar 

  • Almon, Clopper. 1963a. Consistent forecasting in a dynamic multi-sector model.Review of Economics and Statistics 45: 148–162.

    Google Scholar 

  • Almon, Clopper. 1963b. Numerical solution of a modified Leontief dynamic system for consistent forecasting or indicative planning.Econometrica 31: 665–678.

    Google Scholar 

  • Almon, Clopper. 1966.The American Economy to 1975, New York: Harper and Row.

    Google Scholar 

  • Bargur, Jona. 1969.A dynamic interregional input-output programming model of the California and western states water economy. California University Resources Center Contribution, No. 128. Berkeley: University of California.

    Google Scholar 

  • Batten, David F. 1980. A note on the estimation of capital structure in a multisectoral economy.Economics of Planning 16: 87–91.

    Google Scholar 

  • Batten, David F. and Andersson, Åke E. 1983. Toward a hierarchical system of models to coordinate national and regional economic development.Papers, Regional Science Association 51: 21–41.

    Google Scholar 

  • Bourque, P. J., Conway, Jr., Richard, and Howard, C. T. 1977.The Washington projection and simulation model. Input-Output Series, University of Washington Graduate School of Business Administration.

  • Bródy, Andras. 1966. A simplified growth model.Quarterly Journal of Economics 80: 137–46.

    Google Scholar 

  • Bródy, Andras. 1970.Proportions, Prices and Planning. Amsterdam: North Holland.

    Google Scholar 

  • Bruno, M., Dougherty, C., and Fraenkel, J. 1970. “Dynamic input-output, trade and development.” InApplications of input-output analysis: proceedings of the fourth international conference on input-output techniques, Geneva, January, 1968, eds. Anne P. Carter and Andrew Brody. Vol. 2, pp. 48–49. Amsterdam: North-Holland.

    Google Scholar 

  • Carlson, John A. 1973. The production lag.The American Economic Review 63: 73–86.

    Google Scholar 

  • Eckaus, Richard S. and Parikh, Kirit S. 1968.Planning for growth: multisectoral, intertemporal models applied to India. Cambridge: M.I.T.

    Google Scholar 

  • Gossling, W. F. 1975. A dynamic model of capital replacement. InCapital coefficients and dynamic input-output models, ed. W.F. Gossling, pp. 36–52. London: Input-Output Publishing Company.

    Google Scholar 

  • Green, M. J. 1975. Investment matrices for the United Kingdom; their structure and use in forecasting. InCapital coefficients and dynamic input-output models, ed. W. F. Gossling, pp. 14–35. London: Input-Output Publishing Company.

    Google Scholar 

  • Hickman, Bert G. 1965.Investment demand and U.S. economic growth. Washington: The Brookings Institution.

    Google Scholar 

  • Holley, J. 1952. A dynamic model.Econometrica 20: 616–642.

    Google Scholar 

  • Holley, J. 1953. A dynamic model: II. Actual model structures and numerical results.Econometrica 21: 298–324.

    Google Scholar 

  • Johansen, Leif. 1978. On the theory of dynamic input-output models with gestation lags and finite lifetime of capital equipment.Journal of Economic Theory 19: 513–33.

    Google Scholar 

  • Kendrick, David. 1972. On the Leontief dynamic inverse.Quarterly Journal of Economics 86: 693–96.

    Google Scholar 

  • Kreiger, R. G. and Neudecker, H. 1976. Kendrick's forward integration model and the dynamic Leontief multisector model.Quarterly Journal of Economics 90: 505–507.

    Google Scholar 

  • Leontief, Wassily. 1936. Quantitative input and output relations in the economic system of the United States.Review of Economics and Statistics 18: 105–25.

    Google Scholar 

  • Leontief, Wassily. 1941.The structure of American economy 1919–1929. Cambridge, Massachusetts: Harvard University Press.

    Google Scholar 

  • Leontief, Wassily. 1953. Dynamic analysis. InStudies in the structure of the American economy: theoretical and empirical explorations inpinput-output analysis, eds. Wassily Leontief, Hollis B. Chenery, Paul G. Clark, James S. Duesenberrry, Allen R. Ferguson, Anne P. Grosse, Robert N. Grosse, Mathilda Holzman, Walter Isard and Helen Kistin, pp. 53–90. New York: Oxford University Press.

    Google Scholar 

  • Leontief, Wassily. 1961a. Lags and the stability of dynamic systems.Econometrica 29, 4:659–669

    Google Scholar 

  • Leontief, Wassily. 1961b. Lags and the stability of dynamic systems: a rejoinder.Econometrica 29, 4: 674–675.

    Google Scholar 

  • Leontief, Wassily. 1966.Input-output economics, New York: Oxford University Press.

    Google Scholar 

  • Leontief, Wassily. 1970. The dynamic inverse. InContributions to input-output analysis: proceedings of the fourth international conference on input-output techniques. Geneva, January, 1968. Vol. 1 pp. 17–46. Amsterdam: North Holland.

    Google Scholar 

  • Livesey, D. A. 1976. A minimal realization of the Leontief dynamic input-output model InAdvances in input-output analysis: proceedings of the sixth international conference on inputoutput techniques, 1974, pp. 527–541. Cambridge, Massachusetts: Ballinger Publishing.

    Google Scholar 

  • McLewin, W. 1975. A transverse model for change of steady growth rate. InCapital coefficients and dynamic input-output models, ed. W. F. Gossling, pp. 16–36. London: Input-Output Publishing Company.

    Google Scholar 

  • Manne, Alan S. and Weisskopf, Thomas E. 1970. A dynamic multisectoral model for India, 1967–76. InApplications of input-output analysis: proceedings of the fourth international conference on input-output techniques. Geneva, January 1968, eds. Anne P. Carter and Andrew Brody, Vol. 2, pp. 70–102. Amsterdam: North-Holland.

    Google Scholar 

  • Menshikov, Stanislav M. 1975 On new uses of dynamic input-output macroeconomic models. InThe Brookings model: perspective and recent developments, eds. Gary Fromm and Lawrence R. Klein, pp. 633–665. Amsterdam: North-Holland Publishing Company.

    Google Scholar 

  • Miernyk, William H. 1970. The West Virginia dynamic model and its implications.Growth and Change 1: 27–32.

    Google Scholar 

  • Miernyk, William H. and Sears, J. T. 1974.Air pollution abatement and regional economic development: an input-output analysis. Lexington, Massachusetts: D. C. Heath.

    Google Scholar 

  • Miernyk, William H., Shellhammer, Kenneth L., Brown, Douglas L., Coccari, Ronald L., Gallagher, Charles J. and Wineman, Wesley H. 1970.Stimulating regional economic development: an interindustry analysis of the West Virginia economy: Lexington: D. C. Heath and Co., pp. 52–74, 164–168.

    Google Scholar 

  • Miller, R. E. 1966. Interregional feedbacks in input-output models: some preliminary results.Papers, Regional Science Association 17: 105–125.

    Google Scholar 

  • Miller, R. E. 1969. Interregional feedback in input-output models: some experimental results.Western Economic Journal 7: 41–50.

    Google Scholar 

  • Moore, F. T. 1955. Regional economic reaction paths.American Economic Review 45: 139–40.

    Google Scholar 

  • Moore, Frederick T. and Petersen, James W. 1955. Regional analysis: an interindustry model of Utah.The Review of Economics and Statistics 37, 4: 368–83.

    Google Scholar 

  • Murakami, Y., Tokoyama, K. and Tsukui, J. 1970. Efficient paths of accumulation and the turnpike of the Japanese economy. InApplications of input-output analysis: proceedings of the fourth international conference on input-output techniques. Geneva, January 1968, eds. Anne P. Carter and Andrew Brody. Amsterdam: North-Holland.

    Google Scholar 

  • Petri, Peter A. 1972. Convergence and temporal structure in the Leontief dynamic model. InInput-output techniques: proceedings of the fifth international conference on input-output techniques. Geneva, January 1971, eds. Andrew Brody and Anne P. Carter, pp. 563–73. Amsterdam: North-Holland.

    Google Scholar 

  • Preston, R. S. 1976. The Wharton long-term model: input-output within the context of a macro forecasting model. InEconometric model performance: comparative simulations of the U.S. economy, eds. Lawrence R. Klein and Edwin Burmeister, pp. 271–287. Philadelphia, University of Pennsylvania Press.

    Google Scholar 

  • Pritsker, A. Alan B. 1974.The GASP IV simulation language. New York: John Wiley and Sons.

    Google Scholar 

  • Sargan, J. D. 1958. The instability of the Leontief dynamic model.Econometrica 26: 381–92.

    Google Scholar 

  • Schinnar, Arie P. 1978. The Leontief dynamic generalized inverse.Quarterly Journal of Economics 92: 641–52.

    Google Scholar 

  • Tsukui, Jinkich and Murakami, Yasusuke. 1979.Turnpike optimality in input-output systems, Amsterdam: North-Holland.

    Google Scholar 

  • Weisskopf, Thomas E. 1971. Alternative patterns of import substitution in India. InStudies in development planning, ed. Hollis B. Chenery, pp. 95–121. Cambridge, Massachusetts: Harvard University Press.

    Google Scholar 

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Johnson, T. A continuous Leontief dynamic input-output model. Papers of the Regional Science Association 56, 177–188 (1985). https://doi.org/10.1007/BF01887911

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