The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Aggregation of Economic Relations

  • Walter D. Fisher
Reference work entry


A simplification or aggregation problem is faced by a research worker whenever he finds that his data are too numerous or in too much detail to be manageable and feels the need to reduce or combine the detailed data in some manner. He will want to use aggregative measures for his new groups. But what will be the effect of this procedure on his results? How can he choose among alternative procedures? In grouping his data and/or relations he must also decide how many groups to use; a smaller number is more manageable but will cause more of the original information to be lost. The research worker seeks a solution of this problem that will best serve his objectives, or those of some decision-marker who will use his results.

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  1. Chipman, J.S. 1975a. The aggregation problem in econometrics. Advances in Applied Probability 7: 72.CrossRefGoogle Scholar
  2. Chipman, J.S. 1975b. Optimal aggregation in large-scale economic models. Sankhya 37(4): 121–159.Google Scholar
  3. Chipman, J.S. 1976. Estimation and aggregation in economics: An application of the theory of generalized inverses. In Generalized inverses and applications, ed. M.Z. Nashed. New York: Academic.Google Scholar
  4. Chipman, J.S. 1985. Testing for reduction of mean-square error by aggregation in dynamic econometric models. In Multivariate analysis VI: Proceedings of the sixth international symposium on multivariate analysis. Amsterdam: North-Holland.Google Scholar
  5. Day, R.H. 1963. On aggregating linear programming models of production. Journal of Farm Economics 45: 797–813.CrossRefGoogle Scholar
  6. Fei, J.C.H. 1956. A fundamental theorem for the aggregation problem of input–output analysis. Econometrica 24(4): 400–412.CrossRefGoogle Scholar
  7. Fisher, W.D. 1953. On a pooling problem from statistical decision viewpoint. Econometrica 21(4): 567–585.CrossRefGoogle Scholar
  8. Fisher, W.D. 1958. Criteria for aggregation in input–output analysis. Review of Economics and Statistics 40(3): 250–260.CrossRefGoogle Scholar
  9. Fisher, W.D. 1962. Optimal aggregation in multi-equation prediction models. Econometrica 30(4): 744–769.CrossRefGoogle Scholar
  10. Fisher, W.D. 1969. Clustering and aggregation in economics. Baltimore: The Johns Hopkins Press.Google Scholar
  11. Fisher, W.D. 1979. A note on aggregation and disaggregation. Econometrica 47(3): 739–746.CrossRefGoogle Scholar
  12. Fisher, W.D., and P.L. Kelley. 1968. Selecting representative firms in linear programming. Ch. 13. In Economic analysis and agricultural policy, ed. R.H. Day. Ames: Iowa State University Press, 1982.Google Scholar
  13. Gorman, W.M. 1968. The structure of utility functions. Review of Economic Studies 35: 367–390.CrossRefGoogle Scholar
  14. Grunfeld, Y., and Z. Griliches. 1960. Is aggregation necessarily bad? Review of Economics and Statistics 42(1): 1–13.CrossRefGoogle Scholar
  15. Hatanaka, M. 1952. Note on consolidation within a Leontief system. Econometrica 20(3): 301–303.CrossRefGoogle Scholar
  16. Hurwicz, L. 1952. Aggregation in macroeconomic models [abstract]. Econometrica 20(3): 489–491.Google Scholar
  17. Ijiri, Y. 1971. Fundamental queries in aggregation theory. Journal of the American Statistical Association 66: 766–782.CrossRefGoogle Scholar
  18. Klein, L.R. 1946. Remarks on the theory of aggregation. Econometrica 14(4): 303–312.CrossRefGoogle Scholar
  19. Laisney, F. 1984. Theory and practice in optimal aggregation of linear models. Economic Letters 15: 315–324.CrossRefGoogle Scholar
  20. Leontief, W. 1947. Introduction to a theory of the internal structure of functional relationships. Econometrica 15(4): 361–373.CrossRefGoogle Scholar
  21. Malinvaud, E. 1956. L’agrégation dans les modéles économiques, Cahiers du Seminaire d’Econométrie, vol. 4. Paris: Centre National de la Recherche Scientifique.Google Scholar
  22. May, K. 1946. The aggregation problem for a one-industry model. Econometrica 14(4): 285–298.CrossRefGoogle Scholar
  23. May, K. 1947. Technological change and aggregation. Econometrica 15(1): 51–63.CrossRefGoogle Scholar
  24. McCarthy, J. 1956. Aggregation in the Leontief model. Joint Allied Social Science Association meeting in Cleveland, Ohio, 27 December.Google Scholar
  25. Nataf, A. 1960. Résultats et directions de recherche dans la théorie de l’agrégation. In Logic, methodology and philosophy of science. Proceedings of the 1960 International Congress, ed. E. Nagel, P. Suppes, and A. Tarski. Stanford: Stanford University Press, 1962.Google Scholar
  26. Neudecker, H. 1970. Aggregation in input–output analysis: An extension of Fisher’s method. Econometrica 38(6): 921–926.CrossRefGoogle Scholar
  27. Ringwald, K. 1980. A critique of models in linear aggregation structures. Boston: Oelgeschlager, Gunn & Hain.Google Scholar
  28. Schneeweiss, H. 1965. Das Aggregationsproblem. Statistische Hefte. doi:10.1007/BF02922284.Google Scholar
  29. Shou Shan Pu. 1946. A note on macroeconomics. Econometrica 14(4): 299–302.CrossRefGoogle Scholar
  30. Skolka, J. 1964. The aggregation problem in input–output analysis. Prague: Czechoslovakian Academy of Sciences.Google Scholar
  31. Sondermann, D. 1973. Optimale Aggregation von grossen linearen Gleichungssystemen. Zeitschrift für Nationalökonomie 33(3–4): 235–250.CrossRefGoogle Scholar
  32. Theil, H. 1954. Linear aggregation of economic relations. Amsterdam: North-Holland.Google Scholar
  33. Theil, H. 1962. Alternative approaches to the aggregation problem. In Logic, methodology and philosophy of science. Proceedings of the 1960 International Congress, ed. E. Nagel, P. Suppes, and A. Tarski. Stanford: Stanford University Press.Google Scholar
  34. Theil, H. 1967. Economics and information theory. Chicago: Rand McNally.Google Scholar
  35. Tintner, G., and D. Sondermann. 1977. Statistical aspects of economic aggregation. In Mathematical economics and game theory, ed. R. Henn and O. Moeschlin. Berlin: Springer.Google Scholar

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Walter D. Fisher
    • 1
  1. 1.