Summary
It was already fairly late in the development of economic theory that aggregation of individual economic relations into macro relations was recognized as a serious problem. This is illustrated in this paper by pointing to the more or less incidental way in which aggregation problems are mentioned and solved in the older literature till the famous Econometrica debate in the late forties. In particular, we try to disentangle the notions of consistency and representativity.
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References
S.N. Afriat, “The Construction of a Utility Function from Expenditure Data,” International Economic Review, 8 (1967) , pp.67–77.
S.N. Afriat, “On a System of Inequalities in Demand Analysis: An Extension of the Classical Method,” International Economic Review, 14 (1973), pp.460–472.
S.N. Afriat, The Price Index, Cambridge (U.K.): Cambridge University Press, 1977.
R.G.D. Allen, Mathematical Economics, second edition, London: MacMillan, 1964.
R.G.D. Allen, Macro Economic Theory, London: MacMillan, 1967.
G.B. Antonelli, Sulla Teoria Matematica della Economia Politica, Pisa: Nella Tipografia del Folchetto, 1886.
K.J. Arrow, Social Choice and Individual Values, second edition, New York: Wiley, 1963.
W.A. Barnett, Consumer Demand and Labor Supply, Amsterdam: North-Holland, 1981.
C. Blackorby, D. Primont and R.R. Russell, Duality, Separability and Functional Structure, Amsterdam: North-Holland Publishing Company, 1978.
M. Blaug, Economic Theory in Retrospect, third edition, Cambridge (U.K.) : Cambridge University Press, 1978.
A.L. Bowley, “Notes on Index Numbers,” Economic Journal, 38 (1928), pp. 216–237.
W.H. Branson and A.K. Klevorick, “Money Illusion and the Aggregate Consumption Function,” American Economic Review, 59 (1969), pp.832–849.
J.C. Burkill and H. Burkill, A Second Course in Mathematical Analysis, Cambridge (U.K.) : Cambridge University Press, 1970.
E. Burmeister and A.R. Dobell, Mathematical Theories of Economic Growth, New York: The Macmillan Company, 1970.
F. Cajori, A History of Mathematics, third edition, New York: Chelsea, 1980.
L.R. Christensen, D.W. Jorgenson and L.J. Lau, “Transcendental Logarithmic Utility Functions,” American Economic Review, 65 (1975) , pp.367–383.
C.W. Cobb and P.H. Douglas, “A Theory of Production,” The American Economic Review, 18 (1928), Supplement, pp.139–165.
A. Cournot, Recherches sur les Principes Mathématiques de la Théorie des Richesses, Paris: Hachette, 1838 (reprint, Paris: Marcel Riviére & Cie, 1938).
J. van Daal, “Money Illusion and Aggregation Bias,” De Economist, 128 (1980) , pp.86–93.
J. van Daal and A.H.Q.M. Merkies, “A Simple Proof of Nataf’s Theorem on Consistent Aggregation,” Economics Letters, 7 (1981), pp.441–446.
J. van Daal and A.H.Q.M. Merkies, Aggregation in Economic Research, Dordrecht/Boston: Reidel, 1984.
J. van Daal, R.E.D. Henderiks and A.C.F. Vorst, “On Walras’ Model of General Economic Equilibrium,” Zeitschrift für Nationalökonomie, 45 (1985), pp.219–244.
J. van Daal and D.A. Walker, “The problem of Aggregation in Walrasian General Equilibrium Theory,” Report 8701/A, Econometric Institute, Erasmus University Rotterdam, 1987.
F. Divisia, “L’indice Monétaire et la Theorie de la Monnaie,” Revue d’Economie Politique, 29 (1925), pp.842–861, 980–1008, 1121–1151 and 30 (1926), pp. 49–81.
F. Divisia, Economie Rationelle, Paris: Dunod, 1928.
F.W. Dresch, “Index Numbers and the General Economic Equilibrium,” Bulletin of the Amma erican thematical Society, 44 (1938), pp.134–141.
W. Driehuis, Fluctuations and Growth in a Near Full Employment Economy; A Quarterly Econometric Analysis of the Netherlands, Rotterdam: Rotterdam University Press, 1972.
F.Y. Edgeworth, Mathematical Psychics, London: C. Kegan Paul & Co., 1881.
B. Eisenberg, “Aggregation of Utility Functions,” Management Science, 7 (1961), pp. 337–350
I. Fisher, Mathematical Investigation in the Theory of Value and Prices (1892), reprint, New Haven: Yale University Press, 1925.
I. Fisher, The Purchasing Power of Money, New York: MacMillan, 1912.
I. Fisher, The Making of Index Numbers, Boston: Houghton Miffin, 1922.
R. Frisch, “Annual Survey of General Economic Theory: The Problem of Index Numbers,” Econometrica, 4 (1936), pp.1–39.
W.M. Gorman, “Community Preference Fields,” Econometrica, 21 (1953), pp. 63–80.
W.M. Gorman, “The Structure of Utility Functions,” Review of Economic Studies, 35 (1968), pp.367–390.
H.A.J. Green, Aggregation in Economic Analysis, Princeton: Princeton University Press, 1964.
H. den Hartog and H.S. Tjan, “A Clay-Clay Vintage Model Approach for Sectors of Industry in the Netherlands,” De Economist, 128 (1980), pp.129–188.
J.R. Hicks, Value and Capital, second edition, Oxford: Clarendon Press, 1946.
J.R. Hicks, A Revision of Demand Theory, Oxford: Clarendon Press, 1956.
W. Hildenbrand, “On the ’Law of Demand’,” Econometrica, 51 (1983) , pp.997–1020.
W. Jaffe, ed., Correspondence of Leon Walras and Related Papers, 3 vols., Amsterdam: North-Holland, 1965.
W.S. Jevons, Principles of Science, second edition (1877), reprint, London: MacMillan, 1913.
W.S. Jevons, The Theory of Political Economy, second edition (1879) , reprinted in Pelican Books, Harmondsworth: Penguin Books Ltd, 1970.
D.W. Jorgenson, L.J. Lau and T.M. Stoker, “The Transcendental Logarithmic Model of Consumer Behaviour.” Advances in Economics. 1(1982) . pp. 97–238.
L.R. Klein, “Macroeconomics and the Theory of Rational Behavior,” Econometrica, 15 (1946), pp.93–l08.
L.R. Klein, “Remarks on the Theory of Aggregation,” Econometrica, 15 (1946), pp.303–313.
L.R. Klein, Economic Fluctuations in the United States, 1921–1941, New York: Wiley, 1950.
A.A. Konüis, “The Problem of the True Index of the Cost of Living,” translated from Russian (1924), Econometrica, 7 (1939), pp.10–29.
W.W. Leontief, “Composite Commodities and the Problem of Index Numbers,” Econometrica, 4 (1936), pp.39–59.
W.W. Leontief, “Introduction to a Theory of the Internal Structure of Functional Relationships,” Econometrica, 15 (1947), pp.361–373.
A. Lindbeck, “The Price in Economics Science in Memory of Alfred Nobel,” Journal of Economic Literature, 23 (1985), pp.37–56.
K.T. Mak, “On Separability: Functional Structure,” Journal of Economic Theory, 40 (1986), pp. 150–282.
J.A.H. Maks, Empirical Preference Orderings and Applied Demand Analysis, doctor’s thesis, University of Groningen, 1980.
A. Marshall, Principles of Economics, 8th edition, London: MacMillan, 1920.
K. May, “The Aggregation Problem fora One-Industry Model,” Econometrica, 15 (1946) , pp.285–298.
K. May, “Technological Change and Aggregation,” Econometrica, 16 (1947) , pp.51–63.
J. Muellbauer, “Aggregation, Income Distribution and Consumer Demand,” Review of Economic Studies, 62 (1975). pp.525–543.
J. Muellbauer, “Community Preferences and the Representative Consumer,” Econometrica, 44 (1976), pp.979–1000.
A. Nataf, “Sur la Possibilité de Construction de Certains Macromodèles,” Econometrica, 17 (1948). pp.232–244.
V. Pareto, Cours d’ Economie Politique, 2 vols., Lausanne: F. Rouge, 1896–7.
V. Pareto, Manuel d’Economie Politique, Paris: Pichon et Durand-Auzias, 1909.
V. Pareto, “Economie Mathématique,” dans Encyclopédie des sciences mathématiques, Paris: Gauthier-Villars, 1911, t.I, vol. IV, fasc. IV, pp.591–640.
I.F. Pearce, A Contribution to Demand Analysis, Oxford: Clarendon Press, 1964.
L. Philips, Applied Consumption Analysis, second edition, Amsterdam: North-Holland, 1983.
A.C. Pigou, The Economics of Welfare, fourth edition, Lonon: MacMillan, 1938.
F. Pokropp, Aggregation von Produktionsfunctionen, Berlin: Springer, 1972.
S.S. Pu, “A Note on Macroeconomics,” Econometrica 15 (1946), pp.299–302.
F. Quesnay, Tableau Economique, reprint of the third edition (1759), edited by M. Kuczynski, Berlin: Akademie-Verlag, 1965.
D. Ricardo, The Princiles of Political Econom and Taxation, 3rd edition (1821) , reprinted in Everyman’s Library, London: Dent, 1973.
U. E. Roll, A History of Economic Thought, New and revised edition, London: Faber and Faber, 1973.
E. Schlicht, Isolation and aggregation in Economics, Berlin/Heidelberg: Springer, 1985.
J.A. Schumpeter, History of Economic Analysis, London: George Allen & Unwin Ltd, 1954.
W. Shafer and H. Sonnenschein, “Market Demand and Excess Demand Functions,” chapter 14 of K.J. Arrow and M.D. Intriligator (eds.), Handbook of Mathematical Economics, Amsterdam: North-Holland Publishing Company, 1982.
R.M. Solow, “Technical Progress and Productivity Change,” Review of economics ana Statistics, 39 (1957) , pp. 312–320.
W.H. Somermeyer and R. Bannink, A Consumption-Savings Model and its Applications, Amsterdam: North-Holland, 1972.
W.H. Somermeyer and J. van Daal, “Consistent Aggregation — An Alternative Derivation and a Generalization of Nataf’s Theorem,” Zeitschrift für Nationalökonomie, 38 (1978) , pp. 287–303.
M. Sono, “The Effect of Price Changes on the Demand and Supply of Separable Goods,” International Economic Review, 2 (1961), pp. 239–271.
H. Theil, Linear Aggregation of Economic Relations, Amsterdam: North-Holland, 1954.
H. Theil, Theory and Measurement of Consumer Demand, Volume I, Amsterdam: North-Holland. 1975.
R. Theocharis, Early Developments in Mathematical Economics, second edition, London and Basinkstoke: MacMillan, 1983.
J. Tinbergen, “An Economic Policy for 1936,” translated from Dutch (1936) in Selected Papers, edited by L.H. Klaassen, L.M. Koyck and H.J. Witteveen, Amsterdam: North-Holland, 1959, pp.37–84.
J. Tinbergen, Statistical Testing of Business-Cycle Theory, vol. I and II, Geneva: League of Nations, 1939.
H.R. Varian, “The Nonparametric Approach to Demand Analysis,” Econometrics, 50 (1982), pp.945–974.
L. Walras, Elements d’Economie Politique Pure ou Théorie de la Rlchesse Sociale, edition definitive, Paris: Pichon et Durand-Auzias, 1926. (First edition 1874–1877, second edition 1889, third edition 1896, fourth edition 1900, English translation (by W. Jaffe) 1954).
E.R. Weintraub, General Equilibrium Analysis: Studies in Appraisal, Cambridge: Cambridge University Press, 1985.
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van Daal, J., Merkies, A.H.Q.M. (1988). The Problem of Aggregation of Individual Economic Relations; Consistency and Representativity in a Historical Perspective. In: Eichhorn, W. (eds) Measurement in Economics. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-52481-3_41
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DOI: https://doi.org/10.1007/978-3-642-52481-3_41
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