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Published online by Cambridge University Press: 11 May 2010
This paper attempts to illustrate some future areas of quantitative historical research which have not yet received the attention we think they deserve. Our interest is primarily in aggregate economic systems. This emphasis is not motivated by a distaste for the analytical tools of microeconomics. On the contrary, a central premise of this paper is that macroeconomic models are ideally deduced from propositions about the behavior of individual decision-making units, and that they also critically depend on rules for the aggregation of such behavioral relationships. In fact, quantitative economic historians have long recognized the critical role played by aggregation rules in historical analysis. And, in the end, it will be the quantitative economic historian who will best be able to evaluate the efficacy of the employment of such rules in specified historical circumstances.
1 Since these “rules” will never be exactly satisfied in any particular historical reference, we may well be required to develop extensive procedures for dealing with their potential acceptance. Efforts along these lines by Professors Basmann, Battalio, and Kagel in the context of production theories should be noted.
2 Our own views on this debate were briefly dealt with in an earlier paper. Cf. Williamson, J. G. and Swanson, J. A., “The Growth of Cities in the American Northeast, 1820–1870,” Explorations in Entrepreneurial History, 2nd Series, IV, No. 1, Sec. 5.Google Scholar The views expressed there and several remarks in the present paper owe much to the earlier papers by Basmann and Hughes. See Basmann, R. L., “The Role of the Economic Historian in the Predictive Testing of Proffered Economic Laws.” Explorations in Entrepreneurial History, 2nd Series, II, No. 3 (1965), pp. 159–186Google Scholar. Hughes, J. R. T., “Fact and Theory in Economic History,” Explorations in Entrepreneurial History, 2nd Series, III, No. 2 (1966), pp. 75–100Google Scholar.
3 Tsiang, S. C., “A Model of Economic Growth in Rostovian Stages,” Econometrica, XXXII, No. 4 (October 1964), pp. 619–648CrossRefGoogle Scholar, and Rostow, W. W., The Stages of Economic Growth (New York: Cambridge University Press, 1960)Google Scholar.
4 Allen C. Kelley, Jeffrey G. Williamson and Russell J. Cheetham, Economic Dualism in Theory and History (in progress).
5 Jeffrey G. Williamson, “Land Augmenting Extensive Development under. Conditions of Factor Immobility: The Development of the American West, 1870–1910,” (May 1970), unpublished. Many ideas in that paper have stemmed from collaborative research on development problems between Professor Williamson and his colleagues Russell Cheetham and Allen Kelley. In particular, the reader may wish to consult Allen C. Kelley, Jeffrey G. Williamson and Russell J. Cheetham, Economic Dualism in Theory and History, Chapters 7 arid 8. Professor Williamson's interest in spatial aspects of growth can be traced to his earlier work “Regional Inequality and the Process of National Development,” Economic Development and Cultural Change, XIII, No. 4, Part II (July 1965), Supplement.Google Scholar
6 The regions of interest are:
“East”-New England and Middle Atlantic,
“West”-East North Central and West North Central.
For most of the period 1870–1910, the Mountain and Pacific states are an unimportant part of the United States economy. Our important exclusion, of course, is the Southern states.
7 Davis, Lance, “The Investment Market, 1870–1914: The Evolution of a National Market,” The Journal of Economic History, XXV (September 1965), p. 356Google Scholar. See also Sylla, Richard, “Federal Policy, Banking Market Structure, and Capital Mobilization in the United States, 1863–1913,” The Journal of Economic History, XXIX (December 1969), p. 657CrossRefGoogle Scholar.
8 See, for example, Hueckel, Glenn, “A Model of the English Economy During the French Wars, 1783–1815,” The University of Wisconsin (August 1970), unpublishedGoogle Scholar
9 This treatment of interregional migration can be found elsewhere in Allen C. Kelley, Jeffrey G. Williamson and Russell J. Cheetham, Economic Dualism in-Theory and History, Chapter 7.
10 Borts, G., “A Theory of Long-Run International Capital Movements,” Journal of Political Economy, LXXII, 4 (August 1964), pp. 341–359CrossRefGoogle Scholar.
11 See the earlier paper by Williamson and Swanson, and Higgs, R., “The Growth of Cities in a Midwestern Region, 1870–1900,” Journal of Regional Science, IX, No. 3 (1969), pp. 369–375CrossRefGoogle Scholar.
12 For a treatment of the former see E. G. Davis and J. A. Swanson, “On the Distribution of City. Growth Rates in a Theory of Regional Economic Growth,” Economic Development and Cultural Change (forthcoming).
13 Arrow, K. J., “Optimal Capital Policy, the Cost of Capital, and Myopic Decision Rules,” Annals of the Institute of Statistical Mathematics, XVI, No. 1–2 (1964), pp. 21–30CrossRefGoogle Scholar; Smith, V. L., Investment and Production (Cambridge: Harvard University Press, 1960)Google Scholar;, and Jorgenson, D. W., “The Theory of. Investment Behavior,” in Ferber, R., editor, The Determinants of. Investment Behavior (New York: Columbia University Press, 1967), pp. 129–155.Google Scholar
14 The present authors have dealt with this problem, in greater detail in “Firm Location and Optimal City Size; in American History,” in L. F. Schnore, editor, The New Urban History: Quantitative Studies at the Frontier (forthcoming).
15 One of these problems relates to the mechanism employed for collecting payments for use of public services. If these services are purchased by the payment of property taxes, the analytics are simplified considerably, and several interesting propositions may be developed as to optimal taxation. A difficulty of greater gravity relates to the: fixed end point of the maximization problem. It is helpful to consider the prices as fixed over the planning interval (O, T). This premise is difficult to handle in the face of (known) “jumps” in such prices. E.g., given such a jump, can the optimal site remain optimal? Several ways of dealing with this problem are suggested: perhaps the. most fruitful of these would be to turn the problem into one of the variable end point” format, while allowing for variable prices within the planning horizon.
16 It is possible that a complete model of urban growth could be advanced by coupling the model described above with the traditional multiplier analysis of urban growth.
17 We cite but a few studies in this vein: Parks, R. W., “Systems of Demand Equations: An Empirical Comparison of Alternative Functional Forms,” Center for Mathematical Studies in Business and Economics Report 6808 (Chicago, 1968)Google Scholar; Basmann, R. L., “Hypothesis Formulation in Quantitative Economics: A Contribution to Demand Analysis,” in Quirk, J. and Zarley, A., editors, Papers in Quantitative Economics (Lawrence: University Press of Kansas, 1968), pp. 143–202Google Scholar. See also the criticism of Professor Friedman's “theory” of consumption expenditures in Zellner, A., “Tests of Some Basic Propositions in the Theory of Consumption,” American Economic Review, L, No. 2 (May 1960), pp. 565–573Google Scholar, for a treatment suggestive of potential work in economic history. Finally, see Cheetham, Russell J., Kelley, Allen C. and Williamson, Jeffrey G., “Consumer Tastes, Engel Effects and Structural Change in a Duaustic Model of Growth,” Social Systems Research Institute, EDIE 7009, The University of Wisconsin (February 1970).Google Scholar