This study of American manufacturing was conducted under grants from the National Science Foundation. Additional financial support was provided by the Indiana University Graduate School of Business and by the University of Kansas General Research Fund. Jeremy Atack provided considerable research assistance as well as valuable comments, particularly on the section dealing with economies of scale.

¹ The authors will provide the references for each of these hypotheses to interested readers.

² See Bateman, Fred, Foust, James and Weiss, Thomas, “The Participation of Planters in Manufacturing in the Antebellum South,” Agricultural History, XLVIII (April 1974), 277–98Google Scholar and “Profitability in Southern Manufacturing: Estimates for 1860,” Explorations in Economic History (forthcoming). Also see Bateman, Fred and Weiss, Thomas, “Profitability and Industrialization in the Antebellum Southern Economy,” paper presented at the Annual Meeting of the Southern Historical Association, November 1974 (mimeo).Google Scholar

³ Two separate data samples underlie this study. One includes the twenty largest firms (based on output) in each state and the other is a random sample of individual producers selected from the census manuscripts for all states.

⁴ Parker, W. N., “Slavery and Economic Development: An Hypothesis and Some Evidence,” Agricultural History, XLIV (January 1970), 117.Google Scholar

⁵ Our computations include more southern states than do Parker's, including those of the upper South, a fact that enhances the region's relative position.

⁶ Robert Fogel's comment on Eugene Genovese's version of the economies of scale argument as it relates to regional industrial development exemplifies some of the criticism of the conceptual basis of this view. Fogel, Robert W., “The Specification Problem in Economic History,” The Journal of Economic History, XXVII (September 1967), 283–308.CrossRefGoogle Scholar

⁷ The problems are discussed in Walters, A. A., “Production and Cost Functions: An Econometric Survey,” Econometrica, XXXI (January-April 1963), 1–66.CrossRefGoogle Scholar

⁸ See Ibid., and Nerlove, M., Estimation and Identification of Cobb-Douglas Production Functions (New York: Random House, Inc., 1965)Google Scholar, for an examination of these problems as they relate directly to the present form of the estimating equation. Value rather than physical quantity data were used for our analysis, an approach that clouds the distinction between economies of scale and of size, as discussed in Maxwell, W. D., Price Theory and its Applications in Business Administration (Pacific Palisades, California: Goodyear Publishing Co., Inc., 1970), pp. 132–134.Google Scholar

⁹ For example, with the assumption that firms maximized expected profits, ordinary least squares estimates of the output elasticities of capital and labor are neither biased nor inconsistent. See Kmenta, J., Zellner, A. and Dreze, J., “Specification and Estimation of Cobb-Douglas Production Function Models,” Econometrica, XXXIV (October 1966), 784–95.Google Scholar

¹⁰ Two dissertations currently underway should substantially improve upon the present estimates. Jeremy Atack, “Estimation of Economies of Scale in Antebellum U.S. Manufacturing” (dissertation in progress, Indiana University) and Howard Reese, “Estimation and Identification of a Variable Scale Parameter Production Function” (dissertation in progress, University of Kansas).

¹¹ The Cobb-Douglas (CD) function is of the form V = AL^αK^β, where V = value added, K = capital services, L = labor services, A = index of efficiency, α = elasticity of output with respect to labor services, β = elasticity of output with respect to capital services. Unlike the constant elasticity of substitution (CES) production function, the Cobb-Douglas assumes a unitary elasticity of substitution. Purely competitive product and factor market conditions, and profit maximizing behavior are assumed.

Two CD forms were estimated:

1. (1)

   (1)

2. (2)

   (2) log where i = 1 … n over firms within each industry; j = 1,…., 104 over industries; and k = 1,…., 16 over the states. Equation (1) provides direct estimates of α and β and their significance and Equation (2) provides a convenient estimate of the economies of scale and their significance since h = α + β −; 1 is the estimate of the degree of homogeneity of the production function.

¹² Creamer, D., Capital in Manufacturing and Mining (Princeton: Princeton University Press, 1960), pp. 12–14CrossRefGoogle Scholar and Easterlin, Richard in Population Redistribution and Economic Growth, Lee, Everett S., ed. (Philadelphia: American Philosophical Society, 1957), pp. 676–78.Google Scholar

¹³ Superficially there is little to recommend our capital estimates on either theoretical or empirical grounds. However, Griliches determined that use of gross book value of capital as an alternative measure of capital services for his estimates gave similar but somewhat inferior results. Z. Griliches, “Production Functions in Manufacturing: Some Preliminary Results,” in M. Brown, ed., The Theory and Empirical Analysis of Production (New York: National Bureau of Economic Research), Studies in Income and Wealth, Vol. 31, pp. 280–81.

¹⁴ Griliches estimated for 1958 that a 10 percent increase in inputs would result in a 10.5 percent increase in output, i.e., the coefficient, h, was of the order .05. Ibid., p. 298.

¹⁵ While least squares estimates may not identify the true production function, they can still have useful predictive value (see Walters, “Production and Cost Functions”). In the present case, they predict that for the South an increase in both capital and labor would produce a proportionately larger increase in output, implying that the region's manufacturing sector could have been more competitive than it was.

¹⁶ See, for example, Davis, Lance and Stettler, H. Louis, “The New England Textile Industry, 1825–1860: Fluctuations and Trends,” in Output, Employment and Productivity in the United States After 1800 (New York: National Bureau of Economic Research, 1966), pp. 213–238.Google Scholar

¹⁷ Evidence indicates that rates of return were higher in the South than in the West, so that the impact of this technical efficiency factor may be exaggerated. However, investors quite reasonably may have considered the existence of the efficiency sources (e.g., availability of raw materials) as more important than a marginally higher profit rate and so have chosen the West over the South. Profit estimates are shown in Bateman and Weiss, “Profitability and Industrialization.”

¹⁸ See the work of Diane L. Lindstrom, “Demand, Markets and Eastern Economic Development: Philadelphia, 1815–1840,” and Herbst, Lawrence A., “Interregional Commodity Trade from the West to the South, and American Economic Development in the Antebellum Period,” dissertation summaries presented at the Thirty-Fifth Annual Meeting of the Economic History Association, Philadelphia, 1974 (infra, pp. 271 and 264).Google Scholar

¹⁹ These are obviously only lower bounds of the representation since the remaining industries were among the most important of the antebellum period. More than threequarters of New England's 1860 output value, for example, was accounted for by these industries.

²⁰ Even today, the assumption of state, local or regional markets is used by the Census Bureau for a wide variety of products, including sawmilling, meat slaughtering, malt liquor, wooden furniture, milk, bread, and concrete and brick. Industries supplying local or regional markets produced about twenty-five percent of all U.S. manufactured value added in 1963. All told, some fifty-four industries are assumed to serve predominantly a regional market and eleven to supply local ones. See U.S. Bureau of the Census, Concentration Ratios in Manufacturing Industry, 1963, Part II, Prepared by the Bureau of the Census for the Subcommittee on Antitrust and Monopoly of the Committee on the Judiciary, United States Senate, 90th Congress, 1st Session; 1967, Tables 25–26. Also see Schwartzman, David and Bodoff, Joan, “Concentration in Regional and Local Industries,” The Southern Economic Journal, XXXVII (January 1971), 343–48.CrossRefGoogle Scholar In his study of manufacturing, Niemi's calculations are consistent with the position that markets for most industrial goods were geographically small. Only textiles among the important industries in any region appear to have been traded widely in interregional markets in 1860. Outside a few states in the Northeast and only for a few products there, there was similarly little apparent trade across states. While Niemi warns that his calculations are only approximate and to be interpreted cautiously, they do reinforce our general view that the state defined the geographic market for most manufactured goods. Niemi, Albert W. Jr, State and Regional Patterns in American Manufacturing, 1860–1910 (Westport, Conn, and London, England: Greenwood Press, 1974).Google Scholar

²¹ The profit rates were calculated as described in the two papers on profitability cited in footnote 2.