¹ Adelman, Morris A., “The Measurement of Industrial Concentration,” Review of Economics and Statistics, 33 (11 1951), 269–96;CrossRefGoogle ScholarScherer, Frederic M., Industrial Market Structure and Economic Performance, 2nd ed. (Chicago, 1980), pp. 67–70;Google ScholarNutter, G. Warren and Einhorn, Henry, Enterprise Monopoly in the United States: 1899–1958 (New York, 1969), pp. 130–46.Google Scholar

² See, for example, Beard, Charles, The Rise of American Civilization, Vol. 2 (New York, 1933);Google ScholarHiggs, Robert, The Transformation of the American Economy (New York, 1971), pp. 39–47;Google ScholarPorter, Glenn, The Rise of Big Business, 1860–1910 (New York, 1973).Google Scholar

³ Beard, , Rise of American Civilization, p. 198.Google Scholar

⁴ See Hacker, Louis, The Triumph of American Capitalism (New York, 1940);Google ScholarKirkland, Edward, Industry Comes of Age (New York, 1961);Google ScholarChandler, Alfred, Strategy and Structure: Chapters in the History of the Industrial Enterprise (Cambridge, Massachusetts, 1962);Google ScholarDavis, Lance and North, Douglass, Institutional Change and American Economic Growth (Cambridge, 1971);CrossRefGoogle ScholarHiggs, , Transformation, Porter, Rise of Big Business.Google Scholar

⁵ Chandler, Alfred, The Visible Hand: The Managerial Revolution in American Business (Cambridge, Massachusetts, 1977), pp. 8, 337.Google Scholar

⁶ One exception to this generalization is Cain and Paterson's study of biased technical change in U.S. manufacturing over the late nineteenth century. Since they assume a constant returns to scale specification, however, there is no link between technical change and change in industry structure. Cain, Louis and Paterson, Donald, “Factor Biases and Technical Change in Manufacturing: The American System, 1850–1919,” this JOURNAL, 41 (06 1981), 341–60Google Scholar. For a somewhat later period, see Phillips, Almarin, “Concentration, Scale, and Technological Change in Selected Manufacturing Industries, 1899–1939,” Journal of Industrial Economics, 4 (06 1956), 179–93.CrossRefGoogle Scholar

⁷ In the Hicksian sense labor-saving technical progress implies a rise in the ratio of the marginal product of capital to the marginal product of labor over time with the capital-labor ratio being held constant.Google Scholar

⁸ Nelson, Ralph, Merger Movements in American Industry, 1895–1956 (Princeton, 1951), pp. 103–104.Google Scholar

⁹ For detailed discussions of technical innovations in many industries over the period see Clark, Victor, History of Manufactures in the United States, Vol. 2 (New York, 1929);Google ScholarStrassman, W. Paul, Risk and Technological Innovation (Ithaca, New York, 1951);Google Scholar and for a few selected industries such as iron and steel, cotton textiles, or woolens, U.S. Census Office, Tenth Census of the United States, Report on Manufactures, Vol. 11 (Washington, D.C., 1883).Google Scholar

¹⁰ See Clark, , History of Manufactures; Davis and North, Institutional Change;Google ScholarTemin, Peter, Iron and Steel in Nineteenth-Century America (Cambridge, Massachusetts, 1964).Google Scholar

¹¹ Williamson, Jeffrey, “Watersheds and Turning Points: Conjectures on the Long-Term Impact of Civil War Financing,” this JOURNAL, 34 (09 1974), 652–65;Google ScholarDavid, Paul, “Invention and Accumulation in America's Economic Growth: A Nineteenth Century Parable,” in International Organization, National Policies and Economic Development, Carnegie-Rochester Conference Series on Public Policy, Vol. 6, pp. 179–240.Google Scholar

¹² Williamson, , “Watersheds and Turning Points,” p. 653.Google Scholar

¹³ See the discussion in Chandler, , The Visible Hand, pp. 240–83.Google Scholar

¹⁴ See Humphrey, David and Moroney, John, “Substitution among Capital, Labor, and Natural Resource Products in American Manufacturing,” Journal of Political Economy, 83 (02 1975), p. 64.CrossRefGoogle Scholar

¹⁵ Schmitz, Mark, “The Elasticity of Substitution in 19th-Century Manufacturing,” Explorations in Economic History, 18 (07 1981), 290–303.CrossRefGoogle Scholar

¹⁶ Atack, Jeremy, “Returns to Scale in Antebellum United States Manufacturing,” Explorations in Economic History, 14 (10 1977), p. 353.CrossRefGoogle Scholar

¹⁷ As a result, the presence of transport costs could drastically alter the optimal national concentration level in an industry. For example, with a minimum efficient firm size of $4,000,000 value added in flour and meal in 1890 the industry could have supported 26 efficient firms, quite a different picture than natural monopoly. The last column in Table 5 then representing an upper bound to optimal firm size most probably implies an overstatement of market concentration levels dictated by shifts in minimum efficient firm size.Google Scholar

¹⁸ In the South in 1850 and 1860 such industries as men's clothing, cotton goods, and woolen goods, generally regarded as having been relatively unconcentrated and competitive, were also quite concentrated at the state level. Bateman, Fred and Weiss, Thomas, A Deplorable Scarcity: The Failure of Industrialization in the Slave Economy (Chapel Hill, North Carolina, 1981), p. 148.Google Scholar

¹⁹ It perhaps may be possible to simulate the effects of falling transportation costs on market size if industry demand curves could be estimated and used in conjunction with the reported estimated production functions.Google Scholar

²⁰ Of course, the brick market was much closer to a local one than to a national one. In fact, however, the average firm in 1890 was very close to the calculated optimal size. The relationship between average firm size and optimal size appeared to differ between the concentrated and unconcentrated industries group. With the exception of chemicals, where the average firm in 1890 was well into the range of decreasing returns to scale, meatpacking, soap, and machinery, industries in the moderately concentrated and concentrated groups, showed average firm sizes in 1890 substantially less than optimal size. On the other band, in the unconcentrated groups, with the exception of bricks and tiles and printing and publishing, where average firm size and optimal size were close, all industries showed average firm size greater than optimal size, that is, the average firm was operating in the range of decreasing returns to scale.Google Scholar

²¹ For such a decomposition one must assume that the factor-augmenting technical change is exogenous. If the falling relative price of capital, however, induced capital-deepening technical change, then such a separation would not be possible. David, for example, argues that the increased rate of capital accumulation over the last half of the nineteenth century resulted primarily from an upward shift in the real demand for investment. This shift in turn was caused by capitaldeepening technical progress over the century which lowered the relative price of capital goods. David, “Invention and Accumulation.”Google Scholar

²² Chandler, , The Visible Hand, pp. 240–83; Cain and Paterson, “Factor Biases and Technical Change.”Google Scholar

²³ Stigler, George, “Monopoly and Oligopoly by Merger,” American Economic Review, Papers and Proceedings, 40 (05 1950), 23–34.Google Scholar

²⁴ Scherer, , Industrial Market Structure, p. 96;Google ScholarBain, Joe, “Economies of Scale, Concentration and the Condition of Entry in Twenty Manufacturing Industries,” American Economic Review, 44 (03 1954), 15–39.Google Scholar

²⁵ David, , “Invention and Accumulation,” pp. 185–87.Google Scholar

²⁶ Nutter, and Einhorn, , Enterprise Monopoly, pp. 131–39.Google Scholar

²⁷ Chandler, , The Visible Hand, pp. 253–58; Nelson, Merger Movements, pp. 47, 161; Nutter and Einhorn, Enterprise Monopoly, p. 133.Google Scholar

²⁸ Chandler, , The Visible Hand, pp. 250–53; Clark, History of Manufactures, pp. 504–505.Google Scholar

²⁹ Chandler, , The Visible Hand, pp. 300–01; Clark, History of Manufactures, pp. 506–507; Nutter and Einhorn, Enterprise Monopoly, p. 132.Google Scholar

³⁰ Beard, , Rise of American Civilization, p. 175.Google Scholar

³¹ Nelson, , Merger Movements, pp. 47–48; Chandler, The Visible Hand, p. 269.Google Scholar

³² Temin, , Iron and Steel, p. 157;Google ScholarBerck, Peter, “Hard Driving and Efficiency: Iron Production in 1890,” this JOURNAL, 38 (12 1978), 879–900.Google Scholar

³³ Strassman, , Risk and Technological Innovation, p. 48; Temin, Iron and Steel, p. 165.Google Scholar

³⁴ Chandler, , The Visible Hand, p. 250.Google Scholar

³⁵ Nutter, and Einhorn, Enterprise Monopoly, pp. 134, 136; Nelson, Merger Movements, p. 52.Google Scholar

³⁶ Clark, , History of Manufactures, pp. 358–64, 524;Google ScholarRosenberg, Nathan, Perspectives on Technology (Cambridge, 1976), pp. 9–31;CrossRefGoogle ScholarChandler, , The Visible Hand, p. 256.Google Scholar

³⁷ Clark, , History of Manufactures, p. 463; Chandler, The Visible Hand, p. 334.Google Scholar

³⁸ Nelson, , Merger Movements, p. 45; Nutter and Einhorn, Enterprise Monopoly, p. 133.Google Scholar

³⁹ Ibid.; Clark, History of Manufactures, p. 418.

⁴⁰ Nelson, , Merger Movements, p. 45; Clark, History of Manufactures, pp. 482–483.Google Scholar

⁴¹ Nelson, , Merger Movements, p. 52; Chandler, The Visible Hand, pp. 337–344.Google Scholar

⁴² Ibid., p. 247.

⁴³ See, for example, Christensen, Laurits, Jorgensen, Dale, and Lau, Lawrence, “Transcendental Logarithmic Production Frontiers,” Review of Economics and Statistics, 55 (02 1973), 28–45;CrossRefGoogle ScholarBerndt, Ernst and Christensen, Laurits, “The Translog Function and the Substitution of Equipment, Structures, and Labor in U. S. Manufacturing, 1929–1968,” Journal of Econometrics, 1 (03 1973), 81–113;CrossRefGoogle ScholarHumphrey, and Moroney, “Substitution among Capital, Labor, and Natural Resource Products.”Google Scholar

⁴⁴ Cain and Paterson do in fact estimate industry translog cost functions over this period by constructing a price of capital services variables which assumes a rental rate, given by the New England municipal bond yield, constant across the country. In fact, over much of this period there were significant imperfections in the capital market as evidenced by the great geographical variation in local interest rates. Cain, and Paterson, “Factor Biases and Technical Change”;Google ScholarDavis, Lance, “The Investment Market, 1870–1914: The Evolution of a National Market,” this JOURNAL, 25 (09 1965), 355–99;Google ScholarJames, John A., Money and Capital Markets in Posibellum America (Princeton, 1978).Google Scholar

⁴⁵ Burgess, David, “Duality Theory and Pitfalls in the Specification of Technologies,” Journal of Econometrics, 3 (05 1975), 105–21.CrossRefGoogle Scholar

⁴⁶ In other words, strong additive separability between value added and raw material inputs is assumed. To be sure, such separability has been rejected for postwar U.S. and Canadian manufacturing. See Berndt, Ernst and Wood, David, “Technology, Prices, and the Derived Demand for Energy,” Review of Economics and Statistics, 57 (08 1975), 259–68;CrossRefGoogle ScholarDenny, M. and May, J. D., “The Existence of a Real Value-Added Function in the Canadian Manufacturing Sector,” Journal of Econometrics, 5 (01 1977), 55–70.CrossRefGoogle Scholar In both cases, however, constant returns to scale were assumed. Cain and Paterson find a complex pattern of biased technical change in U.S. manufacturing industries over the late nineteenth century, using a four-factor input cost function. In particular, they find that labor-saving technical change was almost as likely to be material-using as capital-using. As noted in note 6, however, that study makes the strong (and questionable for many industries, as is shown in Table 1) assumption of constant returns to scale. This paper will be restricted to the traditional form of the debate, of labor-saving versus capital-saving technical change. Since constant returns to scale is not imposed here, however, it does not necessarily follow that labor-saving technical change, for example, is necessarily capital-using. Cain, and Paterson, “Factor Biases and Technical Change.”Google Scholar

⁴⁷ Hannoch has argued that it is more suitable to define scale economies in terms of the change in costs relative to output along the expansion path where costs are minimized at every output level, since the measures diverge when the function is not homothetic. Since we are unable to estimate the cost function, however, we cannot use this definition. Hannoch, Giora, “The Elasticity of Scale and the Shape of Average Costs,” American Economic Review, 67 (09 1975), 492–97.Google Scholar

⁴⁸ Davis, , “The Investment Market”; James, Money and Capital Markets. If concentration levels were indeed rising over time in some industries, the implicit assumption of a competitive product market embedded in the share equations might appear rather dubious. However, deflating value added by the Warren-Pearson wholesale price index, which should not be subject to an upward bias over time due to increasing monopoly power, and reestimating the equations produced a pattern of results very similar to those discussed in Section II. The actual effect of such a bias should be quite small. One other reason for choosing the labor share equation is that since capital is the residual factor and constant returns to scale are not imposed, we cannot observe the capital share directly.Google Scholar See Fenoaltea, Stefano, “Real Value Added and the Measurement of Industrial Production,” Annals of Economic and Social Measurement, 5 (Winter 1976), 111–38.Google Scholar

⁴⁹ See Maddala, G. S., “The Use of Variance Components Models in Pooling Cross Section and Time Series Data,” Econometrica, 39 (03 1971), 341–58.CrossRefGoogle Scholar

⁵⁰ Wallace, T. D. and Hussain, Ashiq, “The Use of Error Components Models in Combining Cross Section with Time Series Data,” Econometrica, 37 (01 1969), 55–72;CrossRefGoogle ScholarNerlove, Marc, “A Note on Error Components Models,” Econometrica, 39 (03 1971), 383–96;CrossRefGoogle ScholarSwamy, P. A. V. B. and Arora, S. S., “The Exact Finite Sample Properties of the Estimators of Coefficients in the Error Components Regression Models,” Econometrica, 40 (03 1972), 261–76;CrossRefGoogle ScholarFuss, Melvyn, “The Demand for Energy in Canadian Manufacturing: An Example of the Estimation of Production Structures with Many Inputs,” Journal of Econometrics, 5 (01 1977), 89–116.CrossRefGoogle Scholar

⁵¹ Swamy, and Arora, “Exact Finite Sample Properties,” p. 273.Google Scholar

⁵² Griliches further suggests that whatever simultaneous equation bias there may be present would be reduced by the use of regional dummies, as in B.4, which eliminates the systematic components of the correlation between the disturbance and the “independent” variables. Griliches, Zvi, “Production Functions in Manufacturing: Some Preliminary Results,” in Brown, M., ed., The Theory and Empirical Analysis of Production, Studies in Income and Wealth, Vol. 31 (New York, 1967), p. 277.Google Scholar

⁵³ Atack in comparing some 100 percent samples from the Bateman-Weiss sample of the 1850, 1860, and 1870 manuscript censuses with the published figures, found a number of errors in the published summaries—some establishments were misreported, others completely omitted, and so on. Such findings indicate that the published figures should be used with some caution, but not that their value is totally vitiated. There is no evidence of any particular systematic biases in the published reports, such as the omission of the smallest firms, so estimated coefficients should be unaffected, except of course for the perennial errors in variables problem. Atack, Jeremy, “Estimation of Economies of Scale in Nineteenth Century United States Manufacturing and the Form of the Production Function,” unpublished Ph.D. dissertation, Indiana University, 1976, pp. 110–20.Google Scholar

⁵⁴ U.S. Census Office, Ninth Census of the United States, The Statistics of Wealth and Industry, Vol. 3 (Washington, D.C., 1872), pp. 381–82;Google ScholarCreamer, Daniel, Dobrovolsky, Sergei, and Borenstein, Israel, Capital in Manufacturing and Mining (Princeton, 1960).CrossRefGoogle Scholar

⁵⁵ Davis, Lance and Gallman, Robert, “Capital Formation in the United States during the Nineteenth Century,” in Cambridge Economic History of Europe Vol. 7, Pt. 2(Cambridge, 1978), p. 9.Google Scholar

⁵⁶ Easterlin, Richard, “Estimates of Manufacturing Activity,” in Lee, E. et al. , Population Redistribution and Economic Growth: United States, 1870–1950 (Philadelphia, 1957), p. 660.Google Scholar

⁵⁷ Nickless, Pamela, “Productivity in the New England Cotton Textile Industry,” this JOURNAL, 39 (12 1979), 889–910.Google Scholar

⁵⁸ U.S. Senate, Wholesale Prices, Wages, and Transportation, Senate Report No. 1394, 52nd Congress, 2nd Session, Part 2; Brady, Dorothy, “Price Deflators for Final Product Estimates,” in Output, Employment, and Productivity in the United States after 1800, Studies in Income and Wealth, Vol. 30 (New York, 1966), pp. 91–116;Google ScholarWarren, George and Pearson, Frank, Prices (New York, 1933).Google Scholar

⁵⁹ A potential problem in cross-section production function estimation with value added as the dependent variable is the disregard of interstate or interregional variation in the price of output. See Lucas, Robert E., “Labor-Capital Substitution in U.S. Manufacturing,” in Harberger, Arnold and Bailey, Martin, eds., The Taxation of Income from Capital (Washington, D.C., 1969), pp. 223–74. Indeed, this might be a more serious difficulty for the nineteenth century than for today because markets then were more localized and less well integrated interregionally. The Warren-Pearson indexes were derived primarily from New York price observations, while the Aldrich Report data were based on observations from a relatively small number of cities as well. To examine the influence of this interregional price variation, the price series were adjusted by a regional price index. In this case, there were no really substantial differences in the estimates from those reported in the text and the tenor of the results reported in Section II remain unchanged.Google ScholarCoelho, Philip and Shepherd, James, “Differences in Regional Prices: The United States, 1851–1880,” this JOURNAL, 34 (09 1974), 551–91.Google Scholar

⁶⁰ David, Paul, “Measuring Real Net Output: A Proposed Index,” Review of Economics and Statistics, 47 (11 1966), 419–25.CrossRefGoogle Scholar

⁶¹ Fenoaltea argues, however, that the David index of real value added is too sensitive to relative price changes and suggests the alternative technique of adjusting current-price value added in different industries by a single, common deflator. In this case, nominal values added were deflated by the Warren-Pearson wholesale price index and the system of equations was reestimated. The pattern of results reported in Section II remained even using the new dependent variable constructed with the alternative deflator. Fenoaltea, “Real Value Added.”Google Scholar

⁶² Bateman, Fred and Wesis, Thomas, “Comparative Regional Development in Antebellum Manufacturing,” this JOURNAL, 35 (03 1975), 201–07.Google Scholar

⁶³ Goldberger, Arthur, Econometric Theory, (New York, 1964), pp. 227–31.Google Scholar