The results reported in this paper are taken from my doctoral dissertation, “Agricultural Production, Supply and Institutions in the Post-Civil War South,” which is forthcoming (with additions and revisions) from the M.I.T. Press, 1974. I wish to acknowledge Professors Peter Termin and Franklin M. Fisher of M.I.T. for their advice and suggestions throughout the course of the research. The Editor of this Journal and several anonymous referees also made helpful comments on an earlier version of the paper. Responsibility for all remaining errors is mine, however.

¹ Here and throughout, “exploitation” will be used to denote a situation in which the actual wage is lower than the value of the marginal product of labor. The income inequalities arising from unequal ownership of property are thus not attributed to “exploitation” in this sense, since such inequalties arise without any interference in the operation of competitive markets. It is also possible that farmers in general or blacks in particular were excluded from certain non-agricultural pursuits, so that the competitive wage level in agriculture was depressed. The historical debates revolve primarily around conditions within the agricultural sector however, and this paper is directed toward describing the labor market in that sector only.

² Domar, Evsey“The Causes of Slavery or Serfdom: A Hypothesis,” Journal of Economic History, XXX (March 1970), 18–32.CrossRefGoogle Scholar

³ Examples of these outrages are common. See, for example, Schurz, Carl, Report on the Condition of the South (New York: Arno Press and New York Times Reprint, 1969,Google Scholar originally submitted as U.S. Senate, Ex. Doc. No. 2, 39th Congress, 1st Session, 1865), particularly the testimony appended to the Report; also United States Congress, Joint Committee on Reconstruction, Report of the Joint Committee on Reconstruction, 39th Congress, 1st Session (Washington: U.S.G.P.O., 1866), Part II, 54–55Google Scholar, Part III, 31, 142, and Part IV, 39; Hart, Albert Bushnell, The Southern South (New York: D. Appleton & Company, 1910) 283–285;Google Scholar“Two Sorts of Southern Sentiments,” Southern Workman, V (May 1876), 38Google Scholar; Sinclair, William A., The Aftermath of Slavery (Boston: Small, Maynard & Company, 1905), 223–232Google Scholar. This is only a sample of reports of the coercion of labor, and particularly of blacks, which can be found in contemporary accounts. These examples could be multiplied many times.

⁴ The “Black Codes” passed to regulate freedmen by the southern state governments during Andrew Johnson's short-lived direction of “reconstruction” are collected in McPherson, Edward, The Political History of the United States of America During the Period of Reconstruction, from April 15, 1865 to July 15, 1870 (Washington: Philp & Solomon, 1871), 29–43.Google Scholar Documentation and analysis of southern laws attempting to restrict agricultural labor throughout the remainder of the nineteenth century may be found in Zeichner, Oscar, “The Legal Status of the Agricultural Laborer in the South,” Political Science Quarterly, LV (September 1940), 412–428.CrossRefGoogle Scholar

⁵ McPherson, Political History, 36–37, 42; Report of the Joint Committee on Reconstruction, Part I, 107–108, and Part III, 27, 30; DeBow's Review (February 1868), 213, 224.Google Scholar

⁶ Again, innumerable examples could be cited. A few typical cases are: Bruce, Philip A., The Plantation Negro as Freeman (New York: G. P. Putnam's Sons, The Knickerbocker Press, 1889), 177–178;Google Scholar Schurz, Report, 28; Report of the Joint Committee on Reconstruction, Part I, 109, 117, and Part III, 70, 167; Southerner [pseud.], “Agricultural Labor at the South,” The Galaxy, XII (September 1871), 329–339Google Scholar, passim; DeBow's Review (September 1869), 787–788;Google Scholar (July 1869) 564–565; and (February 1870), 168–169; Southern Cultivator, XXVII (July 1869), 214.Google Scholar

⁷ Not only can convincing documentation be built up to support either exploitation of labor or a competitive labor market, but often the same nineteenth-century sources contain conflicting evidence of both competition and exploitation. See notes 3, 5, and 6 above, 3 and 5 giving evidences or exploitation, 6 giving evidence of competition. This point is made in more detail in Stephen DeCanio, “Agricultural Production, Supply and Institutions in the Post-Civil War South,” Unpublished PhD. dissertation, Massachusetts Institute of Technology, 1972, Chapter II.

⁸ The most recent contributions are Reid, Joseph D., “Sharecropping As An Understandable Market Response: The Post-Bellum South,” Journal of Economic History, XXXIII (March 1973), 106–130CrossRefGoogle Scholar; Roger L. Ransom and Richard Sutch, “The Ex-Slave in the Post-Bellum South: A Study of the Economic Impact of Racism in a Market Environment,” Ibid., 131–148; and Robert Higgs, “Race, Tenure, and Resource Allocation in Southern Agriculture, 1910,” Ibid., 149–169.

⁹ This view is suggested in Stampp, Kenneth, The Era of Reconstruction: 1865–1877 (New York: Vintage Books, 1967), 16, 120–121, and in Ransom and Sutch, “The Ex-Slave in the Post-Bellum South,” 136.Google Scholar

¹⁰ The classical account of the hypothetical link between cotton culture and agricultural distress is contained in Hicks, John D., The Populist Revolt (Lincoln: University of Nebraska Press, 1961, originally published by University of Minnesota Press, 1931).Google Scholar For more recent work on the subject, see Ransom, Roger L. and Sutch, Richard, “Debt Peonage in the Cotton South After the Civil War,” Journal of Economic History, XXXII (September 1972), 641–669.CrossRefGoogle Scholar

¹¹ For a more thorough summary of the opposing points of view, see DeCanio, “Agricultural Production, Supply and Institutions,” Chapter II.

¹² More rigorously, it can be shown that equation (1) is the Taylor series linear approximation of the generalized Cobb-Douglas production function

with W = white agricultural labor force input, B = black agricultural labor force input, H = cotton land input, and J = non-cotton land input. Taylor series linearization around arbitrary values (a₀, b₀) and (c₀, d₀) of the productivity parameters (chosen with a₀=b₀ and c₀=d₀ to avoid a priori judgement on the relative magnitudes of a and b or c and d) shows that with L = B+W, T = H+J, R = B/L, and P = H/T, the coefficients of the shift variables R and P in (1) are functions of the productivity parameters a,b,c and d. These functions λ = λ(a,b) and μ = μ(c,d) have the natural properties that λ>0 implies b > a and μ>0 implies c>d. For technical reasons having to do with the choice of the points around which to take the Taylor series expansion of (1a), only the signs of λ and μ, and whether their estimates are significantly different from zero, can be determined by unconstrained estimation of (1).

Also, examination of (1a) shows that if both whites and blacks are paid a wage equal to the value of the marginal product of their respective labors, then labor's share S of total output will be given by

This labor share is independent of the racial composition of the labor force, so the shift variable R may be ignored in computing the labor share which would have prevailed under marginal productivity wage determination. For a complete discussion of these points and of the Taylor series approximation technique, see DeCanio, “Agricultural Production, Supply and Institutions,” Ch. IV.

¹³ The Census volumes which formed the basic data source for the production function estimates were the following:

U.S. Census Office, Tenth Census, 1880, Vol. I:Google ScholarStatistics of the Population of the United States (Washington: U.S.G.P.O., 1883); Vol. III:Google ScholarReport on the Production of Agriculture (Washington: U.S.G.P.O., 1883); Vol. V–VI:Google ScholarReport on Cotton Production in the United States; also Embracing Agricultural and Physico-geographical Descriptions of the Several Cotton States and of California, ed. by Hilgard, Eugene W. (Washington: U.S.G.P.O., 1884).Google Scholar

U.S. Census Office, Eleventh Census, 1890, Vol. I:Google ScholarReport on Population of the United States (Washington: U.S.G.P.O., 1895–1897); Vol. V:Google ScholarReports on the Statistics of Agriculture in the United States, Agriculture by Irrigation in the Western Part of the United States, and Statistics of Fisheries in the United States (Washington: U.S.G.P.O., 1895);Google ScholarCompendium of the Eleventh Census: 1890 (3 Pts., Washington: U.S.G.P.O., 1892–1897).Google Scholar

U.S. Census Office, Twelfth Census, 1900, Vol. I-II: Population (Washington: U.S.G.P.O., 1901–1902); Vol. V–VI:Google ScholarAgriculture (Washington: U.S.G.P.O., 1902).Google Scholar

U.S. Bureau of the Census; Thirteenth Census of the United States: 1910, Vol II: Population, 1910. Reports by States, with Statistics for Counties, Cities and Other Civil Divisions—Alabama-Montana (Washington: U.S.G.P.O., 1913); Vol. III:Google ScholarPopulation, 1910. Reports by States, with Statistics for Counties, Cities and other Civil Divisions—Nebraska-Wyoming, Alaska, Hawaii, and Porto Rico [sic] (Washington: U.S.G.P.O., 1913); Vol. V:Google ScholarAgriculture, 1909 and 1910. General Report and Analysis (Washington: U.S.G.P.O., 1913); Vol. VI:Google ScholarAgriculture, 1909 and 1910. Reports by States, with Statistics for Counties—Alabama-Montana (Washington: U.S.G.P.O. 1913); Vol. III:Google ScholarAgriculture, 1909 and. 1910. Reports by States, with Statistics for Counties—Nebraska-Wyoming, Alaska, Hawaii, and Porto Rico [sic] (Washington: U.S.G.P.O., 1913).Google Scholar

The exact definitions of the variables used are as follows:

Q: Agricultural output is measured by the estimated value of all farm productions in 1879, 1889, and 1899 for the first three census years, and total value of all crops in 1909 for the 1910 census observations. Because the output variable is measured in the year prior to the year for which the inputs are measured, it is necessary to assume that the measurement error involved in using the XXX9 year's output to measure the XXX0 output is not severe. The output variables in succeeding census years are not defined identically, but the first three census years’ values are all net of intermediate products fed to livestock, while the 1910 value uses intermediate farm products fed to livestock to approximate the total livestock output for that year. The change in definitions appears to make little difference in the estimates.

L: L = W+B, where W and B are measured by the total rural population of each race, calculated by deducting. the populations of the cities and towns over 2500 (4000 in 1880) from the total county populations. Counties containing large cities such as Atlanta, New Orleans, etc., were omitted from the samples altogether.

T: Total improved acres in farms, for each of the four census years.

K: The capital input is measured by the dollar value of implements and machinery reported for each of the four census years. Of course implements and machinery were not the only components of agricultural capital. However, farm animals, fertilizer and the value of implements were all highly correlated, so just one of these was chosen as a proxy for all the capital inputs to avoid problems of multicollinearity.

R: R = B/L.

P: P = H/T, where H is total acreage planted in cotton, summing acres in sea island cotton and uplands cotton when the two are reported separately.

S_j: The soil type dummy variables were defined by the physical and chemical soil types reported in Vol. V-VI of the 1880 Census, Report on Cotton Production in the United States, edited by Eugene W. Hilgard. The. counties of each state were as signed to soil type categories according to the classification tables in these reports, so that each state's counties fell into from 4 to 12 distinct soil type categories. In subsequent years, it was assumed that the soil type of a county did not change from what it had been in 1880. A newly created county was assigned to that soil type from which a preponderance of its lands were taken.

¹⁴ Cheung, Steven N.S., The Theory of Share Tenancy (Chicago: University of Chicago Press, 1969);Google Scholar Joseph D. Reid, Jr., “Sharecropping and Agricultural Uncertainty,” Department of Economics Discussion Paper No. 257, University of Pennsylvania, April 1973, and “Sharecropping As An Understandable Market Response”; Joseph E. Stiglitz, “Incentives and Risk-Sharing in Sharecropping,” mimeographed, Yale University, 1972; and RobertHiggs, “Race, Tenure, and Resource Allocation.”

¹⁵ Solow, Robert M., “Capital, Labor and Income in Manufacturing,” The Behavior of Income Shares, National Bureau of Economic Research Conference on Research in Income and Wealth, Studies in Income and Wealth, 27 (Princeton: Princeton University Press, 1964);Google ScholarFisher, Franklin M., “The Existence of Aggregate Production Functions,” Econometrica, XXXVII (October 1969), 553–577.CrossRefGoogle Scholar

¹⁶ Mundlak, Yair and Hoch, Irving, “Consequences of Alternative Specifications in Estimation of Cobb-Douglas Production Functions,” Econometrica, XXXIII (October 1965), 817.Google Scholar In the same article, these authors point out that if the production function disturbance is “partially transmitted” to the inputs (as is most likely in agriculture), both least squares and an alternative estimator proposed by them will be biased. Other techniques have other deficiencies. The detailed factor price data required to estimate the parameters of the production function by the factor shares method do not exist (systematic records of input prices at the county level would be needed). A production model similar to (1) described in Zeuner, A., Kmenta, J., and Drèze, J., “Specification and Estimation of Cobb-Douglas Production Function Models,” Econometrica, XXXIV (October 1966), 784–795Google Scholar, has the property that.if decision-makers maximize expected profits, then ordinary least squares applied to the input and output data produces consistent and unbiased estimates of the parameters, provided the production function exhibits decreasing returns to scale. The presumption that agricultural producers maximize expected profits would be plausible, but unfortunately the proscription of constant returns is contrary to what is required to be able to ignore tenure arrangements and to carry out aggregation to the county level.

¹⁷ For a discussion of the disquieting possibility that a constant labor share leads to estimates of the labor elasticity in the production function equal to that share, rather than the other way around, see Fisher, Franklin M., “Aggregate Production Functions and the Explanation of Wages: A Simulation Experiment,” Review of Economics and Statistics, LIII (November 1971), 305–325.CrossRefGoogle Scholar

¹⁸ The full set of results is reported in DeCanio, “Agricultural Production, Supply and Institutions,” Chs. IV-V.

¹⁹ This sample is presented in Ibid., Appendix 4.

²⁰ For a discussion of the combining of cross-sectional data from different points in time, see Zellner, Arnold, “An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias,” Journal of the American Statistical Association, LVII (June 1962), 348–368;CrossRefGoogle Scholar and Nerlove, Marc, Estimation and Identification of Cobb-Douglas Production Functions (Chicago: Rand McNally & Company, 1965), pp. 157–190.Google Scholar

²¹ If X₁ X₂…, X_n are n random variables, with and Cov (X_i, X_j) = 0 when i ≠ j, then the standard deviation of (1/n)ΣX_i, is given by σ = . If the exact standard deviations of the input elasticity estimates were known, this expression would give the standard deviation of their four-census average exactly. Since the standard deviations are. not known exactly, the standard error of the average may be approximated by where the s_i are the estimated standard errors of the four elasticity estimates. If it is assumed that each census cross-section is a sample drawn from the same population, with α the common value of the labor elasticity, then the statistic will be distributed approximately normally with mean zero and variance one. The significance tests reported in the text are based on approximating the distribution of m by a normal distribution, and in view of this assumption and of the other assumptions made to combine the individual parameter estimates, it should be emphasized that the significance tests are intended only to be suggestive.

²² DeCanio, “Agricultural Production, Supply and Institutions,” 241–244 and Appendix 5.

²³ The details of the somewhat laborious calculations may be found in Ibid., Appendix 5.

²⁴ The “Cotton Belt” as defined here is a geographically coherent unit. A relatively small proportion of Texas’ improved acres was devoted to cotton until the twentieth century, and for this reason, as well as its location, Texas was included in the ‘Periphery.”

²⁵ Siegel, Sidney, Nonparametric Statistics for the Behavioral Sciences (New York: McGraw-Hill Book Company, Inc., 1956), pp. 96–104.Google Scholar

²⁶ Formally, (2) is the result of a Taylor series expansion of

where W₁ and W₂ represent white labor devoted to growing cotton and the noncotton alternatives, respectively; B₁ and B₂ are quantities of black labor defined similarly; H₁ and H₂ are cotton acres farmed by whites and blacks, respectively; and J₁ and J₂ are other improved acres farmed by whites and blacks. The parameters a₁, a₂, b₁, b₂, c₁, c₂, d₁ and d₂ are the associated productivity parameters, and in the Taylor series expansion of (2a), η, θ and φ are complicated functions of these productivity parameters and of other parameters introduced to eliminate those input variables not reported in the censuses of 1880 through 1910. For details and a complete discussion, see DeCanio, “Agricultural Production, Supply and Institutions,” Ch. V.

²⁷ If the Taylor series expansion of equation (2a) of footnote 26 is carried out, it can be shown that the productivities of the various groups can best be assessed by examining the sign frequencies of η, θ, η + φ and θ + φ. This follows from analysis of the coefficients η, θ and φ as functions of the productivity parameters of (2a) when (2) is derived from the Taylor series approximation of (2a). The intuitive interpretation of the sign frequencies of η, θ and φ given in the text corresponds with the interpretation based on the Taylor series coefficients, however, strengthening the argument presented in the text. The complete analysis of η, θ and φ is long and involved, and is omitted here for ease of exposition. The entire discussion is contained in DeCanio, “Agricultural Production, Supply and Institutions,” Ch. V.

²⁸ Ibid.

²⁹ Tebeau, C. W., “Some Aspects of Planter-Freedman Relations, 1865–1880,” Journal of Negro History, XXI (April 1936), 131;Google ScholarZeichner, Oscar, “The Transition from Slave to Free Agricultural Labor in the Southern States,” Agricultural History, XIII (January 1939), 22–32.Google Scholar

³⁰ For a particularly eloquent argument in favor of confiscation and redistribution of the rebels' land to the freedmen, see Thaddeus Stevens' speech “Reconstruction,” delivered at Lancaster, Pennsylvania, September 7, 1865, (Lancaster: Examiner & Herald Printers, 1865).Google Scholar

³¹ According to census literacy data summarized by Ransom and Sutch, the illiteracy rate of southern blacks was much higher than that of southern whites in 1870. See “Debt Peonage,” p. 648. Literacy is not synonymous with farming ability, however.

³² This plausible view is convincingly supported by Wright, Gavin, “‘Economic Democracy and the Concentration of Agricultural Wealth in the Cotton South, 1850–1860,” in The Structure of the Cotton Economy of the Antebellum South, ed. Parker, William (Washington: The Agricultural History Society, 1970), 63–93Google Scholar. See also Shugg, Roger, Origins of Class Struggle in Louisiana: A Social History of White Farmers and Laborers during Slavery and After, 1840–1875 (Baton Rouge: Louisiana State University Press, 1939; paperback edition, 1968), 4–5Google Scholar, 94–95; Banks, Enoch, The Economics of Land Tenure in Georgia, Studies in History, Economics and Public Law, XXIII (New York: Columbia University Press, 1905), 24;Google Scholar and Phillips, Ulrich B., “Plantations with Slave Labor and Free,” Agricultural History, XII (January 1938), 85–86.Google Scholar

³³ Emancipated without resources, blacks had little choice but to remain in agriculture and find employment on the lands of the old plantations. Several accounts of blacks remaining where they had worked as slaves may be found in Fleming, Walter, Doucmentary History of Reconstruction: Political, Military, Social, Religious, Educational and Industrial, 1865 to the Present Time, 2 Vols. (Cleveland: Arthur H. Clark Company, 1907), Vol. II, 301, 309, 439.Google Scholar

³⁴ United States Census Office, Tenth Census, 1880, Vol. III:Google ScholarReport on the Production of Agriculture, xviii; Somers, Robert, Southern States Since the War, 1870–71 (London and New York: Macmillan and Co., 1871), 116–117Google Scholar, and 272–273; Grady, Henry W., “Cotton and Its Kingdom,” Harper's New Monthly Magazine, LXIII (October 1881), 721–722;Google ScholarHammond, Matthew Brown, “Cotton Production in the South,” The South in the Building of the Nation, Vol. VI, prepared by the Southern Historical Publication Society (Richmond: 1909), 89;Google Scholar and Langhorne, Orra, “A Poor White Man's Experience Since the War,” Southern Workman, X (April 1881), 38.Google Scholar