Estimating the share of slave earnings retained in 1800 (A.) The Share of Slave Earnings Retained 1849-1859



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Lindert-Williamson 6 October 2010,

Reformatted 29 May 2011


ESTIMATING THE SHARE OF SLAVE EARNINGS RETAINED IN 1800

(A.) The Share of Slave Earnings Retained 1849-1859
Fogel and Engerman (1974 I: 5-6) claimed slaves retained 90% of what they produced, and thus that “the material … conditions of the lives of slaves compared favorably with those of free industrial workers in the decades before the Civil War” (Whaples 1995: pp. 146-7). That figure, along with subsequent revisions downward, applies to 1859, six decades after 1800. This fact is obviously important for any 1800 estimate, as will be seen below.
In the wake of Time on the Cross, further research reduced the Fogel and Engerman 90% earnings 1859 retention estimate to about 50%: “Current estimates suggest that the typical slave received only about fifty percent of the extra output that he or she produced” (Wahl 2008). In addition to that by Richard Sutch (1975), the best critical assessment, confirming the 50% figure, seems to be an appraisal by Richard Vedder (1975). First, Vedder defines the expropriation rate (ER, following Fogel and Engerman) as the value of the marginal product of the slave (or earnings, w) less his or her actual payment or subsistence (s) divided by the value of the marginal product of the slave, or [w – s]/w = ER. Vedder (1975: p. 455) estimates a range for ER 43.2-72.2%, for an average of 57.7%, well above the more benign Fogel and Engerman 10% rate.
In another study, Vedder reports a 1859 ER figure of 66.7% and a 1849 ER figure of 48%, concluding that the “observed rising rate of slave exploitation over time … reflects rising marginal productivity [of slaves] and a constant [subsistence]” (Vedder 1975: p. 456). This implies that the slave value marginal product rose across the decade 1849-1859 at 4.6% per annum. This huge rate was much lower earlier in the century, but it was still impressive: slave productivity grew at about 1.6% pa 1800-1860, as we shall see.
(B.) Inferring 1800 from the Ante Bellum Trends
The best recent work on slave productivity growth is by Alan Olmstead and Paul Rhode (2010). Using the Craig and Weiss agricultural slave labor force estimates (slaves age 10+: 1998) and 400-pound bale output estimates, cotton bales per worker in the Old South grew at 1.57% per annum 1800-1860 (Olmstead and Rhode: Table 1, p. 37). Old South is defined as Georgia, North Carolina, South Carolina, and Virginia (ibid.: p. 4), the relevant region for our 1800 estimates, and which grew much slower than the New South (East and West South Central). This may overstate average labor productivity growth, since the plantations became more specialization in cotton over time (ibid.: p. 5). Still, even as late as 1880, cotton made up only 16 % of improved acres in the South (with corn 31%: other crops being barley, buckwheat, oats, rye, wheat, hay, tobacco, Irish potatoes, sweet potatoes, rice, and hops). Thus, what about a broader crop-based index? Paul Rhode offers such an index (communication August 22, 2010) based on cotton, tobacco, sugar, molasses, and rice 1800-1860, and it grows at 2.3% per annum for All South (Old plus New South). Applying the same discount to the slower-growing Old South that Olmstead and Rhode report for cotton productivity growth (2010: Table 1, p. 37: 2.44% per annum All South and 1.57% per annum for Old South, or 0.643 discount) implies 1.48% per annum over the six decades. Thus, 1.5% seems like a fair estimate. Cruder but confirming evidence of fast slave productivity growth can be found in earlier work by Conrad and Meyer (1958), Whartenby (1977) and Lebergott (1984).
Assuming an 1859 ER of 57.7%, constant subsistence, and slave productivity growth of 1.5% per annum, then the 1800 ER would have to have been negative! Since we know it was not, subsistence must have grown considerably over the six decades from much lower levels in 1800.
A recent survey (Mancall, Rosenbloom, Weiss 2010) offers confirming evidence on these ante bellum slave consumption growth rates: first, that slave subsistence per capita grew at 0.65% per annum over the 18th century, suggesting the same was true 1800-1860; and second, that in “the nineteenth century, the value of a slave’s diet equaled about 75 percent that of a free person” (p. 399). Their survey also suggests how little we know when they report the slave share of free worker’s diets in the 18th century ranged “anywhere between 20 percent and 75 percent” (p. 399). Presumably, the ratios were smaller for diets than they were for total consumption.
What do we conclude from this? The 1774 and 1800 data on slave consumption and, thus, the retention and exploitation rates, is very sparse, limited mainly to diet. It implies a retention rate ranging between 20 to 75 percent.
(C.) Estimating Slave Consumption in 1800 Directly
Alternatively, we can try to estimate slave consumption in 1800 directly. For this exercise, we lean heavily on Mancall et al. (2010), hereafter MRW. There findings can be summarized by these quotes: “In the nineteenth century, the value of a slave’s diet equaled about 75 percent that of a free person. The information we have found for the colonial period would put the relative value anywhere between 20 percent and 75 percent.” (MRW p. 399) “In estimating the diet of a slave, we assume that its value increased from around 50 percent of a colonist’s diet in 1700 to 75 percent in 1800.” (MRW p. 399. See also fn 37, p. 417) Note that the latter statement interpolates to a share of 67 percent in 1774. Note also that MRW are referring to the value of food (diet or subsistence), and not to non-food consumption like shelter, fuel, clothes and extras which would have loomed much larger in the free laborer’s budget. For example, in 1874-75 Massachusetts, the poorest families (roughly comparable to the average family in 1800), spent 64% on “subsistence” leaving 36% for clothing, rent, fuel and sundries (Historical Statistics 1975: p. 322).
MRW (Table 14.1, pp. 396-7) report the following estimates, which we use to construct Tables 1 and 2:
1800 food consumption (in 1840 prices)

per capita, including slaves slaves, at 75% of free (% LF slave)

US 29.37 23.84 (0.304)

Lower South 27.66 23.80 (0.514)

MC + NE 29.80 22.94 (0.103)

1800 firewood consumption (in 1840 prices)

per capita, including slaves slaves, at 75% of free (% LF slave)

US 6.64 5.39 (0.304)

Lower South 6.10 5.25 (0.514)

MC + NE 6.63 5.10 (0.103)

1800 shelter per capita, free only (in 1840 prices)

US 4.80


1800 shelter per capita, slaves (in 1840 prices, based on rural areas)

US 0.60
Table 1 Total 1800 consumption on food, fuel, shelter, and clothes per slave worker (s, in 1840 prices)

LS: rural farm (23.80+5.25+0.60=29.65; plus 5% for clothes) 31.13 rural non-farm (29.65 plus 10% for better clothes and extras) 32.62

Small town (29.65 plus 10% for higher prices and rents=32.62; plus

10% for better clothes and extras) 35.88

Big city (29.65 plus 20% for higher prices and rents=35.58; plus

20% for better clothes and extras) 42.70

MC+NE: rural farm (22.94+5.10+0.60=28.64; plus 5% for clothes) 30.07 rural non-farm (28.64 plus 10% for better clothes and extras) 31.50

Small town (28.64 plus 10% for higher prices and rents=31.50; plus

10% for better clothes and extras) 34.65

Big city (28.64 plus 20% for higher prices and rents=34.37; plus

20% for better clothes and extras) 41.24



Table 2 Total 1800 consumption on food, fuel, shelter, and clothes per slave worker (s, in 1800 prices: Table 1 1840 figures inflated to 1800 by CPI from http://www.measuringworth.com/uscompare)

s Ratios of s to free-labor w (%)

Lower South: rural farm 45.18 24.05

rural non-farm 47.34 25.75

Small town 52.08 27.63

Big city 61.97 30.68

North (MC+NE): rural farm 43.64 22.71

rural non-farm 45.72 24.87

Small town 50.29 26.68

Big city 59.86 29.64
The ratios of these slave consumption estimates to the relevant location/occupation annual earnings estimates for free labor (from the file “US Earnings Distribution 1800”, using Mid Atlantic = North, and all non-farm = unskilled) are reported in the second column.
Assuming that unskilled slaves and free labor were equally productive, it appears that the slave retention rate in 1800 ranged between 23 and 31%, well below the 50% which the literature has estimated for 1849-1859. Some of the difference can be attributed to the fact that our 1800 estimate tries to cover all consumption, not just diet, but even so the 1800 estimates are well below those of the late ante bellum. They are also below the 1796-1804 slave rental data explored next.
(D.) The Percent of Slave Earnings Retained 1796-1804 for Those Hired
A lessee renting a slave should theoretically pay a rental charge (hire rate per year) such that it plus the upkeep of the slave (the responsibility of the lessee) should be the marginal cost of using the slave. This marginal cost should, in turn, add up to the slave’s marginal product. If so, there is a definitional relationship between the rental price and the exploitation rate (ER).
Let the value of the slave’s marginal product be w, let s be the slave’s consumption, and define ER = [w-s]/w. Logically, R = [w-s], so given an estimate of the slave’s product and consumption, we can infer both the exploitation rate R/[R+s], and the retention rate 1 – (R/[R+s]). We assume that, given skills and occupations, slaves and free labor were close if not prefect substitutes, such that these African-Americans would have received the earnings of free labor had they been free, an assumption supported by qualitative evidence in Goldin’s book (1976: pp. 28-30).
An ICPSR file (constructed by Fogel and Engerman) reports the following average annual hire rates in Queen Anne’s County (Maryland) 1796-1804 for 207 slaves, and we

combine these with the consumption per slave estimates reported in Table 2 above. These hires were for farm work ($):


Table 3 1796-1804 Retention Rates Based on Hire Market
Annual Hire Rental Annual Subsistence (1-ER in parentheses)

Rural Maryland LS: farm MC: farm
All slaves hired 28.44 45.18(61.4) 43.64(60.5)

All male slaves hired 29.62 45.18(60.4) 43.64(59.6)

All male “fellows” 39.42 45.18(54.3) 43.64(52.5)
These slave retention rates are a bit higher than those the post-TOC literature has estimated for 1849-1859 (around 50 percent), with averages of 58.7 percent for the Lower South and 57.5 percent for the Middle Colonies (or Mid Atlantic).


(E.) Bottom Line: Assumed Slave Retention Rates for 1800
We take the farm 1-ER averages from Tables 2 and 3, and the rural-urban gradient in Table 2, to get Table 4. We use the bottom four lines to estimate slave-retained earnings:
Table 4 Slave Retention Rates Estimated for 1800 (%)

Lower South North

Table 2: farm 24.05 22.71

Table 3: farm 58.7 57.5
Average: farm 41.4 40.1

Rural non-farm 44.3 43.9

Small town 47.5 47.1

Big city 52.7 52.3




References
Lee A. Craig and Thomas Weiss (1998), “Rural Agriculture Workforce by County, 1800

to 1900” [http://eh.net/databases/agriculture/])

Alfred H. Conrad and John R. Meyer (1958), “The Economics of Slavery in the Ante

Bellum South,” Journal of Political Economy 66 (April): 95-130.

FE I. Robert William Fogel and Stanley L. Engerman (1974), Time on the Cross: The

Economics of American Negro Slavery. Boston: Little, Brown and Co.

FE II. Robert William Fogel and Stanley L. Engerman (1974), Time on the Cross:



Evidence and Methods-A Supplement. Boston: Little, Brown and Co.

Stanley Lebergott (1984), The Americans: An Economic Record (New York: Norton).

Peter C. Mancall, Joshua L. Rosenbloom and Thomas Weiss, “Conjectural Estimates of

Economic Growth in the Lower South, 1720 to 1800,” in Evidence Matters: Measuring Historical Economic Growth and Demographic Change (forthcoming 2010), pp. 389-424.

Alan Olmstead and Paul Rhode (2010), “Productivity Growth and Regional Dynamics of

Antebellum Southern Development,” in P. Rhode, J. Rosenbloom, and D. Weiman (eds.), Economic Evolution and Revolution (Stanford: Stanford University Press).

Richard Sutch, “The treatment received by American slaves: A critical review of the

evidence presented in Time on the Cross,” Explorations in Economic History 12 (October 1975): 335-438.

Richard Vedder, “The Slave Exploitation (Expropriation) Rate,” Explorations in

Economic History 12 (October 1975): 453-7

Jenny Wahl (2008), “Slavery in the United States.” EH.Net Encyclopedia, edited by Robert Whaples. March 26, 2008. http://eh.net/encyclopedia/article/whal.slavery.us

Robert Whaples, “Where Is There Consensus Among American Economic Historians? The

Results of a Survey on Forty Propositions,” Journal of Economic History 55, 1 (March 1995): 139-154.



F. G. Whartenby (1977), Land and Labor Productivity in United States Cotton

Production, 1800-1840 (New York: Arno Press).


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