Were Slaves More Efficient? Some Doubts About 'Time on the Cross'

Submit a letter:

The carnival of publicity attending the publication of Time on the Cross suggests that the authors, Robert Fogel and Stanley Engerman, desire an audience embracing not only econometric historians but all reasonable men. I am not an econometric historian or a specialist in the history of slavery, but I am a reasonable man and, as such, entitled to judge the plausibility of the authors’ argument. Fogel and Engerman contend that slave labor was more efficient than free labor. This contention appears to rest on a dubious inference that vitiates several of the book’s most striking conclusions.

The most troublesome phase of any quantitative study is the translation of numerical procedures into plain English. In their research and calculations, Fogel and Engerman may have considered all the objections raised below. But even if their conclusions turn out to be procedurally well founded, their presentation still fails, for they have not exposed to the reader’s view any process of reasoning adequate to justify their conclusions.

The crux of the problem is that Fogel and Engerman appear to have drawn unjustifiable inferences from data based on the “geometric index of total factor productivity”—inferences which that index is inherently unable to support. The index is essentially a ratio of output to input. They use it to compare the “efficiency” of Southern (slave) agriculture with Northern (free) agriculture. They conclude that in the single year tested, 1860, “Southern agriculture as a whole was about 35 percent more efficient than northern agriculture….”

One would never know from the authors’ discussion of this index that economists are not entirely sure what it measures, or what causal factors it reflects, even in its most conventional applications. Fogel and Engerman’s interpretation of it as a measure of efficiency is defensible, but it would have been delightfully frank of them to tell their readers that Evsey Domar, the economist who formulated the “geometric” version of the index, was so wary of misinterpretation that he called it simply the “Residual,” rather than an index of efficiency. Commenting on a comparative study of the relative efficiency of the USSR and the US, Domar noted that “if the Index shows that the average factor productivity in one country is markedly inferior to another, greater efficiency of the latter is not an unreasonable hypothesis. But there may be other explanations as well.” Another economist referred to this entire class of aggregate productivity indices as a “measure of our ignorance.”

But let us grant that the index can be construed as a measure of efficiency in some sense. What does it mean in the particular case—a static comparison of Northern and Southern agricultural production in the year 1860—to which Fogel and Engerman apply it?

Continue reading
for just $1 an issue.

Choose a Digital subscription or our best deal—All Access—that includes print and digital issues, full archive access, and the NYR App!

Or register for a free account to read just this article. Register.

Already a subscriber? Sign in

Continue reading for just $1 an issue and get a FREE notebook!

Choose a Digital subscription or our best deal—All Access—and we will send you a free pocket notebook!

Or register for a free account to read just this article. Register.

Already a subscriber? Sign in

Thomas L. Haskell

Thomas Haskell is the McCann Professor of History at Rice University and the author of Objectivity is Not Neutrality: Explanatory Schemes in History. (December 1997)

This Issue

September 19, 1974

1
Robert William Fogel and Stanley L.Engerman, Time on the Cross, volume I: The Economics of American Negro Slavery (Little, Brown, 1974), p. 192, reviewed in NYR, May 2, by C. Vann Woodward. My understanding of the issues has been sharpened by friendly correspondence with Professor Engerman and by the assistance of Rice University colleagues too numerous to name. ↩
2
Evsey D. Domar, “On the Measurement of Technological Change,” The Economic Journal, 71 (December, 1961), pp. 709-729; “On the Measurement of Comparative Efficiency,” in Comparison of Economic Systems: Theoretical and Methodological Approaches, ed., A. Eckstein (University of California, 1971), p. 229; Moses Abramovitz, “Resource and Output Trends in the United States Since 1870,” American Economic Review, Papers and Proceedings 46 (May, 1956), pp 5-23. ↩
3
Fogel and Engerman, Time on the Cross, volume II: Evidence and Methods: A Supplement, pp. 131, 138, emphasis added. The market value of the nation’s agricultural output was taken from estimates by Marvin W. Towne and Wayne D. Rasmussen, “Farm Gross Product and Gross Investment in the Nineteenth Century,” in Trends in the American Economy in the Nineteenth Century: Studies in Income and Wealth, volume 24 (Princeton, 1960), pp. 255-312. Fogel and Engerman describe their initial procedure for calculating regional output as follows: “The allocation of crops [to the two regions] was based on census data regarding the physical product of each crop. Thus in the case of wheat, for example, the Towne-Rasmussen value of national wheat output in 1860 was $151.0 million. According to the 1860 census, the southern and northern shares of national wheat output were 22.4 and 73.2 percent, respectively. Therefore the value of southern wheat output in 1860 was measured as $33.8 million, while that of the North was $110.5 million” (p. 131). ↩
4
Time on the Cross, volume I, p. 210. ↩
5
Some economists have recognized that the index does not discriminate between two different aspects of efficiency, one reflecting producer performance per se, the other reflecting producer responsiveness to consumer demands. Abram Bergson distinguishes between “efficiency in the sense of realization of production possibilities” and efficiency in the sense of “the degree of optimality of the output structure.” He acknowledges that the index measures “performance in the two spheres together.” In short, part of the index’s test of efficiency is whether producers select the optimal mix of outputs, given a certain demand structure. But this supposes that all producers are equally capable of responding to demand. This is a valid assumption in many cases, but it is absurd to suggest that Massachusetts farmers flunked any test of optimality by failing to grow cotton. Edward F. Denison also has recognized the need to take into account the effect of demand pressure upon fluctuations in productivity. See Bergson, “Comparative Productivity and Efficiency in the Soviet Union and the United States,” in Eckstein, op. cit., p. 195, and Denison, What Growth Rates Differ: Postwar Experience in Nine Western Countries (Brookings Institution, 1967), pp. 273-276. In a forthcoming review essay in the Journal of Economic History, Paul A. David and Peter Temin make the same point. ↩
6
Time on the Cross, volume I, p. 209. ↩
7
Ibid., p. 210. ↩
8
Ibid., p. 201. ↩
9
Ibid., p. 208. ↩
10
Ibid. ↩
11
Ibid., pp. 263, 231, 5. ↩
12
Ibid., p. 223. ↩
13
Ibid., p. 215. ↩
14
Ibid., pp. 223, 215. ↩
15
Ibid., p. 93. ↩
16
Stuart Bruchey (ed. and comp.), Cotton and the Growth of the American Economy, 1790-1860: Sources and Readings (Harcourt, Brace & World, 1967), tables 1A, 2A, and 2B. ↩
17
A.W. Silver, Manchester Men and Indian Cotton, 1847-1872 (Manchester University, 1966), pp. 32, 9, 227. ↩
18
E.R.J. Owen, Cotton and the Egyptian Economy, 1820-1914 (London: Oxford University Press, 1969), pp. 50, 31, 199-202; J.A. Todd, The World’s Cotton Crops (London:A. & C. Black, 1924), pp. 239-249. ↩
19
Todd, The World’s Cotton Crops, pp. 98, 395. ↩
20
Gavin Wright, “An Econometric Study of Cotton Production and Trade, 1830-1860,” The Review of Economics and Statistics, 53 (May, 1971), p. 111. I do not claim that planters conspired to control prices. I claim only that the South enjoyed such competitive leeway that it might have realized a profit even if its labor force was neither diligent nor well managed. ↩
21
Time on the Cross, volume I, p. 194. ↩
22
Ibid., p. 196. ↩
23
This is not to say that cotton demand is the only point on which Fogel and Engerman’s efficiency calculation can be challenged. The “efficiency” gap also rests on their dubious assumption that the quality of Northern farmland was 2.5 times higher per acre than Southern farmland. Nor do they consider the possibility that slavery made its chief contribution to “efficiency” by repelling free yeoman farmers, thus reducing land prices and the level of capital investment in Southern agriculture. See also the extensive critique of their labor and land indices by David and Temin in a forthcoming issue of the Journal of Economic History. If the calculations of David and Temin are correct, the “efficiency” gap may not only be reduced, but reversed. ↩