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?
The critical difficulty arises from the fact that the index, which is basically a ratio of output to input, states output not in physical units—bushels, bales, or pounds per worker—but in total market value of the product. It is, therefore, as …
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