In 1968 we undertook to measure and explain the relative technical efficiency of input utilization in the agricultural sectors of the North and South in 1860. The prin- cipal instrument that we employed for this task was the geometric index of the relative total factor productivity, which is defined by equation (1) (symbols are defined in Table 1):
(1) GIG ~ Q ________Q ___ (Ln /L= )'L(K )cK (L / Tn) T
This index' was originally computed from published census data and the results were reported in 1971, both with and with- out adjustments for differences in the qual- ity of outputs and inputs. The ratio of G,/G, yielded by the unadjusted computa- tion was 109.2.2 Crude adjustments for differences between the weights of northern and southern livestock, for land quality, for the proportion of women and children in the labor force, and for other factors, did not reduce this ratio as we thought they would, but increased it to 138.9.3
All differences between the northern and southern indexes of total factor productivity are, in a certain sense, errors of measurement. If output was correctly measured, and if all the inputs and conditions of production were fully specified and correctly measured, the ratio GI/G, would be equal to 100. To explain why GI/Gn deviates from 100, then, is a process of accounting for such errors of measurement as omitted inputs, failure to adjust for differences in the quality of inputs, neglect of economies of scale or of improvements in the organization of production, omitted outputs, disequilibrium in markets, and differences in product mixes.
In order to measure the effect of slavery on the process of production, it is therefore necessary to distinguish those mismeasurements that represent specific features of the slave system from those that are due merely to imperfections in the data, imperfections in methods of aggregation, or other mismeasurements that have no particular bearing on the operation of the slave system. In other words, we wish to obtain a residual measure of efficiency limited exclusively to measurement errors called "specific features of slavery." We then have the further task of identifying which specific features of slavery account for what parts of the aggregate value of the residual.
In our 1971 paper we stressed that a higher productivity index for the South than for the North did not necessarily imply that the southern advantage was due to special features of the slave system. We thought it was possible that slave-using plantations were less efficient than those using free labor, but that for some still un- disclosed reason free southern farms were extraordinarily efficient. The high value of the southern productivity index would then be the consequence of averaging over a high index for free farms and a low index for slave plantations. Another possibility was that both slave and free farms that engaged in diversified agriculture were about as efficient as free farms in the North but plantations specializing in the export staples were highly efficient. In that case the rela- tive productivity of the South might be due not to slavery per se, but merely to an unusually favorable market situation in 1860 for those export staples that happened to be produced by slave labor.
While we did not at that time rule out these alternatives, evidence in the 1860 Census indicated that the large slave plantations produced not only more cotton per capita but also more food per capita than small free farms in the South. It therefore seemed likely that the relative efficiency of southern agriculture was probably related to certain special features of the slave system. We conjectured that two features of slavery were particularly important. The first is that labor, and perhaps other inputs, were employed more intensively under the system of slavery than under the system of farming with free labor. There is much testimony for the proposition that slaves worked more days per year and, perhaps, more hours per day than free farmers. Since our efficiency indexes measured the labor input not in man-hours but in man-years, the more intensive utilization of labor shows up not as greater labor input but as a higher level of productivity. In 1971 we were inclined to believe that our failure to take account of the greater number of hours worked per year by slaves than by free men explained all, or nearly all, of our index of the superior efficiency of slavery. We also considered the much-debated possibility that there were economies of scale in the slave sector of agriculture. Even scholars who thought that slave labor was less efficient than free labor had suggested that the lower quality of labor might have been offset by the superior entrepreneurship associated with large-scale plantations.
To test these hypotheses we launched a search for additional data. A sample of 5,700 estates containing information on the price, age, sex, skills, and handicaps of slaves was retrieved from the probate records of southern courts. Southern archives yielded a sample of the business records of roughly 100 large plantations containing either detailed information on the organization of production, including the daily activities of each slave in the labor force, or demographic information needed to adjust the labor input of women.5 The data in these sources, combined with the data in the Parker-Gallman sample of over 5,000 southern farms listed in the manuscript schedules of the 1860 Census,6 made it possible to refine the input and output measures of G, The net effect of these refinements was to reduce Gs /Gn to 134.7.7 The new data also permitted the computation of total factor productivity indexes by farm size and subregion. Tables 2 and 3 show that the superior efficiency of southern agriculture was not due primarily to the high performance of the free farms of the South. Free farms of the Old South fell be- low the efficiency of northern farms by 2 percent, while free farms in the New South exceeded the efficiency of northern farms by 13 percent. Thus only 4 percent of the efficiency advantage of southern over northern agriculture was due to the superior performance of the free sector. Slave farms accounted for 96 percent of the southern advantage.
Table 3 shows that within each region efficiency increased with farm size, except that in the New South the efficiency index is higher for medium than for large plantations. While we considered the possibility that in the West this intermediate category of slave plantations was actually more efficient than large plantations, we believed that the reversal was probably due to measurement errors. One was a failure to adjust adequately for the locational component of land values, which might have accounted for a much larger share of total land value on slave plantations with 51 or more slaves, especially in the New South, than on slave plantations in the 16 -50 category. Another was the inadequacy of our adjustment for omitted products. Large slave farms, especially in the West, probably engaged much more heavily in home manufacture than did small ones. Large slave farms also appear to have devoted a larger share of the labor force to domestic services than did small plantations. We did not think that when these adjustments were made the entire differential in efficiency between the Old and New South would disappear. The continuous flow of labor from the Old South to the New South suggests that the long-run equilibrium between the two regions had not been attained by 1860. Hence one would expect to find some efficiency advantage in the newer area.