NUTRITION AND SIGNALING IN SLAVE MARKETS: A NEW LOOK AT A PUZZLE WITHIN THE ANTEBELLUM PUZZLE Lee A. Craig Department of Economics North Carolina State University Raleigh, NC 27695-8110 and Robert G. Hammond Department of Economics North Carolina State University Raleigh, NC 27695-8110 Draft: October 8, 2012 Abstract: Between 1800 and 1860 mean adult stature of (U.S.) white males declined by nearly an inch, while real output grew substantially, creating the “Antebellum Puzzle.” In contrast, male slaves did not experience a comparable decrease in heights. To explain this puzzle within a puzzle, we show that the benefit of the marginal nutrient exceeded the cost throughout the antebellum era. As a result, it paid for slave owners to engage in the supplemental feeding of slaves, which increased their stature. While this is consistent with a productivity explanation of increased stature, we also argue that informational asymmetries played an important role in the market for slaves. Slave owners had an incentive to signal that their slaves were high-productivity laborers by supplying them with additional food, which positively impacted slave heights. We provide evidence that, distinct from a productivity explanation, signaling mattered in the trend of slave heights. 0 NUTRITION AND SIGNALING IN SLAVE MARKETS: A NEW LOOK AT A PUZZLE WITHIN THE ANTEBELLUM PUZZLE Abstract: Between 1800 and 1860 mean adult stature of (U.S.) white males declined by nearly an inch, while real output grew substantially, creating the “Antebellum Puzzle.” In contrast, male slaves did not experience a comparable decrease in heights. To explain this puzzle within a puzzle, we show that the benefit of the marginal nutrient exceeded the cost throughout the antebellum era. As a result, it paid for slave owners to engage in the supplemental feeding of slaves, which increased their stature. While this is consistent with a productivity explanation of increased stature, we also argue that informational asymmetries played an important role in the market for slaves. Slave owners had an incentive to signal that their slaves were high-productivity laborers by supplying them with additional food, which positively impacted slave heights. We provide evidence that, distinct from a productivity explanation, signaling mattered in the trend of slave heights. 1 Professional slave traders commanded little respect in southern society, perhaps reflecting moral embarrassment at their occupation but also for much the same reason that used car dealers do in our society. - Daniel Walker Howe What Hath God Wrought In the United States, the mean adult stature of native-born white males of northern European descent declined by nearly an inch between 1800 and 1860 (Haines et al. 2003). During the same period, real per capita GDP grew at an average annual compounded rate of 1.2 percent (Johnston and Williamson 2008). This so-called antebellum puzzle has been much explored in the economic history literature over the past two decades. Explanations of the negative trend in white male stature focus on, among other issues, increasing inequality in the distribution of income, the disamenities of industrialization and urbanization, a decrease in food consumption, and the spread of disease resulting from improvements in the transportation network. (See, for example, Chanda et al. 2008; Craig and Weiss 1998; Haines et al. 2003; Komlos 1987 and 1996; and summaries of the literature in Steckel 1995 and 2009.)1 There remains a puzzle within the antebellum puzzle: male slaves did not experience a comparable decrease in heights (Carson 2008 and 2009; Haines et al. 2011; Komlos and Coclanis 1997; and Margo and Steckel 1982). Of course slaves were less likely than whites to suffer from changes in the distribution of income or the negative effects of industrialization and urbanization. Thus, explanations of the difference between the trends in the statures of slaves and whites during the period typically revolve around changes in the market for nutrients. For example, John Komlos and Peter Coclanis argue that “an increase in the price of nutrients…induced [white] households to substitute carbohydrates for animal proteins. 1 Slaves were not the only exceptions to the puzzle. The very rich also appear to have avoided a downturn in the biological standard of living (Sunder and Woitek 2005). 2 However, slaves fared better [than whites],” as their owners found it profitable to engage in more nutritious feeding practices at the margin (1997, p. 433). 2 (See Figure 1.) Insert Figure 1. We agree with Komlos and Coclanis; the relative price of nutrients played a role in the different trends in stature, and in the next section, we show that the value of the marginal nutrient, as measured by the resulting increase in the productivity of a male slave, exceeded the marginal cost of nutrition throughout the antebellum era. In short, we argue that, from a slave owner’s perspective, it paid to feed. However, we also explore an additional, complementary explanation of the trend in slave heights. Specifically, we argue that the antebellum market for slaves contained informational asymmetries, and the nature of these asymmetries led slave owners to produce taller slaves on average.3 Slave owners, who possessed private information about the productivity of their slaves, had an incentive to sell their least productive, unhealthy, or otherwise most troublesome slaves. Suspecting as much, slave buyers would have expected the slave market to contain some low productivity slaves that were difficult to identify. We argue that, in response to the suspicions of potential buyers, individual slave owners followed feeding practices that maintained the nutritional status of slaves, while that of whites was eroding. To understand the strategic interactions between slave owners and slave buyers, we offer a model of the sequential decision problem of two slave owners: the first owns a high 2 It was also the case that the real price of manufactured goods declined during this period, and free consumers shifted consumption to these relatively lower priced non-food goods. 3 Pritchett and Freudenberger (1992) argue that slaves brought to the market for sale were taller, on average, than the slave population as a whole, which is consistent with our story, as explained below. 3 productivity slave, while the second owns a low-productivity slave. Neither slave has completed his growth years. Under the assumption that productivity levels of individual slaves are not observed by slave buyers, the first owner recognizes that his high-productivity slave will some day yield the same price as a low-productivity slave. In response, he allocates additional food to signal high-productivity by increasing his slave's stature, which studies show reflects productivity (Friedman 1982, Rees et al. 2003, and Steckel 1986 and 1995). Recognizing that this decision can be mimicked, the second owner allocates additional food to his lowproductivity slave. This non-cooperative process would continue until the marginal benefit of additional stature is outweighed by the marginal cost of feeding. The result is a slave market with slaves who were taller than they would have been in the absence of any signaling value of stature.4 Thus our explanation of the relative trend in slave heights during the antebellum period contains two distinct components: One is the productivity explanation, which focuses on the role of feeding in the increase in stature and its resulting impact on productivity. The other is the asymmetric information explanation, which focuses on feeding as a means of masking relatively low-productivity slaves. We argue these two forces, working together, caused the trends in the heights of slaves and whites to diverge during the antebellum era. Nutrition and Slave Productivity Net nutritional status – the difference between nutritional inputs and the demands of work, body maintenance, and disease – is the key to human growth. The consumption of 4 There is a long-running debate in the literature on the extent of adverse selection in slave markets. Greenwald and Glasspiegel (1983) argue that high-productivity slaves were less likely to be sold than low-productivity slaves. Pritchett and Chamberlain (1993) challenge this argument, and their work is in turn challenged by Komlos and Alecke (1996). For our purposes, what matters is the feeding behavior of slave owners and how this feeding behavior is manifested in the heights of the slaves that are ultimately exchanged in the market. 4 nutrients, net of those exhausted during work or while fighting disease, determines whether homo-sapien populations achieve their genetic height potential. Since a positive net nutritional status stimulates growth, adult stature can be viewed as a “cumulative indicator of net nutritional status over the growth years” (Cuff 2005, p. 10). Thus, in making feeding decisions, profitmaximizing slave owners must weigh the marginal cost of nutrients against the marginal value of more productive slaves. The results of previous studies suggest a strong relationship between feeding and productivity. For example, Steckel (1986) studied feeding behavior over a slave’s life course, and Rees et al. (2003) model the optimal allocation of food between childhood and adolescence, explicitly capturing the relationship between a “jump in food allocation” and “the acceleration in physical capacity” once the slave reached his teen years (p. 27). The focus in this section, then, is on measuring and comparing the cost of this “jump,” as measured by the cost of the marginal nutrient, with the market value of the resulting “acceleration in physical capacity.” 5 That measurement is driven by two relationships. One is between nutrition and stature. We call this the effect of nutrition on stature or simply the nutrition effect, and it reflects the impact of net nutrition on human stature. The other is the relationship between stature and output or productivity. We call this the effect of stature on output or simply the stature effect, and it reflects the impact of stature on real output and thus productivity. The literature provides us with estimates of both relationships. 5 Because the model we present below reflects the present value at birth from the marginal nutrient supplied over the slave’s entire growth period, one can think of our estimates as the market value of the integral of increased physical capacity, resulting from the marginal nutrients, as modeled by Rees et al. in their Figure 2(b) (2003, p. 26). 5 With respect to the nutrition effect, Haines et al. (2003) estimate the impact on adult stature of access to protein during an individual’s growth years.6 They estimate: Hi = βNi + ⍺Xi; where Hi is adult stature of the ith individual; Ni is nutrition; and Xi is a vector of other variables that influence stature. Thus ∂H/∂N=β is the nutrition effect on stature. As for the stature effect, Steckel (1995) estimates: Hj = γlnyj + φZj, where Hj is mean stature for the jth country; yj is real per capita income or GDP; and Zj is a vector of other related variables. Because we are interested in stature’s impact on productivity, we invert Steckel’s specification to obtain the stature effect: ∂lny/∂H=1/γ. For the nutrition variable, Ni, Haines et al. estimated, in 100s of grams of protein per adult equivalent per day, the “marketable surplus” protein – i.e. the surplus that could have been consumed on the farm or sent to the market beyond the benchmark food needs of the local population and livestock.7 In making the decision to increase feeding in response to market conditions, slave holders typically would not have kept one hundred percent of this surplus. For the sake of argument, let us say that they kept ten percent of the surplus, i.e. 10 grams per capita per day, to meet the marginal food needs of their slaves.8 In other words, we want to measure the impact on a slave’s productivity when he receives an additional 10 grams of protein per day, every day until he was sold upon reaching adulthood.9 Setting the feeding problem up in this 6 Haines et al. actually measure production rather than consumption, but the way in which they define their net production variable, in the form of a “marketable surplus,” allows us to interpret it as a “shadow” consumption variable – i.e. it reflects the marginal consumption of nutrients. 7 The benchmark is basic metabolic needs. The unit of production was the county in which the individual was born. The technique is derived from Atack and Bateman (1987). While the definition of what constituted a surplus might be debatable, such debates need not trouble us here, as we are only interested in the marginal impact of nutrition, not the overall level of consumption. 8 Though arbitrary, this is not an unreasonable assumption in terms of increasing daily consumption. Ten grams of protein would have been equivalent to 2.5 slices of whole wheat bread. For sources and details, see footnote 11 below. 9 We assume the slave is fully grown by the end of his 20th year. 6 way allows us to pose the following two empirical questions: How much would an additional 10 grams per day for 20 years have cost? And, how much additional output would the slave have produced as a result of that additional protein? Haines et al. provide several different estimates of the nutrition effect, ranging from 0.0656 to 0.1409, with a median figure of 0.1285, which we employ in our estimation below.10 Thus, the equivalent of 10 grams of protein per day from birth to adulthood would have generated, roughly, an additional one-tenth of an inch in adult stature. The source of those marginal grams matters, because the price of a gram of protein differs from source to source. Our analysis includes three common foods from the antebellum diet: wheat, in the form of loafen bread; corn, consumed as cornbread or “johnnycake”; and bacon.11 To conserve space, we explain our results for a linear combination of these three foods, which we call the “mixed” diet.12 With respect to wheat, 10 grams of protein can be found in 2.5 slices of whole wheat bread or 16.66 percent of a loaf.13 Each loaf has two cups of flour at 5.5 ounces each, for 11 ounces of flour per loaf. A bushel of wheat is 59.4 pounds or 86.4 loaves of bread.14 It follows 10 Haines et al. provide an even number of estimates. Our “median” is actually the mean of their two middle figures. For the nutritional contents of these foods, see the following sources: For wheat: http://www.mayoclinic.com/health/whole-grains/nu00204; for corn: http://www.ag.ndsu.edu/pubs/ansci/beef/as1238w.htm; http://www.howmanycaloriesin.com/Calorie_Finder.aspx?FoodID=18024; for pork: http://www.nutritiondata.com/facts/sausages-and-luncheon-meats/1489/2; March 11, 2010. Some foods experience a reduction in nutritional content during processing, in which case the contemporary figures would bias upwards our estimates below; however, refrigeration, trade, and modern agricultural practices have eliminated the loss of nutrients that was associated with seasonal production. We assume these two factors cancel each other out. 12 In the mixed diet, we assume the marginal protein comes from wheat, corn, and pork with the following weights: 0.20 for wheat; 0.40 for corn; 0.40 for pork. This assumption follows from primary sources which noted the relative importance of corn and pork in the slave diet; see Hilliard (1972), passim. 13 These are modern measurements. How you slice the loaf ultimately does not matter. All we are trying to do is convert protein back into bushels of wheat, which were the units that were typically bought and sold on the market and for which we have antebellum prices. 14 59.4/(11/16)=86.4 11 7 that at 15 slices per loaf, each bushel of wheat can generate 1,296 slices of bread.15 Thus 2.5 slices daily, which yields our marginal 10 grams of protein, equals 0.2 percent of a bushel. Throughout the antebellum era wheat traded for around $1.00 a bushel (Atack and Bateman 1987, pp. 232-237; Buley 1950, p. 563; Craig 1993, pp. 107-116; U.S. Bureau of the Census 1975, p. 209). Using 1830 as an example, the price of wheat was $0.96 (in 1860 dollars), which suggests that 10 grams of protein would have cost, on average, roughly $0.0019 a day.16 How much additional output could an owner expect to receive in return for $0.002 worth of protein per slave per day? As noted above, Steckel (1995) provides estimates of the stature effect, which range from 0.204 to 0.252. In other words, an additional centimeter (0.39 inches) in stature would have generated, roughly, an additional 0.20 to 0.25 percent of real output per worker.17 So, from Haines et al., 10 grams of protein gives us an additional 0.10 inches or so in adult stature, and from Steckel, 0.10 inches in stature gives us an additional 0.06 percent in real output, which would be reflected in the market price of a slave. With respect to the other two components of our mixed diet, corn and pork, although corn was typically less expensive per unit than wheat, usually one-half to one-third the price per bushel, the protein content of corn is much less than that of wheat, and it varies depending upon how each grain is processed. We assume the protein content of corn to be only 10 percent that of wheat, which is within the range of estimates provided by the sources in footnote 11. Thus, again using 1830 prices, the price for 10 grams of protein via cornbread or johnnycake was 15 The number of slices is endogenous, depending on the thickness of each slice. The slices-per-loaf figure comes from the assumption that 2.5 slices is one-sixth of a standardized loaf. For details see the sources in footnote 11. 16 Our prices are from the following sources: Wheat prices are from U.S. Bureau of the Census (1975, p. 209); corn prices are from Buley (1950, passim) and Cole (1938, passim); pork prices are from Adams (1986). The antebellum prices are deflated using the CPI from http://measuringworth.com/uscpi/. 17 We rely on Johnston and Williamson’s (2008) aggregate output estimates for the antebellum era. Romer (1989, p. 22) and Balke and Gordon (1989, p. 84) offer dueling estimates of nominal and real GDP dating back to 1869; which for that year are $7.745 billion (in 1869 dollars) and $8.21, respectively. Their figures bound the Johnston and Williamson estimate for that year, $7.85. Thus we argue Johnston and Williamson’s antebellum series can be interpreted as “middle-of-the-road”. 8 $0.0044. As for pork, it had more protein per unit than wheat or corn, but it was also relatively more expensive. Ten grams of protein, or 1.25 ounces of bacon, would have cost $0.0036. We now have most of the pieces we need to address the productivity component of the puzzle within the antebellum puzzle. In terms of cost, we assume the slave owner estimates the cost of an additional 10 grams of protein per day, from the mixed diet, from birth to the end of the slave’s 20th year, at which point the slave is put up for sale. Figure 2 shows, for each year from 1801 through 1860 – i.e. by slave birth-year cohort – the present value of the cost at birth of this nutritional supplement. Note that each observation represents the cost, as measured by the present value at birth, of the feeding supplement for one male slave born in that year and sold on his 20th birthday. For example, the present value at birth of the protein supplement, for a slave child born in 1830 would have been $20.11, in 1860 dollars.18 Insert Figure 2. To obtain the present value of the additional output 10 grams of marginal protein would “purchase,” we model a slave’s productivity over the course of his working life. Field-Hendrey and Craig (1993) show that male slaves did not generate a positive net output until they reached their teenage years; the productivity of a teenager was roughly two-thirds that of an adult male; and males remained productive through age 54. Accordingly, we assume that from ages 13 to 20, the slave owner reaps some gross output reward from the additional food consumed by the slave (specifically, two-thirds of that of an adult male equivalent), and beyond that the owner realized the gain from the market’s valuation of the slave’s enhanced productivity through age 18 We use a six percent discount rate. The yield on long-term U.S. debt hovered around 5.5 percent in the 1840s; for savings deposits in commercial banks the yield was 5.00 to 6.00 percent; and the mean for call money in the 1850s was 6.3 percent. See Homer and Sylla (1991, pp. 304 and 318-319). 9 54. Figure 3 contains three sets of estimates (“high,” “mean,” and “low”) of the present value at birth, in 1860 dollars, of the lifetime productivity increase from the protein supplement over the slave’s first 20 years of life.19 As in Figure 2, each observation represents the present value at birth for a slave born in that year. For example, using the mean series as a reference point, the gross increase in the present value of the output produced by a slave born in 1830 would have been $63.51. Insert Figure 3. Subtracting the cost of protein in Figure 2 from the gross output estimates in Figure 3 generates the net benefit to slave owners from the marginal protein supplement. This net benefit is shown by slave birth cohort in Figure 4. Note that the figure is positive throughout the antebellum era, and, to offer a benchmark from the mean series, the 1830 figure is $43.40.20 In short, at the margin, it paid to feed; and this is what slave owners did (just as Komlos and Coclanis suggested); and as a result slaves were not exposed to the same downward pressure on stature, resulting from the market for nutrients, experienced by antebellum whites.21 Insert Figure 4. 19 The “High” estimate employs Steckel’s upper-bound estimate of the stature effect; the “Low” estimate employs his lower-bound; and the “Mean” estimate uses the mean of these two figures. 20 The estimates in the figure differ from those in Williamson and Cain (2010), because we only estimate the marginal impact of the additional feeding; whereas they provide the full “value” of a slave. 21 In essence, we are arguing slave owners faced the classic Marshallian dilemma. The first elucidation of the problem appears in the calculus of Marshall’s “speculative builder” – though Marshall credits Edgeworth with the initial insight. To wit: “…the marginal outlay which the builder is willing to make for an additional small supply … is equal to … that increment in his total receipts, which he will obtain by the increase” (1920, p. 848). In our case the marginal outlay is for nutrition, and the increment to total receipts is reflected in the resulting increase in the market value of the slave. 10 The results in Figure 4 might reasonably be interpreted as estimates of the quasi-rent imbedded in slave ownership, which was an element of the economic profit associated with slavery. One (perhaps peculiar) manifestation of these quasi-rents was the diverging trends in black and white stature during the antebellum era. Although the source of the quasi-rents in slave agriculture in the American South is much debated in the literature on slavery (Fogel 1989), the willingness and ability to exploit slave labor (or the willingness to have an overseer do it) must be considered as one component. Our estimates in Figure 4 are consistent with evidence, dating from at least Conrad and Meyer (1958), that suggests slave owners were able to capture a substantial portion of their slave’s output, certainly more than they could have had they been forced to pay a market wage. Of course, this particular component of the slave owner’s quasi-rent must be judged against the discount imposed by buyers on all slaves as a result of the suspicion that the market contained low-productivity slaves who were difficult to identify, a result of the informational asymmetries in the antebellum slave market. Evidence from the Historical Record Contemporaneous documents provide narrative support for a link between the food allocation decisions of slave owners and informational asymmetries in the market for slave. There are two components of that link: one is the link between food allocation and stature, and the other is the link between stature and slave prices. With respect to the first component, the anthropometric literature confirms a link between food allocation decisions and stature. This relationship forms the foundation for research on the biological standard of living and is thoroughly reviewed by Cuff (2004) and Steckel (1995 and 2009).22 That relationship was also recognized by the individuals who lived during the period in question. For example, the 22 See also the chapters in Komlos and Baten (1998); and Steckel and Floud (1997). 11 following quote appears in the U.S. Work Projects Administration’s Slave Narrative series, taken from a September 10, 1937 interview with former slave Thomas Hall: The food in many cases that was given the slaves was not given them for their pleasure or by a cheerful giver, but for the simple and practical reason that children would not grow into a large healthy slave unless they were well fed and clothed; and given good warm places in which to live (U.S. Work Projects Administration 1941). As for the other component of the feeding-stature-price link, the documentation from slave markets provides considerable evidence that stature was a prime consideration of slave buyers when choosing among the available slaves. According to Tadman (1989, p. 50), “It was, in fact, very common for children, whose work output would closely relate to their stage of physical development, to be bought by the pound or to be bought according to height. The specialist circulars and price lists of the trade routinely classified children by height or weight (more so than by age), and traders in describing any purchase often gave a note of height and weight.” Eyewitness accounts support this view. Those who observed slave markets in operation reported that slaves were lined up for sale “in the order of their respective heights” (Northup 1855, p. 79), and confirmation of this arrangement by height is widely available (Deyle 2005; Johnson 2001). Of course, for asymmetries in the market to play a substantial role in the food allocation decision, it must be the case that slave owners considered market outcomes as a central concern in their food allocation decisions. If the probability that a slave would be sold was low in some 12 meaningful economic sense, then slave owners should only consider productivity when making their food allocation decisions. If, on the other hand, the probability any particular slave would be sold was sufficiently large, then slave owners should also consider the slave market when allocating food. According to Tadman (1989) slaves were transported from the “Old” (Upper) South to the “New” (Lower) South at an average rate of 200,000 slaves per decade. Further, as discussed by Johnson (2001), The Virginia Times reported that 40,000 slaves were sold in the year 1830. Pritchett (2001) calculates that the number of slaves who were sold out of the Old South to the New South was approximately one-half of the total 835,000 slaves who migrated from the former region to the latter between 1790 and 1860.23 We consider these to be large figures, and relative to those interregional sales, an even larger number of slaves were sold in local markets; though the exact ratio of local to interregional sales is debated, the evidence strongly suggests that local sales comprised a majority of the total sale of slaves (Deyle 2005). In short, the magnitudes of local and interregional sales indicate that a substantial proportion of the total slave population was sold. As a result, the market for slaves would have been important in the decision-making process of slave owners when allocating food to their slaves. To formalize this decision-making process, we now present a theoretical model that illustrates the role of signaling. Model We consider the strategic interactions of slave owners (who want to maximize their return on slave capital) and slave buyers in the context of the asymmetric information and the signaling model of Spence (1973 and 2002). We assume each owner owns one slave and has the 23 See also the references cited by Pritchett (2001), including Fogel and Engerman (1974). 13 option of putting the slave up for sale in a secondary market once the slave achieved adulthood. Slaves differ inherently by the level of their productivity. Accordingly, we divide male slaves into two categories:24 high-productivity (type H) and low-productivity (type L): { L , H }, where L H ; and some fraction, λ, of the slaves are of type H. Each slave’s productivity level is observed by that slave’s owner. Participants in the market observe only the stature of those slaves available for purchase.25 Given that productivity levels are not observed by slave buyers, slave owners have an incentive to send a signal concerning which type of slave is being offered on the market, especially if doing so increases the price received in the market for high-productivity slaves. The dimension of signaling that we consider is in the food allocation decision, which is a function of the slave’s type, e(θ). The cost of signal e to an owner of a slave of type θ is c e, . Signals are discrete: e {e1 , e2 } . We say that the owner has chosen not to signal when choosing e = e1 or has chosen to signal when choosing e = e2. In this sense, choosing e1 is equivalent to making the food allocation decision that would be made in the absence of any asymmetries or signaling value in the market. Given the evidence presented thus far, our objective here is to separate the relationship between stature and productivity from the relationship between stature and signaling. Stature reflects productivity because better fed slaves, who on average were taller, generated more 24 We say “male” slaves because our model strictly refers to the productivity-stature relationship for males. Although our model necessarily omits some features of the market for males, we argue that the market for males is dominated by the productivity-stature relationship; whereas, the market value of females was determined by other complicating factors. Bodenhorn’s (2010) work on the market for manumission more generally confirms differences between the market for male slaves and that for female slaves. 25 It is possible that body-mass index (BMI) is a better indicator here (Bodenhorn and Price 2009); however, since we lack weight data, it is not possible for us to use BMI for this exercise. Further, development economists and researchers from other literatures (e.g., health economics) commonly use data on stature, arguing that it is a better measure of longer-run nutritional status, whereas weight is a better measure of current nutritional status (Strauss and Thomas 1998). 14 output than slaves who were fed less. We take the productive value of stature as given and investigate the role for signaling via stature in addition to stature’s enhancement of productivity. In the notation of the model, e1 is the level of food that a slave owner would allocate to a slave for the sole purpose of raising an optimally productive slave in the absence of informational asymmetries. In contrast, e2 is the (higher) level of food that a slave owner would allocate to a slave for productivity and for the purpose of signaling that the slave is a high-productivity slave. Thus, while some of the food that slaves received was to meet basic metabolic needs and enhance productivity (as explained above), here we are modeling the additional food that owners allocated to their slaves to signal that the slave is an innately high-productivity slave, even when he was not. It follows that there are two types of equilibria that may characterize the market for slaves: separating and pooling. In a separating equilibrium, the owners of high-productivity slaves make different food allocation decisions than the owners of low-productivity slaves. In such a world, there would only be “tall high-productivity” slaves and “short low-productivity” slaves, and the equilibrium market value of slaves would perfectly reflect their productivity. In a pooling equilibrium, all slave owners make the same food allocation decisions and a slave’s stature does not signal his productivity to slave buyers. In such a world, a high-productivity slave sells for the same market price as a low-productivity slave because height ceases to signal productivity. As a result, slave buyers treat both types of slaves as being of average productivity. A pooling equilibrium is found when owners of high-productivity slaves cannot “separate” their slaves from low-productivity slaves, causing both types of slaves to “pool” at the average level of productivity. High and low-productivity slaves do not separate when the signal that is sent by the owners of high-productivity slaves is mimicked by the owners of low-productivity slaves. 15 We argue that the market for slaves exhibited a pooling equilibrium because the owners of low-productivity slaves would have found it profitable to mimic the food allocation decisions made by the owners of high-productivity slaves. The owners of low-productivity slaves were able to mimic because the cost of increasing the stature of low-productivity slaves was sufficiently similar to the cost of increasing the stature of high-productivity slaves. This prevented the owners of high-productivity slaves from making a food allocation decision that separated their slaves such that they yielded a higher market price.26 We now turn to the evidence to support our argument that signaling played a meaningful role in slave markets. Empirical Test of Informational Asymmetries In this section we provide evidence that the stature patterns of slaves are consistent with the presence of informational asymmetries in slave markets. Demonstrating that these asymmetries played an important role in the market for slaves is consistent with our argument that signaling played a role in the divergence of white and slave stature during the antebellum era, a role that is complementary with but separate from the role played by our productivity argument. It seems reasonable to assume that informational asymmetries would be less for slaves sold locally relative to those sold in the interregional trade. One would expect local buyers to have information concerning the treatment of slaves by local slave owners. Indeed, they may have even come in direct contact with the slave who is up for sale. Thus local slaves come to the 26 It is worth contrasting the market for slaves with that for used cars, where owners of high and low quality cars can decide whether or not to place a warranty on the car. The owners of low quality cars find it unprofitable to mimic the owners of high quality cars because it is more costly to warrant a low quality car. As a result, warranties can ameliorate this so-called “lemons’ problem” through a separating equilibrium in the market for used cars. Although there were warranties attached to some slave sales, the probability of enforcement was substantially less than one, and adjudication was costly (Wahl 1996). 16 local market with less uncertainty of their care, feeding, and productivity during their formative years relative to slaves brought to market from a distant location. If informational asymmetries play an important role in the market for slaves, then local slaves should be sold at a premium relative to distant slaves, ceteris paribus. The New Orleans Slave Sale Sample, compiled by Fogel and Engerman, includes data from sales of slaves covering the period from 1804 to 1862. The data include information on the year of sale, the origin of the seller, the price of the slave, and the age and gender of the slave. The origin of the seller can be classified as local (in this case from New Orleans), in-state (from another location in Louisiana), or out-of-state (from a state other than Louisiana). To make a stark comparison, we compare local slaves (for whom informational asymmetries are lowest) to out-of-state slaves (for whom they are highest). Our sample includes male slaves and, in particular, we focus on male slaves who were sold at or below the age of 30.27 These data are used to test for informational asymmetries in an OLS regression model, the results of which are shown in Table 1. Model (1) includes only adult male slaves (between 21 and 30 years old), while Model (2) includes all male slaves (between 0 and 30 years old) with a dummy variable for adults. (The model also includes dummy variables for each decade between 1810 and 1860 as well as a dummy variable that equals one if the sale included multiple slaves.) Our focus is on the local dummy variable, which equals one if the seller originated from New Orleans and zero if the seller originated from a state other than Louisiana.28 Insert Table 1. 27 To facilitate comparison, we make the sample more homogeneous by eliminating any slaves who were noted to have any specialized training or occupation outside of field work. 28 Note that our comparison may be affected by the higher rate of manumission among slaves sold locally (Bodenhorn 2010). However, because the share of manumissions in New Orleans was small after the Louisiana Purchase, manumissions are unlikely to drive the findings that we present. 17 The results support the claim that informational asymmetries were present in slave markets. We can reject the null hypothesis that an adult male slave’s price is independent of his origin. In particular, Model (1) shows that local adults sold for $225.25 more than out-of-state adults (t statistic = 2.04, p-value = 0.04). Further, Model (2) shows that local adults sold for $233.65 more than out-of-state adults.29 In other words, a slave whose productivity is less uncertain (because he is of local origin, which suggests there is more information concerning his care and treatment) sells for a higher price relative to a distant slave, after controlling for the price of children whose productivity is yet to be determined.30 The information gap concerning a slave’s treatment causes a slave buyer to value a credible indicator of the slave’s productivity, demonstrating the potential for signaling to play an important role in slave markets. The fact that a buyer expects to find low-productivity slaves in the market does not keep him away; nor does it destroy the relative value of stature as a signal of productivity. It just drives the offer price down across the board. Thus slave owners face a two-part calculation. The first part involves whether, at the margin, it paid to supply slaves with enough additional nutrients to generate additional productivity, as manifested in their stature. We have shown above that it did. Given this evidence that the benefit exceeded the cost of the marginal nutrient during the antebellum era, one piece remains to complete our argument that a productivity story alone is incomplete. Since it paid to offer a slave more nutrition at the margin, the second part of the owner’s calculation involves whether the net benefit of that supplemental feeding was large enough to overcome the discount buyers imposed on the market price of all slaves. 29 The combined effect of being a local slave and being a local adult slave is found by summing the two associated coefficients, 233.65 = 283.10– 49.45, which is calculated from the table (t statistic = 2.77, p-value = 0.01). 30 The results also hold in a t-test comparison of mean prices by origin, when expressed as a ratio of the price by origin of children (Hinkley 1969). In particular, the local adult-to-child price ratio is 2.07; while the out-of-state adult-to-child price ratio is 1.93 (t statistic = 1.77, p-value = 0.07). 18 The Buyers’ Discount in the Slave Market Exactly how large would that discount have been? Fogel presents estimates of the discount in the market for slaves with various “defects.” The ones of most relevance to our story would seem to be those that possessed the potential to be unobservable (from the buyer’s perspective) defects, such as “runaways” and those with “drinking or other vices” (1989, p. 70). Fogel puts the discount for these slaves at the upper end of the discount range, around 40 percent. (In the language of the model, we assume that the relationship between the productivities of high and low-productivity slaves is L 0.6 H .) However, a figure in this range overstates the mean discount in the market overall for three reasons. One is that although these defects might have been unobservable in the slave’s physical appearance, they were nonetheless known to buyers; otherwise they would not have shown up in the data. Another is that these were among the worst possible defects for a slave. Together these two factors place Fogel’s figure well beyond the bound of estimates for our purposes. Despite the presence of informational asymmetries, not every slave on the market was a drunk or a runaway. In other words, all drunks and runaways might have been low-productivity slaves, but all lowproductivity slaves were not drunks and runaways. The third reason is that in constructing his belief function, the slave buyer includes both the cost of a bad characteristic and the probability that a slave will have that characteristic. The characteristics of the slaves in Fogel’s sample, slaves who happened to display the worst possible characteristics from a prospective owner’s perspective, were known with a probability of one. While the nature of the problem prohibits us from giving a definitive figure here, something in the range of 20 percent of the full market price with no asymmetric information 19 seems on the high end and therefore reasonable for our purposes. Such a discount would be consistent with the buyer expecting a fifty percent chance of acquiring a slave whose productivity matched those with the worst characteristics enumerated by Fogel, i.e. in the model the probability of obtaining a high-productivity slave, λ, is assumed to be fifty percent.31 Furthermore, a discount of this magnitude is consistent with the empirical results of Greenwald and Glasspiegel (1983). Finally, with respect to the prices of slaves, depending on year and location, citing primary sources, Woodman (1966, p. 40) reports that a “prime field hand” could be purchased for between $500 and $1,000 between 1820 and 1850.32 Using the annual means from the New Orleans sales data (Fogel and Engerman 2008), we find that the prices, in 1860 dollars, ranged from a low of $257 in 1813 to a high of $1,339 in 1860, with a mean of $596. Discounting each year’s price by the buyer’s discount discussed above, yields the mean annual adjustment slave buyers would have made to the prices they were willing to offer for a prime field hand at the end of his 20th year. Subtracting this value from the net present value of the protein supplement in Figure 4 yields what we refer to as the “adjusted” net present value at birth of the gains from supplemental feeding, as shown in Figure 5. Using our mean figures, and again using slaves born in 1830 as an example, the adjusted net gain to a slave holder from the marginal net nutrition would have been $16.64. The mean for the period as a whole was $17.46, and in only five of the sixty years was the figure negative. In short, it did pay to feed, and it paid to feed even in the presence of the discount imposed by buyers as the result of their informational 31 Furthermore, buyers who over estimated the probability of obtaining a slave with the worst characteristics would systematically and consistently underbid for slaves, and would thus end up never buying one. 32 These were prices Woodman reported for prime field hands in Georgia in the years 1821, 1828, and 1840 (1966, p. 40). Prices increased dramatically during the 1850s, and there was also a brief run-up in prices just before the Panic of 1837. 20 disadvantages. As a result, slave heights did not decrease; thus there was no antebellum puzzle for slaves. Insert Figure 5. Conclusion Komlos and Coclanis (1997) argue that slave owners found it profitable to engage in more nutritious feeding practices, relative to free whites, than would have been the case in the absence of the market conditions for slaves and food during the antebellum era. We offer empirical support for this position. The increase in the present value at birth of a daily protein supplement would have yielded a real return to slave owners that was greater than the cost of the supplement. However, this was not the only force at work in the market for slaves. The presence of asymmetric information also played a role in the diverging trends in black and white stature during the period. Used cars provided the seminal example of market imperfections in the presence of asymmetric information (Akerlof 1970). As the epigraph to this paper illustrates, historians have compared antebellum slave dealers to used car dealers. Our estimates suggest that the comparison is not ironic. It is also no coincidence that slaves bound for the market tended to be taller than slaves who were not sold by their owners (Pritchett 1997). Slaves possessed traits known only to their owners. Slave buyers knew that slave owners possessed knowledge of those traits, but there was no credible way that such knowledge could be conveyed verbally; just as a sign on a used car that says “Great Value” conveys no credible information about the vehicle’s true market value. 21 As a result, slave owners who wanted to sell a high-productivity slave sought a credible way of signaling to buyers that this slave was not a low-productivity slave. One way to do that was through the overall health of the slave, which would have made the slave more productive and which would have shown up in the slave’s physical characteristics, one the most prominent of which was his stature. The solution, assuming the price of nutrients was low enough relative to the market price of a taller slave (which was the case), was better feeding. However, as thousands of slave owners attempted to send a positive signal concerning their slave’s productivity, even if the slave was not a high-productivity worker, they would have put upward pressure on the mean height of slaves, ceteris paribus. In summary, we combine this signaling explanation, which relies on the presence of informational asymmetries in slave markets, with a productivity explanation.33 Taken together, the two stories suggest that supplemental feeding netted slave owners something in the neighborhood of $17 in present value on average.34 As a result, slave owners fed their slaves more than they otherwise would have, and the trend in slave heights diverged from the trend in white heights, which is consistent with explanations of the puzzle within the antebellum puzzle offered by Komlos and Coclanis and Rees et al. 33 Using dynamic optimization techniques, Copland and Murphy (2010) estimate the optimal amount of protein in slave diets. They find that the actual slave diet was more protein intensive than necessary for profit maximization, providing support for our conclusion that at the margin slave owners provided slaves with a protein supplement. 34 Using slaves born in 1830 as an example, this figure is calculated as follows. The net gains from supplemental feeding, measured as a present value at birth, is equal to the gains from additional output ($63.51) minus the cost of supplemental feeding ($20.11). These net gains ($43.40) are adjusted for the buyers’ discount in slave markets ($26.76) to calculate the adjusted net gains from supplemental feeding ($16.64). Each of these dollar values uses 1860 dollars, the mixed diet, the Haines et al. median nutrition effect, and the mean of Steckel’s stature effect. 22 Table 1 OLS Regression Results Testing for Informational Asymmetries Dependent Variable: Sale Price (in 1860 dollars) (1) (2) Local Slave 225.25 -49.45 (2.04)* (-0.52) Adult Slave 15.48 (0.15) Local X Adult 283.10 (2.30)* Multiple Slaves Sold 500.53 (5.14)*** 389.38 (7.01)*** 1810.Decade 134.75 (0.43) 223.73 (1.50) 1820.Decade -183.29 (-0.60) -37.77 (-0.26) 1830.Decade -208.05 (-0.70) -10.88 (-0.08) 1840.Decade -159.97 (-0.55) -15.68 (-0.11) 1850.Decade 247.28 (0.85) 349.76 (2.55)* 1860.Decade 395.96 (0.98) 548.82 (2.58)** Constant 622.66 (2.09)* 0.049 780 520.04 (3.35)*** 0.070 1521 Adjusted R2 Observations Note: t statistics in parentheses; * the probability of obtaining a t statistic this large when the null hypothesis β=0 is true is less than 0.05; ** p < 0.01; and *** p < 0.001. 23 Note: Data are from Carson (2008 and 2009); Komlos and Coclanis (1997); Komlos (2011); and Steckel (1995). 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