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). Carson’s data are for African Americans rather than slaves; however the
majority of his observations are from slave states.
24
25
26
References
Adams, D.R., Jr. 1986. “Prices and Wages in Maryland, 1750-1850,” Journal of Economic
History 46: 625-645.
Akerlof, George. 1970. “The Market for ‘Lemons’: Quality Uncertainty and the Market
Mechanism.” Quarterly Journal of Economics 84, no. 3: 488-500.
Atack, Jeremy and Fred Bateman. 1987. To Their Own Soil: Agriculture in the Antebellum
North. Ames, IA: Iowa State University Press.
Balke, Nathan S. and Robert J. Gordon. 1989. “The Estimation of Prewar Gross National
Product: Methodology and New Evidence.” Journal of Political Economy 97, no. 1: 3892.
Bodenhorn, Howard. 2010. “Manumission in Nineteenth Century Virginia.” National Bureau of
Economic Research, Working Paper #15704.
Bodenhorn, Howard and Gregory Price. 2009. “Crime and Body Weight in the Nineteenth
Century: Was there a Relationship between Brawn, Employment Opportunities and
Crime?” National Bureau of Economic Research, Working Paper #15099.
Buley, R. Carlyle. 1950. The Old Northwest: Pioneer Period, 1815-1840. Bloomington, IN:
Indiana University Press.
Carson, Scott Alan. 2008. “The Effect of Geography and Vitamin D on African-American
Stature in the Nineteenth Century: Evidence from Prison Records.” Journal of Economic
History 68, no. 3: 812-831.
Carson, Scott Alan. 2009. “Geography, Insolation, and Vitamin D in Nineteenth Century
African-American and White Statures.” Explorations in Economic History 46, no. 1: 149159.
Chanda, Areendam, Lee Craig, and Julianne Treme. 2008. “Convergence (and Divergence) in
the Biological Standard of Living in the USA, 1820–1900.” Cliometrica 2, no. 1: 19-48.
Cole, Arthur Harrison. 1938. Wholesale Commodity Prices in the United States, 1700-1861.
Cambridge, MA: Harvard University Press.
Conrad, Alfred H. and John R. Meyer. 1958. “The Economics of Slavery in the Antebellum
South.” Journal of Political Economy 66, no.1: 95-130.
Copland, Andrew and Robert Murphy. 2010. “The Mathematical Comparison of Historical and
Optimal Slave Diets,” unpublished manuscript.
27
Craig, Lee A. 1993. To Sow One Acre More: Childbearing and Farm Productivity in the
Antebellum North. Baltimore: Johns Hopkins University Press.
Craig, Lee A. and Thomas Weiss. 1998. “Nutritional Status and Agricultural Surpluses in the
Antebellum United States.” In Studies on the Biological Standard of Living in
Comparative Perspectives, edited by John Komlos and Joerg Baten. Stuttgart: Franz
Steiner Verlag.
Cuff, Timothy. 2004. “Historical Anthropometrics.” EH.Net Encyclopedia, edited by Robert
Whaples. August 29. http://eh.net/encyclopedia/article/cuff.anthropometrics
Cuff, Timothy. 2005. The Hidden Cost of Economic Development: The Biological Standard of
Living in Antebellum Pennsylvania. Aldershot, England: Ashgate.
Deyle, Steven. 2005. Carry Me Back: The Domestic Slave Trade in American Life. New York:
Oxford University Press.
Field-Hendrey, Elizabeth and Lee A. Craig. 1993. “Industrialization and the Earnings Gap:
Regional and Sectoral Tests of the Goldin-Sokoloff Hypothesis.” Explorations in
Economic History 30, no. 1: 60-80.
Fogel, Robert W. 1989. Without Consent of Contract: The Rise and Fall of American Slavery.
New York: W.W. Norton.
Fogel, Robert W. and Stanley L. Engerman. 1974. Time on the Cross: The Economics of
American Negro Slavery. Boston: Little, Brown, and Company.
Fogel, Robert W. and Stanley L. Engerman. 2008. “New Orleans Slave Sale Sample, 18041862,” ICPSR07423-v2. Ann Arbor, MI: Inter-university Consortium for Political and
Social Research.
Friedman, Gerald. 1982. “The Heights of Slaves in Trinidad,” Social Science History 6, no. 4:
482-515.
Greenwald, Bruce and R. Glasspiegel. 1983. “Adverse Selection in the Market for Slaves,”
Quarterly Journal of Economics, 98 no. 3: 479-499
Haines, Michael R., Lee A. Craig, and Thomas Weiss. 2003. “The Short and the Dead: Nutrition,
Mortality, and the ‘Antebellum Puzzle’ In the United States.” Journal of Economic
History 63, no. 2: 382.
Haines, Michael R., Lee A. Craig, and Thomas Weiss. 2011. “Did African Americans
Experience the ‘Antebellum Puzzle’? Evidence from the United States Colored Troops
during the Civil War.” Economics and Human Biology, 9, no. 1: 45-55.
28
Hilliard, Sam Bowers. 1972. Hog Meat and Hoecake: Food Supply in the Old South, 1840-1860.
Carbondale, IL: Southern Illinois University Press.
Hinkley, David. 1969. “On the Ratio of Two Correlated Normal Random Variables.” Biometrika
56, no. 3: 635-639.
Homer, Sidney and Richard Sylla. 1992. A History of Interest Rates. New Brunswick, NJ:
Rutgers University Press.
Howe, Daniel Walker. 2007. What Hath God Wrought: The Transformation of America, 18151848. Oxford, UK: Oxford University Press.
Johnston, Louis D. and Samuel H. Williamson. 2008. “What Was the U.S. GDP Then?”
MeasuringWorth. http://eh.net/hmit/
Johnson, Walter. 2001. Soul by Soul: Life Inside the Antebellum Slave Market. Cambridge:
Harvard University Press.
Komlos, John. 1987. “The Height and Weight of West Point Cadets: Dietary Change in
Antebellum America.” Journal of Economic History 47, no. 4: 897-929.
Komlos, John. 1996. “Anomalies in Economic History: Toward a Resolution of the ‘Antebellum
Puzzle.’” Journal of Economic History 56, no. 1: 202-214.
Komlos, John. 2011. “The Postbellum Continuation of the Antebellum Puzzle: Stature in the
United States, 1847-1894,” unpublished manuscript.
Komlos, John, and Bjorn Alecke. 1996. “The Economics of Antebellum Slave Heights
Reconsidered.” Journal of Interdisciplinary History 26, no. 3: 437-457.
Komlos, John and Joerg Baten, eds. 1998. Studies on the Biological Standard of Living in
Comparative Perspectives. Stuttgart: Franz Steiner Verlag.
Komlos, John and Peter Coclanis. 1997. “On the ‘Puzzling’ Antebellum Cycle of the Biological
Standard of Living: The Case of Georgia,” Explorations in Economic History 34, no. 4:
433-459.
Margo, Robert A. and Richard H. Steckel. 1982. “The Heights of American Slaves: New Evidence
on Slave Nutrition and Health.” Social Science History 6, no. 4: 516-538.
Marshall, Alfred. 1920. Principles of Economics, 9th (Variorum) Edition. London: Macmillan and
Company.
Northup , Solomon. 1855. Twelve Years a Slave: Narrative of Solomon Northup, a Citizen of
New-York. New York: Miller, Orton, and Mulligan.
29
Pritchett, Jonathan. 1997. “The Interregional Slave Trade and the Selection of Slaves for the New
Orleans Market.” Journal of Interdisciplinary History 28, no. 1: 57-85.
Pritchett, Jonathan. 2001. “Quantitative Estimates of the United States Interregional Slave Trade,
1820-1860.” Journal of Economic History 61, no. 2: 467-475.
Pritchett, Jonathan and Chamberlain, Richard. 1993. “Selection in the Market for Slaves: New
Orleans, 1830-1860.” Quarterly Journal of Economics 108, no. 2: 461-473.
Pritchett, Jonathan and Freudenberger, Herman. 1992. “A Peculiar Sample: The Selection of
Slaves for the New Orleans Market.” Journal of Economic History 52, no. 1: 109-127.
Rees, R., John Komlos, Ngo V. Long, and Ulrich Woitek. 2003. “Optimal Food Allocation in a
Slave Economy.” Journal of Population Economics 16: 21-36.
Romer, Christina. 1989. “The Prewar Business Cycle Reconsidered: New Estimates of Gross
National Product, 1869-1908.” Journal of Political Economy 97, no. 1: 1-37.
Spence, Michael. 1973. “Job Market Signaling.” Quarterly Journal of Economics 87, no. 3: 355374.
Spence, Michael. 2002. “Signaling in Retrospect and the Informational Structure of Markets.”
American Economic Review 92, no. 3: 434-459.
Steckel, Richard H. 1986. “A Peculiar Population: The Nutrition, Health, and Mortality of Slaves
from Childhood to Maturity.” Journal of Economic History 46, No. 3: 721-741.
Steckel, Richard H. 1995. “Stature and the Standard of Living.” Journal of Economic Literature
33, no. 4: 1903-1941.
Steckel, Richard H. 2009. “Heights and Human Welfare: Recent Developments and New
Directions.” Explorations in Economic History 46, no. 1: 1-23.
Steckel Richard H. and Roderick Floud, eds. 1997. Health and Welfare During Industrialization.
Chicago: University of Chicago Press.
Strauss, John and Duncan Thomas. 1998. “Health, Nutrition, and Economic Development.”
Journal of Economic Literature 36, no. 2: 766-817.
Sunder, Marco and Ulrich Woitek. 2005. “Boom, bust, and the human body: further evidence on
the relationship between height and business cycles.” Economics and Human Biology 3,
no. 3: 450-466.
Tadman, Michael. 1989. Speculators and Slaves: Masters, Traders, and Slaves in the Old South.
Madison: University of Wisconsin Press.
30
U.S. Bureau of the Census. 1975. Historical Statistics of the United States, Colonial Times to
1970, Bicentennial Edition. Washington, DC: Government Printing Office.
U. S. Work Projects Administration. 1941. Slave Narratives: A Folk History of Slavery in the
United States From Interviews with Former Slaves, North Carolina Narratives, Part 1.
Washington, DC: Library of Congress.
Wahl, Jenny B. 1996. “The Jurisprudence of American Slave Sales.” Journal of Economic
History 56, No. 1: 143-169.
Williamson, Samuel H. and Louis P. Cain. 2010. “Measuring Slavery in $2008,” unpublished
manuscript.
31