75

A CALCULATION OF THE BLACK REPARATIONS BILL*

By Julian S imon and Larry Neal

INTRODUCTION

G i v e n the present black rhetoric about "reparat ions" , and given also the successful lawsuits by American Indians concerning tribal lands, it is not unl ikely that somet ime there will be a suit on behalf of American Blacks to be paid for their ancestors ' labor when they were in slavery. While the question is fundamental ly a legal one, this note calculates rough estimates of the economic magni tudes that may be involved in the appropriate size of the reparat ions bill.

The legal questions would be difficult. For example, who should compensate the ex-slave and his descendants , assuming that reparations are to be paid on the basis that slave labor created an "appropriabte surplus" that normal ly would have been retained by the slave? One might argue that the ex-slave- holders and their descendants appropriated the slave's surplus earnings and hence should be liable for reparations (in keeping with Anglo-American legal traditions of third party innocence) . But after all these years b lood descent is impossible to derive. And fur thermore , slaveholders were eventually expropr ia ted of their slave proper ty during the Civil War wi thou t compensa t ion by the victorious North. ~We are grateful to Judah Matras for research assistance and helpful discussions.

76 The Review of Black Political Economy

In contras t to the legal p rob lem, the e c o n o m i c p rob lem would be relatively s t ra ightforward as long as one assumes tha t on ly the private prof i tabi l i ty o f slavery to the slaveholders is involved. E c o n o m i c historians are generally agreed tha t slavery was qui te prof i table to the slaveholders dur ing the ent ire ante-bel lum period. Moreover, reasonably good es t imates can be made o f the actual a m o u n t o f prof i ts m a d e by slaveholders [2 ,7 ,8 ,9 ,16] . But the social prof i tabi l i ty o f slavery is m u c h more problemat ic . Slaveholders were the rul ing class o f the ante-bel lum Sou th and their private prof i ts wou ld , i f any th ing , be larger than the profi ts obta ined by the ent i re non-slave po r t ion o f Sou the rn society. Eugene Genovese [6] has res ta ted a rgument s which were made even dur ing the Civil War [ 1 ] tha t a sys tem o f slavery necessarily genera ted social costs which reduced its social prof i tabi l i ty be low its private prof i tab i l i ty . F o r e m o s t am ong these costs were the social costs o f enforc ing p rope r ty rights in slaves and main ta in ing an "appropr iab le surplus" for the planter wi th his i nves tmen t in h u m a n capital. These social costs s t emmed from the lack o f an educa t iona l sys tem, a t ranspor ta t ion system, and the expense o f ma in ta in ing a police state u n d e r such condi t ions . T h e y were ma in t a ined by the unwil l ingness o f the planter class to equip slaves wi th expensive capital equ ipmen t , including l ivestock. And the Sou the rn planters as a class apparen t ly had a high p ropens i t y to consume, ra ther than to invest, their p roceeds f rom slave- holding. Social affairs and luxur ious living c o m b i n e d wi th a desire for display o f mart ial skills mean t tha t the pr ivate prof i t s o f the S o u t h e r n planters as a class apparen t ly had a h igh p ropens i ty to consume, ra ther than to invest, the i r p roceeds f rom slaveholding. Social affairs and luxur ious living c o m b i n e d wi th a desire for display o f mart ial skills m e a n t tha t the prof i t s o f the S o u t h e r n planters were no t reinvested into the S o u t h e r n e c o n o m y bu t ra ther into the Nor the rn and English economies .

Even wi th these social costs o f the slavery sys tem, the Sou the rn e c o n o m y remained viable and economica l ly eff ic ient as a whole so long as there remained fertile co t t on lands some place wi thin its political domain . FogeI and Enge rman [4] have calculated tha t the rate o f g rowth o f per capita i ncome , the economis t ' s bes t measure for the progress o f e c o n o m i c eff ic iency in an e c o n o m y , was roughly the same in the s laveholding Sou th as in the N o r t h f rom 1840 to 1960. This g rowth was based pr imari ly u p o n the development o f the rich c o t t o n lands o f the Sou thwes t where per capita i n c o m e was

A Calculation of the Black Reparations Bill 77

more than double that in the old South. It is clear that this growth of economic efficiency, derived solely f rom rapid exploitat ion of the rich co t ton lands of the Southwest , was due to the effort o f the enslaved Blacks transported from the Old South. I t is extremely doubt fu l that the South have maintained this growth of economic efficiency with a growing problem of soil exhaustion in the old South [3,6] and the reaching of the

geographical limits to the new cot ton lands [ 1 1 ]. But the Civil War intervened before the effects of these facts could be felt in the Southern economy.

In s~arl, there is no solid quantitative historical evidence on which I:o build a case that the social rate o f return to slavery was sig:aificantly lower than the private return. In the absence of such evidence it makes sense to concentra te upon the reparations due from the initial and direct appropriat ion of slave labor surplus.

The quant i ty sought in the following calculations is the d i f fe rerce between (a) what black slaves' labor was wor th on the open market and (b) what was expended upon their unkeep and consumption by their owners. That is, we seek to estimate the difference between w h a t slave-owners would have had to pay free black men and w o m e n for the same tasks, and what they actually spent on their slaves. No account is taken here of any indirect economic damage to slaves and their off-spring due to the cultural impoverishment of slavery, both because any such account is extraordinari ly speculative and also because it is contrary to the practice o f American courts in according damages. Nor is any accounting made for menta l and physical suffering due to slavery and its af termath.

This is a partial model which assumes that wages and prices would have been the same i f the slaves had been free. It may be thought tha t such an assumption leads to an overest imate of the free labor marke t wage because the addition o f freed slaves to the pool of free labor would tend to drive down the marke t wage. But if all Blacks had been free they could have acquired the educat ion and skills denied them while in servile status. This would have increased their marginal product and hence their marke t wage. These effects o f f reedom on the marginal p roduc t would have been enhanced by the additional work efforts Blacks would have exer ted if the wages were retained by the Black instead o f by his master. If increases in marginal p roduc t resulting f rom f reedom for the Blacks would have increased demand for their labor, it m a y have been that the ruling marke t

78 The Review of Black Political Economy

wage u n d e r f r e edom would have been greater t han i t was in fact unde r slavery. Our use o f the actual m a r k e t evaluat ion o f Blacks' wages unde r the ante-bel lum cond i t i ons m a y , therefore , represent an underes t imate o f the appropr ia te wage for calcu- lat ing reparations~

There are three parts to the work . The fi.rst j ob is to es t imate the m a r k e t value o f the unpaid ne t wages o f slaves who lived at various t imes before emancipa t ion . The calcula t ions will be made as present-value sums at single po in t s in t ime -- the po in t s being the e igh teen th years o f the slaves. The second job is to es t imate the n u m b e r o f slaves w h o labored w i t h o u t fair pay. Slaves will be c o u n t e d in the years t hey t u r n e d 18 years o f age. The th i rd job is to mul t ip ly the a m o u n t s by the n u m b e r o f slaves, f ind the i r value as o f the present , and aggregate them.

T H E UNPAID WAGES OF SLAVES IN V A R I O U S Y E A R S

The marke t pr ice o f a slave at t he age o f 18 m a y be considered to be the present value, in tha t year, o f the s t ream o f his fu tu re earnings less upkeep costs. We m a y reasonably assume tha t this sum was appraised accurate ly by the slave marke t . 1 Slave-price da ta are convenient ly available in Conrad and Meyer [2, Ch. 3 ]. To es t imate the overall l i fe t ime ne t unpa id wages o f a slave, however , one mus t also take accoun t o f the costs o f raising the slave to age 18, and the revenues f rom his labor before age 18, such ch i ldhood expend i tu re s and revenues being c o m p o u n d e d to age 18. Let t ing

V t = value o f slave at age 18 in year t V t = m a r k e t price o f slave at age 18 in year t L = value o f labor pe r fo rmed by slave M = m a in t enance costs o f slave

we can summar ize this a lgor i thm b y the fo rmula 18

Vt= Pt + s ~= 1 [(Lt-s -Mt-s) (1 + r)S].

L is zero unt i l t h e child is six years old; i.e., f r o m s=13 to s=18. In t he first yea r o f life the m a i n t e n a n c e costs inc lude nursery costs and the value o f the m o t h e r ' s los t t ime in the fields, in add i t i on to t he no rma l ma in t enance costs o f food , c lothing, and housing. The rate o f in teres t obvious ly has great effect on the

A Calculation of the Black Reparations Bill 79

final ,~stimate when considering the present value o f the sums as o f 1974. But the calculations of the values as of age 18 are not much affected by the rate o f interest. Suffice it for now that since it does not affect the order of magnitude of the final sum f o r our purposes here we shall (a) note Conrad and Meyer's reasoning and judgment that 7 percent is appropriate, and work with ~:hat rate; and (b) also calculate using a 3 percent rate.

Table 1 shows estimates of pre-18 slaveholder's expenses and revenues as of 1840 based on Conrad and Meyer's da ta (pp. 62-65). One must take into account that some slave children died at ages young enough that they represented net losses to the slaveholders. As an adjustment we use the crude expedient o f doubling all costs and revenues that occurred in the first 9 year~ and we therefore use the adjusted totals in columns 6 and 7, in:;tead of those in columns 4 and 5, Table I.

Now we add the adjusted pre-18 total to the value of the slave at age 18. As of the 1840 period we may use marke t prices for a male slave of $925, and for a female slave 2 $825. We shall hencefor th average the two ($875). This gives a sum of $520 net unpaid wages for the slaves' lifetime, computed at 7 percent and $853 computed at 3 percent.

In t800 slave prices were 57 percent of the 1840 price [2] , so we shall arbitrarily use the same proport ion of the total 1840 value: above as the appropriate lifetime value for 1790. For the year~,; be tween 1790 and 1840 a linear interpolat ion is used as seen in column 6 of Table 2. The actual course of slave prices in four slave markets from 1795 to 1860 [ I0 , p. 177] indicates that this procedure underest imates the present value of the appropriable surplus in most of the intervening years, especially for the 1830s. No estimates will be made for slaves who came to matur i ty before 1790, on the dubious ground that our present society is responsible only for the debts of its politically independent life. And no estimates will be made for slaves reac t ing matur i ty after 1840, on the ground that the work years af ter 1863 of slaves who matured in or before 1840 are some balance to the work lives before t863 o f slaves who matured after 1840.

TA

BL

E 1

: C

osts

and

Rev

enue

s A

ssoc

iate

d w

ith

Rai

sing

a S

lave

to

Age

18

in 1

840

03

o

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Ex

pe

ns

e o

r

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ge

Re

ve

nu

e

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sery

Cos

ts

Mo

the

r's

tim

e l

ost

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nten

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M

aint

enan

ce

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nten

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aint

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ce

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nten

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aint

enan

ce

imp

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d W

ages

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pu

ted

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es

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ute

d W

ages

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es

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d W

ages

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nten

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aint

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ce

Mai

nten

ance

M

aint

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ce

Mai

nten

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M

aint

enan

ce

Mai

nten

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M

aint

enan

ce

Mai

nten

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M

aint

enan

ce

Mai

nten

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Am

ou

nt

in

Yea

r D

olla

rs

Bir

th -

1 y

ear

old

= t

-18

$ -

50

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th -

1 y

ear

old

= t

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16

0-1

= t-

18

- 10

1-

2 =

t-17

-

10

2-3

= t-

16

10

3-4

=t-

15

~

10

4-5

= t-

14

10

5-6

= t-

13

10

6-7

= t-

12

+ 5

6-7

= t-

12

10

7-8

=t-

ll

+ 10

7-

8 =

t-ll

.

15

8~9

= t-

lO

+ 15

8-

9 =

t-lO

15

9-

10

-= t-

9

+ 20

9-

10

= t-

9

15

10-1

1 =

t-

8 +

30

10

-11

=t-

8

15

11-1

2 =

t-

7 +

40

Va

lue

V

alue

at

age

at

age

V

alue

at

age

Val

ue a

t ag

e 1

8 a

t 18

at

18

at

3%

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at

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just

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r A

dju

ste

d f

or

(Ro

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ty

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t dol

lar)

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. 3

0.

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+

11,

+ 14

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r

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Tot

als

TA

BL

E 1

: C

osts

and

Rev

enue

s A

ssoc

iate

d w

ith

Rai

sing

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lave

to A

ge 1

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184

0 (C

on

t'd)

(2)

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ou

nt

in

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r D

olla

rs

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nten

ance

11

-12

= t-

7

. 15

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aint

enan

ce

12-1

3 =

t-

6 +

50

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nten

ance

13

-13

= t-

6

15

Mai

nten

ance

13

-14

= t-

5

+ 6

0

Mai

nten

ance

13

-14

= t-

5

20

Mai

nten

ance

14

-15

= t-

4

+ 70

M

aint

enan

ce

14-1

5 =

t-

4 20

M

aint

enan

ce

15-1

6 =

t-

3 +

80

Mai

nten

ance

t5

-16

=

t-

3 -

20

Mai

nten

ance

16

-17

= t-

2

+ 9

0

Mai

nten

ance

16

-17

= t-

2

20

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nten

ance

17

-18

= t-

1

+10

0 M

aint

enan

ce

17-1

8 =

t-

1 -

20

(4)

(5)

Val

ue

Val

ue

at a

ge

at a

ge

18 a

t 18

at

3%

7%

(Rou

nded

to

nea

r-

est d

olla

r)

18.

- 24

. +

60.

+ 75

. 18

. -

23.

+ 70

. +

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23.

28.

+ 79

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23.

. 26

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+ 98

. 22

. 25

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+10

3.

21,

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7.

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ue

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ge

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t 3%

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dju

ste

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or

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rta

lity

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. +

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. 23

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22,

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. 2

i.

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3.

21.

$ 22

.

(7)

Val

ue a

t ag

e 18

at

7%

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just

ed

fo

r M

ort

alit

y

24.

+ 75

. -

23.

+ 84

.

- 28

. +

92.

- 26

. +

98,

- 25

. +

103,

23

. +

107.

21.

$ -

355.

o o _=

O

~0

_=

Cos

t and

Rev

enue

s A

ssoc

iate

d w

ith

Rai

sing

a S

lave

to

Age

18

in 1

840

oo

...t

TA

BLE

2:

The

Pre

sent

Val

ue o

f th

e A

ppro

pria

ble

Sur

plus

of

Sla

ves

Age

d 18

, 17

90-1

840

r~

(1)

(2)

(3)

(4)

(5)

Sla

ves

Age

d 18

Li

near

A

djus

ted

Inte

rpol

atio

n E

stim

ates

S

lave

s A

ged

from

pre

viou

s fo

r 18

14

-

25

colu

mns

ye

ars

of a

ge

in T

hous

ands

(T

hous

ands

) (T

hous

ands

) T

otal

Sla

ve P

opul

atio

n in

Tho

usan

ds

1246

+ 1

241=

18

40

2487

Sla

ves

Age

d 10

-

23

in T

hous

ands

781

1013

+ 9

96 =

18

30

2009

62

1

786

+ 75

22 =

18

20

1538

(6)

Net

Val

ue*

of s

lave

at

age

18

@ 7

%

1810

11

91

1800

89

4

1790

69

8

*Slig

ht d

evia

tions

from

str

ict

linea

rity

are

acc

ount

ed f

or

by r

ound

ing.

55.7

8 55

$

520

(7)

Num

ber

of

Sla

ve=

Age

d 18

T

imes

Val

ue

(Tho

usan

ds)

$ 28

,600

44.3

5 44

47

5 20

,900

430

386

341

296

34

26

20

15

404

33.6

7 14

,620

10,0

36

6,82

0

4,44

0

t~

o w~

pq

o o

A Calculation of the Black Reparations Bill 83

THE NUMBER OF SLAVES COMING TO AGE 18 IN V A R I O U S YEARS

G o o d censuses o f slaves were no t made . (Nor were censuses wi th mode rn detail made for non-slaves, ei ther , o f course). There fore rough app rox ima t ions are necessary. The source for data unless otherwise m e n t i o n e d is the U.S. D e p a r t m e n t o f C o m m e r c e [ 12 ].

Co lumns 2 and 3 o f Table 2 give available age d is t r ibut ions f r o m censuses in 1820 to 1840. Linear ex t rapo la t ions over the intervals yield age 18 es t imates as in c o l u m n 4. Because age 18 is above the middle o f t he 10-23 interval the linear inter- po la t ions for 1830 and 1840 are scaled d o w n w a r d s slightly as in Coluran 5. The es t imate for 1820 is similarly scaled upwards for t he same reason.

We may now es t imate the p r o p o r t i o n s (age 18/ total popula- t ion) , which are app rox ima te ly 2.2 pe rcen t in 1840, 1830, and 1820 This est imate may be applied backwards to the 1810, 1800 and 1790 es t imates o f to ta l slave popu la t i on to get the remaining est imates in c o l u m n 5, Table 2.

The above est imates are confused by the fact tha t no accoun t was taken o f the "free co lo red" popu la t i on which was, for example , 113,000 o f a to ta l o f 899 ,000 Negro males in 1820. (The age est imates above exc lude "free co lored") . As long as the marke t price ref lected the possibil i ty that the slave might b e c o m e free, however , no p rob l em should occur. But this m a t t e r prevents us f rom work ing backward f rom the Negro popu la t i on in, sag, 1880 to check our earlier est imates.

A GGREGATIO N AND P R E S E N T V A L U E AS O F 1974

Now we mus t first mu l t i p ly the n u m b e r o f slaves age 18 by the i r values. This is d o n e for the decennial dates in c o l u m n 7 o f Table 2. For years in be tween , linear ex t rapo la t ions can now be made . This gives us a series o f amoun t s for each year f rom 1790 to 1840.

The only remaining p rob lem is to decide on the appropr ia te in teres t rate to c o m p o u n d the sums to 1974. This decision is u n e x p e c t e d l y easy. It is qu i te clear that no interes t rate be low 3 pe rcen t makes any e c o n o m i c sense. Since 1880, and very likely since 1840, the Uni ted States e c o n o m y has been growing at a rate o f approximate ly 3 percent annual ly. Any asset which fails to yield this rate of re tu rn is unprof i tab le and m u s t be replaced

84 The Review of Black Political Economy

by ano the r which yields at least the three percent . So we begin by c o m p u t i n g the present value at that rate, wh ich comes to $67.9 bill ion as o f 1974. We also c o m p u t e the a m o u n t for 6 percent , which comes to $6,786.3 bill ion. These a m o u n t s are in te rms o f ante-bel lum dollars and should be inflated by the rise in the general price level which has occurred since then to give the appropr ia te reparat ions bill. The GNP def la tor in 1973 was roughly 4.5 t imes its 1860 level [ 13 ,14] . Using this scale factor , t he repara t ions bill in 1973 dollars wou ld range f rom $305.6 billion to $30 ,583 .4 bill ion. Nei ther o f t he c o m p o u n d i n g rates is as high as the 7 percent which Conrad and Meyer t h o u g h t reasonable for pre-Civil War t imes, and ye t even 6 pe rcen t p roduces a sum so as t ronomical as to be a lmost meaningless . Therefore , we need no t bo the r to decide which rate is m o s t reasonable. Even 3 percent , w i th price level ad jus tmen t s , p roduces a sum large e n o u g h for a lmos t anyone ' s purposes .

CONCLUSION

The sums calculated above m a y seem to the reader large compared wi th , say, the present GNP o f the U.S. o f $1.3 trillion. But ref lect this way: Present weal th is a func t ion o f past savings. N o n - c o n s u m p t i o n (saving) ordinar i ly has run 10-15 percent per year in the U.S. But Blacks were no t consuming perhaps 80 pe rcen t o f more o f their income, ra ther than 10-15 percent ; and 80 percent savings rate c o m p o u n d s remarkab ly fast. In light o f this the c o m p o u n d e d sums do no t seem unreasonably high.

The sums calculated above represent accumula ted s tocks o f debt . In set t l ing the deb t two alternatives are possible which are economica l ly equivalent . One wou ld be to transfer t i t le on an equivalent s tock o f assets held in the U.S. to present -day descendan t s o f fo rmer slaves. The o the r alternative would be to assign the annual earnings o f the ou t s tand ing deb t to slave descendants . In the lat ter case, the annual p a y m e n t s would range f rom $9 bil l ion to $1,831.5 bill ion depend ing on w h e t h e r the inf la ted 3 pe rcen t or 6 percen t c o m p o u n d i n g rate is used. These sums compare to the $11.2 bill ion spen t in fiscal 1973 on publ ic assistance p a y m e n t s [15] . Viewed this way, the lower b o u n d repara t ions bill we have calculated appears to be a reasonable, even conservative, figure.

If one calculated the tota l o f governmenta l t ransfer p a y m e n t s

A Calculation of the Black Reparations Bill 85

to Blacks today, he would likely f ind that the Uni ted States is, in fact, paying interest on the black reparat ions bill bu t no t recognizing it as such. More than the i rony o f h is tory is involved here. The economic legacy o f sys temat ic d iscr iminat ion against Black,~ is a reduct ion in the level o f possible na t ional p r o d u c t i o n and a con t inued bu rden f rom the social costs o f sustaining discri~aaination. The legacy surely represents a larger annual toll on the nat ional resources than is represen ted by the annual in teres t we have calculated on the repara t ions bill.

FOOTNOTES

1There can be l i t t le doubt that participants in the market for slaves were making this sort of calculation. For example: " . . .nor would I w i l l ing ly sell the slaves as long as there remains any prospect of paying my debts wi th their labor. In this I am governed solely by views to their happiness which wi l l render i t wor th their whi le to use extraoT'dinary exertions for some t ime to enable me to put them ul t imate ly on an easier foot ing, which I wi l l do the moment they have paid the debt due f rom the estate, two-thirds of which have been contracted by purchasing them." , Thomas Jefferson, Writings (Ford) IV, 416-417.

2The market value of a woman was almost as high as that of a man, part ly because she had value for breeding more slaves in addi t ion to her f ie ldwork product ion. H o w e ~ r , Fogel and Engerman have calculated that only 13% of the woman's market price was due to the discounted value of expected prof i ts f rom breeding. (Time on the C~oss, forthcoming) And to include the breeding revenues would be double counti ng.

REFERENCES

1. J. E. Cairness, The Slave Power (London: Macmillan, 1862).

2. Alfred H. Conrad and John R. Meyer, The Economics o f Slavery (Chicago: Aldine, 1964).

3. Avery Craven, Soil Exhaustion as a Factor in the Agr icu l tura l History o f Virginia and Maryland, 1606-1860 (Urbana, Il l inois, 1926).

4. Robert Fogel and Stanley Engerman, eds., The Re-Interpretat ion o f American Economic History (New York : Harper and Row, 1971 ).

5. Time on the Cross ( forthcoming).

6. Eugene Genovese, The Po/it ica/ Economy o f Slavery: Studies in the Economy and Society o f the Slave South (New York : Vintage, 1967).

7. Lewis Cecil Gray, History o f Agr icu l ture in the Southern Uni ted States to 1860 (Washington, D,C.: Carnegies Inst i tu t ion of Washington, 1933).

86 The Review of Black Political Economy

8. Ulrich B. Phillips, American Negro Slavery (New York: D. Appleton and Co., 1918).

9. , "The Economic Cost of Slaveholding in the C o , o n Belt ," Political Science Quarterly, XX, (June, 1905).

10. , Li fe and Labor in the Old South (Boston: Lit t le, Brown and Company, 1929).

11. Charles Ramsdell, '~l'he Natural Limits of Slavery Expansion," Mississippi Valley Historical Review, XVI (September, 1929).

12. U.S. Department of Commerce�9 Bureau of the Census, Historical Statistics o f the United States, Colonial Times to 1957 (Washington: G PO, 1961 ).

13. ton: GPO, 1966).

�9 Long Term Economic Growth, 1860-1965 (Washing-

14. �9 Survey o f Current Business (July 1973).

15. U.S. Department of Health, Education and Welfare, Social Security Bulletin (September 1973).

16. Yasuki Yasuba, "Prof i tabi l i ty and Viabil i ty of Slavery in the Ante-Bellum South, "�9 in Fogel and Engerman, eds., q.v.