. 12
( 14)


employment, then we would expect to see an increase in relative female
employment in agriculture. In fact we observe the opposite. The per-
centage of day-laborers who were female declined between 1750 and
1850. Based on a sample of wage accounts from sixty-¬ve farms,
I estimated that, among agricultural day-laborers, the percentage of days
worked by females fell from 13.6 percent in 1751 to 10.6 percent in
1851. The fact that both relative female wages and relative female
employment fell suggests that there was also a decline in the demand for
female labor in agriculture.
What could have caused this decline in demand for female agricultural
laborers? Snell suggested that in the southeast it was due to increased
specialization in arable agriculture, combined with the replacement of
the sickle by the scythe, which reduced women™s role in harvest.18 As
discussed in Chapter 3, women did not use the scythe because it
required too much strength. Both women and men used the sickle, and
when the sickle was used to cut grain women had an active part in
harvest. The increased use of the scythe caused a decrease in the
demand for female labor during harvest. This raises the question of why
the scythe replaced the sickle.
The scythe had been used for centuries to mow grass or harvest less
valuable grains, but its use expanded to more valuable grains at the

Snell, Annals of the Laboring Poor, ch. 1
312 Gender, Work and Wages in Industrial Revolution Britain

beginning of the nineteenth century. Pamela Sharpe suggests that the
move from the sickle to the scythe cannot explain the declining
employment of women in agriculture because the sickle and the scythe
co-existed.19 However, the fact that two technologies can co-exist does
not contradict the claim that economic forces caused the changes
observed. The sickle and the scythe each had their own advantages, and
it was changes in relative prices that determined which technology would
be used, and thus the demand for male and female labor. The scythe was
not a new technology, and had been used since the Roman era.20
However, various properties of the tool limited its use. The scythe cut
the grain closer to the ground, and in an open-¬elds system, where the
stubble was common property, the use of the scythe was sometimes
forbidden.21 Grain could be cut faster with a scythe, but the sickle was
neater, and spilled less grain on the ground,22 so a farmer considering
using the scythe would have to trade the savings in labor costs from
using the scythe against the loss of grain that would result. The scythe
was a grain-using and labor-saving technology, while the sickle was a
grain-saving and labor-using technology. This difference explains why
the scythe was ¬rst used for the cheaper grains, and applied to wheat
last. It also explains why high-wage areas were more likely to use the
scythe. In 1769 Young found the scythe being used for wheat near Hull,
though cutting wheat with a scythe was unusual at that time. The reason
for the region™s deviation from normal practice is clear; Young notes that
“The prices of labor are most of them extremely high.”23
The tendency for the wage of male laborers to rise relative to the price
of grain caused the scythe to replace the sickle. In the eighteenth century
the scythe was used to cut grass, and sometimes cheaper grains. It was
used for oats, barley, peas, and beans in early modern England, but was
not used for wheat until the nineteenth century.24 Its application to the
wheat harvest began in the south during the Napoleonic Wars and then
spread north. Overton claims that 90 percent of the wheat harvest was
cut with a sickle in 1790, and only 20 percent in 1870.25 The cause of
the shift from the sickle to the scythe was not technological change, since
the scythe was not a new tool, but a shift in prices that induced farmers
to choose a different harvest technology.

Sharpe, Adapting to Capitalism, p. 75. “This straightforward economic reason for the
growing demarcation of labor can then be dispelled immediately.”
Roberts, “Sickles and Scythes,” p. 4. 21 Ibid., p. 14.
Ibid., p. 16, and Roberts, “Sickles and Scythes Revisited,” p. 92.
Young, Northern Tour, vol. I, p. 113. 24 Roberts, “Sickles and Scythes,” p. 15.
Overton, Agricultural Revolution in England, p. 124.
Women™s labor force participation 313

The change in harvest technologies is probably not the only reason for
decreasing demand for female agricultural laborers. Even farms which
were primarily pastoral, such as that of the Oakes family in Norton,
experienced a decline in demand for female agricultural laborers.26
Another possible explanation for the declining demand for women is
institutional rather than technological. The early nineteenth century saw
a large increase in poor law payments, and farmers began to be more
concerned about the amount of money spent on the poor. Since poor
rates were paid locally, farmers, especially large farmers, were concerned
about the level of the rates, and were willing to adjust their hiring pat-
terns to minimize the rates.27 Farmers would have preferred hiring men
if male unemployment increased poor law payments but female
employment did not. If a woman™s husband was already employed and
not receiving poor relief, employing the woman would not further
reduce poor law payments. A preference for hiring males may have been
a method of spreading the work out among the greatest possible number
of families, in order to minimize poor relief payments.
Declining demand most likely reduced female labor force participa-
tion as the market wage fell below some women™s reservations wages.
The value of the woman™s contribution to the household was high
enough that low wages barely covered the opportunity cost of working.
Austin estimates: “Where a girl is hired to take care of children, she is
paid about 9d. a-week, and has her food besides, which is a serious
deduction from the wages of the woman at work.”28 If the cost of food
doubled the cost of hiring child care, a working woman would have to
pay about a third of her earnings for child care. Mrs. Sumbler, some-
times an agricultural laborer from Wiltshire, told parliamentary inves-
tigator Alfred Austin that she did not think working outside the home
increased the family™s net income:
I do not think a great deal is got by a mother of a family going out to work;
perhaps she has to hire a girl to look after the children, and there is a great waste
of victuals and spoiling of things; and then working in the ¬elds makes people eat
so much more. I know it was so with me always. I often say there is not
fourpence got in the year by my working out.29

If the net bene¬t of work was so small, even a small decrease in the wage
could cause a woman to drop out of the labor force.

Burnette, “Labourers at the Oakes.”
For a model that incorporates poor law payments in the farmer™s maximization
problem, see Boyer, Economic History of the English Poor Law, ch. 3.
Women and Children in Agriculture, p. 26.
Women and Children in Agriculture, pp. 67“8.
314 Gender, Work and Wages in Industrial Revolution Britain

II. Barriers to employment
Decline in the demand for female labor decreased the options available to
women and thus made them worse off. Barriers preventing women from
entering certain occupations also decreased the women™s options. One
possible cause of declining female participation was increased barriers that
pushed women out of various occupations. If they were pushed out of many
occupations, women may not have been able to ¬nd alternative employ-
ment, and may have dropped out of the labor force. In some cases we have
direct evidence of such barriers. Commercial directories show no tendency
toward increased occupational segregation over the nineteenth century,
but census data do indicate increased segregation between 1851 and 1871.
We know that there were barriers preventing women from being
employed in certain occupations because we hear women complain about
not being able to work where they chose. One tailoress responded to news
of a tailors™ strike against women™s employment by writing this to The
Pioneer: “surely the men might think of a better method of bene¬ting
themselves than that of driving so many industrious women out of
employment. Surely, while they loudly complain of oppression, they will
not turn oppressors themselves.”30 Women were pushed out of mule-
spinning. Women who tried to work as mule spinners at James Dunlop™s
mill in Glasgow were “waylaid and attacked, in going to, and returning
from their work” and “beaten and abused” by male mule spinners.31
Chapters 5 and 6 contain numerous examples of occupations which set up
barriers to women™s employment, including mule-spinning, wool-combing,
law, medicine, and the church. The occupations from which women
were excluded were those where male workers had enough economic
power to monopolize an industry and exclude women. Many of these
barriers were new during the Industrial Revolution. Women had been
mule spinners and midwives, but were pushed out of these occupations.
To investigate whether a general increase in occupational barriers may
have contributed to declining female participation, I examined occu-
pational segregation in commercial directories and the censuses. The
usual method for measuring occupational segregation is to calculate the
index of segregation, or the Duncan index. The index is:
jmi À fi j

The Pioneer, March 19, 1834, quoted in Taylor, Eve and the New Jerusalem, p. 108.
BPP 1824 (51) V, p. 525.
Women™s labor force participation 315

where mi is the percentage of males in occupation i, and fi is the
percentage of females in occupation i. For example, if there are 200
women listed in the town™s directory, and 40 of them are milliners, then
the fi for the occupation milliner is 20 percent. If men and women have
exactly the same occupational distribution, so that the female percentage
in each occupation is equal to the percentage of women in the workforce
as a whole, then the index will equal zero. If occupations are completely
segregated, so that women never work in male occupations and men
never work in female occupations, then the index is equal to 100.
Humphries used census data to calculate the index of occupational
segregation for each county in 1851 and 1871, and found that the index
“rose for all counties between 1851 and 1871.”32 The smallest increase
was in Northamptonshire, where the index rose from 65.1 to 65.4, and
the largest increase was in Cumberland, where the index rose from 50.8
to 69.3. The average increase in the index was 7.1 points. We have seen
that the nineteenth-century censuses were not very accurate measures of
women™s employment (see Chapter 1). Here, however, we are interested
in trends rather than levels, and if the extent of measurement error is
constant over time it will not affect the trend. Thus there does seem to have
been an increase in occupational segregation between 1851 and 1871.
Unfortunately it is not possible to use the census to examine whether
occupational segregation was increasing during the ¬rst half of the
eighteenth century because individual-level occupational data are not
available before 1841. The most comprehensive measure of occupations
available for the Industrial Revolution period is the commercial direc-
tories, and these record only business owners in manufacturing and
trade. We can, however, examine whether there was increasing occu-
pational segregation among this group.
The index of segregation is very sensitive to the de¬nition of occupa-
tional categories, so I have adjusted the occupational categories in the
directories to make them as similar as possible. Because the index is so
sensitive in this respect, these indexes cannot be meaningfully compared
to other indexes from other studies. The indexes of segregation are
presented in Table 7.2. While the highest level of segregation seems to be
in Derby in 1850, within towns there is no evidence of increasing segre-
gation over time. The index of segregation for Manchester is slightly lower
in 1846 than in either 1788 or 1824“5. The index of segregation for
Coventry also falls over time. Overall there is no evidence of an upward
trend in occupational segregation in commercial directories.

Humphries, “Most Free from Objection,” p. 932.
316 Gender, Work and Wages in Industrial Revolution Britain
Table 7.2. Indexes of occupational segregation from commercial directories

Index of
Date Town segregation Percent female

1788 Manchester 0.593 8.9
1791 Coventry 0.658 9.0
1824“5 Manchester 0.606 6.6
1835 Coventry 0.589 9.2
1846 Manchester 0.577 9.3
1850 Birmingham 0.645 11.8
1850 Derby 0.685 12.1
1892 Coventry 0.568 14.2

Notes: Occupational categories were made as similar as possible. Persons of
undetermined sex were assigned a sex based on the sex ratio within the occupation.
Sources: Lewis™s Manchester Directory for 1788; Universal British Directory, 1791; Pigot
and Dean™s Directory for Manchester, 1825; Pigot & Co.™s National Commercial
Directory, 1835; Slater™s National Commercial Directory of Ireland, 1846; Slater™s
Royal National and Commercial Directory, 1850; Kelly™s Directory, 1892.

Table 7.3 shows the progression over the years in the percentage
of tradeswomen in some of the larger occupational categories, for
Manchester and Coventry. This table tells the same story as the indexes;
there is no clear downward trend in the participation of women. In
Manchester the relative number of women drapers decreased, but the
proportion of women butchers increased. Between 1788 and 1846, the
proportion of women increased in eight occupations and decreased in
seven. Most of these changes were very small. Taken together, shop-
keepers and grocers were 14 percent female in 1788, 12 percent in 1824,
and 13 percent in 1846. Dyers were 6 percent female in 1788, 4 percent
in 1824, and 5 percent in 1846. Part B of Table 7.3, which examines
Coventry, shows that the same pattern also holds during the second half
of the nineteenth century. Between 1791 and 1835, the portion of
women increased in eight occupations and decreased in four, while
between 1835 and 1892 the portion of women increased in eight occu-
pations and decreased in ¬ve. While women drapers seem to have been
disappearing in Manchester, they were on the rise in Coventry. Overall
there is no evidence of increasing occupational segregation in the com-
mercial directories. In fact, this table shows surprising stability over time.
Evidence from commercial directories, then, leads to a different
conclusion than evidence from the census. The difference must be due
to the fact that the directories measure only a limited segment of the
workforce. The segment of the labor force that appeared in commercial
directories, business owners in trade and manufacturing, did not
Women™s labor force participation 317
Table 7.3. Trends in female participation in some of the largest occupations
(percentage of business owners who were female)

A. Manchester 1788 1824“5 1846

Agent 0.0 0.0 0.3
Attorney 0.0 0.0 0.6
Baker and ¬‚our dealer 7.7 9.6 6.1
Boot and shoe maker 0.0 6.5 2.1
Butcher 2.9 8.5
Calico printer 0.0 0.0 0.0
Cotton spinner 5.3 0.0 0.0
Draper, mercer 24.6 7.8 11.2
Dyer 6.4 4.1 5.4
Manufacturer of cloth 1.9 0.2 1.1
Merchant 1.7 0.0 0.6
Publican 9.4 15.2 15.5
Schoolmaster/mistress 35.7 48.6 43.8
Shopkeeper, grocer 13.9 12.1 12.7
Tailor 0.0 1.6 0.4
Warehouseman 0.0 5.3 7.3

B. Coventry 1791 1835 1892

Agent 0.0 0.0
Attorney 0.0 0.0 0.0
Baker and ¬‚our dealer 11.1 6.7 18.8
Boot and shoe maker 0.0 8.8 4.0
Butcher 6.3 1.4 2.4
Cloth manufacturer 0.0 20.0 0.0
Cycle manufacturer 0.0
Draper, mercer 0.0 13.3 21.4
Dressmaker 100.0 100.0 100.0
Dyer 1.7 0.0 40.0
Maltster 0.0 5.6 0.0
Physician and surgeon 0.0 0.0 0.0
Publican 14.7 7.3 13.4
Ribbon manufacturer 2.3 2.7 4.9
Schoolmaster/mistress 40.0 55.9 50.0
Shopkeeper, grocer 6.3 12.5 22.2
Tailor 0.0 0.0 7.2
Watch and clock maker 0.0 6.7 0.4

Notes: I took the ten largest occupations in each year (except “fustian cutter,” which
appears only in 1788). Butchers are missing from the 1824“5 directory. For 1791 the
“Shopkeeper, grocer” category includes “Grocers, victuallers, and hucksters.”
Sources: Lewis™s Manchester Directory for 1788; Pigot and Dean™s Directory for Manchester, 1825;
Slater™s National Commercial Directory of Ireland, 1846. The Universal British Directory, 1791;
Pigot & Co.™s National Commercial Directory, 1835; Kelly™s Directory, 1892.
318 Gender, Work and Wages in Industrial Revolution Britain

experience increasing occupational segregation. However, there was
increasing occupational segregation in the labor force as a whole
between 1851 and 1871. Thus the increasing segregation seems to have
occurred among workers who were employees.

III. Increased household incomes
Some of the decline in female labor force participation can be explained
by an increase in incomes. If market goods were inferior, then an
increase in income would increase the demand for home-produced
goods. For example, if purchased child care is inferior, an increase in
income may lead a family to use the labor of the wife for child care, even
if it is more expensive to do so. An increase in household income would
encourage the mother to spend more time at home. This may provide an
explanation of the withdrawal of women from the labor market over the
course of the nineteenth century; as incomes increased, women were
better able to afford the consumption good of raising their own children.
Numerous studies have found that women™s time out of the labor
force is a normal good, in the sense that increases in family income will
increase the consumption of this good.33 There are many possible rea-
sons why households may value women™s time out of the labor force.
They may value the goods and services produced in the household, or
higher social status, or women™s leisure, or all of these. If time out of the
labor force is a normal good, then we would expect it to go up, and
women™s labor force participation to go down, when male incomes rise.
For the ¬rst half of the nineteenth century, rising income cannot be an
important cause of the general decline in female labor force participation
simply because incomes were not rising. There is an extensive and lively
literature on the course of real wages over the early nineteenth century.
Optimists argue that the Industrial Revolution led to increases in the
real wage, and pessimists argue that real wages did not rise during the
Industrial Revolution. The argument, though, is mainly about the timing
of real wage increases. Lindert and Williamson suggest that real male
wages began to grow after 1820, and more than doubled between 1819
and 1851.34 Feinstein, using more accurate measures of the cost of living,
¬nds much smaller increases before 1851. All sides of the debate, though,
agree that real wages rose during the second half of the nineteenth

See, for example, Horrell and Humphries, “Women™s Labour Force Participation,” and
James Smith and Michael Ward, “Time-Series Growth in the Female Labor Force,”
Journal of Labor Economics 3 (1985), S59“S90.
Lindert and Williamson, “English Workers™ Living Standards.”
Women™s labor force participation 319


Real Earnings (1778/82=100)





1770 1780 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920

Figure 7.3 Feinstein™s estimates of real earnings
Source: Feinstein, “Pessimism Perpetuated”; Feinstein, “New Estimates of
Average Earnings.” The price index used is the Board of Trade Wholesale Price
Index from Mitchell, Abstract of British Historical Statistics, p. 476.

century. Figure 7.3 graphs Feinstein™s 1998 estimates of average full-
employment real earnings for 1770 to 1882, combined with his 1990 esti-
mates of average money earnings for 1880 to 1913, corrected for in¬‚ation
using wholesale prices.35 Most of the nineteenth-century increase in real
wages took place during the last three decades of the century. Real wages
rose only 17 percent between 1770 and 1840, but rose 80 percent between
1870 and 1900. Thus it is not surprising that Horrell and Humphries ¬nd
that, even after controlling for income, there is still a downward trend in
female participation during the ¬rst half of the nineteenth century.36 Given
the pattern of real wages, it is likely that increases in income had the largest
impact on female labor force participation in the second half of the nine-
teenth century.

Charles Feinstein, “Pessimism Perpetuated: Real Wages and the Standard of Living in
Britain during and after the Industrial Revolution,” Journal of Economic History 58
(1998), pp. 625“58; Charles Feinstein, “New Estimates of Average Earnings in the
United Kingdom, 1880“1913,” Economic History Review 43 (1990), pp. 595“632. The
price index used is the Board of Trade Wholesale Price Index from B. R. Mitchell,
Abstract of British Historical Statistics (Cambridge: Cambridge University Press, 1962),
p. 476.
Horrell and Humphries, “Women™s Labour Force Participation,” p. 112.
320 Gender, Work and Wages in Industrial Revolution Britain
Table 7.4. The predicted effect of changes in real earnings on married
women™s labor force participation

1801“41 1841“61 1861“1901

Percent change in real earnings 31.2 14.4 111.9
Predicted effect on married women™s LFP
À12.5 À5.8 À44.8
Upper bound
À0.5 À0.2 À1.7
Lower bound
À12.5 À21.2 À58.4
Actual change in married women™s LFP
Percent predicted by income change
Upper bound 100.0 27.1 76.7
Lower bound 3.8 1.0 2.9

Sources: Real Earnings; Feinstein, “Pessimism Perpetuated”; Feinstein, “New Estimates
of Average Earnings”; Mitchell, Abstract of British Historical Statistics, p. 476. Elasticities
for calculating the predicted effect: Horrell and Humphries, “Women™s Labour Force
Participation,” p. 112; Goldin, “The Changing Economic Role of Women,” p. 568.
Actual changes in LFP, 1801“41 and 1841“61: Horrell and Humphries, “Women™s
Labour Force Participation,” p. 98. Actual Changes in LFP, 1861“1901: Land, “The
Family Wage,” p. 61; McKay, “Married Women and Work.”

To estimate the effect of changing income on female labor force
participation, I combine Feinstein™s real earnings estimates with the
income elasticity of female participation. Based on their sample of
working-class household budgets, Horrell and Humphries estimate that
the elasticity of married women™s participation with respect to real male
earnings is “0.4.37 If the participation of poor women was more
responsive to male earnings than that of non-poor women, this elasticity
may overstate the response for the population as a whole. Claudia
Goldin ¬nds a much smaller elasticity, of “0.015, for US women in the
twentieth century.38 The elasticity of the participation response for all
married women in nineteenth-century Britain was probably somewhere
between these two elasticities. I use these two elasticities, combined with
wages changes from Figure 7.3, to calculate the upper- and lower-
bound estimates of what effect changes in income had on female par-
ticipation (see Table 7.4). Because the elasticity of the response is so
low, the lower-bound estimates suggest that change in income had
little effect on female participation in the nineteenth century. The
upper-bound estimates suggest a greater role for rising incomes. During
the 1801“41 period, the upper-bound estimate can explain the entire

Claudia Goldin, “The Changing Economic Role of Women: A Quantitative Approach,”
in Robert Whalpes and Dianne Betts, eds., Historical Perspectives on the American Economy
(Cambridge: Cambridge University Press, 1995), p. 568.
Women™s labor force participation 321

12 percent decline in married women™s labor force participation. For the
shorter period of 1841 to 1861, participation declines at a faster rate,
and rising real incomes explain only 27 percent of the decline. For the
end of the nineteenth century, the decline in participation is very large,
58 percent, but because incomes increased so rapidly, rising income can
explain 77 percent of the decline if we use the upper-bound estimate.
While the actual contribution of rising incomes was probably smaller
than the upper-bound estimates, these calculations suggest that rising
incomes may have been a signi¬cant factor in causing the decline in the
labor force participation rate of married women during the nineteenth

IV. Value of home production
Jan DeVries explains the declining female participation of the later
nineteenth century as the result of increased preferences for home-
produced goods and services, which he terms “Z goods”:
As real earnings rose in the second half of the nineteenth century (the timing varies
by social class and country), a new set of Z goods, associated with the health and
training of children and the achievement of new standards of domesticity in the
home, came to appear superior to the available range of market-provided goods
and services. To acquire these Z goods the labor of wives and children was
withdrawn from the labor force as the incomes of adult male workers rose.39

This process was the exact opposite of the “industrious revolution,”
which had drawn women and children into the workforce as a result of
an increased demand for market-provided goods and services.
Mokyr suggests a possible explanation for this shift in preferences
toward home-produced goods and services: new scienti¬c knowledge
about germs.40 While the idea of germs had been proposed by others,
Pasteur was ¬nally able to demonstrate that germ theory was true in the
1860s.41 Mokyr calls the discovery of germs “one of the most signi¬cant
technological breakthroughs in history.”42 Suddenly, new techniques for
avoiding disease were available. Households had always valued health,
and with new information about the relationship between cleanliness
and health, households placed greater value on cleanliness, not only for

Jan DeVries, “Between Purchasing Power and the World of Goods: Understanding the
Household Economy in Early Modern Europe,” in Pamela Sharpe, ed., Women™s Work:
The English Experience, 1650“1914 (London: Arnold, 1998), p. 229.
Joel Mokyr, The Gifts of Athena: Historical Origins of the Knowledge Economy (Princeton:
Princeton University Press, 2002), p. 200.
Ibid., p. 184. 42 Ibid., p. 185.
322 Gender, Work and Wages in Industrial Revolution Britain

itself, but also for the better health that it provided. The result was an
increase in the demand for home-produced goods and services.
However, the increased demand for cleanliness caused by the dis-
covery of germs probably did not affect female labor force participation
until late in the nineteenth century, and thus could explain only the last
few decades of the decline. Even after Pasteur demonstrated the exist-
ence of germs, this new knowledge still had to be transmitted to the
public. Housewives had to be convinced that germ theory was true, and
that it had implications for the health of their families. Organizations
such as the British Ladies™ National Association for the Diffusion of
Sanitary Knowledge helped to convince women of the value of cleanli-
ness.43 Their message was reinforced by advertisements for soap, and
soon women were made to feel guilty if their homes were not spotless.
By the early twentieth century, women had been persuaded of the
importance of eliminating dirt from their homes, and their labor force
participation had reached a low point. By 1901 married women™s labor
force participation had already reached its nadir of about 10 percent,
where it stayed until it began to rise in the 1930s.44

V. Gender ideology and changes in preferences
When they observe a change, economists generally seek to explain that
change as a response to the constraints faced by decision-makers. It is
possible, however, that changes in preferences may explain the change in
behavior. There is evidence that women™s preferences for work changed
over the course of the nineteenth century and contributed to the decline
of labor force participation.
The nineteenth century saw the creation of the idea that a married
woman should not need to work and her husband should be able to
support the family. Previously it was expected that women would con-
tribute to the family income. An eighteenth-century pamphlet warns
women that “you cannot expect to marry in such a manner as neither of
you shall have occasion to work, and none but a fool will take a wife whose
bread must be earned solely by his labor and who will contribute nothing
toward it herself.”45 By the nineteenth century this attitude had changed,
and middle-class families were ashamed if the wife had to work.46 Men

Ibid., p. 189. 44 Hatton and Bailey, “Women™s Work in Census and Survey,” Figure 1.
A Present for a Servant Maid, 1743, quoted in George, London Life in the Eighteenth
Century, pp. 168“9.
Rose, “Gender Antagonism,” p. 205.
Women™s labor force participation 323

commonly expressed concern that married women who were working
would neglect their domestic duties. Seeing to the domestic comforts of
the home, even if it was a small cottage, came to be seen as important
work that paid employment would detract from. In the 1843 report on
Women and Children in Agriculture we see men expressing concern about
the families of women who worked in the ¬elds. Revd Howman from
Bexwell, Norfolk, did not approve of women being employed in out-
door agricultural work because:

It produces also a bad moral effect on the men. Observation shows that women
employed in ¬eld-work are not so careful and clean as others; consequently, the
home to which the man returns, after his day™s work, is not so comfortable as it
ought to be, and he is driven to the ale-house and beer-shop to avoid the dis-
comforts, and to seek for that comfort which he ought to ¬nd at home.47

Somewhat later, in 1865, the managers of a Scottish paper mill report
that “with a view to prevent the neglect of children in their homes, we do
not employ the mothers of young children in our works.”48 For women
of the upper classes, the avoidance of paid work was particularly
important. In 1839 Mrs. Ellis wrote that:
It is a curious anomaly in the structure of modern society, that gentlemen may
employ their hours of business in almost any degrading occupation and, if they
but have the means of supporting a respectable establishment at home, may be
gentlemen still; while, if a lady but touch any article, no matter how delicate, in
the way of trade, she loses caste, and ceases to be a lady.49

Veblen explains this enforced leisure for women as a form of con-
spicuous consumption demonstrating the household™s high status. While
middle-class husbands could not afford to refrain from work, “the
middle-class wife still carries on the business of vicarious leisure, for the
good name of the household and its master.”50 This ideology probably
encouraged many women to stay out of the labor market.
Certainly nineteenth-century individuals thought about themselves in
gendered ways. This may have affected women™s employment oppor-
tunities in various ways. Craft and professional organizations used
gender ideology to support their restrictions on female employment.
Gender ideology worked through customer preferences, by reducing the

Women and Children in Agriculture, p. 244.
Quoted in Simonton, European Women™s Work, p. 141.
Mrs. Ellis, The Women of England and their Social Duties and Domestic Habits, 2nd edn
(London: Fisher, Son, and Co., 1839), pp. 344“5.
Thorstein Veblen, The Theory of the Leisure Class (Boston: Houghton Mif¬‚in [1899]
1973), p. 68.
324 Gender, Work and Wages in Industrial Revolution Britain

demand for the services of females in certain occupations. Gender
ideology also created a social cost to female employment. Families that
did not follow the male-breadwinner norm lost social status. As incomes
rose in the later nineteenth century, more families could afford to pur-
chase the higher social status that came with a wife who did not work
outside the home. Gender ideology may also have changed women™s
preferences; even if they could have found employment, women may
have preferred to remain out of the labor force. Even Ivy Pinchbeck, an
educated and accomplished woman, voiced this preference. She noted
that, in spite of the fact that “the majority of married women lost their
economic independence,”
the industrial revolution marked a real advance, since it led to the assumption
that men™s wages should be paid on a family basis, and prepared the way for the
more modern conception that in the rearing of children and in home-making,
the married woman makes an adequate economic contribution.51

In valuing the opportunity to remain out of the labor force above eco-
nomic independence, Pinchbeck demonstrated that her preferences
were different from those of many women today, who would prefer
economic independence. There is no basis for saying which set of
preferences is better, but the difference in preferences surely had
implications for labor force participation.
However, the fact that the culture increasingly associated women with
the household at a time when women™s labor market participation fell
does not necessarily mean that the changing ideology caused the change
in participation. Correlation is not causation. Unfortunately, this is
dif¬cult to determine because both economic incentives and gender
ideology were changing at the same time, and both implied declining
female participation. It is not clear whether the change in gender
ideology was independent of economic changes, or was itself driven by
those economic changes. Perhaps participation declined because of
changes in economic incentives, and only then did ideology change.52

Pinchbeck, Women Workers and the Industrial Revolution, pp. 312“13.
Snell argues that changes in women™s agricultural employment came before changes in
attitudes: “The historical determinant of women™s economic and domestic roles would
appear to be located primarily in seemingly autonomous changes in the structure of the
economy, rather than in shifts of social attitudes. Moral sentiments antagonistic to
female labor in the nineteenth century may have reinforced the pattern of change
described here, and contributed to the process begun in the mid-eighteenth century.
But insofar as they cannot readily be dated from before 1800, at the very earliest, their
signi¬cance seems heavily undercut by the evidence that the major sexual division of
labor began at least ¬fty years before such ˜middle-class™ attitudes toward the roles of
women can have had in¬‚uence.” Snell, Annals of the Laboring Poor, p. 66.
Women™s labor force participation 325

Perhaps gender ideology was created as a marketing tool to convince
people to accept the restrictions on female employment that bene¬ted
particular groups of male workers.
Nor should we assume that the ideological statements we hear from
Victorians were accurate descriptions of reality. To a large extent female
domesticity was an aspiration rather than a description of reality. Vickery
criticizes the literature on separate spheres for failing to ask important
questions about the primary sources used: “Did men and women
actually conform to prescribed models of authority? . . . Did women
deploy the rhetoric of submission selectively, with irony, or quite
cynically?”53 After reviewing some of the evidence, Vickery suggests that
“doubts now circulate within women™s history about the conceptual
usefulness of the separate spheres framework.”54 The power of gender
ideology to direct women™s activities should not be overstated.

The explanations for declining participation presented here suggest that
before 1850 it had different causes and consequences than it had after
1850. Before 1850, declining participation was caused mainly by
declining demand for female labor, which made women worse off. After
1850, declining participation resulted from the expansion of women™s
choice set as well as from its contraction. Census data suggest increasing
occupational segregation after 1851, so part of the declining participation
of the later nineteenth century may have been due to mounting occupa-
tional barriers, which made women worse off. Some of the decline,
though, was also due to increasing family income, combined with new
information about health that increased the demand for home-produced
goods and services. Both of these changes made women better off.
Gender ideology also contributed to declining female participation by
changing women™s preferences for home versus market work. Did these
changes make women worse off or better off ? There is no basis for
answering this question because we would have to chose one value
system over the other in order to rank the outcomes. Declines in female
participation rates are seen by some historians as part of a patriarchal
system that ensured men continued to enjoy the services of women.55
They made women worse off in the sense that they made them more
dependent on men. The women™s movement of the twentieth century
included a rejection of this model of the family, largely because of the

Vickery, “Golden Age to Separate Spheres?” p. 385. 54 Ibid., p. 393.
Hartmann, “Capitalism, Patriarchy, and Job Segregation.”
326 Gender, Work and Wages in Industrial Revolution Britain

differences in power that it implied. The women at the time, however,
did not experience the change as a bad thing. Withdrawal from market
work is not necessarily bad. We consider retirement a good thing, and as
Benjamin and Brandt note:
We cannot attach a welfare interpretation to female labor force participation . . .
If the household was suf¬ciently wealthy, the women could stay at home, con-
suming “leisure,” assuming leisure is a normal good. Put another way, just
because draft animals do a lot of farm work does not mean they enjoy a high
position in society or that they are better off than animals grazing in the ¬elds.56

There is no basis for concluding that Pinchbeck or her contemporaries
were wrong to favor home production over market production.
Declining female participation during the later nineteenth century did
not necessarily represent declines in women™s welfare. To the extent that
it was caused by increasing employment barriers, it made women worse
off, but to the extent that it was caused by increasing household incomes
and new information about health, it improved women™s lives. During
the ¬rst half of the century, however, the decline in female participation
resulted from declining demand for female labor, and thus does seem to
indicate a decline in women™s welfare.

Benjamin and Brandt, “Markets, Discrimination, and the Economic Contribution of
Women,” p. 67.
8 Conclusion

Competition is the great, the only, the all-prevailing evil.
“ a male tailor and unionist, 18341

During the Industrial Revolution, women earned lower wages than men,
and worked in different occupations. This book has analyzed the reasons
for these differences. In competitive portions of the labor market,
women were disadvantaged by their lesser strength, since strength was
important in most jobs. Women™s wages were on average lower than
men™s wages because women were on average less productive than men.
Occupational segregation was not the cause of the wage gap, but a
method of minimizing it. If men and women had worked in the same
occupations, the wage gap would have been even larger. Occupational
segregation minimized the wage gap by directing women to occupations
where wages were least sensitive to strength. While individuals used
gender ideology to interpret the wage differences they saw, that does not
necessarily mean that gender ideology was the cause of those differences;
people often create myths to explain things they do not understand, or to
justify institutions that bene¬t them economically. In competitive por-
tions of the labor market the gender division of labor was determined by
comparative advantage. Women worked in jobs requiring less strength,
except for a few exceptional women who were strong enough to do jobs
such as hewing coal. Comparative advantage also directed women to
child-care tasks, so women preferred work in cottage industry, which
could more easily be combined with child care.
In less competitive portions of the labor market, male workers were
able to raise their own wages by limiting the supply of labor, and usually
this involved barriers to female employment. Where men worked as
skilled employees, unions were the most important source of gender
constraints during the Industrial Revolution. Guilds had become inef-
fective, and employers sought to hire women because they could pro¬t

The Pioneer, May 9, 1834, quoted in Taylor, Eve and the New Jerusalem, p. 115.

328 Gender, Work and Wages in Industrial Revolution Britain

from doing so. Only workers with scarce skills, and thus some monopoly
power, were successful in excluding women. Unskilled workers faced
competition from other unskilled workers; unskilled workers tried to
erect such barriers, but were unsuccessful. While men often used gender
ideology to justify the exclusion of women, the real cause of their actions
was economic. While employers shared the same gender ideology, they
fought for the right to hire women because they could pro¬t from doing
so. When economic incentives and gender ideology con¬‚icted, men were
willing to abandon the ideology.
Professional organizations acted much like unions in seeking to limit
female employment. Male physicians edged out female midwives by
convincing the public that formal education made physicians more skil-
led. Strict limits on who could enter an occupation, such as examinations
for apothecaries, also allowed professions to limit entry. Lawyers, doctors,
and the clergy were all successful in erecting barriers to women™s
employment, severely limiting women™s opportunities for high-paid
work. Teaching at the primary level, which was not yet professionalized,
remained open to women, and success was determined by the com-
petitive market.
A woman™s ability to go into business herself was limited by a wider
range of factors, all of which were immune to competition. Customers did
not compete with each other, and in certain occupations customers pre-
ferred to patronize men, limiting women™s opportunities. How else can we
explain the absence of women from hair dressing? Women™s opportunities
were also limited by the law. Married women had no legal existence, and
their husbands controlled all their assets. While the feme sole exception
allowed married women to conduct their own businesses, the law of
couverture led to women having more limited access to capital. Daughters
received their inheritances in trust, which protected the money from loss
by current or future husbands, but also prevented women from using the
money for a business venture. None of these factors, however, was as
important in determining the gender division of labor as either strength
or barriers erected by powerful groups of male workers.
Historians of women workers tend to think that free-market forces
were detrimental to women. Perhaps they have been in¬‚uenced by the
trade union movement, which (rightly) saw competition as a threat to its
power. I believe, however, that competition was bene¬cial to women,
and that English women would have been worse off if there had been
less competition in the economy. In fact, competition was a woman™s
strongest and most consistent ally in the struggle for economic oppor-
tunity. Institutions such as the law and the family were more likely to be
swayed by gender ideology, but competition was blind.
Conclusion 329

While competition hurt organized male workers by eroding their
market power, it helped women. Where there were no barriers to female
employment, competitive markets guided women to the occupations
where strength was least important, minimizing the wage penalty caused
by women™s lesser strength. Where women faced barriers to employ-
ment, competition was the most powerful force in breaking down those
barriers. The powerful tailors™ union was eventually defeated by com-
petition, and the trade was opened to women. Weavers were never able
to erect barriers to female employment because the trade was too easily
learned, and thus too competitive. It was competition that convinced
employers to hire women, even though their ideology opposed it. Only
where monopoly power limited competition could barriers to female
employment be maintained. The advantage of competition can also be
seen in the fact that women in the British economy fared better than
women in other less competitive economies; in Germany guilds had
more power than in England, and the number of trades which were
monopolized by men was much greater.
Competition was not the source of women™s lower wages. Competi-
tion led to occupational sorting in competitive markets, but in this case
occupational sorting actually increased women™s wages, by directing
them to the occupations where the penalty for their lesser strength was
the smallest. The only places where occupational segregation reduced
the wages that women could earn were places where entry to those
occupations was non-competitive. Where men monopolized an occu-
pation and did not allow women to enter, women lost, and their wages
suffered. Many of the highest-paying occupations were so monopolized,
severely limiting opportunities for the most educated women. The cause
of these limited opportunities, though, was insuf¬cient competition.
British women faced fewer economic constraints than German
women because British markets were more competitive. Ogilvie notes
that in Germany guilds were strong and were able to exclude outsiders.
Only males could be apprenticed, and apprenticeship was required in
“most economic activities in both towns and villages. The only exceptions
were farming, laboring, spinning, and housework”.2 Most unmarried
women had limited occupational opportunities; most worked in either
agriculture or spinning.3 Wages and occupations were not determined
by individual ability because markets were not competitive.4 British
women, by contrast, faced fewer constraints, and participated in a wider
range of occupations. They were less likely to do heavy jobs for which

2 3 4
Ogilvie, A Bitter Living, p. 96. Ibid., pp. 272“3. Ibid., p. 324.
330 Gender, Work and Wages in Industrial Revolution Britain

they were ill-suited, such as plowing, and participated in a wide
range of commercial activity. Competitive markets bene¬ted women
In identifying the desire for economic gain as the main motive behind
barriers to female employment, and in identifying competition as the
most powerful defender of women™s opportunities, I am suggesting that
economic motives, rather than gender ideology, determined the division
of labor. While I do not dispute the fact that individuals used gender
ideology to make sense of their experiences, that does not mean that
ideology was really the driving force behind those experiences. Gender
ideology was an important part of the life experiences of men and
women of Industrial Revolution Britain. It played an important role in
how the British understood their world, and it could be decisive in areas
where competition was weak, such as family decisions about how to
educate children, or university admission decisions. When male workers
sought to limit the supply of labor to their occupations, gender ideology
guided them to target women. But gender ideology was not itself
exogenous to the market, and was formed in response to needs created
by the market. In some cases, gender ideology was used to explain the
otherwise inexplicable, such as women™s lower wages. In some cases, it
was a tool used to persuade the broader society that women should be
excluded from certain occupations.
In learning about the British labor market two hundred years ago, we
have learned some useful lessons. We have learned that competition can
be bene¬cial to women. This should not be taken to imply that laissez-
faire bene¬ts women. Competition is not the absence of government
involvement. In fact, government intervention is often required to allow
competition to survive. While competition tends to protect women from
discrimination, this certainly does not mean that capitalist societies are
free from discrimination because capitalist societies do not always, or
even usually, produce competitive markets. Competition is a frail plant
that, without constant tending by the gardener, will be strangled by the
weeds of distributional coalitions. Accepting the conclusion that com-
petition helps women does not imply that we should favor inactive
government. It does imply, though, that we should try to use the power
of competition to bene¬t women, writing policies that reduce monopoly
power and thus help the market to function well, rather than trying to
overrule the market.
We have also learned that equal opportunity does not guarantee equal
outcomes. In situations requiring strength, men and women are not
equally capable. In certain cases, equal outcomes can only be obtained
from unequal opportunities. One example is ¬rearms tests at the FBI. In
Conclusion 331

1995 two women complained that a test requiring new agents to pull the
trigger of a handgun 29 times in 30 seconds was used to discriminate
against women.5 Another example is a debate over whether the military
should set different standards for men and women combat pilots. The
problem is that:
If women are expected to carry 150-pound water pumps and take the same G
forces as men, a truly gender-neutral assignment policy could well lead to an
across-the-board reduction in opportunities for women in the armed forces
because many of them lack the strength and endurance to qualify.6

We must choose whether we want equal opportunities or equal out-
comes, rather than pretending that we can always have both. Current
military policy is something of a compromise. Physical standards for
women are set lower than those for men, but the difference in require-
ments is less than the difference in the average abilities of the sexes, so
that women still ¬nd it more dif¬cult to meet the standard.7
Today the gender gaps are smaller, but women™s wages and occupa-
tions still do not look identical to men™s. The ratio of women™s to men™s
median hourly earnings rose from 63 percent in 1972 to 79 percent in
1991.8 The gender gap is now smaller than that reported in Table 2.1.
The labor force participation rates of married women have increased
from 10 percent at the beginning of the twentieth century to over 60
percent in 1991.9 Women have greater opportunities than they once did
for well-paid work, and have entered professions in medicine, the law,
and the church. The extent of occupational segregation has decreased,
but it has not disappeared.
One reason that women™s opportunities in the labor market have
changed is that the law has changed. Married women gained control of
their earnings and wealth in the second half of the nineteenth century,
eliminating the disadvantages discussed in Chapter 7. In Britain, the
Married Women™s Property Act of 1870 gave married women control of

“Female FBI Trainees: Gun Test Discriminates”, Chicago Tribune, October 5, 1995.
David Evans, “Women in Combat: Raised Expectations, Lowered Standards?” Chicago
Tribune, May 7, 1993, sec. 1, p. 23.
Bernadette M. Marriott and Judith Grumstrup-Scott, “Introduction and Background”,
in Marriott and Grumstrup-Scott, eds., Body Composition and Physical Performance
(Washington, DC: National Academy Press, 1992), p. 19.
Jane Waldfogel, “The Price of Motherhood: Family Status and Women™s Pay in a Young
British Cohort”, Oxford Economic Papers 47 (1995), p. 584. Blau and Kahn report, for
the 1990s, ratios of 0.75 in the UK and 0.76 in the US. Francine Blau and Lawrence
Kahn, “Gender Differences in Pay”, Journal of Economic Perspectives 14 (2000), p. 92.
Data for England and Wales. Hatton and Bailey, “Women™s Work in Census and
Survey”, p. 88.
332 Gender, Work and Wages in Industrial Revolution Britain

their personal property and the right to their own earnings. Further acts
in 1882 and 1893 gave women full control of all property they brought
to the marriage or acquired after marriage. In the US, Maine was the
¬rst state to grant married women ownership of their property, in 1844,
and of their own earnings, in 1857. Other states followed during the
second half of the century, and by 1895, forty-four states had passed
some type of law expanding the ownership rights of married women.10
Women had to wait until the 1960s for laws against employment dis-
crimination. In the US, the Equal Pay Act of 1963 and Title VII of the
1964 Civil Rights Act forbade discrimination against women in hiring
and pay.11 In Britain gender discrimination was outlawed by the Equal
Pay Act of 1970 and the Sex Discrimination Act of 1975.12 Instead of
denying married women a legal voice, the law now enforces equal
opportunity in employment.
In 1825 William Thompson identi¬ed two causes of women™s lower
wages: their lesser strength, and child-bearing. Over the past two cen-
turies strength has become much less important in determining women™s
labor market opportunities. It still plays a role in some occupations;
those that require high levels of strength are overwhelmingly male.
However, in most occupations strength is not a factor. Table 8.1 shows
the gender division of labor in jobs of different strength intensity in the
US labor force. The Dictionary of Occupational Titles categorizes the
strength required for each of the jobs it lists as sedentary, light, medium,
heavy, or very heavy. Table 8.1 shows that the percentage of women in
an occupation decreases monotonically as the strength requirement of
the job increases. While 55 percent of the workers in sedentary jobs are
female, only 12 percent of workers in heavy jobs, and only 6 percent of
workers in very heavy jobs, are female. However, strength is much less
important for determining wages than it was two hundred years ago
because only 12 percent of all workers are employed in occupations
whose strength requirements are heavy or very heavy. Strength, then, is
not in such high demand, so it does not command the wage premium
that it once did. It can no longer explain the overall wage gap because
there are enough jobs where strength is unnecessary to employ all the
women in the labor force. Strength, though, can still explain why women
are rare in certain occupations, such as ¬re-¬ghting and construction.

Khan, “Married Women™s Property Laws”, pp. 363“4.
Kermit Hall, ed., The Oxford Companion to American Law (Oxford: Oxford University
Press, 2002), p. 219.
David Walker, The Oxford Companion to Law (Oxford: Clarendon Press, 1980),
p. 1137.
Conclusion 333

Table 8.1. Gender division of labor by strength category of occupation

Number of workers in April,
1971 (1000s)

Strength Percent Percent of all Cumulative
category Males Female female workers percent

Sedentary 8,172 9,926 54.8 21.4 21.4
Light 17,405 16,120 48.1 39.7 61.1
Medium 16,236 6,238 27.8 26.6 87.7
Heavy 7,585 1,038 12.0 10.2 97.9
Very Heavy 1,578 102 6.0 2.0 100.0
Total 50,976 33,423 39.6

Note: The number of workers in each category is the total in the US labor force estimated
from the April 1971 CPS sample, using the CPS weights.
Source: National Academy of Sciences, Committee on Occupational Classi¬cation and
Analysis, Dictionary of Occupational Titles (DOT): Part I “ Current Population Survey, April
1971, Augmented with DOT Characteristics, [Computer ¬le]. ICPSR version. Washington,
DC: US Department of Commerce, Bureau of the Census [producer], 1981. Ann Arbor,
MI: Inter-university Consortium for Political and Social Research [distributor], 2001.

While strength has become irrelevant in most occupations, child-
bearing still has important effects on women™s labor market outcomes.
The gender wage gap is smaller for women without children than it is for
mothers. Waldfogel ¬nds that, for British women who were 33 in 1991,
mothers earned 64 percent as much as men, while women with no
children earned 84 percent as much as men. Single women earn 83
percent as much as single men, but married women earn only 56 percent
as much as married men.13 Marriage and family have different effects on
men™s and women™s earnings. The presence of children decreases female
wages but increases male wages. Marriage increases wages for both men
and women, but the effect is more than twice as large for men as it is for
women.14 A substantial part of the wage gap is actually a “family gap”;
the labor market penalizes women, but not men, for having families.
The family gap may result from the fact that women still do most of
the household labor. Table 8.2 shows the gender gap in hours spent in
household work. While there has been remarkable convergence in most
countries, women still do most of the household labor. Even women
who work full-time do more housework than men who work full-time.

Jane Waldfogel, “Understanding the ˜Family Gap™ in Pay for Women with Children”,
Journal of Economic Perspectives 12 (1998), p. 142.
Ibid., p. 146.
334 Gender, Work and Wages in Industrial Revolution Britain
Table 8.2. Men™s hours of housework as a percentage of
women™s hours of housework

US Full-time
Denmark Norway Japan USSR US workers

1964 12.3
1965 35.0 8.9 31.1 27.5
1971 37.3
1980 50.9
1981 45.2
1985 11.3 44.1
1987 55.4
2003 57.6 67.4

Sources: 2003 data from Daniel Hammermesh, Harley Frazis, and Jay Stewart,
“Data Watch: The American Time Use Survey”, Journal of Economic Perspectives,
19 (2005), p. 224. All other data from F. Thomas Juster and Frank P. Stafford,
“The Allocation of Time: Empirical Findings, Behavioral Models, and Problems
of Measurement”, Journal of Economic Literature, 29 (1991), p. 477.

This gender division of labor in household work is currently one of the
major obstacles to gender equality in the labor market. Joshi and Paci
¬nd that, while the wage penalty for being female declined between
1972 and 1991, the penalty for motherhood did not decline.15 Men and
women will not reach equality in the labor market until there is equality
within the family.
Fortunately there are signs that behavior is changing. The conver-
gence of housework time evident in Table 8.2 is encouraging, as is the
increase in the number of teenage girls who expect to be in the labor
market as adults. While in 1968 only 30 to 35 percent of teenage girls
in the US expected to be working at age 35, by 1980 between 80 and
85 percent expected to be working at age 35. This change in expect-
ations contributed to women™s increasing college enrollment rates, and
today female college students outnumber male college students.16
Technology also seems to be helping women to reduce the con¬‚ict
between child bearing and market work. Martha Bailey ¬nds that the
release of the pill in the US did not change total fertility, but it did lead
to an increase in the number of female professionals because it allowed
women to change the timing of births: “By providing a low-cost means

Joshi and Paci, Unequal Pay for Women and Men, p. 124.
Claudia Goldin, Lawrence Katz, and Ilyana Kuziemko, “The Homecoming of
American College Women: The Reversal of the College Gender Gap”, Journal of
Economic Perspectives 20 (2006), pp. 133“56.
Conclusion 335

of delaying childbearing, oral contraception allowed women to remain in
school, pursue longer-term careers, and work more in the paid labor
force during ages historically associated with childrearing”.17 While the
occupations and wages of men and women may never be identical, labor
markets are clearly moving in that direction. Women of the twenty-¬rst
century may not have occupations and wages identical to men™s, but
they will face less occupational segregation and smaller wage gaps than
women of the Industrial Revolution.

Martha Bailey, “More Power to the Pill: The Impact of Contraceptive Freedom on
Women™s Life Cycle Labor Supply”, Quarterly Journal of Economics 121 (2006), p. 295.
Appendix to Chapter 3

This appendix presents more mathematical versions of the sorting
models presented in Chapter 3. All of these models assume that indi-
viduals do not differ by skill, but only in their strength endowment.

Model A
Here I expand Model A to allow the possibility that the distributions
may overlap. Individuals get strength endowments that are random
draws from normal distributions. Males and females draw their strength
endowments from different distributions, and the male distribution has a
higher mean. In general individuals can freely choose among T occu-
pations. In occupation i individual j will produce qij ¼ ai þ biSj units of
output and will have earnings of piqij, where pi is the piece-rate. An
individual will choose the occupation in which he or she has the highest
earnings. Since earnings functions are linear, each occupation will have
at most one interval of possible S values over which it is the best
occupational choice. (It is possible that an occupation will attract no
workers if its earnings are always below those of another occupation.)
What will happen if we take the income functions from Figures 3.2 and
3.5, but allow the strength endowments to overlap? Suppose that females
have strength endowments that are normally distributed with a mean of
25 and a standard deviation of 15. Males have strength endowments that
are normally distributed with a mean of 75 and a standard deviation of 15.
With these assumptions the male mean is 3 1 standard deviations above
the female mean, which approximately matches the distance between
the means in maximum lift capacity presented in Table 2.4.
In Figure 3.2, individuals with strength between 0 and 25 will choose
occupation A. Since 25 is the mean female strength score, half of the
women will choose occupation A and half will choose occupation B.
A strength score of 25 is 3 1 standard deviations below the mean on the
male distribution, so the probability of observing a man in occupation
A is less than one-tenth of 1 percent. The outcome is essentially the

Appendix to Chapter 3 337

same as above, except for the possibility of ¬nding a very unusual man in
occupation A.
Given the opportunities described in Figure 3.5, individuals with a
strength score below 20 will choose occupation A, those between 20 and
60 will choose occupation B, and those above 60 will choose occupation
C. We would expect that 20 percent of women will choose occupation
A, 79 percent occupation B, and 1 percent occupation C, while 84 percent
of men will choose occupation C, and 16 percent of men will choose
occupation B. Clearly, occupations A and B are “women™s work” and
occupation C is “men™s work,” but the gender division of labor is not
perfect. If there are equal numbers of male and female workers, we
would expect to observe that about 1 percent of workers in occupation
C are female, and 17 percent of workers in occupation B are male. It
could even happen that we observe men in occupation A, though that
would be a rare occurrence.
If we allow the male and female strength distributions to overlap, the
general pattern remains, with one gender dominating most occupations,
but the division of labor by gender is not as strict, and we could observe
more than one occupation hiring members of both genders.

Model B
In this model I assume that employers can observe the worker™s gender
but not the worker™s strength score. The employer will treat all women
the same, acting as if each female worker has a strength score of:

Sf ¼ E °Sj j j is femaleÞ

Similarly, the employer will treat all men the same, acting as if each male
worker has a strength score of:
Sm ¼ E °Sj j j is maleÞ

Since men are stronger than women, Sm > Sf.
The labor power provided by an individual is a function of that
individual™s strength:
Lij ¼ ai þ bi Sj

The relationship between labor power and strength can be different at
different ¬rms. At some ¬rms strength may not matter (bi ¼ 0), in which
case the ¬rm will not prefer men. If strength does matter (bi > 0), then
the average man provides more labor power than the average woman.
338 Gender, Work and Wages in Industrial Revolution Britain

The ¬rm cannot observe an individual™s level of strength, but does
observe gender. Given gender, the ¬rm forms a conditional expectation
of strength. The ¬rm thus expects different amounts of labor power from
each gender:

Lif ¼ E°Lij j j is femaleÞ ¼ ai þ bi Sf
Lim ¼ E°Lij j j is maleÞ ¼ ai þ bi Sm

Since Sm > Sf, then Lim > Lif if bi > 0. We could also write the labor
power provided by a male as:

Lim ¼ Lif þ bi °Sm À Sf Þ

This suggests that we can think of the labor power provided by an individual
as a base level of labor power, plus a strength upgrade if the worker is male.
We can normalize labor power so that the base level of labor power is one:
Lij ¼ 1 if j is female
bi °Sm À Sf Þ
¼1þ if j is male

If we sum this up over all the workers that the ¬rm hires, then the total
amount of (normalized) labor power hired by the ¬rm is:

N þ qi M

where N is the total number of male and female workers hired by the
¬rm (N ¼ F þ M) and M is the number of male workers hired. The
parameter qi is the value of the strength upgrade to ¬rm i.
Including this equation for labor power in a Cobb-Douglass production
function we get:
Q ¼ A°N þ qM Þa K b

The marginal product of a female worker is:
dQ aQ
¼ Aa°N þ qM ÞaÀ1 K b ¼
dF N þ qM

and the marginal product of a male worker is:
dQ aQ°1 þ qÞ
¼ Aa°N þ qM ÞaÀ1 K b °1 þ qÞ ¼
dM N þ qM
Appendix to Chapter 3 339

The ¬rm™s ri, which I have de¬ned as the ratio of the female marginal
product to the male marginal product is simply:
dQ=dF 1
r¼ ¼
dQ=dM °1 þ qÞ

The ¬rm will choose to hire men if (1 þ qi) > wm/wf (or qi > (wm À wf)/wf ,
or ri < wf /wm) and to hire women if (1þqi) < wm/wf (or qi < (wm À wf)/wf ,
or ri > wf /wm). This is the same thing as saying that the ¬rm will buy the
strength upgrade if the value of the upgrade is greater than its price.
In general each ¬rm™s demand for workers will depend on the price of
the ¬rm™s output and the level of wages. Wages will adjust so that the
demand for each type of worker is equal to the supply. If we assume that
the number of workers each ¬rm will hire is ¬xed, then the wage ratio
can be easily determined in a simple graph. In Figure 3.6, the length of
the x-axis is the total amount of labor supplied and demanded in the
economy. There are OX females and XL males. Firms are ordered by ri,
and the “r-pro¬le” is constructed by giving each ¬rm a line segment
whose height is ri and whose length is proportional to the number of
workers it hires. The wage ratio is then determined by the point at which
the vertical line originating at point X intersects the r-pro¬le. The
marginal ¬rm may hire both males and females, but all other ¬rms will
hire only one gender. Changes in the number of workers hired by a ¬rm,
or the entry and exit of new ¬rms, will change the r-pro¬le and, if
substantial enough, will shift the market wage ratio.

Model C: the learning model
This model provides an intermediate case between Model A and Model
B. Model A assumes that the employer can perfectly observe the indi-
vidual worker™s output, and Model B assumes that the employer has no
information about the individual worker™s output, and must use gender to
estimate the worker™s productivity. In this model the employer receives a
noisy signal of the worker™s output. At ¬rst the employer has little infor-
mation, and pays the worker according to gender as in Model B. Over
time the employer learns about the workers and pays a wage more closely
matched to the individual™s productivity, and the model evolves into one
more like Model A. As in the two previous models, I assume that prod-
uctivity differs only because of strength, so that an individual™s product-
ivity can be completely described by the strength score S.
We might expect that when an employer ¬rst hires a worker he or she
does not know that individual™s strength score (Sj), but that over time
340 Gender, Work and Wages in Industrial Revolution Britain

the employer learns and can adjust the wage to reward actual product-
ivity. I assume that in each industry there is a function that relates an
individual™s output, qj, to his or her strength score, Sj:
qj ¼ f °Sj Þ

The employer pays each worker his or her expected productivity, which
varies over time as the employer receives more information. Thus:
wtj ¼ Et q j

When ¬rst hired, each worker receives a wage equal to the average
productivity of that worker™s sex:

wtj ¼ lj where lj ¼ lf ¼ f °Sf Þ if j ¼ f
¼ lm ¼ f °Sm Þ if j ¼ m

Each period the employer receives a signal, stj, of productivity that will
allow him or her to update the estimate of the worker™s productivity. The
employer observes:
stj ¼ qj þ etj

where etj is a random error that is normally distributed with mean zero
and variance r2 . Since qj is the individual™s true productivity, it is
not stochastic, so the signal stj is normally distributed with mean qj
and variance r2 :
In the second period, one signal has been observed. The expected
value of the individual™s productivity is a weighted average of the
observed signal and the mean productivity of the worker™s sex:

r2 r2
l þ 2 i 2 s1j
w2j ¼ E2 qj ¼ 2 2i
ri þ re ri þ re

where li and r2 (i ¼ m, f ) are the mean and variance of the true
productivity of individuals in the worker™s sex. This equation can
also be written:
1 1
li þ r2 s1j
w2j ¼ e
1 1
r2 r2

In the third period, the expected value of the worker™s productivity will
be a weighted average of E2qj and s2j, which reduces to:
Appendix to Chapter 3 341

1 1
li þ r2 °s1j þ s2j Þ
w3j ¼ e
1 1
þ 2 r2
r2 e

The wage in subsequent periods is updated according to observed
values of s:
1 1
li þ r2 skj
r2 e
wtj ¼ 1 1
þ t r2
r2 e

As t gets large, this approaches an average of the stj™s, and thus will
converge to the true productivity, qj. In the ¬rst period of employment,
the individual is paid the average productivity of his or her sex, as in
Model A. In the limit, though, the employer learns the true productivity
of the worker, as in Model B.
In some cases, however, this process may fail to achieve the correct
allocation of labor according to individual ability. Correct sorting may
never occur for women with high strength scores. In order to learn the
true productivity of a worker, the employer must ¬rst be willing to hire
that individual. An unfamiliar employer may not be willing to hire a
woman for any positive wage. For example, if the productivity of a
worker at a ¬rm is:

qj ¼ S 2 À 900

and the average female strength score is less than 30, then the expected
productivity of a woman is negative, and the employer will be unwilling
to hire women. A woman whose strength score was 40 could be pro-
ductive in this occupation, but the employer will not discover that
because he will never hire her in the ¬rst place.
Appendix to Chapter 4


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