Gender Roles and Technological Progress

Gender Roles and Technological Progress
The views expressed in this paper are those of the author(s) and not those of the funding organization(s) or of CEPR, which takes no
institutional policy positions.
We are grateful to the Banco de España for their financial and organizational support.
Stefania Albanesi and Claudia Olivetti
Gender Roles and Technological
Progress
Tarragona, Spain; 20-25 May 2008
Hosted by
Banco de España
European Summer Symposium in International
Macroeconomics (ESSIM) 2008
Gender Roles and Technological Progress
Stefania Albanesiyand Claudia Olivettiz
August 3, 2007
Abstract
Until the early decades of the 20th century, women spent more than 60% of their primeage years either pregnant or nursing. Since then, improved medical knowledge and obstetric
practices reduced the time cost associated with women’s reproductive role. The introduction
of infant formula also reduced women’s comparative advantage in infant care, by providing an
e¤ective breast milk substitute. Our hypothesis is that these developments enabled married
women to increase their participation in the labor force, thus providing the incentive to invest in
market skills, potentially narrowing gender earnings di¤erentials. We document these changes
and develop a quantitative model that aims to capture their impact. Our results suggest that
progress in medical technologies related to motherhood was essential to generate the signi…cant
rise in the participation of married women between 1920 and 1960, in particular those with
children. By enabling women to reconcile work and motherhood, these medical advancements
laid the ground for the revolutionary change in women’s economic role.
1
Introduction
The dramatic rise in the labor force participation of married women is one of the most notable
economic phenomena of the twentieth century. The trend is particularly prominent for those with
young children and has led to a revolutionary change in women’s economic role. We examine the
contribution of progress in medical technologies related to motherhood to this process and …nd
that these advancements played a critical role.
Our point of departure is that women’s maternal role was associated with a considerable time
commitment until the early decades of the twentieth century. Consider a typical woman in 1920.
Her life expectancy was 55 years at age 10. She married at age 21 and had on average more than
3 children, with her …rst birth at age 23 and her last at age 33. Her total number of pregnancies
was higher than the number of births, given the high fetal mortality rate. In total, she would be
pregnant for 34% of the time during her fertile years.
For useful comments, we wish to thank Raquel Fernández, Simon Gilchrist, Claudia Goldin, Jeremy Greenwood,
John Knowles, Roberto Samaniego, Michele Tertilt, and seminar participants at Boston University, Chicago Fed,
LSE, UCLA, UT Austin, George Washington University, USC, the NBER Summer Institute, the LAEF conference
on "Gender, Households and Fertility" at UCSB, the New York/Philadelphia Workshop on Macroeconomics, the
SED 2006 Annual Meeting, and the North American Econometric Society Meetings. We thank Natalie Bau, Jenya
Kahn-Lang, Mikhail Pyatigorski, and Justin Svec for excellent research assistance. This research is supported by
the National Science Foundation under Grant No. 0551511.
y
Columbia University, NBER, and CEPR. Sa2310@columbia.edu. Corresponding author.
z
Boston University. Olivetti@bu.edu.
1
Health risks in connection to childbirth were severe. The pre- and post-partum phases, as well
as labor, were associated with considerable su¤ering that could lead to physical disability and, in
the extreme, death. One mother died for each 125 living births in 1920. The four main causes
of death were septicemia, toxaemia, trauma and hemorrhages. At a rate of 3.6 pregnancies per
woman, the compounded risk of death was 2.9% or 1 in 34, a very considerable number. Add to
this that, for every maternal death, twenty times as many mothers su¤ered di¤erent degrees of
disablement annually (Kerr, 1933). Indeed, infection, toxemia, and trauma were also the main
causes of maternal morbidity. The duration of the corresponding disablement ranged between 7
months and 7 years. An additional factor to consider for the early decades of the 20th century
is that most infants were breast fed in their …rst year of life. Women would then be nursing for
33% of the time between age 23 and 33. Since the time required to breast feed one child ranges
between 14 and 17 hours per week for the …rst 12 months, this means that 35% to 43% of women’s
working time was devoted to nursing for a 40 hour workweek.
Not surprisingly, these biological demands signi…cantly hindered women’s ability to participate
in the labor force and substantially weakened their incentives to invest in marketable skills. Only
9% of married women were in the labor force in 1920, and only 3% among those with preschool
children. Starting in the 1930’s there were signi…cant advancements in medical “technologies”
related to motherhood. We show that these developments were critical to the rise in married
women’s labor force participation. We …rst provide evidence on progress in this area and argue
that it reduced the time spent by women in reproductive duties. We then develop a quantitative
model that aims to capture their impact.
We consider two dimensions of medical progress. The …rst corresponds to scienti…c discoveries that determined a substantial improvement in maternal health and a decline in the time
cost associated with pregnancy, childbirth and recovery. Leading examples are the development
of bacteriology and the introduction of sulfa drugs and antibiotics that dramatically decreased
mortality risk from sepsis, blood banking that reduced the risk from hemorrhages, and standardization of obstetric interventions that brought the incidence of trauma during labor to a minimum.
These same advancements also contributed to a fall in stillbirths and miscarriages and the consequent decline in the number of pregnancies for given live births. The second dimension is the
development and commercialization of infant formula, which, by providing an e¤ective breast
milk substitute, reduced women’s comparative advantage in infant feeding and degendered home
production. Advancements in both these areas were largely exhausted by the mid 1950’s.
We construct measures of this progress using a variety of data sources. For the …rst component,
we derive an index of maternal health based on historical data on births, fetal and maternal deaths.
We use this index to proxy the reduction in the time cost associated with pregnancy, childbirth
and recovery. For the second component, we posit that the progress in infant feeding technologies
is embodied in baby formula and measure it with the time price of Similac, the earliest and most
popular modern formula. We collect the data from advertisements in historical newspapers.
The model features overlapping generations of agents who are born single and then marry.
When single, they can invest in market skills, which increases their wages in future periods. In
addition to consumption and leisure, agents value two home goods. The general household good
corresponds to activities such as meal preparation, cleaning, and other household chores. Both
spouses can contribute to the production of this good. The infant good represents those activities
strictly connected to the existence of infants in the household, that is pregnancy, childbirth and
feeding. This home good is only valued in the fecund years of life, and only wives can contribute
to its production. Two technologies, old and new, can be adopted for the production of each home
2
good. Households must pay to adopt the new technologies, which are less labor intensive than
the old. This cost re‡ects the value of additional market goods required in production. If the new
technology is adopted, infant feeding becomes a general household good since both spouses can
now take on the task. Households decisions are Pareto e¢ cient and fertility is exogenous. Both
the division of labor within the household and gender di¤erences in wages are endogenous. The
only exogenous gender asymmetry built into the model is the assumption that only the wives’
time is required for the production of infant goods.
Progress in medical technologies that leads to a reduction in the time required from mothers’
for infant care is a necessary condition for the rise in labor force participation of married women
at all ages in the model. A decline in time cost of pregnancy and the price of infant formula
increases the labor force participation of women in the fecund period, which raises investment in
market skills when single and reduces their earning di¤erential relative to men. This outcome also
reduces women’s home hours and increases their participation beyond the fecund years of life.
Our quantitative analysis allows for four exogenous sources of technological progress. The
reduction in the time cost of pregnancy, childbirth and recovery, and the introduction and improvement of infant formula have a direct impact on women only. The improvement in general household technologies, advocated by Greenwood, Seshadri and Yorugoklu (2005), and the
economy-wide increase in real wages a¤ect the opportunity cost of home production for both
genders. To examine the role of these factors, we calibrate the model to 1920 and we feed in
measures of technological progress for the time period between 1920 and 1970 to examine the
properties of the transition and to evaluate the impact of each source of progress in isolation.
Our results suggests that medical progress is indeed a powerful force. The reduction in the time
cost of pregnancy, childbirth and recovery alone can account for the fourfold increase in the labor
force participation of married women with children between 1920 and 1960. Progress in home
appliances only plays an important role between 1950 and 1970.
Our simulations overpredict the labor force participation rate of married women and the
closing of the gender earnings gap. This is not surprising since technological progress is the only
force at work in our model. In reality, a variety of o¤setting factors were at work. Among those, a
very important one until the 1950’s was the presence of “marriage bars,”consisting in the practice
of not hiring married women or dismissing female employees when they married. Marriage bars
were prevalent and pervasive in teaching and clerical work, which accounted for half of single
women’s employment in that period (Goldin, 1991). Cultural forces and preference formation, as
emphasized in Fernández, Fogli and Olivetti (2004) and Fernández and Fogli (2005), or statistical
discrimination driving gender earnings di¤erentials as in Albanesi and Olivetti (2006), may also
have played an important role in slowing down the increase in women’s labor force participation.
We are the …rst to analyze the impact of progress in medical technologies related to motherhood
on married women’s labor force participation. Our contribution is to isolate and measure sources
of technological change that are intrinsically gendered and directly a¤ect women, and to quantify
their impact. Given that the public health considerations and general scienti…c discoveries that
led to these advancements date as far back as the mid 19th century and largely preceded the rise
in married women’s participation, they can be considered exogenous. By contrast, the di¤usion
of modern home appliances largely occurred after World War II and may well have been driven
by rising demand from working women. Perhaps more importantly, the new medical technologies
generated a tangible e¤ect on women’s lives in the late 1920s and early 1930s, the years in which
married women’s participation started to rise. By making it feasible for women to reconcile work
and motherhood these advancements set forth the process of change that revolutionized women’s
3
economic role.
The paper is organized as follows. Section 2 documents progress in medical technologies
related to motherhood and constructs measures of this progress. Section 3 describes our analytical
framework. Section 4 discusses our calibration strategy and presents the results of our quantitative
analysis. Section 5 concludes.
2
Progress in medical technologies related to motherhood
This section documents two aspects of technological progress that contributed to reduce the time
commitment associated to women’s maternal role: the medical advancements that reduced the
time cost of pregnancy, childbirth and subsequent recovery, and the introduction and di¤usion of
‘humanized’infant formula.
2.1
Progress in Maternal Health
The risk of temporary or permanent disability, and potentially death, associated with labor,
delivery and post-partum conditions substantially contributed to the cost of women’s maternal
role, as documented in Loudon (1992) and Leavitt (1986). The four main causes of maternal
death were septicemia (40%), toxemia (27%), traumatic accidents of labor (10%) and hemorrhages
(10%)1 . Infection, toxaemia and trauma were also the main causes of maternal morbidity and gave
rise to the most debilitating ailments associated with the child bearing process, such as puerperal
fever, prolonged labor, vesico-vaginal …stula and other severe forms of perineal lacerations. A
variety of complications associated with the puerperium, due to pelvic deformation and lack of
strength from poor nutrition, also contributed to imperil the health of the mother, as well as that
of the child.
It is hard to comprehensively assess the toll of childbearing on women’s health and productivity given the great variety of possible debilitating conditions. Systematic data on the duration and
intensity of the disablements are not available even for the most recent years.2 Yet, a few hospital
based studies suggest that certain type of conditions can lead to very persistent disablement. Perineal lacerations are perhaps amongst the most debilitating traumatic consequences of childbirth.
Kerr (1933) reports that the duration of complaints ranged from seven months for vesico-vaginal
…stula to 3.5 years for perineal lacerations, and up to 7/13 years for incomplete/complete prolapse
of the uterus.3
We focus on maternal mortality as an index of medical progress in maternal health, given the
di¢ culties in obtaining more comprehensive measures of disablement. As shown in …gure 1, there
were 60.8 maternal deaths per 10,000 live births in 1915. After a temporary rise due to the 1918
in‡uenza outbreak, the rate of maternal deaths averaged 68 per 10,000 live births in the 1920s.
The decline in maternal mortality occurred gradually in the early 1930s and precipitously starting
in 1936. The phase of sharply declining maternal mortality rates - from 56.8 deaths per 10,000
1
Data from U.S. Department of Commerce, Bureau of the Census, Mortality Statistics, 1921. Cause-of-death
codes prior to this date do not allow to identify deaths due to traumatic accidents of labor.
2
The World Health Organization estimates that even today 42 percent of the women who give birth annually
experience at least mild complications during pregnancy. Despite the large numbers of women who are a¤ected by
such morbidity, especially in developing countries, little is known about how to measure it systematically and about
the social and economic consequences of di¤erent types of morbidities (see Holly, Koblinsky and Mosley, 2000).
3
This study is based on a sample of 2000 patients seeking treatment between 1928 and 1931 in Glasgow’s Royal
Samaritan Hospital, a facility devoted exclusively to gynecological cases.
4
100
90
Maternal Mortality Rate, 10,000 live births
80
10,000 live births
70
60
50
40
30
20
10
0
1915 1918 1921 1924 1927 1930 1933 1936 1939 1942 1945 1948 1951 1954 1957 1960 1963 1966 1969
Figure 1: Trends in maternal mortality.
5
30.00
Toxemias
25.00
Hemorrhage
Sepsis
Traumatic Accidents of Labor
15.00
10.00
5.00
0.00
19
21
19
23
19
25
19
27
19
29
19
31
19
33
19
35
19
37
19
39
19
41
19
43
19
45
19
47
19
49
19
51
19
53
19
55
19
57
19
59
19
61
19
63
19
65
19
67
19
69
10,000 live births
20.00
Figure 2: Trends in causes of maternal deaths.
6
live births in 1936 to 4.7 in 1955, was associated with the surge in the rate of hospital births
starting in 1935.4 As shown in …gure 2, the most striking decline occurs for deaths due to sepsis,
which drop from 27.5 in 1921 to less than 1 per 10,000 live births in 1955. All other factors of
mortality also precipitously decline in the same period. As shown in …gure 1, maternal mortality
rates continued to decline after 1955, but only gradually, reaching 2 deaths per 10,000 live births
in 1970.5
What led to these dramatic improvements in maternal health? Table 1 lists the major medical
discoveries and innovations connected to pregnancy, labor and parturition between 1800 and 1940,
which we discuss in detail in the Appendix.6 The improvements between 1936 and the mid 1950s
can be attributed to the application of the new obstetric practices developed by trial and error
in the late 1800s and early 20th century that reduced the incidence of trauma during labor, as
well as to the general availability of antibiotics and penicillin to treat infection and sepsis, and of
transfusions to replace blood lost in hemorrhages. Improved pre-natal care determined a decline
in the incidence of death by toxaemia.
Table 1: Timeline for Maternal Health
1843
1852
1861
1867
1879
1898
1915
1928
1930
1935
1936
Puerperal fever found contagious. Notion of prevention via hygienic measures introduced.
Methods for vesico-vaginal …stula repair …rst published. Additional progress in 1914 and 1928.
Findings on preventing post-partum infections in maternity wards …rst published in Vienna.
First published paper on surgical antisepsis, …rst clinical application of bacteriological principles.
Pasteur links puerperal fever to streptococcus.
X-ray pelvimetry …rst used for di¢ cult obstetric cases. Becomes routine in 1930s.
Low cervical cesarean section developed.
Penicillin discovered, becomes widely available at the end of WWII.
American Board of Obstetrics and Gynecology established.
Antibiotic action of sulfonamides discovered.
Hospital blood banks established. Aids with post-partum hemorrhages.
An additional consequence of poor maternal health was the high frequency of stillbirths and
miscarriages. Many stillbirths were the outcome of fetal asphyxia in the frequent cases of di¢ cult
labor. Both stillbirths and miscarriages were often due to bad health and poor nutrition of the
mother, as well as lack of prenatal monitoring (see O’Dowd and Phillipp, 1994). The evolution
of fetal mortality rates is similar to that of maternal mortality. Figure 3 plots the time series for
fetal deaths starting in 1918.7 The fetal death rate is stationary around 4% between 1918 and
1930. Between 1931 and 1953 it gradually declines to 2%, and remains at that level thereafter.
4
Information on maternal mortality by causes is from the U.S. Department of Commerce, Bureau of the Census
and U.S. Department of Health, Education and Welfare, several volumes. Maternal mortality rates are from U.S.
Census Bureau, Statistical Abstracts of the United States (2003).
5
The gradual decline continued in the following decades down to a maternal mortality rate of 0.1 per 10,000 live
births in 2001.
6
See also Thomasson and Treber (2004) for an empirical analysis of the consequences of the hospitalization of
childbirth on maternal mortality.
7
Following the WHO standard, fetal deaths are de…ned as "death prior to the complete extraction or expulsion
from its mother of a product of conception, irrespective of the duration of pregnancy." This measure includes both
stillbirths and miscarriages and abortions. The stillbirth rate only include fetal deaths in which the period of
gestation was 20 weeks or more.
7
Fetal deaths per 1,000 live births
45
40
35
1,000 live births
30
25
20
15
10
5
0
1918 1921 1924 1927 1930 1933 1936 1939 1942 1945 1948 1951 1954 1957 1960 1963 1966 1969
Year
Figure 3: Trends in fetal deaths
This decline is driven by the same medical advancements that result in improved maternal health.
Improved obstetric practices, see Table 1, reducing the incidence of di¢ cult labor were a main
contributor. The systematic e¤orts to provide prenatal monitoring beginning in the mid 1920s
also played an important role.
2.1.1
Evolution of the Time Cost of Pregnancy, Childbirth and Recovery
The improvements in maternal health arguably led to a decline in the time cost of pregnancy,
childbirth and recovery. We construct a measure of maternal mortality risk that compounds the
risk of death for each pregnancy over the lifetime number of pregnancies and use it to proxy this
decline.
The …rst step in this process is to derive a correct estimate of the number of pregnancies.
Our measure of completed fertility is the Total Fertility Rate (TFR), that is based on live birth
registration data.8 To estimate the corresponding number of pregnancies, we use data on fetal
deaths.
The …rst adjustment we apply corrects for measurement error. As reported in Loudon (1992),
8
See Jones and Tertilt (2007) for an extensive discussion of lifetime fertility measures.
8
this was a serious issue in birth registration. There were two potential problems. Since no
guidelines were available, children that had died by the time of registration were often registered
as stillbirths even if they were born alive. In addition, many births simply went unregistered.
We adjust for measurement error using the stillbirth rate, which was equal to approximately 4%
in 1920. According to Woodbury (1926), births fell short of their true value by 8.7%, so this
adjustment is quite conservative. With this adjustment, our measure of live births is T F R =
T F R (1 + s) ; where s is the rate of stillbirth. We refer to T F R as adjusted total fertility.
To calculate the number of pregnancies for given adjusted fertility, we treat the fetal death
rate as a measure of the incidence of unsuccessful pregnancies. Denoting with f the probability
of a fetal death and using T F R as the number of live births, the resulting number of pregnancies
amounts to P = T F R = (1 f ) : The resulting adjustment is quite signi…cant. In 1920, while
the T F R from registration data was 3.3, the number of pregnancies was equal to 3.6. By 1950,
for a T F R of 3.03, the number of pregnancies totaled 3.17.
Our measure of maternal mortality risk is simply given by the product of the probability of
death per pregnancy, the maternal mortality rate, by the number of pregnancies P : Improvements
in fetal and maternal mortality both contribute to the decline of this variable over the period of
interest. This variable is plotted in …gure 6.
2.2
Progress in Infant Feeding
Until the early decades of the 20th century, cows’milk and hiring a wet nurse were the only two
alternatives to mother’s milk. In the last decades of the 19th century, both these alternatives
were proven inadequate.9 The new discoveries in physiology, bacteriology and nutritional science
in the second half of the 19th century revealed the connection between infant mortality, poor
nutrition and tainted milk supplies (Mokyr, 2000). This led to a variety of initiatives to improve
public health and develop e¤ective substitutes for mother’s milk.
Table 2 lists the main developments in the area of public health.10 Given the prevalence
of diarrhea and dehydration as a major factor in infant mortality, initiatives were targeted to
two main concerns: water and sewage treatment, and the quality of milk supplies. The major
urban areas were at the forefront of this e¤ort, which was initially local in nature. Various cities
introduced milk certi…cation at the end of the 19th century. Progress was slow and uneven. With
the link between children’s health and environmental conditions …rmly established in the public
debate, the …rst federal piece of legislation on the purity of food supplies was …nally passed in
1906. By the 1940s most major metropolitan areas had developed water treatment and sewage
disposal systems.
9
After a failed attempt to medicalize the practice of wet nursing in the late 19th century, concerns about
transmission of siphylis and other deseases led to its virtual disappearance by the mid-twentieth century. See
Golden (1996) for more details.
10
Sources: http://www.sewerhistory.org/chronos/roots.htm and Wolfe (2001).
9
Table 2: Timeline in Public Health Initiatives
1838
1854
1892
1893
1906
1908
1912
1921
First chemical analysis of human and cow’s milk.
Cholera …rst demonstrated to spread via water supplies in London.
First US city to treat sewage waters with chlorine.
Bureau of Milk Inspection established in Chicago.
First Federal Pure Food and Drug Act passed by Congress.
First Bureau of Child Hygiene established in New York City.
US Children’s Bureau established.
Sheppard-Towner Maternity and Infancy Protection act enacted by Congress.
The …rst breakthrough in infant nutrition was the realization that cow’s milk was a very poor
alternative to mother’s milk.11 In 1838, the …rst chemical analysis showed that cow’s milk contains
a much higher level of proteins and a lower amount of fat and carbohydrates than human milk.
This discovery led to the …rst generation of cow’s milk modi…ers, such as Leibig’s, Nestle’s and
Mellin’s infant food, developed and introduced commercially between the 1870s and the 1890s.
These powdered formulas contained a combination of malt, wheat ‡our and sugar to be mixed
with hot cow’s milk and diluted with water. Although better than cow’s milk, the resulting infant
food was still nutritionally inferior to maternal milk.12
Pediatricians strongly opposed these products and discouraged mothers from buying them.
Infant feeding studies became the most important sub-…eld in pediatrics as doctors worked to
develop more scienti…c methodologies for modifying cow’s milk. The most successful method was
Rotch’s “percentage method,” the medical gold standard for infant feeding between 1890 and
1915. This formula had several drawbacks. It was still nutritionally inadequate and so complex
that it was mostly prepared in milk laboratories and distributed through pediatricians13 .
The most important innovation in infant feeding occurred in the early 1920s when nutrition
scientists succeeded in creating a so called ‘humanized’infant formula that exactly matched the
composition of maternal milk in terms of its fat/proteins/carbohydrates content. The …rst two
formulas with this property, SMA (for “simulated milk adapter”) and Similac (for “similar to
lactation”), were created in 1919/1920 and are still sold in stores today. These humanized formulas
were approved by the medical profession14 and pediatricians encouraged mothers to use them if
they encountered problems breast feeding.
The introduction of e¤ective and easy-to-prepare infant formulas, as well as improvements in
baby bottles, induced a dramatic shift from breast- to bottle-feeding between 1920 and the early
1970s. To document this phenomenon, we rely on three sources: the studies by Hirschman and
Hendershot (1979) and Hirschman and Butler (1981) for children born between the early 1930s
and the early 1970s, and Apple (1987) for the years before 1930.
Figure 4 displays the resulting trend in breast feeding rates. In 1920, the breast feeding rate
was 88% and it had declined to less than 25% by the early 1970s. This decline was very dramatic
and sudden, and was particularly strong at longer breast feeding durations. While approximately
11
See Packard and Vernal (1982), Apple (1987) and Schuman (2003) for a more detailed account of the history
of infant formula in the United States.
12
See Table A2 in the appendix.
13
The formula could also be made at home through a complicated and time and labor intensive process. Newspapers from the time include a very large number of classi…ed ads for nurses specialized in making formula according
to Rotch’s percentage method.
14
The name Similac was proposed by Morris Fishbein, the editor of the Journal of the American Medical Association in the 1920s (Schuman, 2003).
10
50% of newborns were exclusively breast fed at 6 months in 1920, this number had fallen to 3%
in 1970. Hirschman and Butler (1981) show that from 1950 to 1970 breast-feeding rates declined
both for working and for non-working mothers, although non-working women were more likely to
breast feed for more than 3 months. The evidence on trends in the use of commercially prepared
formulas is not systematic and is only available since the 1950s. The fraction of 2 to 3 month-old
infants fed using commercially prepared formulas increased from 30% in 1955 to 70% in 1970
(Fomon, 2001).
According to all records, the 1970s marked the lowest incidence of breast feeding of the entire
20th century. Breast feeding rates have increased steadily since then, owing to new medical
…ndings on the immunization properties of human milk. In 2004, approximately 63% of mothers
breast fed their baby at 1 week. While this rate is comparable to those observed in the 1920s, the
duration of breast feeding is now much lower: only 14.2% of babies are exclusively breast fed at
6 months.15
As the new medical discoveries increasingly pointed to the importance of mothers’ milk for
children’s development, the introduction of portable breast pumps allowed women to reconcile
market work with breast feeding. Although rudimental breast pumps existed since the 16th
century, the …rst successful mechanical pump for humans was created in 1956. The historically
high rates of participation of women with young children likely spurred the development of light
and e¢ cient portable breast pumps, introduced in 1996.16
2.2.1
Price of Similac
We posit that progress in infant feeding technologies is embodied in infant formula and measure
it by constructing a series for the time price of infant formula.
We collect the data from advertisements from the Chicago Tribune, the Los Angeles Times
and the Washington Post.17 The historical ads provide information on price, quantity and type
of formula in drugstore chains such as Walgreens and Stineway. The price observations refer to
items on sale, hence, we interpret them as a lower bound for the price. For each year in the
sample and for each city we have monthly observations that we use to construct our yearly series.
To derive a measure of the opportunity cost of infant formula, we construct the series for its time
price. This is obtained by de‡ating the original price series by hourly wages in manufacturing.18
In Figure 5, we report the time price series for the …rst generation of milk modi…ers. Mellin’s
and Nestle’s are in blue and the one for Similac is in red. The …rst observation on Similac
dates to 1935. While there was a large drop in the time price of the …rst generation of formulas
before 1935, we focus on Similac because it was the …rst commercially available formula to be
deemed equivalent to mother’s milk and to become popular. In 1975, 52% of infants receiving
commercially available milk-based formulas were fed Similac (see Table III in Fomon, 1975.) The
formula remains very popular today.19
15
National Immunization Survey, CDC, 2004.
See http://www.slate.com/id/2138639/#ContinueArticle.
17
This information is available from ProQuest Historical Newspapers Chicago Tribune (1849-1985), Los Angeles
Times (1881-1985) and The Washington Post (1877 - 1990). We are grateful to Claudia Goldin for suggesting this
data source. The details about the construction of the price series are discussed in the appendix.
18
Throughout the paper our measures of hourly wages is from Margo (2006a.) Hourly wages and prices are
expressed in 1982-1984 U.S. dollars. See appendix for details.
19
SMA did not achieve great popularity in the U.S, and in 1975 it accounted for less than 12% of the market
for commercially prepared formulas (Fomon, 1975). Alternative scienti…c infant formulas, such as Enfamil, were
launched on the market much later, in 1959.
16
11
100
90
80
70
Percentage
60
50
40
30
20
10
0
1920
1925
1930
1935
1940
1945
1950
Year of Birth of Infant
Figure 4: Trends in breast-feeding
12
1955
1960
1965
1970
3.5
3
Milk Modifiers
Similac
2.5
percentages
2
1.5
1
0.5
85
81
19
77
19
73
19
69
19
65
19
61
19
57
19
53
19
49
19
45
19
41
19
37
19
19
33
29
19
25
19
19
21
17
19
13
19
19
09
05
19
01
19
19
97
18
18
93
0
year
Figure 5: Time price of Infant Formula
The time price should be interpreted as follows. The value of 2 for 1935 means that the
cost of 1 liquid ounce of Similac corresponds to 2% of the hourly wage in manufacturing in that
year. Given that 4 liquid ounces are needed for the typical feeding, the opportunity cost of one
feeding was approximately 5 minutes of work. This time price declined by an average of 5.1% per
year between 1935 and 1970. The decline in the time price of formula parallels the decline in its
monetary cost. In 1920, the cost of bottle-feeding a baby boy of median weight during his …rst
year of life ranged between 39 and 48 percent of disposable income. By year 1970 this cost had
fallen to approximately 2 percent of personal disposable income.20
3
Model
We assume the economy is populated by overlapping generations of agents who live for three
periods, r; with r = 0; 1; 2. Each generation comprises a continuum of agents who di¤er in their
productivity in market production, ; and by gender. Cohorts and the overall population are
split equally by gender and the distribution of market productivity is the same across genders. In
20
These calculations take into account the fact that the amount of formula needed varies by weight and the
number of feedings varies by age. See Data Appendix for details.
13
the …rst age of their life, all agents are single. In the second period of life, they all marry to an
agent of di¤erent gender and with the same productivity and remain married in the third period.
In each model period, t; a new generation of single agents is born, and total population size is
constant.
Agents value private consumption, c; and leisure, l; in all periods. Individual preferences can
be represented by the following lifetime utility function:
!
r
X
Y
s u (cr ; lr ) ;
r=0;1;2
s=0
where
u (c; l) =
c1
1
+ v (l) ;
and v (l) represents the sub-utility from leisure:
v (l) =
l1
0
1
;
with ; 0 ;
0. The parameters r 2 (0; 1) represent the discount factor from age r to age
r 1: with 0 = 1: We allow for di¤erential discount factors to accommodate ages of di¤erent
duration.
Leisure is de…ned as:
l = T h pn;
where T is the individual time endowment, p 2 [0; 1] denotes labor force participation, n corresponds to the …xed number of work hours an employed individual works on the market, and h
denotes home hours.
Home hours are applied to the production of two home goods. The general household good,
G; corresponds to activities such as meal preparation, cleaning, helping children with homework,
vacation planning, yard work and other activities. This good must be produced at all ages of life.
In the …rst period of marriage and only in that period, households must also produce the infant
good, I; which corresponds to activities deriving from the existence of infants in the household,
such as pregnancy, childbirth and feeding. Hence, the …rst period of marriage can be interpreted
as the fecund period of life:
The next section describes in detail the production technology for each home good.
3.1
Home Production
For each good, both time and market goods are inputs in production. The key assumption is that
women and men can equally contribute to the production of general household goods. Instead,
only the wife’s time is used as an input in the production of infant goods. This asymmetry is
clearly extreme, since the husbands’contribution to the production of infant goods is necessary,
at least at conception. However, it provides a simple and realistic way of modelling women’s
comparative advantage in the production of infant goods, based on the fact that only women can
give birth and breast feed.
The ratio of home hours to market goods in home production depends on technology. There
are two technologies for the production of each home good, old and new. The new technologies are
less time intensive than the old. The old technologies are free, while there is a …xed cost to adopt
14
the new technologies expressed as a time price. This cost corresponds to the monetary value of
the market goods associated with the new technologies translated into units of time. The time
price of the new technologies can change over time. A decline in this price re‡ects technological
progress embodied in the market goods used in production. Households choose which technology
to adopt for each home good in each period of their life.
3.1.1
Infant Goods
The infant goods are produced exclusively using the wife’s time. Their level of production is
denoted with I and does not vary with the technology, which only in‡uences the time intensity of
production. Let hf I denotes the time required by the wife to produce I: Under the old technology:
n
o
I = min I I ; hf I (0) ;
(1)
where hf I (0) =
I I
> 0: Under the new technology:
n
o
I = 1 min I ; hf I (1) ;
(2)
with hf I (1) = I > 0: The parameter I > 1 measure the reduction in time intensity associated
with the new technology, with hf I (0) = I I > hf I (1) = I : The quantity I I under the new
technology can be interpreted as the quantity of market goods associated with production, such
as infant formula. The old technology is free and we denote the price of the new technology with
qI .
A few words of interpretation are in order here. The total time devoted by wives to infant
good production represents the sum of feeding time plus the time associated with pregnancy,
childbirth and recovery. This is based on the notion that the physical cost of pregnancy reduces
a woman’s ability to perform market work. The parameter I measures this cost in equivalent
time units. Based on the evidence on progress in medicine and obstetrics, most households were
just confronted with “best” practices for behavior during pregnancy, childbirth and recovery,
while they chose how to feed their child. Correspondingly, we treat the time cost of pregnancy,
childbirth and recovery, I ; as a parameter, and we model bottle feeding as a choice.
To incorporate the e¤ects of the reduction in the physical cost of pregnancy over time re‡ecting
progress in medical knowledge and obstetric practices, as well as changes in fertility, we will allow
I to vary over time with the measure of maternal mortality risk constructed in section 2. We
posit that breast feeding is the only feeding method under the old technology, while under the new
technology infants are fed formula with a bottle. Adoption of the new technology allows infant
feeding, which under the old technology can solely be produced by the mother, to become a general
household good that could be produced by both spouses. After all, there is no di¤erence between
bottle feeding an infant and general household goods, such as helping children with homework
or meal preparation, in terms of comparative advantage by gender. Hence, under the new I
technology, the mother’s time required for infant feeding drops to zero, a saving that corresponds
in percentage terms to ( I 1) : On the other hand, the time required for general good production
rises by the amount I ( I 1) ; the time devoted to breast feeding. Implicit in this treatment is
the assumption that the time required for infant feeding does not depend on the method. Even
under the new technology, the asymmetry in the spouses’contribution to infant good production
remains since mothers still have to bear the physical cost of pregnancy I .
We now describe the production technology for general household goods.
15
3.1.2
General Household Goods
Our model for general household good production is similar to Greenwood, Seshadri, and Yorugoklu (2005).
Let H G denote the contribution of home hours to production under technology G = 0; 1;
where G denotes whether the old ( G = 0) or the new ( G = 1) technology is used. The
production function for singles and old married households is:
G = min f
G =
G G; H
(0)g ;
(3)
G min f G ; H
(1)g :
The parameter G > 1 denotes the time savings associated with the new G technology, so that
the new technology requires fewer home hours, that is H (0) = G G > H (1) = G : The quantity
G G under the new technology can be interpreted as the quantity of market goods associated
with the production of the general household good. We denote with q G the time price of the new
home durables technology, which re‡ects the market value of the market goods associated with
the new G technology, such as home appliances, groceries etc. The old technology is free.
For married households, spouses contribute to the production of G according to:
1=
H = 0:5 hf G
+ 0:5 (hm )
;
(4)
where the parameter determines the substitutability of husbands’and wives’home hours in the
production process. The spouses’contribution is symmetric, irrespective of the technology used.
For young married households, we incorporate the complementarity between infant and general
household good production by letting the time requirement H vary with the technology adopted
for producing the infant good, as described above. Speci…cally:
G
I
G
I
= min
=
G G; H
G min
G; H
0;
I
;
1;
I
;
(5)
where H 0; I = G G + I I ( I 1) and H 1; I = G + I I ( I 1) ; and I ( I 1) is the
time required for infant feeding, an activity that becomes a general household good if the new I
technology is adopted.21
We now describe the agents’optimization problems at each age in life.
3.2
Single Agents’Problem
Agents are born with no wealth and cannot borrow against future income. At age 0; they are
single. They decide on whether to participate in the labor force in that period, on whether to
acquire market skills, on how to produce the home good G and on how much to save. The
acquisition of market skills has a time cost of > 0 and a¤ects their labor market productivity
at ages r = 1; 2; as follows:
j
= 1 + "ej ;
(6)
21
This is an analytically tractable way to model this complementarity, given our technological assumption. Of
course, since the choice of technology does not a¤ect the level of production or utility directly, many other strategies
would be equivalent.
16
where the parameter " represents the returns to skills and ej = 0 when no skills are acquired and
ej = 1 otherwise.
A single individual’s problem is:
j
0(
)=
aj1
u c; T
max
0;p;e2f0;1g;
e
h
c + aj1
w
G
pn +
G
1
j
1
aj1 ; e;
;
(Problem S)
subject to (6), (3) and:
G G
p
q
;
for j = f; m: Here, j1 aj1 ; e;
denotes the maximized present discounted value of individual
lifetime utility at the beginning of period 1; which will be derived below. The variable w denotes economy-wide real wages in e¢ ciency units of labor and may change over time, due to
improvements in the market production technology.22
3.3
Household Problem
We model married individuals according to Chiappori’s (1988, 1997) collective labor supply approach. Under this paradigm, household decisions are Pareto e¢ cient. Households choose a
sequence of private consumption, participation, and home hours for each spouse, as well as technologies for the production of the home goods, subject to an intertemporal budget constraint and
to the technological and feasibility constraints.23
We …rst describe the optimal choice of home hours in each period, taking as given the production technology. This step amounts to solving the following cost minimization problem:
C H; hf I =
min
hm 2[0;h];hf G 2[0;h hf I ]
1 + "ef hf + (1 + "em ) hm
subject to
h f = hf I + h f G ;
1=
0:5 (hm ) + 0:5 hf G
H;
hf I ;
hf I
for some H = H G ; I and hf I = hf I I :
The …rst order necessary conditions for hf G and hm for interior solutions are:
1 + "ef
(hf G )
1
=
(1 + "em )
(hm )
1
;
(7)
22
We assume that progress in market technology is not gender biased and that the distribution of individual productivities, which is symmetric across genders, remains constant over time. For an analysis of skill bias technological
change and its e¤ects on female participation and fertility, see Galor and Weil (1996).
23
The Pareto problem can be decentralized by allowing each spouses to individually choose labor force participation and private consumption in each period. Households then jointly choose a rule for sharing household wealth,
savings, the allocation of home hours and the technologies for producing the home goods. The fact that saving is a
joint household decision implies that individual problems are static. Moreover, the household is implicitely assumed
to have commitment in the joint choices.
17
1=
0:5 (hm ) + 0:5 hf G
= H;
hf I = hf I :
We will denote with hj G ; I for j = f; m the policy functions for the cost minimization
problem. By (7), if ef = em , then, the solution is hf G = hm : If instead ef
em ; then, the only
f
G
m
solution has h > h : Hence, the symmetry in the spousal allocation of home hours devoted to
the production of G depends on the opportunity cost of home hours, that is potential wages, for
each spouse.
Let Zt denote total household expenditures net of total household income in period t:
h
i
X
Z G; I ; qG; qI ; w =
cj + j lj + w C H G ; hf I I + q G G + q I I
j=f;m
Tw
X
j
:
j=f;m
Substituting in the expressions for the cost of production of the two public goods, we obtain:
X
X
j j
Z G; I ; qG; qI ; w =
cj + w q G G + q I I
w
p n;
j=f;m
j=f;m
where w corresponds to the contemporaneous value of economy-wide real wages. Hence, the
household’s intertemporal budget constraint is given by:
Z1
G I G I
1 ; 1 ; q1 ; q 1 ; w1
+
Z2
G; I ; qG; qI ; w
2
2
2 2
2
1 + R2
a1 ;
(8)
where a1 is household wealth at the beginning of age 124 : The households initial wealth a1 is given
(1 + R1 ) ; where the
by the sum of the spouses’wealth at the beginning of age 1; a1 = af1 + am
1
values of aj1 solve the spouses’individual optimization problem when single.
The households’Pareto problem is given by:
X
X
r 1
j
I
max
hjr G
pjr n
j u cr ; T
r ; r
2
I ; cj ;pj ; G
1 f r r r gr=1;2;j=f;m r=1;2
j=f;m
subject to (8) and (3), (1)-(2), (6), with ejr = 0 for r = 1; 2; hf2 I = 0 and hf2 = hf2 G and where
j = f; m denote the spouses’Pareto weights.
The …rst order necessary conditions for the household problem are:
j
j uc;1
j
j 2 uc;2
j
j ul;1
j
j 2 ul;2
= 0; for j = f; m;
j
(9)
(1 + R2 ) = 0; for j = f; m;
(10)
w1 ej = 0; for j = f; m;
(11)
(1 + R2 ) w2 ej = 0; for j = f; m;
24
(12)
Here, the home goods are not marketable, so their production level does not enter in the household budget
constraint. See Chiappori (1997) for a discussion.
18
I
for given values of G
is the
r and 1 ; as well as the intertemporal budget constraint (8). Here,
multiplier on the intertemporal budget constraint.
The intertemporal pattern of consumption is independent from the distribution of the Pareto
weights or the choice of technology and labor force participation patterns over time. Instead, the
higher the Pareto weight of a spouse, the higher the optimal level of consumption and leisure.
It follows that pjr is decreasing in j ceteris paribus, so that wives will participate more if their
Pareto weight is lower.
The Euler equation for the individual saving choice at age 0 is:
u0 pj0
aj1 ; T
ej0
pj0 n +
j
1;a
1
aj1 ; e;
0;
= 0 for aj1 > 0:
(13)
The envelope condition for this problem is:
j
1;a
aj1 ; e;
=
; for j = f; m:
(14)
j
Intuitively, a spouse with a higher Pareto weight will obtain a larger share of resources when
married and …nds it optimal to bring lower wealth levels into the marriage, other things equal.
Here, as previously noted, j1 aj1 ; e;
is the maximized present discounted value of lifetime
utility at the beginning of period 1: Given that this corresponds to the individual value function
for the household’s optimization problem, it is possible to incorporate the agent’s problem when
single into the household problem, to simplify the derivation of lifetime consumption, home hours
and participation paths. We describe this strategy of solving the household problem in detail in
the Model Appendix.
3.4
Market Production and Equilibrium
A continuum of identical, perfectly competitive …rms in each period produce an undi¤erentiated
output using labor only, and then convert it into consumption goods and goods used in the
production of general household and infant goods.
The representative …rm produces the undi¤erentiated output, Y; according to the production
function:
Y
N;
(15)
where the variable Y denotes per capita production of the undi¤erentiated good and N is per
capita (average) labor input in e¢ ciency units, given by:
Z
N = p (i) i (1 + ei ) d (i) ;
(16)
i
where i indexes individuals in the population. Here, corresponds to average labor productivity.
may grow over time to re‡ect technological advancements in market production. Y can be
transformed into home durables, D; commodities used in the production of infant goods K; and
private consumption goods, C; according to the technology:
G
D+
I
K +C
19
Y:
(17)
Given that all technologies are constant returns to scale and that the production sector is
competitive, w = in equilibrium, so that wages will grow one to one with market productivity.
In addition, competitive pricing pins down the equilibrium values of q l as a function of the
technological marginal rates of transformation l ; for l = G; I.
We describe the representative …rm’s problem and the derivation of the equilibrium in the
Model Appendix.
4
Quantitative Analysis
We calibrate parameters to match the equilibrium of our model to a variety of data statistics in
1920. We then simulate the transition between 1920 and 1970 predicted by the model, by feeding
in measures of technological progress in general and infant good technologies, as well as the rise
in economywide real wages over this period. Finally, we run several experiments to gauge the
contribution of the introduction of each source of technological progress in isolation.
4.1
Calibration
We set f = m = 0:5 so that spouses have equal bargaining power: We …x = 1 and = 1;
so that utility is logarithmic in private and public consumption. This implies that wealth and
substitution e¤ects of changing new technology prices and aggregate wages exactly cancel. We
interpret the single period as covering ages 15-22, and the second period as covering ages 23-35.
We consider the last period as corresponding to ages 36-60. We set the yearly interest rate at 5%,
and …x 1 = exp( 0:05 7) and 2 = exp ( 0:05 13) ; with Rr = 1= r 1 for r = 1; 2:
We calibrate the remaining parameters to match certain data statistics of interest in 1920.
We parameterize the G technology as follows. Given our assumption that spouses have a
symmetric role in the production of G; we set = 0:9; which corresponds to an elasticity of
substitution between husbands’and wives’home hours in the production of G equal to 10. We
set the parameters G and G based on the assumption that all households in which the wife
participates in the labor force adopt the new technologies in 1920. Using the value of home hours
of married women, conditional on participation in the labor force, and of married men in 1920,
this delivers:
"
#1=
4
51
0:5
+ 0:5
= 0:2346;
G G =
112
112
"
#1=
4
25
0:5
+ 0:5
= 0:1256;
G =
112
112
which implies G = 1:87.25
For the infant good technology, recall that the parameter I corresponds to the time cost of
pregnancy, childbirth and recovery as a fraction of the time endowment, while the parameter I
corresponds to the time saving associated with bottle feeding relative to breast-feeding.
We use our estimate for the number of pregnancies, P ; based on the calculations described
in Section 2 to obtain a value for I , under the assumption that for each pregnancy, women
25
Data sources on home hours are reported in the data appendix.
20
experience 4.5 unproductive months. Then, as a fraction of their time endowment during the
young married period, this component of the cost is equal to:
I
(1920) =
P1920 (4:5=12)
:
35 23
To compute the time cost associated with infant feeding, we use infant feeding charts from the
National Association of Pediatrics, according to which the average time required to breast-feed
one child for the …rst 12 months ranges between 14 and 17.30 hours per week. Given the adjusted
completed fertility rate, T F R , the fraction of the time endowment that women spent nursing is
T F R1920 (17=112)
: The total time commitment then adds to:
35 23
I
(1920) =
I
(1920) + T F R1920 (17=112) = (35
I (1920)
23)
:
Based on T F R1920 = 3:4 and P = 3:6; this implies I = 0:1141 and I = 1:35:
Agents in our model need to know the evolution of economy-wide wages, w; and new home
technology prices, q I and q G ; to solve their decision problems. To compute the equilibrium in
1920, we assume that agents forecast future values of new technology prices and wages based on
their expectation for the rate of growth of each of these variables. We then take this expectation
to correspond to the average annual rate of change of the data counterparts of these variables
over the time period 1920-1970. As discussed in Section 2, we adopt the notion that technological
progress in the infant good is embodied in the market goods used in its production under the
new technology and will be re‡ected in their time price. So we take the time price of the new
I technology, q I , to correspond to the time price of Similac. Since this series starts in 1935 we
extrapolate it back to 1920 using the average yearly price change between 1935 and 1970 which
is equal to 5.08%.
Similarly, we posit that technological progress in general household goods is embodied in home
durables and we use their time price to proxy such progress. We take q G ; the time price of the new
general household technology in the model, to correspond to the real value of the quality-adjusted
Divisia price index for eight appliances built by Gordon (1990), rescaled by the real hourly wage
in manufacturing. This price series is available only since 1947. We extrapolate it back to 1920
applying to home durables the methodology developed by Cummins and Violante (2002).26 The
average yearly rate of decline in this variable is 4.6%.
We calibrate the relative price of the new home technologies, the ratio q I =q G ; using information
on the monetary cost of formula and on historical prices for home appliances. We assume that
a household who adopts the new G technology purchases a refrigerator, a washer and a vacuum
cleaner and that the appliances need to be replaced every 5 years. Thus, a household must replace
them twice in the young married period. The replacement cost corresponds to their price in the
year of replacement, computed using the series for the price of home durables. Similarly, we
convert the cost of feeding one child with infant formula to 1920 dollars. The ratio of the cost
of feeding one child with infant formula and the cost of buying the three major home appliances
in 1920 is 0:084: We then multiply this ratio by the adjusted total fertility rate in 1920, which is
equal to 3:4: This delivers: q I =q G = 0:3:
We assume the distribution of is log-normal, with mean and standard deviation . This
leaves six remaining parameters: q G ; "; ; 0 ; and : which we calibrate to match the value in
26
Details about the construction of the price series for home durables are in the appendix.
21
1920 of the following population statistics: home hours of married women who participate in the
labor force, home hours of married women who do not participate in the labor force, home hours
of men, the average rate of adoption of new general household technologies, the average rate of
bottle feeding, and labor force participation of married women by cohort as a ratio to the labor
force participation of men. Speci…cally, our target for the labor force participation of old married
women in our model is the labor force participation rate in 1920 of white married women born
between 1866 and 1885 over the labor force participation of men in 1920. Our target for the labor
force participation of young married women in our model corresponds to the participation rate in
1920 of white married women born between 1886 and 1895 over the labor force participation of
men in 1920. We select the parameterization that minimizes the sum of squares of the distance of
the values predicted by our model for those parameters and the corresponding data statistic. The
population statistics and the corresponding model values are listed in Table 3. The calibrated
parameters are reported in Table 4.
Table 3: Calibration Targets
Population Statistic
Home hours of married women who do not participate in the labor force
Home hours of married women who participate in the labor force
Male home hours
Average adoption of new general household technology
Average adoption of bottle feeding technology
Labor force participation of young married women
Labor force participation of old married women
Value in 1920
51
25
4
7%
15%
9%
6.5%
Model Value
49
22
7
8%
15%
9%
6.5%
The data on labor force participation of married women by cohort in 1920 is reported in
Goldin (1990). The 1920 targets for home hours by gender and employment status of wives are
described in the Data Appendix. In order to obtain the targets in model units, we simply divide
the statistics for home hours per week by 112, the non-sleeping hours per week. We obtain: T = 1;
n = 0:36; hfG = 0:456 for wives who do not participate in the labor force, hf = 0:223 for wives
who participate, and …nally hm = 0:0357 for husbands. The target value of 15% for the adoption
rate of the new infant feeding technology is based on the fact that, as discussed in Section 2.2,
approximately 85% of infants were breast-fed in 1920. The target value of 7% for the adoption
rate of new general household goods technologies is based on an average of the percentage of
households with washing machines, refrigerators and vacuum cleaners, from Bowden and O¤er
(1994).
Table 4: Calibrated Parameters
;
G;
I;
1;
G
I
2
1
0.9
0.126, 1.87
0.114, 1.35
0.74, 0.41
3:6
22
qG
q I =q G
"
0
1.6
0.27
0.25
0.08
1.54
0:7
4.2
Equilibrium at 1920 Prices
We now discuss the main cross-sectional properties of the equilibrium in 1920.
All men participate in the labor force and invest in market skills, and all single women participate in the labor force. All single men adopt the new general household goods technology,
while only a fraction of single women do. Male home hours are highest when single. Labor force
participation of married women and investment in market skills are increasing in productivity and
decreasing in age, though for married women, their participation is higher when old than when
young. Home hours devoted to the production of G goods are highest for young married women,
followed by old married women and by single women. Home hours of women are decreasing in
productivity and female and male home hours in a given cohort converge as productivity increases.
This is due to the fact that adoption of new home goods technologies is increasing in productivity.
The adoption of new home goods technologies is necessary for married women to participate in
market work, as participation of the wife occurs only for households that have adopted both new
technologies.
The female/male earnings ratio in the model depends on the relative investment in skills across
genders. Investment in market skills is lower for the older cohorts of women in the model, leading
to a lower female/male earnings ratio for the old relative to the young. This cohort e¤ect stems
from the fact that the old married cohort faces higher prices for the new home technologies and
lower real wages. This leads to lower adoption rates at both ages of marriage and, therefore, lower
participation of women when married, and lower investment in market skills when single. This
property of the model is consistent with empirical evidence for the US that average gender wage
di¤erentials are increasing with age and higher for older cohorts.27
The model predicts higher home hours for men with working wives relative to the data. This
is due to the fact that more married women who participate in the labor force in the model have
invested in market skills than in data. Since they have the same wage as their husbands, the
allocation of home hours is symmetric in those households in the old period.
4.3
Transition
Our model features four exogenous sources of technological change. The …rst is the reduction in
the time cost of pregnancy, childbirth and recovery driven by improved medical knowledge and
obstetric practices leading to lower maternal mortality rates, as well as by changes in fertility.
The second is the introduction of infant formula and its improvement over time, re‡ected in the
decline of its the time price. These factors have a direct impact on women only. Third, the
improvement in general household technologies as re‡ected in the decline in the time price of new
home appliances. Lastly, the increase in economy wide labor productivity, due to technological
progress in market good production, re‡ected in the increasing average real wage. The third and
fourth factor in‡uence the opportunity cost of home production for both genders.
To evaluate the role of these factors, we feed measures of these variables into the model to
examine the properties of the transition between 1920 and 1970. For market productivity, we use
27
In the data, there isn’t a substantial di¤erence in average years of formal schooling across genders for the period,
though the statistic is slightly lower for women. Median years of school completed by people 25 and over are equal
to 8.6 for men and 8.7 for women in 1940. See Table A1 - http://www.census.gov/population/www/socdemo/educattn.html. In our interpretation, investment in market skills in the model does not precisely correspond to formal
schooling, but to e¤ort exerted in early labor market experiences that may in‡uence future carrier paths and earning
potential.
23
G
q ,q
I
Real w ages
2
3
1.5
2.5
1
2
1.5
0.5
1920
1930
1940
1950
1960
1
1920
1970
1930
1940
year
ν
1950
1960
1970
year
I
f
h , old and new technology
I
0.15
0.1
0.08
0.1
0.06
0.05
0.04
0.02
1920
1930
1940
1950
1960
0
1920
1970
1930
1940
year
1950
1960
1970
year
Figure 6: Forces of technological progress in the model.
real wages. For the new general household technology, we use Gordon’s Divisia price index as
described in Section 4.1. For the new infant good technology, we use the time price of Similac.
Finally, we use the index of maternal death risk as a proxy for the decline in the time cost of
pregnancy, childbirth and recovery, as discussed in section 2. We set:
I
I
~t
(t) = M M
(t) = 1 +
I
(1920) ;
T F Rt (17=112)
;
(33 23) I (t)
~ t = M atM ortt =M atM ort1920 ; and M atM ortt is the maternal mortality rate at time
where M M
~ t.
t: The index of technological progress then corresponds to the variable M M
Figure 6 plots the transitional forces at work in our model over the period of interest. Consistent with our calibration strategy, we assume that agents forecast the change in new technology
prices and real wages over their lifetime using the yearly average change over the period of interest. Our results for the transition are displayed in …gure 7, where the solid red lines correspond
to data and the dashed black lines correspond to model predictions.
The model over predicts the rise in the labor force participation of young married women and
in the adoption of the new infant good technology. By 1970, 83% of all young married women
participate in the labor force when young (dashed-line in panel 5), and 90% of young married
households adopt the new infant good technology (panel 1), whereas in the data only 47% of
young married women participate and the formula feeding rate is 75%.28 This outcome is due to
28
We compute period averages by cohort in the model simulations. This is required since the young married
period lasts 11 years, the old married period lasts 27 years, which is longer than the 10 year time interval we adopt
for our simulations. Hence, when we compute the transition, 1/11 agents that were young in 1920 will still be
24
Av erage τ
I
Av erage τ
100
100
80
80
G
f
m
h ,h , married
60
e
f
100
50
80
40
60
60
60
30
40
40
40
20
20
0
1920
20
1940
1960
0
1920
year
1940
0
1920
1960
year
f
1940
1960
0
1920
year
f
p , y oung
20
10
p , old
F/M Earnings
100
100
100
100
80
80
80
80
60
60
60
60
40
40
40
40
20
20
20
20
0
1920
1940
year
1960
0
1920
1940
0
1920
1960
year
1940
1960
year
f
p , y oung when old
1940
1960
year
0
1920
1940
1960
year
Figure 7: Model transition.
the fact that the decline in q I is very rapid between 1920 and 1950. The adoption of the new G
technology is slightly slower than in the data. The slow adoption of the new general household
technologies in the model re‡ects that fact that until 1940 there is no signi…cant reduction in its
time price.
The ability to invest in market skills ampli…es the e¤ect of the new home technologies on
women’s labor force participation and accelerates the transition in the model. We plot the fraction
of married women that have invested in market skills in each year in panel 4. In 1920, this fraction
is equal to 3%, it then declines to 1% in 1930, re‡ecting the higher fertility rates in that cohort,
and it takes o¤ in 1940 rising to 45% in 1970. We interpret this variable broadly, re‡ecting not
only years of formal education but also additional time invested in their careers that workers
can only pursue early in their employment history. This implies that there is no single summary
measure of this variable that we can use to compare the model’s prediction with the data along
this dimension. In …gure 7, we compare women’s investment in market skills in the model with
the percentage of white women graduating from college by cohort.29 The college graduation rate
young in 1930. Similarly, 7/27 agents that were old married in 1920 will still be old married in 1940, 10/27 will still
be old married in 1930. To take this into account in the transition, we treat 1920 as if everybody is a new single
agent, a new young married agent and a new old agent, consistent with our calibration. In 1930 we compute all the
decisions for the new single, young married and old married agents. The population statistics on the young married
and old married that we report for 1930 re‡ect the fact that 10/11 young marrieds in 1930 are new young marrieds
and 1/11 young marrieds made their decisions in 1920 and behave accordingly. Similarly for the old married agents
and for all successive years.
This treatment is consistent with the maintained assumption that at each stage in life agents make all their
decision at the beginning of the period based on the current prices/wages and expected future prices.
29
Source: U.S. Bureau of the Census, Current Population Reports, Series P-20, Educational Attainment in the
United States.
25
is 6% in 1920 and rise to 25% in 1970. Interestingly, the take o¤ for women’s college graduation
rates in the data occurs in 1940, as predicted by our model.
We report the female/male ratio of average labor earnings in panel 8 (dashed line) and we
compare it to the ratio of wage income for the white married population from the Census. The
model predicts a value of 30% for 1920, higher than its empirical counterpart equal to 21%. The
earnings ratio drops in the model in 1930 and 1940, to 15%. This is mainly a compositional
e¤ect, due to the entry of unskilled married women in the labor force in that time period, which
determines a decline of average wage income of women, conditional on participation. The earnings
ratio rises steadily from 1950 onward in the model, reaching 50% in 1970, whereas in the data it
is only 28% at the same date.
Labor force participation of married women increases with age in the model, consistent with
the data. This can be seen from panels 5 and 6, where the dashed-dotted line corresponds to
the labor force participation rate of young married women when old. The value predicted by our
model is quite close to the data until 1940 after which it rises at a faster rate. This outcome is
driven by the acceleration in women’s investment in market skills in 1940, which is more intense
in the model than in the data, as well as by the fast adoption of new infant good technologies in
1930.
The rates of participation for old married women is very close to the data. In all years, young
married women (dashed line in panel 5) exhibit higher participation rates than old married women
(panel 7). This cohort e¤ect, which is also present in the data, is due to the fact that old married
women face lower lifetime earnings due to rising real wages and higher new home technology
prices. This reduces their incentive to invest in market skills and their opportunity cost of home
production relative to men.
Finally, home hours of married women decline signi…cantly, while male home hours increase
over time. This outcome is mostly driven by the rising rates of women’s investment in market
skills at all ages, which induces greater symmetry in the household allocation of home hours. Total
leisure for married men then decreases substantially relative to total leisure of married women
who participate in the labor force. Home and market work for participating married women,
excluding the time devoted to the production of infant goods, totals to 65 hours in 1920, and falls
to 54 hours in 1970. For married men, total work amounts to 48 hours in 1920 and rises to 53
hours in 1970 in the model.
This prediction is consistent with empirical evidence for the US, on the decline in leisure
time for men married to women who participate in the labor force relative to their wives. This
phenomenon is discussed by Knowles (2005), who focusses on the time period 1965-2003. For
our period of interest, it is not possible to measure home hours of husbands conditional on the
participation status of their wife. However, the downward trend in married men’s leisure relative
to their wife is clearly present. Knowles (2005) argues that the decline in married men’s relative
leisure is due to an increase of wives’ bargaining power within the household. In our model,
this outcome stems from the fact that women’s lower comparative advantage in home production
increases wives’earning potential on the labor market and induces a more equal distribution of
home hours.
4.3.1
Discussion
How do we interpret the fact that the model largely overpredicts the labor force participation
of young married women and the rate of adoption of new infant good technologies relative to
26
the data? The evolution of household technologies and labor productivity is the only force that
in‡uences female labor force participation and gender earnings di¤erentials in the model, while
other factors may also play a role and dampen the e¤ect of improving technologies in practice.
One very important factor which we abstract from is the presence of “marriage bars” for
women until the 1950’s. Marriage bars consisted in the practice of not hiring married women or
dismissing female employees when they married. Marriage bars were prevalent in teaching and
clerical work, which accounted for approximately 50% of single women’s employment between 1920
and 1950. Goldin (1991) extensively documents the pervasiveness of these practices for di¤erent
school districts and for …rms hiring o¢ ce workers. The probability of not retaining single female
worker upon marriage ranged between 47.5% to 58.4% for school districts between 1928 and 1942,
and between 25% and 46% for …rms hiring o¢ ce workers between 1931 and 1940. The probability
of not hiring a married woman ranged between 62% and 78% for school districts and between
39% and 61% for …rms hiring o¢ ce workers over the same periods.
Conditional on employment, di¤erences in wages across genders are purely driven by di¤erences in investment in market skills in our model. We do not allow for statistical or taste based
discrimination. Yet, even in current years approximately 10% of the gender di¤erences in earnings
cannot be accounted for by observable di¤erences in characteristics that are related to productivity (O’Neill, 2000). Albanesi and Olivetti (2006) argue that this unexplained gender earnings
di¤erential could be due to statistical discrimination. Gender discrimination would greatly reduce
women’s incentive to invest in market skills and participate in the labor force in our model.30
Cultural factors may also have played an important role in slowing down the increase in
women’s labor force participation. Fernández and Fogli (2005) document the strong role of
country of origin, a proxy for cultural di¤erences in attitudes with respect to women’s work,
in second-generation American women’s labor force participation behavior. Based on survey evidence reported in Fogli and Veldkamp (2007) and Fernández (2007), only 20% of respondents
believed that a married woman should work in the period between 1935 and 1945. By 1970, this
number went up to 55%, a very signi…cant rise to a level that still suggests a signi…cant cultural
barrier to women’s employment.31
We also assume that the distribution of bargaining power in the household is exogenous, constant over time and equal across spouses. Empirical evidence32 suggests that the distribution of
bargaining power across spouses depends on relative wages. Based on this, the assumption that
spouses have symmetric bargaining power in the 1920’s seems unrealistic since married women had
lower earning potential. Institutional factors, such as divorce laws, lack of political representation
and marriage bars in the labor market may also have contributed to reduce women’s bargaining
power in the household. The gradual lifting of these constraints over the course of the twentieth
century can be represented as an increase of the wives’Pareto weight in the household problem
in the context of our model.33 Knowles (2005) argues that the reduction in female/male earnings
di¤erential indeed increased the bargaining power of women and led to a decline in gender di¤er30
Numerical experiments suggest that di¤erential returns to work or skill investment by gender do not signi…cantly
a¤ect the transition. This is due to the fact that the conventional measures of these gender di¤erentials do not vary
much over this time period.
31
Fogli and Veldkamp (2007) and Fernández (2007) point to uncertainty about the e¤ect of mother’s work on the
welfare of young children as an important determinant of these attitudes.
32
See Browning, Bourguignon, Chiappori, and Lechene (1994) and Mazzocco (2007).
33
Doepke and Tertilt (2007) argue that the rise in returns to education at the beginning of the twentieth century
increased women’s importance in the household and spurred a process of equalization in their economic and social
rights.
27
entials in home hours. In our model, a rising Pareto weight for married women would lead to a
slower increase in their participation, since this is inversely related to their Pareto weight in the
household problem.
Lastly, we assume that the only cost associated to the adoption of new infant good technology is
the monetary cost and that infant formula was readily available in all locations after its commercial
introduction. In practice, there could be additional learning costs associated with the use of infant
formula that slow down its di¤usion in the population or uncertainty about the e¤ectiveness of
formula as a substitute for mother’s milk. For example, formula was initially not available in all
locations. In the 1920s and early 1930s, di¤usion of knowledge on infant formula mainly occurred
via women giving birth in hospitals. For this period, the rate of hospital birth can in fact be
considered an upper bound on the possible rate of di¤usion of infant formula. In addition, as
discussed in Section 2, in the early 1970s, new scienti…c discoveries regarding the positive e¤ect of
mother’s milk on the immune status of the baby and on the child’s resistance to infections brought
about a resurgence in breast feeding. The inclusion of additional adoption costs for infant formula,
as well as constraints on di¤usion, would dampen the adoption rate of infant formula in the model
and slow down the rise in married women’s labor force participation.34
4.4
Experiments
We now run several experiments to isolate the role of each source of technological progress in
isolation. The experiments are summarized in Table 5.35
Table 5: Experiments
Experiment 1 q I and q G constant
Experiment 2 q G constant
Experiment 3 Constant q G and I
Experiment 4 q I and I constant
Experiment 5 Constant I
We report the behavior of all variables in Table 6 and selected results from the experiments
in …gures 8-11. In all …gures, the dashed lines correspond to the transition in the full model, the
dash-dotted line correspond to the transition in the experiment, while the solid lines correspond
to the data.
Experiment 1 …xes q I and q G to their value in 1920, so that the only dynamic force is the
decline in I . Results are displayed in …gure 8. There is no increase in the adoption of new infant
and general household technologies over the entire period in this experiment. Changes in the
labor force participation of young married women exclusively re‡ect changes in the time cost of
pregnancy. Despite this, labor force participation for young married women rises as much as in
the data between 1920 and 1950. The reduction in the time cost of pregnancy, childbirth and
34
The new discoveries on the immunization properties of mother’s milk could be modelled as a negative shock to
the productivity of the new infant good technology. That is, adopting the new technology, would still save time but
deliver a lower quantity of infant good. If preferences were de…ned over the quantity of infant goods, this would
lead, other things equal, to higher breast feeding rates.
35
We do not conduct and experiment with constant real wages, since due our logarithmic speci…cation for preferences, substitution and wealth e¤ects associated with a generalized rise in the level of real wages exactly cancel.
This implies that the transition with constant real wages is exactly the same as with rising real wages. In all the
experiments, real wages are held constant.
28
Averageτ
I
Averageτ
100
100
80
80
60
60
40
40
20
20
0
1920
1930
1940
1950
1960
0
1920
1970
1930
year
LFP, young m arri ed wom en
80
80
60
60
40
40
20
20
1940
1950
1960
1970
LFP, old m arried wom en
100
1930
1950
year
100
0
1920
1940
G
1960
0
1920
1970
1930
year
1940
1950
1960
1970
year
Figure 8: Experiment 1
recovery alone can account for the rise in the participation of married women in the fecund period
of life over these years. Labor force participation of old married women does not increase beyond
1940. Table 6 also shows that there is no reduction in female home hours and no increase in the
investment in market skills.
It is a feature of the model that single women’s investment in markets skills is strongly linked
to the expectation of being in the workforce in the old married period. This stems from the fact
that this period is the longest in the agents’ lifetime in the model, and returns to investment
in market skills are mostly reaped in those years. On the other hand, adoption of the new
infant good technology in the young married period also encourages investment in market skills.
This mechanism generates a strong complementarity between adoption of the new infant good
technology, investment in market skills and work in the old married period for women, which
emerges in all the experiments. Investment in market skills also leads to a more symmetric
household allocation of home hours, because it eliminates gender di¤erentials in earnings. Hence,
women’s participation in the old married period is associated with a relatively high female/male
earnings ratio.
In experiment 2, q G is held constant so that there is no improvement in the general household
technology and the transition is exclusively driven by the decline in I and q I . Results are
displayed in …gure 9. Not surprisingly, the average G remains at 1920 levels for the entire time
period, however, I is unchanged relative to the full transition. Married women’s labor force
participation rises less than in the data and in the full model between 1950 and 1970, while
it’s virtually una¤ected between 1920 and 1950. This suggests that improvements in general
household technologies play a strong role in the later time period. In the early period, rising
female participation rates are mostly driven by young married women entering the labor force
as I declines and households adopt the new infant good technology, and this pattern is mostly
29
Averageτ
I
Averageτ
100
100
80
80
60
60
40
40
20
20
0
1920
1930
1940
1950
1960
0
1920
1970
1930
year
LFP, young m arried wom en
80
80
60
60
40
40
20
20
1940
1960
1970
LFP, old m arried wom en
100
1930
1950
year
100
0
1920
1940
G
1950
1960
0
1920
1970
1930
year
1940
1950
1960
1970
year
Figure 9: Experiment 2
una¤ected by the constant value of q G : The high value of q G has a direct negative e¤ect on
participation of old married women. This discourages investment in market skills and indirectly
also a¤ects young married women’s participation in the labor force between 1950 and 1970, despite
the high rates of adoption of new infant good technologies.
We report the results for experiment 3 in Table 6. This experiment isolates the e¤ect of a
decline in q I since both I and q G are constant. Labor force participation of young married
women rises from 9% in 1920 to 20% in 1970. This suggests that the declining cost of infant
formula alone can account for only a small fraction of the rise in participation of young married
women, and the decline in the time cost of pregnancy, childbirth and recovery instead has a much
stronger impact over those years.
Experiment 4 isolates the e¤ect of the decline in q G : The results are displayed in …gure 10.
With q I and I constant, I is also constant. The labor force participation of young married
women is lower than in the full transition and much lower than in the data between 1920 and
1950. Absent any decline in q I or I ; young married women’s labor force participation is 9%
lower than in the data in 1930, 13% lower in 1940, 3% lower in 1950. This suggests that in the
model the rise in the labor force participation of young married women is strongly driven by
progress in medical technologies. By contrast, old married women’s labor force participation and
the adoption of new general household technologies are virtually una¤ected with respect to the
model with all sources of technological progress. As reported in Table 6, investment in market
skills is lower in 1960 and 1970, which depresses the F/M earnings ratio for that period.
Results for experiment 5, in which I is kept constant at the 1920 level are reported in …gure
11. The transition is only driven by the decline in price of the new infant and general household
technologies in this experiment. The lack of progress in medical technologies mostly e¤ects the
participation of young married women, which is approximately 10% lower in all years relative to
30
Averageτ
I
Averageτ
100
100
80
80
60
60
40
40
20
20
0
1920
1930
1940
1950
1960
0
1920
1970
1930
1940
year
LFP, young m arried wom en
80
80
60
60
40
40
20
20
1940
1960
1970
LFP, old m arried wom en
100
1930
1950
year
100
0
1920
G
1950
1960
0
1920
1970
1930
1940
year
1950
1960
1970
year
Figure 10: Experiment 4
the full version of the model and approximately 5% lower than in the data in 1930 and 1940.
Once again, the decline in the time cost of pregnancy emerges as the essential factor for the rise
in participation of young married women before 1950.
We also conducted an experiment to evaluate the role of fertility, by allowing all sources of
progress and …xing fertility at the 1920 level. The transition is virtually unchanged relative to
the full model. This suggests that high fertility is not in itself detrimental to rising participation
of married women if the time cost of pregnancy is declining and households can adopt the new
home technologies.
Summing up, the reduction in the time cost of pregnancy, childbirth and recovery appears to
be the most important force behind the rise in the participation of married women with children
between 1920 and 1960. Its impact is stronger than the decline in the price of infant formula
over that period. Improvements in medical technologies alone can fully account for the rise in
the participation of young married women between 1920 and 1950. Improvements in general
household technologies mostly a¤ect labor force participation of young and old married women
between 1950 and 1970. The ability to adopt both the new infant good technology and the new
general household technology are essential for the rise in labor force participation of old married
women between 1950 and 1970.
5
Concluding Remarks
Our results suggest that the advancements in medical technologies that reduced the time cost of
pregnancy, childbirth and recovery were essential for the rise in labor force participation of young
married women with children between 1920 and 1960, while infant formula played a smaller role
over that time period. The introduction and improvement in home appliances accounts for a
31
Averageτ
I
Averageτ
100
100
80
80
60
60
40
40
20
20
0
1920
1930
1940
1950
1960
0
1920
1970
1930
1940
year
LFP, young m arried wom en
80
80
60
60
40
40
20
20
1940
1960
1970
LFP, old m arried wom en
100
1930
1950
year
100
0
1920
G
1950
1960
0
1920
1970
1930
1940
year
1950
1960
1970
year
Figure 11: Experiment 5
signi…cant fraction of the rise in female labor force participation between 1950 and 1970.
We concentrate on the years before 1970 since we are interested in medical advancements
that occurred (and plateaued) before then. As discussed in the literature, after 1970 additional
factors such as the availability of oral contraception and the change in divorce laws played a
role in explaining the increase in women’s investment in education, labor force participation and
wages. Goldin and Katz (2002) show that the availability of oral contraceptives starting in the
late 1960’s contributed to the increase in the number of college graduated women into professional
programs and to the decline in the age at …rst marriage. Bailey (2006) shows that legal access to
the pill before age 21 signi…cantly reduced the likelihood of having a …rst birth before age 22 and
increased the number of women in the paid labor force.
We focus on the time intensive nature of the commitments associated with motherhood. An
additional factor to consider is that for professional women the career clock and the biological
clock almost exactly coincide. This is a recent phenomenon, connected to the shift from "jobs
to careers" in women’s work choices which was, as argued by Goldin (2006), in part induced
by the availability of oral contraceptives. This concurrence may account for the high drop out
rates of highly educated women, as well as for their under-representation in executive positions in
many professions. Albanesi and Olivetti (2007) argue that the greater cost associated with career
investment for women may explain the di¤erences in the level and structure of compensation by
gender for top executives.
One important property of our model is that, by considering medical advancements related to
motherhood, it can reproduce the contemporaneous rise in fertility36 and in labor force participation of married women with young children that took place in the US in the late 1930s. Our
current analysis, however, abstracts from fertility decisions. A version of our model with fertility
36
See Greenwood, Seshadri and Vanderbroucke (2005).
32
choice has the potential to endogenously generate the rise in fertility, as well as account for the
dynamics of labor force participation. While this is beyond the scope of this paper, we plan to
explore the role of fertility decisions in future work.
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34
[31] Haines, Michael R., and Richard Sutch. 2006. Population, by marital status, sex, and race:
1880–1990. Table Aa614-683 in Historical Statistics of the United States, Earliest Times to
the Present: Millennial Edition, edited by Susan B. Carter, Scott Sigmund Gartner, Michael
R. Haines, Alan L. Olmstead, Richard Sutch, and Gavin Wright. New York: Cambridge
University Press.
[32] Hambraeus, L. 1977. Proprietary milk versus human breast milk in human feeding. Pediatric
Clinics of North America 24: 17-36.
[33] Hanes, Christopher. 1996. Changes in the Cyclical Behavior of Real Wage Rates 1870–1990,”
Journal of Economic History 56: 856–7, December.
[34] Hauser, Robert. 1976. Fertility Tables for Birth Cohorts by Color: United States 1901-1973.
Rockville, MD: National Center for Health Statistics.
[35] Hirschman, Charles and Marilyn Butler. 1981. Trends and Di¤erentials in Breast Feeding:
An Update. Demography 18 (February):39-54.
[36] Hirschman, Charles and Gerry E. Hendershot. 1979. Trends in breast feeding among American mothers. Vital Health Statistics 23 3:1-46. National Center for Health Statistics.
[37] Holly E. Reed, Marjorie A. Koblinsky, and W. Henry Mosley. 2000. The Consequences of Maternal Morbidity and Maternal Mortality: Report of a Workshop. National Research Council
(U.S.), Committee on Population. Washington, DC: National Academy Press.
[38] Jones, Larry E. and Michele Tertilt. 2007. An Economic History of Fertility in the U.S.:
1826-1960. The Handbook of Family Economics, Peter Rupert, Ed., forthcoming.
[39] Kerr, J.M. Munro. 1933. Maternal Mortality and Morbidity. Edinburgh
[40] Knowles, John. 2005. Why Are Married Men Working So Much? Manuscript, University of
Pennsylvania.
[41] Leavitt, Judith W. 1988. Brought to Bed: Childbearing in America, 1750-1950. Oxford
University Press.
[42] Loudon, Irvine 1992. Death in Childbirth: An International Study of Maternal Care and
Maternal Mortality 1800-1950. Oxford University Press.
[43] Margo, Robert A. 2006a Hourly and weekly earnings of production workers in manufacturing:
1909–1995. Table Ba4361-4366 in Historical Statistics of the United States, Earliest Times to
the Present: Millennial Edition, edited by Susan B. Carter, Scott Sigmund Gartner, Michael
R. Haines, Alan L. Olmstead, Richard Sutch, and Gavin Wright. New York: Cambridge
University Press.
[44] Margo, Robert A. 2006b Hourly and weekly earnings of production workers in manufacturing,
by sex and degree of skill: 1914–1948.” Table Ba4381-4390 in Historical Statistics of the
United States, Earliest Times to the Present: Millennial Edition, edited by Susan B. Carter,
Scott Sigmund Gartner, Michael R. Haines, Alan L. Olmstead, Richard Sutch, and Gavin
Wright. New York: Cambridge University Press.
35
[45] Martinez, Gilbert A. and John P. Nalezienski. 1979. The Recent Trend in Breastfeeding.
Pediatrics 64: 686-692, November.
[46] Mazzocco, Maurizio. 2007. Household Intertemporal Behavior: a Collective Characterization
and a Test of Commitment. Forthcoming, The Review of Economic Studies.
[47] Mokyr, Joel. 2000. Why “More Work for Mother?”Knowledge and Household behavior 18701945. Journal of Economic History 60: 1-41.
[48] National Center for Health Statistics. 2000. Infant Growth Charts from the Center for Disease
Control of the National Center of Health Statistics. http://www.cdc.gov/growthcharts/.
[49] O’Dowd, M.J. and E.E. Philipp. 1994. The History of Obstetrics and Gynaecology. Informa
Healthcare.
[50] O’Neill, June. 2003. The Gender Wage Gap in Wages, circa 2000. The American Economic
Review, Papers and Proceedings 93 (2): 309-314.
[51] Packard A. and S. Vernal. 1982. Human Milk and Infant Formula. Academic Press, Inc., New
York, NY.
[52] Ramey, Valerie A. and Francis Neville. 2006. A Century of Work and Leisure. NBER Working
Papers 12264, National Bureau of Economic Research, Inc.
[53] Rios-Rull, Victor. 1993. Working in the Market, Working at Home, and the Acquisition of
Skills: A General equilibrium Approach. The American Economic Review 83: 893-907.
[54] Robinson, John P., 1985. Changes in Time Use: an Historical Overview. In Juster F. Thomas
and Frank P. Sta¤ord eds. Time Goods and Well-Being, Institute for Social Research, The
University of Michigan.
[55] ProQuest Historical Newspapers Chicago Tribune (1849-1985), Los Angeles Times (18811985) and The Washington Post (1877 - 1990).
[56] Schuman, Andrew J., 2003. A Concise History of Infant Formulas (twists and turns included),
Contemporary Pedriatics, February.
[57] Thomasson, Melissa A. and Jaret Treber. 2004. From Home to Hospital: The Evolution of
Childbirth in the United States, 1927-1940. NBER Working Papers 10873.
[58] U.S. Census Bureau. 1975. Historical Statistics of the United States, Colonial Times to 1970,
Bicentennial Edition.
[59] U.S. Census Bureau, Statistical Abstracts of the United States, 2003. Mini-Historical Statistics, Tables HS-13 and HS-30.
[60] U.S. Department of Commerce, Bureau of the Census, Mortality Statistics. 1920 to 1937.
[61] U.S. Department of Commerce, Bureau of the Census, Birth, Stillbirths and Infant Mortality
Statistics. 1931 to 1936.
[62] U.S. Department of Commerce, Bureau of the Census, Vital Statistics of the United States,
Part I, Natality and Mortality Data for the United States. 1938 to 1944.
36
[63] U.S. Department of Health, Education and Welfare, Vital Statistics of the United States,
Volume II, Mortality Data. 1950 to 1959.
[64] U.S. Public Health Service, Federal Security Agency, Vital Statistics of the United States,
Part I, Natality and Mortality Data for the United States. 1945 to 1949.
[65] U.S. Department of Health, Education and Welfare, Vital Statistics of the United States,
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[66] Vanek, Joanna. 1973. Keeping Busy: Time Spent in Housework, United States, 1920-1970.
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in the Nineteen and Twentieth Centuries. Ohio State University Press, Columbus, OH.
6
Model Appendix
6.1
Household Problem
Given that individuals are born without any initial wealth, they will all participate in the labor
force when single. Then, we can write a uni…ed intertemporal budget constraint, valued in terms
of age 1 consumption goods, given by:
3
2
X
Z2
42
Z1 +
(18)
cj0 w0 pj0 5 (1 + R1 ) :
1 + R2
j=f;m
The households’uni…ed Pareto problem is:
X
maxo
0:5
u cj0 ; T
n
ej0 ; I1 ;
+
1
G(j)
cjr ;pjr ; r
2
4
X
r=1;2
r 1
2
ju
hj0
pj0 n + g0 Gj0
G I
0; 0
Gj
0
j=f;m
r=0;1;2;j=f;m
X
ej0
cjr ; T
hjr
G I
r ; r
pjr n + g1 G1
G
1
; I1
I
1
+
2 g2
G2
G
2
j=f;m
subject to (18) and (3), (1)-(2), (6), hf2 I = 0 and hf2 = hf2 G : Here, the Pareto weights over age 0
utility are symmetric, consistent with the fact that agents choose the age 0 allocation individually.
Combining (9) and (13):
cj0
=
cj1
j
1 (1
+ R1 )
0:5
1=
; for j = f; m:
(19)
Similarly, combining (9) and (10):
cj2 = cj1 [
2 (1
+ R2 )]1= ; for j = f; m:
37
(20)
3
5
Using (9) for f and m :
m
f
cm
1 = c1
1=
:
(21)
f
Equations (18)-(21), jointly with (9), give rise to a system of six equations in the six unknowns
cjr for j = f; m and r = 0; 1; 2:
6.2
Market Production and Equilibrium
The problem for the representative …rm is given by:
max y
d;k;c
wN
subject to (15) and (17), where w is corresponds to economy wide labor productivity in the current
period. Hence, in equilibrium, w will be equal to at each date.
The resource constraint is:
Z
Z
I (j)
X
G (j)
1
G
I
I
r
0 =
n (r) q G
(j)
d
dj
+
q
n
(r)
dj
r
r
1 (j) k
j
r=1;2
+
X
r=1;2
1
n (r) Cr + a01 +
3
Z
i
j
a00 (i) + (1 + ei ) p (i) di
Y
X
n (r) ar (1 + R) ;
r=1;2
where j indexes households in the population, n (r) denotes the fraction of agents of age r in the
population and:
Z
Cr =
(sr (i) + (i) (1 + ei ) pr (i)) di;
i
Z
X
Y =
n (r) pr (i)
(i) (1 + ei ) di;
i
r=0;1;2
where i indexes individuals in the population and capital letters denote aggregate values.
Integrating budget constraints over all households in the population:
Z
Z
Z
I
G
G
I
I
A (1 + R) +
p (i) di = C + q
(j) dj + q
(j) k I (j) dj A0 ;
i
j
j
where i indexesR all living individuals
and j all living Rhouseholds.
R
G
I
Since Y = p (i)
(i) di = j G (j) d (j) dj + j I (j) k (j) dj + C + A0 A (1 + R) from
the resource constraint, then:
Z
Z
Z
Z
G
I
G
I
G
G
I
I
(j) d (j) dj +
(j) k (j) dj = q
(j) dj + q
(j) (j) dj;
(22)
j
j
j
j
R
R
I
G
where market clearing requires j I (j) k (j) dj = K and j G (j) d (j) dj = D: Then, under
competitive pricing, (22) pins down the equilibrium values of q l as a function of the technological
marginal rates of transformation l ; for l = G; I.
38
7
Data Appendix
7.1
Demographics
Data on total fertility rate and number of live births are from Hauser (1976). Data for median age
at …rst marriage correspond to Series A 158-159 in Historical Statistics of the United States (1975).
Data for median age at …rst birth are obtained by using information on …rst births by age of mother
from the National Center of Health Statistics (http://www.cdc.gov/nchs/data/statab/t991x02.pdf).
We use information on number of women in each age group (Series A 119-134, Historical Statistics
of the United States, 1975) in order to obtain the median age at …rst birth in 1920. We take the
statistic for median age at last birth from Glick (1977, Table 1.)
7.2
7.2.1
Wages and Prices
Prices
Nominal prices are de‡ated by using the U.S. Bureau of Labor Statistics All Urban Consumers
Price Index (CPI-U) with base 1982-1984. This index is an average of prices for all items in
the CPI and across all major U.S. cities. We de‡ate monthly and yearly data by using the
corresponding (monthly or early) CPI-U.
7.2.2
Real Wages
The historical real wage series that is most commonly used in the literature is the series discussed
in Hanes (1996). However, the series starts in 1923 and has a break during WWII (1941 to 1946).
Given that we focus on the 1920-1970 period, we use real hourly wages in manufacturing (or
full-time year-round workers) from Margo (2006a.) This series is available for every year between
1909 and 1995. The two series move very closely although for every year, real wages in Hanes’
series are larger than in Margo’s.
7.2.3
Wage Rates by Gender
We use the 1920-1948 series on hourly wages of production workers in manufacturing by gender
from Margo (2006b.) This series is based on aggregate payroll data collected by the National
Industrial Conference Board (NICB.) Unfortunately, information on wage rates by gender is not
readily available after 1948. Hence we use data from the Handbook of Labor Statistics, 1970,
Table 109 (Number and Average Straight-Time Hourly Earnings of Production Workers in Selected Manufacturing Industries, 1967-69) to compute the male and female hourly wage in 1968.
Unfortunately these data are only available for selected industries. Therefore, we scale the wages
upwards to match (1967-69 average of) series Ba4361 (the aggregate hourly wages based on the
NICB sample.) We use simple linear interpolation to …ll in the missing data between 1948 and
1968.
7.2.4
Female/Male Earnings Ratios
Data on the female/male earnings ratio are from Goldin (1990, Table 3.1). This is the standard
series used in the literature and it provides information on the gender gap for full-time year-round
workers. We also use Census data to construct a measure of the average gender earnings ratio for
the overall population. In this case we use the IPUMS Census 1% samples from 1940 to 1970 (for
39
1970, we use the 1% State sample). Our sample includes white men and women, aged 16 through
64, living in non-farm households. We further restrict the sample to observations with group
quarters status equal 1, “Households under 1970 de…nition.”We use the information on wage and
salary income (INCWAGE). For all years N/A code (999999) is treated as missing data. Since
the information on income in the 1940 and 1950 Censuses is only available for sample-line persons
the statistics by gender are obtained as weighted averages using sample-line weights (SLWT). For
1960 and 1970 sample-line weights coincide with person weights (PERWT).
7.3
7.3.1
Trends in Labor Force Participation of Married Women
By Age and Cohort
We construct cohort and time series measures of labor force participation (LFP) of married women
using comparable 1890 to 1980 LFP data constructed by Goldin (1990, Table 2.2). The data are
disaggregated into …ve age groups: 15-24, 25-34, 35-44, 45-54, 55-64. Since data are not available
for 1910 we obtain LFP by age for this decade by linear interpolation of the appropriate statistics
between 1890 and 1920.
Based on these data we compute the LFP statistics used in section 4.1, 4.3 and 4.4, as follows.
The 1920 calibration target for LFP of "young" (age 23 to 35) married women corresponds to the
LFP of women born in 1886-1895 (that is, married women age 25-34 in 1920). The 1920 target for
LFP of "old" (age 36 to 60) married women is obtained by averaging LFP statistics for the 35-64
age group across three cohorts: 1856-1865, 1866-1875 and 1876-1885. The time series data for
LFP of old married women used in Figure 7-11 and in Table 6 is obtained by averaging (with the
appropriate population weight obtained from Haines and Sutch (2006)) LFP of married women
aged 35-44, 45-54 and 55-64 in each decade. The corresponding data points for LFP of young
married women correspond to LFP of women aged 25-34 in 1920, 1930, ..., 1970.
7.3.2
By Number of Children
We use 1920 to 1970 IPUMS Census data to compute LFP by number of children. Our sample
inclusion rules are the same as in section 7.2.4.
We count individuals whose imputed labor status is "employed" or "unemployed" (variable
EMPSTAT, codes 1 and 2) as participating in the labor force (see IPUMS documentation for
information on consistency of this variable across time and comparability to other measures of
participation.) Because employment status information is not available in 1920, we use occupation data for that year instead. Using the 1950-standardized variable (OCC1950), we count all
individuals with an "occupational response" (codes 0 through 970) as participating in the labor
force. Observations with a "non-occupational response," unknown occupation or no data are,
therefore, counted as non-participants. We report LFP by presence of children within various
age categories, as well as for women with no children. These statistics are obtained by using
information on the total number of children living in the household (variable NCHILD), the total
number of children less than 5 years old (NCHLT5) and on the age of the youngest child (variable
YNGCH). Averages are weighted using person weights (variable PERWT). Table A1 presents the
data on LFP by presence of children for married and never married white women age 23 to 35.
40
Table A1: Female LFP by marital status and presence of children (percentages)
1920
1930
1940
1950
1960
1970
Married
no children
children
15
4
27
6
38
10
54
14
66
22
74
32
1920-1950
1920-1960
1950-1970
1960-1970
262
342
37
12
12
242
443
129
44
Never Married
no children
children
80
63
83
62
86
61
86
62
86
63
86
64
9
8
-1
0.3
12
-1
0
2
1
B a se d o n IP U M S d a ta . L F P b a se d o n E M P S TAT (c o d e = 1 -2 ) in ye a rs 1 9 3 0 to 1 9 7 0 . L F P b a se d o n O C C 1 9 5 0 (c o d e = 0 -9 7 0 ) in 1 9 2 0 .
C h ild re n va ria b le s b a se d o n N C H IL D , N C H LT 5 , a n d Y N G C H . R e stric te d to G Q = 1 , w e ig hts= P E RW T . A g e 2 5 -3 5 .
7.4
Home Hours
The “1920”value for married men’s home hours is from Table 11.1 in Robinson (1985.) According
to this source, men only spent 4 hours per week in family care activities. A reported in Vanek
(1973), housewives spent 51 hours per week attending to household chores. For employed married
women, de…ned as working for pay more than 15 hours per week, Vanek (1973, page 194) reports
26.8 hours per weeks for rural employed women and 23.6 hours per week for urban employed
women. Following Ramey and Francis (2006) we take the average of these two statistics (25 hours
per week). The numbers that we use for home hours are consensus estimates. Vanek (1973)
reports information from a compilation of time-use studies conducted by the Bureau of Nutrition
and the Bureau of Home Economics between 1924 and 1928. In all these studies home hours by
housewives range from 50 hours per week to 60 hours per week. The few studies that report home
hours for men show that men spent on average between 3 and 5 hours per week in home activities.
See also Ramey and Francis (2006) and Bryant (1996).
7.5
Progress in Maternal Health
We can identify three phases in the history of childbirth in the US.37 Until 1850s, only women
were admitted in the birthroom and deliveries were assisted exclusively by midwives. Between
1850 and 1935, physicians gradually entered the birthroom. After 1935, births rapidly shifted to
the hospital. While rates of maternal mortality only declined substantially starting in the last
phase, the changes to the birthing process that led to this outcome began in the second part of
the 19th century. In the …rst phase, midwives, despite their extensive experience, did not have
su¢ cient medical knowledge to deal with the potential complications associated with parturition
and physicians were not trained to deal with women’s health. In the late 18th century, a- uent
families in the North-East started to invite male physicians to assist with deliveries. Physicians
used drugs to alleviate pain during labor and hasten delivery, and often resorted to bloodletting
37
See Loudon (1992) and Leavitt (1986) for further details.
41
in hospital
not in hosp.- physicians
not in hosp. - midwife
120
100
Percentage
80
60
40
20
0
1935
1940
1945
1950
1955
1960
1965
1970
1975
Year of Birth of Child
Figure 12: Percentage of live births in hospital by place of delivery and type of attendant.
and forceps. This practice steadily grew in the second half of the 19th century. In 1900, 50% of
all births were assisted by midwives and the rest by physicians.
The presence of formally trained physicians was instrumental in preventing maternal and
neonatal deaths in many instances. However, the initial lack of experience and the practice of
avoiding visual examination of female patients undermined their ability to intervene e¤ectively
during parturition. Experimentation and excessive operative interventions, such as aggressive use
of forceps, were common. In addition, physicians’exposure to other patients with communicable
diseases actually increased the risk and incidence of post-partum infections before germ theory
was widely accepted and antibiotics were available.
Even if initially the intervention of physicians did not contribute to a substantial reduction
in maternal mortality, it led to the introduction of new procedures that laid the ground for an
improvement in obstetric practices that substantially reduced the risk of maternal disability and
death during the …rst half of the twentieth century. The most notable developments were surgical
procedures to correct perineal lacerations, and the adoption of new hygiene standards following
the discoveries in bacteriology of the late 1800s.
The perceived iatrogenic nature of women’s birthing and post-partum conditions in the early
part of the 20th century led to the move from home to hospital. This shift was part of a broader
42
e¤ort in the medical profession to standardize and monitor obstetric practices. While until the
mid 1920s, only poor women gave birth in hospitals, starting in the 1930s, with the advent of
electronic imaging and advanced neonatal therapies that could only be administered in a hospital
setting, wealthy women also started giving birth in hospitals. As shown in Figure 12, 36.9% of
all births took place in hospitals in 1935. By 1955, 94.4% of all births took place in hospitals.
7.6
Physical and Monetary Cost of Breast Feeding
Our estimates of the total time and monetary cost of breast feeding are based on information from
the National Association of Pediatrics (http://www.med.umich.edu/1libr/pa/pa_formula_hhg.htm).
According to this source, the number of feedings per day varies by the infant’s age. That is, an
infant should be fed 6 to 8 formula feedings per day for the …rst month, 5 to 6 formula feedings
per day from 1 to 3 months, 4 to 5 formula feedings per day from 3 to 7 months, 3 to 4 formula
feedings per day from 7 to 12 months. The number of daily feedings decreases with the age of the
child as solid food is introduced in the later period.
7.6.1
Physical Cost
Based on accounts from pediatric journals, it is reasonable to assume that the time spent for each
feeding (time for the actual feeding and cleaning up) ranges from 20 to 30 minutes. Combining
this information with the number of daily feedings by age, we can obtain rough estimates of the
average weekly time cost of feeding an infant. We …nd that a mother would spend 700 to 900
hours breast feeding a baby during his …rst 12 months of life. This calculation implies that she
would spend on average 13.6 to 17.3 hours per week in this activity.
7.6.2
Monetary Cost
According to the National Association of Pediatrics, the amount of formula needed for a baby
varies by the infant’s weight. Newborns usually start with 1 ounce per feeding, by 7 days they can
take 3 ounces per feeding. The amount of formula that most babies take per feeding (in ounces)
can be calculated by dividing the baby’s weight (in pounds) in half. We use this information as
well as the 2000 Infant Growth Charts from the Center for Disease Control of the National Center
of Health Statistics (available at: http://www.cdc.gov/growthcharts/) to obtain our estimates of
the average daily intake of infant formula (in liquid ounces) for a baby of median weight during
the …rst 12 months of his life. The average daily cost of exclusively breast feeding an infant is
then obtained by multiplying the resulting average daily quantity of formula by the price of a
‘ready-to-feed’liquid ounce of Similac.
We use the 2000 CDC Infant Growth Chart since it is based on a representative sample of
formula- and breast-fed infants. Also available are the 1977 Growth Charts that are based on a
study conducted in Ohio from 1929 to 1975. The babies in this study were primarily fed formula
or a combination of breast milk and formula and often started solids before 4 months. Since
the mode of infant feeding in‡uences the pattern of infant growth we think that the 2000 CDC
Growth Char provides a better approximation for the weight growth of (exclusively breast fed)
infants in 1920.
43
7.7
Infant Formula
Table A2 reports di¤erences in the composition of di¤erent types of milk and of …rst and second
generation infant formulas. Data on human and cow milk are from Packard and Vernal (1982,
page 140). Data for Nestle are from Apple (1987). Data on the more contemporary formula are
from Hambraeus (1977). Entries are percentages of grams of fatnproteinsncarbohydrates per 1,000
grams of milk/formula. We use the composition of SMA for the 1920s as a proxi for Similac’s. We
think that this is a reasonable assumption since, as shown in the last two columns of the table,
the two formulas are nutritionally equivalent in 1977. In the 1970s, nutritional scientists realized
that it was wrong to design the formula to exactly match human milk. As a consequence there
was a drastic change in the composition of these formulas relative to those created in the 1920s.
No further path breaking discovery has occurred ever since. Similac products currently in stores
are nutritionally equivalent to those sold in 1977.
Table A2: Percentage composition of di¤erent types of milk
Proteins
Fat
Carbs
7.7.1
Human Milk
Cow’s Milk
0.9%
4.4%
6.6%
3.4%
3.6%
4.8%
Nestle
1929
2.3%
2.3%
5.7%
SMA
1920s
0.9%
4.6%
6.5%
SMA
1977
1.5%
3.5%
7%
SimilacnEnfamil
1977
1.5%
3.6%
6.8%
Humanized Infant Formula: Similac
The infant formula that became known as Similac was developed in the early 1920s by two Boston
based scientists, Alfred W. Bosworth, a milk chemist, and Henry Bodwidtch, a pediatrician. The
formula, marketed by the Moores and Ross Milk Company in 1924, was initially sold only through
physicians, who would place their own label on the plain cans. By 1926, it was commercialized
under the name Similac (see Schuman, 2003.)
As discussed in Section 2, we measure technological progress embedded in infant formula based
on a time series for the real price of Similac constructed from historical ads from the Chicago
Tribune, the Los Angeles Times and the Washington Post. For each year between the mid 1930s
and the mid 1980s we have monthly information on price, quantity and type (powder, concentrated
liquid, ready-to-feed) of Similac products on sale in drugstore chains in these three cities.
Since there are very few observations on ready-to-feed formula we only use information on the
price of powder and concentrated liquid Similac. These products did not di¤er in terms of their
chemical composition. The only di¤erences between powder and liquid formula were (and still
are) related to the proportion of water that needs to be added in order to obtain one ready-to-feed
liquid ounce of formula and in the di¤erential amount of time required to e¤ectively mix powder or
concentrated liquid with water. Since this di¤erence is negligible, we consider the two products as
equivalent in terms of their quality. In order to average their prices, we express them in the same
unit of measure (that is, one ready-to-feed liquid ounce of formula) using the following conversion
rules. According to the instructions reported on the current Similac labels, 25.6 ounces of powder
can make approximately 196 ‡uid ounces of formula whereas 13 ounces of concentrated liquid
Similac can make 26 ‡uid ounces of formula. Therefore, the price of one unit (i.e. one liquid
44
$0.10
$0.09
LA
$0.08
Washington
$0.07
Chicago
$0.06
$0.05
$0.04
$0.03
$0.02
$0.01
Jan-83
Jan-79
Jan-75
Jan-71
Jan-67
Jan-63
Jan-59
Jan-55
Jan-51
Jan-47
Jan-43
Jan-39
Jan-35
$0.00
Figure 13: Average Monthly Price of Similac
ounce) of formula in real terms is obtained by dividing the (real) price of the can by the quantity
of formula (in liquid ounces) that can be obtained by using the content of the can.
Figure 11 shows the monthly city-level data for the unit price of Similac thus obtained. Interestingly, there is little price variation across cities before 1970. As shown in the …gure, we do not
have information for each month/year. If the information for one year is missing we interpolate
prices across the two adjacent years. There is no record on the price of Similac in the Los Angeles
Times from July 1936 to March 1948 and in the Washington Post from October 1942 to May 1948.
Hence, for some of the early years our series is based on the price of Similac for the Chicago area
alone. For some years we also have information on the regular (non sale) price of the product.
However, this information is very limited and cannot be used to obtain a consistent price series.
Nonetheless, it is interesting to note that a 16 ounces can was often referred to as the ‘$1.25
Similac’and not by its weight. This seems to suggest that the non-sale price of the product was
$1.25 for a long time (from 1935 to the late 1940s/early 1950s). Over time we …nd more and more
ads of the ‘$1.25 Similac’ at discount prices suggesting that the price of the formula was closer
to its sale price in the early 1950s than it was in the mid 1930s. It follows that we are probably
underestimating the decline in the price of Similac over this period.
45
Over time the nutritional content of Similac has improved with the introduction of iron-forti…ed
formulas in 1959 and of the ready-to-feed version of the product in the 1970s. Since we are using
sale prices we actually have very few observations for these improved products. Hence we have
excluded them from our calculations. We also have data for Enfamil, a formula that became
available in the late 1950s/early 1960s. However, data on Enfamil are only available since 1961,
hence we have excluded these observations from our analysis. However, nothing would change if
we were to include them in our calculations.
7.7.2
Milk Modi…ers: Nestle’s and Mellin’s
We have also extended the price series backward by collecting the prices of the …rst-generation
of milk-based formulas (Mellin’s and Nestle’s) that were commercially introduced in the late
19th century. These formulas were milk modi…ers, that is, they were mixed in given proportions
to cow milk. The information collected from the ads, however, did not include quantities only
prices. We obtain estimates for the quantities of these products by using a variety of sources
- …gures from Apple (1987) and historical ads, labels and bottles sold on Ebay.38 Below we
describe our procedures for computing the sizes of Mellin’s and Nestle’s products. Since the
powdered formulas had to be mixed with milk (and water) in given proportions we add to our
calculations the price of cow milk. To this aim we use the series of retail price of “delivered”
‡uid milk (series 195 from the Statistical Abstract of the United States: Bicentennial Edition).
The price reported in this series is an order of magnitude higher than the one reported in the
wholesale price series from the NBER. However, the retail price is reasonable when compared
with a more recent series on the retail price of milk sold in stores (and not ‘delivered’ milk)
available from the University of Wisconsin Dairy Marketing and Risk Management Program
(http://future.aae.wisc.edu/data/monthly_values/by_area/307?tab=prices&grid=true) for the
period 1980-1997. Below we report the calculations that we used to obtain the price of one
liquid ounce of ‘ready to feed’formula.
Nestle’s Sizes: Nestle’s infant food came in di¤erent sizes:
1. The size sold for $0.5 at regular price would correspond to 1lb of powder formula. We …nd
this information from historical ads on Ebay.
2. The “hospital size” can of powder Nestle’s weighted 4.5lb. This information is reported in
Figure 3.3, Apple (1987).
There seem to be also additional, unknown, sizes of the Nestle’s cans. Since we do not have
this information we drop these price observations from our sample. Size and type may have
changed in the 1920s. Therefore, non-hospital size packages sold at a regular price of more than
$0.5 (essentially all non-hospital packages after about 1919) are excluded from the series.
Conversion factor: We use the following calculations in order to obtain the price of one
liquid ounce of ‘ready to feed’formula: 6 table spoons + 20 oz of cow’s milk + 15 oz water = 38oz
of liquid (where 2 table spoons are equal to 1 liquid oz). This information is taken from page 12
in the August 1929 issue of the Journal of the American Economic Association. The calculation
above assumes that 1 table spoon of powder is equal to 9 gr of powder, based on current package
descriptions (where, generally, 1 scoop = 9 gr, approximately). The conversion factor that we use
38
See http://americanhistory.si.edu/collections/object.cfm?key=35&objkey=110 for an example.
46
to go from table spoons to liquid oz is as follows: 1oz = 28.35 grams = 3.15 tbsp = 0.53 servings
of 6 tbsp.
Mellin’s Sizes: There were only two sizes of Mellin’s – small and large bottles. The large
bottle had a net weight of 10oz (Figure 5.6, Apple (1987)), an approximate volume of 16oz
(authors communication with ebay seller), and approximate dimension of 6” to 6 34 ” height and
3” diameter. The small bottle’s approximate dimensions are 5 12 ” height and 2 12 ” diameter
(authors communication with ebay seller). Based on dimensions, we can estimate that the small
bottle should contain 60% to 64% as much formula as the large bottle. If we use 60%, it’s net
weight is 6oz and it’s volume is 9.6oz.
Type: Data for Mellin’s do not report whether the product was sold in powdered or liquid
form. The mixing directions for Mellin’s formula call for use of “level tablespoons.” Combined
with information on types of formula generally available in the relevant time period, we assume
that Mellin sold only powder formula.
Conversion factor: We use the following calculations in order to obtain the price of 1 liquid
oz of ‘ready to feed’formula (assuming that the large size corresponds to a 16oz bottle and the
small one corresponds to a 9.6oz bottle): 6tbsp + 16oz cow’s milk + 12oz water = 31oz of liquid.
This information is taken from Figure 5.4 in Apple (1987). Since 6tbsp = 3 oz, by volume this
implies that 1oz of powder = 31/3 liquid oz of usable ready to use formula.
7.7.3
Additional Information on Breast Feeding Practices
Our data on changes in breast-feeding practices for children born between the early 1930s and
the early 1970s are from the 1965 National Fertility Study and the 1973 National Survey of
Family Growth (Cycle I) conducted by the National Center of Health Statistics (as reported in
Hirschman and Hendershot (1979) and Hirschman and Butler (1981).) The evidence on breastand bottle-feeding rates before 1930 is based on a series of studies conducted by the Children
Bureau for di¤erent geographical areas during the period 1917-1919 (see Apple, 1987, Table 9.1).
The evidence on trends in the use of commercially prepared formulas is mainly based on the
Ross Mother’s Survey that was conducted by Ross Laboratories in Ohio, the current producer of
Similac, from 1955 to the late 1980s.39
The data from Hirschman and Hendershot (1979) and Hirschman and Butler (1981) are based
on retrospective surveys. This might pose problems related to the precision of the information
especially for older cohorts of women. However, the numbers that we report are consistent with
evidence from hospital discharge records and, at least to our knowledge, represents the most
accurate description of trends in breast feeding over this period. The sporadic evidence from
alternative records (hospital discharge records and the Ross Mother’s survey,) although not extensive, consistently shows that by the early 1970s less than 25% of newborn babies were breast
fed (at hospital discharge or at 1 week.)
The study by Hirschman and Hendershot (1979) also present interesting evidence on how
breast feeding rates vary with indicators of social status over this period. They show that, for all
cohorts, college educated women are more likely to breast feed than women with lower levels of
educational attainment. However, statistically signi…cant di¤erentials in breast feeding incidence
by education do not extend to the duration of breast feeding. The relation between the incidence
of breast feeding and education has changed over time. For births occurring in 1950 or earlier, the
39
See Martinez and Nalezienski (1979).
47
variation in breast feeding rates by education was small. In the late 1950s, a U-shape relationship
emerged, with breast feeding more likely among women with the least or most years of education.
By the 1970s, breast feeding was least common among women with the lowest levels of education,
a pattern that persists to the year 2000.
7.8
Household Appliances
We use Gordon’s quality-adjusted Divisia price index for household appliances (Gordon, 1990)
rescaled by real wages as a measure of the time price of new general household technologies.
This price series is available from 1947 to 1984. In order to obtain a series starting in 1920
we extrapolate the quality-adjusted price index backward by applying to home durables the
procedure developed by Cummins and Violante (2002) to construct a quality-adjusted post-1984
price index for the capital goods that make up equipment and software. Their procedure is
based on the assumption that the speed of technological change for these goods can be measured
as the di¤erence between the growth rate of constant-quality consumption and the growth rate
of the good’s quality-adjusted price index. Since NIPA data on household durables are not
disaggregated by type of appliance we cannot perform the full-‡edged adjustment proposed in
Violante and Cummins but simply apply the relevant part of their procedure to our aggregate
series for household appliances. In our application we use the NIPA price index for kitchen and
other household appliances (NIPA Table 2.5.4, row 30) and Gordon’s Divisia price index for eight
household appliances. Both series are available for the period 1947-1984. Following Cummins
and Violante we use the pairs of price indexes over the entire period to estimate an econometric
model of Gordon’s quality adjusted price index (in logs) as function of a time trend, the current
value of the NIPA price index (in logs) and the growth rate of lagged GDP (from NIPA.) The
estimated quality bias implicit in the NIPA series is the coe¢ cient on the NIPA log price. We then
extrapolate the Gordon’s quality-adjusted price index backward by using the NIPA price series
for the pre-1947 period and our estimate of the quality bias. In our exercise we use the Gordon’s
quality-adjusted price index that does not include further ‘adjustments’ for energy e¢ ciency or
repair costs since these changes occurred post 1970.
We estimate a quality-adjustment of -3.04% per year between the two series over the 1947-1984
period. The …rst available year for the NIPA series is 1929. The NIPA price index for kitchen
and household appliances increased by 0.98% per year between 1929 and 1947. By combining this
information with the estimated quality adjustment we obtain an (estimated) exponential decline in
the quality-adjusted price index for household durables of 2.06% (0.98%-3.04%) per year between
1947 and 1929. Since we need to obtain a price series starting in 1920 we extrapolate this adjusted
price index backward by assuming that the rate of NIPA price change between 1920 and 1929 is
the same as the one observed between 1929 and 1947.
The appliance prices that we use for our calibration are as follows. From Cowan (1983) and
General Electric Catalogues, the cheapest model or refrigerators sold at $450 dollars in 1924,
whereas the latest model Frigidaire refrigerator sold for 714$ in 1922. The price of the most
recent model of Maytag electric washing machine was 165$ in 1922. The …rst information of the
price of a vacuum cleaner dates to 1947 when the most recent Hoover model sold for 249.50$.
To estimate q I =q G in section 4.1, for each appliance, we convert the …rst available price to 1920
dollars and we de‡ate it back to 1920 using the average rate of growth for the time price of home
durables.
48
year
1920
1930
1940
1950
1960
1970
Data
9%
14%
21%
27%
34%
47%
Model
year
1920
1930
1940
1950
1960
1970
Data
6%
10%
14%
27%
44%
55%
Model
year
1920
1930
1940
1950
1960
1970
Data
15
20
36
50
64
75
Model
year
1920
1930
1940
1950
1960
1970
Data
49
48
48
47
44
37
Model
year
1920
1930
1940
1950
1960
1970
Data
21%
21%
21%
25%
24%
28%
Model
9%
14%
23%
51%
77%
83%
7%
11%
14%
24%
47%
70%
14%
28%
73%
82%
90%
90%
47
49
48
43
33
29
30%
15%
15%
23%
38%
50%
Table 6: Transition and experiments
LFP of Young Married Women
Experiment 1 Experiment 2 Experiment 3 Experiment 4 Experiment 5
Data
9%
9%
9%
9%
9%
14%
14%
14%
7%
5%
7%
26%
22%
22%
11%
10%
15%
42%
25%
38%
18%
24%
37%
52%
30%
45%
23%
42%
61%
63%
29%
33%
20%
58%
75%
77%
LFP of Old Married Women
Experiment 1 Experiment 2 Experiment 3 Experiment 4 Experiment 5
Data
7%
7%
7%
7%
7%
6
11%
11%
11%
11%
11%
7
11%
9%
9%
14%
15%
8
9%
8%
9%
24%
27%
11
11%
8%
13%
44%
44%
17
12%
8%
8%
66%
68%
25
Adoption of new infant good technology
Experiment 1 Experiment 2 Experiment 3 Experiment 4 Experiment 5
Data
14%
14%
10%
10%
14%
7
8%
28%
28%
8%
16%
21
8%
73%
69%
11%
62%
41
8%
82%
82%
11%
80%
63
8%
90%
90%
11%
90%
82
5%
90%
90%
11%
87%
93
Married Women's Home Hours
Experiment 1 Experiment 2 Experiment 3 Experiment 4 Experiment 5
Data
47
47
47
47
47
4
48
49
49
48
48
4
49
49
47
46
46
4
49
48
48
43
44
6
49
47
46
41
39
9
49
49
47
33
29
10
F/M Earnings
Experiment 1 Experiment 2 Experiment 3 Experiment 4 Experiment 5
30%
25%
16%
14%
13%
13%
30%
15%
11%
16%
17%
12%
30%
15%
11%
11%
13%
13%
30%
22%
35%
32%
30%
42%
30%
19%
19%
21%
31%
47%
Model
16%
20%
37%
63%
87%
94%
Model
4%
2%
5%
13%
37%
47%
Model
9%
9%
15%
27%
54%
71%
Model
7
7
7
7
8
9
LFP of Young Married Women when "Old"
Experiment 1 Experiment 2 Experiment 3 Experiment 4 Experiment 5
16%
14%
11%
15%
16%
14%
16%
11%
10%
10%
10%
10%
16%
11%
11%
10%
10%
10%
16%
20%
37%
64%
82%
91%
16%
21%
42%
64%
82%
93%
Women's Investment in Market Skills
Experiment 1 Experiment 2 Experiment 3 Experiment 4 Experiment 5
4%
2%
1%
4%
4%
2%
4%
2%
1%
4%
4%
2%
4%
2%
1%
4%
7%
4%
4%
2%
5%
14%
20%
36%
4%
2%
5%
11%
20%
51%
Adoption of new general household technology
Experiment 1 Experiment 2 Experiment 3 Experiment 4 Experiment 5
9%
9%
9%
9%
9%
9%
9%
9%
9%
9%
9%
9%
9%
9%
9%
9%
9%
9%
9%
9%
15%
27%
51%
70%
9%
9%
15%
27%
51%
71%
Men's Home Hours
Experiment 1 Experiment 2 Experiment 3 Experiment 4 Experiment 5
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
8
7
7
7
7
8
8
9
7
7
7
7
7
9
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