The Baby Boom and World War II:
A Macroeconomic Analysis
Matthias Doepke, Moshe Hazan, and Yishay Maoz
• The baby boom started right after World War II.
• Is there a relation between the two?
The Total Fertility Rate in the United States:
4
3
2
1
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
The Traditional View Versus Our View:
• Tradition: Baby boom is too big and lasts too long to be
explained by the war.
• This argument applies only to “catch up” fertility.
• Our view: The war mattered because it resulted in a
large, temporary demand shock for female labor.
• This shock had an asymmetric effect on older and younger
women.
The Mechanism:
• World War II draws women into the labor market. The
war generation gathers labor market experience.
• Many war-generation women stay at work after the war,
raising female labor force participation.
• Higher effective labor supply induces young women NOT
to enter the labor market and to have children instead.
• Crowding-out effect reverses when war generation
retires from the labor market.
Labor Supply of Young and Old Women in the U.S.:
0.6
0.55
Labo
or Supply
0.5
0.45
0.4
Women 20-32
0.35
Women 33-60
0.3
0.25
0.2
1940
1950
1960
1970
1980
Fertility by Age in the U.S.:
300
Birth Rate
250
Women 15-19
200
Women 20-24
150
Women 25-29
Women 30-34
100
Women 35-39
50
Women 40-44
0
1940
1950
1960
1970
1980
Outline:
• Existing theories of the baby boom.
• Model and calibration.
• Effect of the World War II shock.
• The baby boom in other countries.
Existing Theories
• Easterlin (1961):
The “relative income hypothesis.”
People growing up in the Great Depression had low
material aspirations, and had lots of children instead.
• Greenwood, Seshadri, Vandenbroucke (2005):
The “household technology hypothesis.”
Household technology became more productive from
the 1930s to the 1950s, which lowered the cost of
having children.
Some Problems:
• “Relative income hypothesis:”
• Many mothers of the baby boom were born after the
Great Depression.
• Fertility highest in 20-24 age group; fertility peaks
1957.
• The “household technology hypothesis:”
• Difficult to quantify.
• The abrupt end of the baby boom cannot be accounted
for.
• Fertility should rise for all age groups.
Model
• Overlapping generations of households consisting of a
man and a woman.
• Period corresponds to 2.5 years. People turn adult at
age 20, retire at 60, and live until age 70.
• Women can have one child per period until age 32.5.
• Men supply labor inelastically.
• When not having children, women decide whether to
enter the labor market.
• Endogenous accumulation of experience.
Preferences and Constraints:
• Utility:
U=
T
β
j−1
log(cj ) + σxi log(xj ) + σn log(n).
j=1
• Budget constraint:
f f
cj + aj+1 = (1 + rj )aj + wjmem
+
w
j
j ej lj .
• The female time constraint:
xj = h − κbj − φ(nyj )ψ − lj − zj .
The Female Labor Market:
• Labor supply is discrete: lj ∈ {0, 1}. Supply decision
on the extensive margin.
• Fixed cost zj ∈ {0, 1} of re-entering the labor market
captures adjustment costs and, possibly, cultural norms
opposed to working mothers.
• Implications:
• All women enter initially since they don’t have
children yet.
• After having children, most women don’t resume work
because of scarcity of time and adjustment cost.
• Heterogeneity in labor supply and fertility due to
differences in leisure weight σxi.
Endogenous Experience:
• Initial experience normalized to one for both sexes:
f
=
e
em
1
1 = 1.
• Labor market experience evolves according to:
m
em
j+1 =(1 + ηm )ej ,
efj+1 =(1 + ηf lj − ν(1 − lj ))efj .
• Implies that gender gap is larger at older ages.
Fertility Decisions:
• It is optimal to have children as late as possible to
extend the initial earnings period.
• Thus, exit from labor market depends on desired
number of children.
Technology:
• Production function with limited substitutability between
male and female labor:
F ρ
1−α
α
M ρ ρ
.
Yt = AtKt θ(Lt ) + (1 − θ)(Lt )
• Aggregate stock of capital is sum of households’ assets.
• Aggregate labor supply is sum of households’ efficiency
units of labor.
• Capital depreciates at constant rate δ.
• Productivity At grows at constant rate γ.
Calibration
• Overall strategy:
• Match technology to U.S. long-run growth
observations.
• Match fertility rate, female labor force participation,
experience accumulation, and relative female wages
to U.S. data in 1940.
• Choose fixed cost of labor-market reentry to match
old female LFP in 1950.
Standard Macro Targets:
• Capital share α = 0.3.
• TFP growth matched to 1.8 percent growth in GDP/capita
per year.
• Depreciation rate 4.7 percent per year.
• Return on capital 6.9 percent per year (pins down
discount factor: β = 0.91).
• Full-time work takes one-third of available time: h = 3.
Experience Accumulation and Cost of Children:
• Return to experience matches male experience profile
in 1940 Census data.
• Depreciation of female experience matches relative
earnings of women at 20 and 33.
• Resulting parameters: ηm = ηf = 0.625, ν = 0.0196.
• Haveman and Wolfe (1995): Total private cost of a child
(including forgone earnings) 38 percent of GDP/capita.
• Estimate additional cost of young children and returns
to scale from having children from time use data.
• Resulting parameters: bj = 0.23, φ = 0.46, ψ = 0.33.
Male versus Female Labor:
• Elasticity of substitution between male and female
labor: 2.9 (Acemoglu, Autor, and Lyle 2004).
• Ratio of average female to male wages in 1940 Census:
0.66.
• Resulting parameters: ρ = 0.65, θ = 0.34.
Utility Weights and Reentry Cost:
• Targets for four remaining parameters σn, min(σx),
max(σx), z:
• Completed fertility rate of 1911-1915 cohort: 2.4.
(i.e., model families have either 2 or 3 children).
• Labor force participation rate of married women 33
and older in 1940: 13 percent.
• Labor force participation rate of married women 33
and older in 1950: 18 percent.
• Change in labor force participation rate of women 20
to 32 in 1940–1950: -9 percent.
• Sensitivity analysis for dispersion of leisure taste.
• Baseline parameters:
σn = 1.52, σx ∼ U (0.98, 1.23), z = 0.8.
Labor Force Participation by Age in Steady State:
Steady State
Labor Force Participation Rate
1
0.8
0.6
0.4
0.2
0
20
30
40
50
Age
60
70
The World War II Shock:
• Shock is modeled as a sudden, large decrease in male
labor supply (-30 percent) as well as a one-time decline
in the fixed cost e.
• Shock increases labor force participation of older women.
• Size of shock matched to increase in total female
participation in war period.
• Due to fixed cost of entry, increase in participation
persists after the war and lowers female wages.
• Result: Young women after the war experience
worsened labor market conditions, exit earlier, and have
another child.
Total Fertility Rate in Model:
3.8
3.6
3.4
Total Fertility Rate
3.2
3
2.8
2.6
2.4
2.2
2
1.8
1940
1945
1950
1955
1960
1965
1970
1975
1980
Total Fertility Rate in Model and Data:
3.8
Model
Data
3.6
3.4
Total Fertility Rate
3.2
3
2.8
2.6
2.4
2.2
2
1.8
1940
1945
1950
1955
1960
1965
1970
1975
1980
Cohort Fertility Rate in Model:
3.2
Completed Fertility Rate
3
2.8
2.6
2.4
2.2
2
1910
1920
1930
1940
1950
1960
Cohort Fertility Rate in Model and Data:
Model
Data
3.2
Completed Fertility Rate
3
2.8
2.6
2.4
2.2
2
1910
1920
1930
1940
1950
1960
Labor Force Participation Profile:
Steady State
Labor Force Participation Rate
1
0.8
0.6
0.4
0.2
0
20
30
40
50
Age
60
70
Labor Force Participation Profile:
Steady State
Cohort Born in 1905
Labor Force Participation Rate
1
0.8
0.6
0.4
0.2
0
20
30
40
50
Age
60
70
Labor Force Participation Profile:
Steady State
Cohort Born in 1905
Cohort Born in 1925
Labor Force Participation Rate
1
0.8
0.6
0.4
0.2
0
20
30
40
50
Age
60
70
Average Age at First Birth in Model:
Average Age at First Birth (Deviation from 1940)
1
0.5
0
−0.5
−1
−1.5
−2
1940
1945
1950
1955
1960
1965
1970
1975
1980
Average Age at First Birth in Model and Data:
Average Age at First Birth (Deviation from 1940)
1
Model
Data
0.5
0
−0.5
−1
−1.5
−2
1940
1945
1950
1955
1960
1965
1970
1975
1980
LFP 33−60 relative to 1940
LFP 20−32 relative to 1940
Labor Force Participation over Time in Model:
0.15
0.1
0.05
0
−0.05
−0.1
1940
1945
1950
1955
1960
1965
1970
1975
1980
1945
1950
1955
1960
1965
1970
1975
1980
0.2
0.15
0.1
0.05
0
−0.05
1940
LFP 33−60 relative to 1940
LFP 20−32 relative to 1940
Labor Force Participation over Time in Model and Data:
0.15
0.1
Model
Data
0.05
0
−0.05
−0.1
1940
0.2
1945
1950
1955
1960
1965
1970
1975
1980
1955
1960
1965
1970
1975
1980
Model
Data
0.15
0.1
0.05
0
−0.05
1940
1945
1950
Gender Gap, Overall
The Gender Gap over Time in Model:
0.74
0.72
0.7
0.68
0.66
Gender Gap, 20−24
0.64
1940
1945
1950
1955
1960
1965
1970
1975
1980
1945
1950
1955
1960
1965
1970
1975
1980
0.86
0.85
0.84
0.83
0.82
0.81
1940
Gender Gap, Overall
The Gender Gap over Time in Model and Data:
0.74
0.72
0.7
0.68
0.66
0.64
1940
Gender Gap, 20−24
Model
Data
1945
1950
1955
1960
1965
1970
1975
1980
0.86
0.85
0.84
0.83
Model
Data
0.82
0.81
1940
1945
1950
1955
1960
1965
1970
1975
1980
Sensitivity Analysis: Baseline
3
2.9
Completed Fertility Rate
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2
1910
1920
1930
1940
1950
1960
Sensitivity Analysis: Dispersed Leisure Taste
3
2.9
Completed Fertility Rate
2.8
2.7
2.6
2.5
2.4
2.3
2.2
Baseline
Dispersed Leisure Taste
High Reentry Cost
2.1
2
1910
1920
1930
1940
1950
1960
Sensitivity Analysis: Higher LFP Target
3
2.9
Completed Fertility Rate
2.8
2.7
2.6
2.5
2.4
2.3
2.2
Baseline
Dispersed Leisure Taste
High Reentry Cost
2.1
2
1910
1920
1930
1940
1950
1960
The Baby Boom in other Countries
• Most industrialized countries experienced a post-war baby
boom.
• Size and duration of boom varies substantially.
• Compare two groups:
• Countries with similar war experience to U.S.:
Canada, Australia, New Zealand.
• Neutral countries:
Sweden, Switzerland, Portugal, Spain.
The Baby Boom in Countries Similar to U.S.:
4.00
3.50
United States
3.00
Australia
2 50
2.50
New Zealand
Canada
2.00
1.50
1910
1920
1930
1940
1950
1960
The Baby Boom in Neutral Countries:
4.00
3.50
United States
3.00
Sweden
Switzerland
2 50
2.50
Spain
2.00
Portugal
1.50
1910
1920
1930
1940
1950
1960
Summary
• If labor supply is persistent, one-time demand shock
leads to long-lived, asymmetric effects on younger and
older workers.
• World War II was a huge demand shock for
female labor.
• Qualitatively, cohort-specific participation rates,
wages, fertility, and the timing of births behave as they
should after such a shock.
• Quantitative exercise suggests that mechanism can
account for a major part of the baby boom and
baby bust.
The Effect of Increased Participation on Wages:
• Analyzed by Acemoglu, Autor, and Lyle (2004).
• Use of mobilization rates as a source of exogenous
variation.
• Main findings:
• Mobilization led to increased female labor supply
after the war.
• 10 percent increase in female employment lowers
female wages by 7 to 11 percent.
• 10 percent increase in female employment lowers male
wages by 3 to 4 percent.