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 0.5 Labo or Supply 0.45 0.4 0.35 0.3 0.25 0.2 1940 1950 1960 1970 1980 Women 20-32 Women 33-60
Fertility by Age in the U.S.: 300 rth Rate Bi 250 200 150 100 50 0 1940 1950 1960 1970 1980 Women 15-19 Women 20-24 Women 25-29 Women 30-34 Women 35-39 Women 40-44
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(c j )+σ xi log(x j ) ] + σ n log(n). j=1 Budget constraint: c j + a j+1 =(1+r j )a j + wj m e m j + w f j ef j l j. The female time constraint: x j = h κb j φ(n y j )ψ l j z j.
The Female Labor Market: Labor supply is discrete: l j {0, 1}. Supply decision on the extensive margin. Fixed cost z j {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 σ xi.
Endogenous Experience: Initial experience normalized to one for both sexes: e m 1 = ef 1 =1. Labor market experience evolves according to: e m j+1 =(1 + η m )e m j, e f j+1 =(1 + η fl j ν(1 l j ))e f j. 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: ( Y t = A t Kt α θ(l F t ) ρ +(1 θ)(l M t ) ρ) 1 α ρ. 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 A t 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: η m = η f =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: b j =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 σ n, min(σ x ), max(σ x ), 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: σ n =1.52, σ x U(0.98, 1.23), z =0.8.
Labor Force Participation by Age in Steady State: 1 Steady State Labor Force Participation Rate 0.8 0.6 0.4 0.2 0 20 30 40 50 60 70 Age
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 3.2 Total Fertility Rate 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 3.6 Model Data 3.4 3.2 Total Fertility Rate 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 3 Completed Fertility Rate 2.8 2.6 2.4 2.2 2 1910 1920 1930 1940 1950 1960
Cohort Fertility Rate in Model and Data: 3.2 Model Data 3 Completed Fertility Rate 2.8 2.6 2.4 2.2 2 1910 1920 1930 1940 1950 1960
Labor Force Participation Profile: 1 Steady State Labor Force Participation Rate 0.8 0.6 0.4 0.2 0 20 30 40 50 60 70 Age
Labor Force Participation Profile: 1 Steady State Cohort Born in 1905 Labor Force Participation Rate 0.8 0.6 0.4 0.2 0 20 30 40 50 60 70 Age
Labor Force Participation Profile: 1 Steady State Cohort Born in 1905 Cohort Born in 1925 Labor Force Participation Rate 0.8 0.6 0.4 0.2 0 20 30 40 50 60 70 Age
Average Age at First Birth in Model: 1 Average Age at First Birth (Deviation from 1940) 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 0.5 0 0.5 1 1.5 Model Data 2 1940 1945 1950 1955 1960 1965 1970 1975 1980
Labor Force Participation over Time in Model: LFP 20 32 relative to 1940 0.15 0.1 0.05 0 0.05 0.1 1940 1945 1950 1955 1960 1965 1970 1975 1980 LFP 33 60 relative to 1940 0.2 0.15 0.1 0.05 0 0.05 1940 1945 1950 1955 1960 1965 1970 1975 1980
Labor Force Participation over Time in Model and Data: LFP 20 32 relative to 1940 0.15 0.1 0.05 0 0.05 0.1 Model Data 1940 1945 1950 1955 1960 1965 1970 1975 1980 LFP 33 60 relative to 1940 0.2 0.15 0.1 0.05 0 Model Data 0.05 1940 1945 1950 1955 1960 1965 1970 1975 1980
The Gender Gap over Time in Model: Gender Gap, Overall 0.74 0.72 0.7 0.68 0.66 0.64 1940 1945 1950 1955 1960 1965 1970 1975 1980 Gender Gap, 20 24 0.86 0.85 0.84 0.83 0.82 0.81 1940 1945 1950 1955 1960 1965 1970 1975 1980
The Gender Gap over Time in Model and Data: Gender Gap, Overall 0.74 0.72 0.7 0.68 0.66 Model Data 0.64 1940 1945 1950 1955 1960 1965 1970 1975 1980 Gender Gap, 20 24 0.86 0.85 0.84 0.83 0.82 Model Data 0.81 1940 1945 1950 1955 1960 1965 1970 1975 1980
Sensitivity Analysis: Baseline 3 2.9 2.8 Completed Fertility Rate 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 2.8 Completed Fertility Rate 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2 Baseline Dispersed Leisure Taste High Reentry Cost 1910 1920 1930 1940 1950 1960
Sensitivity Analysis: Higher LFP Target 3 2.9 2.8 Completed Fertility Rate 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2 Baseline Dispersed Leisure Taste High Reentry Cost 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 3.00 250 2.50 2.00 United States Australia New Zealand Canada 1.50 1910 1920 1930 1940 1950 1960
The Baby Boom in Neutral Countries: 4.00 3.50 3.00 250 2.50 2.00 United States Sweden Switzerland Spain 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.