Fertility Theories: Can They Explain the Negative Fertility-Income Relationship? Larry Jones1

Alice Schoonbroodt2 1 University 2 University

Michèle Tertilt3

of Minnesota

of Southampton

3 Stanford

University

University of Texas at Austin April 2009

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Motivation I

Income and fertility I

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Fertility decline over time (demographic transition), often thought to be related to growing incomes. Fertility and GDP negatively related across countries. Cross-section: poorer people have more children.

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Large literature on understanding demographic transition (increasing returns to schooling, mortality decline, technological progress, . . . ), but still no consensus.

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Separate theories of cross-section.

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Are “time series” and cross-section connected? (If so, should focus on theories that can get both.)

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Today’s Remaining Agenda I

Data on fertility-income relationship over time (Jones and Tertilt 2007). I I

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Find a robust negative relationship over 150 years. Consecutive cross-sections look like they lie on one overall curve.

New look at theories of relationship btw income and fertility (Jones, Schoonbroodt and Tertilt 2008). I

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Most theories of demographic transition have little to say about cross-section. Weaknesses of existing micro theories. Taste for life-style – an alternative? (but has nothing to say about time series)

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The Data in Jones and Tertilt (2007) I

IPUMS: US Census data (1% public use sample) on Fertility, Occupation, Income (partial), . . .

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CEB: “How many children have you had in your life?” (Not including stillbirths, not asked to unmarrieds for many census years . . . ) - what age should we use?

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Asked in 1900 US census first, and then in most census years up to and including 1990 (not 2000).

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Measures of economic well-being: Occupation data from 1900, Education data from 1940, Current years income data since 1950.

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Actual Data Used Cohort label 1828 1838 1848 1858 1868 1878 1888 1898 1908 1918 1928 1938 1948 1958

Actual cohorts 1826-1830 1836-1840 1846-1850 1856-1860 1866-1870 1876-1880 1886-1890 1996-1900 1906-1910 1916-1920 1926-1930 1936-1940 1946-1950 1956-1960

Census year 1900 1900 1900 1900 1910 1940 1940 1940 1950 1960 1970 1980 1990 1990

Age 70-74 60-64 50-54 40-44 40-44 60-64 50-54 40-44 40-44 40-44 40-44 40-44 40-44 30-34

CEB 5.5861 5.4942 5.3561 4.9002 4.4952 3.2457 3.1504 2.8222 2.3019 2.5939 3.1074 3.0104 2.2160 1.7991

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Caveats/Questions I

Data Quality - Particulary Birth Cohorts from early on?

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They use CEB of 40-50 yr old women, sometimes older. Mortality bias?

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Occupation as a measure of Economic Well-Being?

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VS. what alternative?

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Other selection issues? (currently married, husband with valid occupation)

Useful to do more work on these.

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Related Empirical Literature I

Large empirical literature on fertility.

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Most studies focus on either time series or cross section.

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“Consensus” from cross-sectional studies: fertility is negatively related to women’s income, and little correlation with male earnings (e.g. Borg 1979, Schultz 1990, Heckman 1990). Studies suffer from lack of wage information. Identification often from cohort variation.

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Some studies at business cycle frequency (e.g. Simon 1969, Butz and Ward 1979): switch from pro-cyclical to counter-cyclical fertility?

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Cross-country studies: negative relationship between income and fertility (e.g. Docquier 2004, Manuelli and Seshadri 2008).

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Background: Fertility Transition 6 5.5

CEB TFR CEB27

5

Number of Children

4.5 4 3.5 3 2.5 2 1.5 1 1800

1820

1840

1860

1880 1900 1920 Birth Cohort / Actual Year

1940

1960

1980

2000

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Fertility and Economic Wealth Occupational Income: Measure of husband’s life-time income I

Occupations recorded in all Censuses. Incomes not until 1950.

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Most women have no recorded occupations (in early time period).

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OIS constructed as Median Income for a given Occupation in 1950.

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Adjust OIS to account for GDP p.c. growth.

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Movement over time to higher income occupations.

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Adjust for trend growth so that exogenous component PLUS occupation change = 2% ↑ per year.

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Cross Sections: Fertility and Occ. Income Figure 3: CEB vs. Occupational Income in 2000 Dollars 6.5 Birth Cohort

6.0

1828 1848 1868 1888 1908 1928 1948

Children ever Born

5.5 5.0 4.5 4.0

1838 1858 1878 1898 1918 1938 1958

3.5 3.0 2.5 2.0 1.5 0

20,000

40,000

60,000

80,000

Occupational Income in 2000 Dollars

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Fertility and Occ. Income: Transformed Data 2.0

Birth Cohort

1828 1848 1868 1888 1908 1928 1948 Reg

Log of Children ever Born

1.8

1.6

1.4

1.2

1838 1858 1878 1898 1918 1938 1958

1.0

0.8

0.6

0.4 7.7

8.2

8.7

9.2

9.7

10.2

10.7

11.2

Log of Occupational Income in 2000 Dollars

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Income Elasticity I

Overall estimate: -0.38;

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Fairly stable over time, but not perfect: Birth Cohort 1828 1848 1868 1898 1918 1938 1958

Income Elasticity -0.33 -0.32 -0.34 -0.50 -0.25 -0.19 -0.22

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Accounting Exercise I

CEB in 1928 = 5.6, in 1958 = 1.8.

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OI in 1828 = $4,154;

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OI in 1958 = $54,517;

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Overall Increase = $54,517/$4,154 about 13;

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Elasticity from 1828 cohort = -0.33;

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Predicted fall is to CEB = 2.4 in 1958;

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Actual CEB in 1958 is 1.8;

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84% of fall from change in OI.

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Data Summary I

Negative fertility-income relationship for 150 years of birth cohorts.

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Fertility is negatively related to male income at time where (most) women did not work in the market.

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Cross-sectional data and time series lie almost on same curve (increasing incomes “explain” 84% of fertility decline)

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Overall income elasticity of fertility ≈ -0.38

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Where does this take us for different theories . . . ?

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Which Theories are Consistent with Picture?

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Theories of Demographic Transition Most theories of the demographic transition rely on change in technology/prices/institutions over time and thus have little to say about the cross-section: I

Demographers: decline in infant and child mortality & “process of development ” (also Jones and Schoonbroodt 2008)

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Technological progress (Greenwood and Seshadri 2002)

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Rising demand for human capital (during second phase of Industrial Revolution) (Galor and Weil 1999, 2000)

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Education and child labor policies (Doepke 2004)

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Old age security hypothesis (Caldwell 1976, Boldrin, de Nardi and Jones 2005)

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What about Micro Theories of Fertility? I

Let’s collect some ideas

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Let’s try to capture those ideas in simple examples

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Micro Theories of Fertility and Income Not so obvious: higher income → spend more on all goods, i.e. more kids. 1. Opportunity cost of time (Mincer 1963, Becker 1965, Willis 1973) I I I

need high elasticity of substitution (or non-homotheticity) theory does not work if child-care can be purchased in fact, need father’s time (or assortative matching)

2. Q/Q trade-off (e.g. Becker and Tomes 1976) I

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Specific assumptions on child quality production function (need quality elasticity to increase with inputs). parental time crucial

3. Heterogeneity in taste for kids (not much theory yet)

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Which Micro Theories also get Time Series?

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Heterogeneity in Taste for Children I

People differ in relative importance of consumption vs. procreation (religion?)

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People with taste for consumption goods invest more in human capital to increase their future wage. Same people also have fewer children.

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People with taste for procreation invest less in human capital and thus have a lower wage. Same people also have more children.

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Ultimately it is the relative desire for children that drives wage differences.

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No assumptions on elasticity of substitution are needed.

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Theory works even when child-care can be outsourced.

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Taste for Children – An Example

max

αc log(c) + αn log(n)

s. t.

ls + lw + bn ≤ 1

c,n,lw ,ls

w = als c ≤ wlw Assume: People differ in αc or αn

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Example Continued n∗ =

1 b(1 + 2 ααcn )

w∗ =

αn αc

a +2

dn∗ /d αn > 0 and dw ∗ /d αn < 0 implies: dn∗ /dw ∗ < 0. 1 2 [1 − w ∗ ] b a ∗ ∗ Note: dn /dw < 0 does not depend on income and substitution effects. n∗ =

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Taste Theory – Time Series? 8 low TFP, low cost medium TFP, medium cost high TFP, high cost highest TFP, highest cost

7

Fertility

6 5 4 3 2 1 0 0

1

2

3

4 Wage

5

6

7

8 4

x 10

Time series: increase in child cost. Why??? 23 / 35

Quantity-Quality Tradeoff

max

αc log c + αn log n + αq log q

s. t.

c + sn ≤ w (1 − bn)

c,n,q,s

q = f (s) 

αn αc +αn

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n∗ =

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n∗ ↓ in w iff



s∗ w

1 ∗ b+ sw

↑ in w . ∂



sf 0 (s) f (s)



> 0.

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Which happens iff

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Most functional forms: constant or decreasing elasticity.

∂s

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Special Case (Becker and Tomes 1976) f (s) = d0 + d1 s n = ∗

αn −αq αc +αn d0 b − wd 1

d0 − wd ∂n/∂w 1 ε= = d0 n/w b − wd 1

Note: as w → ∞, ε = 0. Not consistent with stable elasticity.

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Quantity-Quality Tradeoff 6 low wages medium wages and d0 up 5

high wages + d0 even higher highest wages + d up

Fertility

1

4

3

2 0

1

2

3

4 Wage

5

6

7

8 4

x 10

But why should quality production parameters change systematically? 26 / 35

Price of Time Theory: Homothetic Preferences

max c,n

s.t.

c 1−σ − 1 n1−σ − 1 + αn 1−σ 1−σ c ≤ (1 − bn)w αc

n∗ = 

1 1/σ 1−σ αc b1 w σ +b αn

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Price of Time Theory: Homothetic Preferences 7 low wages medium wages high wages highest wages

6

Fertility

5 4 3 2 1 0

1

2

3

4 Wage

5

6

7

8 4

x 10

Only decreasing if σ < 1. 28 / 35

Price of Time Theory: Non-homoth. Prefs.

max c,n

s.t.

n1−σ − 1 1−σ c ≤ (1 − b1 n)w αc c + αn



αn n = αc b1 ∗

1/σ

(1)

w −1/σ

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Price of Time Theory: Non-hom. Prefs. (σ = 3) 6 low wage medium wage high wage highest wage

Fertility

5

4

3

2

1 0

1

2

3

4 Wage

5

6

7

8 4

x 10

Income elasticity of demand for children = -0.333 works well! 30 / 35

Asking for More: Couples I

In data: fertility decreasing in male wages.

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Which theories can explain this?

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Price of time: need father’s time to be crucial for child-rearing or assortative mating in productivities.

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Preference heterogeneity: I I I

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can get result even if father’s time not necessary. Needed: spouses match along preference lines. Why? Couples with a high desire for consumption goods: both invest more in schooling → higher wage. He will enjoy less leisure (work more) and she will spend less time with children (work more).

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Asking for More: Nannies • Fairly obvious that raising children takes time. • Whose time? • Many historical examples of “outsourcing” childcare: nannies, aupair, wet nurses, grand-mothers, neighbors. • But then theories imply that higher wage people should have more children. • What’s missing? Next: Taste theory can be extended to allow for nannies, price of time theories cannot!

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Comparison Ability vs. Taste Heterogeneity Assumptions and Robustness

Ability

Tastes

Elasticity (c,n)

σ<1

σ irrelevant

Parental time

crucial

not necessary

2-parent families

corr (wm , wf ) > 0 or complementarities in home production

need matching along preference lines

Can also get dq/dw > 0?

yes, plus may help relax σ assumption

depends on details of preference heterogeneity

Time series?

yes

no

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Summary I

dn/dw < 0 robust fact over last 150 years in U.S.

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Even at time when women did not work in the market.

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Income elasticity of fertility ≈ -0.38.

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Most theories of demographic transition cannot account for cross section.

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Not all theories of cross-section have time series implications.

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Seems to work best: Price of time theory.

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Directions for Future Research I

Needed: quantitative theory that can account for time series and cross section of fertility.

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Price of time theory most promising?? → Full dynamic model? → but recall: fertility negatively related to male income. → Assortative mating? Male time input into child-rearing?

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Almost all theories rely on parental time being a non-substitutable input → need for new theories.

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Mechanism for time series and cross-section necessarily related?

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Ways to test taste vs. ability driven theories empirically?

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