### Class 7 Fertilityx

```Economics 2333: Topic #7,
Fertility
Professor Robert A. Margo
Spring 2014
Outline
• Demographic Basics. The Demographic
Transition and Long-Term Trends in Fertility
• General Explanations
• Jones and Tertlit. Bailey, et. al.
• Baby Boom: Greenwood, et al vs. Bailey and
Collins. Other Explanations.
Demographic Basics (1)
• G = B – D + M. G = growth rate of population, B = birth
rate, D = death rate, M = net migration.
• These are “period” rates. B = weighted average of age
specific fertility rates (women) x share of women of
relevant ages in the population.
• If we sum the period age-specific fertility rates = period
TFR. Cohort vs. Period. Cohort = TFR of women born
in year t.
• TFR = [(L – F)/S + 1] x β. Β = proportion of women ever
bearing a child, L = age at last birth, F = first birth, S =
spacing interval. L, F, S are bounded (fuzzy) by human
physiology.
Demographic Basics (2)
• In C19 (but not “today”) fertility is very closely tied to marriage.
Age at first birth very close to age at first marriage, and proportion
ever bearing a child is approximately proportion ever marrying.
• Sources of historical fertility information: state and federal
censuses, genealogies, birth registration.
• US federal census records marital status first in 1880, CEB/CS not
until C20. Some state censuses have information earlier than this.
• Published TFR rates in Historical Statistics begin in 1800 BUT C19,
especially ante-bellum are extrapolated on child-woman ratios.
Child-woman ratio: # of children ages 0-5/women ages 15-44.
• Leading authority is Michael Haines, see his various essays on
population in Historical Statistics of the US.
Demographic Transition
• Demographic transition move from high
fertility/mortality to low fertility/mortality.
• Modern demographic transition: mortality
(usually infant/child) declines first, followed by
fertility. Many macro implications.
• US demographic transition is NOT like this.
Fertility seems to decline continuously from day
#1, with exception of baby boom.
• Recent work by J. David Hacker (Demography
2003) challenges traditional views on US fertility
decline in C19.
Hacker Estimates
• Recent work by J. David Hacker is changing views on US fertility
decline in C19.
• Hacker has prepared new estimates of crude birth rates beginning
• Argues against a decline in marital fertility in the first half of the
C19. If there was decrease in TFR, came about because of
decreases in proportion marrying and/or age at first marriage.
• Own-child methods using IPUMS suggest decreases after 1840.
Mean age at first birth increases over C19, some decline in marital
fertility after 1850 but less perhaps than previously thought.
Decline in marital fertility appears in 1860s, suggest Civil War effect.
• Suggests work in economic history should focus more on timing of
age of first birth (marriage).
Explaining Long-Term Fertility Decline
in US
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Easterlin relative income hypothesis. Applied to frontier/settled areas. Also to baby boom.
Very difficult to assess empirically.
Becker quantity-quality model. As incomes rise parents “demand” higher quality children
where quality is investment in human capital. Depending on size of quality effect, quantity
can be negatively correlated with income. Minimal investigation for C19.
Child default/financial markets: David/Sundstrom vs. Ransom/Sutch. Steckel: antebellum
fertility rates in cross-section are negatively correlated with banks per capita.
Economic growth increases opportunity cost of time input into child-rearing. Clearly true for
C20 as a secular trend. Relevance for C19 not yet investigated in a serious way. Closely
related to Greenwood, et. al.; return to this point later in lecture.
Decreases in infant and maternal mortality. Infant mortality does not appear to decrease
much until after 1880. Maternal mortality may have different effects in short vs. long run.
Supply side: changes in contraceptive access. Until recently, thought to be relatively
unimportant but this has been changed by various papers by Martha Bailey.
Jones and Tertlit (2006)
• Primary focus is on the empirical relationship
(negative) between fertility and “occupational income”
(OI) of male household heads, married to women ages
40-49.
• Uses 1900-1990 census data on CEB. C19 results are
back-cast from 1900 age-specific TFRs, i.e., women
ages 70-74 in 1900 yield data point on CEB for 1826-30
birth cohort.
• Match each women to OI of her husband.
• Important issue: back-casted CEB is affected by
maternal and infant mortality. “Forward-projected”
CEB ≤ back-casted CEB because of maternal mortality.
Main Findings of Jones and Tertlit
(2006)
Main Findings, Continued
Bailey, Guldi, and Hershbein
• Forthcoming in Boustan, Frydman, and Margo,
ed. Human Capital in History.
• Focuses on C20: are there two demographic
transitions or just one?
decline in the aggregate looks very much like
pre-WW2 decline.
• HOWEVER, there are some distinctive
differences.
BGH: Changes in Fertility Behavior
• Variance of completed fertility declined
substantially. Couples much more likely to
have exactly two children AND proportion
childless also declined.
• De-coupling of marriage and fertility but NOT
(so much) household formation. Age at “first
household formation” more or less than same
today as in the 1920s (role today of
cohabitation).
The Other Three Facts
The Baby Boom
• US fertility decline in C19 and early C20 seems
relentless until the “baby boom”.
• Baby boom is NOT just delayed fertility (i.e.
response to baby bust in 1930s). Clearly
present in completed fertility.
• To demographers, explaining the baby boom is
a central puzzle, similar to Great Depression
among economists.
Baby Boom and Baby Bust (1)
Baby Boom and Baby Bust (2)
Discussion of Comparative Statics
• Why does this model generate a negative
effect of w on n? Suppose that market
productivity goes up; this causes w to rise.
Consider the first order condition:
Discussion continued
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If w increases, dC/dn goes up because costs of childrearing are homogenous of degree 1 in w.
But if w goes up, the agent is richer, and demands more consumption, causing the marginal utility
of consumption to decline.
BUT (in the model) consumption has a fixed component. This causes the MU of consumption to
decline less than the increase in MC of time spent in childrearing → rhs of equation increases,
meaning that n must fall to restore FOC.
NOTE that if fixed component of consumption were zero → a given % increase in w would cause c
to increase by %, leaving the ratio of w/c unchanged, causing the solution to the first order
equation for n to be the same. In this model, n is a constant, if c = 0, and w is increasing due to real
wage growth. Is this a reasonable story? Vast majority of time spent in childrearing in C19 is
performed by women. U-shaped pattern of LFP (Goldin; Olivetti) implies that LFP declining over
most of C19; overwhelming majority of married women are not in the labor force (BUT are engaged
in household production). Not clear how one can generate a rising opportunity cost of married
women’s time in childrearing in C19. (C20 is another story).
Possible story: C19 fertility is within marriage, rise in w for men causes an increase in age of first
marriage.
Follow logic of FOC for rise in x (productivity of childrearing), dn/ dx is positive, while dn/dg is
negative.
Aggregate time series: trends in
household productivity
• Long term trend in TFP within household due
to diffusion of labor saving innovations.
• Figure 2: trend pre-dates baby boom.
• Figure 3: real wage changes are smooth.
• Figure 4: trend in consumer durables prices
relative to producer durables is smooth,
except for WW2 blip.
• Moral: difficult to reconcile with baby boom
Regression analysis
• Bailey and Collins assemble county and state
level data on period and completed fertility.
• Regress these on proportion of households
with appliances and also (cohort) exposure to
electricity. Cross-section w/controls and also
first differenced.
• Result: correlation between fertility and
measure of household technology is negative.
Very robust.
Amish
• Final piece of evidence: Old Order Amish
• Amish do not use electricity. Should not
exhibit behavior similar to general population.
• And yet the Amish also had a baby boom.
Theoretical Critique
• Greenwood, et. al. model implies a negative
effect of prices on fertility: if price of
complementary technology falls, families have
more kids.
• But if model is extended to have three goods:
composite commodity, children, and home
produced good, implication is no longer valid.
• See Bailey-Collins Slutsky equation.
Other Explanations
Albanesi and Olivetti
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