Large Shocks and Small Changes in the Marriage Market for Famine Born Cohorts in China
ABSTRACT Between 1958 and 1961, China experienced one of its worst famines in history. Birth rates plummeted during these years, but recovered immediately afterwards. The famine-born cohorts were relatively scarce in the marriage and labor markets. The famine also adversely affected the health of these cohorts. This paper decomposes these two effects on the marital outcomes of the famine-born and adjacent cohorts in the rural areas of two hard hit provinces, Sichuan and Anhui. Individuals born pre and post-famine, who were in surplus relative to their customary spouses, were able to marry. Using the Choo Siow model of marriage matching, the paper shows that the famine substantially reduced the marital attractiveness of the famine born cohort. The modest decline in educational attainment of the famine born cohort does not explain the change in spousal quality of that cohort. Thus, the famine-born cohort, who were relatively scarce compared with their customary spouses, did not have significant above average marriage rates.
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ABSTRACT: The human costs of famines outlast the famines themselves. An increasing body of research points to their adverse long-run consequences for those born or in utero during them. This paper offers an introduction to the burgeoning literature on fetal origins and famine through a review of research on one well-known case study and a bibliography of published work in the field generally.SSRN Electronic Journal 01/2012;
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ABSTRACT: In a transferable utility context, Choo and Siow (2006) introduced a competitive model of the marriage market, and derived its equilibrium output, a marriage matching function. The marriage matching function denes the gains generated by a marriage between agents of prescribed types in terms of the observed frequency of such marriages within the population, relative to the number of unmarried individuals of the same types. Left open in their work is the question of whether, for a given population whose frequency of types is known, this gains data captures all of the statistical information used to dene it. Equivalently, it is not known whether the Choo-Siow model of the marriage market admits a unique equilibrium. We resolve this question in the armative, assuming the norm of the gains matrix (viewed as an operator) to be less than two. The analytical diculty of showing uniqueness of positive roots of polyno- mial systems has generated a growing literature that provides numerical techniques for tackling such problems. Our method adapts a strategy called the continuity method, more commonly used to solve elliptic par- tial dierential
University of T oronto
Department of Ec onomic s
September 8, 2008
By Loren Brandt, Aloysius Siow and Carl Vogel
Large Shocks and Small Changes in the Marriage Market for
Famine Born Cohorts in China
Working Paper 334
Large Shocks and Small Changes in the
Marriage Market for Famine Born Cohorts in
University of Toronto
University of Toronto
NERA Economic Consulting
September 6, 2008
Between 1958 and 1961, China experienced one of its worst famines in
history. Birth rates plummeted during these years, but recovered imme-
diately afterwards. The famine-born cohorts were relatively scarce in the
marriage and labor markets. The famine also adversely a¤ected the health
of these cohorts. This paper decomposes these two e¤ects on the marital
outcomes of the famine-born and adjacent cohorts in the rural areas of two
hard hit provinces, Sichuan and Anhui. Individuals born pre and post-
famine, who were in surplus relative to their customary spouses, were able
to marry. Using the Choo Siow model of marriage matching, the paper
shows that the famine substantially reduced the marital attractiveness of
the famine born cohort. The modest decline in educational attainment
of the famine born cohort does not explain the change in spousal quality
of that cohort. Thus, the famine-born cohort, who were relatively scarce
compared with their customary spouses, did not have signi…cant above
average marriage rates.
?We thank SSHRC for …nancial support.
The “Great Leap Forward” was a national-level political and economic exper-
iment carried out in China between 1958-1961.1
which began in the mid-…fties, increased in speed and scope. Rural labor was
reallocated from agriculture towards industry: People were moved from vil-
lages to work in urban factories, while agricultural land and labor were directed
towards steel production in “backyard furnaces”. In many localities, strong po-
litical incentives contributed to o¢cial exaggeration of grain yields, which led
to a reduction in sown area, and excessive state procurement and export based
on these exaggerated reports. This was in addition to a state rationing system
that already favored urban industrial workers to the detriment of the villages.
The Greap Leap Forward resulted in the most severe famine in China in the
20th century. Estimates of famine-related mortality range from 15 to 30 million
deaths. Peng (1987) estimates that births lost or postponed resulted in about 25
million fewer births.2In general, the countryside was struck much harder than
cities.3The economic experiment was abandoned by early 1962. The mortality
rate quickly fell and the birth rate also quickly recovered.
While the drop in birth rates is widely recognized, much less is known about
the e¤ects on those who were born during the famine. The medical literature
reports that there are severe deleterious long-run health e¤ects for individuals
su¤ering nutritional deprivation either in utero or in their infancy (See Barker,
1992). Recent research by Gorgens et. al. (2005), St. Clair et. al. (2005),
and Luo, Mu and Zhang (2006) provide some direct con…rmation for this in the
case of China, focusing on such health-related outcomes as stunting, obesity,
Not all the e¤ects of the famine on the famine-born cohorts were negative.
Due to the drop in the birth rates, the famine-born cohorts were small relative
to adjacent birth cohorts. This scarcity should increase their relative values in
both the marriage and labor market. Their increased value in the labor market
should also further add to their desirability in the marriage market.
The net e¤ect of the famine on marital outcomes of famine-born cohorts is an
aggregation of three e¤ects: (1) a negative attractiveness e¤ect due to adverse
health outcomes that reduces demand for famine-born spouses; (2) a positive
attractiveness (wage) e¤ect due to relative scarcity of famine-born cohorts in the
labor market that increases their demand as spouses; and (3) due to customary
gender di¤erences in ages of marriage, there is an increase in spousal demand for
famine-born cohorts because of their relative scarcity in the marriage market.
Collectivization of farming,
1For an overview of the Great Leap Forward, see Lardy (1987).
2Ashton et. al. (1984) provide estimates at the national level of the magnitude of the
demographic crisis. See Peng (1987) for a detailed analysis of the impact of the famine at the
provincial level. Lin and Yang (2000) and Li and Yang (2006) examine causes of the famine.
Becker (1997) provides a narrative account.
3The famine also extended beyond China’s traditional famine belt region. For example,
Sichuan province, in which mass famines were historically rare, was one of the hardest struck.
The objective of this paper is to study the e¤ect of the famine on the marital
outcomes of the famine-born and adjacent cohorts. We will decompose the
observed changes in marital outcomes into those due to changes in relative
scarcity versus those due to changes in attractiveness.
The change in marital attractiveness due to the famine is di¢cult to mea-
sure. In the censuses that we use, there are no wage measures that might capture
attractiveness. Instead, we will use educational attainment as a proxy for at-
tractiveness, but such proxies provide a noisy measure of the actual change in
marital attractiveness.4To get around these di¢culties, we will use a residual
accounting approach to measure the unobserved changes in attractiveness where
the di¤erences in marital outcomes, after accounting for quantity changes, are
attributed to changes in attractiveness.5To do so, we need a model of the mar-
riage market that will provide an estimate of what a change in quantity, ceteris
paribus, will do.6Our empirical model will be the CS marriage matching func-
tion (Choo and Siow 2006).7The main bene…t of the CS marriage matching
function is that it has substitution e¤ects, a central focus of this paper.8
Sichuan and Anhui, two primarily agricultural provinces located in western
and eastern China, respectively, were two of the most severely a¤ected provinces
by the famine.9Because the famine disproportionately a¤ected rural rather than
urban communities,10we will focus our analysis on the rural population in both
provinces. Thus, all …gures and statistics in this paper pertain to the rural
Figures 1 and 1a show the distributions of individuals by age in the 1990
Census for Sichuan and Anhui, respectively. Due to a high long-run birth rate
and mortality rates that increase with age, population by age should be declining
with age. As we can see in Figure 1 for Sichuan, there is a sharp drop in the
population of the famine-born cohort, 29-31 year old men and women, or those
4Unobserved marital attractiveness is a standard concern.
(2005), for example, show that individuals born in deterministic “unlucky” years in Japan
and Korea respectively, have worse marriage market outcomes. These worse outcomes occur
in spite of their relative scarcity in the marriage market as parents try to avoid those unlucky
5Residual accounting methods are common in economics. See, for example, Oxaca decom-
positions in labor economics and Solow residuals in growth accounting.
6Oxaca decompositions in labor economics use earnings regressions and Solow residuals in
growth accounting use the Solow growth model.
7A marriage matching function is a production function for marriages (Pollard 1997, Pollack
1990). Inputs are population vectors of types of individuals. Output is a matrix of who marries
whom, and who remains unmarried.
8The workhorse marriage matching function of demography, the harmonic mean marriage
matching function, e.g. Schoen(1981), does not have substitution e¤ects.
9In 1957, 86 and 92 percent of the labor force were in the primary (agriculture, …sheries and
forestry) sector in Sichuan and Anhui, respectively. Between 65-70 percent of GDP originated
in the primary sector. These data are taken from Xin Zhongguo wushi nian tongji ziliao
huibian, 2005). Further details are in Peng (1987).
10Peng(1987) documents that excess mortality was more severe in rural than in urban areas.
At the national level, the excess crude death rate for the urban population between 1958-1962
was 13.84 compared to 7.94 for the two preceding years. By comparison, the excess crude
death rate for the rural population rose from 11.45 to 24.45 over the same period. See Peng
(1987), p. 646.
Akabayashi (2006) and Lee
born between 1959-1961. The panel also shows the quick recovery in fertility
after the famine. Figure 1a plots population by age for Anhui, which was also
heavily a¤ected by the famine. Again, there is a sharp drop in the size of the
famine-born cohort as well as a quick recovery in fertility after the famine.
Our empirical strategy is to compare the marital behavior of the famine-
a¤ected cohorts in 1990 to their same age counterparts in 1982. The famine-
born cohort were between ages 29 to 31 in 1990. We consider the pre and post
famine-born cohorts to be those between ages 32-34 and ages 26-28 in 1990,
respectively. Thus we will compare the marital behavior of individuals between
the ages of 26 to 34 in 1990 to their same age counterparts in 1982.
What Figures 1 and 1a cannot show are the quality e¤ects of the famine
on the famine-born cohort. Using national samples, Almond et. al.(2007) show
that educational attainment fell for the famine-born cohort. In this paper, we
will investigate the changes in educational attainment for the famine-a¤ected
cohorts as a proxy for the changes in marital attractiveness of those cohorts.
We will also investigate the e¤ects of the changes in educational attainment on
changes in marital behavior.
Our results show that famine-a¤ected women in 1990 had approximately the
same long-run marriage rates as their same age non-famine-a¤ected peers did
in 1982. Pre famine-born men in 1990 had approximately the same marriage
rates as their same age 1982 peers. Famine-born and post famine-born men
had higher marriage rates than their same age 1982 peers. Taken as a whole,
famine-a¤ected individuals had weakly higher marriage rates than their non-
famine a¤ected peers. Given the large changes in customary sex ratios for the
famine-a¤ected cohorts, these individuals had to show substantial ‡exibility in
their choices of spouses. For many of these individuals, marrying, albeit to a
non-customary spouse, is substantially preferred to remaining unmarried.
We …rst consider a CS marriage matching function (MMF) where individuals
are di¤erentiated by gender and age. We estimate this model using the 1982
census for both provinces. Using these estimates, we predict what the marriage
rates would have been in 1990 given the changes in population supplies a¤ected
by the famine. The predicted marriage rates are marginally higher than the ac-
tual marriage rates for famine-born women and marginally lower for pre-famine
born women. The predicted marriage rates are signi…cantly higher than the ac-
tual marriage rates for famine-born men and signi…cantly lower for pre-famine
born men. The large discrepancies between predicted and actual marriage rates
of the famine-a¤ected individuals imply that there was substantial decline in
the marital attractiveness of the famine-born cohorts relative to their pre and
post famine-born cohorts.
A natural question that arises is the extent to which the decline in mari-
tal attractiveness of the famine-born cohort can be captured by di¤erences in
educational attainment of the various cohorts. To answer this question, we
re-estimate the CS model, allowing now for matching by both age and educa-
tional attainment. We show that the changes in educational attainment for the
famine-born cohort are insu¢cient to explain changes in marital behavior of that
cohort. Alternatively, the change in marital attractiveness of the famine-born
cohort is not well captured by the changes in their educational attainment.
Our paper is related to two literatures. First, it is related to the literature
that studies the e¤ects of the “Great Leap Forward” on social and economic
outcomes (E.g. Almond, et. al. 2007; Chen 2007; Geogens, et. al. 2004; Porter
2007). Of these papers, Almond et. al. and Porter study the e¤ects on the
marriage market. We build on their work.
In addition to other outcomes, both of these two papers use a regression
framework to study the causal e¤ects of the famine on marital behavior of the
a¤ected cohorts. These include marriage rates, age at marriage, spousal age
di¤erences and other spousal characteristics. They concluded that the famine
had modest e¤ects on marriage rates, caused the a¤ected cohorts to marry
later, increased their spousal age gaps, and decreased their spousal education
gaps. However, the two papers attribute the outcomes to di¤erent causal mech-
anisms. Almond et. al. emphasize the decline in marital attractiveness of the
famine-born cohort whereas Porter emphasizes the relative scarcity of famine-
born cohort in the marriage market. Almond et. al. use variations in provincial
mortality rates of the famine-a¤ected cohorts as a regressor and interpret its
estimated e¤ect as due to changes in marital attractiveness. Porter uses marital
share weighted adult sex ratios of the famine-a¤ected cohorts within and across
provinces as a regressor and interprets its estimated e¤ect as due to changes in
sex ratios. Since the famine increased mortality and decreased birth rates (and
therefore eventual population supplies to the marriage market), it is di¢cult
to disentangle empirically the two e¤ects in a regression framework. To relax
the “either or” hypothesis, we use a structural model of marriage matching to
decompose observed marital behavior to both of these mechanisms.
A famine e¤ect on marital behavior is a general equilibrium e¤ect. For exam-
ple, the sum of all men of a particular type that di¤erent types of women marry
must be less than or equal to the number of men of that type. A regression using
individual level data of spousal characteristics on individual attributes ignores
these general equilibrium constraints.11General equilibrium e¤ects are poten-
tially signi…cant due to the large imbalances in customary sex ratios caused by
the famine. These e¤ects apply to both causal mechanisms discussed above. By
construction, the CS model imposes all relevant general equilibrium constraints.
In general, our empirical results agree qualitatively with those found by Al-
mond et. al. and Porter.12We also show that both relative scarcity and changes
in marital attractiveness matter, and there are …rst-order general equilibrium
e¤ects. Ignoring these general equilibrium e¤ects lead to inadmissible predicted
marital behavior such as predicted marriage rates that are above one.
A caveat is in order. While there are de…ciencies to the regression approach
to study the e¤ects of the famine on marital behavior, our approach is based on
the untestable assumption that the CS model is the appropriate model of the
11The inability of the regression framework using individual level data to deal with general
equilibrium e¤ects are well known (E.g. Imbens and Woolridge 2008; Heckman, Lochner and
Taber 1999). In the marriage context, see Choo and Siow.
12Finer comparisons are misleading because of the di¤erences in samples and methodologies.
We use rural Sichuan and Anhui samples and they use national samples.
marriage market. Such an assumption is standard to most residual accounting
methods. Thus we view our paper as complimentary to the above two papers.
Our paper is also related to the literature which studies the e¤ect of ex-
ogenous variations in the sex ratios on marital outcomes (Akabayashi, 2006;
Bhrolchain 2001; Brainard 2006; Esteve i and Cabré 2004; Francis 2007). Many
of the exogenous variations in sex ratios have both a quality and quantity di-
mension due to the e¤ects of war (E.g. Brainard; Esteve i and Cabré; and
Francis). Even the variations in sex ratios due to superstition about being born
in “unlucky” years have a quality dimension (Akabayashi). Individuals born in
these “unlucky” years su¤er a social stigma which makes them less desirable in
the marriage market. But they bene…t from being relatively scarce in the labor
and marriage market. Our framework can be applied to disentangle these two
e¤ects in these environments.
In this paper, we will use three statistics to study marital behavior: marriage
rates (which measure the gains to marrying versus not marrying), marriage
shares (which measure who marries whom) and a marital accounting scheme,
total gains to marriage (which combine the …rst two concerns).
Let t denote the year of the census, t = f1982;1990). At each year, indi-
viduals are di¤erentiated by their age and or education. Let j denote type j
women and i denote type i men. j = 1;::;J and i = 1;::I. nt
women of type j in year t. nt
number of married women of type j year t. ?t
type i year t. Let ?t
ijbe the number of type i men married to type j women.
There are I ? J types of marriages at time t.
The sex ratio between type i men and type j women, St
jis the number of
iis the number of men of type i in year t. ?t
iis the number of married men of
ij, is de…ned as:
; i = 1;::;I; j = 1;::J (1)
In general, we expect adult sex ratios to be close to one.
The marriage rate is:
;g = i;j; i = 1;::;I; j = 1;::J(2)
An equivalent measure to the marriage rate is the marriage odds ratio:
(1 ? rtg);
g = i;j; i = 1;::;I; j = 1;::J (3)
The marriage rates or odds ratios are informative about the choice of whether
to marry or not. They are equivalent univariate measures of marital behavior.
The marriage rates or odds ratios are not informative about substitution pat-
terns in marriage, i.e. who marries whom.
To study who marries whom, we …rst study spousal shares by types of hus-
bands and wives:
; i = 1;::;I; j = 1;::J(4)
; i = 1;::;I; j = 1;::J(5)
ijjis the share of type j spouses among type i’s wives. st
type i spouses among type j’s husbands. Shares are informative about spousal
subsitution patterns, i.e. who to marry. By de…nition, the sum of the shares
across di¤erent types of spouses for the same type of individual is one. Thus
the shares are not informative about the choice of whether to marry or not. Nor
are they informative about how shares will change if the sex ratio changes.
To investigate how substitution a¤ects the decision to marry and vice versa,
we need a statistic that will link the two e¤ects. To that end, let ?t
total gains to a fi;jg marriage relative to them not marrying:
The numerator is the number of fi;jg marriages. The denominator is the
geometric average of the number of unmarrieds. Total gains, ?t
complete (alternative to ?ij) characterization of the marriage distribution.13
ijis an accounting scheme for marriage distributions.
We can rewrite total gains as:
The total gains to fi;jg marriages is the average of the log odds of marriages
for i type men and j type men plus the average of the log shares. Thus total
gains to marriage combines substitution patterns with marriage rates.
Consider a new time t0with di¤erent marital matches and population sup-
jjiis the share of
; i = 1;::;I;j = 1;::J (6)
ij, provides a
i, for all i and j, we can recover the marriage distribution, ?t
jji; i = 1;::;I;j = 1;::J(7)
j. We can estimate new total gains, ?t0
; i = 1;::;I;j = 1;::J (8)
ijfor all i and j is a complete description of the marriage distribution in
time t0. So ??t0t
ijfor all i and j is a complete description of the
13It cannot deal with marital choices with zero observation. I.e. ?t
ijmust be …nite.
changes in the marriage distributions between the two periods.14
Tautologically, changes in total gains, ??t0t
population supplies and changes in marital preferences. In order to disentangle
observed changes in marital behavior between e¤ects due to changes in marital
preference and e¤ects due to population supplies, we need a model of marital
behavior. CS is such a model. It provides a behavioral derivation of ?t
their model, total gains measures the expected marital gain to a random fi;jg
pair marrying relative to them not marrying. The thought experiment is as
follows. Consider a randomly chosen a type i male marrying a randomly chosen
type j female. We compare the marital output of this random chosen couple
to the geometric average of what they would have obtained if they had remain
unmarried. So once the individuals are chosen, they could only compare whether
to marry or forever remain unmarried. This measure of relative expected marital
gain is una¤ected by marriage market conditions because we are not choosing
the couple based on relative scarcity, nor do we allow them to marry other
Thus in CS, ?t
j, or other determinants of marriage market conditions. If we have estimates
jfor all i and j using equations (6), we can predict
what the new marriage distribution b ?t0
In our context, let time t individuals be those whose marital behavior were
una¤ected by the famine. Let t0individuals be those who were a¤ected by
the famine. If the only e¤ect of the famine was to change population supplies
between t and t0, then ?t0
be b ?t0
marriage distribution, b ?t0
Because total gains completely describe the marriage distribution, the previous
statement is always true. Without a model of marital behavior, we do not know
how much of ??t0t
ijis due to changes in marital attractiveness and how much
is due to changes in population supplies. The bite of CS is that it implies that
ij, the changes in total gains, only measure changes in marital attractiveness
due to the famine.
In demography, CS is known as a MMF with substitution e¤ects. The stan-
dard demographic MMF is the harmonic mean MMF (E.g. Schoen 1981) which
ij, are due to both changes in
ijare exogenous, independent of population vectors, nt
ijwill be with new population vectors nt0
ijfor all i and j by solving:
j, and ?t0
i? b ?t0
j? b ?t0
; i = 1;::;I;j = 1;::J (9)
ijand the marital distribution at time t0should
ijas in the system of equations (9).
So if the new actual marriage distribution, ?t0
ij, di¤ers from the predicted
ij, the total gains of marriage must have changed be-
tween the old and the new environments, i.e. ?t0
ijfor at least some fi;jg.
14CS has a proof of local uniqueness. Although there is no proof of global uniqueness, our
experience with it using US (CS), Canadian (Choo and Siow 2006a) and Chinese data here
do not suggest otherwise empirically.
excludes substitution e¤ects,
The absence of substitution e¤ects means that changes in ni0 for i 6= i0or
nj0 for j 6= j0will not a¤ect ?ij. ?ij also describes the marriage distribution
completely. But if CS is correct, ?ijis a function of marital preferences as well
as population vectors. Using estimated ?ijto predict changes in the marriage
distribution due to population changes will result in biased predictions. As will
be discussed later, the harmonic mean MMF generates inadmissible predictions
in our context.15
Summary Data and Sex Ratios
All the data presented here come from the one percent household sample of the
1982 Census of China and the one percent clustered sample of the 1990 Census
of China. Wang (2000) and Mason and Lavely (2001) are useful resources on the
details of the censuses and data samples. In our analysis, we only use those data
pertaining to individuals who reside in rural counties. This can be rationalized
on two grounds: …rst, the countryside was more a¤ected by the famine than the
cities,16and second, the rural marriage market was largely self-contained, and
highly local in nature. There was some cross-provincial migration for marriage,
but the numbers are relatively small. In the Data Appendix, we discuss how
rural is de…ned, and several other data-related issues, including migration.
Tables 1 and 2 provide some summary statistics for rural counties in Anhui
and Sichuan from the 1982 and 1990 censuses. The average spousal age dif-
ferences in the two provinces ranged between two to four years. Any observed
spousal age di¤erence is an equilibrium outcome determined by marriage mar-
ket conditions. Under average marriage market conditions existing in China at
the times of the 1982 and 1990 censuses, the average spousal age di¤erence was
about three years. Because the censuses collect ages by years, we assume that
the customary equilibrium spousal age di¤erence is three years.
The …rst-order impact of the famine on the marital behavior of individu-
als would have been on the famine-born cohort and their customary spouses.
For men who usually marry women three years younger, the customary spouses
for the famine-born men were the post-famine-born women. For famine-born
women, their customary spouses were the pre famine-born men. Thus, we con-
sider individuals born between 1956 to 1964 to be the famine-a¤ected cohorts.
We observe the marital behavior of individuals in 1982 and 1990. For conve-
nience, the ages of these individuals in 1990 are given below.
15The search for empirically tractable MMF with substitution e¤ects is ongoing (Pollak
1990, Pollard 1997). CS provides a solution.
16See footnote 10.
Our main interest is to examine the behavior of the famine on marital be-
havior in the 1990 census. The reason for focusing on the 1990 census is that
by 1990, the post-famine cohort was 26-28 years old. Most women of that age
category and older would have acquired their permanent marital status. Except
for 26 and 27 year olds, most men of that age category and older would also
have acquired their permanent marital status.
We will use individuals of the same age and characteristics in 1982 as con-
trols for their counterparts in 1990. That is, the control group for post famine
individuals are those who were 26-28 in 1982, the control group for famine-born
cohort are those who were 29-31 in 1982, and the control group for the pre-
famine cohort are those who were 32-34 in 1982. In general, as shown in the
immediate table above, individuals in the control groups, of age 26 and older
in 1982, were not a¤ected at birth by the famine. There is one year of overlap.
Individuals of age 26 in 1982, used as a control group for pre-famine 26 year olds
in 1990, are also in the post-famine group in 1990. There was also no signi…cant
social or legal change to the labor and marriage markets between 1982 and 1990.
Thus, it is reasonable to use individuals of the same age and characteristics in
1982 as controls for their counterparts in 1990.
Figure 1 shows the number of individuals by age in rural counties in Sichuan in
1990. The pre-famine cohort, 32-34, were a¤ected by the famine. There were
less of them than 35 or 36 year olds. Absent the famine, due to population
growth and mortality risk, there should be less older individuals rather than
more in a given census year. Thus the 32-34 year olds were adversely a¤ected
by the famine.
The famine-born cohort, 29-31, is substantially smaller than the adjacent
cohorts, re‡ecting primarily the fall in the birth rates of that cohort. Recovery
of the birth rates after the famine was very rapid. There is no visible impact of
the famine on cohort sizes after 1964, ages 25 or younger in 1990.
Figure 1 also shows that there were less 35 and 36 year olds than 37 olds,
which implies that these cohorts were also a¤ected by the famine. We do not
directly study their marital behavior because of our focus on the marital behav-
ior of the famine-born cohort with their adjacent aged peers. The analysis of
the famine-a¤ected cohorts takes into account that they could and did marry
these 35 year olds and older individuals in 1990.
2.1 Marriage rates
Figure 2 shows two sex ratios by age. The dashed line is the sex ratio of men
to women for same age men and women. It shows that the famine had little
to no impact on the sex ratio; there is no evidence that male children were
favored over female children among the famine-a¤ected cohorts. The solid line
is the sex ratio by women’s age where the men were three years older than the
women. Here, the e¤ect of the famine is very clear. The sex ratio was above
2.5 for famine-born women because there were relatively more pre-famine-born
men. Also the sex ratio fell to 0.25 for post-famine-born women because there
was a relative scarcity of famine-born men. If individuals valued the customary
age of marriage, there should have been large marriage market e¤ects on the
Figure 3 plots the marriages rates for men and women by age in 1990 and
1982. In both census years and at all ages, female marriage rates exceed 0.95
whereas male marriage rates are less than 0.9.
For women younger than age 40, marriage rates for women of the same age
were essentially the same in 1990 and 1982. In other words, the famine-a¤ected
women in 1990 had the same marriage rates as their same age peers in 1982.
Figure 2 earlier showed that the famine-born women were in relative scarcity
and the post-famine women were in relative surplus when compared to their
customary spouses. This strongly suggests that the famine-a¤ected women also
married non-customary spouses and that these substitutions to a …rst order left
the marriage rates of famine-a¤ected women unchanged.
In 1990, the marriage rates for famine-a¤ected men were di¤erent from un-
a¤ected cohorts. The marriage rates of pre-famine-born men, 32-34, were lower
than their adjacent older peers. They were also lower than that of the famine-
born men, 29-31. Interestingly, post famine-born men had higher marriage rates
than the famine-born men even though post famine-born men were not scarce
relative to their customary spouses.
Compared with 1982 men of the same ages, the marriage rates of pre famine-
born men in 1990 were not signi…cantly di¤erent. Thus the lower marriage rates
of pre famine-born men in 1990 compared to their adjacent older peers may have
been a lifecycle e¤ect rather than a famine-related e¤ect.
Compared with 1982 men of the same ages, the marriage rates of famine and
post famine-born men in 1990 were signi…cantly higher. Thus, both within year
comparisons in 1990 and across years comparisons suggest that the marriage
rates of famine and post famine-born men were positively a¤ected by the famine.
Based on marriage rates between 1990 and 1982, a tentative conclusion is
that the marriage rates of famine-a¤ected women in 1990 were unchanged. The
marriage rates of pre famine-born men were una¤ected whereas the marriage
rates of famine-born and post famine-born men increased in 1990. These con-
clusions are summarized in Figure 4. The marriage rates of famine-born men
increased by less than 5 percent compared to their 1982 peers. The marriage
rates of post famine-born men increased by substantially more, 5 to 15 percent
more than their 1982 peers. But famine-born men are scarce. It is therefore
surprising that their increased marriage rates were so modest.
Previous researchers who have studied marriage rates and large exogenous
sex ratio changes in other contexts have also often found small e¤ects of these
changes on marriage rates, e.g. Bergstrom and Lam (1994) and Bhrolchain
(2001). As we do in this paper, these researchers interpret these small e¤ects as
due to ‡exible spousal choices in the face of large changes in sex ratios. But there
are anomalies in these common …ndings of small e¤ects. If a large change in the
sex ratio leads to a particular gender and age cohort being relatively scarce in
the marriage market, that cohort should experience a substantial increase in its
marriage rate. It is anomalous that the increased marriage rates of famine-born
men in 1990 compared to their 1982 peers were signi…cantly smaller than the
post famine-born men. The behavior is less puzzling for famine-born women
because marriage rates for women were already high. The marriage rate of
famine-born women in 1990 could not have been signi…cantly higher. On the
other hand, it is anomalous that the marriage rate of post-famine women in
1990 was not signi…cantly lower than their famine-born counterparts because
the post-famine women were in relative surplus.
To get an appreciation of the quantitative discrepancies to be explained and
the …rst order importance of accounting for general equilibrium considerations,
we estimate the CS MMF using 1982 data where the type of an individual
is their age.17
With the same data, we also estimate the parameters of the
harmonic mean MMF. Using the estimates from the two models and population
supplies in 1990, we predict what the 1990 marriages rates would have been due
to changes in population supplies alone.
Figures 4b and 4c show for Sichuan, the predicted male and female marriage
rates from the two models respectively. For both genders, the predicted marriage
rates from the harmonic mean MMF often exceed 1, an inadmissible prediction.
These violations occurred because the harmonic mean MMF does not impose
required general equilibrium accounting identities and the changes in sex ratios
of customary spousal age di¤erences were large. Thus as previous researchers
have observed, the standard MMF used by demographers is a poor empirical
On the other hand, the predicted marriage rates from the CS MMF behave
sensibly. In …gures 4b and 4c, the predicted marriage rates are above average
for the famine-born cohorts and below average for the adjacent aged birth co-
horts. No accounting constraint is violated. Note that actual female marriage
rates were over 0.95 for most ages. Even with large changes in sex ratios of
the customary spousal age di¤erences for the famine-born cohorts, their pre-
dicted marriage rates remained below 1. The predicted female marriage rates
for famine-born cohorts were very similar to those predicted for adjacent aged
cohorts. In other words, the CS MMF respects both the general equilibrium
accounting constraints of MMFs and also captures the ‡exibility of individuals
in their marital choices. These two attributes show the advantage of the CS
MMF over the harmonic mean MMF.
17Details of the the estimation are in section 2.3.
In …gure 4b, famine born males had lower marriage rates than predicted
by CS and pre famine-born males had higher marriage rates than predicted by
CS. So changes in relative scarcities of the di¤erent types of individuals caused
by the famine cannot explain these discrepancies. The famine must have also
changed marital attractiveness or total gains to marriage for these cohorts.
Figure 4c shows that the discrepancies between predicted and actual female
marriage rates were small. CS is able to generate predicted male marriage
rates that substantially responded to changes in population supplies and female
marriage rates that marginally responded. It is clear that changes in population
supplies alone cannot explain the observed changes in marriage rates. We also
need to account for changes in marital attractiveness of the famine-a¤ected
2.2 Marriage shares
To set the stage, it is convenient to have an idea of what customary marital
shares were. Figure 5 plots the distributions of husbands by spousal age dif-
ferences for women who were 33, 30 and 27 in 1982. Because they were born
substantially before the famine, the marital behavior of 1982 women of those
ages should have been una¤ected by the famine. We di¤erentiate husbands by
their age gaps over their wives, from -3 years to +6 years. Husbands within
these 10 years ages interval account for 83-96% of all husbands. The …gure
shows that there is essentially no di¤erence in the distributions of husbands by
spousal age di¤erences for these di¤erent aged women in 1982. The marital
behavior of 1982 women of those ages was una¤ected by the famine; and their
spousal choices as represented by spousal age di¤erences did not change with
their age in 1982.
Turning to the e¤ects of the famine, Figure 6 shows the marital partners of
three age cohorts of women in 1990: 27 (post famine-born), 30 (famine-born)
and 33 (pre famine-born). First consider 33 year old women who were born
before the famine. Since women generally marry older men, Figure 2 tells us
that the customary husbands of these women are not scarce.
husbands were in the 10 years age interval with the remainder primarily among
older men. The largest share of husbands was two years older. For 33 year old
women in 1990, the age distribution of their spouses looks the same as their
same age peers in 1982 in Figure 5.
30 year old women were famine-born women. They are scarce relative to
their customary husbands. Compared with the shares of 33 year old women,
their marriage shares distribution shifted to the right. Although they could
replicate the share distribution of the pre-famine women because they were
scarce relative to older men, more of them chose to marry older husbands. One
potential explanation is that they avoided competing with younger women.
27 year old women were born after the famine. They su¤er a relative scarcity
of customary husbands. As shown in the …gure, their marriage share distribution
is almost symmetric around age gap [?2;2]. It ‡attens out between age gap
2 to 4 and then increases. Thus, post-famine women married a much larger
90% of their
share of own age or younger men, and also signi…cantly older men. The share of
husbands in the age gap [?2;2] was 0.83. A larger share of these women married
signi…cantly older men than the other cohorts of women. Figure 6 shows that in
1990, the distributions of husbands by spousal age di¤erences were signi…cantly
di¤erent between pre famine-born, famine-born and post famine-born women.
Using the behavior of women in 1982 as control groups, Figure 7 plots the
ratio of 1990 husbands’ shares to 1982 shares for 27, 30 and 33 year old women.
If there is no di¤erence in shares between 1982 and 1990 for the same age women,
then the ratio should be 1. Consider the case of 33 year old women. The ratio
of shares are slightly above 1 for age gap between [0,4]. In both 1982 and 1990,
most of the husbands of these 33 year old women fell in the age gap between
[0,4] years. The ratio of shares are lower than 1 outside [0,4]. This says that in
the [0,4] range, and to a …rst approximation, pre famine-born women in 1990
had the same relative distribution of husbands by spousal age di¤erences as
their 1982 counterparts. But pre-famine women in 1990 had substantially less
younger or older husbands outside the range. Less younger husbands can be
explained by the relative scarcity of famine-born men. Why older men outside
the range was lower in 1990 will be discussed later.
Famine-born women in 1990, age 30, behaved very di¤erently from their 1982
counterparts. They were far more likely to marry older men and far less likely
to marry men of the same age or younger. Since these women are relatively
scarce, they could have married their customary partners. But they did not do
Post-famine women in 1990, age 27, also behaved very di¤erently from their
1982 counterparts. They were far more likely to marry same age or younger men,
also pre famine-born men, and far less likely to marry famine-born men. So here,
post-famine women avoided the scarce famine-born men. What is interesting is
that their increased demand for substantially older, pre famine-born men. Both
27 and 30 year old women in 1990 had relatively more demand for signi…cantly
older men, which may partially explain why 33 year old women in 1990 had
relatively lower demand for husbands older than 4 years.
Taken as a whole, Figure 7 shows that di¤erent cohorts of famine-a¤ected
women responded di¤erently in their spousal choices. This …nding is anticipated
by the observation that female marriage rates did not di¤er much across di¤erent
cohorts of famine-a¤ected women.
To preview what we will …nd, recall that marriages rates of famine-born women
were the same as their pre and post famine-born peers. The marriage rates of
famine-born men were lower than their post famine-born peers. But famine-
born men and women are relatively scarce in the marriage market. Let j denote
the cohort of famine-born women and i denote their customary spouses. To a
…rst order, ot
jdid not change and j type women are scarce relative to type i men.
ijmust fall. Under the CS interpretation,
the expected gains to marriage for a random fi;jg pair relative to them not
jjimust fall and by equation (7), ?t