For Better or for Worse: Have the Gains from Marrying and Living

For Better or for Worse: Have the Gains from Marrying and Living
Together Changed?
Evidence by Age in Trinidad and Tobago
Michael Henry,
Aston Business School
Sandra Sookram,
SALISES
and
Eric Strobl,
Ecole Polytechnique and SALISES
PRELIMINARY AND INCOMPLETE; PLEASE DO NOT QUOTE
Abstract
We investigate whether gains derived from marrying and cohabitating have changed in Trinidad since the
1980s. Our starting point is to consider a marriage market in which individuals are matched according to
their age group and marriage and cohabitation generate surpluses that may be enjoyed by those involved.
Using data on marital and cohabitating status generated from the 1980 and 2000 Population Status as well
as Vital Statistics we then employ a recently developed non-parametric method to estimate the actual total
net gains for marriage and cohabitation for each age group specific match. Our results indicate that there
have been important shifts over time.
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Section I: Introduction
Love and compatibility have long been held to be the main reasons for marriage. The act of
marriage is also associated with bringing financial stability, children and social acceptance. For
example, in most cultures, remaining single beyond reproductive years, often carries the stigma
of being unwanted by the marriage markets (Saardchom, 2003).
These factors aside, the age at marriage and differential age at marriage between men and
women are seen as been important for social security researchers and actuaries involved in the
design of second-to-die nursing home and long-term care. Additionally, demographers have long
been interested in studying marital matching or who marries whom (Choo and Siow, 2005).
In this paper we investigate whether gains derived from marrying and cohabitating have changed
in Trinidad since the 1980s. Our starting point is to consider a marriage market in which
individuals are matched according to their age group and marriage and cohabitation generate
surpluses that may be enjoyed by those involved. Using data on marital and cohabitating status
generated from the 1980 and 2000 Population Status as well as Vital Statistics we then employ a
recently developed non-parametric method to estimate the actual total net gains for marriage and
cohabitation for each age group specific match.
Our results indicate that there have been
important shifts over time.
The remainder of this paper is divided as follows: Section II provides a detailed explanation of
the methodology adopted in the paper. Section III describes the data employed in the empirical
analysis and the main sources from which the data originate. The results from the empirical
exercise are presented in Section IV, while Section V concludes the paper.
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Section II: Methodology
Our empirical estimator of the gains to marriage is based on the marriage matching
function developed by Choo and Siow (2006).
Accordingly, one can consider the marriage
market consisting of I types of men and J types of women who may potentially form a {i,j} type
marriage. Consequently, there are I x J different marriage submarkets. In any {i,j} marriage a
systematic marriage surplus, ∏ij in the spirit of that first proposed by Becker’s transferable utility
model of the marriage market, is assumed to be generated.
This surplus ∏ij will be shared
between the husband and the wife, where τ ij is the share obtained by the wife and ∏ij - τ ij that
retained by the husband. These shares are determined by the separate contribution of each
spouse to the marital surplus. It is also assumed that the husband and the wife each also get
idiosyncratic payoffs that are particular to each of them and depends solely on the type of the
spouse that he/she marries but not the spouse’s specific identity.
One should note an
idiosyncratic payoff of this form implies that every type i male (regards) all other type j females
as perfect substitutes. Moreover, it is assumed that the idiosyncratic payoff is independent of
their shares of marital surplus received. More specifically, the utilities of a g male of type i and k
female of type j will of being married are, respectively:
Vijg = ∏ij - τ ij +εijg
(1)
Vijk = τ ij +εijk
(2)
where εijg and εijk are the husband’s and wife’s idiosyncratic payoffs, respectively. Individuals
who remain unmarried will receive get a systematic as well as an idiosyncratic payoff. For the a
g male and k female these will be:
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Vijg = ∏i0 + εi0g
(3)
Vijk = ∏0j + ε0jk
(4)
where the systematic and idiosyncratic payoffs are defined analogously to above.
Given the spousal choices and their payoffs, systematic as well as idiosyncratic, a g
male’s and k female’s optimal choice of marriage partner or lack thereof will satisify,
respectively:
vig = max[vi0g,…, vijg,…, viJg]
(5)
vjk = max[v0jk,…, vijk,…, vIjk]
(6)
Choo and Siow (2006) show that if there is equilibrium in each of the IxJ marriage submarkets,
so that demand for spouses equals their supply, then the net gains for an {i,j} type marriage for
the husband and wife will be:
ln(µij/µi0) = ∏ij - τ ij- ∏i0
(7)
ln(µij/µ0j) = τ ij- ∏oj
(8)
where µij, µi0, and µ0j are observed number of {i,j} marriages, i type single males, and j type
single females, respectively. Also, denoting mi and fj as the total number of males type i and
females type j that marry, then the marriage rates:
4
∑µ
k
ik
≈ ln(mi/µi0)
(9)
ik
≈ ln(fj/µ0j)
(10)
mi
∑µ
k
mi
measure the expected benefit to a type i male and type j female, respectively, from being able to
participate in the marriage market.
One should note that while the total net gains can be easily calculated from data on
marriages and available individuals by type, the left hand side components of (7) and (8) are not
directly observable by the researcher from such data. Moreover, will τ
change as population supplies change.
ij
be endogenous and
However, Choo and Siow (2006) show that the per
spouse total net gains, i.e., the sum of the individual net marriage gains, denoted as πij, is just:
π ij =
Π ij − Π i 0 − Π 0 j
2
= ln
µ ij
µi 0 µ 0 j
(11)
which is observable and is independent of population changes.
Within this framework it is easy to allow for cohabitation by adding this as another type
of living arrangement. More precisely, one extend the type of living arrangement l to include
both marriage, m, and cohabitation, c. Thus, apart from remaining single each male (female) now
faces 2xJ (2xI) choices of living arrangements when choosing a spouse, which generates 2xIxJ
living arrangemtents for every combination of male and female. Assuming markets clear, Choo
and Siow (2006) show that this implies for males and females, respectively, total net gains of
ln(µlij/µi0) and ln(µlij/µ0j) for living arrangements l Є {m, c}, as well as a systematic gain of:
5
π l ij == ln
µ l ij
µi 0 µ0 j
for l Є {m, c}
(12)
One can also define cohabitation rates analogous to (9) and (10) that measure the expected
benefit to a type i male and type j female, respectively, from being able to participate in the
marriage market.
Section IV: Data
The first part of our analysis focuses solely on measuring the gains associated with
getting married. This necessitates identifying the number of single individuals and marriages
according to some predefined {i, j} classification scheme. To this end we resort to two main data
sources: (1) Population Censuses and (2) Vital Statistics. The population census, which is a
household survey that collects individual level as well as household level information on all
known households in Trinidad, allows us to identify the number of non-married individuals at
any point in time, and we have access to the exhaustive data for two waves, 1980 and 2000. The
Vital Statistics provides the number of registered marriages according to age groups of the
individuals involved and we thus use age as {i,j} classification of males and females. In this
regard, marriages in the data are aggregated into the following groups: less than 15, 15-19, 2024, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60-64, and 64+. One should note that while
the legal minimum age for marriage is 18, in practice the minimum age is determined by
tradition as defined by religious denomination. For instance, under the Muslim Marriage and
Divorce Act, the minimum legal age of marriage is 16 for males and 12 for females, while under
the Hindu Marriage Act and the Orisha Marriage Act, the minimum legal age of marriage is 18
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for males and 16 for females. We hence do not restrict our analysis to those aged 18 and over.
One problem with the Vital Statistics data is that for some {i,j} matches only a few number of
marriages at any point in time are observed. In order to minimize problems associated with such
‘thin cells’ we, as Choo and Siow (2006), aggregated the number of marriages resulting from the
pool of ‘singles’ in 1980 and 2000 over the two, rather than one, subsequent years; marriages
that took place in 1981 and 1982 for the 1980 and those recorded for 2001 and 2002 for the year
2000 pool. Nevertheless, the number of empty cells was large for the groups less than 15 and
64+ and hence we restrict our analysis to all age groups falling within the 15-64 age range.
We also want to compare the gains associated with cohabitation relative to those derived
from being married.
A challenge in this regard is identifying cohabitating couples.
The
population census fortunately identifies within a household both the marital spouse of the head of
household as well as the cohabitating partner of the head if the head is unmarried. We thus can
identify cohabitating, but unmarried, couples involving the household head. Additionally, any
spouses and/or partners of any children of the household head residing on the same premises can
be identified in the population censuses. Thus we can also isolate cohabitating couples that
involve a child of the head of household - as long as there is only child of the household head
residing within the residency, or the gender of the listed partner(s) clearly eliminates the child
from being the (heterosexual) partner. To create an analogous group of married couples we
employ an analogous identification procedure to determine married couples. For singles we limit
these to be the unmarried residents that are either the head of household or their children, as long
as no partner was listed as living within the household, or in those cases where it is clear which
child is the one with the married spouse. One should note that the population census allow us
neither to determine the length of the cohabiting nor the marriage living arrangement.
This
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means that the interpretation of any gains as defined above is necessarily different from
aforementioned sample. More specifically, gains need to be interpreted as gains to being married
or cohabiting rather than gains associated with becoming married or deciding to cohabitate.
Section V: Results
In Figures 1a and 1b we show the bivariate age distributions of the married in 1981/2 and 2001/2
respectively. These graphs indicate that in both years most marriages occurred between young
adults. However, distribution of marriages in the second graph (1b) is more dispersed and
indicates that there are fewer marriages in 2001/2 and also that people married at a later age.
This latter finding is consistent with similar findings for several countries of the world,
particularly in the case of males. According to Saardchom (2003), whereas forty years ago the
mean age of marriage was less than 30 for both males and females for all countries in a 156
country sample, more recent data from the United Nations (2000) show the age of marriage for
men exceeded 30, on average, in 12 of out of the 156 countries. Additionally, the female mean
age of marriage exceeded 30 in four countries – Iceland, Sweden, Barbados and Jamaica.
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Figure 1 Marriage Distribution by Age Group 1980 and 2000
a : 1980
b: 2000
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Figure 2 graphs the 1980 and 2000 age distributions of the population vectors. In both decades,
for the age groups 15-19, 20-24 & 25-29 there were more available males than females and in
2000/1 the same is true for the age group 30-34. The finding in the latter decade clearly indicates
that males were getting married at a later age than females compared to 1980/81. Figure 3 shows
the converse of the finding shown in Figure 2 but this time in terms of marriage rates.
Figure 2
0
20000
40000
60000
Availables in 1980 and 2000
15-19
25-29
20-24
35-39
30-34
40-44
age
females 1980
males 1980
45-49
55-60
50-54
60-64
females 2000
males 2000
10
Figure 3
0
.02
.04
.06
.08
.1
Marriage Rates
15-19
25-29
20-24
35-39
30-34
40-44
age
males 1980
females 1980
45-49
55-60
50-54
60-64
males 2000
females 2000
Figures 4 & 5 plot the systematic net gains from marrying relative to not marrying for each party
in any {i,j}marriage for the two periods under study. Females in the 20-24 age group receive the
largest systematic net gains from marrying a slightly older man while males in the 20-24 age
group receive the largest systematic net gains from marrying a female roughly in the same group
(Figure 4). In the 40-44 age group males receive the highest systematic net gains from marrying
a slightly younger female, while a female receives the highest net gains when she marries
someone slightly older or at least in her same age group. There is little or no change in the
systematic net gains for both genders in the two age groups in 2000/1 (Figure 5).
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Figure 4
-10
-8
-6
-4
-2
Systematic Gender Specific Net Marriage Gains
15-19
25-29
20-24
35-39
30-34
40-44
age
males 20-24 1980
females 20-24 1980
45-49
55-60
50-54
60-64
males 40-44 1980
females 40-44 1980
Figures 6 and 7, using age as the only differentiating criterion show the smoothed systematic
total gains from marriage for 1980/1 and 2000/1 respectively. Compared to Figures 1a and 1b,
the distributions of the estimated total gains are less peaked and less concentrated.
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Figure 5
-10
-8
-6
-4
-2
Systematic Gender Specific Net Marriage Gains
15-19
25-29
20-24
35-39
30-34
40-44
age
males 20-24 2000
females 20-24 2000
45-49
55-60
50-54
60-64
males 40-44 2000
females 40-44 2000
13
Figure 6
Figure 7
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Figure 8 graphs the change in the total systematic gains to marriage between 1980/1 and 2000/1
for spouses who are close in age. It shows a sharp fall in the total systematic gains to marriage
for young adults between the age of 15 and 34 in 2000/1. Both technological and social factors
are the most likely causes of the fall in the gains to marriage over the period.
Figure 8
-1.5
-1
-.5
0
.5
Change in Total Systematic Marriage Gains: 1980-2000
15-19
25-29
20-24
35-39
30-34
same age
male 5 years older
40-44
age
45-49
55-60
50-54
60-64
male 5 years younger
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Figures 9 and 10, show data for single, cohabitating and married men and women, for the two
individual years under review. In 1980, the number of single males between the ages of 15-29
exceeded the number of single females. The highest amount of cohabitation appears to be in the
age range of 20-29. Additionally, whereas in 1980 the highest number of marriages occurred in
the 30-34 age group, in 2000 it was in the 35-39 age group.
Finally, Figure 11 shows the total systematic gains to marriage and cohabitation for same aged
couples. In 1980, the highest systematic gains from marriage for same age couples were in age
group 30-34. In 2000, however, the highest gains occurred in the 35-39 age group. In terms of
systematic gains to cohabitation for same age couples, the highest gains occurred at lower age
groups compared to those of married couples for the two years examined. For instance, in 1980
the highest systematic gains from cohabitation was in the 20-24 age group while in 2000, these
occurred in the slightly higher age group of 25-29 years. This clearly indicates that due to
economic and social factors, as well as cultural acceptance that couples are cohabitating for
longer periods before getting married.
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10000 20000 30000 40000 50000
0
Single-Cohabitating-Married Men and & Women 1980
15-19
25-29
20-24
35-39
30-34
married couples 1980
single males 1980
55-60
50-54
60-64
cohabitating couples 1980
single females 1980
Single-Cohabitating-Married Men and & Women 2000
0
10000 20000 30000 40000 50000
45-49
40-44
age
15-19
25-29
20-24
35-39
30-34
married couples 2000
single males 2000
40-44
age
45-49
55-60
50-54
60-64
cohabitating couples 2000
single females 2000
17
-10
-5
0
5
Total Systematic Gains for Same Aged Couples
15-19
25-29
20-24
35-39
30-34
40-44
age
marriage 2000
cohabitation 2000
45-49
55-60
50-54
60-64
marriage 1980
cohabitation 1980
Section VI: Conclusion
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