Household production and sexual orientation.
Allen, Douglas W.
Homosexual unions do not result in children, and generally they
have a less extensive division of labor and less marital-specific
capital than heterosexual marriages.
(Becker 1981, p. 225)
I. INTRODUCTION
It is conventional economic wisdom that the gains from household
production are lower for same-sex couples compared to opposite-sex
couples because the former obviously lack the benefits that come from a
sexual division of labor within the home. Even with the presence of
children, these specialization gains would seem lacking because
differences across sexes are absent, and therefore, opposite-sexed
couples should receive larger household benefits. Indeed, the lower
benefits within same-sex households have long been a cornerstone in the
explanation of duration instability among these couples. (1)
Yet, none of these long-held beliefs are based on any large sample
empirical estimates.
The challenges in estimating the value of household commodities
among same-sex couples are large, and until very recently, were
impossible to overcome. Gays and lesbians make up a very small fraction
of any population. Among this small fraction, few are in common law or
married relationships, and still fewer have children. Furthermore,
within the United States same-sex marriage is legal only within a
handful of states, and though the number of states continues to grow, no
census or other large probability sample directly identifies same-sex
couples. In smaller samples that might identify same-sex couples, seldom
is data collected on time devoted to household activities, or the labor
market variables necessary to estimate home production. So on the one
hand, estimation requires a specific set of economic data on time use,
market activity, and expenditures that are lacking in any sociological
data that includes same-sex couples. While on the other hand, large
probability sample datasets with market and household information often
fail to identify sexual orientation.
The 2006 Canada census solves almost all of these problems. (2)
First, same-sex marriage became legal across all of Canada in 2005. (3)
As a result, the 2006 census self-identifies same-sex couples: both
married and common law. (4) The census also measures time use within the
household, income (based on tax records), and other demographic
characteristics for both spouses. Most importantly, the census is large
enough to contain a random sample of same-sex couples to allow for
estimation. Thus, although not perfect, the census contains the minimum
amount of information necessary to estimate differences in the household
production functions across different couple-types.
Given that the household commodity output is unobservable, it is
necessary to do this estimation within the context of a specific
household model. Here the Graham and Green (1984) model is used. (5)
This model exploits a simple Cobb-Douglas production function, in which
household output depends on the amount of time each household member
devotes to the household and the amount of market goods that are
utilized. The empirical findings are rather interesting, and robust.
First, same-sex couples respond differently than opposite-sex couples to
time cost changes with respect to their allocation of household time.
This finding is consistent with other social science findings that show
same-sex couples are less likely to specialize within the household.
However, by far the most important element in determining the value of
total household production is the value of market goods employed. As a
result, differences in the value of household production that arise over
differences in the sexual division of labor between same-and
opposite-sex homes are swamped by the role that market goods play in
producing household commodities. Thus, based on the findings here, one
would conclude that the loss of a sexual division of labor is not an
important factor in the determination of the value of household
production for gays and lesbians.
Differences in household production across different couple-types
may be caused by many different factors. However, here the objective is
to test the long-held conjecture of Becker, quoted above, by
investigating time use patterns within the household and providing the
first estimates of the value of household commodities for gay and
lesbian households. That is, the goal is simply to see if such a
difference actually exists.
II. MATCHING, SOCIAL NORMS, AND HOUSEHOLD PRODUCTION
Individuals do not randomly match with others to form couples.
Rather, selection takes place within the context of a matching market,
and individuals choose the best match possible given the competition of
others. These matches depend on the size of the matching market, the
social norms of the subculture the individuals live in, as well as
observable and unobservable (to third parties) individual
characteristics. In the end, we only observe those matches that result
from this process.
Given the nonrandom assignment of individuals into couples, the
actual amount of household goods produced depends on the matching
process. For example, there is a gender studies literature that suggests
lesbians allocate household labor based in part on strong subculture
social norms of equality and a rejection of traditional gender
differences. (6) Hence, despite the lack of biological difference,
inability to jointly bear children, and matching on similar income
levels, further reductions in specialization may result from these
social norm differences.
In addition to the role of social norms, same-sex couples may match
differently than opposite-sex couples, and gay couples may match
differently from lesbian couples. For example, differences in the
expectation of
marriage, future children, or life expectancy might lead to
systematic differences in couple-specific human capital investment
decisions, which influence the quantity of household production that
takes place. (7) In addition, higher search costs for same-sex couples
could lead to fewer couplings and lower quality matches on average. This
may lead to different parts of the distribution of men and women forming
couples for the different couple-types, and differences in the value of
household production could result from this different composition of the
sample.
Hence, actual differences found in the value of household
production, without the context of a specific model being tested, cannot
be directly attributed to the "same-sexness" of the couple.
The differences may reflect differences in social norms, differences in
sorting, or some other systematic difference between same and
opposite-sex couples. However, the objective here is not to sort through
these different factors, but rather to first establish whether any
difference in household output actually exists between opposite- and
same-sex couples and if it does exist, how large is it?
III. THE GRAHAM AND GREEN MODEL
Directly estimating a household production function, in general, is
difficult because there are almost no instances where household outputs
are reported in surveys. (8) Without measures of the dependent variable,
various indirect procedures have been used, many of which exploit
detailed information on time and market goods used in home production.
(9) When the data are more aggregated and less detailed, usually various
restrictions are in order to separate the role of household preferences
from production. (10)
Here the parsimonious nature of the census expenditure data forces
the use of the indirect method developed by Graham and Green (1984),
which (1) has the critical (and unappealing) assumption that market
goods and home production are perfect substitutes, and (2) allows for
time spent at home to be a combination of leisure and production. Within
this model the household maximizes a household utility function defined
over consumption and leisure subject to a series of standard time and
budget constraints, and a Cobb-Douglas household production
function." Appendix A describes the basic equations of the model,
but here it is only necessary to address the household production
function:
(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [H.sub.1] and [H.sub.2] are the quantities of time each
devotes to the household, [M.sub.1] and [M.sub.2] are respective human
capital measures of the "effective" home production time that
takes into account jointness in production, [X.sub.z] is the composite
market good used within the home, and A is a scale parameter (see
Appendix A). (12) The key parameters that need to be estimated are a, b,
[[gamma].sub.1], [[gamma].sub.2], and [beta].
The parameters a and b measure an individual's relative
productivity in the home versus the market. Values a = b = 1 imply that
both persons 1 and 2 are equally productive across the two sectors and
have no specialized human capital for the home or market. A comparative
advantage in the home for person 1 would imply a > 1. The parameters
[[gamma].sub.1], [[gamma].sub.2], and [beta] are the returns to scale
parameters of the household production function, and measure the
relative importance of person 1's and 2's time and market
goods. Hence, [[gamma].sub.1] + [[gamma].sub.2] + [beta] = 1 would imply
constant returns to scale in the household. The Graham and Green model
would suggest that a strong division of labor would exist when there is
a large difference between a and b, and the [gamma] of one spouse is
relatively large. According to conventional wisdom, this division of
labor is enhanced by sexual differences between the couple. Thus, across
the different sexual orientations there should be significant
differences in these parameter values if sex differences in couples
matter for household production.
A twist in the Graham and Green model is that it allows for
"jointness" in leisure and household production. That is, time
spent in the home can be both productive and enjoyable (e.g., gardening
or cooking). This relationship is defined by Equations (A6) and (A7) in
Appendix A, but here it is only necessary to understand the parameter
[[delta].sub.i], which measures the degree of jointness for each person.
Thus, [[delta].sub.1] =0 means no jointness for person 1--housework is
only a chore. On the other hand, [[delta].sub.2] = [infinity] means
perfect jointness for person 2--housework is like a vacation.
The Graham and Green set-up is purely neoclassical: the household
maximizes utility subject to all of the various time, goods, and
production constraints listed in Appendix A. Solving from the system of
first-order conditions, Graham and Green derive a simple log-linear
demand equation based on observable variables, which includes the
following demand for [H.sub.2]:
(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
where [W.sub.1] and [W.sub.2] are the respective wages, c' is
a constant, and
q = (1 - [beta]) (1 + [[delta].sub.2]) - [[gamma].sub.2]
- ([[gamma].sub.1] (1 + [[delta].sub.2]))/(1 + [[delta].sub.1]).
Equation (2) can be estimated with census data as
(3) ln [H.sub.2] = [c.sub.0] + [c.sub.1] ln A + [c.sub.2] ln
[W.sub.2] + [c.sub.3] ln [W.sub.1] + [c.sub.4] ln [M.sub.2] + [c.sub.5]
ln [M.sub.1].
Here, the [c.sub.i] coefficients are the compound functions of the
model parameters found in Equation (2). Graham and Green provide
formulas for backing all of the relevant household production function
parameters (a, b, [[gamma].sub.1], [[gamma].sub.2], and [beta]) from the
[c.sub.i] coefficients. (13)
The Graham and Green system is under-identified by two. (14) To
solve this identification problem Graham and Green must impose two
additional restrictions on the model, and this results in nine different
cases. These are Case 1, no jointness in household production
([[delta].sub.1] = [[delta].sub.2] = 0); Case 2, equal productivity in
home and market (a = b = 1); Case 3A, constant returns to scale (CRS)
and no jointness for person 1 ([[gamma].sub.1] + [[gamma].sub.2] +
[beta] = 1, [[delta].sub.1] = 0); Case 3B, CRS and no jointness for
person 2 ([[gamma].sub.1] + [[gamma].sub.2] + [beta] = 1,
[[delta].sub.2] = 0); Case 3C, CRS and neutrality of person 1 's
time ([[gamma].sub.1] + [[gamma].sub.2] + [beta] = 1, a = 1); Case 3D,
CRS and neutrality of person 2's time ([[gamma].sub.1] +
[[gamma].sub.2] + [beta] = 1, b = 1); Case 3E, CRS and equality of
relative productivities at home and in the market ([[gamma].sub.1] +
[[gamma].sub.2] + [beta] = 1, a = b); Case 3F, CRS and equal jointness
of time ([[gamma].sub.1] + [[gamma].sub.2] + [beta] = 1, [[delta].sub.1]
= [[delta].sub.2]); and finally, Case 4, equal jointness and relative
marginal productivity (a = b, [[delta].sub.1] = [[delta].sub.1]).
Following Graham and Green, the household production function is
estimated for each one of these cases. No argument is made in favor of
one restriction over another given that the objective is to compare the
value of household production across different couple-types.
Once Equation (3) is estimated, the household production parameters
are calculated under the various case restrictions, and combined with
the average values of the variables in Equation (1) to estimate the
value of household production for a given home. When these values are
averaged over all the individuals within a group, a measure of the
average value of household production within that group is arrived. The
procedure is not perfect and makes some heroic assumptions, but it works
with the level of data available, and provides for a comparison across
different types of couples.
IV. DATA
The 2006 Canada census is a 20% random sample of the
noninstitutionalized Canadian population. It contains 6,470,472
individual records and represents 1,813,576 census families. From all
records the married or cohabitating couples (with or without children)
were selected, leading to a total sample of 1,463,895 couples. Table 1
provides some descriptive statistics for the six groups under
consideration, and variable definitions are found in Table A1 of
Appendix B. (15)
The census contains measures of time at home spent on housework,
child care, and senior care. Following the theory of household
production, the time spent on these three activities was combined to
create a total household time variable for each spouse. The census
contains annual income and wage information, as well as market place
hours information for the week prior to the census. (16) The variable
for weekly hours worked in the workforce often contained too many
missing observations to be useful. As a result, wages were calculated
using the annual after-tax income and total annual hours of work. (17)
Because many couples are made up of one spouse who does not work outside
the home, the Heckman two-step procedure is used to estimate a selection
equation and then adjust the wage equation to come up with estimated
wages for all individuals. (18)
Table 1 reports the estimated population averages among the
different family types for the variables of interest. Several
interesting features stand out. First, heterosexual households with
children are larger on average than gay or lesbian households with
children. (19) Second, the differences in family income across the
different couple-types are typical: gay households with the highest,
followed by lesbian and heterosexual households. Third, the income
differences between the spouses are high and similar for gays and
heterosexuals (with and without children), but lower for lesbian
couples. Correspondingly, the average amount of time spent on household
activities varies considerably across the different couple-types. There
is a considerable difference in spouse time spent in the household for
heterosexual couples, with very little difference for gays and lesbians.
Finally, there is a larger age gap for heterosexual and gay couples,
compared to the small age gap for lesbian couples. Just looking at these
averages suggests that gay and lesbian couples are less likely to be
specializing in household production and market work--Becker's
prediction seems confirmed.
One of the most significant facts comes from the last row of Table
1; the estimated population sample sizes are low for gay and lesbian
households. Whereas there are millions of heterosexual households, there
are very few gay and lesbian households with children, and even the
total population estimates of 23,065 gay and 19,585 lesbian couples is
relatively small. (20)
V. ESTIMATION
Estimation of a household production function begins with
estimating the demand for household time in Equation (3) for the six
different household types in the sample. Equation (3) regresses
household time of person 2 on wages for both spouses, a general scale
parameter, and each spouse's human capital. Following Graham and
Green, the scale parameter is a vector combination of household
characteristics. To the extent possible, I used variables similar to
Graham and Green: the value and size of the home, family size, and the
age of the youngest child. Likewise, the human capital variables follow
Graham and Green, and are combinations of age and education levels. The
estimates for Equation (3) are found in Table 2.
Table 2 shows that in terms of responses to the cost of time,
heterosexual households behave as general household theory would
predict: increases in the cost of time to person 2 leads to reductions
in his/her time spent at home (coefficients for after-tax income are
-.54 and -.87), and increases in the cost of time to person 1 leads to
an increase in person 2's time spent at home (coefficients are .63
and . 18). Both heterosexual regressions (with and without children)
show that as the human capital levels of person 2 increase, the hours at
home increase (coefficients for [M.sub.2] are 0.30 and 1.14). Similarly,
as the scale parameter increases, person 2 spends more time at home
(coefficients for A are .16 and .17). All of the heterosexual results
make sense in terms of traditional household models and are very similar
in size and sign with those found by Graham and Green. (21)
The regression coefficients for the other four household types show
some considerable differences. Most notable is the reduced precision and
lack of statistical significance even though the sample size is
substantial. In addition, same-sex couples do not systematically behave
the way heterosexual couples do with respect to the cost of time.
Indeed, with respect to the reaction of person 2's household hours
to the cost of time, with the exception of gay households without
children, the other household types behave in the opposite way of
heterosexual households; that is, the coefficients for after-tax income
have the opposite signs compared to those for heterosexuals. This may be
caused by different household behavior and bargaining, but it reflects a
reduced sexual division of labor.
The difference in coefficients between opposite- and same-sex
households is not quite as striking for the human capital variables (M)
and the household scale parameter (A). In general, with respect to
changes in these variables the same-sex households respond in a similar
fashion to opposite-sex households. Thus, when human capital improves,
family members from all types of families increase the amount of time in
household production. When the scale of household production increases,
all types of households again increase the amount of time in producing
household commodities. If gay and lesbian families respond to human
capital and scale changes in ways similar to heterosexual households,
then their different response to changes in the costs of time may be due
to a lack of sexual division of labor since the other alternative
explanations are likely to affect human capital and scale variables as
well. (22)
As mentioned, Graham and Green provide closed form solutions of all
the parameters of the production function based on the coefficient
estimates of Table 2. (23) Here I produce the final calculated parameter
values based on each special case in Table 3, only for the couples with
children. (24) Although a complicated and daunting table, Table 3
provides the essential parameter estimates of Equation (1) necessary to
arrive at a value of household production (Z). Consider the top panel of
Table 3 for heterosexuals with children. The [[gamma].sub.1] and
[[gamma].sub.2] parameters measure the importance of time in home
production. Looking across all of the cases, the values are all small
and generally positive. On the other hand, [beta] measures the
importance of market goods in household production. In all the cases
[beta] is slightly bigger than 1. Together these mean that heterosexual
households effectively experience constant returns to scale, and scale
is driven almost entirely by [beta].
Looking at the same rows for the gay and lesbian households shows
that lesbian households are almost identical to heterosexual homes in
terms of scale and the magnitudes of the parameters, and that gay
households are slightly different. Although gay households generally
experience constant returns to scale (i.e., [[gamma].sub.1] +
[[gamma].sub.2] + [beta] [approximately equal to] 1), [beta] is 10%
higher and [[gamma].sub.2] tends to be more negative. This means that
market goods play an even more important role in gay household
production and for person 2 there is a greater amount of jointness
between leisure and housework. (25)
Consider now the values of a and b across the different cases and
household types in Table 3. These parameters measure the relative
productivity of each spouse in the home versus the market. In almost all
of the cases, except for gay person 1, these values are less than 1.
Almost everyone is more productive in the market rather than the home.
These three general findings--that all households experience
constant returns to scale; that the home production elasticity with
respect to market goods ([beta]) is always greater than the elasticity
with respect to time ([[gamma].sub.1] and [[gamma].sub.2]); and that
when a and b are not constrained to be 1, they are almost always less
than 1--were also found by Graham and Green. They also play a
significant role in the household production estimates because they mean
that (1) market goods play a much larger role in the production of
household commodities than time, and (2) time devoted to market activity
to generate income is more productive than time used in the home
producing household commodities directly. No doubt this reflects the
ease with which goods and technology can easily substitute for
time--especially in the modern home.
The importance of [beta] in determining the value of household
production means that [X.sub.z] is the critical input. However, market
goods within the home are a function of income, and so income
differences across different household types will mostly drive
differences in the value of household production. For example, gay
households, on average, tend to have higher joint incomes and higher
levels of education. This means these households generate lots of market
goods, and given the higher value of [beta] for gay households, they use
these market goods effectively in the home. Similarly for lesbian
households, their high joint household income contributes to large
values of household production. Thus, even though gay and lesbian
households are "same-sex" and likely have reduced sexual
division of labor gains (based on Table 2), the general elasticity
differences in the key parameters will more than compensate for the
inability to exploit sexual differences in spouses.
A. The Value of Household Production
The final step to estimate the value of household production
requires a return to Equation (1). This equation provides the
relationship between household production (Z), the parameters, and
choice variables. Table 3 provides the parameter estimates for a, b,
[[gamma].sub.1], [[gamma].sub.2] and [beta] that can now be plugged into
Equation (1). The value for hours [H.sub.1] and [H.sub.2] comes directly
from the data, and Graham and Green provide a procedure to indirectly
estimate the values of A, [M.sub.1], and [M.sub.2]. This procedure
involves taking a weighted average (the weights are based on the
estimated coefficients) of the mean values of the variables that make up
A, [M.sub.1], and [M.sub.2]. (26) More problematic is [X.sub.z] the
value of market goods used to produce household commodities. Since the
census contains no variable comparable to [X.sub.z], I use a procedure
similar to that used by Graham and Green and approximate [X.sub.z] using
the after-tax income levels of both spouses multiplied by the average
fraction of after-tax income that is spent on household consumption by
income quintiles. These fractions come from other Statistics Canada
documents, and moving from the lowest to the highest quintiles, these
fractions are 1.17, .907, .790, .694, and .538. (27) Thus, to calculate
[X.sub.z], the total after-tax income of the household is multiplied by
the relevant fraction.
Once all parameter and choice variable values are calculated, they
are plugged back into Equation (1) to calculate the value of household
production for a given couple. Following this procedure for every couple
gives a distribution of household production values for each household
class. The averages and standard errors of each class are reported in
Table 4. Each value in the table is the average of the estimated value
of household production (with its standard error in parentheses below)
for a given household type and for a given set of restrictions on the
production function. Considering only the heterosexual couples, the
values in Table 4 (adjusting for inflation) are comparable to the values
found by Graham and Green almost 30 years earlier. (28)
What can be said about the value of household production across the
different sexual orientations? First, given the large standard errors,
there is no statistical difference across the different household types,
and perhaps this is the most important lesson. Given the role and wide
dispersion of income across couples, and given the relative unimportance
of time in household production, the gender combination of the couple is
not important. Other factors dominate this effect. In particular, given
the relative size of the [beta] parameter to the [gamma]'s, the
value of household production is driven mostly by the amount of
[X.sub.z] used, and this is determined by income. Since the income
distribution within any class is enormous compared to the differences
across a class, there is no statistical difference in Z across
heterosexual, gay, or lesbian homes.
On the other hand, if we just consider the average of the estimated
values of household production, some interesting features appear that
may be worthy of speculation and further study. First, heterosexual
households produce about the same value of household production, with or
without children, at around $48,000. Given this similarity, and the
similarity between both types of heterosexual households in Table 2, it
can be concluded that these two types of households are specializing in
similar ways. This no doubt reflects the expectation of future children
within all opposite-sex households, leading to similar levels of
specialization, total income, spouse income differences, and spouse age
differences. For example, from Table 1 there is a strong similarity in
the age gap between opposite-sex couples with and without children: 2.69
versus 2.58 years--again, suggesting similar behavior regardless of
children.
For both gay and lesbian households the presence of children makes
a large difference, but in opposite ways. The average value of household
production for gay couples with children is $79,256, but only $24,712
for couples without children. Indeed, gay households with children
produce the largest value of household production. (29) Referring back
to Table 1, this type of couple has the higher level of total income,
and the largest spouse income difference. Hence gay couples with
children have a large elasticity of home production with respect to
market goods (income), and they have large levels of income. On the
other hand, gay households without children produce the lowest values of
household production, almost 1/3 of their "with child"
counterparts. The difference in household production levels is driven
mostly by the value of [beta] for gays without children, which equals
.99--identical to both types of lesbian couples. The large difference
between the two types of gay households suggests that most gay
households without children are not on the path to becoming parents.
(30)
Finally, for lesbians with children the average value of household
production is $36,997, but it is $53,033 when children are not present.
Lesbian couples would appear similar to heterosexuals when there are no
children, but have lower values of household production when children
are present. Of all couple-types, lesbians are the most similar to each
other. Their age and income differences are small, they are younger on
average, and their incomes are similar to heterosexuals. (31)
VI. CONCLUSION
Estimating household production functions involves a number of
(heroic) assumptions, and the specific levels estimated cannot be taken
too literally. This caution has to be heeded even more so when the data
limitations and conceptual difficulties of different sexual orientations
are added to the mix. However, these problems are less of a concern when
examining differences between different household types. Thus,
conditional on the procedure, this article has made the first estimates
of household production values for gay and lesbian households in
comparison to heterosexual ones. (32) In terms of fundamentals, gays and
lesbians would appear to behave differently than heterosexual couples.
They are more similar in age and income, their hours of work in the
household generally do not respond in similar ways to changes in the
cost of time, and there would appear to be large differences between gay
and lesbian households, with and without children. (33)
However, for all couple-types the input of market goods (driven by
income) plays a much more important role in the household production
function than the role of time, and human capital skills are much more
valuable in the market than in the home. These effects swamp any
differences that arise from a loss of sexual division of labor. Perhaps
most important, given the wide dispersion of income within each type of
sexual orientation, the variance in the estimates of the value of
household production are so large that there is no statistical
difference between the different types of sexual orientations. Thus,
although the point estimates found here confirm other findings that
these three couple-types are likely different in their behavior and that
Becker was right in terms of the sexual specialization of same-sex
households, as a practical matter, sexual specialization in household
production is dominated by the ability to generate income.
In almost every U.S. legal case dealing with same-sex marriage the
issue of household production arises. Those in favor claim that marriage
would encourage more household production. Those opposed claim that
same-sex couples amount to roommates and that any gains to household
production would be small. The results of this article would suggest
that both are right to some extent. The gains from a sexual division of
labor are smaller for same-sex couples, but this does not matter much
for household production. In other words, the question of same-sex
marriage should not rest on household production.
ABBREVIATIONS
CRS: Constant Returns to Scale
OLS: Ordinary Least Squares
doi: 10.1111/ecin.12095
Online Early publication April 30, 2014
APPENDIX A
The Graham and Green model consists of the six equations. First is
a household utility function that depends on consumption, C, and
"effective" leisure [M.sub.i][L.sub.i]:
(A1) U = U (C, [M.sub.1][L.sub.i], [M.sub.2][L.sub.2])
C is the sum of goods purchased in the market [X.sub.m], and
household commodities Z.
(A2) C - [X.sub.m] + Z
Equation (A2) is the critical "perfect substitute"
assumption in the model, which implies that choice is a matter of
opportunity costs alone, and that time in household production is
independent of nonlabor income. The household commodities are produced
according to a Cobb-Douglas function:
(A3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [H.sub.1] and [H.sub.2] are the time inputs of person 1 and
2. [X.sub.z] are those purchased market goods that are used in household
production. The household faces several constraints. First, a budget
constraint:
(A4) [X.sub.m] + [X.sub.z] = [W.sub.1] [N.sub.1] +
[W.sub.2][N.sub.2] + v
where [W.sub.1], [W.sub.2], [N.sub.1], [N.sub.2] are the respective
wages and hours worked, and v is the amount of unearned income. Next
there is a time constraint, where total time T is divided between work
at home H, the market N, and a residual l:
(A5) [l.sub.i] + [H.sub.i] + [N.sub.i] = T, i = 1, 2.
Finally, Equation (A6) reflects the possibility of joint production
within the household:
(A6) [L.sub.i] - [l.sub.i] + g ([H.sub.i]), i = 1, 2.
and where
(A7) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Leisure [L.sub.i] is the sum of the residual time, plus a fraction
of the time spent doing housework. In the Graham and Green model the
household maximizes Equation (Al) subject to the constraints in
Equations (A2)-(A7).
APPENDIX B
TABLE B1
Definitions of Variables
Variable Name Definition
Wage variable
After-tax income = After-tax income as reported on income
tax or self-reported
Human capital variables
Age = Age in years
Education = 1 if no high school diploma
= 2 if only high school diploma
= 3 if trades certificate
= 4 if registered apprentice
= 5 if college credit less than 1 year
= 6 if college credit 1-2 years
= 7 if college credit greater than
2 years
= 8 if college diploma
= 9 if earned Bachelor's degree
= 10 if Bachelor plus college diploma
= 11 if professional degree
= 12 if earned Master's degree
= 13 if earned PhD
Scale variables
Family size = The number of people in the household
Value of home = Dollar value of occupied residence
Number of rooms = Number of all rooms in residence
Age youngest child = Age in years of youngest child
REFERENCES
Allen, D.W., and S.E. Lu. "Marriage and Children: Differences
Across Sexual Orientations." Working Paper, Simon Fraser
University, 2013.
Badgett, M. V. L. "Gender, Sexuality, and Sexual Orientation:
All in the Feminist Family?" Feminist Economics, 1(1), 1995,
121-39.
--. Money, Myths, and Change: The Economic Lives of Lesbians and
Gay Men. Chicago: University of Chicago Press, 2001.
Becker, G. A. Treatise on the Family. Cambridge, MA: Harvard
University Press, 1981.
Biblarz, T., and E. Savci. "Lesbian, Gay, Bisexual, and
Transgender Families." Journal of Marriage and Family, 72(3), 2010,
480-97.
Carrington, C. No Place Like Home: Relationships and Family Life
Among Lesbians and Gay Men. Chicago: University of Chicago Press, 1999.
Experian Information Solutions. The 2012 LGBT Report: Demographic
Spotlight. New York: Experian Simmons, 2012.
Fitzgerald, J., M. Swenson, and J. Hicks. "Valuation of
Household Production at Market Prices and Estimation of Production
Functions." Review of Income and Wealth, 42(2), 1996, 165-80.
Giddings, L. "But Who Mows the Lawn? The Division of Labor
within Same-Sex Households," in Women, Family, and Work: Writings
on the Economics of Gender, edited by K. Moe. Malden, MA: Blackwell
Publishing Ltd., 2003.
Graham, J., and C. Green. "Estimating the Parameters of a
Household Production Function with Joint Products." Review of
Economics and Statistics, 1984, 277-83.
Gronau, R. "Home Production--A Forgotten Industry."
Review of Economics and Statistics, 62, 1980, 408-16.
Jespen, L., and C. Jespen. "An Empirical Analysis of the
Matching Patterns of Same-Sex and Opposite-Sex Couples."
Demography, 39(3), 2002, 435-53.
Kooreman, P., and A. Kapteyn. "A Disaggregated Analysis of the
Allocation of Time within the Household." Journal of Political
Economy, 97(2). 1987, 223-49.
Kurdek, L. "The Allocation of Household Labor by Partners in
Gay and Lesbian Couples." Journal of Family Issues, 28(1), 2007,
132-48.
Nock, S., and M. Brinig "Weak Men and Disorderly Women:
Divorce and the Division of Labor," in The Law and Economics of
Marriage and Divorce, edited by A. W. Dnes and B. Rowthorn. Cambridge:
Cambridge University Press, 2002.
Oerton, S. "Reclaiming the 'Housewife'? Lesbians and
Household Work," in Living "Difference": Lesbian
Perspectives on Work and Family Life, edited by G. Dunne. Stroud, UK:
Haworth Press, 1998.
Patterson, C., E. Stufin, and M. Fulcher. "Division of Labor
Among Lesbians and Heterosexual Parenting Couples: Correlates of
Specialized Versus Shared Patterns." Journal of Adult Development,
11(3), 2004, 179-89.
Pollak, R., and M. Wachter. "The Relevance of the Household
Production Function and Its Implications for the Allocation of
Time." Journal of Political Economy, 83, 1975, 255-77.
Rosenzweig, M., and P. Schultz. "Estimating a Household
Production Function: Heterogeneity, the Demand for Health Inputs, and
Their Effects on Birth Weight." Journal of Political Economy, 91,
1983, 723-46.
Suen, W., and H. K. Lui. "A Direct Test of the Efficient
Marriage Market Hypothesis." Economic Inquiry, 37(1), 1999, 29-46.
(1.) See Nock and Brinig (2002) for a nice summary of the role that
sexual division of labor has played in divorce. Becker (1981), and
Badgett (1995) discuss the effect sexual orientation can have on the
sexual division of labor and the subsequent marriage benefits.
(2.) The 2011 census rules were changed to allow voluntary
responses. Hence the 2011 census may not be a true probability sample,
and to-date is still not available.
(3.) Same-sex couples in Canada have had all taxation and
government benefits since 1997. The first Canadian same-sex marriage
took place on January 14, 2001 at the Toronto Metropolitan Community
Church. These early marriages became the basis of a successful legal
challenge which ended at the court of appeal on June 10, 2003. On July
20, 2005, the Federal government passed the Civil Marriage Act that made
Canada the fourth country in the world to legalize same-sex marriage.
Thus, different people date the arrival of same-sex marriage in Canada
as 2001,2003, or 2005. Biblarz and Savci (2010, p. 490) note that
legalization has reduced the stress and stigma of homosexuality in
Canada, which makes it more likely that respondents would be
unintimidated to respond correctly to Statistics Canada surveys.
(4.) Here, for the purpose of estimating the household production
function, I make no distinction between married and cohabitating
couples. First, the census groups them together for same-sex couples.
Second, in Canada the distinction has had no legal implication since
1997 when cohabitating couples were granted all legal rights and
responsibilities as married couples.
(5.) Suen and Lui (1999) provide another model for estimating
household production.
(6.) See Giddings (2003), Kurdek (2007), or Patterson, Stufin, and
Fulcher (2004) for small sample studies of equal allocation of household
labor for lesbian couples. Oerton (1998) points out that lesbian couples
may still have a "housewife," but this identification is not
based on traditional gender roles. Two other book-length treatments that
discuss the relationship between the market and home for same-sex
couples are Carrington (1999) and Badgett (2001).
(7.) See Jespen and Jespen (2002), who show some differences in the
matching of different types of couples.
(8.) There are a few exceptions. For example, Fitzgerald, Swenson,
and Wicks (1996) are able to directly estimate a household production
function given the unique design and extremely small dataset they
collected. Rosenzweig and Schultz (1983) use birth weight as a measure
of output. In both cases, the special features of the data collected
allowed for a direct estimation. As Fitzgerald, Swenson, and Wicks point
out, however, "With data only on time use in household production,
indirect estimation of household production functions and the use of
these production functions to estimate the value of production is the
best that can be done" (p. 166).
(9.) For example, see Kooreman and Kapteyn (1987), Gronau (1980),
and Graham and Green (1984).
(10.) See Poliak and Wachter (1975).
(11.) The presence of same-sex and cohabitating unions means that
the use of nouns like "husband" and "wife" or
"male" and "female" are not appropriate. Here I
simply refer to person "I" and "2" where person 1 is
self-identified in the census as the "main provider." Later,
household production values are reported when person 2 is switched to be
the main provider.
(12.) The variables on the right-hand side are observable (although
[M.sub.1], [M.sub.2] and A are the linear combinations of various
observable variables), while Z is not observable. A household commodity
(Z) could be something like clean teeth or a meal. Keeping teeth clean
requires time (H) and a tooth brush ([X.sub.z]).
(13.) See Graham and Green (1984, p. 279). The actual formulas
depend on the various identification assumptions. For example, if there
is no jointness (8|=52=0), then [[gamma].sub.1] = - [c.sub.4]/C], but if
there is neutrality in human capital (a = b = 1), then [[gamma].sub.1] =
[c.sub.5]/[c.sub.1].
(14.) Examination of Equation (2) shows that there are only five
variables to estimate seven parameters.
(15.) The census file used is not a public dataset. To use the
data, a proposal is screened by the Social Sciences Research Council of
Canada, a Royal Canadian Mounted Police criminal check is conducted, and
the researcher becomes a deemed employee of Statistics Canada subject to
the penalties of the Statistics Act. Empirical work was conducted at the
SFU Research Data Center, and all results were screened by Statistics
Canada before release. Statistics Canada does not allow the release of
the sample means, nor maximums or minimums of any variables.
Furthermore, population sizes are rounded off to the nearest 5. Hence
the averages reported in Table 1 are the averages of the estimated
population variables.
(16.) For most respondents the income information comes from their
tax return. Otherwise it is self-reported.
(17.) In Canada individuals are taxed, not households.
(18.) This procedure is used by Kooreman and Kapteyn (1987).
(19.) All of the heterosexual means, for both those with and
without children, are statistically different from the means for gays
and lesbians. However, most of the gay and lesbian means are not
statistically different from each other. For example, the 95% confidence
intervals for family size for couples with children are 3.869-3.873 for
heterosexuals, 3.32-3.64 for gays, and 3.48-3.60 for lesbians.
(20.) Allen and Lu (2013), using the Canadian Community Health
Survey that directly identifies sexual orientation, find a population
estimate of 80,209 lesbians and 143,038 gay men in Canada. This amounts
to .83% of the population and does not include bisexuals. Hence the
estimates here for the number of same-sex couples is consistent with the
data from the health survey.
(21.) The core Graham and Green results to the same regression
(1984, Table 3, p. 280), compared to the base results of Table 2 for
heterosexual couples with children are shown below (standard errors in
parentheses). With one exception, the signs are all the same for each
variable.
Variable Graham and Green Table 2
Husband's wage 0.047 (0.07) 0.627 (0.007)
Wife's wage -0.169 (0.05) -0.544 (0.007)
Wife's age 0.129(0.07) 0.246 (0.01)
Husband's education -0.091 (0.11) -0.124 (0.002)
Wife's education -0.191 (0.14) 0.057 (0.002)
Family size 0.577 (0.13) 0.452 (0.005)
Number of rooms 0.207 (0.08) 0.080 (0.004)
Age of youngest child -0.343 (0.002)
Owing to a collinearity problem, Graham and Green do not include
the Husband's age as a regressor--this was not a problem with the
2006 Canada census. They also use four dummy variables to mark the ages
of children, whereas Table 2 uses the age of the youngest child. Graham
and Green find that as more older children are present, the wife's
home production time falls, which is consistent with the result above
that when the age of the youngest child increases, the wife's
household time falls.
(22.) An alternative approach to estimating Equation (3) pooled all
of the data across the different household types, using the same-sex
indicators interacted with the variables in the equation. This was
estimated multiple times, starting with just the wage variables, adding
the human capital variables, and then finally adding the scale
variables. When all variables are included, the results are essentially
the same, and the general conclusion of the article follows. There is no
getting around the problem that same-sex households are rare, and this
results in a lack of estimation precision. When just the wage variables
are included, all of the coefficients are statistically significant, but
also they are all negative.
(23.) See Graham and Green (1984. p. 279).
(24.) With the exception of one parameter for one household type
(brought up below), the parameters for households without children are
similar.
(25.) A value of [gamma] < 0 means that the home can have more
by reducing the amount of time in home production. Hence, the time spent
must be generating utility directly through the enjoyment of the
housework.
(26.) The human capital variables [M.sub.1] and [M.sub.2] are
linear combinations of the Age and Education variables. If [c.sub.a] and
[c.sub.e] are the coefficients from estimating Equation (3), then
[M.sub.1] is [c.sub.a]/([c.sub.a] + [c.sub.e]) x Age +
[c.sub.e]/([c.sub.a] + [c.sub.e]) x Education.
A similar procedure is followed for [M.sub.2]. Similarly, the scale
variable A is a linear combination of Family Size, the Value of Home,
the Number of Rooms, and the Age of Youngest Child. The weights for this
combination are again the coefficient of each variable from the
estimation of Equation (2) divided by the sum of the coefficients on
these four variables. This follows the procedure of Graham and Green
(1984, p. 282).
(27.) See Statistics Canada, Survey of Household Spending, Table
RY2007 C2FPY0032 IncomeQuintiles. To date there is no evidence to
suggest different propensities to consume for the different
couple-types. Although there may be a difference across the
couple-types, a recent consumer report finds essentially no difference
in average household consumption expenditures across heterosexual, gay,
and lesbian homes. According to the consumer report, the higher
household incomes for gays and lesbians is offset by "the fact that
both lesbian and gay adults tend to reside in larger cities where the
cost of living can be considerably higher" (Experian Information
Solutions 2012, p. 8). Although slight, this may justify using the same
income shares for the different household types to estimate [X.sub.z].
(28.) Dropping the two estimates by Graham and Green that make no
sense (i.e., the household production value estimates equal to $178 and
$1,636), and using the Canadian consumer price index for adjustment, the
average Graham and Green estimate of household production value is
$41,917. This is well within the range of values found in Table 4 for
heterosexual couples.
(29.) Allen and Lu (2013) investigate several behaviors (drug use,
smoking, sexual behavior, and sorting) across different sexual
orientations using the Canadian Community Health Survey, and they also
find the presence of children in same-sex households makes an enormous
difference in behavior, but not for opposite-sex households.
(30.) Allen and Lu (2013) find large differences in the way gay
couples with children behave compared to gay couples without children,
with respect to drug use, smoking, and sexual behavior. This difference
is much smaller for heterosexual couples, with or without children.
(31.) As noted, within the census an individual self identifies as
the "main provider," and for heterosexual couples this is
almost always the male. Such a distinction may be irrelevant in a
same-sex household, and the person self identified as the main provider
may be arbitrary. The Graham and Green exercise was repeated, switching
person 1 and person 2, with some interesting results. The average values
of estimated household production across all the different cases
becomes:
Heterosexuals Gays
With Without With
Children Children Children Children
Average HP $30,303 $43,893 $57,447 $24,875
Lesbians
With
Children Children
Average HP $39,661 $52,582
Three things are noteworthy. First, the values of household
production are all lower, reflecting the on average lower incomes of
person 2 in the household. Second, the only household estimate that
changes in a large way is heterosexual households with children. This
reflects the sexual division of labor in opposite-sex homes. However,
all of the household production values remain statistically
insignificant from each other, and so the main conclusion remains:
although there is evidence of differences in specialization across
sexual orientations, these differences are swamped by variation within a
household type.
Case 1 Case 2 Case 3A Case 3B Case 3C
Gays and lesbians with children
Average over all cases: $44,193
39,489 47,165 48,867 48.862 47.652
(21,345) (25,228) (26,118) (26,528) (26,869)
Gays and lesbians without children
Average over all cases: $23,149
19,714 25,087 22,628 23,532 22,601
(16,417) (22,058) (19,881) (19.568) (19,831)
Case 3D Case 3E Case 3F Case 4
Gays and lesbians with children
Average over all cases: $44,193
47,462 48.864 48,863 20,517
(25,406) (26.196) (26,560) (10,972)
Gays and lesbians without children
Average over all cases: $23,149
22,423 22,622 22,601 27,141
(18,912) (19.870) (19,832) (23,954)
(32.) It would have been more sophisticated to estimate the
parameters directly using a nonlinear estimator. However, such a
procedure rests on the assumption that the specified model is correct,
and most canned programs are very sensitive to missing data. Here the
ordinary least squares (OLS) estimates likely provide a more robust
method.
(33.) There are enough differences between gay and lesbian
households to justify treating them in separate regressions. When they
are combined, the following estimates of household production values
(and standard errors) are obtained:
The results, as might be expected, lie between the values found in
Table 4 for gays and lesbians.
DOUGLAS W. ALLEN, Thanks to Krishna Pendakur and two anonymous
referees for their productive comments.
Allen: Burnaby Mountain Professor of Economics, Department of
Economics, Simon Fraser University, Burnaby, BC, Canada. Phone 778
7823445, Fax 778 7824955, E-mail allen@sfu.ca
TABLE 1
Estimated Population Averages (Weighted Observations)
Heterosexuals Gays
With Without With Without
Children Children Children Children
Family size 3.87 2 3.48 2
Value home 249,283 202,017 237,432 227,791
Number of rooms 7.62 6.58 7.28 6.03
Age youngest child 11.83 14.59
Age person 2 42.6 53.88 44.25 42.25
Age person 1 (a) 45.31 56.50 46.07 44.64
Education person 2 4.95 4.20 5.63 6.04
Education person 1 5.27 4.58 5.88 6.76
After-tax income 1 42,960 36,073 47,257 42,320
After-tax income 2 29,333 24,696 33,490 32,660
Age difference 2.69 2.58 2.11 2.22
Income difference 28,681 23,017 33,294 25,320
HH hours 1 1782.86 928.68 1756.66 680.11
HH hours 2 2514.61 1208.77 1892.60 680.33
Hours difference 731.75 280.09 135.94 0.22
N 3,953,255 3,242,765 760 22,305
Lesbians
With Without
Children Children
Family size 3.54 2
Value home 223,016 182,296
Number of rooms 7.30 6.12
Age youngest child 9.41
Age person 2 40.17 43.03
Age person 1 (a) 40.81 44.07
Education person 2 6.11 6.19
Education person 1 6.64 6.66
After-tax income 1 40,413 36,280
After-tax income 2 32,749 31,641
Age difference 0.56 0.91
Income difference 20,786 19,244
HH hours 1 2397.30 813.70
HH hours 2 2452.43 816.94
Hours difference 55.13 3.24
N 3,330 16,255
(a) For gay and lesbian couples "Person 1" refers to the person who is
identified as the "head" of the household.
TABLE 2
Estimated Hours Equation (Weighted Observations, Variables Logged;
Dependent Variable; Logarithm of Person 2's Household Time)
Heterosexuals Gays
With Without With Without
Children Children Children Children
Wage variables
After-tax income 1 0.627 0.183 -0.243 0.031
(0.007) * (0.009) * (0.973) (0.212)
After-tax income 2 -0.544 -0.870 * 3.90 -0.239
(0.007) * (0.010) * (2.015) * (0.310)
Human capital
variables
M Person 1 -0.577 0.214 0.778 0.211
(0.013) * (0.016) * (1.090) (0.191)
M Person 2 0.304 1.142 -3.11 0.541
(0.015) * (0.016) * (1.66) ** (0.242) *
Scale variable
A 0.166 0.174 1.60 0.410
(0.007) * (0.004) * (0.712) * (0.054) *
Constant 7.55 9.04 -29.37 5.05
(0.106) * (0.133) * (15.02) * (3.19)
N (a)
F 13,641 6,769 7.85 19.08
[R.sup.2] 0.212 0.118 0.340 0.064
Lesbians
With Without
Children Children
Wage variables
After-tax income 1 -0.288 -0.215
(0.338) (0.152)
After-tax income 2 0.217 0.130
(0.517) (0.230)
Human capital
variables
M Person 1 0.214 0.663
(0.505) (0.215) *
M Person 2 0.370 0.095
(0.651) (0.266)
Scale variable
A -.0001 0.201
(0.285) (0.061) *
Constant 9.03 4.06
(3.18) * (1.73) *
N (a)
F 9.84 9.72
[R.sup.2] 0.234 0.040
Note: Standard errors in parentheses.
(a) Statistics Canada does not allow the release of the sample
sizes for each regression.
* Significant at the 5% level.
TABLE 3
Estimated Production Function Parameters (for Couples with Children)
Case 1 Case 2 Case 3A
Heterosexuals with children
[[gamma].sub.1] -.05 -.04 .05
(0.002) * (0.001) * (0.002) *
[[gamma].sub.2] .03 .02 .04
(0.001) * (0.001) * (0.001) *
[beta] 1.006 1.006 1.006
(0.055) * (0.055) * (0.055) *
a .92 1 .92
(0.019) * (0.019) *
b .66 1 .55
(0.043) * (0.031) *
Gays with children
[[gamma].sub.1] .006 .02 .006
(0.06) (0.03) (0.02)
[[gamma].sub.2] -.14 .08 -.11
(0.046) ** (0.46) * (0.67) **
[beta] 1.10 1.10 1.10
(0.44) * (0.44) * (0.44) *
a 3.19 1 3.19
(9.74) (9.74)
b .63 1 .79
(0.13) * (14.95)
Lesbians with children
[[gamma].sub.1] .02 .02 .02
(0.014) (0.008) * (0.014)
[[gamma].sub.2] -.10 .03 .01
(0.034) * (0.08) (0.028)
[beta] .99 .99 .99
(0.86) (0.86) (0.86)
a .74 1 .74
(0.38) (0.38) **
b .08 1 1.69
(0.23) (5.12)
Case 3B Case 3C Case 3D
Heterosexuals with children
[[gamma].sub.1] .03 .04 -.03
(0.001) * (0.001) * (0.001) *
[[gamma].sub.2] -.03 .04 .02
(0.001) * (0.002) * (0.001) *
[beta] 1.006 1.006 1.006
(0.055) * (0.055) * (0.055) *
a -1.54 1 .04
(0.056) * (0.002) *
b -.66 .61 1
(0.042) * (0.019) *
Gays with children
[[gamma].sub.1] .03 .02 -.01
(0.02) (0.02) (0.02)
[[gamma].sub.2] -.14 -.12 .08
(0.75) ** (0.07) ** (0.46) **
[beta] 1.10 1.10 1.10
(0.44) * (0.44) * (0.44) *
a .62 1 -.02
(0.58) (0.02)
b .63 .70 1
(0.13) * (0.13) *
Lesbians with children
[[gamma].sub.1] .10 .02 .03
(0.031) * (0.008) * (0.602)
[[gamma].sub.2] -.10 -.01 -.03
(0.034) * (0.005) ** (0.081)
[beta] .99 .99 .99
(0.86) (0.86) (0.86)
a .16 1 -.01
(0.039) * (0.021)
b .30 2.56 1
(0.881) (8.258)
Case 3E Case 3F Case 4
Heterosexuals with children
[[gamma].sub.1] .01 .58 -.05
(0.001) * (0.099) * (0.002) *
[[gamma].sub.2] .007 -.58 .12
(0.0008) * (0.097) * (0.012) *
[beta] 1.006 1.006 1.006
(0.055) * (0.055) * (0.055) *
a 3.30 -.08 .197
(0.386) * (0.013) * (0.009) *
b 3.30 -.04 .197
(0.386) * (0.005) * (0.009) *
Gays with children
[[gamma].sub.1] .03 .005 -.001
(0.04) (0.02) * (0.02) *
[[gamma].sub.2] -.13 -.10 .009
(0.08) ** (0.06) (0.04)
[beta] 1.10 1.10 1.10
(0.44) * (0.44) * (0.44) *
a .64 4.39 -9.35
(0.17) * (14.63) (35.90)
b .64 .81 -9.35
(0.17) * (0.16) * (35.90)
Lesbians with children
[[gamma].sub.1] -.008 .36 -.03
(0.050) (0.85) (0.85)
[[gamma].sub.2] .01 -.35 .14
(0.047) (0.875) (0.35)
[beta] .99 .99 .99
(0.86) (0.86) (0.86)
a -2.19 .05 .20
(5.21) (0.20) (0.18)
b -2.19 .08 .20
(5.21) (0.40) (0.18)
TABLE 4
Estimates of Household Production
Case 1 Case 2 Case 3A Case 3B Case 3C
Heterosexuals with children
Average over all cases: $48,080
24,795 40,569 45,817 43,684 45,730
(22,234) (36,897) (41,814) (39,323) (41,657)
Heterosexuals without children
Average over all cases: $48,064
31,773 72,933 54,285 51,973 49,863
(21,803) (57,103) (38,789) (36,764) (38,847)
Gays with children
Average over all cases: $79,256
56,951 91,194 69,723 69,785 69,751
(69,644) (110,972) (84,674) (86,551) (85,669)
Gays without children
Average over all cases: $24,712
21,679 26,711 25,290 25,378 25,459
(18,287) (24,444) (22,039) (21,817) (21,958)
Lesbians with children
Average over all cases: $36,997
23,426 37,970 43,755 43,857 43,755
(8,703) (13,630) (15,668) (16,248) (15,649)
Lesbians without children
Average over all cases: $53,033
34,823 81,357 59,029 59,199 59,071
(13,762) (35,443) (22,599) (22,833) (22,580)
Case 3D Case 3E Case 3F Case 4
Heterosexuals with children
Average over all cases: $48,080
53,076 45,061 41,769 92,226
(48,025) (40,503) (52,751) (85,570)
Heterosexuals without children
Average over all cases: $48,064
50,739 49,993 54,689 16,332
(36,826) (39,110) (39,680) (11,352)
Gays with children
Average over all cases: $79,256
66,490 69,783 69,720 149,908
(78,080) (86,500) (84,551) (177,774)
Gays without children
Average over all cases: $24,712
24,692 24,243 25,308 23,654
(21,554) (22,138) (22,073) (19,977)
Lesbians with children
Average over all cases: $36,997
41,490 43,379 45,472 10,055
(14,901) (16,073) (22,65!) (3,996)
Lesbians without children
Average over all cases: $53,033
48,126 56,812 60,020 18,860
(19,085) (24,889) (25,185) (8,156)
