Married Women’s Labour Supply and Intra-Household Bargaining Power * Safoura Moeeni † March 15, 2016 Abstract In some developing countries, labour force participation (LFP) of women is low and de- creasing, despite an increase in education levels and decline in fertility rates. Such trends are different from those observed in many developed countries. This paper provides an explana- tion for the female labour supply puzzle, by estimating a household bargaining model using data from 2006 to 2013 Iranian Household Income and Expenditure. I build and estimate a structural model of education, marriage, fertility and labour supply in an intra-household collective decision framework, in which bargaining power is an endogenous variable. In the model, women can increase their bargaining power in the household by obtaining education. The estimated model exhibits the features that are consistent with the data; women’s LFP is an inverse U-shaped function of bargaining power. As a woman’s bargaining power increases, she participates more in the labour market. However, over a certain level of bargaining power, women are less likely to work outside the home. Moreover, the data shows bargaining power inequality in Iran has increased, so number of women with very low and very high level of bargaining power has increased. According to the results, these two groups are less likely to participate in labour market. Thus, women’s LFP in Iran has decreased. * I am grateful to Atsuko Tanaka, Assistant Professor at University of Calgary, for her advice and valuable suggestions during the planning and development of this research. I wish to thank my referees B. Curtis Eaton and Daniel Gordon for their helpful feedback. † PhD Student, Department of Economics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada, E-mail: [email protected]1
Transcript
Married Women’s Labour Supply
and
Intra-Household Bargaining Power∗
Safoura Moeeni†
March 15, 2016
Abstract
In some developing countries, labour force participation (LFP) of women is low and de-
creasing, despite an increase in education levels and decline in fertility rates. Such trends are
different from those observed in many developed countries. This paper provides an explana-
tion for the female labour supply puzzle, by estimating a household bargaining model using
data from 2006 to 2013 Iranian Household Income and Expenditure. I build and estimate
a structural model of education, marriage, fertility and labour supply in an intra-household
collective decision framework, in which bargaining power is an endogenous variable. In the
model, women can increase their bargaining power in the household by obtaining education.
The estimated model exhibits the features that are consistent with the data; women’s LFP is
an inverse U-shaped function of bargaining power. As a woman’s bargaining power increases,
she participates more in the labour market. However, over a certain level of bargaining power,
women are less likely to work outside the home. Moreover, the data shows bargaining power
inequality in Iran has increased, so number of women with very low and very high level of
bargaining power has increased. According to the results, these two groups are less likely to
participate in labour market. Thus, women’s LFP in Iran has decreased.
∗I am grateful to Atsuko Tanaka, Assistant Professor at University of Calgary, for her advice and valuablesuggestions during the planning and development of this research. I wish to thank my referees B. Curtis Eaton andDaniel Gordon for their helpful feedback.
†PhD Student, Department of Economics, University of Calgary, 2500 University Drive NW, Calgary, Alberta,Canada, E-mail: [email protected]
1
1 Introduction
Aggregated time series data for developed countries reveal a negative relationship between fertility1
and labour force participation (LFP)2 of women, and a positive relationship between LFP of women
and their level of education.3 In contrast, data for Iran reveal a positive relationship between fertility
and LFP of women, and a negative relationship between LFP of women and their level of education.4
Figure 1 shows the low and decreasing rate of LFP of women despite an increase in the education
level and a decline in the fertility rate. While similar trends are observed in some other developing
countries, such as India and Middle Eastern and North African (MENA) countries (Syria, Morocco,
etc.), little is known about the mechanism. 5
In this paper, I develop and estimate a model of education, marriage and the household to
explain the surprising relationship seen in the Iranian data. This model would explain why we
see one pattern in developed countries and another in MENA countries. My proposed explanation
for this apparent anomaly involves changes in the intra-household bargaining power of women.
Bargaining power is the relative capacity of each of the parties to negotiate or dispute to compel
or secure agreements on its own terms. I measure women’s bargaining power by using various
indicators, including the ratio of wife’s education relative to her husband’s, 6 and find that Iranian
women’s bargaining power has been increasing substantially over the past decades. As is often the
case with countries in MENA region, Iranian women historically have had much less bargaining
1 The average number of children that would be born to a woman over her lifetime.
2 The percentage of working-age persons in an economy who are employed or unemployed but looking for a job.
3 For example, in OECD countries female LFP increased from 60 percent to 62 percent, while women averageyears of schooling has increased and fertility rate has declined between 2006 and 2013. Theoretically, education ispositively related to women’s labour force participation because education raises income as well as the opportunitycost of non-market activities. Also, the inverse relationship between fertility and female LFP rate has proven to beempirically significant and robust (Bloom et al. (2009) [11]). The economic conceptualization of the relationshipbetween women’s LFP and fertility emphasizes the opportunity cost of children.
4 According to data published by Statistical Center of Iran (SCI), fertility has declined from six births per womanin the 80’s to two births in recent years, and the number of women who attended university increased 131 percentin the last ten years. At the same time, female LFP fell by five percentage points, from 17 percent to 12 percent.
5 For example, Indian female LFP fell by seven percentage points, from 37 percent to 28 percent and Syrian femaleLFP fell from 16 percent to 14 percent, despite rapidly increasing educational attainment for girls and decliningfertility between 2006 and 2013.
6 One indicator for women’s bargaining power is the ratio of wife’s education relative to her husband’s. Accordingto this indicator, a couple with same education level have equal power in decision making within the household. Aseducation gap with wife and husband increases, the balance of the power will be disrupted.
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Women's LFP
Figure 1: Education, Fertility and LFP
Source: Statistical Center of Iran (SCI)
power within the household than women in developed countries. For example, in many developed
countries there is not much difference between male and female in years of education. 7 While
women in Iran used to attain less education and have more children, women’s bargaining power in
Iran has substantially increased as a result of the recent increase in their education level. Greater
bargaining power allows women to steer allocations in their preferred direction. For instance,
women with larger bargaining power tend to have fewer children and prefer staying at home to
working outside if they find little opportunity in the labor market. Thus, an increase in women’s
household bargaining power can account for a negative education-LFP relationship as well as a
negative education-fertility relationship. 8
The goal of this paper is to investigate my hypothesis by developing a model of intra-household
bargaining power using Iranian household data and to provide an explanation for seemingly incon-
7 Maitra and Ray (2005) [33] showed that the average value of the female share of education is approximately 0.5for Australian household.
8 During this time other factors which affect women’s LFP (e.g. husband’s income, access to and cost of daycareand education cost) didn’t change. Moreover, I control for economic conditions.
3
gruent labor supply trend observed in some developing countries. This paper develops a general
collective model of household (Chiappori (1992) [18]) by allowing the education, marriage and fer-
tility decisions to be endogenous. Unlike the existing literature of household bargaining, my model
allows women to choose their bargaining power through education. So, in my model not only the
bargaining power is endogenous but also every factor that affects the bargaining power (such as
the husband-wife ratio of education and earnings) is endogenous. Such modification is critical to
model implication since, in real world, education and husband properties are not exogenous for
women. Furthermore, the model captures two counteracting effects of education on labour force
participation. On the one hand, higher education increases the potential wage and thus increases
the probability of participation in the labour market. On the other hand, female’s bargaining power
is positively affected by the woman’s education level. While the first effect of education is well ac-
knowledged, the second effect is not considered as of the foremost importance and is often ignored
in the economic literature. Consistent with this explanation, Figures 2 and 3 show that according
to Iranian data, women with relatively low and relatively high bargaining power, participate less in
the labour market, and if they participate, they work less hours.
The model of this study is a four-part static model. Women make decisions for all parts at time
zero. They first independently invest in human capital; their decision is driven by their cost and the
expected returns of education. Education has two roles: first, within a human capital framework,
education augments natural abilities that are sold in the labour market; second, education provides
a way for individuals to sort themselves by ability. Therefore, education acts as a signaling and/or
4
screening device for unobservable ability in both the labour and the marriage market. In the second
part of the model, women find their mate on the marriage market based on their human capital and
their characteristics. The third part of the model considers the wife and husband’s decision after
marriage regarding the number of children. Finally, in the last part, couples consume private goods,
save and supply labour, subject to household budget and time constraints. Household decisions in
the last two parts depend on the bargaining power of wife and husband, which is determined
by the education level. I assume Pareto efficiency and full commitment in marriage.9 I find that
women’s LFP is an inverse U-shaped function of bargaining power. Women’s LFP initially increases
as bargaining power goes up, but start decreasing after bargaining power reaches a certain level.
Therefore, as a woman’s bargaining power increases, she participates more in the labour market.
However, over a certain level of bargaining power, women are less likely to work outside the home.
Moreover, the data shows bargaining power inequality in Iran has increased, so number of women
with very low and very high level of bargaining power has increased. According to the results, these
two groups are less likely to participate in labour market. Thus, in the case of Iran, women’s LFP
has decreased, despite an increase in education levels and decline in fertility rates.
In the general collective model (Chiappori (1992) [18]) the education level, number of children
and bargaining power are considered exogenous. Thus, the link between the education level, fertility
rate, and bargaining power are missed. With the missing link between the education level and
the bargaining power, Chiappori’s model always predicts that LFP is positively correlated with
education because the sole effect of the education is an increase in the potential wage. Moreover,
due to missing link between the fertility rate and the bargaining power, the general collective model
cannot explain a positive correlation between fertility rate and LFP.
This paper uses data from 2006 to 2013 Iranian Household Income and Expenditure Survey
(HIES) for estimation and testing fitness of the model. The advantage of this survey is that it not
only contains very rich information on individuals’ demographic characteristics (such as age, years
of schooling, relation with the head of family and gender), but also includes detailed information
on individuals’ socioeconomic characteristics (i.e. employment, income, expenditures, etc.). I use
Iran as an example because this rich data is not available for other MENA countries. However,
understanding the case of Iran also has implications for other economies, especially those in the
9 I abstract from issues relating to divorce by full commitment assumption in marriage.
5
MENA region which have similar labour market conditions.
The remainder of the paper is organized as follows. Theoretical and empirical literature surveys
are presented in Section 2. The theoretical framework of the model is covered in Section 3. Section
4 solves the model. Section 5 provides a description of the sample used. Section 6 and 7 estimate
and simulate the model, respectively. Section 8 solves the puzzle. Finally section 9 concludes.
2 Literature review
In neo-classical family economics, the household is the unit of study. The household’s problem is to
maximize a single utility function subject to a household budget constraint. Allocation is carried
out such that the marginal utility of consumption is equalized across family members. With the
unitary approach, who earns the income should not matter to household consumption patterns. In
other words, income is pooled (Samuelson (1956) [50]) and Becker (1981) [8]).
Although this approach seems to be very convenient in theoretical modeling and empirical
analysis, its application has been strongly criticized in the past decades by Manser and Brown
(1980) [35], Apps and Rees (1988) [2], Chiappori (1992) [18], Bourguignon and Chiappori (1993) [12],
Browning and Chiappori(1998) [15]. First, it is argued that treating the family as the representative
agent violates the individualism principle, which states each individual must be characterized by
own preferences. Second, since the unitary model considers the family as a whole, it does not
allow for raising any intra-household related issues, that might have a significant effect on each
member’s welfare. The family is a place of conflict and cooperation. Third, income pooling imposes
restrictions on the labour supply of individual household members and the unitary model (Slutsky
conditions), which are often rejected by empirical studies for households with more than one member
(Bloemen (2010) [10]).
There are three alternative approaches that address these issues: the Nash cooperative bargain-
ing, the non-cooperative bargaining, and the collective settings. Crucial to the non-unitary model
is the relative power of individual members in the household (Pollak (1994) [42]). All of these
alternative models use a game-theoretic approach. Cooperative Nash bargaining household models
is the earliest attempt to explicitly describe the decision-making process within the household. The
earliest papers that established the Nash bargaining approach to the household include Manser and
6
Brown (1980) [35] and McElroy and Horney (1981) [37]. This approach consider household members
as agents who try to come to an agreement on how to divide the gain of cooperation while living
together. In this bargaining model, individuals, given their relative bargaining power in the family,
have to reach an efficient allocation of the gain obtained from living together. The generalized Nash
framework has important empirical implications. However, those implications are not immediately
testable with observable data. For instance, there is no reason to assume that the threat point10
of utility functions are observable. If threat points are not observable, no explicit restrictions can
be put on the bargaining power matrix. Another important criticism of this approach is that if its
empirical implications are rejected, then it is impossible to determine whether the particular choice
itself is rejected or the bargaining setting in general causes this rejection (Zeyn Xu (2007) [53]).
Moreover, cooperative bargaining models make the more restrictive assumption of invariant utility
across marital statuses (McElroy (1990) [36]).
The second alternative game theoretic approach is non-cooperative bargaining model. In this
framework, household members are assumed to maximize their utility taking the other’s behavior as
given (Leuthold (1968) [28], Ash worth and Ulph (1981) [3], Browning (2000) [13], Chen and Woolley
(2001) [16] and Lundberg and Pollak (1993) [30]). 11 These models are typically characterized by
a two-stage decision making process with non-cooperative solutions integrated into a generalized
Nash cooperative game. In cooperative models Pareto efficiency can be realized if information is
symmetric and agreement resulting from the game is binding and enforceable. On the contrary,
non-cooperative models have the advantage of focusing on self-enforcing equilibrium, which may
be Pareto optimal (Lundberg and Pollak (1996) [32], Basu (2006) [7] and Ligon (2002) [29]). So,
non-cooperative bargaining models do not always lead to Pareto efficient outcomes.
Chiappori (1988, 1992) [17] [18] and Apps and Rees (1988) [2] initiate an alternative theory
that assumes Pareto efficiency in the intra-household decisions. This approach was extended by
Browning, Bourguignon, Chiappori, and Lechene (1994) [14], Browning and Chiappori (1998) [15].
These types of models are called collective household models or Pareto efficient models, due to the
fact that they only make the minimal assumption that the outcomes of intra-household conflict
and collaboration are Pareto efficient. The collective approach relaxes the restrictive features of
10 Threat point as the reservation utility is one of the key features of the cooperative bargaining model.
11 Cournot Equilibrium
7
the unitary model by specifying household welfare to be a weighted combination of the individuals’
utilities. These welfare weights turn out to be proxies for the power of each member of the household.
In its general form, the collective model nests cooperative Nash bargaining models as particular
cases, since the latter are based on axioms that include Pareto efficiency. Unlike the cooperative
bargaining models, no household games or decision-making mechanisms are specified. Like the
cooperative bargaining model, the outcomes are efficient. It also nests non-cooperative bargaining
models as long as they lead to Pareto efficient outcomes(Lundberg and Pollak (1994) [31]).
The main drawback of the collective model is that power of each member in the household is
fixed and exogenous. While a household’s balance of power influences its choices, the choices can
in turn affect the household’s balance of power. This feature of households is well recognised in
the descriptive and sociological literature but it has been formally modelled relatively rarely and
usually for special contexts (Basu (2006) [7]). Basu (2001a) [6] is the first attempt at endogenising
the bargaining power in a model of intra-household behaviour. To be more specific, consider a
household with two members, a man and a woman. Following the collective approach, the household
welfare function is a weighted sum of the wife’s and husband’s utility functions in which the weights
capture the balance of power within the household. In the traditional collective model of the
household, variables that determine the intra-household powers typically consists of variables that
are exogenous to the household. Basu(2001a) [6] criticises this assumption and argues that there
are reasons to believe that changes in the household’s choice vector may affect the intra-household
bargaining power. Koolwal and Ray (2002) [43] extended Basu (2001a) [6] in several ways: (i) they
generalised Basu’s framework to allow a simple test of his assumption that the female’s share of
adult wage earnings is a measure of her bargaining power, (ii) they used the relative educational
experience of the woman vis a vis the man, as a measure of her bargaining power (iii) they presented
empirical evidence on the endogenously determined welfare weight, on its variation with female
education, and on its impact on household expenditure patterns. They showed education plays an
effective role in enhancing the power of women inside the household. In their study education is
exogenous. So, their model does not allow women to choose their bargaining power. The current
study is also an attempt to endogenise bargaining power. In my model, every factor that affects the
power of the woman is endogenous and chosen by her. Moreover, this paper consider the possibility
of nonparticipation in the labour market which is neglected in Chiappori model.
8
I use this framework to explain the observed positive correlation between fertility and married
women’s LFP, and negative correlation between education and married women’s LFP in Iran. There
are two groups of potential alternative explanation in the literature for these stylized facts. The
first group concerns labour supply. In particular, the prevalence of conservative attitudes towards
gender roles, especially among the urban middle classes, seems to be the preferred explanation
among researchers in the field (Salehi Esfahani and Shajari (2010) [20], Hijab (2001) [25], Gunduz-
Hosgor and Smits (2008) [22]). Although, culture and tradition account for some of the reasons
behind low female LFP, they are not the only reason. For example, Malaysia, a country with
comparable fertility and education, and similar culture,12 has twice the female LFP as Iran. 13
Moreover, cultural factors can not explain the decreasing trend of women’s LFP in Iran.
Another probable explanation is related to labour demand. International sanctions against
Iran,14 which intensified in late 2010,15 reduced Iran’s oil income by half and disrupted Iran’s import
of intermediate and capital goods that have caused factories to shut down or work with less than
half their normal capacity (Haidar (2015) [24]). As a result, employment opportunities for many
women decreased. However, international sanctions cannot explain the puzzle completely because
low and decreasing rates of LFP and employment were recorded even before sanctions. Moreover,
as Figure 4 shows in Iran, there is an inverse relationship between real GDP per capita and female
LFP. As real GDP per capita decreases, some women are laid off, but they stay in the the labour
12 Islam is central to and dominant in Iranian and Malay cultures. Muslim women are permitted to work outside thehome, but need to obtain their husbands’ permission for this. Therefore, financial responsibility for the family restssquarely on the husband, and the wife has no duty to contribute to family expenses. So, the society’s norms in thesecountries ensure that non-market activities especially homemaking are assigned to women.
13 Data Source: World Bank / World Development Indicators
14 Following the Iranian Revolution of 1979, the United States imposed sanctions against Iran and expanded themin 1995 to include firms dealing with the Iranian government. In 2006, the UN Security Council passed Resolution1696 and imposed sanctions after Iran refused to suspend its uranium enrichment program. U.S. sanctions initiallytargeted investments in oil, gas and petrochemicals, exports of refined petroleum products, and business dealingswith the Iranian Revolutionary Guard Corps. This encompasses banking and insurance transactions (including withthe Central Bank of Iran), shipping, web-hosting services for commercial endeavors, and domain name registrationservices.
15 United Nations Security Council Resolution 1929 passed in 2010, banned Iran from participating in any activitiesrelated to ballistic missiles, tightened the arms embargo, travel bans on individuals involved with the program, frozethe funds and assets of the Iranian Revolutionary Guard and Islamic Republic of Iran Shipping Lines, and recom-mended that states inspect Iranian cargo, prohibit the servicing of Iranian vessels involved in prohibited activities,prevent the provision of financial services used for sensitive nuclear activities, closely watch Iranian individuals andentities when dealing with them, prohibit the opening of Iranian banks on their territory and prevent Iranian banksfrom entering into relationship with their banks if it might contribute to the nuclear program, and prevent financialinstitutions operating in their territory from opening offices and accounts in Iran.
9
market and look for jobs. Moreover, in recession some men are laid off or their income decrease,
so the necessity for supplemental income motivates inactive wives to search for a job (Karshenas
(1997) [26], Karshenas and Moghadam (2001) [27], Mirzaie (2014) [41]). This inverse relationship
is consistent with the declining portion of the U-shape relation between female participation and
GDP during the process of economic development.
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Women LFP Real GDP per capita
Figure 4: Real GDP per capita and Women LFP
Source: Central Bank of Iran (CBI), Statistical Center of Iran (SCI)
In addition, there have been a number of attempts to assess the role of education and family
size in women’s LFP and employment in Iran. However, most of these studies are qualitative or use
simple statistical approaches that do not discern and measure the effects of various factors (e.g.,
(2005) [46]; Rezai-Rashti and James (2009) [44]; Bahramitash and Esfahani (2009 and 2011) [5] [4]).
The studies that rely on quantitative methods are quite limited and none of them considers the
effect of intra-household bargaining power. 16
16 Salehi-Isfahani (2005) [48] analyzes the determinants of LFP and paid employment, using a Probit method and asample survey of about 6000 observations in 2001. Salehi-Isfahani and Marku (2008) [49] use a pseudo-panel based onannual household surveys during 1984-2004 to identify the age, cohort, and period effects on female LFP. Majbouri(2010) [34] employs a short panel with about 16000 observations during 1992-1995 to examine the impact of economicstability in that period on LFP.
10
3 The model
This paper is a direct extension of the collective approach developed by Chiappori (1992) [18].
My model extends his theory by allowing the education, marriage and fertility decisions to be
endogenous. Thus, in this model not only the bargaining power is endogenous but also every factor
that affects the bargaining power is endogenous and chosen by women. The model of this study
is a four-part static model.17 I assume Pareto effciency18. Women make decisions for all parts at
time zero. First, the women independently invest in human capital; their decision is driven by
their ability and their cost. I assume that human capital is equal to years of schooling. When
investing in human capital, women must anticipate the outcome of their investment. This outcome
has two distinct components: (i) education augments and sorts natural abilities that are sold in
the labour market; (ii) a higher educational level has an impact on marital prospects, it affects
the expected income of the future spouse, the total utility generated within the household and the
intra-household allocation of this utility. So, education acts as a signaling and/or screening device
for unobservable ability in both the labour and marriage market. Women choose level of education
to maximize their utility, but it’s costly.
maxEduf
U(Eduf )− cost(Eduf , ability) (1)
where Eduf is female education and U is utility function.
In the second stage, women and men match on the marriage market. They choose their mate
based on their education levels, preferences for marriage and characteristics. A matching is stable
if one cannot find a woman who is currently married but would rather be single, a man who is
currently married but would rather be single, or a woman and a man who are not currently married
together but would both rather be married together than remain in their current situation. Formally,
each woman decides about her mate’s properties (education level, non-labour income and utility
preferences) to maximize gain of marriage subject to her own properties. In addition, her decision
17 Static model is time-invariant and women make decisions for all parts at time zero.
18 Keshavarz Haddad (2015) [23] shows validity of this assumption for Iranian households.
11
should satisfy her husband.
maxEdum,Ym,αm
U fmarried (2)
st : M(Eduf , Y f , αf , φ) (3)
U fmarried ≥ U f
single (4)
Ummarried ≥ Um
single (5)
where Eduf and Edum are wife and husband’s education levels, Y f and Y m are wife and husband’s
non-labour income, and αf and αm are wife and husband’s preferences.
The two conditions (4) and (5) imply that married women and men would not prefer remaining
single. U fsingle and Um
single are reservation utility levels that a woman and a man require to participate
in any marriage, and U fmarried and Um
married are their utility if they marry. I assume that such
matching is feasible, so women do not need to think about the next-best solution. Moreover, I
assume full commitment assumption in marriage to avoid issues related to divorce.
After marriage, wife and husband make decisions together. In the functioning and decision
making of households, bargaining power has an important role. Bargaining power is the relative
capacity of each of the parties to negotiate or dispute to compel or secure agreements on its own
terms. Since bargaining power is unobservable, it is not possible to actually measure it. So, I need to
find a proxy for women’s bargaining power. Measures that are frequently used to proxy for women’s
bargaining power include income and employment, asset ownership (both current assets and assets
brought to marriage) and education. Koolwal and Ray (2002) [43] showed that a ceteris paribus
increase in the females educational experience leads to a significant increase in her bargaining power
inside the household; and a similar increase in the males educational experience has an opposite
effect. 19 While any woman probably prefers to have a higher-earning partner, a large difference
between their potential income decreases the wife’s bargaining power. So, if a woman can find a
mate who has similar preferences and a lower education level, she has more power in family decisions
but less money to consume. Following them, I use the wife’s share of education in the household
19 Basu (2001a[6]) used the female’s share of adult earnings to measure her bargaining power, but Koolwal and Ray(2002) [43] showed share of potential income is a better proxy for bargaining power. Since the education level isone of the most important factors in determining the income level, they used women share of education to measurebargaining power.
12
(µ = Eduf
Eduf+Edum) as her bargaining power for two reasons. First, other proxies are exogenous while
there are reasons to believe that a woman’s choices can affect her bargaining power. 20 Second,
I am trying to understand the role of education and marriage in determination of the women’s
bargaining power. Since wife’s share of education in the household can reflect woman’s decision
about her education level and husband’s properties, I use this proxy to measure women’s bargaining
power.
After marriage, wife and husband decide about the number of children. Fertility decision is a
function of wife and husband’s preferences and the costs of children, given an income constraint
(Becker 2009 [9]). Parents receive utility from being mother and father but it is costly for them. 21
Since their utility and cost function are different, the final decision depends on their bargaining
power. So, wife and husband maximize a weighted sum of utility functions minus cost functions:
where µ is the wife’s bargaining power and (1− µ) is her husband’s. Mom is wife’s utility of being
the mother that is the function of her preferences θf and the number of children N . Similarly,
Dad is husband’s utility of being the father. These two functions are an inverted-U function of the
number of children (N). The functions costf and costm are cost functions of having children for the
mother and the father. µ is the wife’s bargaining power and (1− µ) is her husband’s.
Finally, in the last part couples and their children consume goods and supply labour subject to
the family budget and time constraints. Following Chiappori (1992) [18], wife and husband behave
as a single decision maker maximizing the weighted sum of the spouses’ utilities:
maxCf ,Cm,Cc,lf ,lm,Lf ,Lm
µ ∗ U f (Cf , lf ) + (1− µ) ∗ Um(Cm, lm) +N ∗ Uk(Ck) (7)
st : p ∗ (Cf + Cm +N ∗ Ck) +W f ∗ lf +Wm ∗ lm < Y +W f ∗ Lf +Wm ∗ Lm (8)
T f = Lf + lf , Tm = Lm + lm (9)
20 Basu(2001a) [6]
21 The costs of children include opportunity costs (the earning loss from reduced labour supply), child-care costs(including the availability of child-care) and time costs of raising and educating a child (including the domesticdivision of labour).
13
where U f and Um are wife and husband’s utility functions that depend on both consumption C
and leisure l. Also, Uk is child’s utility functions that is a function of consumption Ck. I assume
that all children are homogeneous. Assuming the preferences are rational, monotonic, convex and
continuous, the utility functions are increasing and quasi-concave. It is assumed that spouses know
each other’s and their children’s preferences. Furthermore, I assume that each household member
is endowed with direct preferences on her/his own leisure and consumption. Therefore, household
members have egoistic preferences. However, as Chiappori (1992) [18] showed, “caring” form of
individual preferences would lead to identical results. p is the price of consumption, and Lf and
Lm are labour supply by wife and husband. T is the individual’s total time. Y is the non-labour
income of the family. 22 W f and Wm are wife and husband’s wage that are functions of their
characteristics such as education, age, and economic conditions. I assume wife and husband pool
their labour and non-labour earnings between themselves. Women participate in the labour force if
their market wage exceeds their reservation wage. This decision depends on a vector of explanatory
variables including the personal and family characteristics of the woman such as age, education,
number of children, household income without her wage income, the characteristic of her husband
(status of work and education), and economic conditions. Again, since wife’s and husband’s utility
functions are different, their decision depends on bargaining power. Internal decision processes are
cooperative, in the sense that they systematically lead to Pareto-efficient outcomes. Figure 5 shows
the relationship between all variables of the model.
Figure 5: Schematic Diagram of Whole Model
22 The non-labour income includes financial transferred aids, real estate incomes, subsidies, interest on bank deposits,bounds yield and share dividends, scholarships and cash gifts from others.
14
I solve the model by working backwards from the last part. So, I start with the labour supply
and consumption decisions. At the third stage they decide about the number of children. Then
I move to the second stage, i.e. the marriage market. The marriage decision is made by women
based on preferences and education levels. However, her decision should satisfy her husband. The
solution of this stage allows me to construct the utility of woman, conditional on her education level
that is chosen at the first part. Table 6 in appendix B shows a list of all variables of the model.
As this table shows, price index (p), non-labour income (y), individuals’ total time (T f&Tm) and
age (agef&agem) are pre-determined variables. The price index (p) and individuals’ total time
(T f&Tm) are normalized to 1. The source of other exogenous variables is HIES. Other variables
of the model including wife and husband’s consumption (Cf&Cm), leisure (lf&lm), labour supply
(Lf&Lm), wage (W f&Wm) and education level (Eduf&Edum) are endogenous. Wife and husband’s
consumption (Cf&Cm) are unobservable, but I can observe total consumption from HIES. Also, I
have wage (W f&Wm), education level (Eduf&Edum) and labour supply (Lf&Lm) from the data
set. By having labour supply, I can calculate leisure (lf = 1 − Lf&lm = 1 − Lm). Moreover,
wife’s intra-household bargaining power is endogenous and is determined by wife and her husband’s
education levels.
4 Solving the model
I solve the model by working backwards from the last stage. Since my focus in this paper is on
LFP not fertility, I solve the model for couples with no children (N = 0). 23 In this framework,
the household consists of two individuals with distinct utility functions and the decision process
leads to Pareto efficient outcomes. I start with the labour supply and consumption decisions and
23 Allowing for children is left for the future work.
st : p ∗ (Cf + Cm) +W f ∗ lf +Wm ∗ lm < Y +W f ∗ Lf +Wm ∗ Lm (11)
T f = Lf + lf (12)
Tm = Lm + lm (13)
The price index (p) and individuals’ total time (T f&Tm) are normalized to 1. I assume that
individuals’ preferences (αf and αm), and so the optimal level of consumption and leisure are
different during lifetime. After solving F.O.Cs of this maximization problem, I have four equations
in four unknowns (Cf , Cm, lf , lm):
Cf = αf ∗ µ ∗ (Y +W f +Wm) (14)
Cm = αm ∗ (1− µ) ∗ (Y +W f +Wm) (15)
lf =(1− αf ) ∗ µ ∗ (Y +W f +Wm)
2W f(16)
lm =(1− αm) ∗ µ ∗ (Y +W f +Wm)
2Wm(17)
Cf and Cm are unobservable. In fact, I can only observe total consumption (C = Cf + Cm).
As equation(16) implies the optimal amount of wife’s labour supply (1−lf ) is an inverse function
of her bargaining power (µ) and her non-labour earning 24 (Y +Wm). Another variable that affects
a woman’s labour supply is her wage (W f ). If wage increases, on the one hand, the opportunity
cost of leisure increases. This tends to cause the woman to give up leisure and work more (the
substitution effect). On the other hand, the higher wage increases her income for a given number
of hours. This increase in income tends to cause her to supply less labour in order to spend the
higher income on leisure (the income effect).
I now move to the second stage (the marriage market). Women and men match on the marriage
24 As I mentioned before, I assume wife and husband pool their labour and non-labour earnings between themselves.So, wife’s labour income is W f and her non-labour earning is sum of family non-labour income (Y ) and her husband’swage (Wm).
16
market and their decision constrained by preferences, non-labour incomes and education levels.
Although, there is the emotional gain from being married relative to remaining single, for simplicity
I assume the gain of marriage is only economics gain. A woman will marry if :
st : p ∗ (Cf + Cm) +W f ∗ lf +Wm ∗ lm < Y +W f ∗ Lf +Wm ∗ Lm (30)
Y f +W f
Y f +W f + Y m +Wm∗ (2)1−αf ≤ µ ≤ Y m +Wm
Y f +W f + Y m +Wm∗ (2)1−αm (31)
µ =Eduf
Eduf + Edum(32)
F.O.C:
Edum = F1(Eduf ;αf , αm,W
f ,Wm, Y ) (33)
F.O.C of this problem is nonlinear function of Edum and analytical solution is impossible, so I have
to apply numerical methods in order to find the solution. Edum is a function of parameters (αf , αm),
incomes (wages and non-labour income) and Eduf . Family non-labour income is exogenous and
Eduf is chosen at the first part. In this model, wages are endogenous. Individual’s wage varies
by gender and education. Most papers also use the experience as explanatory variable in the wage
equation, but for the HIES data set I can not observe any variable to calculate the experience.
Since there is negative correlation between experience and education, 26 omitting this variable
would therefore produce a bias to the estimated effect of the education level on the wage (β1f 6= β1f
and β1m 6= β1m ). To solve this omitted variable bias problem, age is commonly used as a proxy
for years of work experience. 27 For simplicity, I consider the wage equation as a linear function of
25 For simplicity, I assume husband’s non-labour income and utility preference are exogenous for women.
26 People who pursue higher education have lower levels of experience.
27 Mincer (1974) [40] uses the transformation experience = age - years of schooling - 6, which assumes that a workerbegins full-time work immediately after completing his education and the age of school completion is years of schooling+ 6.
18
education, age, square of age and time: 28
W f = β0f + β1f ∗ Eduf + β2f ∗ agef + β3f ∗ (agef )2
F.O.C of this problem is a nonlinear equation and analytical solution is impossible, so I apply
numerical methods to find Eduf . After solving this problem and finding Eduf , I have W f by using
equation (34). By substitution Eduf in F.O.C of second stage (equation (33)), I have Edum and
then µ (equation(32)) and Wm (equation (35)). Now, I have all variables that I need for computing
Cf , Cm, lf and lm.
28 t is a time trend variable introduced to control for time-varying factors such as economic conditions. I do notinclude the square of education in wage equations because this variable is not significant.
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5 Data
This paper uses a pseudo-panel data:29 Iran’s Household Income and Expenditure Survey (HIES)
from 2006 to 2013 for estimation and testing the fitness of the model. 30 The statistical Center of
Iran (SCI) reports this database, which covers near 60000 households every year. For my analysis,
the sample consists of couples in which wives and husbands are aged between 15 and 65 and do not
have children. I also exclude from the sample all students, men who are doing mandatory military
services, those who are physically unable to work, and those who are prohibited by law from working.
Since the behaviour of rural and urban households is different, I only study households who live in
urban regions of the country.
The advantage of this survey is that it not only contains very rich information on individuals’
demographic characteristics (such as age, gender, marital status, relation with the head of fam-
ily and years of education), but also includes detailed information on individuals’ socioeconomic
characteristics (i.e. employment, income, expenditures, etc). Although true panel data for Iranian
families is not available, Deaton (1985) [19] identified four advantages of pseudo panel data. First,
data from different sources can be combined into a single set of pseudo panel data if comparable
cohorts can be defined in each source. Second, attrition problems often found in true panel data are
minimized. Third, the use of cohort means and errors-invariables methods smooth and control the
problem of the individuals’ response errors. Fourth, moving from individual data to larger cohorts
and to one macro cohort can analyze inconsistencies between micro and macro analysis.
However, this data set has some limitations. The HIES does not provide “annual” hours of
work. Instead, individuals are asked to report the “daily” hours of work and the number of days
they worked during the last week. So, I calculate the annual hours of work as (daily hours of work ×
number of work days during the last week × number of weeks in a year). Moreover, HIES does not
provide the wage rate, which is the average hourly earnings. I define the wage rate by dividing total
net yearly labour income including permanent and nonpermanent incomes (over time working) for
29 Individuals and families are not followed over time. However, this data set is constructed by defining cohorts usingindividual characteristics that are stable over (e.g., income, family size, ...) to reduce year to year fluctuations andto make consecutive year samples more similar. So, this database is pooling comparable cross-section data collectedrepeatedly over time. However, this database is not true panel data and it is not possible to apply the normal paneldata techniques on this data set.
30 This data set is available from 1984 but some essential variables for this study such as hours of work were notasked before 2006.
20
wage earners, and net labour income for employees with private and self employed jobs, over annual
working hours. Another limitation of HIES is that it does not provide the non-labour income, but
it reports detailed composition of individuals’ income. So, I consider the non-labour income as
summation of financial transferred aids, real estate incomes, subsidies, interest on bank deposits,
bonds yield and share dividends, scholarships, and cash gifts from others.
Table 1: Sample Descriptive Statistics for Married Individuals
over the eight census years, there is a potential of 96 cells of cohort mean data. Table 5
32 I check wife’s asset share in the household as another indicator for women’s bargaining power and I observe similartrends.
22
(in appendix A) lists the number of individuals contained in each cohort.
2. Differentiating between age, period, and cohort (APC) effects
When a data set contains observations on many individuals over an extended period of time,
observed variance can be attributed to three related effects: (a) differences between cohorts,
which are labeled the cohort effects; (b) differences associated with different points in the life
cycle, which are labeled the age effects; and/or (c) differences associated with different periods,
which are labeled the period effects. 33 We cannot identify these three effects simultaneously
because only one time dimension and one individual or cohort dimension exists. More specif-
ically, the functional relationship between all three effects causes perfect collinearity when all
three effects are fully specified (period=age+cohort) (Fienberg and Mason (1985) [21] and
Ryder (1965) [47]). The question of how best to solve this identification problem has gener-
ated controversy, especially among sociologists (Rodgers (1982) [45] and Smith, Mason, and
Fienberg (1982) [51]). Although there is a variety of approaches to solve the APC conundrum,
each has limitations. One common approach is to impose a linear restriction on any pair of
age, period, or cohort variables (e.g., if the membership in the cohort born 1971-1980 is no
different from membership in the 1981-1990 cohort, then I can restrict the cohort effects to be
equal for this pair). For estimating parameters of utility functions, I address the age, period,
and cohort identification problem by using a linear restriction that all age effects are equal
and are included in the constant term. Thus, individuals’ preferences differ across cohorts,
and an individual’s preferences change over time. However, this change is related to time
effect, not age effect.
33 The difference between age effects, period effects and cohort effects is well explicated by this fictional dialogue bySuzuki (2012) [52]:A: I can’t seem to shake off this tired feeling. Guess I’m just getting old. [Age effect]B: Do you think it’s stress? Business is down this year, and you’ve let your fatigue build up.[Period effect]A: Maybe. What about you?B: Actually, I’m exhausted too! My body feels really heavy.A: You’re kidding. You’re still young. I could work all day long when I was your age.B: Oh, really?A: Yeah, young people these days are quick to whine. We were not like that. [Cohort effect]
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6 Estimation
In this section, I use the mechanism described in section 4 to estimate the model described in sec-
tion 3. This model has two groups of parameters: utility function parameters (αf , αm), and wage
functions parameters (β0f , β1f , β2f , β3f , λf , β0m, β1m, β2m, β3m, λm). I have six equations ((14) to
Equation 1 : Real Wage per hourβ1f : years of schooling 3002.443∗∗ (259.296)β2f : age 11911.328∗∗ (947.624)β3f : age2 -146.615∗∗ (12.884)λf : t -3397.757∗∗ (199.667)
The estimated coefficient of the selection equation shows that age has a positive but decreasing
effect on women’s LFP. We expect age to affect participation through two mechanisms: (i) its
impact on an individual’s work-leisure preferences, and (ii) through the impact of experience in
the labour market. Younger women are more likely to be enrolled in full-time education and thus
less likely to participate in the labour market. Middle-aged women will have more experience and
likely more family responsibilities than their younger counterparts and will thus be more inclined to
35 Literacy level is measured by the years of schooling
36 I tried some other variables such as non-labour income (i.e. rent, interest, financial aid, transfers and income ofhomemade products) and family’s income from selling used durable goods. But they are insignificant. Also, I triedhusband’s income, but it has collinearity with bargaining power.
25
participate in the labour force. Older women are more likely to have significant resources available
for retirement and are less likely to participate as they approach the regular age of retirement.
Regarding the effect of bargaining power on women’s LFP, the estimated results show that
bargaining power has a positive but decreasing effect. As a woman’s bargaining power increases,
she participates more in the labour market. However, over a certain level of bargaining power,
women are less likely to work outside the home. Moreover, the time effect is negative, which means
time-varying factors such as economic conditions make women less likely to participate in the labour
market.
Table 2 also shows the estimated coefficient of the wage equation. Concerning the education
variable, I find that a higher education level increases the hourly wage and the effect is statistically
significant. Moreover, the age has a positive and significant effect on the hourly wage. However,
the effect of the square of the age is negative, which means that over a certain age, the wage does
not increase any more. Furthermore, the time effect is negative, which shows a decreasing trend of
real hourly wage for women over time. Table 7 (in appendix C) provides more details of Heckman’s
method for regression and selection equations.
Since 99% of husbands are employed in my sample, I assume all men participate in the labour
market. Thus, I do not need to estimate the selection equation for them. I estimate the wage
equation for men as a linear function of education, age, square of age and time:
p price index normalized to 1Y non-labour income (real estate incomes, subsidies, ...) HIEST f&Tm individual’s total time normalized to 1agef wife’s age HIESagem husband’s age HIES
