INEFFICIENCY OF MALE AND FEMALE LABOR SUPPLY IN
AGRICULTURAL HOUSEHOLDS: EVIDENCE FROM UGANDA
MARTYN J. ANDREWS, JENNIFER GOLAN, AND JANN LAY
This article analyzes the efficiency of the intra-household allocation of female and male labor
inputs in agricultural production. In a collective household model, spouses’ optimal on-farm
labor supply is such that the marginal rate of technical substitution between male and female
labor is equated over different crops. Using the Uganda National Household Survey 2005/06, we
test whether this condition holds by estimating production functions and controlling for endogeneity using a method proposed by Gandhi, Navarro, and Rivers (2009). We find that women are less
productive than men, that there is more female labor input on low productivity parcels, and that
men are relatively more productive on female-controlled plots compared with male-controlled
plots. Total farm output could be higher and Pareto improvements could be possible if male labor
was reallocated to female-controlled plots and/or female labor was reallocated to male-controlled
plots.
Key words: Intra-household allocation, labor supply, gender, Uganda.
JEL codes: D13, J16, O12, Q12.
In many developing countries, smallholder
production remains the main source of
livelihood for poor rural households. The
literature on agricultural households has
stressed the role of missing insurance, credit,
and labor markets in explaining the moderate supply response to market reforms of
smallholders (Key, Sadoulet, and De Janvry
2000; Taylor and Adelman 2003). In addition to these market constraints, smallholder
labor allocation decisions may be affected
by norms and rules that may cause suboptimal outcomes. Specifically, gender roles
in agriculture have been previously shown to
potentially cause inefficiencies in agricultural
Martyn Andrews is a Professor of Economics and Jennifer
Golan is a Lecturer in Development Economics, both at
the University of Manchester, UK. Jann Lay is head of the
Research Program “Development and Globalization” at the
GIGA German Institute of Global and Area Studies, Hamburg, Germany, and Assistant Professor at the University of
Göttingen, Germany.
Jennifer Golan gratefully acknowledges financial support of
the Poverty Reduction, Equity, and Growth Network, and
the Economics Department of the University of Manchester
for funding her PhD. The authors are thankful for comments
received by participants of the Royal Economic Society Conference in London, seminar participants at Purdue University,
the Econometric Society World Congress in Shanghai, the
Bolivian Conference on Development Economics in La Paz,
and the German Economic Association Meeting in Göttingen.
The authors also thank Mette Christensen, David Colman,
Mika Kortelainen, Andy McKay, Ed Taylor, Bernard Walters,
and various referees for useful comments that substantially
improved this paper.
production, though rigorous evidence on this
is scarce.
The so-called collective model has been
established as the “workhorse” for analyzing
intra-household resource allocation. Like all
other cooperative models, a key assumption
of the model is that household decision outcomes are Pareto efficient. The predictions of
the collective model for consumption behavior have been tested in different contexts.
While studies using data from developed
countries tend to support the collective
model (Bourguignon et al. 1994; Browning
and Chiappori 1998; Thomas and Chen 1994),
evidence from developing countries often
does not support efficiency (Udry 1996; Duflo
and Udry 2004; Goldstein and Udry 2008;
Quisumbing and Maluccio 2003). In particular, production decisions have been found
to be sub-optimal when households have to
adjust to new agricultural conditions such
as deeper market integration or changes in
relative prices (Jones 1983; McPeak and Doss
2006).
In this article, we use a version of the
collective model that is characterized by
an efficient allocation of factor inputs to
evaluate the optimality of on-farm labor allocations in agricultural households in Uganda.
The model is based on the original model of
Chiappori (1992), which has been extended
for household production by Udry (1996),
Amer. J. Agr. Econ. 97(3): 998–1019; doi: 10.1093/ajae/aau091
Published online October 27, 2014
© The Author 2014. Published by Oxford University Press on behalf of the Agricultural and Applied Economics
Association. All rights reserved. For permissions, please e-mail: [email protected]
Andrews, Golan, and Lay
Inefficiency of Male and Female Labor Supply in Agricultural Households
Apps and Rees (1997), Chiappori (1997),
and Donni (2008). For consumption choices,
the model predicts certain conditions for
domestic production decisions. Domesticallyproduced goods can be divided into those
that can be sold or bought in the market (e.g.,
crop production) and non-marketable goods
(e.g., children’s welfare). Chiappori (1997)
and Donni (2008) show that if the good has
a market substitute, then the allocation of
resources in production can be analyzed
independently from consumption decisions;
essentially this is the same as the standard
unitary agricultural household model, where
the household has no restrictions in accessing
product markets (Singh, Squire, and Strauss
1986). In other words, factors of production
are allocated to home production as if the
household maximizes domestic profits.
Apart from this marketability assumption,
a further challenge for collective models
with domestic production is that data on
inputs and outputs are seldom available in
standard datasets. However, in developing
countries, domestic production of marketable
crops is a main source of household income
and standard survey data often also collects
input, output, and price information of farm
production. There is an increasing body of
evidence that female and male labor inputs
are allocated sub-optimally in smallholder
households. This evidence suggests that intrahousehold farm behavior may be better
described by alternative household models
in which conflicts of interest between the
partners may produce inefficient outcomes.
Udry’s seminal (1996) study concludes
that productive resources are allocated inefficiently in rural Burkina Faso. Efficiency
requires that two equal plots should have
identical yield and input allocations, and
so any deviation should be only a function
of plot characteristics. Controlling for plot
characteristics and household-year-crop fixed
effects, Udry finds that yields per acre of
identical crops are lower for plots controlled
by women than men by approximately 30%.
This can be explained by fertilizer and labor
inputs being more intensely used on maletended plots. In other words, were Burkinabe
households to allocate resources efficiently,
given diminishing returns, they would reallocate resources to female-tended plots. Using
CES production function estimates, Udry
shows that male and female labor inputs are
equally productive, while all labor inputs are
highly substitutable on identical crop-plots.
999
Also, the results indicate no differences in
production technology between the plots.
This means that, amongst other factors, labor
could be reallocated so as to increase output
(see Akresh (2005) for further evidence for
Burkina Faso).
Preceding Udry (1996), Jacoby (1992) studies the division of labor of men and women
in livestock and crop production in Peru; he
finds that women are more productive in
livestock and men in crop production, which
means that the efficiency requirement would
be violated if labor inputs were allocated in
equal proportions. However, the data used
does not disaggregate male and female labor
inputs by activity, which undermines this test.
Nonetheless, Jacoby’s results illustrate that
the efficiency of allocating male and female
labor not only depends on relative factor
productivity, but also on the production
technology employed.
Udry (1996) and Jacoby (1992) are consistent with the earlier findings of Jones
(1983), who explains why married women,
compared to widowed women, allocate
“insufficient labor” to paddy rice plots in
North Cameroon. Incomes from rice production are controlled by the husband, but
cultivation relies on both husband’s and
wife’s labor inputs. Jones estimates the compensation rate to female labor input in rice
production; her results suggest that the suboptimal labor allocation can be explained by
the low rate of compensation that married
women receive relative to the opportunity
costs faced; that is, income from sorghum
production, agricultural wage labor, and
other incomes. In other words, if households
were to allocate resources so as to maximize
incomes, compensation to married women
would need to increase.
In this article, we analyze the efficiency
of intra-household allocation of female and
male labor inputs in the farm production of
various crops in the context of Uganda. Our
contribution to the literature is as follows.
First, we derive a test of the efficiency of
male and female labor allocation over various crops using the collective model derived
by Browning and Gørtz (2012). Second, our
empirical strategy is based on theoretical
conditions that allow us to identify all relevant parameters for testing efficiency, but
without suffering from the inherent endogeneity problems of estimating production
functions. Third, we use the Uganda National
Household Survey (UNHS) 2005/06, which
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April 2015
contains information on who controls the
output from a given piece of land. Our study
is related to but distinct from Udry’s. While
Udry analyzes efficiency within crops across
different plots, we analyze labor allocation
both between plots as well as between crops
(within the same household), partly using a
different theoretical restriction. Further, this
dataset records information on farmers who
are much more integrated into markets than
those analyzed by Udry.
The next section analyzes the literature
on traditional gender roles and social norms
in agricultural production in Sub-Saharan
Africa (SSA) and Uganda. In the following
section, we derive a test of efficiency considering different scenarios of labor supply. We
then describe the data and discuss econometric issues, particularly relating to the possible
endogeneity of labor inputs. The penultimate
section discusses the results and the final
section concludes.
Gender Roles and On-farm Labor Allocation
Anthropological, sociological, and anecdotal
evidence points to a “gendered division” of
crops and tasks in SSA that might explain
intra-household labor allocation. In the SSA
context, traditional gender roles not only
reflect and reinforce comparative advantages
in agriculture, but are in many countries a
mechanism for the division of income within
the household. If established structures become incompatible with new incentives, such
as through price increments for a certain type
of crop, this might cause difficulties when
adjusting the distribution of benefits. While
this does not necessarily impact on the effort
and amount of labor applied, achieving a
compensation rule compatible with profit
maximizing production behavior may be
fairly complicated under rigid traditions and
gender roles.
For instance, in many SSA countries,
women grow food crops mainly to guarantee
domestic food consumption, while men tend
to control output from cash crop production
while still relying on the female and family
labor inputs (FAO, IFAD, and ILO 2010).
As noted, Jones’s (1983) study shows that
if women do not feel adequately compensated, they tend to supply insufficient labor.
Dolan (2001) provides evidence of struggles
over resources in horticulture-producing
households in Meru, Kenya. French beans,
Amer. J. Agr. Econ.
a crop originally within the female domain,
were expanded for export purposes. The
resulting shift in the productive focus of the
household increased the labor burden on
females. At the same time, men tried to
extend their control to the proceeds of
French bean production, but thereby adversely impacted the female position within
the household, and presumably negatively
affected female labor effort in the production
process.
Traditional gender roles have also been
named as a reason for men being reluctant
to contribute to food crop production in
Africa (Boserup 1976), despite the possibility that they might be more efficient at
performing certain tasks. Both men and more
often women may be excluded from certain
tasks as well as entire income-generating
spheres, thereby illustrating the rigidity and
persistence of traditional gender roles, in
particular with regard to the allocation of
labor within the household (Dey 1981; Jones
1983; and von Braun and Webb 1989). Still,
whether a certain cropping pattern follows
gendered lines has been found to depend on
the cultural context as well as agro-ecological
context (Doss 2002).
We analyze data from Uganda. Here, there
is also evidence that cash crop production—
particularly coffee production—relies on
female labor inputs in the production process,
while marketing and income control lie in
male hands (Kyomuhendo and McIntosh
2006; Elson and Evers 1996; Evers and
Walters 2001; Kasente 1997). In addition
to an amount of time-consuming home duties
such as fetching water and collecting firewood, producing food crops and specific tasks
(such as weeding) required to produce other
crops are typically performed by women
(Kasente et al. 2000; Dolan 2001). Social
norms have been named as a factor constraining women’s ability to mobilize male
labor within the household (Hill & Vigneri
2011). Doss and Morris (2001) note that in
many African countries men can command
women’s labor while the reverse is not true.
This is also true for Uganda, and Evers and
Walters (2001) argue that this pattern is reinforced by social norms such as obligatory
dowry payments to the spouse’s family.
Traditional gender roles may be challenged by changes in the structure of the
economy and the corresponding changes in
economic incentives. One important feature
of structural change in SSA is the increasing
Andrews, Golan, and Lay
Inefficiency of Male and Female Labor Supply in Agricultural Households
market integration of rural households
(Hazell et al. 2010) that causes a less clear-cut
distinction between cash and food crops. For
instance, increased prices for leafy vegetables
in Kampala, Uganda, shifted men’s focus on
its production (World Bank, FAO, and IFAD
2009). Increased marketed production of
traditional food crops may cause conflicts of
interest between the partners over crops, for
example in the case of banana production
in Uganda (Ministry of Gender, Labor, and
Social Development 2005). These conflicts
may result in sub-optimal resource allocations, as previous gender roles and associated
compensation rules do not necessarily lead
to optimal outcomes under new market
conditions.
The evidence surveyed in this section
hence suggests that sub-optimal production
outcomes may be caused inter alia by an inefficient allocation of labor, which in turn may
be linked to rigid gender roles in agricultural
production. In addition, intra-household compensation for labor inputs in domestic farm
production typically depends on control over
proceeds from certain crops. Again, control
over crop output is determined by traditions
and social norms and the evidence above
suggests that these may not provide adequate
incentives for efficient labor allocation.
The Collective Farm Model and Testable
Implications
The evidence surveyed in the previous
section suggests that intra-household struggles over labor input and income control may
give rise to production inefficiencies. To test
whether this is the case, we derive a condition
for the optimal allocation of male and female
on-farm labor inputs using a collective farm
model based on Browning and Gørtz (2012);
the model also draws on Singh, Squire, and
Strauss (1986), Udry (1996), and Apps and
Rees (1997).
The Collective Farm Model
The household consists of two partners,
labeled A and B. Partner A’s utility depends
on the consumption of a good bought
in the market qm
A , hours of leisure lA , a
f
domestically-produced subsistence good qA ,
a non-rival household public good Q,
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and a vector of preference factors aA 1 :
f
uA = uA (qm
A , lA , qA , Q; aA ). Partner B’s utility
B
u depends on exactly the same arguments:
f
uB = uB (qm
B , lB , qB , Q; aB ). Partner A cares
about B in the sense that her total utility
comprises her own uA plus a proportion λA
of B’s. In other words, her welfare function
is defined as A = uA + λA uB , with λA ∈
[0, 1]. If λA = 0, A is said to be egoistic, that
is, she does not care about B’s utility. If
λA = 1, A is completely indifferent between
her own utility and her partner’s utility. We
rule out the possibility that λA < 0, namely
that she dislikes her partner, or λA > 1, that
she cares more about her partner than herself. The same considerations apply for B:
B = uB + λB uA , with λB ∈ [0, 1].
Further, h is the household’s welfare
function, that is, a weighted average of the
individual welfare functions: h = μ̃A +
(1 − μ̃)B , with μ̃ ∈ [0, 1]. The weight μ̃
reflects the so-called “balance of power”
within the household. If μ̃ = 1, then A is
all-powerful. Economic theory does not provide a framework explaining the content
of μ̃, but it is hypothesized to be a function
of so-called distribution factors. These are
exogenous factors that impact the allocation
of power within the household but not on
preferences, like aA and aB , or the budget
constraint (Browning and Chiappori 1998).
Substituting the individual utility functions
into household welfare, we can redefine h
as μuA + uB . The so-called Pareto weight μ
is a composite index of μ̃, λA , and λB , and
captures the relative weight of partner A in
the decision process.
Each partner has a total time endowment of T hours a day. For A, T can be
allocated to leisure lA , food crop fA , cash
crop cA , public good production hA , or offfarm employment activities (self- or wage
employment), mA . In maximizing household welfare, the partners face the following constraints on their allocation of time,
namely T = lA + mA + fA + cA + hA and T =
lB + mB + fB + cB + hB .
Total food crop production qf can be allof
f
cated to subsistence consumption qA + qB ,
f
or traded in the local market, qm , at price pf .
The food crop production function F f uses
domestic labor inputs fA and fB , and land L:
1
For the sake of simplicity, we assume that children can be
treated as public goods.
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April 2015
f
f
Amer. J. Agr. Econ.
f
qf = qA + qB + qm = F f (fA , fB , L). The variable L is assumed to be fixed and exogenous,
which allows the analysis to focus on the
short-run intra-household allocation of labor
inputs in which labor can be more flexibly
reallocated between crops than land. The
same applies for cash crop production, except
that this crop is entirely traded in the market
at the cash crop price pc : qc = F c (cA , cB , L).
The production of the household public good
Q depends on each partners’ time input,
hA , hB , and material inputs bought in the
market, qH : Q = F Q (hA , hB , qH ).
All three production functions, namely
food crop F f (.), cash crop F c (.), and public good F Q (.) are increasing in all inputs,
and satisfy standard concavity conditions.
In addition, domestic on-farm labor inputs
and off-farm employment activities are nonnegative. For simplicity, we assume that both
partners supply a positive amount of labor
to domestic cash crop production. Also, we
consider that A’s optimal off-farm labor supply, m∗A , could be limited by social norms to
a sub-optimal level m̄A . This means that she
may be forced to allocate her time between
leisure, public goods, and domestic farm production beyond the desired level. Further,
there is an income constraint stating that
expenses on consumption goods and material
inputs into public good production cannot
exceed the total of on-farm profits, nonwage income, y, and labor incomes, mA wA
and mB wB . This constraint is written as
follows:
(1)
m
H H
pm (qm
A + qB ) + p q
f
f
= pf [F f (fA , fB , L) − (qA + qB )]
+ pc F c (cA , cB , L) + y + mA wA
+ m B wB .
The household’s problem is to maximize
total household welfare μuA + uB subject to
the 5 constraints and 3 production functions.
The two relevant first-order conditions are as
follows:
(2)
pf
∂F f
∂F c
= pc
= wA
∂fA
∂cA
(3)
pf
∂F f
∂F c
= pc
= wB .
∂fB
∂cB
If both partners supply labor to both crops,
equations (2) and (3) are interpreted as if
the farm is maximizing the profit of jointly
producing the food crop f and the cash
crop c. For partner A, the marginal revenue
products of labor for both crops are equal
to each other and equal to her marginal
cost wA . As this is also true for partner B,
the marginal rate of technical substitution
(MRTS) between male and female labor is
equated over the two crops:
(4)
∂F f
∂fA
∂F f
∂F c
=
∂fB
∂cA
∂F c
= wA /wB .
∂cB
The left-hand equality is what we test in the
rest of this paper; hereafter, we refer to
this as our test of allocative efficiency. We
also define the two MRTSs as θf and θc ,
respectively.
It can also be shown that if partner A supplies no labor to off-farm activities and she
is constrained to supply all the desired labor
to the local labor market, this condition still
holds. In other words, within the same household, male and female labor inputs cannot
be reallocated so as to increase output if the
marginal rates of technical substitution are
equated over crops, that is, θc = θf . This condition does not depend on the distribution
of power within the household. Equation
(4) also holds in the presence of market
imperfections; more specifically, it does not
depend on the existence of a functioning
labor market.
In the rest of this section, we show how
to apply our test of allocative efficiency
when estimating production functions for
food and cash crops. These different kinds
of crops should be seen as a stylized separation of different agricultural production
activities. In our empirical analysis we distinguish between plots “controlled” by males or
females, respectively.
Testing Allocative Efficiency
To implement our test, we estimate the four
marginal products in equations (2) and (3),
which means estimating the parameters of
F f (fA , fB , L) and F c (cA , cB , L). However, first
we need to address a well-known problem, that is, the labor inputs are likely to be
endogenous. There are two possible reasons,
both of which are gender-specific. This exacerbates the problem because the biases in
estimating the effects of fA and fB will not
Andrews, Golan, and Lay
Inefficiency of Male and Female Labor Supply in Agricultural Households
cancel out when computing θ. The first reason is that there may be idiosyncratic shocks
caused by the weather, crop pests, diseases,
and so on. These affect men and women
differently because they grow and control
different crops. Accordingly, male and female
marginal products will be systematically different from each other and these differences
would be incorrectly interpreted as inefficiencies. The second reason is that men are more
likely to self-select themselves into farming
plots and crops that yield higher returns.
The issue of endogenous labor inputs was
noted in the developing country context by,
for example, Fafchamps (1993), who analyzed data for Burkina Faso. Similarly, Udry
(1996) was cautious in interpreting his results
because it is difficult to find valid instruments
that affect factor inputs but are not correlated with production shocks. Like Udry,
we are unable to pursue an instrumentalvariables type strategy, and so we follow
closely an approach proposed by Gandhi,
Navarro, and Rivers (2009).
We can view the household’s problem as
choosing its inputs fA and fB by maximizing its profits for the food crop: pf F f (fA ,
fB , L)ev − wA fA − wB fB , where v captures
these shock and selection issues, and is
observed by the household. Not only is v
correlated with fA and fB , the two correlations might well be different. At the same
time, the household maximizes its profits
for the cash crop, but here we focus solely
on the food crop. The first-order conditions
equations (2) and (3) are rewritten as follows:
(5a)
pf
∂F f (fA , fB , L) v
e = wA
∂fA
(5b)
pf
∂F f (fA , fB , L) v
e = wB .
∂fB
Once fA and fB are chosen, actual food crop
output is given by:
(6)
yf = F f (fA , fB , L)ev e ≡ qf e
equations (6) and (5b), so that, for partner B:
p f yf
log(1/sB ) ≡ log
w B fB
fB ∂F f ( )
= − log
+ .
F f ( ) ∂fB
(7)
There is a symmetric equation for Partner
A. We emphasize that wB fB is hypothetical
in the sense that it is the cost that would be
incurred by supplying fB hours at a market
wage rate wB . The same applies to wA fA .
Both wA and wB reflect the opportunity
cost of an hour of labor, while wA fA and
wB fB are different from the labor incomes
earned in the market, wA mA and wB mB ,
as in equation (1). Hence, the dependent
variable 1/sB , when logged, is the (inverse)
share of revenue earned in producing yf that
would be paid to partner B for supplying fB
hours. Lastly, is the only unobserved variable left in the model. The right-hand side of
equation (7) depends on the functional form
of the production function.
We choose the Constant Elasticity of Substitution (CES) production function because
the elasticity of substitution between the
labor inputs for partners A and B can be
estimated unrestrictedly. Because we want to
focus on the elasticity of substitution between
fA and fB only, we write the production
function for the food crop as:
(8)
log F f (fA , fB , L)
νf
−ρ
−ρ
= − log[δAf fA f + δBf fB f ] + γf Lf
ρf
where νf is the returns to labor parameter,
ρf is the substitution parameter, and δAf and
δBf are the distribution parameters that capture the marginal products of partners A and
B. Note that 0 ≤ δAf , δBf < 1 and, because
of land Lf and other possible labor inputs,
δAf + δBf < 1. Equations (6), (5a), and (5b),
respectively, become:
(9)
(10)
where is another variable, this time not
observed by the household nor the “econometrician.” The key insight of Gandhi,
Navarro, and Rivers (2009) is to recognize that v can be substituted out between
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log yf = log F f + v + log wA /pf
= log F f − (1 + ρf ) log fA
−ρ
−ρ
− log δAf fA f + δBf fB f
+ log(νf δAf ) + v
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April 2015
Amer. J. Agr. Econ.
and
(11)
regression parameters as follows:
log wB /pf
(14)
f
θf ≡ MRTSAB ≡
= log F f − (1 + ρf ) log fB
−ρ
−ρ
− log δAf fA f + δBf fB f
+ log(νf δBf ) + v.
−ρf
1+ρf
.
(15)
δAf
δBf
fA
fB
−(1+ρf )
δAc
=
δBc
cA
cB
−(1+ρc )
.
−ρ
+ δBf fB f ]
+ ρf log fB − log(νf δBf ) + ≈ − ρf λAf log fA + ρf (1 − λBf ) log fB
− ρ2f λBf λAf g(fB , fA )
− log(νf δBf ) + where λAf ≡ δAf /(δAf + δBf ) and λBf ≡
δBf /(δAf + δBf ). The last line of equation (12)
is a linear approximation that comes from a
Taylor series expansion (Kmenta 1967). We
note that
(13)
fB
fA
This is a non-linear restriction involving
six parameters: δAf , δBf , ρf , δAc , δBc , and ρc .
The four labor inputs are evaluated at their
sample means.
log(1/sB )
f f py
≡ log
w B fB
= log[δAf fA
Using the equivalent expression for the cash
crop, our test is written as
It is v that causes the labor inputs to be
endogenous; differencing out v between
equations (9) and (11) results in:
(12)
δAf
=
δBf
∂F f ∂F f
/
∂fA ∂fB
g(fA , fB ) ≡ −(log fA − log fB )2 /2.
Unique estimates of δAf , δBf , and ρf are
identified from equation (12). By symmetry,
there is another equation for log(1/sA ), but
we do not estimate this equation, as there
are issues relating to the quality of the data
we have for female wages wA , discussed later.
Similarly, we identify δAc , δBc , and ρc from the
analogous equation for the cash crop. In what
follows, we refer to output as the “dependent
variable” because we seek to estimate the
parameters of production functions, even
though the left-hand side of our regression
model is log(1/sB ).
Our test of the theory is whether the
marginal rate of technical substitution
between male and female labor inputs is
the same across both crops (see equation (4)
above). For the food crop, the marginal rate
of substitution is written as a function of the
Data
In this section we describe the Uganda
National Household Survey (UNHS) and
the variables we construct for our empirical
analyses.
Samples
The data we use come from the Uganda
National Household Survey 2005/06, and was
collected by the Ugandan Bureau of Statistics. The UNHS is nationally and regionally
representative and contains detailed information on agricultural activities. The agricultural
questionnaire covers two cropping seasons: July to December 2004 and January
to June 2005, which are labeled “Season
t = 1” and “Season t = 2,” respectively.2
We restrict our analysis to male-headed
households that live with one or more
spouses; this is because analyzing bargaining between spouses is more straightforward
in male-headed households.3 After dropping
observations with missing values, this gives
a sample of 3,665 male-headed households.
Hereafter “spouse” and “female” are used
interchangeably.
2
Uganda has two rainy seasons. The first starts around March,
can last until June/mid-June, and affects the first harvest (t = 2).
The second starts around August, lasts until November, and affects
the second harvest (t = 1). In northern regions of Uganda, the
two rainy seasons tend to merge into each other.
3
In this sample, 21.2% of households are polygamous, the rest
are monogamous.
Andrews, Golan, and Lay
Inefficiency of Male and Female Labor Supply in Agricultural Households
1005
Table 1. Sample Characteristics
Households
Parcels
Plots
of which:
Monocropped
Intercropped
Changersc
t=1
t=2
t = 1&2
Unitsa
Total obsb
3,268
6,407
9,337
3,380
7,092
13,489
2,983
5,225
6,915
3,665
8,274
15,911
6,648
13,499
22,826
4,025
3,309
2,003
6,260
5,226
2,003
2,421
2,491
2,003
7,864
6,044
2,003
10,285
8,535
4,006
Note: Sample is defined as male-headed households with one or more spouses (3,665 households).
a indicates column (4) = (1) + (2) − (3), and provides total number of households/parcels/plots.
b indicates column (5) = (1) + (2), and provides the total number of household obs./parcel obs./plot obs.
c indicates monocropped in one season, intercropped in the other.
Table 1 summarizes the sample characteristics of these 3,665 households. Of these,
2,983 are observed in both seasons, resulting in 6,648 household-season observations.
Households have land parcels that comprise either monocropped plots, where only
one crop is grown, or intercropped plots,
where more than one crop is grown. We
observe 15,911 plots on 8,274 parcels for
the 3,665 households. A parcel is a group
of plots with similar soil characteristics, discussed in more detail below. Because there is
more rainfall in the first rainy season, households use more plots (13,489) in Season t = 2
compared with Season t = 1 (9,337). This
results in 22,826 plot-seasons. Of the 15,911
plots, 7,864 are monocropped (10,285 plotseasons) and 6,044 are intercropped (8,535
plot-seasons), and 2,003 plots change from
monocropped to intercropped, or vice versa,
between the two seasons. There are 13,499
parcel-seasons for these 3,665 households.
Because some permanent crops such as
coffee have a two-season growing cycle,
we define the dependent variable yp as
the total annual value of plot output. Our
empirical analysis is based on this plot-level
cross-section comprising 15,911 annual plot
observations. We also create a crop-level
cross-section, where the unit of observation
is the total annual value of crop output for a
given household for 7,152 household crops.
Here, the variable being modeled is denoted
as yhc .
Generally, the information we require from
the agricultural questionnaire is observed at
different “levels” (households, parcels, and
plots) depending on the variable of interest.
This has implications for our empirical analysis. For a given household-season, a) labor
inputs are recorded for each plot, whereas
b) output is recorded for each crop at the
household-season level, but not for each crop
on each plot.4 Unfortunately, a) implies that
we cannot tell how much time is spent on
each crop on an intercropped plot. However,
b) implies that output for each plot (at the
household-season level) can be constructed
from the output for each crop and the area
used.5 To do this, we assume that—for a
given crop grown on different plots within
a household-season—output per acre is the
same for all plots.
To illustrate, consider a household with
two plots labeled p = 1, 2. If these two plots
are monocropped (say, coffee on p = 1 and
peas on p = 2), we can match the respective labor inputs for both plots with the
household-season information on coffee and
peas output. However, if the household produces some coffee on p = 2 as well—so that
this plot is intercropped—we use the assumption above to share the output value of coffee
between the two plots.6 The econometric
implications of this “output sharing” rule are
discussed below, and the appendix details the
actual procedure.
The resulting plot-level dataset comprises
information on total output value and labor
4
Households are much more likely to report with accuracy
their labor inputs by plot, and their output by crop. This is because
they may not know from which plot the output of a given crop
came, but are more likely to know how much time they spent
working on a given plot.
5
The acreage of a specific crop on an intercropped plot
is derived from the following survey questions: “If the plot is
intercropped, the total plot area should be entered ... for each crop
and then the percentage of the plot area under the component
crops.”
6
Suppose there are two acres of coffee on the mono-cropped
plot and one acre of coffee on the second intercropped plot. In
this case, two-thirds of the household’s coffee output would be
“allocated” to plot 1 and one-third to plot 2.
1006
April 2015
Amer. J. Agr. Econ.
Table 2. Sample Averages by Plot Type, Parcel Control, and Marketed Share
Plot type
All
Output value per
acrea
Male labor per acreb
Female labor per acre
Total labor per acrec
Propn zero female
labor
Propn zero male labor
Marketed shared
Area (acres)
Weather shocke
Male wagesf
No plots
No parcels
Percent of total
167.3
Mono
167.9
23.1
27.1
53.1
60.7
100.6
115.8
0.053
0.075
0.035
0.289
1.035
0.331
2.013
15,911
0.050
0.277
0.919
0.255
7,864
Parcel control
Inter
166.6
All
174.1
194.0
19.1
45.6
85.7
0.031
24.7
48.0
96.9
0.050
22.2
35.4
73.4
0.075
0.020
0.302
1.147
0.406
0.032
0.315
1.310
0.357
0.015
0.371
1.552
0.351
Spouse
170.2
Marketed share
Joint
153.3
50.6
3,496
42.3
None
121.2
10.2
35.8
24.3
59.6
55.9
69.6
92.4
126.4
123.3
0.018
0.039
0.046
0.071
0.214
1.052
0.376
0.031
0.308
1.178
0.352
8,047
8,274
49.4
Head
1,742
21.0
3,036
36.7
0.053
0.000
0.673
0.305
<Half
≥Half
192.7
207.0
19.5
46.6
87.8
0.030
25.6
35.7
81.2
0.090
0.020
0.255
1.094
0.371
0.027
0.777
1.518
0.324
6,514
5,164
4,233
40.9
32.5
26.6
Note: The unit of observation is a plot or a parcel. Superscripts indicate the following.
a Output value in ,000’s Uganda Shillings.
b Labor inputs are measured in person days per year.
c Total labor is the aggregate of domestic, hired, and other labor inputs.
d Marketed share is defined as the ratio of revenue to output value.
e Dummy for whether at least one crop on the plot was affected by drought or floods.
f Median, in ,000’s Uganda Shillings, per day; varies at the household-level only.
inputs (see table 2). To estimate production functions by crop, we can only use
monocropped plots, where, by definition,
the crop coincides with the plot, which means
we observe the labor inputs used in producing each crop, and the output produced.
From this we can create a crop-level dataset
by aggregating the data for each crop at the
household level. Note that we still have to
apply the above rule to share the output
between intercropped and monocropped
plots if a crop grown on a monocropped plot
is also grown on an intercropped plot for a
given household-season. This is the case for
49.9% of the household-crop observations.
The resulting dataset comprises 22 different
crops grown by 3,219 households, totaling
7,982 observations. Given the asymptotic
properties of our test, we further restrict
this dataset to crops with a minimum of 100
observations. This leaves a final sample of
11 crops grown by 3,128 households, totaling 7,152 crop observations (see table 3).
We use the latter for testing whether the
marginal rate of technical substitution is the
same across the crops. We now detail the key
variables used in our analysis.
(table 2) or per crop (table 3). This is the
quantity harvested (minus quantity wasted)
times the producer price, both of which are
observed. We use output value (in thousands
of Ugandan shillings) rather than output (in
kilograms) because we need to aggregate
across crops on a given plot in our plot-level
dataset. Notice that we do not use the term
revenue, because not all output is sold, a
distinction that becomes important below.
It may be that the price of a crop depends
on the gender of the crop manager. For
instance, Hill and Vigneri (2011) find that
access to coffee markets in Uganda crucially
depends on the ownership of means of transportation, and the quantity sold, which differ
by the gender of the household head. Once
these differences are accounted for, there
is no gender difference in accessing markets. In markets, female heads of households
receive lower coffee prices than male household heads, but this difference seems due to
the marketing channel chosen, rather than
gender-based price discrimination. We discuss the possibility of gender-based price
differentials in our empirical analysis.
Labor Inputs
Output
The “dependent variable” is the annual
value of the output harvested, either per plot
Labor inputs are measured in person-days
per year. The second, third, and fourth rows
of tables 2 and 3 report domestic adult (i.e.,
Andrews, Golan, and Lay
Table 3. Sample Averages by Crop
Coffee
Cotton
Maize
Mtooke
Grdnts
Beans
Sorghm
Peas
Millet
Cassva
Pots
146.3
27.1
61.2
116.7
0.054
0.068
0.238
1.070
0.263
2.010
7,152
178.0
29.3
22.9
63.2
0.222
0.044
0.940
1.824
0.153
101.5
51.8
44.4
121.5
0.053
0.053
0.943
1.407
0.228
128.8
19.2
30.7
69.0
0.059
0.041
0.399
1.643
0.373
177.4
15.8
24.8
58.0
0.112
0.046
0.215
1.514
0.192
156.5
25.5
65.0
119.0
0.042
0.087
0.223
0.702
0.363
106.3
15.2
44.9
76.9
0.030
0.103
0.215
0.809
0.369
101.6
17.2
45.0
87.3
0.036
0.058
0.185
1.059
0.341
76.1
13.8
38.8
67.2
0.031
0.145
0.178
0.684
0.313
116.9
30.7
79.9
141.0
0.019
0.178
0.148
0.730
0.245
141.4
66.6
93.7
223.0
0.057
0.048
0.134
1.119
0.122
181.1
17.8
91.2
136.8
0.022
0.068
0.071
0.627
0.247
275
189
761
427
667
414
1109
131
376
1044
Note: The unit of observation is a household crop. This table refers to the 11 crops for which there are at least 100 observations. Table columns are ordered by marketed share. Superscripts indicate the following.
a Output value in ,000’s Uganda Shillings.
b Labor inputs are measured in person days per year.
c Total labor is the aggregate of domestic, hired, and other labor inputs.
d Marketed share is defined as the ratio of revenue to output value.
e Dummy for whether at least one crop on the plot was affected by drought or floods.
f Median, in ,000’s Uganda Shillings, per day; varies at the household-level only.
1759
Inefficiency of Male and Female Labor Supply in Agricultural Households
Output value per acrea
Male labor per acreb
Female labor per acre
Total labor per acrec
Propn zero female labor
Propn zero male labor
Marketed shared
Area (acres)
Weather shocke
Male wagesf
No. crops
All
1007
1008
April 2015
18 years or older) male, female, and total
labor inputs, per acre. On average, women
supply about half the total household annual
hours (53.1%), twice that of men (23.1%). In
addition to domestic adult female and male
labor, total labor also includes domestic child
labor, hired labor, and other labor inputs. The
information on child labor is not available by
gender. Also, 5.3% of plots have no female
labor and 3.5% have no male labor. This
very much depends on which crops are being
cultivated.
In table 3, among those crops with more
than 100 observations, cassava stands out as
the most labor-intensive crop, while coffee,
maize, matooke, and peas require considerably less labor. The table confirms that adult
female labor supply is substantial. For most
crops, this is about half of total labor input,
and is typically about two to three times
higher than adult male labor input. This is
not true, however, for traditional cash crops
such as coffee and cotton, where, on average, the male input exceeds that of females.
This division of work between crops is also
reflected in the next two rows of table 3,
which report the proportion of observations
where there is no male or no female labor
input. There is no female labor on 22.2%
of coffee plots (4.4% for males), whereas
only 1.9% of the millet plots have no female
input (17.8% for males). To summarize, as
is well-known, whilst women supply roughly
twice as much labor as men, this varies considerably by crops, as does the proportion of
crops wholly farmed by one partner or the
other.
Wages
The left-hand side of our regression models is
log(1/sB ) ≡ log(pf yf /wB fB ), the hypothetical
(inverse) share of revenue earned in producing yf that would be paid to partner B for
supplying fB hours (see equation (12)). The
final component of log(1/sB ) that we discuss
is the wage of the male in the household, wB .
There are two sources of information in
the survey. The first is constructed from all
individuals who report having worked for
pay during the previous 12 months. Using
information on the last cash payment and the
estimated cash value of in-kind payments,
we create a daily earnings measure. In our
sample of male household heads and female
spouses, only 28% of individuals report the
information we require, and the majority of
Amer. J. Agr. Econ.
these (78%) are men. This is one reason why
we do not model partner A’s income share in
the value of output log(1/sA ).
The second variable is the agricultural community person-day wage, recorded in the community module of the survey, and is observed
for everybody in our sample. We use this
variable to impute wages for those individuals not reporting a wage using a standard
Mincer-style regression, additionally controlling for age, gender, years of schooling, a
dummy variable if the individual is responsible for a non-farm enterprise, regional fixedeffects, and a dummy variable for urban areas.
We also include interaction terms between the
gender dummy, the business dummy, and the
community wage variable.
Using these imputed daily wages, we
find that female median earnings are 38%
lower than male median earnings. We also
find that this mark-down does not vary much
by household, only at the community level. In
the absence of household variation in wA /wB ,
it is meaningless to use both first-order conditions in equation (5); this is the second reason
why we do not model log(1/sA ).
Adverse Shocks
Adverse shocks are endemic in agriculture,
and can have sizeable effects on output. Our
data allow us to control for this, and so we
construct a set of dummy variables for such
shocks, using the following question: “Before
it was harvested, what was the main cause
of crop damage?” The possible responses
are drought, flood, disease, insects, animals,
birds, theft, or some other cause. In the crop
dataset, we create dummies for each cause,
and assign the value of one if affected in
either season. In the plot dataset, the dummies adopt the value of one if at least one
crop on a given plot was affected by the said
cause. For example, 31.9% of plots were
affected by drought, 14.0% were affected by
disease, 7.7% were affected by insects, and
5.0% by animals. Because they refer to the
crop, these dummies are included in all our
regressions. Including the dummies should
affect the male and female labor coefficients
if the impact of shocks has an important gender dimension. Finally, using the dummies for
drought and flood, we create a dummy for
adverse weather, which is included in table 2
and table 3; we do this to illustrate the extent
to which plots and crops were affected by
adverse weather shocks.
Andrews, Golan, and Lay
Inefficiency of Male and Female Labor Supply in Agricultural Households
Gender Control of Crops and Plots
As already discussed, table 3 demonstrates
that the intra-household allocation of labor
between men and women varies by crop.
Such a gender division of labor can be efficient if it is made according to comparative
advantage and compatible with the production technology employed. If the division of
labor reflects the distribution of crop output
between partners, and one partner feels inadequately compensated for the labor supplied
for crops that are controlled by their spouse,
they may either under-allocate labor or supply less effort. Alternatively, if one partner
has the power to dictate intra-household
labor allocation, too much labor may be
supplied to this partner’s crops.
To investigate whether any deviations
from an efficient labor allocation system are
related to who controls the output, we use
the following question asked of households
(our emphasis added): “Who mainly manages
or controls the output from this parcel among
the household members?”. From the replies
to this question we construct three categories
to record whether output is controlled by
a) the head only, b) the spouse only, or c)
by both and/or other household members
and/or other people (see the middle panel
of table 2). Just because one partner (typically the man) controls output on some or
all of the parcels on a farm does not mean
that the allocation of factor inputs on the
farm is inefficient, as the theory allows for
all-powerful men or women. However, the
literature for SSA agriculture cited above
suggests that inefficiencies may arise when
partners feel inadequately compensated for
their labor inputs.
A total of 36.7% of the parcels are jointly
managed or managed by someone else; of
the rest, men exert control over twice the
number of parcels as women (our sample
only consists of male-headed households
with at least one female spouse). Table 2 also
shows that much less male labor per acre is
used on their spouse-controlled parcels, and
vice versa; in fact, men spend about twice
as much time on their own parcels compared with their spouses’ parcels, whereas
their spouses spend six times more time on
their own than on their husbands’ parcels.
The table also shows that female spousecontrolled parcels are much smaller (by
32%) and have a lower output value than
male-controlled parcels (by 12%). For similar
1009
findings for Malawi, see Kilic, Palacios-Lopez,
and Goldstein (2013). We accordingly stratify
the sample to determine whether our test of
inefficiencies is related to gender roles in the
household.
In addition, we are interested in examining
whether the role of market integration possibly causes such inefficiencies, as conflicts over
labor allocation are likely to arise once a
certain proportion of the household’s output
is traded in the market. As we observe the
revenue from a given plot when its output
is sold on the market, we define a marketed
share variable, r, as the ratio of revenue to
output value. Table 2 shows that this proportion does not vary between the monocropped
and intercropped plots, but table 3 shows
that it varies considerably over crops in the
crop-level dataset. As expected, the share
is higher for cash crops: 94% of the output
value of all coffee produced is sold, whereas
this figure is 7.1% for potatoes. The 11 crops
we analyze are listed in order of marketed
share in table 3.
To capture the idea that men’s interests in
controlling traditionally female-dominated
crops will increase with the amount of output
that is sold, we define the following three
categories: no output is sold in the market (r = 0); “some” output is traded on the
market (0 < r ≤ 0.50); and “lots” of output
is traded on the market (r > 0.50). Table 2
shows that the average time that females
spend per acre is about twice as high (69.6
days per year, per acre) when the market
share is zero compared with when more than
50% of the output is sold in the market (35.7
days per year per acre). For men, there are
no substantial differences. The same pattern
occurs when we examine single food crops
that traditionally fall under female control.
Accordingly, table 2 shows that the marketed share and control variables are correlated, as expected. The proportion of output
sold, r, is much larger for male-controlled
parcels (37.1%) than female-controlled
parcels (21.2%). When we regress r on two
control dummies and a constant, this difference in means of 0.152 is highly significant
with a household-cluster robust standard
error of 0.0109. When parcels are jointly
controlled, the marketed share is 30.8%.
While these are interesting correlations,
both endogeneity of the marketed share variable (higher output causes a higher marketed
share) and simultaneity with labor allocation
decisions preclude using it as an explanatory
April 2015
variable in a production function. Nor can
we stratify the sample by marketed shares.
Nonetheless, these descriptive statistics and
correlations are a strong indication that
market integration and gender roles are
interrelated.
Households integrate into markets not
only by selling more of a given crop portfolio,
but also by adopting more marketable crops.
We have shown that the marketed shares
differ considerably between crops. This is
also why we are interested in investigating
the equality of the MRTS between male
and female labor across crops within the
household. We have pointed out that labor
input choices and the marketed share of a
specific crop are likely to be simultaneously
determined. This is less of a problem if we
compare the MRTS between crops, as one
can reasonably assume that labor allocation
decisions are being made once a specific crop
choice has been made.
Parcels
A unique feature of the data is that it records
information at the parcel level as well as for
plots. A parcel is a contiguous piece of land
with identical (uniform) tenure and physical
characteristics and is entirely surrounded
by land with other tenure and/or physical
characteristics or infrastructure, for example,
water, a road, forest, etc., that does not form
part of the holding.7 This implies that a parcel
is part of a holding that is physically separate
from other parts of the holding; a holding is
made up of one or more parcels.
To assess the extent to which parcels differ
from plots, we note that the number of plots
per parcel is Poisson distributed, with a mean
of 1.72. First note that the distribution of the
number of crops per parcel-season is very
similar to that of the number of crops per
plot-season. Similarly, when we compare the
distribution of the number of crops per plot
with the distribution of the average number
of crops per plot over the 13,499 parcelseasons, we see that the standard deviation
of the former—the total variation—is very
similar to that of the latter—the betweenparcel variation—which means that there is
very little within-parcel variation. Figure 1
illustrates why there is so much between
variation: of 13,499 parcel-seasons, 5,734 have
7
A holding is a household in our terminology.
Amer. J. Agr. Econ.
6000
4000
Frequency
1010
2000
0
0
2
4
6
8
avge no crops per parcel-season
10
Figure 1. Distribution of average number of
crops per plot by parcel
exactly one crop on every plot (these are the
monocropped plots), whereas another 3,494
parcel-seasons have an average of exactly
two crops per plot, and 1,210 parcel-seasons
have an average of exactly 3 crops per plot.
In other words, there is considerable variation in how households use the plots within a
given parcel in terms of how many crops they
grow.8
This information at the parcel-level allows
us to do two things. First, we observe who
controls each parcel, namely the male, the
spouse, or whether the parcel is jointly controlled. We can then investigate which control
regimes are more productive, and then test
whether the MRTS between female and male
labor is equated across plots under different
control regimes (head, spouse, joint control).
Second, in both the plot and crop datasets, we
have repeated observations on parcels and
are able to control for parcel fixed-effects
in our regressions. In other words, using
parcel fixed-effects allows us to control for
soil fertility characteristics that potentially
determine which plots and crops are farmed
by men rather than women in the same
household.
Specification and Econometric Issues
In this section we specify the empirical
model. Each household h owns a number
8
Crop diversification is a typical feature of poor rural households. On the one hand, diversification results from optimal
portfolio choices of crops given differences in expected returns
and risks. On the other hand, it is well-established that agricultural households simultaneously decide on production and
consumption in the presence of different combinations of market
imperfections. This implies that crop choice is determined by
shadow prices that reflect the household’s factor endowments,
technology, and preferences.
Andrews, Golan, and Lay
Inefficiency of Male and Female Labor Supply in Agricultural Households
of parcels, denoted a, that are sub-divided
into plots, denoted p. For the plot dataset, our
estimating equation is written:
(16)
yp = x p β + η a + v p
where implicitly p = p(a(h)). This is standard
notation for a nested data structure such as
ours, and indicates that p varies as parcels
vary in the data, which themselves vary
as households vary. Comparing this with
equation (12), it is clear that yp replaces
log(1/sB ) ≡ log(pf yf /wB fB ). Similarly, the
vector xp contains log fA and log fB , the labor
inputs of partners A and B, g(fA , fB ), the CES
variable defined in equation (13) above, other
labor inputs (including domestic children
and hired labor), and any remaining control
variables. Even though there is a γf Lf term
in equation (8), because we assume that the
production function is additively separable
in Lf , it does not appear in the first-order
conditions, and hence the model being estimated. This is clearly true of the plot acreage.
However, we do not drop all the other labor
inputs because they could have been specified as part of a larger aggregated labor input
in the CES production function. We choose
not to do this because we are not interested
in estimating these other substitution elasticities, but they should be added as controls
nonetheless. Further, ηa is a parcel-level
fixed-effect that controls for soil-quality or
the slope/steepness of the cultivation area,
while vp is the idiosyncratic error term. In
some regressions, we replace ηa by ηh , a
household fixed-effect.
From the estimates on log fA , log fB , and g,
we compute δA , δB , and ρ, and then, using the
sample averages for fA and fB , we compute
the MRTS parameter θ (see equation (14)
above). To test for the equality of the MRTS
across plots, we then stratify the sample using
our gender control variable.
In the crop dataset, we focus on monocropped plots only, and then compute
household-crop-level aggregates for all variables in the data. We then examine each of
the 11 crops—coffee, cotton, maize, matooke,
groundnuts, beans, sorghum, peas, millet, cassava, and potatoes—separately. In effect, we
replace p by hc:
(17)
yhc = x hc β + ηa + vhc ,
c = 1, . . . , 11.
1011
As above, we can control for ηa or ηh , or neither. To ensure that we estimate the same ηa
or ηh across all crops, we pool the data and
use crop-dummy interactions. Finally, we test
the null hypothesis that the MRTS parameter
is the same for all 11 crops.
A potential problem arises because output is recorded for each crop, but not each
plot. As described in the appendix, for a
given crop grown across different plots in the
same household, we assume that the output
per acre is the same for all plots cultivating
the same crop. This is a possible concern if
this assumption is violated because some
plots are more productive than others and it
is these plots that males choose to control.
We control for this potential endogeneity
in three different ways: using the method of
Gandhi, Navarro, and Rivers (2009), specifying parcel fixed-effects, and using information
on who actually controls each plot. This
means there are no bias implications for our
estimates because all that is left is standard
measurement error in the dependent variable. Finally, for the same reason, we do not
need to be concerned about the fact that the
male wage rate is measured with error (this
variable is derived from the community wage
and other observable characteristics for some
males in the sample).
Results
We first discuss our estimates of the underlying production function using the plot-level
dataset; in the following sub-section, we
examine the crop-level dataset.
Evidence from Plot Data
Following our discussion of inefficiency
above, we first test whether the MRTS
between female and male labor is equated
across plots under different control regimes
(head, spouse, joint control). In table 4,
columns 2 and 3 report what happens when
equation (16) is estimated controlling for
household fixed effects ηh , and parcel fixedeffects, ηa , respectively. Column 1 reports
ordinary least squares (OLS) estimates.
There are three important features of
table 4. In all our regressions, the elasticity of
substitution parameter ρ is estimated slightly
out of its legal range of ρ < −1. It is wrong to
interpret the production functions as having
linear isoquants (ρ = −1) because there are
1012
April 2015
Table 4.
Plots
Amer. J. Agr. Econ.
Fixed Effects Estimates for All
(1)
OLS
Female labor log fA
Male labor log fB
CES variable
g(fA , fB )
Log child labor
Log hired labor
Log other labor
Drought dummy
Disease dummy
Head control
dummy (parcel
variable)
Spouse control
dummy (parcel
variable)
0.1142
(0.0113)
−0.7233
(0.0108)
−0.0526
(0.0037)
0.0423
(0.0068)
0.1335
(0.0080)
0.0719
(0.0088)
−0.2162
(0.0279)
−0.2452
(0.0383)
−0.0123
(0.0373)
(2)
(3)
Household Parcel
0.1375
(0.0110)
−0.7329
(0.0098)
−0.0494
(0.0033)
0.0426
(0.0071)
0.1090
(0.0060)
0.0396
(0.0071)
−0.0585
(0.0249)
−0.0706
(0.0325)
0.2198
(0.0696)
−0.0857 −0.0640
(0.0520) (0.0691)
0.1692
(0.0132)
−0.7406
(0.0124)
−0.0505
(0.0041)
0.0479
(0.0092)
0.0982
(0.0081)
0.0401
(0.0100)
−0.0613
(0.0311)
−0.0288
(0.0396)
·
·
·
·
Female share λA
0.0964
0.1258
0.1629
(0.0132) (0.0134) (0.0165)
Male share λB
0.3891
0.3290
0.2872
(0.0297) (0.0246) (0.0259)
Elast. param. ρ
−1.1841 −1.0923 −1.0389
(0.0499) (0.0328) (0.0283)
MRTSAB param.θ
0.2799
0.4064
0.5819
(0.0484) (0.0616) (0.0944)
No. Household
dummies
No. Parcel
dummies
3,665
8,274
Notes: Estimates of equation (12); household cluster standard errors
appear in parentheses. Column (3) includes parcel fixed-effects; column
(2) restricts these to household fixed-effects. All specifications include
crop and shock dummies. The sample size is 15,911 plots. The parameters λA , λB , ρ, and θ are derived from the estimates above. See equation
(14) of main text for how the MRTS parameter θ is estimated.
very few observations where either the male
or female exclusively works on the plot or
crop (see table 3). It is better to interpret
these estimates as meaning that one day of
male labor input is being easily substituted by
one day of female labor input; this is consistent with ρ being, for example, −0.9 (which
lies inside the 95% confidence interval in
most regressions). Rather than drop observations where either fA = 0 or fB = 0, we follow
standard practice and add a small number of
hours to fA or fB .
Second, because the MRTS parameter θ
is estimated less than unity, the data imply
that men are more productive than women.
In all three regressions, the parameter is
significantly lower than unity.
The third feature is that the estimate of
θ increases from 0.280 when there are no
fixed-effects, to 0.406 when we control for
ηh , and to 0.582 when we control for ηa .
This is because, as we move from left to
right, the estimated female share parameter,
λA —which is closely related to the marginal
productivity of women—almost doubles,
whilst that of men, λB , drops by one quarter.
Said differently, the more we control for, the
more productive are women, as the following
correlations also illustrate:
ηh
ηa
log fA log fB g(fA , fB )
ηh
1.0000
0.8731 1.0000
ηa
−0.0441 −0.0980 1.0000
log fA
−0.0194 0.0190 0.2086 1.0000
log fB
g(fA , fB ) −0.0149 0.0248 0.0425 0.7166 1.0000 .
The correlation between the parcel fixedeffect η̂a from column (3) and log fA is
−0.098, but is 0.019 for men. When we compute the correlation between η̂h and log fA ,
it is smaller at −0.044.9 This is evidence that
the parcel fixed-effects indeed capture parcel
characteristics that matter for productivity, and so we are not purely picking up a
household effect when taking parcel effects
into account. Whilst it is often suspected
that women cultivate less productive land,
we believe that concrete econometric evidence for this finding is scarce. For example,
the World Bank, FAO, and IFAD (2009) note
that “Women—especially if they are the main
providers of staple food crops—are particularly affected by declining soil fertility. Men
often control the best land with the best soil
to produce commercial crops, and women
more often farm marginal land.”
Two other features of our results are noteworthy. First, almost all of the adverse shock
variables have a negative effect on output
9
Obviously η̂a and η̂h are highly correlated. Hausman tests in
the two fixed-effects regressions confirm that the observed labor
inputs are indeed strongly correlated with the estimates of ηa
and ηh .
Andrews, Golan, and Lay
Inefficiency of Male and Female Labor Supply in Agricultural Households
in the OLS regression. This is because the
shocks are correlated with output in the pf yf
component of sB , and not with labor inputs
or wages. Table 4 reports that the estimate
for drought is −0.216 and for disease it is
−0.245, and both are significant and substantial. The table does not report the rest, but
in fact, insects (−0.181), animals (−0.159),
and stealing (−0.294) are also significant.
In the other two regressions, the effects are
much weaker, suggesting limited variation in
shocks across plots within the same household or parcel. However, when we drop these
dummies, in none of the three regressions
do the estimates on log fA , log fB , or g(fA , fB )
alter at all, and so θ is unaffected too. This
means that the shocks are not correlated with
labor inputs, which in turn implies that there
is no gender dimension to these observed
shock adjustments. To see that there is no
correlation between the weather shock
dummy—either drought or flood—and who
controls the parcel, see table 2.
Second, we also include the parcel-level
control variables discussed above. The variables are small and insignificant in column
(1), but when we control for household
fixed-effects, we find that when the parcel
is controlled by males, such plots are 22%
more productive than all other plots. This is
consistent with our findings just reported.
We now investigate this further; in table 5,
we report what happens when column (3)
of table 4 is stratified by who controls the
parcel (see also table 2). The key finding is
that θ is significantly smaller, at 0.212, when
the spouse (female) controls the parcel compared with the head (male) controlling the
parcel, where θ is estimated as 0.591. On
jointly-controlled parcels the estimate is even
higher at 0.708. This reinforces the finding
above: not only is more female labor applied
on low-productivity parcels, the marginal
productivity of female labor is much lower
and the marginal productivity of male labor
is much higher on a female-controlled parcel.
Recalling that there is much less labor
input when females control parcels compared with male- and joint-controlled parcels,
these results mean that households fail to
allocate labor optimally across different
parcels when these are under the control
of different household members. In other
words, total output could be higher—a Pareto
improvement—if male labor were reallocated from male- to female-controlled parcels
or vice versa. Using the estimates for the
1013
Table 5. Parcel Fixed-effects Estimates for
All Plots, Stratified by Who Controls the
Parcel
(1)
Head
(2)
Spouse
(3)
Joint
0.1824
(0.0204)
−0.7306
(0.0192)
−0.0574
(0.0069)
0.0414
(0.0157)
0.1026
(0.0138)
0.0433
(0.0168)
−0.0419
(0.0497)
−0.0778
(0.0623)
0.0780
(0.0377)
−0.7098
(0.0327)
−0.0689
(0.0094)
0.0741
(0.0197)
0.0809
(0.0190)
0.0597
(0.0246)
−0.0080
(0.0748)
−0.0815
(0.0841)
0.1664
(0.0196)
−0.7574
(0.0179)
−0.0389
(0.0061)
0.0458
(0.0138)
0.0935
(0.0110)
0.0350
(0.0139)
−0.1020
(0.0469)
0.0569
(0.0623)
0.1745
(0.0249)
Male share λB
0.3009
(0.0367)
Elast. param. ρ
−1.0451
(0.0403)
MRTSAB param. θ
0.5909
(0.1356)
No. of Parcel
3,496
dummies
No. of Plots
6,752
0.0490
(0.0381)
0.5544
(0.1432)
−1.5929
(0.4744)
0.2118
(0.0714)
1,742
0.1679
(0.0247)
0.2358
(0.0392)
−0.9912
(0.0379)
0.7080
(0.1891)
3,036
3,148
6,011
Female labor log fA
Male labor log fB
CES variable
g(fA , fB )
Log child labor
Log hired labor
Log other labor
Drought dummy
Disease dummy
Female share λA
Notes: See table 4 column (3), but re-estimated for head, spouse, and
joint/other controlled parcels separately.
“Head” and “Spouse” columns in table 5,
if all the female labor (the 59.6 figure in
table 2) were moved from spouse-controlled
to head-controlled plots, total output from
spouse-controlled and head-controlled plots
would increase by 0.092 log-points. Similarly, if all the male labor (the 22.2 figure in
table 2) were moved in the opposite direction, total output would increase by 0.189
log-points. These are sizeable and significant
effects.
The finding that the MRTS is highest on
jointly-controlled parcels is in line with a
recent study by Kazianga and Wahhaj (2013),
who argue that in Burkina Faso jointlycontrolled plots serve for the household
provision of public goods which, given social
norms, enables joint plot managers to draw
1014
April 2015
more household resources towards its cultivation than individually-controlled plots can
command. It may be that jointly-controlled
plots overcome individual incentive problems
in terms of labor supply and effort application. In addition, our results suggest strong
productivity differences between head- and
spouse-controlled plots.
One explanation for our finding that θ
varies by who controls the output is that men
and women face different prices for trading
identical crops; if so, this would explain why
marginal products are not equated over the
crops. To investigate this further, for each
plot we construct a price-index for the output
sold by dividing revenue per kilogram sold
by the actual output sold, in kilograms. We
then regress this variable on the three control dummies, controlling for crop and shock
dummies and household fixed-effects.
It turns out that we do not find any
price differentials between spouse- and
male- or jointly-controlled parcels. In fact,
our estimated price differential between
head-controlled and spouse-controlled is 25.8
Ugandan shillings in favor of spouses, with
a robust standard error of 27.8 (the average
kilogram price is 342.86 shillings). Unfortunately, we cannot explore the determinants of
potential price differentials further because
our data does not contain disaggregated
information on the ownership of means of
transport, access to networks, or other factors
that may explain why and if gender-based
price differentials exist. See also Hill &
Vigneri (2011), who examine this issue for a
sample of female heads of households.
Before we turn to the crop-level dataset
and test the equality of the MRTS across
crops, we examine whether we can detect
any systematic differences between monocropped and intercropped plots. This allows
us to assess whether the crop-level dataset
that is constructed using only monocropped
plots is a representative sub-sample of
the plot dataset. We therefore stratify the
data into monocropped and intercropped
sub-samples to examine whether any sample selection issues are likely to affect our
results. For example, it is possible that intercropped plots are more likely to be farmed
by women and to be food crops instead
of cash crops like coffee or cotton. In fact,
table 2 shows that monocropped plots have
slightly higher factor input levels per acre
than intercropped plots. However, the proportion of male labor out of total labor is
Amer. J. Agr. Econ.
almost the same for both sub-samples, as it
is for female labor. Also, the average output
value per acre is the same, on average, for
both sub-samples.
As parcel fixed-effects should deal with
such potential selection effects, we simply
re-estimate the model in table 4, column 3,
to see whether the same results are obtained
for the two plot-types (not reported). It
turns out that the MRTS parameter θ is the
same, estimated as 0.518 for monocropped
plots and 0.682 for intercropped plots. The
F-statistic for testing their equality is 1.53,
with a p-value of 0.22. In other words, we
conclude that sample selection is not driving
our subsequent results using our crop-level
dataset.
Evidence from Crop Data
We now analyze the 7,152 crop observations
for 3,128 households by estimating equation
(17) above (see table 6). The three blocks
report estimates of the MRTS parameter, θ,
by crop. At the top, we report OLS estimates;
we also control for household fixed-effects
(middle block) and for parcel fixed-effects
(bottom block). For the OLS regression,
the estimates of θ across the 11 crops are
robust, considering the relatively low number
of observations for each crop. Eight of the
estimates lie between 0.28 and 1.07, that is,
they are consistent with all earlier estimates
of θ reported in the previous subsection. For
three crops—beans, sorghum, and millet—θ
is estimated above unity (the peas and millet
estimates have particularly large standard
errors). In general, the standard errors are
much larger when we stratify by crops, which
reflects small sample sizes and the non-linear
nature of how θ is computed. This means that
we are unable to reject the null hypothesis
that θ is unity for nine crops.
Our test of efficiency is whether these 11
estimates are the same as each other; the
F-statistic is 0.84 (p-value = 0.46). Because
the estimates for peas and millet have very
high standard errors, we could exclude
them from the test, but nothing changes:
the F-statistic is 0.99 (p-value = 0.44). This
constitutes evidence in favor of efficiency in
the allocation of labor across the crops. The
household and parcel fixed-effects estimates
are similar, albeit slightly more variable, and
usually higher. For cotton, maize, matooke,
groundnuts, millet, and cassava, the results
are fairly robust. For the rest, the standard
Andrews, Golan, and Lay
Inefficiency of Male and Female Labor Supply in Agricultural Households
1015
Table 6. Estimates of MRTS Parameter θ, by Crop
Coffee Cotton Maize Mtooke Grdnts Beans Sorghm
Peas
Millet
Cassva
Pots
F-stata
OLS
0.297
0.925
0.667
1.067
0.501
1.544
1.302
0.280
1.568
0.825
0.873
0.84
(0.200) (0.565) (0.153) (0.290) (0.414) (0.724) (0.886) (2.476) (1.904) (0.230) (0.312) [0.59]
Household FEb
0.687
1.327
0.804
1.352
0.457
1.233
6.597
1.288
0.512
0.835
1.965
0.88
(0.200) (1.231) (0.199) (0.385) (0.207) (0.890) (13.195) (1.452) (0.287) (0.232) (0.714) [0.55]
Parcel FEc
1.371
0.607
0.690
1.106
0.460
4.185
3.613
1.892
0.795
1.379
4.583
0.67
(0.475) (0.903) (0.263) (0.432) (0.413) (6.066) (3.603) (2.118) (0.418) (0.501) (4.142) [0.75]
275
189
1109
761
427
667
414
131
376
1044
1759
Notes: This table refers to the 11 crops for which there are at least 100 observations. Fixed effects estimates of equation (17), household-cluster
robust standard errors in parentheses. All models estimated as one equation, so that fixed-effects constrained equal across the columns. In all 33
cases, we cannot reject the hypothesis that ρ = −0.9 (that is, the two factor inputs are highly substitutable for each other); θ is computed imposing
this restriction. Adverse shock dummies are included. There are 7,152 household-crop observations. Table columns are ordered by “marketed share.”
Superscript a indicates F-statistics in the first block have a F(10, 3127) distribution under the null; the second block they have a F(10, 3127) distribution; and in the third block they have a F(10, 5065) distribution; P-values in brackets.
b indicates 3,128 household fixed-effects.
c indicates 5,066 parcel fixed-effects.
errors increase appreciably. The F-statistics
are now 0.88 (p-value = 0.55) for householdfixed effects and 0.67 (p-value = 0.75) for
parcel-fixed effects, and so lead to the same
outcome. The OLS test statistic is the most
reliable, and OLS provides the most precise
estimates of the three blocks.
Using the OLS estimates, we now see what
happens when we explicitly control for who
controls the output. For this purpose, we
construct a household-level version of the
parcel-level control variable analyzed earlier, and use interactions in the regression
to generate estimates for “head,” “spouse,”
and “joint.”10 We do this for each crop; the
estimates are reported in table 7.
We have already established that labor
inputs are correlated with who controls the
plot, and that θ falls when it is the female
spouse in control. Recall that our estimates
of θ from table 5 are 0.59 if the parcel is
head-controlled, 0.21 if spouse-controlled,
and 0.71 for joint control. In addition to
corroborating our previous finding of inefficiencies, the aim here is to also determine
whether there are any variations across
crops. We would, for example, be able to see
whether cash crops—traditionally controlled
my males—are more prone to inefficiencies than female-controlled food crops. It
is worth reporting that the proportion of
household-crop observations that are “joint”
10
The household-level control variable classifies households
as head-, spouse-, or jointly-controlled if all the parcels for given
household are either controlled by the head or the spouse;
otherwise, a household is categorized as jointly-controlled.
is constant over the 11 crops, but that some
crops are less likely to be spouse-controlled
than others. For example, for coffee and
cotton, the proportions are 14% and 11%;
these are double for millet, beans, and peas.
Note that the rows of the table are ordered
by the marketed share variable, which is
why the traditional cash crops of coffee and
cotton are in the left-most columns.
There are only three crops with significant
differences in male and female labor input
coefficients across the three control regimes:
coffee, cassava, and potatoes. For coffee, θ
varies considerably across head-controlled,
spouse-controlled, and jointly-controlled
crops. Table 3 shows that coffee is typically
controlled by the head of the household and
female labor input is relatively low. For headcontrolled coffee, θ is negative, which is due
to λA being negative. It is interesting that on
female-controlled coffee crops, female labor
input is relatively productive, but there are
very few such cases.
Cassava and potatoes are traditional food
crops that are mostly consumed within the
household. Still, the market share for cassava is higher than for potatoes and there
are relatively few spouse-controlled cassava
crops (see table 3). Also, male labor input is
higher on cassava relative to potato crops.
Interestingly, for both crops, θ is highest on
jointly-controlled crops, which might reflect
that most of the proceeds from cassava and
potato production are used for the provision
of household consumption. The low MRTS
on spouse-controlled compared to headcontrolled cassava is surprising; it is driven
1016
April 2015
Amer. J. Agr. Econ.
Table 7. OLS Estimates of MRTS Parameter θ, by Crop and by Who Controls the Parcel
Coffee Cotton Maize Mtooke Grdnts Beans Sorghm
Head control
−0.083
(0.275)
0.51
Spouse control
1.336
(0.842)
0.14
Joint control
0.050
(0.231)
0.36
Obs
275
p−valuea [0.03]
Peas
Millet
Cassva
Pots
0.768 0.796
0.711
0.432 1.920
1.786 −1.296 1.189 1.143
(0.843) (0.268) (0.289) (0.416) (1.177) (1.810) (1.813) (1.379) (0.563)
0.57
0.50
0.41
0.36
0.33
0.39
0.33
0.34
0.44
0.929
(0.327)
0.37
1.183 0.369
0.891
0.423 1.062
0.669 −0.435 0.719 0.157
(3.996) (0.199) (0.435) (0.342) (0.707) (0.763) (6.119) (0.755) (0.130)
0.11
0.13
0.20
0.22
0.26
0.19
0.24
0.27
0.18
0.434
(0.149)
0.24
1.030 0.745
2.124
0.762 1.659
1.156
0.456 2.313 1.211
1.415
(0.682) (0.249) (1.125) (0.930) (0.779) (1.108) (1.485) (4.301) (0.470) (0.753)
0.32
0.37
0.39
0.42
0.41
0.43
0.43
0.39
0.38
0.39
189
1109
761
427
667
414
131
376
1044
1759
[0.53] [0.45] [0.46] [0.55] [0.09] [0.96] [0.41] [0.58] [0.0001] [0.0003]
Notes: See tablenotes to table 6. The estimates on log fA and log fB are interacted with the 3 control dummies, thereby generating 3 different estimates of θ. The third row in each block is the proportion of observations controlled.
Superscript a denotes 4 degrees of freedom, testing whether the 6 parameters can be restricted to 2, associated with the variables log fA , log fB .
by λA being higher on head-controlled than
on spouse-controlled cassava. An explanation
for this could be that women tend to oversupply labor to the crop, hence yielding low
returns. In contrast, for potatoes, men seem
to under-supply labor to spouse-controlled
crops, with θ being higher under head control,
and λA being similar under both control
regimes, while λB is higher under spouse
control.
The results by crop are hence partially
consistent with inefficient allocations across
crops. We observe inefficient labor allocations, in particular for coffee, cassava, and
potatoes. These again imply that output could
be increased by labor reallocations and/or
changes in control regimes.
Conclusion
This article analyzes the efficiency of female
and male labor allocation in agricultural
households using data from the Uganda
National Household Survey 2005/06. In
particular, in Sub-Saharan Africa, previous
empirical evidence hints at the possibility
of sub-optimal labor allocations due to traditional gender roles in agriculture. These
gender roles may limit the flexibility of labor
allocation in agricultural production. In addition, gender roles also govern the control of
the proceeds of production, which constitutes
an element of intra-household compensation
mechanisms.
We provide evidence that farm households
indeed fail to efficiently allocate female and
male labor in agricultural production. We test
whether the marginal rate of technical substitution between female and male labor inputs
is equated over different agricultural production activities. This optimality condition
does not hold when we compare male- and
female-controlled plots. The findings imply
that total farm output could be increased by
reallocating male labor to female-controlled
plots, or vice versa.
An alternative explanation for our finding
is that men and women face different prices
for identical crops, which would also imply
that the marginal products are not equated
over the crops. Partners may, for example,
face different (transaction) costs for trading
identical crops. This might be particularly
relevant once an individual controls or manages the output of a certain crop. While we
do not find gender-based price differentials to
explain our results, we find that women operate on less productive parcels of the farm.
In addition, the inefficient intra-household
allocation of labor results in a severe lack
of male labor on female-controlled parcels.
These findings are confirmed by production function estimates for single crops. For
crops with significant labor input differences
across the different control regimes, we
also find that households do not equate the
MRTS of male and female labor for the same
crop when output is controlled by different
members of the household.
The finding that inefficiencies arise when
comparing plots controlled by different
individuals in the households implies that the
household’s intra-household compensation
Andrews, Golan, and Lay
Inefficiency of Male and Female Labor Supply in Agricultural Households
rules do not yield Pareto-optimal outcomes.
Control over output can be thought of as
a constituent component of such compensation rules and our results suggest that, in
many agricultural households in Uganda,
these rules do not seem to generate adequate incentives. It is important to note
that our findings are not driven by different
opportunity costs of male and female labor.
These may be due to male-female earnings
differentials on labor markets or different
responsibilities within the household, such as
caring for children or the elderly. All these
factors may affect the relative productivity
of males and females. Despite the resulting
relative productivity differences, households
should still allocate labor between different agricultural activities so as to maximize
output.
Finally, possible inefficiencies are often
considered in the context of increasing market integration of farmers and changes in
relative prices. There is anecdotal evidence
that traditional norms and gender roles may
not respond quickly enough to new incentives, and therefore lead to sub-optimal
outcomes in the presence of such changes.
Our findings are not generally supportive
of such a view. In fact, more market integration does not appear to be related to
higher inefficiencies in allocating male and
female labor. In light of previous findings
from less market-integrated households with
large inefficiencies, our results may also be
taken as a sign that market integration is
not necessarily related to less cooperation in
production, given that a considerable fraction of output is jointly controlled for crops
that are mainly traded in markets. Yet our
evidence for these relationships is at best
indicative. In our view, assessing the causal
relationship between gender roles, market
integration, and productivity therefore constitutes an interesting avenue for future
research.
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Appendix
Measurement Error when Constructing Crop
Output?
A potential problem arises because, for a
given household–season, output is recorded
for each crop, but not each plot. In this
appendix, we describe our crop-sharing rule.
First write the production function for crop
β β
c as q = kAfAA fBB . Explicitly subscripting
by c, kc is an unobserved crop-specific technical factor that captures the idea that k1
coffee-plants can be grown on an acre of
1019
land (because of the distance between plants
etc.), and is different from k2 for potatoes,
and so on. Next, we consider crop c grown by
household h over a number of plots. For each
plot, we observe the area on which the crop
is grown, Apc , but we only observe crop output, qc , for the whole household. We assume
that output per acre is the same for all plots,
which means we can compute
q̂p = qc
Apc
Ac
where Ac ≡ p Apc .
Note that out of 12,288 observations on
crop output, 49.9% were created using this
method (note that there are more crop observations than in table 3, precisely because
some households grow the same crop on
different plots).
The potential problem is that kc might not
be constant from plot to plot within a given
household. Of the 6,129 observations that
were imputed, 36.3% come from the same
parcel, where it is reasonable to assume that
kc is constant (because parcels have the same
soil characteristics, etc.). Of the remaining
3,902 observations, suppose that some plots
are better than others in the sense that one
can produce more coffee output per acre,
then it is possible that males may choose to
control those plots rather than poorer plots.
However, also note that there are only 408
households (out of 3,665) where the control
variable varies within a household across
different parcels. None of this is an issue once
our econometric procedures control for the
endogeneity of labor inputs, as discussed in
the main text.