affil0affil0affiliationtext: Department of Agricultural and Resource
Economics, University of Arizona
<EMAIL_ADDRESS>
# Intra-Household Management of Resources: Evidence from Malawi

Anna Josephson

###### Abstract

In models of intra-household resource allocation, the earnings from joint work
between two or more household members are often omitted. I test assumptions
about complete pooling of resources within a household, by accounting for
income earned jointly by multiple household members, in addition to income
earned individually by men and women. Applied in the case of Malawi, I find
that by explicitly including intra-household collaboration, I find evidence of
partial income pooling and partial insurance within the household,
specifically for expenditures on food. Importantly, including joint income
reveals dynamics between household members, as well as opportunities and
vulnerabilities which may previously be obfuscated in simpler, binary
specifications. Contrasting with previous studies and empirical practice, my
findings suggest that understanding detailed intra-household interactions and
their outcomes on household behavior have important consequences for household
resource allocation and decision making.

_JEL Classification_ : O12, D13, J16
_Keywords_ : households, intra-household income allocation, joint income,
gender, Malawi

##  1 Introduction

Household decision making traditionally assumes that all income is earned by a
single household member, who is then responsible for those earnings in intra-
household resource allocation (Chiappori, 1992; Browning et al., 1994;
Browning and Chiappori, 1998). Much of the existing literature addresses this
issue by accounting for interactions between these individuals within the
household, focusing on the interactions between men and women (Udry, 1996;
Duflo and Udry, 2004; Basu, 2006; Bobonis, 2009). But for many households,
income earned jointly, by two or more household members, constitutes a large
proportion of earned income. Work from Africa shows that between 12 percent
and 70 percent of household plots are jointly managed, resulting in a
substantial amount of shared income (Kilic et al., 2015; Slavchevska, 2015;
Harmony et al., 2021). The failure to consider these joint income-earning
relationships has likely led to inaccuracies, misestimation, and
misunderstanding of household dynamics in studies of intra-household income
and resource allocation. In this paper, I relax assumptions about income
earning, including income earned jointly between two or more household
members, so as to better understand how households internally cope with and
manage transitory shocks. This elucidates intra-household functioning and
behavior, helping us to better understand how households operate during times
of stress.

In many households, income earned jointly by two or more household members,
constitutes a large proportion of earned income. This is particularly true in
Malawi, the context for this paper. Malawi is a nation in which intra-
household collaboration is common, particularly in agriculture (Kilic et al.,
2015; McCarthy and Kilic, 2017; Doss and Quisumbing, 2020). To evaluate these
collaborative interactions, I empirically test assumptions about household
resource allocations. Specifically, I explore disparities in expenditure by
different income earners, after the experience of a short term shock. My
analysis focuses on three types of income earned in Malawi: that earned
exclusively by a man, that earned exclusively by a woman, and that earned
jointly by two or more people. I use these groups to test a restriction of the
collective household model: that income from all of these income types is
always pooled. The central observation underlying my methodological approach
and empirical estimation is that if households completely pool income, then
households members with different income types fully insure one another
against short term fluctuations in their incomes. Thus, non-persistent income
shocks will not result in changes in allocation of resources within the
household.

I reject the hypothesis of complete income pooling within the household. This
means that household members do not fully insure one another against short
term fluctuations in income. However, I find evidence that household members
partially pool income for expenditures on food. This behavior results in
partial pooling and partial insurance for the household on the most important
purchase for many households, as well as the largest single expenditure item
in household budgets. So, although households do not completely pool income,
they exhibit a strategic pooling behavior for an essential expenditure.
Further, my results reveal trends in income stability among household members
and elucidate how households account for changes in income - and in particular
how household members adjust their incomes when there are shocks to different
household income types. In particular, the results reveal how changes in
income from women shifts expenditure on a variety of goods. When including
joint income, the impacts of changes in women’s income on expenditure are
evident, relative to men’s and joint incomes. These findings elucidate intra-
household dynamics further than previous studies. Overall, while I observe
similar aggregate trends when including or excluding joint income, its
inclusion demonstrates the inequities felt among household members, due to
short term shocks.

Further, I examine the role of household structure on intra-household resource
allocation. I consider differences between male- and female-headed households,
as well as households with patrilineal and matrilineal lineage. I find that
both male- and female-headed households, as well as patrilineal and
matrilineal lineage households, exhibit similar same behavior as the pooled
sample. This suggests that regardless of household makeup, extending the
standard specification to include joint income elucidates structural decisions
as well as opportunities and vulnerabilities therein. This, interestingly,
differs from previous literature which suggests there are likely to be
significant differences based on lineage and household headship. Some of this
may be due to the unique context that is Malawi: more than two thirds of
households report a matrilineal heritage, but still nearly 80 percent of
households are male-headed. This configuration may explain some of the
disparities from previous literature, at least with respect to household
structures.

To test the assumption that all household income is pooled, I use a model
developed by Duflo and Udry (2004), which allows me to explore the disparities
in expenditure by different income earners resulting from exogenous variation
in rainfall. The central observation underlying the methodological approach
and empirical estimation is that if households completely pool income, then
household members fully insure one another against short term fluctuations in
income. If this is the case, then non-persistent income variations will not
result in changes to the allocation of resources within the household.

The identification strategy relies on observing the impact of exogenous
variation in rainfall on income and expenditure. I examine short term
variations in rainfall, which are covariate at the household level. All
members of a household experience the same rainfall, but the pattern of
rainfall may have different impacts on individual household members, due to
discrepancies in input use, cultivated crops, and plot quality. As previous
work has shown, women and men tend to cultivate different portfolios of crops
and do so on plots of different qualities and different quantities and
qualities of inputs (Udry et al., 1995; Udry, 1996; de Brauw, 2015; Chen and
Collins, 2014; Kilic et al., 2015; Oseni et al., 2015; Slavchevska, 2015;
Doss, 2018). Thus, rainfall may have different impacts on the income of
different household members and household labor allocation may be disparately
impacted, by gender, after the experience of a shock (Branco and Feres, 2020;
Josephson and Shively, 2021). In a household with complete insurance from the
pooling of resources of all household earners, the different impacts of
rainfall on different income earners, conditional on total expenditure, should
not translate into differences in the allocation of a particular expenditure
to different purposes within the household.

The results of this study suggests that by omitting joint relationships in the
analysis of household behavior, research has failed to account for important
dynamics in household analyses. Individual resource allocation decisions are
integral to overall household income and spending behaviors. Interactions
between these individuals are an essential part of understanding household
behavior. This study extends our understanding of these important dynamics by
including jointly earned income in the analysis. This paper is among the first
to explicitly incorporate jointly earned income with individual income into
the analysis of household income pooling.111There is a growing body of
literature, centered in West Africa, which explores the concept of shared
plots, which are generally managed by men. Although this literature highlights
income which, in principle, may be classified as joint, it is not identified
in this way (Duflo and Udry, 2004; Kazianga and Wahhaj, 2013). While other
areas have included aspects of joint management, this consideration has been
omitted from studies of gender-specific household resource
allocation.222Bobonis (2009), Kilic et al. (2015), Oseni et al. (2015),
Slavchevska (2015), McCarthy and Kilic (2017) all include a discussion of
joint collaboration but focus on production and shared household and
agricultural responsibilities. Similarly, the idea of joint household appears
in Bernard et al. (2020) and Ambler et al. (2022), though related to survey
design and the importance of household structure in that process. The evidence
presented in this study supports the validity and empirical relevance of
including income earned jointly in intra-household analyses. It further
contributes to a growing literature on how detailed understanding of intra-
household dynamics and intra-household estimation may better help inform
effective and targeted policy (D’Souza and Tandon, 2020; Brown et al., 2021;
Dizon et al., 2022).

##  2 Country Context and Data

###  2.1 Country Context

The context for this study is Malawi. Malawi is an ideal location to examine
intra-household relationships as collaboration in agricultural household
activities is common in the country (Kilic et al., 2015; McCarthy and Kilic,
2017). Inheritance is matrilineal, with matrilineal settlement practices
(Walther, 2018). However, traditional behavior gender behavior is also
standard, especially in rural areas, and drives different household practices
and outcomes: while more than two thirds of households report a matrilineal
heritage, but still nearly 80 percent of households are male-headed. These
circumstances lead to differential outcomes, in literacy, income, labor market
participation, and poverty, for men and women. Poverty in the country is
widespread and poverty rates differ between female- and male-headed
households. While poverty rates for male-headed households have fallen, rates
for female-headed households are stagnant (Kilic et al., 2015). Further, Kilic
et al. (2015) find that, on average, female-managed plots are 25 percent less
productive than male-managed plots. This discrepancy in productivity may drive
some of the observed gendered poverty gap.

Crop choice and cropping behavior may also drive some of this observed gap. As
Eicher and Staatz (1990) report, cash crops and agricultural technologies in
Malawi were historically introduced only to men. Thus, men developed a cash-
crop, export-oriented agricultural practice while women continued cultivation
of subsistence crops. This trend persists, as Mathiassen et al. (2005) find
that men are more likely to grow hybrid maize and tobacco, while women are
more likely to grow local maize varieties. We observe similar trends, reported
in Table 1: while maize is grown at similar rates, regardless of if the plot
is managed by men, women, or managed jointly, men’s and jointly managed plots
are much more likely to grow tobacco, while women’s plots are more likely to
grow beans, including soybeans and pigeonpea.

###  2.2 Data

Data for this study comes from two rounds of the Malawi Integrated Household
Panel Survey (IHPS) which was implemented by the National Statistical Office
under the Living Standard Measurement Survey - Integrated Household Surveys on
Agriculture (LSMS-ISA) program with the World Bank. The sample was designed to
be representative at the national, urban/rural, and regional levels. Efforts
were made to track resettled and split off households. In 2013, the IHPS
succeeded in tracking 3,246 households across 204 enumeration areas, which
were surveyed in the previous round in 2010. Attrition is low, at 3.8 percent
for households and 7.4 percent for individuals (McCarthy and Kilic, 2017). The
data set contains information on demographics, expenditure, and agriculture,
as well as household-specific rainfall measurements.

The empirical analysis uses a balanced panel from households whose data was
collected in both 2010 and 2013. Due to interest in income earned by
agricultural households, I omit from the analysis households which did not
report income from crop sales. Each household included in the sample has at
least one household member who earned some income from the sale of crops. In
2010, 1,198 individuals (46 percent of individuals in the first round)
reported selling some crops. In 2013, 1,720 individuals (52 percent of
individuals in the second round) reported selling some crops. In total, 850
households appear in both years, yielding a total of 1,700 household
observations. Because of the focus on a subset of the population, one cannot
consider the sample nationally representative of Malawi. However, it is
representative of individuals and households who participate in crop markets
in Malawi. Further, rising sales and expanding markets across Africa suggest
that these trends will be instructive, as more households begin to participate
in crop and output markets (Timmer, 2017).

Summary statistics for the variables used in our specifications are presented
in Table 2. I use three types of data. First, I use income data, which are
classified according to two types of specifications: first a “traditional”
specification, which includes only income from men and women, and next an
“extended” specification, which includes joint income. Next, I use expenditure
data, for a series of ten different types of household expenditures, including
food; alcohol and tobacco; clothing; recreation; education; healthcare;
housing and utilities; transportation; communication; and hotels and
restaurants. Finally, I use rainfall data, in order to estimate the short term
shocks experienced by household members. Each of these are discussed in more
detail below.

First, I consider the various types of income. In addition to details on the
crops sold by a household, the LSMS surveys designate the household member who
is responsible for decisions about the income earned from the sale of each
crop. Respondents are asked to report the primary income manager and, as
appropriate, a secondary income manager. The data are used to classify income
managers. First, I create the “traditional” measure: only male and female
income included (Table 2, Panel 1 “Omitted Joint Income”). In this measure, I
consider only the primary manager and designate male and female income based
on the gender of the individual reported. Next, I create the “extended”
measure: with male, female, and joint income included (Table 2, Panel 1 “Joint
Income”). To do this, I designate income as joint if a secondary income
manager is identified. The analysis is indifferent about whether joint funds
are controlled by multiple women, multiple men, or both a man and a
woman.333Of jointly managed income, in 2010, 1 percent is managed by
individuals of the same gender, 1 percent a primary female manager and a
secondary male manager, and the remaining 98 percent has a primary male
manager and a secondary female manager. In 2013, 2 percent is managed by
individuals of the same gender, 3 percent has a primary female manager and a
secondary male manager, and the remaining 95 percent has a primary male
manager and a secondary female manager. Excluding the 2-5 percent of
households which are not male primary, female secondary managed has no
significant impact on results. Thus, in the analysis, all shared income is
designated as “joint”. If no secondary manager is identified, income is
classified as either male or female, following the gender of the primary
manager. In these definitions, male income is earned by men and female income
is earned by women. Joint income is earned by a combination of two
individuals, of any gender.

Considering the differences between these definitions: the primary
discrepancy, when joint income is omitted, there is an over-attribution of
earned income to men. Women’s income remains similar, regardless of whether
joint income is included. The percent difference between specifications is
approximately 5 percent (on average, 2,828 MK without joint income, compared
with 2,686 MK with joint income). In contrast, men’s income is vastly
different when joint income is included, with a percent difference of around
70 percent (on average, 19,555 MK without joint income, compared with 5,846 MK
with joint income).

Next, I use expenditure data, which also come from the LSMS surveys. An
aggregate measure includes all household expenditure, but also include seven
measures of disaggregated expenditure for different types of goods.
Unsurprisingly, food comprises the largest share of the household’s budget on
average, followed by housing and utilities expenses.444This measure generally
does not include rent. Of the households included in the analysis,
approximately 2 percent do not own their properties, and thus may pay some
rent on the building in which they live. Exclusion of renter households does
not significantly influence results. Recreation, hotels and restaurants, and
healthcare comprise the smallest budget shares. Table 2 reports these figures
in Panel 2.

Finally, I use exogenous measures of rainfall to measure the short term shocks
which are experienced by households. Table 2 reports relevant summary
statistics in Panel 3. Rainfall data are derived from the CHIRPS rainfall data
set, which is produced by the Climate Hazards Group at University of
California, Santa Barbara (Funk et al., 2015). CHIRPS makes use of a monthly
climatology CHPclim, Tropical Rainfall Measuring Mission Multi-satellite
Precipitation Analysis version 7 (TMPA 3B42 v7) and global Thermal Infrared
Cold Cloud Duration (TIR CCD) from two NOAA archives. The remote sensing data
are then merged with gauge data from five public archives, including the
Global Historical Climatology Network (GHCN) and GTS, several private sources,
and meteorological agencies. CHRIPS data is measured daily at a 0.05 degree
resolution.

Using data from the LSMS, rainfall can be measured at the household level
(Michler et al., 2021). The data provide a record of rainfall variation across
households within a village, although fluctuations within a village for a
point in time are relatively small. I use total seasonal rainfall (measured in
mm) as my variable of interest. Per Michler et al. (2021), I also test a
series of other rainfall specifications with no significant differences.

As rainfall is defined at the household-level, all household members are
subject to the same rainfall patterns, but the same level and pattern
precipitation may have different effects on the income produced by different
crops. That is, a particular rainfall pattern will likely differently impact
crops that tend to be produced by women and crops that tend to be produced by
men (see Table 1). These different impacts are an integral part of our
identification strategy, discussed in the subsequent sections.

##  3 Theoretical Model

Many household models assume that households reach Pareto efficient outcomes.
This assumption is often unchallenged. Udry (1996) was among the first to
question the fundamental assumption that households in developing countries
must be Pareto efficient. Though Udry argues for the rationality of Pareto
efficiency, he posits that it is not mandatory. He demonstrates empirically
that for farming households in Burkina Faso, Pareto efficient allocation of
resources is not achieved. Subsequent research has upheld Udry’s findings,
demonstrating that many households do not pool income and are not Pareto
efficient. Similar behavior is observed in literature on gender relations and
bargaining (Duflo, 2003; Udry et al., 1995; Basu, 2006; Li and Wu, ; Doss,
2013; Antman, 2015; Fiala and He, 2016).

To take these ideas a step further and incorporate ideas of joint and
collaborative work, I adapt a model developed by Duflo and Udry (2004) and
include jointly earned income. A household consists of two individuals, each
of whom produces one crop on a plot and who together produce a joint crop on a
shared plot ($i\in\\{m,f,j\\}$). Farms are cultivated using labor ($L_{i}$)
which for men ($m$) and women ($f$), can be traded in a competitive market at
wage $w$. The agricultural production function is $f_{i}(L_{i},v)$ where
$v\equiv(v_{1},v_{2})^{{}^{\prime}}$ is a vector of two measures of rainfall
which impact cultivation on the plot of each individual.

Rainfall is experienced and each individual consumes a vector of private goods
$x_{m}$, $x_{f}$ and some shared public goods $x_{p}$ at prices $p$.
Preferences of men and women follow the expected utility function
$\mathrm{E}u_{i}(x_{i},x_{p})$, where expectations are taken over potential
realizations of rainfall. Rainfall influences the efficient allocation of
resources only through its impact on cultivation.555This is a strong
assumption also taken by Duflo and Udry (2004), which I explore further in
Appendix A.1. If this is the case, non-persistent income variations will not
result in changes to the allocation of resources within the household.

Any _ex ante_ efficient allocation of resources can be characterized as a
solution to:

$\displaystyle\max_{x_{i},L_{i}}$
$\displaystyle\mathrm{E}\big{\\{}[u_{f}(x_{f},x_{p})]+\Lambda[u_{m}(x_{m},x_{p})]\big{\\}}$
(1) s.t. $\displaystyle p\cdot(x_{m}+x_{f}+x_{p})\leq
f_{f}(L_{f},v)+f_{m}(L_{m},v)+f_{j}(L_{j},v)-w(L_{f}+L_{m}),$

where $\Lambda$ represents some Pareto weight or bargaining power, which
depends on the observable and unobservable attributes of household members.
This Pareto weight does not depend on $v$, as with an efficient allocation of
resources, risk is pooled. Recall that, if risk is pooled, households insure
one another against rainfall variation and over the period of interest and
thus there is no a change in bargaining power.

With expenditure as $e\equiv p\cdot(x_{m}+x_{f}+x_{p})$:

$x_{i}=x_{i}(\Lambda,p,e)\ \ \ \ \ \ \forall\ \ i\in\\{m,f\\}.$ (2)

Consumption of any particular good is independent of the rainfall realization
$v$, conditional on expenditures, prices, preferences, and the Pareto weight
parameter. So, the impact of rainfall realizations on expenditure for a
particular commodity depends only on the expenditure elasticity of demand for
that commodity and on the effect of rainfall on overall expenditure.

Equation (2) implies that the impact of rainfall realizations on expenditure
for any particular commodity depends only on the expenditure elasticity of
demand for that commodity and on the effect of rainfall on overall
expenditure. And so, assuming that the relative prices of consumption are not
related to rainfall realizations ($\frac{\partial p}{\partial v}=0$).

For any $i$ and period $t\in\\{1,2\\}$ and any good $g$:

$\frac{dx_{i}^{g}}{dv_{t}}=\frac{dx_{i}^{g}}{de}\cdot\frac{de}{dv_{t}}.$ (3)

Equation (3) demonstrates the effect of rainfall in period $t$ on consumption
of good $g$ by $i$. Its impact on total expenditure should be equal across all
rainfall realizations:

$\frac{\frac{dx_{i}^{g}}{dv_{1}}}{\frac{de}{dv_{1}}}=\frac{\frac{dx_{i}^{g}}{dv_{2}}}{\frac{de}{dv_{2}}}.$
(4)

What is crucial in equation (4) is that $dv_{t}$ impacts collective household
decision making through its influence on the household’s budget
constraint.666Only data on rainfall and expenditures is required in order to
estimate equations (2) and (4).
$f_{f}(L_{f},r)+f_{m}(L_{m},r)+f_{j}(L_{j},r)-w(L_{f}+L_{m})$ is not observed
and such data is not required for empirical analysis.

Equation (4) serves as an overidentifying restriction, which is tested in the
empirical analysis. The restriction specifies that realized rainfall
influences demand for a particular good in proportion to its impact on
expenditure.

##  4 Empirical Implementation and Identification

To implement the overidentifying restriction test in equation (4), a log-
linear approximation of demand is taken for a certain commodity $g$ by
household $h$ in period $t$:

$\log(x_{ght})=\alpha\cdot\log(e_{ht})+f(\Lambda)+Z_{ht}\beta+\gamma_{h}+\nu_{ht}$
(5)

where $e_{ht}$ again denotes expenditure, while $Z_{ht}$ represents location
and time indicators, $\gamma_{h}$ represents a household fixed effect, and
$\nu_{ht}$ represents an error term. Markets are assumed to be regionally
integrated. With this assumption, at any point in time, prices are the same
within a region and so is the effect of rainfall on relative prices. Demand is
captured by the region-time indicator.

Next assuming a log-linear relationship between total expenditure and profit,
for the rainfall vector, the relationship between rainfall and household
expenditure (total and on a particular commodity) is represented:

$\log(e_{ht})=V_{ht}\alpha+Z_{ht}\beta+\epsilon_{ht}$ (6)

From this, I can specify the reduced form relationship:

$\log(x_{hgt})=V_{ht}\pi+f(\Lambda)+X_{ht}\beta+\gamma_{h}+\nu_{ht}$ (7)

Equation (6) and (7) are differenced, giving reduced form equations for
estimation:

$\Delta\log(e_{hit})=\Delta V_{ht}\alpha+\Delta
X_{ht}\beta+\Delta\epsilon_{ht}$ (8)

$\Delta\log(x_{hgt})=\Delta V_{ht}\pi+\Delta X_{ht}\beta+\Delta\nu_{ht}$ (9)

Equation (6) allows for the analysis of changes over time, and controls for
unobserved household heterogeneity, which, if neglected, could bias
coefficient estimates. To test the restriction proposed in equation (4), I use
the following overidentification test:

$f_{f}(L_{f},v)+f_{m}(L_{m},v)+f_{j}(L_{j},v)-w(L_{f}+L_{m})=\chi\alpha$ (10)

for some scalar $\chi$. To test this empirically, I employ a proportional non-
linear Wald test. However, this test is limited as it does not explicitly link
variation in income with its respective gendered or joint origin.777Results of
the unrestricted test are presented in Table A.1 in Appendix A.2.

To address this limitation, I generate linear differences in rainfall for each
of the income earners within a household. First differenced income ($y_{iht}$)
regressions are estimated for the first stage:

$\Delta log(y_{iht})=\Delta V_{ht}\psi_{yi}+\Delta
Z_{ht}\delta_{yi}+\Delta\gamma_{it}.$ (11)

And calculate predicted values ($\Delta V_{ht}\hat{\psi}_{yi}$). Then, I
estimate for the second stage:

$\Delta\log(e_{ht})=\sum_{g=1}^{G}\Delta V_{ght}\hat{\psi}_{gyh}+\Delta
Z_{ht}\beta+\Delta\epsilon_{ht},$ (12)

is estimated, where terms are as previously defined. Equation (12) allows for
the testing of the impact of rainfall on expenditure, distinguished by
different income sources. Instead of broadly considering rainfall’s impact on
expenditure. I estimate its impact while also testing assumptions of household
behavior.

In implementing this analysis, I control for heteroskedasticity and
correlation within households using a clustered bootstrap procedure at the
household level.

##  5 Results and Discussion

In this section, I present and discuss the results of the traditional and
extended specifications, as well as several robustness checks on those
findings. First, I discuss the results and compare the extended and
traditional specifications which include and do not include joint income
earned by multiple earners, respectively, for my standard overidentification
test. These results are presented in Tables 3 and 4. I then also discuss two
additional robustness checks, which account for heterogeneity across household
type and cultures. These results are presented in Tables 5 and 6.

###  5.1 Extended and Traditional Specifications

I first consider the results of the first stage, the relationship between
income and rainfall, presented in Table 3. Panel 1 presents the specification
with inclusion of male, female, and joint income, while Panel 2 presents the
specification with just male and female income.888Appendix section A.2
presents and discusses the results if this stage did not exist. In both
panels, it is evident that total seasonal rainfall has a positive and
significant, albeit small, impact on incomes. In Panel 1, all income types all
have a positive relationship with total seasonal rainfall, although the
coefficient on male income is more than twice as large as the coefficients on
joint and female income. This suggests - following expectations - that as
rainfall increases, incomes increase and as rainfall decreases, incomes
decrease.

Interestingly, in Panel 2, the coefficient on female income is more than twice
as large as the coefficient on male income. If we assume that larger
coefficients are an indicator of greater response to changes in total
rainfall, then this suggests that when joint income is not included, as in the
traditional specification, men’s income becomes less vulnerable to, but also
less able to benefit from, fluctuations and short term shocks in seasonal
rainfall. Similarly, this suggests that women’s income becomes more vulnerable
to and more able to benefit from the same fluctuations.

Using the predicted values from the first stage, I estimate the restricted
overidentification test that is the second stage. The results are presented in
Table 4. Recall that the impacts on income by earner, measured conditional on
total expenditure, determine discrepancies and shifts in the allocation of
income to different expenditure purposes within the household. Panel 1
presents the results of the extended specification which includes joint
income. Considering these results, I fail to reject equality for the case of
food. Failure to reject equality indicates that income is pooled for this
expenditure and that households insure one another for expenditures on goods
in this category. That is, I find evidence that households are insuring one
another against short term shocks for expenses that the household makes on
food. As this comprises a large portion of the household budget and percentage
of total household expenditures, this represents a significant expense for the
household that is insured. Still, though, I reject equality for expenditures
on alcohol and tobacco, clothing, recreation, education, healthcare, housing
and utilities, transportation, communication, and hotels and restaurants. That
is, all other household expenses. This suggests a strategic - though
incomplete - pooling mechanism employed by households.

I also consider the size and significance of coefficients presented in Panel
1, with particular attention to the magnitudes of these coefficients. The
coefficients are interpreted as percentages changes in expenditure, with
related changes in income. I observe that there are more significant
coefficients associated with predicted changes in women’s income, then with
men’s income or with joint income. About 80 percent of coefficients are
significant, suggesting that expenditures on various goods are vulnerable to
the predicted changes in women’s income. These coefficients are all positive
and indicate shifts between 2.5 and 5 percent, depending on the expenditure.
This suggests potentially consequential changes in expenditure to various good
categories, as women’s income changes, though not necessarily for men’s income
or income from joint sources.

In Panel 2, the results of the traditional specification are presented, which
does not include joint income. Similarly to the extended specification, I fail
to reject equality for the case of food. Again: failure to reject equality
indicates that income is pooled for this expenditure and households insure one
another for expenditures on goods in this category. Further, as before, I
reject equality for expenditures on alcohol and tobacco, clothing, recreation,
education, healthcare, housing and utilities, transportation, communication,
and hotels and restaurants. Overall, this indicates that the findings do not
differ across the extended and traditional specification, at least with
respect to the broad conclusions about insurance of expenditures by household
members in the presence of short term shocks.

It is worth noting, however, that while the overall interpretation of results
are the same, there are differences in the magnitude and significance of
coefficients across the two specifications. In the traditional specification,
only 40 percent of the predicted changes in women’s income have a significant
relationship with expenditure - half as many as in the extended specification.
Further, all of the magnitudes are greater in the traditional specification.
Considering the implications of these differences, this change suggests that
actual household behaviors may be masked to some extent in the traditional
specification. While to some degree, the predicted changes, particularly in
women’s income, suggest a smaller percentage change in magnitude of the
coefficients when joint income is included, but a greater number of categories
of expenditure overall show a significant change in predicted income and
corresponding changes in expenditure. This suggests that there is a shift in
type of allocation behavior demonstrated, that is important for understanding
dynamics and functioning of households and their responses to coping with
short term shocks and fluctuations in income. It suggests that women’s income
changes result in changes to expenditure - if women’s incomes increase,
expenditure increases, but if women’s income decreases, expenditure decreases.
This is observed particularly for healthcare and transportation, which see no
changes in expenditure associated with changes in income from men or joint
sources. The differences observed in allocation behavior between Panel 1 and 2
suggests that the complete story of household allocation behavior is not
evident in the traditional specification, but is only revealed in the extended
specification, which includes income earned jointly.

These results suggest the importance in and value for including joint
relationships in analyses of household behavior and resource allocation. The
evidence of this study elucidates and differs from previous work, and moves
beyond the usual conceptions of the household, extending the discussion about
intra-household relationships and behavior. Although I find evidence of
partial income pooling, that behavior is likely strategic, as it is for the
greatest single expenditure source within most households’ budgets. In
addition to this, however, the findings in this section suggest that
understanding detailed intra-household interactions and their outcomes on
household behavior have important consequences for household resource
allocation and decision making, as related to income allocation in the
presence of shocks. Understanding the dynamics of household members’
allocation of resources to various expenditures is essential for appreciating
how decisions are made within households and how members individually and
households at large, cope with shocks to their incomes.

###  5.2 Heterogeneity across Households

Next, I present two robustness checks. To consider household composition may
change the allocation of household resources, I consider some potential
alternative household structures, including households with matrilineal
traditions and households with female headship. It is possible that a subset
of households may behave in different ways based on different compositions and
structures, which are consistent with disparate types of income pooling
behaviors.

In Table 5, Panel 1 presents the male, female, and joint specification, while
Panel 2 presents simply the male and female specification. Within each panel,
there are two sections. In each, section A presents the results for non-
matrilineal households while section B presents the results for matrilineal
households. This is similar in Table 6, though in this case, section A
presents the results for non-female-headed households and section B presents
the results for female-headed households.

First, I consider differences in income pooling driven by societal
characteristics, in particular matrilineal inheritance traditions. Walther
(2018) finds that there may be disparities in cooperative decision making
behavior in Malawi, depending on women’s status in the household.
Specifically, those residing in communities with matrilineal lineage may
exhibit different behavior, due to women’s relative power in these
communities. To explore this, I consider whether the community reports being
matrilineal. The data includes responses to the question: “Do individuals in
this community trace their descent through their father, their mother, or are
both kinds of descent traced?” Communities which respond “their mother” are
deemed to be matrilineal.999Less than 10 percent of respondents indicated
“both” and so these communities were grouped with those communities which
trace lineage from their father. This entire group is simply classified as
“non-matrilineal”.

The results of the specifications related to matrilineal inheritance
traditions are presented in Table 5. In the table, Panel 1 presents the
extended specification which includes male, female, and joint incomes, while
Panel 2 presents the traditional specification, which includes only male and
female incomes. Within each panel, there are two sections. In each, section A
presents the results for non-matrilineal households while section B presents
the results for matrilineal households. As in both the extended and
traditional specification presented in Table 4, I fail to reject equality for
the case of food. Failure to reject equality indicates that income is pooled
for this expenditure and that households insure one another for expenditures
on goods in this category. This is the case for all variations, including
matrilineal and non-matrilineal households, in both specifications. Again, I
reject equality for expenditures on alcohol and tobacco, clothing, recreation,
education, healthcare, housing and utilities, transportation, communication,
and hotels and restaurants. This may a strategic pooling behavior employed by
households to pool income for their greatest household expenditure, although
the overall household expenditure pooling is thus incomplete.

I observe some differences when examining matrilineal households in the
different specifications. In matrilineal households in the extended
specification, predicted changes in women’s income are significantly
associated with expenditures in about half of the cases; but this falls to
just about 40 percent in the non-matrilineal specification. However, in
matrilineal households, very few joint income coefficients are significant,
while in the non-matrilineal households, more than 30 percent are significant.
Notably, coefficients are also smaller in the non-matrilineal specification,
between 2 and 4 percent, rather than 3 to 6 percent as in the matrilineal
specification. Taking this further, in the traditional specification, in non-
matrilineal households, two thirds of the coefficients are significant for
women’s income, while only 25 percent are significant for men’s income. Again,
this falls in the matrilineal specification: just over 15 percent are
significant for women’s income, while none are significant for men’s income.
This seems to suggest that there are disparities in results, with respect to
the magnitude and significance of coefficients, when considering the
traditional and extended specifications, and, as such, conclusions may
ultimately vary based on what specification is considered. In particular, some
specifications, particularly when considering matrilineal households, may hide
women’s allocation of resources in response to short term shocks.

The results of the specification related to male and female household headship
are presented in Table 6. In the table, Panel 1 presents the extended
specification which includes male, female, and joint incomes, while Panel 2
presents the traditional specification, which includes only male and female
incomes. Within each panel, there are two sections. In each, section A
presents the results for non-female-headed households while section B presents
the results for female-headed households. Once again, I fail to reject
equality for the case of food. Failure to reject equality indicates that
income is pooled for this expenditures and that households insure one another
for expenditures on goods in this category. This is the case for all
variations, including matrilineal and non-matrilineal households, in both
specifications. And again, I reject equality for expenditures on alcohol and
tobacco, clothing, recreation, education, healthcare, housing and utilities,
transportation, communication, and hotels and restaurants. There is one
exception to this finding: in the case of female-headed households in the
extended specification. In this case, we fail to reject equality for the case
of hotels and restaurants. This relationship however, is likely spurious,
simply based on the consistency of results throughout the rest of the
analysis.

In the case of female- and male-headed households, I see very similar results
to the findings for matrilineal and non-matrilineal households: predicted
changes in women’s income are significantly associated with expenditures in
two thirds of the non-female-headed specification, this falls to just over 15
percent in the female-headed specification. Interestingly, in neither case for
the extended specification are the joint incomes subject to many significant
relationships. Coefficient are also very large in the non-female-headed
specification, with coefficients between 9 and 17 percent, relative to the
female-headed specification, with coefficients around 1 or 2 percent. This
suggests that in non-female-headed households, changes in women’s income due
to positive or negative short term shocks are associated with changes to
expenditure - positive or negative, depending on the direction of the shock.
Further, in the traditional specification, in both the female and non-female-
headed household specifications only about 15 percent of coefficients for
women’s income are significant. And, it is not the case that coefficients on
male incomes are significant instead. In both cases, very little is
significant. Again, this suggests that the traditional specification
obfuscates and masks some information about how households cope within
households and how expenditures are adjusted, after the experience of a short
term shock. The specification used in an analysis may obfuscate the role of
women in household resource allocation and understanding household
expenditures, in response to shock events.

It is worth noting that the differences in these robustness checks, differ
somewhat from previous literature. Previous work suggests that there are
likely to be significant differences based on lineage and household headship.
But, I find little evidence of that, with respect to intra-household resource
allocation. I suspect that the context of Malawi may be important to consider:
more than two thirds of households report a matrilineal heritage, but still
nearly 80 percent of households are male-headed. This configuration may
explain some of the disparities from previous literature, at least with
respect to these robustness checks focused on household structures and
traditions.

The differences in potential expenditure changes revealed by considering both
the extended and traditional specifications demonstrates the vulnerabilities
of and opportunities to benefit in households’ livelihoods associated with
changes in women’s incomes, resulting from these short term shocks. Shocks and
resulting changes to women’s income is significantly affects expenditure more
often then changes in men’s and joint income. This is a fact often hidden in
the traditional specification when only men’s and women’s incomes are
included. These changes are likely to affect household expenditures and, in
turn, impact household livelihoods and outcomes as a result. The results
reveal a partial, strategic pooling of household incomes on food - the largest
expenditure within most households’ budgets. However, overall, households do
not pool income completely. These findings help further to elucidate intra-
household behavior. Understanding these dynamics and the full picture of
household vulnerabilities is revealed only in the extended specification, but
is imperative for fully understanding household dynamics and intra-household
resource allocation in the presence of short term, transient shocks.

##  6 Conclusions

I reject the hypothesis of complete income pooling within the household when
income earned jointly by two or more individuals is included in the empirical
analysis, I find evidence that household members partially insure one another
for expenditures on food. Food is a significant component of a household’s
expenditure and so this pooling behavior is for large percentage of a
household’s shared expenditures. This may a strategic pooling behavior
employed by households to pool income for their greatest household
expenditure, although the overall household pooling is still incomplete. But,
this finding is important as they are generally contrary to previous studies,
which fail to find even partial pooling or insurance within households. This
finding is robust across all of the specifications considered in this paper,
including the traditional and extended specifications, as well as robustness
checks of household structure, considering dynamics of matrilineal households
and households headed by women.

The inclusion of joint income reveals vulnerabilities of and opportunities for
households not previously revealed in most traditional analyses of household
behavior. Short term, non-persistent shocks often result in a predicted change
in women’s income, which is positively associated with changes in various
household expenditures. This suggests that as women’s income increases,
household expenditures also increase. However, it further suggests that if
women’s income decline, then expenditures may decrease - and these
expenditures are not insured by other household members and so may result in
shifts in the overall household expenditure. This is an important dynamic of
household resource allocation, which is not evident in a binary, traditional
conception of the collective household model, but is evident when joint income
is fully included in the analysis.

Household models have been a cornerstone of microeconomic analysis for more
than half a century, but many of the analyses on intra-household allocation of
resources has assumed that all income is earned by a single household member,
who is then responsible for those earnings in intra-household resource
allocation. In these circumstances, findings indicate that households tend not
to pool income. In this paper, I have relaxed this assumption and reveal
differential household behavior, not previously shown in standard, traditional
models, which only consider men and women and their income in the analysis. In
this way, this study moves beyond standard unitary, collective, and non-
cooperative conceptions of the household, extending the existing discussion
about intra-household dynamics. In contrast with previous studies and
prevailing empirical practice, the results suggest that understanding joint
interactions and their outcomes on household behavior have important
consequences for households and are imperative for our understanding of
households dynamics and interactions. Consideration of these relationships,
combined with efforts to learn about the intricate, shared relationships
within households will be imperative for understanding those dynamics.

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Table 1: Crop Cultivation, By Management Type

| 2010 | 2013
---|---|---
|  Women |  Men |  Joint |  Women |  Men |  Joint
Maize | $30.93$ | $28.61$ | $29.41$ | $25.20$ | $25.58$ | $25.39$
Tobacco | $7.18$ | $25.85$ | $24.37$ | $4.46$ | $12.00$ | $11.99$
Groundnut | $21.0$ | $17.69$ | $19.32$ | $23.17$ | $22.79$ | $23.82$
Rice | $2.75$ | $2.0$ | $2.24$ | $3.26$ | $2.41$ | $2.85$
Beans | $20.99$ | $14.45$ | $13.16$ | $26.84$ | $20.37$ | $20.35$
Potato | $3.31$ | $3.07$ | $3.36$ | $3.26$ | $3.15$ | $3.00$
Millet | $1.66$ | $0.62$ | $0.84$ | $0.00$ | $0.24$ | $0.16$
Sorghum | $1.10$ | $0.31$ | $0.56$ | $2.03$ | $0.97$ | $0.79$
Other | $11.08$ | $7.4$ | $6.29$ | $11.78$ | $12.49$ | $11.65$
Note: Table reports the crops cultivated, classified by management type.
Management type includes “male”, “female”, or “joint”, following the joint
specification as describe in section 2.2. Reallocated and omitted
specifications are not included. Maize includes: local maize and hybrid maize.
Beans include: “beans”, soybeans, and pigeonpea. Other crops include: cotton,
sugarcane, cotton, tomato, okra, and various vegetables and spices.

Table 2: Summary Statistics for Income, Expenditure, and Rainfall

| Mean | Std Dev
---|---|---
_Panel 1: Income_
Joint Income |  |
Female Income | $2,686$ | $53,023$
Male Income | $5,846$ | $39,134$
Joint Income | $13,871$ | $103,771$
Omitted Joint Income |  |
Female Income | $2,828$ | $53,325$
Male Income | $19,555$ | $111,606$
_Panel 2: Expenditures_
Total | $611,834$ | $670,837$
Food | $359,981$ | $318,225$
Cigarettes and Alcohol | $17,746$ | $47,288$
Clothing | $20,548$ | $47,523$
Recreation | $4,664$ | $17,225$
Education | $9,847$ | $41,409$
Healthcare | $7,709$ | $18,966$
Housing and Utilities | $119,296$ | $167,730$
Transportation | $30,182$ | $107,582$
Communication | $19,722$ | $94,566$
Hotels and Restaurants | $7,012$ | $17,200$
_Panel 3: Rainfall_
Total Seasonal Rainfall | $1,163$ | $551$
Note: Income and expenditure values are in Malawian Kwacha real terms with 2010 base. Rainfall measured in millimeters. |

Table 3: First Stage Rainfall Estimates

|  Joint Income |  Female Income |  Male Income
---|---|---|---
_Panel 1: Male, Female, and Joint_
Total Seasonal Rainfall | $0.00039^{*}$ | $0.00045^{**}$ | $0.00113^{**}$
| $(0.00016)$ | $(0.00014)$ | $(0.00022)$
$R^{2}$ | 0.020 | 0.022 | 0.048
_Panel 2: Male and Female_
Total Seasonal Rainfall |  | $0.00167^{**}$ | $0.00050^{**}$
|  | $(0.00024)$ | $(0.00014)$
$R^{2}$ |  | 0.075 | 0.023
Note: N = 850. Fully robust standard errors are in parentheses. (∗ $p<0.05$,
∗∗ $p<0.01$). Regressions also include agro-ecological zone indicators.

Table 4: Restricted Overidentification Tests

| (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
---|---|---|---|---|---|---|---|---|---|---|---
| Aggregate | Food | Alcohol & Tobacco | Clothing | Recreation | Education | Healthcare | Housing & Utilities | Transportation | Communication | Hotels & Restaurants
_Panel 1: Male, Female, and Joint_
Predicted change in male income | $5.008^{**}$ | $5.029^{*}$ | $-0.142$ | $-2.603$ | $3.568^{*}$ | $3.113^{*}$ | $1.043$ | $3.944^{*}$ | $1.160$ | $0.145$ | $2.180$
| $(1.921)$ | $(2.021)$ | $(1.814)$ | $(2.026)$ | $(1.462)$ | $(1.534)$ | $(1.918)$ | $(1.555)$ | $(1.891)$ | $(1.679)$ | $(1.729)$
Predicted change in female income | $4.127^{**}$ | $4.176^{**}$ | $1.664$ | $2.666^{**}$ | $3.006^{**}$ | $2.985^{**}$ | $2.585^{**}$ | $3.007^{**}$ | $2.170^{*}$ | $2.112^{*}$ | $0.455$
| $(0.953)$ | $(1.003)$ | $(0.900)$ | $(1.005)$ | $(0.725)$ | $(0.761)$ | $(0.951)$ | $(0.771)$ | $(0.938)$ | $(0.833)$ | $(0.858)$
Predicted change in joint income | $0.601$ | $0.570$ | $0.865$ | $2.045^{*}$ | $-1.054$ | $-0.574$ | $0.354$ | $0.224$ | $0.586$ | $0.239$ | $0.237$
| $(0.848)$ | $(0.892)$ | $(0.801)$ | $(0.895)$ | $(0.645)$ | $(0.678)$ | $(0.847)$ | $(0.687)$ | $(0.835)$ | $(0.742)$ | $(0.763)$
Overidentification - Wald Test |  | 0.26 | 73.25 | 215.62 | 206.78 | 109.73 | 35.58 | 24.38 | 40.63 | 69.68 | 63.82
|  | (0.968) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | 0(.000) | (0.000)
$R^{2}$ | 0.214 | 0.196 | 0.064 | 0.080 | 0.060 | 0.075 | 0.061 | 0.201 | 0.060 | 0.031 | 0.056
_Panel 2: Male and Female_
Predicted change in male income | $0.228$ | $0.190$ | $0.872$ | $2.229^{*}$ | $-1.488$ | $-0.935$ | $0.204$ | $-0.083$ | $0.481$ | $0.140$ | $0.148$
| $(1.049)$ | $(1.103)$ | $(0.990)$ | $(1.106)$ | $(0.798)$ | $(0.838)$ | $(1.047)$ | $(0.849)$ | $(1.032)$ | $(0.917)$ | $(0.944)$
Predicted change in female income | $8.229^{*}$ | $8.347^{*}$ | $0.418$ | $-2.481$ | $8.097^{**}$ | $6.954^{*}$ | $3.258$ | $6.578^{*}$ | $2.575$ | $2.084$ | $2.158$
| $(3.576)$ | $(3.762)$ | $(3.377)$ | $(3.771)$ | $(2.721)$ | $(2.856)$ | $(3.570)$ | $(2.894)$ | $(3.520)$ | $(3.126)$ | $(3.218)$
Overidentification - Wald Test |  | 0.19 | 72.20 | 211.56 | 205.81 | 109.57 | 34.10 | 24.23 | 39.97 | 67.02 | 63.24
|  | (0.909) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000)
$R^{2}$ | 0.224 | 0.200 | 0.080 | 0.076 | 0.056 | 0.076 | 0.053 | 0.197 | 0.068 | 0.028 | 0.054
Note: N = 850. The table presents coefficients of the difference in log
consumption of each item on the difference in predicted log income, as from
Table 3. Regressions include agro-ecological zone indicators. Fully robust
standard errors clustered at the household are in parentheses (∗ $p<0.05$, ∗∗
$p<0.01$) below the predicted change variables. Below the Wald test in
parentheses is the probability $>\chi^{2}$.

Table 5: Restricted Overidentification Tests - Log of Consumption
(Matrilineal)

| (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
---|---|---|---|---|---|---|---|---|---|---|---
| Aggregate | Food | Alcohol & Tobacco | Clothing | Recreation | Education | Healthcare | Housing & Utilities | Transportation | Communication | Hotels & Restaurants
_Panel 1: Male, Female, and Joint_
Section A: Non-Matrilineal |  |  |  |  |  |  |  |  |  |  |
Predicted change in male income | $5.021$ | $5.847$ | $-1.062$ | $-14.590$ | $8.385$ | $7.257$ | $-9.556$ | $6.327$ | $5.430$ | $7.792$ | $8.488$
| $(8.342)$ | $(8.877)$ | $(7.480)$ | $(8.264)$ | $(6.425)$ | $(6.854)$ | $(7.913)$ | $(7.066)$ | $(8.287)$ | $(7.264)$ | $(7.354)$
Predicted change in female income | $3.628^{**}$ | $3.517^{**}$ | $1.455$ | $2.358$ | $2.585^{**}$ | $2.106^{*}$ | $1.373$ | $2.972^{**}$ | $2.216$ | $2.998^{**}$ | $1.260$
| $(1.256)$ | $(1.337)$ | $(1.127)$ | $(1.245)$ | $(0.968)$ | $(1.032)$ | $(1.192)$ | $(1.064)$ | $(1.248)$ | $(1.094)$ | $(1.108)$
Predicted change in joint income | $2.723^{**}$ | $2.731^{**}$ | $0.461$ | $2.145^{**}$ | $0.436$ | $0.840$ | $1.705^{*}$ | $1.707^{**}$ | $0.835$ | $0.260$ | $0.894$
| $(0.718)$ | $(0.764)$ | $(0.644)$ | $(0.712)$ | $(0.553)$ | $(0.590)$ | $(0.681)$ | $(0.608)$ | $(0.713)$ | $(0.625)$ | $(0.633)$
Overidentification Wald-Test |  | 3.13 | 36.08 | 139.32 | 26.02 | 30.79 | 123.07 | 8.47 | 13.03 | 25.86 | 29.46
|  | (0.373) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.037) | (0.005) | (0.000) | (0.000)
Observations | 269 | 269 | 269 | 269 | 269 | 269 | 269 | 269 | 269 | 269 | 269
$R^{2}$ | 0.213 | 0.199 | 0.045 | 0.113 | 0.084 | 0.076 | 0.089 | 0.229 | 0.063 | 0.058 | 0.099
Section B: Matrilineal |  |  |  |  |  |  |  |  |  |  |
Predicted change in male income | $1.644^{*}$ | $1.382$ | $-0.408$ | $-1.191$ | $-0.154$ | $-0.617$ | $-0.252$ | $1.441^{*}$ | $-0.228$ | $-0.539$ | $1.048$
| $(0.966)$ | $(1.014)$ | $(0.936)$ | $(1.045)$ | $(0.732)$ | $(0.765)$ | $(0.990)$ | $(0.760)$ | $(0.948)$ | $(0.846)$ | $(0.875)$
Predicted change in female income | $5.276^{***}$ | $5.428^{***}$ | $2.545$ | $3.711^{**}$ | $4.026^{***}$ | $4.450^{***}$ | $4.967^{***}$ | $3.340^{**}$ | $2.292$ | $0.899$ | $-0.769$
| $(1.685)$ | $(1.767)$ | $(1.632)$ | $(1.822)$ | $(1.277)$ | $(1.334)$ | $(1.726)$ | $(1.326)$ | $(1.652)$ | $(1.475)$ | $(1.524)$
Predicted change in joint income | $0.655$ | $0.681$ | $0.778$ | $1.024$ | $-0.572$ | $-0.153$ | $-0.502$ | $0.426$ | $0.941$ | $0.838$ | $0.775$
| $(0.638)$ | $(0.669)$ | $(0.618)$ | $(0.690)$ | $(0.483)$ | $(0.505)$ | $(0.653)$ | $(0.502)$ | $(0.625)$ | $(0.558)$ | $(0.577)$
Overidentification Wald-Test |  | 4.19 | 186.88 | 490.29 | 998.09 | 539.79 | 715.04 | 24.26 | 268.85 | 262.08 | 154.41
|  | (0.241) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000)
Observations | 581 | 581 | 581 | 581 | 581 | 581 | 581 | 581 | 581 | 581 | 581
$R^{2}$ | 0.224 | 0.200 | 0.080 | 0.076 | 0.056 | 0.076 | 0.053 | 0.197 | 0.068 | 0.028 | 0.054
_Panel 2: Male and Female_
Section A: Non-Matrilineal |  |  |  |  |  |  |  |  |  |  |
Predicted change in male income | $2.061^{**}$ | $2.110^{**}$ | $0.228$ | $0.749^{*}$ | $0.626^{*}$ | $0.876^{**}$ | $0.711^{*}$ | $1.421^{**}$ | $0.781^{*}$ | $0.457$ | $1.003^{**}$
| $(0.370)$ | $(0.394)$ | $(0.332)$ | $(0.366)$ | $(0.285)$ | $(0.304)$ | $(0.351)$ | $(0.313)$ | $(0.367)$ | $(0.322)$ | $(0.326)$
Predicted change in female income | $2.687^{**}$ | $2.496^{*}$ | $1.464$ | $3.451^{**}$ | $1.643^{*}$ | $1.232$ | $2.053^{*}$ | $2.054^{*}$ | $1.520$ | $2.128^{*}$ | $0.278$
| $(1.031)$ | $(1.097)$ | $(0.924)$ | $(1.021)$ | $(0.794)$ | $(0.847)$ | $(0.978)$ | $(0.873)$ | $(1.024)$ | $(0.898)$ | $(0.909)$
Overidentification Wald-Test |  | 2.62 | 22.15 | 10.23 | 18.03 | 26.53 | 12.75 | 7.25 | 12.69 | 18.79 | 22.15
|  | (0.269) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.027) | (0.002) | (0.000) | (0.000)
Observations | 269 | 269 | 269 | 269 | 269 | 269 | 269 | 269 | 269 | 269 | 269
$R^{2}$ | 0.213 | 0.199 | 0.045 | 0.113 | 0.084 | 0.076 | 0.089 | 0.229 | 0.063 | 0.058 | 0.099
Section B: Matrilineal |  |  |  |  |  |  |  |  |  |  |
Predicted change in male income | $0.689$ | $0.397$ | $-0.927$ | $-1.939$ | $-0.773$ | $-1.356$ | $-1.039$ | $0.838$ | $-0.721$ | $-0.787$ | $1.100$
| $(1.129)$ | $(1.184)$ | $(1.094)$ | $(1.221)$ | $(0.856)$ | $(0.894)$ | $(1.157)$ | $(0.888)$ | $(1.107)$ | $(0.989)$ | $(1.022)$
Predicted change in female income | $5.745$ | $6.539$ | $6.226$ | $10.002^{**}$ | $4.678$ | $7.171^{**}$ | $6.368$ | $2.869$ | $5.888$ | $4.292$ | $-1.361$
| $(3.454)$ | $(3.623)$ | $(3.346)$ | $(3.736)$ | $(2.618)$ | $(2.734)$ | $(3.538)$ | $(2.718)$ | $(3.386)$ | $(3.025)$ | $(3.125)$
Overidentification Wald-Test |  | 3.34 | 155.49 | 404.64 | 216.83 | 233.04 | 96.13 | 18.46 | 177.89 | 169.11 | 71.06
|  | (0.189) | (0.000) | (0.000) | (0.014) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000)
Observations | 581 | 581 | 581 | 581 | 581 | 581 | 581 | 581 | 581 | 581 | 581
$R^{2}$ | 0.224 | 0.200 | 0.080 | 0.076 | 0.056 | 0.076 | 0.053 | 0.197 | 0.068 | 0.028 | 0.054
Note: N = 850. The table presents coefficients of the difference in log
consumption of each item on the difference in predicted log income, as from
Table 3. Regressions include agro-ecological zone indicators. Fully robust
standard errors clustered at the household are in parentheses (∗ $p<0.05$, ∗∗
$p<0.01$) below the predicted change variables. Below the Wald test in
parentheses is the probability $>\chi^{2}$.

Table 6: Restricted Overidentification Tests - Log of Consumption (Female-
Headed)

| (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
---|---|---|---|---|---|---|---|---|---|---|---
| Aggregate | Food | Alcohol & Tobacco | Clothing | Recreation | Education | Healthcare | Housing & Utilities | Transportation | Communication | Hotels & Restaurants
_Panel 1: Male, Female, and Joint_
Section A: Non-Female-Headed |  |  |  |  |  |  |  |  |  |  |
Predicted change in male income | $1.608$ | $1.460$ | $-2.443$ | $-5.472^{**}$ | $-0.536$ | $0.772$ | $-1.875$ | $-0.619$ | $-2.820$ | $-1.955$ | $1.877$
| $(1.747)$ | $(1.857)$ | $(1.694)$ | $(1.871)$ | $(1.398)$ | $(1.384)$ | $(1.769)$ | $(1.440)$ | $(1.772)$ | $(1.614)$ | $(1.607)$
Predicted change in female income | $13.805^{**}$ | $14.604^{**}$ | $7.605$ | $10.979^{*}$ | $16.898^{**}$ | $9.638^{*}$ | $10.398^{*}$ | $15.327^{**}$ | $13.540^{**}$ | $9.234^{*}$ | $0.338$
| $(4.819)$ | $(5.122)$ | $(4.673)$ | $(5.161)$ | $(3.857)$ | $(3.818)$ | $(4.879)$ | $(3.973)$ | $(4.887)$ | $(4.452)$ | $(4.432)$
Predicted change in joint income | $0.857$ | $0.855$ | $1.049$ | $2.380^{**}$ | $-0.603$ | $-0.373$ | $0.596$ | $0.582$ | $0.946$ | $0.512$ | $0.232$
| $(0.798)$ | $(0.848)$ | $(0.774)$ | $(0.855)$ | $(0.639)$ | $(0.632)$ | $(0.808)$ | $(0.658)$ | $(0.809)$ | $(0.737)$ | $(0.734)$
Overidentification Wald-Test |  | 0.49 | 731.10 | 332.45 | 374.67 | 88.83 | 357.82 | 18.67 | 563.16 | 878.65 | 48.80
|  | (0.921) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000)
Observations | 677 | 677 | 677 | 677 | 677 | 677 | 677 | 677 | 677 | 677 | 677
$R^{2}$ | 0.220 | 0.205 | 0.061 | 0.081 | 0.081 | 0.062 | 0.053 | 0.210 | 0.075 | 0.034 | 0.048
Section B: Female-Headed |  |  |  |  |  |  |  |  |  |  |
Predicted change in male income | $-17.254$ | $-13.829$ | $-20.866$ | $-5.289$ | $3.530$ | $-15.054$ | $-20.371$ | $-34.773^{**}$ | $-22.431$ | $1.491$ | $-13.172$
| $(16.195)$ | $(16.332)$ | $(14.103)$ | $(16.496)$ | $(8.961)$ | $(13.536)$ | $(15.677)$ | $(12.219)$ | $(13.935)$ | $(10.556)$ | $(13.346)$
Predicted change in female income | $1.551^{*}$ | $1.559^{*}$ | $0.094$ | $0.926$ | $0.026$ | $1.195^{*}$ | $0.475$ | $-0.306$ | $-0.618$ | $0.722$ | $-0.016$
| $(0.711)$ | $(0.717)$ | $(0.619)$ | $(0.724)$ | $(0.393)$ | $(0.594)$ | $(0.688)$ | $(0.536)$ | $(0.612)$ | $(0.463)$ | $(0.586)$
Predicted change in joint income | $3.114^{*}$ | $3.109^{*}$ | $0.728$ | $1.337$ | $0.411$ | $0.700$ | $1.600$ | $-0.077$ | $0.646$ | $0.242$ | $-0.177$
| $(1.210)$ | $(1.221)$ | $(1.054)$ | $(1.233)$ | $(0.670)$ | $(1.012)$ | $(1.172)$ | $(0.913)$ | $(1.041)$ | $(0.789)$ | $(0.997)$
Overidentification Wald-Test |  | 1.95 | 337.29 | 60.22 | 411.48 | 27.42 | 203.48 | 633.58 | 785.60 | 606.50 | 371.41
|  | (0.583) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.139)
Observations | 173 | 173 | 173 | 173 | 173 | 173 | 173 | 173 | 173 | 173 | 173
$R^{2}$ | 0.252 | 0.225 | 0.093 | 0.096 | 0.076 | 0.158 | 0.118 | 0.212 | 0.046 | 0.050 | 0.146
_Panel 2: Male and Female_
Section A: Non-Female Headed |  |  |  |  |  |  |  |  |  |  |
Predicted change in male income | $0.861$ | $0.850$ | $0.823$ | $1.882^{*}$ | $-0.621$ | $-0.320$ | $0.429$ | $0.478$ | $0.695$ | $0.349$ | $0.320$
| $(0.684)$ | $(0.727)$ | $(0.663)$ | $(0.733)$ | $(0.548)$ | $(0.542)$ | $(0.693)$ | $(0.564)$ | $(0.694)$ | $(0.632)$ | $(0.629)$
Predicted change in female income | $14.048$ | $14.539$ | $-0.561$ | $-7.248$ | $17.237^{**}$ | $12.041^{*}$ | $4.647$ | $11.970$ | $4.795$ | $3.607$ | $3.330$
| $(7.603)$ | $(8.080)$ | $(7.371)$ | $(8.142)$ | $(6.085)$ | $(6.023)$ | $(7.697)$ | $(6.267)$ | $(7.709)$ | $(7.023)$ | $(6.992)$
Overidentification Wald-Test |  | 0.26 | 60.65 | 171.26 | 136.08 | 87.19 | 33.31 | 15.85 | 26.58 | 47.56 | 48.10
|  | (0.880) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000)
Observations | 677 | 677 | 677 | 677 | 677 | 677 | 677 | 677 | 677 | 677 | 677
$R^{2}$ | 0.220 | 0.205 | 0.061 | 0.081 | 0.081 | 0.062 | 0.053 | 0.210 | 0.075 | 0.034 | 0.048
Section B: Female-Headed |  |  |  |  |  |  |  |  |  |  |
Predicted change in male income | $-19.360$ | $-15.905$ | $-21.994$ | $-5.577$ | $2.829$ | $-13.526$ | $-22.215$ | $-35.353^{**}$ | $-25.091$ | $2.750$ | $-12.881$
| $(16.783)$ | $(16.925)$ | $(14.615)$ | $(17.095)$ | $(9.286)$ | $(14.027)$ | $(16.246)$ | $(12.663)$ | $(14.440)$ | $(10.939)$ | $(13.830)$
Predicted change in female income | $1.524^{*}$ | $1.533^{*}$ | $0.083$ | $0.919$ | $0.019$ | $1.203^{*}$ | $0.455$ | $-0.310$ | $-0.640$ | $0.731$ | $-0.013$
| $(0.715)$ | $(0.721)$ | $(0.623)$ | $(0.729)$ | $(0.396)$ | $(0.598)$ | $(0.693)$ | $(0.540)$ | $(0.616)$ | $(0.466)$ | $(0.590)$
Overidentification Wald-Test |  | 1.60 | 249.64 | 39.76 | 356.35 | 13.51 | 126.35 | 536.35 | 487.23 | 119.47 | 296.85
|  | (0.448) | (0.000) | (0.000) | (0.000) | (0.001) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000)
Observations | 173 | 173 | 173 | 173 | 173 | 173 | 173 | 173 | 173 | 173 | 173
$R^{2}$ | 0.252 | 0.225 | 0.093 | 0.096 | 0.076 | 0.158 | 0.118 | 0.212 | 0.046 | 0.050 | 0.146
Note: N = 850. The table presents coefficients of the difference in log
consumption of each item on the difference in predicted log income, as from
Table 3. Regressions include agro-ecological zone indicators. Fully robust
standard errors clustered at the household are in parentheses (∗ $p<0.05$, ∗∗
$p<0.01$) below the predicted change variables. Below the Wald test in
parentheses is the probability $>\chi^{2}$.

##  Appendix A Appendix

###  A.1 Prices and Price Stability

An essential assumption in the theoretical and empirical models is that
changes in consumption are driven by only changes in rainfall. This assumption
implies that there is no indirect link between rainfall and consumption. An
indirect link might exist if changes in rainfall induce changes in price,
which impact consumption and thus household expenditures. In this section I
briefly discuss some of the relevant literature which supports this
assumption.

Timmer (2000) suggests that price stability has an essential role in the
process of structural transformation and policies which work to stabilize
prices are common around the world. Additional evidence in this area is
supported by Fox et al. (2011); Chavas et al. (2005). Price stability observed
is often the result of government and development agency policy efforts
throughout Southern Africa (Jayne et al., 2006; d’Hotel et al., 2013). Efforts
towards coordination, transparency, and consultation between stakeholders have
improved price stability in recent years. Much of this achievement has come
from the compiling of strategic grain reserves, as modeled in Tran et al.
(2015) and Mason and Myers (2013).

Several studies, from Southern Africa generally and Malawi in particular, have
explored the existence of price stability in cases where changes would be
expected to shift prices. Ricker-Gilbert et al. (2013) considers the impact of
fertilizer subsidy programs on maize price stability in Zambia and Malawi:
they find that even doubling the subsidy results in only small price changes.
The conclusions of this work are supported by Denning et al. (2009) who
determine that input subsidies and maize surpluses improved price stability in
Malawi.

Price stability is a reasonable assumption across much of Southern Africa,
including Malawi, due to the prevalence of such programs and efforts to
stabilize prices throughout the region. These findings and relevant literature
support the assumption that changes in consumption are driven by only changes
in rainfall experienced.

###  A.2 Additional Tests and Analyses

Table A.1 presents the unconstrained estimates of the relationship between
expenditure and rainfall. For each regression, nine rainfall variables, are
included, as well as location indicators. These results are not disaggregated
by gender and hence cannot address the potentially gendered nature of income
earning and expenditure.

Table A.1: Unrestricted Overidentification Tests

| (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
---|---|---|---|---|---|---|---|---|---|---|---
| Aggregate | Food | Alcohol & Tobacco | Clothing | Recreation | Education | Healthcare | Housing & Utilities | Transportation | Communication | Hotels & Restaurants
Total seasonal rainfall | $0.00447^{**}$ | $0.00446^{**}$ | $0.00167^{**}$ | $0.00249^{**}$ | $0.00154^{**}$ | $0.00189^{**}$ | $0.00196^{**}$ | $0.00313^{**}$ | $0.00208^{**}$ | $0.00127^{**}$ | $0.00132^{**}$
| $(0.00035)$ | $(0.00034)$ | $(0.00030)$ | $(0.00031)$ | $(0.00025)$ | $(0.00025)$ | $(0.00031)$ | $(0.00026)$ | $(0.00030)$ | $(0.00028)$ | $(0.00028)$
$R^{2}$ | 0.214 | 0.196 | 0.064 | 0.080 | 0.060 | 0.075 | 0.061 | 0.201 | 0.060 | 0.031 | 0.056
Note: N = 850. Regressions include agro-ecological zone indicators. Fully
robust standard errors clustered at the household are in parentheses (∗
$p<0.05$, ∗∗ $p<0.01$).