INFORMAL SAVINGS AND INTRA-HOUSEHOLD
STRATEGIES:
THEORY & EVIDENCE FROM URBAN BENIN∗
Vincent Somville†
September 2012
Abstract
Daily collectors operate worldwide; they charge a fee in exchange for the collection of their
client's deposits. The clients recover their savings after one month. With a negative nominal
return of -3.3% per month, the service is quite expensive but nonetheless prevalent among the
very poor. In the sample one third of the people make deposits and they deposit on average one
third of their income.
The economic literature so far emphasizes one motive for making deposits: people want to
commit to save. I show that deposits are determined by the income inequality within households
and I argue that people make deposits in order to reduce their contribution to the household's
expenditures and increase their private consumption. This intra-household motive is rst modelled
and then tested using a unique panel data-set collected in Benin.
Additionally, I show that daily collectors enable women to make more gifts to their children
and acquaintances, and allow men to reduce those gifts and their participation to household's
public goods. There is large positive eect of the deposits on people's purchase of new clothes,
and making deposits increases women's expenditures on frivolous goods substantially. Finally, the
commitment motive appears to be an another determinant of men's deposits.
JEL: D13, O12
∗ This paper is produced as part of the project Actors, Markets, and Institutions in Developing Countries: A microempirical approach (AMID), a Marie Curie Initial Training Network (ITN) funded by the European Commission under
its Seventh Framework Programme Contract Number 214705 PITN-GA-2008-214705. Data collection was funded by
the Belgian National Bank and the Fondation Universitaire pour la Coopération Internationale au Développement.
Thanks are due to Matteo Bobba, Marcel Fafchamps, Clémentine Gavouyère, Raphaël Godefroy, Catherine Guirkinger,
Romain Houssa, Sylvie Lambert, Jean-Philippe Platteau, Vijayendra Rao, Daniel Stein, Vincenzo Verardi and seminar
participants at Paris School of Economics, Namur University and the 9th EUDN conference for useful comments and
discussions. I am very grateful to Olivier Dagnelie and Philippe Lemay-Boucher, with whom I collected the data, and
to Joël Noret for many fruitful discussions and to our team of enumerators: Félicité Chadare, Maurille Gandemey,
Shadia Gbaguidi, Calixte Houedey, Euphrem Lankoutin, Pierre Meliho, Raoul Tchiakpe, Aristide, Hilarion Sylvestre
and especially Charlemagne Tomavo.
† Centre of Research in the Economics of Development (CRED), Department of economics, University of Namur and
Chr. Michelsen Institute, Norway. Address: P.O.Box 6033 Bedriftssenteret, N-5892 Bergen, Norway, fax: +4747938001,
tel: +4747938014, email: [email protected].
1
1
Introduction
1 charge a fee in exchange for collecting daily the deposits of their clients. After one
Daily collectors
month, the clients recover their savings minus the fee, which is equal to one deposit. In other words,
the clients earn a negative nominal return of -3.3% per month on their savings.
As documented by Rutherford et al. (1999) and Rutherford (2000), daily collectors exist in various
places of the world and they handle a large part of informal savings in urban areas. Daily collectors
have been studied by economists in dierent contexts and they are generally mentioned by researchers
in micro-nance (see for instance Besley, 1995; Rutherford, 2000; Collins et al., 2009 and Armendariz
and Murdoch, 2010).
Aryeetey and Gockel (1991) include daily collectors in their work on capital
formation in Ghana and Aryeetey and Udry (1997) and Steel et al. (1997) describe them more generally
in Sub-Saharan Africa.
Nevertheless, very few researchers have really focused on this institution.
Among them, Ashraf
et al. (2006a) use a randomized control trial in the Philippines to investigate the determinants of
participation in a deposit collection service and evaluate its impact (see also Ashraf et al., 2009).
Being married is one important determinant of take up, which suggests that intra-household issues
matter. The physical distance to the bank is the other important determinant of take-up. The authors
also nd that oering the service of deposit collection increased the level of savings and decreased
borrowing.
The service that they oer has however important dierences with the daily collectors
because it is a costless monthly collection instead of a costly daily collection.
In the same line, Dupas and Robinson (2011) provide a randomly selected sample of self-employed
individuals in rural Kenya with access to an interest-free bank account. One of their main ndings
is that the daily private expenditures of women in the treatment group became 27% to 40% higher
than those of women in the comparison group. One interpretation of the authors is that women in the
treatment group might have been better able to shield their income from others.
An important feature of the the daily collection is that the clients commit to deposit the same xed
amount of cash everyday, for 30 days. If a client does not deposit as planned, he has to pay a fee.
Therefore some clients are likely to use the daily collection service as a commitment device.
There is an important literature arguing that individuals' level of impatience is lower for future
trade-os than for near-term trade-os. The rst models were developed by Strotz (1955) and Phelps
1 Daily collectors have dierent names in dierent countries. For instance, they are usually called tontinier in Benin,
susu in Ghana and esusu in Nigeria. They are more generally known as mobile bankers in West Africa and deposit
collectors in India.
2
and Pollak (1968). Time-inconsistent choices may be due to hyperbolic preferences, temptations, or
dual-self agents (see Ashraf et al., 2006b for a review).
This literature is however predominantly
theoretical. In fact, Ashraf et al. (2006b) are the rst to provide eld evidence linking hypothetical
time discount questions to the decision to use a commitment device. They use a randomized control
methodology to determine the motives behind the take-up of a commitment saving product. They nd
that women who exhibit time-inconsistent choices, and hence could have a preference for commitment,
are more likely to choose the commitment product. In a recent paper, Brune et al. (2011) also nd
that Malawian farmers who were randomly oered commitment savings account were able to increase
substantially their savings, agricultural inputs and crop sales (among other outcome measures) while
ordinary accounts did not have any signicant impact on those measures. The authors provide further
evidence that the farmers in fact commit themselves not to share their revenues with their kith and
kin.
While the literature has focused so far on the clients time-inconsistent behaviour to explain why they
make deposit rather than simply keeping the money home, I claim that deposits are also explained by
one's desire to increase his private consumption at the expense of his household's public consumption.
I rst write a formal model to introduce and analyse this motive. I then provide empirical evidence
supporting this claim.
The evidence comes from a survey carried out in Cotonou. The daily collection service is extensively
used in Benin. In the sample 36% of people with positive income make deposits. On average, they
deposit CFAF 516 (1.03$) per day. This is relatively high: on average a client's daily income is equal
to CFAF 1 708, of which he deposits around one third.
The population under study is poor, and
therefore the prevalent use of the daily collection service raises a number of important questions. In
particular, a direct policy recommendation for reducing poverty could be to provide the same service
at a lower cost. The design of sound policies however requires a clear understanding of the motives
that prompt people to make costly deposits rather than choose other forms of savings.
The commitment motive is already well understood but the intra-household motive is, to my knowledge, new to the literature on daily deposits. As a theoretical contribution, this paper provides an
analytical examination of the conditions that determine the optimal amount that a consumer will
deposit in order to lower his contributions to his household's public goods and to increase his private
consumption. The main prediction of the model is that deposits are determined by the within households income inequality.
It is only when household's members have similar incomes that they will
3
nd it optimal to make deposits. The intuition is as follows: in a model of voluntary contributions to
household's public goods, when household's members have very unequal incomes, the poorest member
shall not contribute to the public good and therefore has no reason to make costly deposits since he
will anyway consume his whole income privately. Simultaneously, the richest member could in theory
be tempted to make deposits, restricting his disposable income and constraining his contribution to
the public good in a way that is sucient to prompt the other member to compensate and nance
part of the public good. However, the higher the income inequality and the more deposits must the
richest member make to lead to positive contributions by the poorest member. Because the cost of the
deposits is proportional to the amounts of deposits, there will exist a level of inequality above which
the richest member nds it optimal not to incur that cost even if it means that he is the only one in
charge of the public good.
Empirically, both the commitment motive and the intra-household motive could play a role. To
assess the relative importance of the commitment motive I use time discount questions similar to those
used by Ashraf et al. (2006b) and Brune et al. (2011) to identify time-inconsistent individuals.
I
then run two sets of regressions. In the rst one I check whether individual's deposits are explained
by within household income inequality and time-inconsistent preferences. The panel structure of the
data is crucial to these regressions as it allows to eliminate all time constant unobserved variables and
thereby limits potential endogeneity issues. In the second one I compare the expenditures made by
users and non-users of the deposit collection. There also I use the panel to control for individual xed
eects and I additionally use instruments to correct for the self-selection of users. If the intra-household
motive is important, then we expect users to spend less on the household's public goods and more on
private goods. The methods and instruments are explained in greater details in section 4.2.
The results support the theory. Income inequality within households is a strong and robust determinant of people's deposits. The commitment motive, proxied by the time discount questions, also
partly determines the deposits.
Moreover, men who make deposits contribute less to some of the
main household's public goods (electricity bills mainly).
Both men and women who make deposits
spend much more on personal clothes. When they make deposits, women, but not men, increase their
purchase of frivolous goods, such as tobacco, alcohol, or candies.
This last result is unexpected. Even though is in line with the ndings of Dupas and Robinson
(2011) mentioned above, it contrasts a lot with the literature on the divergence between women and
men's preferences. For instance, Hoddinott and Haddad (1995) show that in Ivory Coast, men spend
4
relatively more than women on goods such as alcohol and cigarettes and less on goods that benet
children or the household as a whole (see also Bruce, 1989; Thomas, 1990; Browning, 2000; Duo and
Udry, 2004; Ashraf et al., 2009). In Cotonou men also spend more then women on frivolous goods, but
the data suggest that women use their deposits to sharply increase their purchase of frivolous goods.
Finally deposits could also be a way to protect income against nancial claims. Therefore, those
using the service should eectively transfer less money if they consider the claims illegitimate.
On
the other hand, using the daily collector enables the accumulation of a lump sum that may be used
for legitimate transfers. I provide suggestive evidence that men who make deposits give less to their
children and parish fellows, while women who make deposits give less to their husbands.
The next section discusses some critical characteristics of Beninese households and of the access
to banking services in Cotonou. In section 3, the model of strategic interactions between household
members shows how deposits are related to one's income share.
The model provides the welfare
implications of policies improving access to deposit collection service, which are discussed at the end
of the section. The empirical evidence is presented in section 4: rst the description of the data and
of the identication strategy and then the econometric results. Section 5 concludes.
2
Context
Some characteristics of the Beninese households and of the access to banking services in Cotonou are
essential to the model and the empirical analysis.
First, as shown by Dagnelie and LeMay-Boucher (2007), Beninese households do not pool their resources. There is no common budget between spouses and the contributions to the household's public
goods are made independently by the members. As Falen, an anthropologist who conducted research
2
among the Fon for more than a decade , concludes: the notion of a married couple's communal prop-
erty or joint bank accounts is totally foreign to most Fon people.(...) Keeping common nances would
be dangerous since money is always scarce and people are generally willing to take, borrow, beg, or in
other ways extract money from another , and he adds that most Fon view descent in patrilinear terms,
husbands and wives belong to dierent families, and have few common kinship loyalties. (...) Having
the option of diverting money from a conjugal account for use by one's own family could cause irreparable damage (Falen, 2011, p.103-104). Some anthropologists and economists already documented the
disconnection between household member's nancial spheres (see for instance Moock, 1986; Hoddinott
2 Fon
is the most populous ethnic group in Benin.
5
3 Therefore,
and Haddad, 1995; Attanasio and Lechene, 2002; Rangel and Thomas, 2006 for reviews).
I assume that the household's members take their decisions independently from one another. They
are however assumed to behave strategically: their decisions depend on their partner's decisions and
vice-versa.
Second, the only alternative to deposits is to accumulate cash at home. The data come from the
outskirts of Cotonou, where people live in high density slums.
Accumulating assets such as gold,
cattle, or land for example is too risky when not simply impossible. Also, most people cannot use an
account in a bank or a micro-nance institution (MFI). The rst reason is that the minimum balance
required by banks is out of reach for most of the population under study.
Houssa and Verpoorten
(ming) report that, at the time of the study, it varied from CFAF 100 000 to CFAF 500 000. In the
sample only 7% of the people earn more than CFAF 100 000 per month and the average monthly
income is around CFAF 40 000. People would thus need to accumulate savings in order to open an
account. Moreover, most of them cannot aord to keep hundreds of thousands of CFAF unused on a
bank account as they live in poverty and have pressing needs. In addition to the minimum balance
requirement, people are reluctant to deposit money with banks due to high transport costs. Helms
et al. (2005) estimate weekly costs to be equal to CFAF 5000 for banks and CFAF 150 for MFIs.
When taking into account the nominal interest rates on deposits, Helms et al. (2005) conclude that
one needs to save CFAF 130 000 in a bank or CFAF 36 000 in a MFI, per month, to cover these costs
and choose these institutions rather than a daily collector. Moreover, the attractiveness of the daily
collector increases furthermore when the opportunity cost of transportation and queuing are accounted
for. Finally, as described by Houssa and Verpoorten (ming), the banking sector in Benin went through
a severe crisis and collapsed at the beginning of the nineties. The collapse was partly due to adverse
economic conditions and partly to the actions of the Kerekou government. Among other policies, the
government nationalized all private banks. The banks then started to make loans with zero interest
rate and without collateral to politicians and their supporters (Girardon, 1989). Most of these loans
were not reimbursed and the banks were liquidated.
Households incomes were severely hit by the
4 More recently, in
collapse of the banks and people today continue to distrust the banking sector.
what is called l'aaire ICC-Services, a micronance institution lost the savings of thousands of people
while playing a Ponzi scheme. The aaire provoked a big scandal as close supporters of the President
3 See
also Dercon and Krishnan (2000), Duo and Udry (2004) and Munro et al. (2006), who cast doubt on the unitary
model as a relevant representation of household's functioning.
4 Mathieu Kerekou only left power in 2006.
6
are allegedly involved, and it undermined further the trust that people had in formal saving institutions
(for a brief account of the aair, see Nossiter, 2010).
Rotating savings and credit associations (ROSCA), which are very common in Cotonou (Dagnelie
and LeMay, 2008), could be another alternative to daily collectors. ROSCA members meet regularly
and they bring a pre-dened amount of cash money in each meeting.
given the total amount collected, called the pot.
One of the member is then
The main indirect costs are the cost of attending
the meetings, the imposed saving rate that potentially diers from one's optimal level of saving, and
5 In Cotonou, ROSCAs generally
the risk that the ROSCA collapses before each member gets the pot.
meet every two weeks or every month.
Therefore, people still need to accumulate money either at
home or through the daily collector if they want to participate in a ROSCA. ROSCAs are used to pool
bigger amounts of money, and not to avoid bringing daily incomes home. They also involve a lot of
6
people and it takes several months or even years before all members get the pot.
Finally, Anderson and Baland (2002) investigate individual motives to participate in ROSCAs in
Nairobi. Using a Nash bargaining model, they argue that the wives participate in ROSCAs to protect
their savings against claims by their husband for immediate consumption.
Their argument is close
to the intra-household motive that I investigate, but is nevertheless very dierent because they do
not allow for strategic interactions between spouses; only the wife has the possibility to join ROSCAs
in order to inuence the nal household's consumption. Their main results would be aected if the
husband were also allowed to join a ROSCA or to divert money from the household in reaction to his
wife's strategy.
In the context of Cotonou, restricting the set of strategies available to players, as done in Anderson
and Baland (2002), would be too strong an assumption. Besides, my main result arises precisely from
the strategic interaction that is at play between household's members. When an individual decides
how much to deposit, he must take into account how much the other deposits since it aects the money
that is available for the household's consumption.
5 References about ROSCAs include Besley et al. (1993); Bouman (1995); Handa and Kirton (1999); Anderson and
Baland (2002); Basu (2008); Anderson et al. (2009). About Benin, see Dagnelie and LeMay (2008) and Dagnelie (2008).
6 One might wonder why people do not join daily ROSCAs that would replicate the service oered by daily collectors.
For an equal deposit, setting up a ROSCA would however require that at least 30 people meet everyday. Even if one
can nd 29 other persons who are willing to meet everyday, the cost in time and organization is simply too high.
7
3
Theoretical framework
The model is written to capture the essential characteristic of daily collection:
using the service
amounts to paying someone to be able to bring less money home. The model depicts a world where
people have no access to banks to store their revenues. In order to transfer their current income to
future periods, they have to keep some money at home or to make deposits to the daily collector. I
assume that there is no credit market.
There are two agents,
a
and
b,
who live for 2 periods. Each agent
in the rst period and decides how much to deposit,
to contribute to a public good,
g,
di .
i = {a; b}
receives an income
The remaining income,
w i − di
wi
can be used
or it can be saved to the second period. I allow these savings,
si ,
to
enter directly into the utility function. The savings allow the agents to purchase indivisible goods, or
simply to delay their expenditures to a more appropriate day, such as the market day. I do not model
explicitly the various reasons that push people to save. I am not trying to explain savings per se, but
rather the choice of paying a daily collector rather than simply keeping the money at home. Agent
i
utility is given by:
U i = u g; si
The function
u(.)
is assumed to be twice continuously dierentiable. For simplicity, I also assume
that the second derivatives with respect to each argument are strictly negative:
Another important assumption is that
00
ugsi
u(0; si ) = 0.
00
is not negative: higher savings do not cause a lower marginal
utility from increased consumption of the public good.
assuming that
00
ugg < 0 and usi si < 0.
Finally, the discussion is also simplied by
This assumption guarantees that there will always be some positive
7
provision of the public good.
The total provision of public good is the sum of the individual contributions:
g = ga + gb .
The
individual savings are equal to the sum of:
ˆ
the part of the deposits that is recovered:
ˆ
the part of the income that is saved at home:
kdi
with
k ∈ ]0; 1[;
hi = wi − di − g i .
The utility function can therefore be written as:
U i = u g i + g j ; wi − (1 − k) di − g i
7 The main results do not change when u(0; si ) > 0, but this assumption leads to trivial discussions of cases where
the agents save or deposit their whole income because they do not care suciently about the public good.
8
The precise steps of the game are as follows:
1. In the rst period, the agents receive their incomes,
wi ,
and simultaneously and independently
choose the level of deposits that they make to the collector,
2. Each agent brings
w i − di
di ∈ 0; wi .
at home and chooses the level of his contribution,
gi ,
to the public
good.
3. In the second period, the agents consume their savings,
wi − (1 − k) di − g i .
The solution concept used is the standard Nash equilibrium in pure strategies. The game is solved by
backward induction.
3.1
Contributions to the public good (step 2)
The agents simultaneously choose the contribution to the public good that maximizes their utility:
M ax
i
{g }
u g i + g j ; wi − (1 − k) di − g i
∀i = {a; b} and j 6= i
The rst order conditions of each agent lead to a system of two equations (the reaction functions,
Ri ):



u0g − u0sa = 0 ≡ Ra g b


u0g − u0 b = 0
s
(1)
≡ Rb (g a )
It is not guaranteed that a solution to this system exists in the set of feasible values of
ga
and
gb .
Lemma 1 claries the conditions under which an interior solution exists.
Lemma 1.
Existence: if (i)
0
0
ug (0) − usa (0) > 0
and (ii)
Ri
−1
(0) > Rj (0),
then there exists a solution
to the system of equations (1) and the contributions corresponding to this solution are positive.
Condition (i) means that each agent would like to contribute at least a little if the other agent does
not contribute, and condition (ii) that agent
exceeds agent i's contribution when
j
i's
contribution that induces agent
j
to contribute zero
does not contribute. The proof of Lemma 1 is a direct replication
of the proof of existence of a Nash equilibrium in the standard Cournot model (see for instance Tirole
(1990), p.224-225).
Note that it cannot be guaranteed at this stage that the solution respects the constraint on the
maximum level of contributions:
g i ≤ wi − di , ∀i = {a; b}.
The next lemma states that if there exists a solution to the system (1), then the solution is unique.
9
Lemma 2.
Uniqueness: if it exists, the solution to the system of equations
Proof. Suppose there exists an intersection between
(1)
0
0
0
0
Ra g b ≡ ug −usa = 0 and Rb (g a ) ≡ ug −usb = 0.
We know that a sucient condition for this intersection to be unique is that
whenever they intersect.
Moreover, a sucient condition to guarantee
i = {a; b}
It is therefore sucient to prove the lemma,
(Tirole, 1990).
is unique.
Ra
is steeper than
0
i this, is that Rg j < 1
0
i to show that Rg j < 1
Rb
for
for
i = {a; b}.
By the implicit function
00
usa g ≥ 0
The assumption that
denominator and
0
a
Rgb 0
0 u0g −u0sa 00
00
a
gb − 00 ugg00−usa g 00 theorem:R b = −
=
0
g
(u0 −u0 a ) ugg +usa sa −2usa g g
s
ga implies that in absolute value the numerator is lower than the
is lower than one.
The proof is similar for
b's
reaction function.
We can now discuss the rst step of the game: how much the agents choose to deposit, taking into
account the eect of the deposits on the equilibrium contributions to the public good.
3.2
Equilibrium deposits (Step 1)
First of all, it should be clear that making deposits is a protable strategy only if it eectively constrains
one's contribution to the public good in Step 2. If in Step 2, agent
than his available income allows,
deposits.
In this case, if
i
g i < w i − di ,
decreases
di ,
then
i
i's
optimal contribution is lower
can always increase his utility by making less
he will still be able to contribute
gi
in Step 2 and he will
save on the costs of the deposits. In other words, deposits make sense only if in Step 2, they are such
that the agent would prefer to choose a contribution higher than his available income. This result is
formally established in the next lemma.
Lemma 3. ∀ i = {a; b}
: agent
i
gi = 0
or
is decreasing in i's deposits,
di .
makes deposits only if his deposits are such that in step 2,
g i = wi − di .
Proof. Suppose that
i
makes deposits and that in Step 2,
g i < w i − di .
First I show that in Step 2 the equilibrium level of public good,
g∗
is the sum of
g a∗
and
g b∗ ,
g∗ ,
the solution to equations (1). The eect of
0
(g ∗ )di
0
=
(g a∗ )di + g b∗
10
0
di
di
on
g∗
is equal to:
i's
By the implicit function theorem, the eect of the deposits on
g
i∗
0
−
=
di
0
0
ug −usi
contribution is:
0
di
0
(u0g −u0si )gi
00
00
= − (1 − k) u00
usi si −ugsi
(2)
00
00
gg +usi si −2usi g
<
and the eect on
j 's
0
contribution is:
g j∗
0
di
gj
=
gi
00
=
0
− u00
i's
g
i∗
0
di
00
ugg −usj g
0
di
+ g
j∗
0
di
g i∗
and it is negative because
i
di
0
=
g
i∗
0
di
g
i∗
+ − u00
00
makes deposits,
j 's
0
di
00
ugg −usj g
gi
00
00
gg +usj sj −2usj g
0
00
di
1−
00
0
di
(4)
ugg −usj g
00
00
u00
gg +usj sj −2usj g
<
When
(3)
0
deposits on the level of public good is therefore equal to:
=
2).
gi
00
00
gg +usj sj −2usj g
>
The total eect of
gi
0
00
is negative and
00
ugg −usj g
00
00
u00
gg +usj sj −2usj g
is lower than 1 (from lemma
increased contributions do not compensate for the decrease of
i's
contributions.
The second part of the proof establishes that
The equilibrium savings of
i
are given by
i0 s
savings decrease with
si = wi − (1 − k) di − g i∗ .
his savings is:
11
i's
deposits.
The eect of
i's
deposits on
si
0
di
− (1 − k) − g i∗
=
0
di
00
= − (1 − k) − (1 − k) u00
00
usi si −ugsi
00
00
gg +usi si −2usi g
00
00
usi si −ugsi
00
00
00
ugg +u i i −2u i
s g
s s
00
− (1 − k) 1 +
=
00
usi si −ugsi
u00
gg +u
<
0
is negative but lower than one and
si
0
di
(5)
00
00
−2u i
s g
si si
is thus negative.
It follows from Lemma 3 that the agents may only make deposits if it leads them to contribute
their whole available income in Step 2. There are two possibilities: (i) when one agent deposits his
di = wi
whole income:
is such that
and (ii) when one agent's deposits constrains his equilibrium contribution:
g i = wi − di .
I discuss these two possibilities in turn.
It is always possible for an agent to deposit his whole income. Suppose that
that
di
di = wi .
This implies
g i = 0: i cannot contribute to the public good since all his money is kept by the deposit collector.
j 's
For a given value of
ˆ
if
di = w i
ˆ
if
di = 0
g i = 0, g = g j
then
then
contribution,
g = gbi + g j
and
g j > 0:
and
si = kdi = kwi ;
si = wi − gbi ,
where
Clearly, the total level of public good is lower when
condition for
di = w i
gbi
is
i's
di = wi
to be a protable strategy, is that
i's
best response to
than when
gj .
di = 0.
So a necessary
deposits lead to an increase in
i's
savings
that compensate the lower level of public good. The dierence in i's savings when i's deposits go from
zero to
wi
is given by:
4si = kwi − wi − gbi
i's
savings are therefore lower when
di = wi
than when
kwi
<
wi − gbi
(1 − k) wi
>
gbi
This condition is sucient to guarantee that the strategy
is not satised, then
di = wi
di = 0
di = 0 dominates di = wi .
may be an equilibrium strategy.
12
if:
(6)
If the condition
The last case to be discussed is when
are equal to
kdi = k wi − g i
di = di
g i = g i = wi − di .
is such that
In this case, i's savings
. The change in savings compared to the case where
di = 0
is:
4si = kdi − wi − gbi
4si = k wi − g i − wi − gbi
4si
is negative if:
(1 − k) wi > gbi − kg i
(7)
Note that if condition (6) is satised then condition (7) is also satised. This tells us that if
cannot be an equilibrium strategy then
di = di
such that
g i = wi −di
di = wi
cannot be an equilibrium strategy
either.
The main nding from the discussion of the choice of the level of deposits is that condition (6) is
sucient to ensure that making deposits is never an equilibrium strategy. Condition (6) is more easily
satised when:
ˆ
the cost of making deposits is high (k is low)
ˆ i's income is high
relative to j
's income.
wi
enters directly on the left hand side of the condition
and indirectly on the right hand side through
through
gbi . wj
enters indirectly on the right hand side
gbi .
The ndings of the discussion are summarized in the following proposition.
Proposition 1.
Making deposits to contribute less to the public good and save more money for future
consumption can be an equilibrium strategy only when (i) the agents have suciently similar incomes
and (ii) the cost of the deposit collection is not too high.
The story behind Proposition 1 goes as follows. The equilibrium contribution of an agent to the
public good is not determined by the income of that agent alone, but by the level of his income relative
to the other agent's income. The richer is
good and the less
b will contribute.
a
compared to
b,
the more
a
will contribute to the public
This is a well-known result commonly referred to as the exploitation
of the great by the small after Mancur Olson's work (Olson, 1971). This result is the key to understand
the eects of the deposits. Consider the extreme case where
13
a's income is so high compared to b's that
only
a
contributes to the public good. In this case,
prompt
b
a
would need to make high deposits before they
to contribute more. Because the cost of deposits is proportional to the deposits, this means
that the higher is
a's income compared to b, the higher is the cost that a must incur before his deposits
have any favourable eect. If the incomes of the two agents are suciently dierent, the richer one
will never nd it protable to make deposits. The poorer agent on the other hand has no reason to
make deposits, his contribution is already minimal and he uses his income exactly as he wishes.
The role played by the income inequality is illustrated in Figures 5 and 5. In Figure 5, the agents
have similar incomes and if
i
makes deposits, that will directly aect the equilibrium contributions.
In Figure 5 on the other hand, incomes are very unequal. In this case,
there are no deposits only
on
j 's
contributions,
i
i
i
is richer than
j
and when
contributes to the public good. In order for his deposits to have an eect
must deposit an important part of his income. And the higher is the income
inequality, the further away from each other are the reactions functions and the higher the deposits
have to be before they inuence the other agent's contributions.
HERE IS FIGURE 1
HERE IS FIGURE 2
It is very important to understand that the result of Proposition 1 is also robust to important
structural changes in the game.
It could be argued in particular that a model of repeated interactions would be more realistic since
we will apply the model to people living together for years. It therefore sounds reasonable to allow the
agents to reach mutually benecial agreements that limit the deposits that they make.
This does not aect the main result which is that people do not make deposits when they have
very dierent incomes. If the agents can reach an agreement that limits their deposits:
ˆ
those who had dierent incomes did not make deposits before the agreement and they keep not
making deposits after ;
ˆ
those who had similar incomes, and were making deposits before the agreement, may make less
deposits (and maybe no deposits at all) after.
The conclusion is unchanged: when income inequality is high, people do not make deposits and it is
only when they have similar incomes that deposits may be observed.
14
The model is until now very general.
Without using specic utility functions I cannot however
prove that there always exists a level of income inequality that is sucient to ensure that the agents
never make deposits. Using standard utility functions, I can nonetheless show that the level of income
inequality that prevents deposits not only exists, but is reasonable and likely to be observed in reality.
3.3
Cobb-Douglas Utility Functions
For example, with Cobb-Douglas utility functions:
U i = (g)
With
0
Ui > 0
and
00
U i < 0 (α
β
and
The eect of
i's
α+β
α+2β
=
deposits on
The eect of
i's
deposits on
β
∀i = {a; b}
0
j 6= i:
j
w − (1 − k) dj
is:
α+β
β
= − (1 − k) α+2β
+ (1 − k) α+2β
di
=
α
− (1 − k) α+2β
<
0
si = wi − (1 − k) di − g i∗
si
and
β
α+2β
i
w − (1 − k) di −
g ∗ = g i∗ + g j∗
g i∗ + g j∗
si
are positive and smaller than one).
The equilibrium contributions in Step 2 are,
g i∗
α
0
di
is:
=
0
− (1 − k) − g i∗ di
α+β
(1 − k) α+2β
−1
<
0
=
as expected from Lemma 3.
To illustrate Proposition 1, suppose that
g i = 0, g ∗ = g j∗ =
α
j
α+β w and
i chooses to deposit his whole income and dj = 0: di = wi ,
si = kdi = kwi .
ci =
U
On the other hand, if
In this case,
α
wj
α+β
α
i's
kwi
utility is given by:
β
i decides not to make deposits then g ∗ = g i∗ + g j∗
15
is given by the equilibrium
contributions in (1),
si = wi − g i∗
and
i's
Ui =
where
w = wi + wj .
Agent
i
utility is given by:
α
w
α + 2β
α β
w
α + 2β
β
will prefer not to make deposits if:
α
α+2β w
Ui
α β
α+2β w
By rearranging the terms and replacing
1−
wi
w
α
ci
U
α
>
β
>
wj
w by
wi
w
β
1−
<
1
kβ
α
j
α+β w
kwi
β
wi
w , the condition becomes:
α+β
α+2β
α β
α+2β
β
(8)
The right hand side is a positive constant. The left hand side is a positive and concave function of
i
w
w . It follows that
i will prefer not to make deposits if his income,
or low. It is only when
i
j
and
Suppose for instance that
α
relative to
j 's income,
is either high
have similar incomes that making deposits can be a protable strategy.
and
β
are equal to one and that
k = 17/18.
Then making deposits is
never an equilibrium strategy when the richest agent earns more than 74% of the total income.
We can now examine the welfare consequences of the model.
3.4
Welfare
The welfare implications of the model follow directly from its resolution.
They are summarized in
Proposition 2, where the welfare is simply dened as the sum of the agents' utilities.
Proposition 2. ∀i = {a, b}
and
j 6= i,
compared with the situation where deposits are not possible,
when one agent makes deposits, his utility increases and the other agent's utility decreases ; the total
welfare can either increase or decrease
Proposition 2 informs us that the existence of the daily collection service has an ambiguous impact
on total welfare.
To know whether it would be benecial for the agents that the State, or other
economic actors such as non-governmental organizations, provide an equivalent service at a lower cost,
the impact of an increase of
k
on total welfare must be determined.
It follows from the analysis made so far that an increase in
16
k
could have a positive or negative
eect on the agent's utilities. If the agents did not make any deposit before
k
increases, and one of
them makes deposits after, Proposition 2 tells us that the user's utility increases, the non user's utility
decreases and the total welfare could increase or decrease. If one of the agents already made deposits
before
k
increases, his utility increases. The eects on the other agent's utility and on total welfare
are ambiguous.
If people make deposits only to control their time-inconsistent behaviour, reducing the cost of the
service should increase the people's welfare. On the other hand, if the intra-household motive plays
a part, the loss incurred by the non-users may not be compensated by the gain of the users.
The
policy recommendations may then be reversed. I return to the policy implications of the model in the
conclusion.
4
Empirical results
In this section I turn to the empirical analysis of the motives explaining the deposits. I rst describe
the data before introducing the identication strategy and the results.
4.1
The data
The data were collected in 2004 and 2006, in three districts (Vossa, Enagnon, Enagnon-plage) of
Cotonou's outskirts. Households were randomly selected and all members were interviewed. Men and
women were always interviewed separately by an enumerator of the same gender: 1179 people older
than 16 were interviewed in 2004 and 873 in 2006 (717 in both years). Information about their jobs,
earnings, belongings, expenditures, nancial transfers, education, religion, etc. was gathered, as well
as detailed data about the ROSCAs, informal insurance groups and the use of the daily collectors.
Most variables that are used in the analysis are standard and do not require any specic explanation.
Only the Time inconsistent variable is not trivial. As in Ashraf et al. (2006b) and Brune et al. (2011),
this is a dummy variable that is equal to one when an individual is identied as likely to make timeinconsistent choices. The individuals were asked the following hypothetical questions:
A
Would you prefer to receive CFAF 1000 guaranteed in one week or CFAF 1500 guaranteed in one
week and one month ?
and later in the survey:
17
B
Do you prefer to receive CFAF 2000 guaranteed in one year or CFAF 3000 guaranteed in one year
and one month ?
People who are impatient today but prefer to be patient in the future are expected to make time
inconsistent choices: because in the future they will be in the same situation as today, they will choose
not to wait. If they are sophisticated (i.e. aware of their time inconsistent choices), they could look
for a commitment device. The results of these questions are given in Table 1:
HERE IS TABLE 1
The result is that 17% of the individuals are identied as susceptible of looking for a commitment
device.
This identication of time-inconsistent individuals is very imperfect. For instance, it depends on
the amounts and the time frame used in the questions. Despite its shortcomings, it is certainly worth
checking whether the proxy aects the deposits and assessing the magnitude of its impact.
Basic descriptive statistics are presented in Table 5. The incomes are expressed in CFAF 1 000.
We see that 31% of sample individuals are clients of a daily collector (36% if the sample is restricted to
the individuals who actually earn an income). Most of these clients are women, working in a market.
This is not very surprising since collectors are mainly active in markets and most people working in the
markets are women. There is also a larger proportion of people living in a couple, both monogamist
and polygamist, among the clients. Clients are on average richer than non-clients, and they come from
poorer households.
These rst statistics also come into line with Proposition 1: 57% of the clients have an income that
represents between 25% and 75% of their total household income; only 33% of the non-clients do. As
8 The fact that some clients
predicted by Proposition 1, the non-clients rather have a low income share.
have high income shares does not contradict the theory: one should control for dierent variables. For
instance, richer people have higher income shares and are more likely to make deposits. Therefore the
multivariate analysis is required to properly test the main prediction of the model.
Finally, there are more men identied as time-inconsistent among clients than non-clients. This is
however not true for women.
HERE IS TABLE 2
8 Note
that most of the individuals whose income share equals 100% are living alone and should not be aected by
the intra-household motive.
18
Table 5 presents additional information about the importance of the deposits.
The sample is
restricted to the people who make deposits. Deposits are relatively high, since on average the clients
deposit 36% of their income with a daily collector. Moreover, half of the clients deposit more than
one-fourth of their income. Deposits compose a rather large share of people's incomes, although they
are small amounts in absolute values: the median of CFAF 9 000 corresponds to
¿
13.72.
HERE IS TABLE 3
It can be added that 21% of the people who did not use the services of a daily collector in 2004
were making deposits in 2006, while 45% of the people who did use a daily collector in 2004 were
not resorting to it anymore in 2006. This variation is large and will be exploited in the econometric
analysis.
The survey also includes precise measures of the people's expenditures. I use the purchase of one
private good, clothes, and three public goods: the electricity bills, house repairs and school charges.
These are the most common expenditures on goods that are not immediate, current, consumption. On
average, they amount to 64% of those expenditures. Table 4 shows the mean expenditures made by
men and women, daily collector clients and non-clients. As expected from the intra-household motive,
9
clients spend less then non-clients on all three public goods and more on the private good.
Additionally, I look at the expenditures on frivolous goods. Frivolous expenditures are the sum of
the expenditures made on tobacco, alcohol, candies and other fancy food during the week that preceded
the survey. According to the intra-household motive, daily collector clients shall use their deposits to
increase their consumption of frivolous goods. On the other hand, according to the commitment motive
and temptation theories, the clients may make deposits in order to decrease their consumption of
frivolous goods. Nevertheless, without proper controls, descriptive statistics could be very misleading.
For instance, richer people are expected to purchase more frivolous goods and be less likely to make
deposits (they have a higher income share). This could also explain that women seem to spend more
on electricity when they make deposits.
HERE IS TABLE 4
Finally, here is a brief and descriptive discussion of the way deposits may aect the transfers made
to the kith and kin.
9 Except
for the expenditures that women make on electricity and house repairs.
19
As discussed by Platteau (2012), redistributive norms are pervasive and persistent in African countries, compared with countries of other continents. Making deposits could be a way to protect income
against nancial claims since deposits cannot be readily redrawn. Therefore, those using the service
should eectively transfer less money if they consider the claims illegitimate. On the other hand, using
the daily collector enables the accumulation of a lump sum that may be used for legitimate transfers.
Consequently, it is expected that daily collector's clients increase some transfers and reduce others.
In Table 5, the amount of transfers given are presented for four categories of recipients: kids, spouse,
acquaintances and parish fellows.
10
From the all sample columns, it seems that using the daily collector permits to decrease all transfers.
The decomposition by gender however oers a more subtle pattern. Transfers by men-users all decrease,
but women's use of a daily collector seems to enable them to reduce their transfers to their husband
and to increase their transfers to their kids and friends.
Unfortunately, there are not enough transfers made to allow for a successful econometric analysis
of those items. The data does not allow to obtain more information than is provided by Table 5.
HERE IS TABLE 5
4.2
Strategy
Both the commitment and the intra-household motives may determine the deposits, and the same
individual may be subject to both motives. The paper provides a new theory to explain why people
make deposits rather than saving on their own. The objective of this empirical section is to explore
whether the data can provide some evidence for or against that theory.
The model provides two
important conjectures:
Conjecture 1.
Deposits are determined by the within households income inequality - it is only when
household's members have similar incomes that they will nd it optimal to make deposits.
Conjecture 2.
Compared to non-users, those who make deposits spend more on private goods and
contribute less to their household public goods.
10 Only the irregular transfers appear in the table. For example if a father gives his son CFAF 150 every morning for
his lunch, this transfer is not in the table. But if the son asks his father some help to buy a bicycle, it is included. The
reason is that regular transfers are the results of longer terms arrangements (as documented by Falen, 2011). A husband
for example will give CFAF 2 000 to his wife on the market days and CFAF 150 to his son each morning for his lunch
and that long-lasting arrangement shall not be interrupted or modied in the month in which the husband decides to
make deposits.
20
To check the rst conjecture, I regress the deposits on the individual income share and the income
share squared.
11 There are however other factors that are expected to inuence people's deposits.
Deposits shall depend on the individual's level of income and his household income independently
from his income share.
Given that the variable of interest is the individual income divided by his
household income, I cannot control for both the household and the individual's income in addition to
the income share. In the following tables, I control for the individual income. The regressions with
12
the household income instead of the individual income give similar results.
The daily collectors have oces, where people can go to make deposits, and they also operate in
the markets where they go from client to client in order to collect the deposits. People working in the
markets have thus a better access to the service. The taxi-moto drivers, who ride around the city all
day long also have a better access because they may easily stop by a daily collector's oce. Hence
the inclusion of two dummy variables indicating whether the individual works on the market or is a
taxi-moto driver.
I include binary variables that indicate whether the individual owns a bank account or is a member
of a ROSCA, since those individuals have a possible alternative to the daily collector.
I also control for the size and the composition of the household. Most regressions include controls
for the time of the survey (2004 or 2006) and for the neighbourhood of the individual (Vossa, Enagnon
and Enagnon plage).
Given that the dependent variable, the deposits, is censored at zero and that nearly 70% of the
13 As is often the case with expenditures data, the
observations are zeroes, I use a Tobit estimator.
residuals are not normally distributed when the level of the expenditures is used. Because the nonnormality of the residuals causes a bias of the Tobit estimates, I follow Cameron and Trivedi (2009) by
using the logarithm of the positive expenditures and then setting the truncation point to zero. Given
the panel dimension of the data, standard errors are clustered at the individual level.
The estimations are however vulnerable to the following endogeneity problem: since individuals
who are versed in nancial matters would better manage their income, their savings and their business,
such unobserved ability would simultaneously aect the income of the individuals and the use of a daily
11 There
exist dierent ways of testing the non-monotonic relationship between deposits and income share. Here
are displayed estimations that include the income share and the income share squared. I obtain similar results with
regressions that allow the eect of income shares to change with their level or with semi-parametric regressions (see the
appendix for the results of Robinson (1988) semi-parametric estimation).
12 See Figure 5 below.
13 The increasing-decreasing relationship between the income share and the deposits is very robust to the model
specication. As can be seen from Figure 5, it remains intact for instance if I use OLS estimators and standard panel
Fixed Eects estimators.
21
collector. In this case, the positive eect of the income share would be over-estimated and its negative
eect under-estimated. There is no reason, however, to believe that this ability would have changed
between the two observed periods and therefore controlling for individual xed eects eliminates the
problem.
Another possibility is that clients use their deposits to invest in their business. In this case, using
the service would have a positive impact on income. This is not plausible though: the savings recovered
are small (23¿ on average, and below 44¿ in 95% of the cases) and insucient to purchase the capital
goods that would increase labour productivity. For example, there are many shermen in the sample.
To increase their productivity signicantly, shermen need to rent bigger and quicker boats or larger
nets, things that are considerably more expensive than what they can save from a month income.
Moreover, only 5% of the clients deposit the money recovered each month on their bank account or in
a ROSCA. The remaining 95% spend it immediately on consumption goods. Also, during the last six
months before they were interviewed, the collector's clients have made professional investments worth
CFAF 918 on average, while the non-clients have spent CFAF 1292 on average. The dierence is not
statistically dierent from zero (Weald test), which indicates that the clients do not invest more in
their business then the non-clients.
The xed eects regressions should also clear the other motive for making deposits - commitment
- under the assumption that the individual's preference for commitment did not change between the
two periods of observation.
Because it is not possible to consistently estimate a standard Tobit model with individual xed
eects, I use the trimmed least absolute deviation (Tlad) estimates as described by Honoré (1992).
Finally, I add regressions that include the proxy identifying time-inconsistent behaviour. Because
this proxy is only available in the second survey I use the Tobit only and not the Tlad.
To check the second conjecture - those who make deposits spend more on private goods and
contribute less to their household public goods, I provide dierent estimations of the factors that
determine the expenditures made on various public and private goods. The main concern here is that
people with specic preferences for private or public goods may self-select and be more likely to make
deposits. As a result, there would be an important and unobserved dierence between the users and
the non-users of a daily collector. For example, those who have a very low preference for the education
of their children are simultaneously less likely to contribute to the school charges and to make deposits.
If that is the case, the Tobit estimation will underestimate the eect of making deposits on the various
22
expenditures. This problem is solved by the inclusion of individual xed eects (Tlad estimator) if this
specic characteristic of the people did not change between the two surveys. In addition to the Tobit
and Tlad estimators, I also use an instrumental variable approach. The endogenous variables are (i)
a dummy equal to 1 if the individual makes deposits and (ii) the interaction of that dummy variable
with the variable being a woman. The instruments are two binary variables: the rst one is equal to
one if the individual is a taxi-moto (zem) and the other one is equal to one if he works in a market.
As mentioned above, being a zem and working in a market facilitates the access to the daily collectors
and thereby increases the likelihood that one makes deposits. Conditional on the other independent
variables of the regressions, being zem or working in the market does not inuence one's expenditures.
This is absolutely clear for expenditures such as electricity, house repairs and school charges. It is also
a reasonable assumption regarding the other goods - clothes and frivolous goods - given that those
goods are easily available to anyone, thanks to the many shops and street vendors.
The results of these estimations are presented and discussed in the next section.
4.3
Results
The results of the Tobit and Tlad estimations of deposits are displayed in Table 6.
In the rst six
columns, the whole sample is used. Columns 7 to 12 give the results for the sub-sample of women and
columns 13 to 18 for the sub-sample of men.
As expected from the theory, the relationship between the deposits and income share is rst increasing and then decreasing. Depending on the regressions, the impact of the income share becomes
negative when the income share exceeds around 70%. The impact of the income share is quantitatively
very high. According to the regression All sample - Tobit III, everything else being equal, when the
income share increases from 20% to 30%, the deposits increase by 75%. The impact goes down to 6.5%
when the income share increases from 60% to 70%. Deposits decrease by 28% when the income share
goes from 80% to 90%.
HERE IS TABLE 6
In Figure 5 the deposits predicted by other econometric models are plotted against the individual
income share. The controls used are the same as in regressions III of Table 6, except for the income:
in Figure 5 it is either the individual (i curves) or the household income (hh curves) that is used.
In all estimations (Tobit, Tlad, OLS, Fixed eects) the relationship between the income share and
23
the deposits is strong, statistically signicant, rst increasing and then decreasing. Even though this
relationship may not prove the theory proposed in this paper, it certainly is a strong evidence in its
favour.
HERE IS FIGURE 3
In Table 7 the estimations of the deposits include the binary T.I. which equals one if the individual
is identied has making time inconsistent choices, and T.I.*woman , the interaction of being a woman
and T.I.. The estimations are the result of a Tobit model applied to the second round of the survey
(the T.I. variable is not available for the rst round). In contrast with the ndings of Ashraf et al.
(2006b), who nd a positive eect for women but not for men, the eect here is positive for men,
but negative for women
.
I do not have enough information on the people's preferences to further
investigate the negative eect on women. The positive eect on men is very high: deposits increase by
14 among the men identied as time-inconsistent. The eect of the income share remains similar
201%
to the estimations of Table 6.
HERE IS TABLE 7
The intra-household motive asserts that people make deposits to lower their contributions to the
household's current expenditures and increase their private consumption. Therefore, we should observe
dierent patterns of consumption between clients and non clients. Nevertheless, if the other motives
are at play, making deposits may also allow people to resist temptations and increase their expenditures
on various public goods as well as private goods. The results of the comparison of the expenditures
made by those who make deposits and those who do not are presented in Table 8.
For each good,
the rst column gives the result of the Tobit estimation, the second column the Tobit where making
deposits is instrumented
15 , and the third column the Tlad estimates.
As explained in section 4.2, it is feared that the people who choose to make deposits and those who
do not have dierent preferences for the public and private goods. For example those who care less
about the household's access to electricity could make more deposits and decrease their contribution to
the purchase of electricity. If that is the case the Tobit regressions underestimate the eect of making
deposits. This is exactly what the comparison of the Tobit and IV estimates show for all items.
14 e1.106 -1=201%.
15 The rst stages
of the two-stage procedure are not reproduced here but the correlation between the endogenous
variables and the instruments is clearly established, the F-stats for instance are all above 50.
24
Men who make deposits contribute much less to the purchase of electricity. Everything else equal,
when a man makes deposits his expenditures on electricity drop by 95% (Tlad:e
−3.1
− 1 = −0.95)
to
100% (IV). There is however no signicant eect for women.
As for the school charges and house repairs, making deposits has a signicant eect according to
the Tlad estimations only.
It is therefore dicult to conclude with certainty that making deposits
matters.
Making deposits however has a very strong and unambiguous eect on the expenditures made on
new clothes and on frivolous goods. Both men's and women's expenditures on personal clothes increase
sharply when they make deposits. Women who make deposits, but not men, also spend much more
on frivolous goods.
The way the pattern of expenditures is aected by the deposits is entirely consistent with the theory
behind the intra-household motive and it adds evidence supporting it.
HERE IS TABLE 8
5
Conclusion
I wrote a model of strategic interactions between two members of a single household. In equilibrium,
the agents use the daily collection service in order to bring less money home and constrain their own
contribution to the household's public current expenditures. By doing so they divert some resources
from the household's public consumption toward their own private consumption and drive their partner
to increase his contribution to the public good. I called this strategy the intra-household motive for
making deposits.
The main prediction of the model is that deposits are determined by the within households income
inequality. It is only when household's members have similar incomes that they will nd it optimal to
make deposits.
In the empirical part, I rst show that deposits are massive: in Cotonou, one third of the people
make deposits and they deposit on average one third of their income.
I then provide strong evidence in support of the intra-household motive. I used the panel structure
of the data and xed eects at the individual level to clear the estimations from the time constant
motive of commitment.
Moreover, using a proxy that identies time-inconsistent individuals, I showed that the commitment
25
motive is an important determinant of men's deposits, but not of women's.
I nally showed that users and non-users of the daily collection service exhibit dierent patterns
of consumption: men users contribute less to the purchase of electricity, both men and women spend
more on new personal clothes.
Women consumption of frivolous goods also increase sensibly when
they make deposits.
The data also suggests that men who make deposits make fewer gifts to their children and parish
fellows, while women give less money to their spouse if they make deposits.
These ndings are important for the understanding of a widespread informal saving device.
In
particular, the intra-household motive has strong policy implications. As the model showed, improving
the access to the daily collectors may hurt rather than favour the population as a whole. Now that
big donors are pushing small nancial institutions to encourage savings,
16 the negative eects that I
underlined need to be evaluated.
The evidence also emphasizes the importance of savings among the poorest members of society and
lead me to disagree with the researchers who pretend that the poor cannot and do not save.
I believe that the popularity of the daily collection service and the relevance of the two motives -
safety and commitment - arise from the possibility to deposit savings in the same day as the income
is received. This is a service that most formal institutions such as banks or MFIs do not oer at this
moment. Nevertheless, if one wants to increase the level of formal savings in developing countries then
using new technologies such as 'mobile money ', where deposits on a bank account could be made at a
very low cost and at any time using a mobile phone, sounds promising and certainly deserves further
attention.
17
16 The Bill & Melinda Gates Foundation for instance announced grants worth $38m to MFIs in South Asia, Latin
America and Africa to encourage them to expand their savings oerings (The Economist, 2010).
17 For examples of 'mobile money ' see The Economist (2009) and The Economist (2011).
26
Appendix A: Robinson (1988) semi-parametric estimator
The results of semi-parametric estimations, following Robinson (1988), conrm that deposits are increasing in the income share when the income share is low, and decreasing when it is high. The turning
point computed also corresponds to the results of the Ols, Tobit and panel Fixed Eects displayed
above. The econometric model controls for the linear relationship between the deposits and all the
controls used in the Chapter (corresponding to column 3 of Tables 6 and 8), although the relationship
between deposits and income share is not constrained to be linear. The routine developed by Verardi
and Debarsy (2011) is used to compute the coecients. The results are presented in the gure below.
The predicted values of the logarithm of the deposits are on the vertical axis and the income share on
the horizontal axis.
Figure A1: Robinson estimator
-2
-1
Log(deposits)
0
1
2
Lncome
2
-1
-2
.Log(deposits)
0
.2
.4
.6
I.8
1
Income
2og(deposits)
share
0
.2
.4
.6
Income share
27
.8
1
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31
semiparametric regression estimator in
Table 1: Time-inconsistent choices
Later (B)
Now (A)
Patient
Impatient
Total
Patient
Impatient Total
414 (74%) 144 (26%)
558
221 (83%)
267
365
825
46 (17%)
460
32
Table 2: Descriptive statistics
All sample D.C. clients Non-clients
Number of observations
2052
644
1408
Women
52%
72%
42%
Man's monthly income (if >0)
61
64
60
Woman's monthly income (if >0)
40
48
33
***
123
112
127
**
Household monthly income
***
Income share
< 25%
38%
15%
49%
***
Income share
∈ [25%; 50%[
22%
32%
18%
***
Income share
∈ [50%; 75%[
18%
25%
15%
***
Income share
∈ [75%; 100%[
6%
8%
5%
***
Income share
= 100%
15%
20%
13%
***
Time inconsistent women
15%
15%
15%
Time inconsistent men
20%
27%
19%
*
Literacy rate
51%
34%
59%
***
Age
34
37
33
***
Household size
5.2
4.8
5.3
***
Living in a monogamous couple
38%
47%
34%
***
Living in a polygamous couple
11%
15%
9%
***
Works in a market
37%
66%
23%
***
Works as taxi-motorbike
2.2%
3.3%
1.7%
**
Has a bank account
10.4%
8%
11.6%
***
Participates in a ROSCA
16.6%
21%
15%
***
*, ** and *** indicates that the dierence in means between clients and non-clients is signicant at
10%, 5% and 1%.
33
Table 3: Information on deposits (CFAF)
mean
s.d.
25%
15 317 21 258 6 000
median
9 000
75%
95%
15 000 45 000
34
mean deposit/income
36%
35
36
11 087
School
1 811
Frivolous
1 835
15 924
7 098
1 061
5 025
1799
10 050
12 912
3 096
5 872
DC clients Non-clients
***
***
*
2 681
15 896
13 427
1 336
7 908
2 364
11 137
17 019
5 237
9 019
DC clients Non-clients
Men
***
1 507
15 936
4 643
954
3 907
1 040
8 586
7 380
213
1 635
DC clients Non-clients
Women
***
***
*
***
*, ** and *** indicates that the dierence in means between clients and non-clients is signicant at 10%, 5% and 1% (unilateral test).
11 900
Clothes
Private goods:
2 458
5 606
House repairs
Electricity
Public goods:
All
All sample
Table 4: Expenditures on household public goods and private goods (CFAF)
37
38
same parish
People of the
Acquaintances
Spouse
Children
Transfers given to:
76
(0.21%)
24
(0.05%)
37
(0.06%)
4
(0.02%)
156
(0.4%)
60
(0.17%)
90
(0.2%)
59
(0.14%)
Nonclients
DC
clients
All Sample
DC
(0%)
0
(0%)
3
(0.61%)
211
(0%)
0
clients
Men
Non-
(0.05%)
32
(0.33%)
127
(0.63%)
247
(0.29%)
141
clients
(0.03%)
6
(0.08%)
51
(0%)
2
(0.19%)
82
clients
DC
(0.04%)
13
(0.06%)
7
(0.09%)
33
(0.08%)
22
clients
Non-
Women
Mean value of the gifts in CFAF and (% of Income)
Table 5: Summary of gifts
39
40
-3.97***
(0.23)
Yes
Yes
0.076
2052
2052
No
No
Tlad I
b (s.e.)
-0.00
(0.00)
7.11***
(1.26)
-5.31***
(1.05)
-4.80***
(0.25)
Yes
Yes
0.131
2052
2052
No
No
Tobit III
b (s.e.)
-0.00
(0.00)
11.72***
(0.91)
-8.55***
(0.78)
1.18***
(0.21)
1.33***
(0.20)
1.63***
(0.47)
-0.63**
(0.29)
-0.21
(0.19)
0.08***
(0.03)
-5.29***
(0.32)
Yes
Yes
0.132
2052
2052
No
No
0.37
(0.36)
1.58
(0.99)
-0.28
(0.37)
0.08
(0.24)
0.13*
(0.07)
Tlad III
b (s.e.)
-0.00
(0.00)
6.56***
(1.44)
-4.74***
(1.17)
-2.56***
(0.23)
Yes
Yes
0.102
1064
Tobit I
b (s.e.)
0.01**
(0.00)
11.33***
(1.07)
-8.68***
(0.91)
1064
No
No
Tlad I
b (s.e.)
0.00
(0.01)
5.33***
(1.64)
-4.09***
(1.26)
-2.90***
(0.24)
Yes
Yes
0.125
1064
1064
No
No
Women
Tobit II Tlad II
b (s.e.)
b (s.e.)
0.01*** 0.00
(0.00)
(0.01)
7.68*** 4.36**
(1.13)
(1.76)
-6.04*** -3.48***
(0.94)
(1.32)
.
.
1.58*** 0.61*
(0.24)
(0.33)
.
0.00
.
(0.00)
-0.36
-0.08
(0.39)
(0.54)
-0.29
-0.17
(0.22)
(0.28)
Tobit III
b (s.e.)
0.01**
(0.00)
8.41***
(1.20)
-6.38***
(0.96)
.
.
1.52***
(0.24)
.
.
-0.34
(0.39)
-0.32
(0.22)
0.09**
(0.04)
-3.41***
(0.36)
Yes
Yes
0.127
1064
1064
No
No
0.66**
(0.31)
0.00
(0.00)
-0.01
(0.49)
-0.15
(0.28)
0.15*
(0.08)
Tlad III
b (s.e.)
0.00
(0.00)
4.36**
(1.73)
-3.27**
(1.34)
-7.41***
(0.56)
Yes
Yes
0.081
988
Tobit I
b (s.e.)
-0.00
(0.00)
15.47***
(1.84)
-10.46***
(1.72)
Table 6: Tobit and Tlad estimations of log(deposits)
Standard errors clustered at the individual level
*** signicant at 1%, ** signicant at 5%, * signicant at 10%
Time F.E.
Location F.E.
Pseudo-R2
Sample size
Constant
Household size
ROSCA
Bank account
Working in
a market
Taxi (moto)
Income share
squared
Woman
Income share
Earnings
Tobit I
b (s.e.)
-0.00
(0.00)
13.27***
(0.80)
-9.85***
(0.76)
All sample
Tobit II Tlad II
b (s.e.)
b (s.e.)
0.00
-0.00
(0.00)
(0.00)
11.44*** 6.70***
(0.90)
(1.43)
-8.58*** -5.02***
(0.79)
(1.16)
1.20***
(0.21)
1.34***
0.33
(0.20)
(0.35)
1.62***
1.67*
(0.46)
(0.96)
-0.63**
-0.28
(0.29)
(0.37)
-0.17
0.06
(0.19)
(0.23)
988
No
No
Tlad I
b (s.e.)
-0.01
(0.00)
9.36***
(2.75)
-6.82***
(2.45)
-7.28***
(0.57)
Yes
Yes
0.093
988
988
No
No
Men
Tobit II
Tlad II
b (s.e.)
b (s.e.)
-0.00
-0.01*
(0.00)
(0.00)
15.41*** 9.81***
(1.92)
(3.32)
-10.49*** -6.84**
(1.73)
(2.94)
.
.
0.68
-0.64
(0.53)
(0.99)
1.66***
1.72
(0.59)
(1.07)
-1.29**
-0.62
(0.51)
(0.53)
-0.26
0.67
(0.40)
(0.49)
Tobit III
b (s.e.)
-0.00
(0.00)
15.45***
(1.93)
-10.46***
(1.73)
.
.
0.69
(0.54)
1.66***
(0.59)
-1.29**
(0.51)
-0.27
(0.40)
0.01
(0.08)
-7.38***
(0.76)
Yes
Yes
0.093
988
988
No
No
-0.62
(0.86)
1.69
(1.09)
-0.63
(0.48)
0.65
(0.52)
0.06
(0.14)
Tlad III
b (s.e.)
-0.01*
(0.00)
9.53***
(2.96)
-6.54**
(2.67)
41
13.304***
(1.298)
(1.292)
(0.003)
(0.003)
13.234***
0.005*
0.005*
b (se)
b (se)
2
(1.448)
825
0.120
825
0.122
Yes
(0.409)
(0.398)
Yes
-5.916***
-5.725***
(1.945)
7.933***
(0.005)
0.013**
b (se)
(1.319)
.
.
(0.336)
-0.738**
.
.
(1.534)
825
0.137
Yes
(0.498)
442
0.108
Yes
(0.311)
442
0.110
Yes
(0.313)
442
0.138
Yes
(0.500)
Men
(0.005)
0.002
b (se)
II
(0.004)
0.003
b (se)
III
(3.374)
.
.
(2.864)
383
0.091
Yes
(1.051)
383
0.096
Yes
(1.062)
-8.561***
.
.
(0.642)
1.183*
.
.
(2.910)
-8.703***
(3.452)
383
0.108
Yes
(1.277)
-8.591***
(0.128)
0.014
(0.721)
-1.097
(0.750)
-1.300*
(0.925)
0.199
(0.917)
0.743
.
.
(0.649)
1.103*
.
.
(2.938)
-9.274***
(3.493)
14.022*** 14.284*** 15.230***
(0.005)
0.002
b (se)
I
-3.393*** -8.275***
(0.053)
(0.049)
-5.673***
0.071
(0.326)
(0.317)
0.063
0.061
(0.569)
(0.425)
-0.228
-0.650
.
(0.769)
-0.760*
.
0.773
(0.430)
-2.539***
.
.
(0.357)
-0.563
.
.
(0.351)
-2.620***
.
.
(1.316)
1.848***
(0.636)
(1.575)
12.503***
(0.006)
0.011*
b (se)
III
1.456***
-1.552**
(0.626)
-1.423**
(0.498)
(0.505)
(0.380)
0.843*
(0.289)
(0.258)
1.671***
(1.222)
0.876*
2.853***
(1.153)
2.581***
(1.148)
Women
II
-10.252*** -10.285*** -6.630*** -8.567***
(1.570)
*** signicant at 1%, ** signicant at 5%, * signicant at 10%
Robust standard errors
Sample size
Pseudo-R
Location xed eects
Constant
Household size
Member of a ROSCA
Bank account holder
Taxi (moto)
Working in a market
T.I. * woman
T.I.
Woman
(0.006)
0.011*
b (se)
I
11.236*** 12.516***
(0.003)
0.005*
b (se)
III
Income share squared -10.093*** -10.172*** -8.460***
Income share
Earnings
II
All sample
I
Table 7: The commitment motive
42
43
House repairs
Tobit
IV
Tlad
b (s.e.) b (s.e.) b (s.e.)
-1.16
-288.11 5.38*
(3.30)
(8964.65) (3.08)
-2.29
292.51
-8.74
(5.55)
(8975.11) (7.31)
0.00
0.03
0.12
(0.03)
(0.78)
(0.09)
-0.00
-0.02
-0.07
(0.03)
(0.54)
(0.04)
0.10**
0.24
0.02
(0.05)
(4.59)
(0.04)
23.10*** 51.04
-2.92
(3.97)
(883.47) (0.00)
-0.46
-0.70
1.65
(0.54)
(7.19)
(1.22)
7.91*** -3.24
2.34
(2.98)
(343.05) (4.81)
-2.50
-42.42
(3.58)
(1124.86)
-60.35*** -24.08
(5.58)
(1084.00)
Yes
Yes
Yes
Yes
Yes
Yes
0.119
2052
2052
2052
Tobit
b (s.e.)
2.55***
(0.55)
1.47**
(0.74)
0.02**
(0.01)
-0.00
(0.00)
-0.01
(0.01)
7.29***
(0.57)
-0.26***
(0.09)
-1.31***
(0.41)
4.04***
(0.51)
-4.50***
(0.78)
Yes
Yes
0.080
2052
Yes
Yes
2052
2052
Tlad
b (s.e.)
1.39**
(0.68)
0.01
(0.89)
-0.00
(0.00)
0.00
(0.00)
0.00
(0.01)
-0.37
(1.25)
-0.00
(0.14)
-1.13
(0.72)
Clothes
IV
b (s.e.)
11.99**
(4.85)
1.89
(5.04)
0.01***
(0.00)
0.00
(0.00)
-0.03**
(0.01)
5.96***
(0.72)
-0.27***
(0.09)
-0.74
(0.50)
0.64
(1.06)
-5.23***
(1.04)
Yes
Yes
Table 8: Tobit, IV and Tlad estimations of public and private expenditures
Electricity
School charges
Tobit
IV
Tlad
Tobit
IV
Tlad
b (s.e.) b (s.e.) b (s.e.) b (s.e.) b (s.e.) b (s.e.)
DC user
-2.68** -21.46** -3.10** -0.05
4.58
-1.52*
(1.26)
(9.90)
(1.38) (0.86)
(6.43)
(0.89)
Female X DC
4.03**
26.21** 5.93*** 2.41*
3.31
0.39
(2.02)
(10.42) (2.30) (1.38)
(6.87)
(1.64)
Earnings
0.02
0.02**
-0.01
0.03**
0.02*** 0.01
(0.01)
(0.01)
(0.01) (0.01)
(0.01)
(0.01)
Household's
0.00
0.00
0.02
-0.01
-0.01
-0.01
earnings
(0.01)
(0.01)
(0.01) (0.01)
(0.00)
(0.00)
Other hh's
0.02
0.02
-0.01
-0.01
-0.02
-0.01
members deposit
(0.02)
(0.02)
(0.01) (0.02)
(0.02)
(0.01)
Chief
17.76*** 19.52*** 9.81*** 18.01*** 17.38*** 6.03***
(1.21)
(1.72)
(1.93) (0.98)
(1.19)
(1.82)
Household size
0.41**
0.38**
0.00
1.56*** 1.55*** 0.83***
(0.19)
(0.18)
(0.26) (0.14)
(0.14)
(0.21)
Owner
3.02*** 2.28**
-1.17
0.64
0.94
-0.65
(1.08)
(1.09)
(1.86) (0.84)
(0.78)
(1.58)
Woman
-3.17*** -7.31***
0.73
-1.33
(1.23)
(2.31)
(0.97)
(1.68)
Constant
-23.33*** -20.58***
-25.49*** -25.86***
(1.75)
(2.41)
(1.45)
(1.87)
Time xed eect
Yes
Yes
Yes
Yes
Yes
Yes
Location xed eects Yes
Yes
Yes
Yes
Yes
Yes
Pseudo-R2
0.128
0.154
Sample size
2052
2052
2052
2052
2052
2052
Standard errors clustered at the individual level
*** signicant at 1%, ** signicant at 5%, * signicant at 10%
Frivolous goods
Tobit
IV
Tlad
b (s.e.) b (s.e.) b (s.e.)
0.46*
2.94
-0.41
(0.27) (2.44)
(0.41)
1.80*** 4.08
1.57***
(0.37) (2.54)
(0.56)
0.01
0.00*
0.01
(0.00) (0.00)
(0.00)
0.00*** 0.00*** 0.00
(0.00) (0.00)
(0.00)
-0.02*** -0.02 *** -0.01
(0.01) (0.01)
(0.01)
3.19*** 2.77*** -0.32
(0.30) (0.35)
(0.62)
-0.01
-0.02
-0.11
(0.04) (0.04)
(0.09)
-0.59*** -0.41*
-0.61
(0.19) (0.25)
(0.37)
-0.22
-2.10***
(0.27) (0.51)
2.69*** 2.60***
(0.37) (0.49)
Yes
Yes
Yes
Yes
Yes
Yes
0.054
2052
2052
2052
Figure 1: Equilibrium contributions when
i
and
j
have similar incomes
gi
wi
NE
wi-di
NE'
Ri
Rj
gj
44
Figure 2: Equilibrium contributions when income inequality is high
gi
wi
NE
Ri
wi-di
NE'
Rj
gj
45
Figure 3: Predicted deposits as a function of the income share
46