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Massachusetts Institute of Technology
Department of Economics
Working Paper Series
Institutional
Change
in
the Non-Market
Endogenous Matching
Economy:
Chennai's
Chit Fund Auctions
in
Jan Eeckhout
Kaivan Munshi
Working Paper 03-01
December 2002
Room
E52-251
50 Memorial Drive
Cambridge,
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http://papers.ssm.com/abstract_id4572801
3
Change
Institutional
Endogenous Matching
Non-Market Economy:
in the
Chennai's Chit Fund Auctions*
in
Jan Eeckhout^
Kaivan Munshi*
December 2002
Abstract
This paper tests the proposition that non-market institutions can respond flexibly to changes
in
the economic environment that they operate
in,
using data from Chennai's chit fund auctions.
These auctions bring borrowers and lenders together
1993, legal restrictions exogenously capped the
of
endogenous matching
is
proposed,
in
Data
small groups, and starting from September
in
the auctions.
A
theory
which borrowers and lenders sort themselves into groups
with different characteristics, which also predicts
policy experiment.
in
amount that could be bid
collected before
and
how
after the
new
institution settles remarkably quickly into its
the participants will re-sort following the
experiment reveals that this non-market
equilibrium.
Consistent with the theory, a
completely different composition of borrowers and lenders in the groups, and a completely different
group structure
is
observed.
Keywords. Roscas. Non-market Institutions. Endogenous Matching. Financial Intermediation.
JEL. 012. 017. G20. D40.
Introduction
1
The importance and
the persistence of non-market institutions in developing economies has gener-
ated a great deal of interest
among economists
While the analysis of comparative
in recent years.
agrarian institutions, notably sharecropping, has a long history in the economics literature, this line
of research has been extended over the last decade to rotating savings
*We thank
Ajit
Menon and
in collecting the data.
cicJ
his
team of
Poorti Marino,
field investigators,
Nauman
support from the McArthur Foundation, and
Newman,
is
lison, Sergei
gratefully acknowledged.
and the
staff at
and credit associations
Shriram Chit Funds,
and Aldo Colussi provided superb research
for their assistance
assistance.
Finan-
initial collaboration on this project with Patrick Legros and
Andrew
Ilias
We have benefited
from many helpful discussions with R. Chandrasekar, Glenn El-
Izmalkov, R. Kanan, George Mailath, Marco Manacorda, Steve Matthews, Volker Nocke,
Nancy Rose, R. Sadanandam, R. Thyagarajan, and seminar participants
'University of Pennsylvania, eeckhout@ssc.upeiin.edu
^University of Pennsylvania
(Besley,
and MIT, munshiOmit edu
.
at
UPenn, Maryland,
Andy
MIT and
Postlewaite,
Georgetown.
Coate and Loiiry 1993, 1994), cooperatives (Banerjee, Besley and Guinnane 1995), mutual insurance
arrangements (Townsend 1994), and informal credit institutions (Udry 1994). The prevailing view
this research
is
that non-market institutions are opportunistic arrangements that exploit social ties to
overcome information, enforcement, and coordination problems. Despite
these institutions
may
still
their obvious inefficiencies,
do better than their competitors when market institutions function imper-
In this view, non-market institutions should not be seen as vestiges of a traditional economy,
fectly.
dominated by
tutions
may
social ties
and reciprocal exchange, that
encouraged, or at the very least
been the case
The
essentially hinder change. Instead, these insti-
economy
actually play an active role in the transition from the traditional
market economy. As a policy recommendation,
in
many
left
this suggests that
alone, instead of being discoiuraged
and
strictly regulated as
we have
just described relies
more appropriate
as the economic environment changes over the course of the development process.
empirical work that studies
how
different
the economic environment that they operate
may
in.^
marriage and
traditional societies (see, for example,
se,
position in this paper
Non-market
institutions,
But there has
in
institutions often use social sanctions
is
fertility
and such
social
has been documented to be remarkably rigid in
Munshi and Myaux
that this rigidity
is
2002).
not a feature of non-market institutions per
but a consequence of the restrictions that sometimes keep them
social regulation will decline as these institutions evolve,
improvement
on the
leave these institutions relatively unresponsive to change. Consistent with this view,
social regulation surrounding
Our
has
non-market institutions respond to changes
to ensure that individuals do not deviate from cooperative patterns of behavior,
regulation
modern
developing economies.
optimistic assessment of non-market institutions that
little
to the
non-market institutions should be
idea that these institutions will alter their structure, or be replaced by
been
in
in their flexibility.
We
which has evolved to the point where
test this
it
The importance
in place.
of
and we would expect to see a corresponding
view by studying a
classic
non-market institution,
displays several features, such as relative anonymity
competition, that are associated with the market. As expected,
we
and
will see this particular institution
respond swiftly and appropriately to an exogenous economic change.
The
subject of this paper
is
the rotating savings and credit association (Rosea).
Roscas are
informal financial institutions, which are popular throughout the developing world, and are even
found among migrant groups
in the U.S.
and other advanced economies. In
Rosea consists of a small group of individuals with
amount
of
money
to a "pot," at fixed intervals of time.
period, either by lot or by auction,
In
its
social ties to each other
The amount
and each participant
in
in the
its
traditional form, the
who
pot
is
contribute a fixed
disbursed in each
the Rosea receives the pot once only.
simplest form, as analyzed by Besley, Coate and Loury (1993, 1994), the Rosea facilitates the
consumption of consumer durables. For example, imagine that ten residents of a
village get together
Previous empirical work on non-market institutions has typically taken a static approach to analyze the structure
and the performance of these
institutions (as in
Udry
1994, Banerjee et
al.
2001).
to save ten dollars each every month.
one hundred
dollars.
Once a
member
first
month,
won the
participant has
period until every
all
interested in purchasing a bicycle, which costs
each individual saved independently
If
month, starting from the
autarky.
are
With the random Rosea, one member
the bicycle.
in each
They
group drawn at random receives the bicycle
of the
so everyone
pot, he
must
would take him ten months to buy
it
at least as well off as they
is
still
would be
in
continue to contribute his share in each
of the group has received the pot, so social ties play an important role in
ensuring that the Rosea participants do not renege on their institutional obligations.
Turning to the setting of
this paper, while simple
South India, the institution that we study
system was nationalized
in
in this
Roscas have been popular
paper
is
based in the
city.
for centuries in rural
The Indian banking
known
the early 1970s, and the urban Roscas, or chit funds as they are
in
South India, emerged shortly
them
legal loop-hole that allowed
Chit funds apparently took advantage of a
after nationalization.
to function as financial intermediaries, in competition with the
banks, as long as their organizational structure precisely matched the basic structure of the simple
Roscas described above.
that
members
What
distinguishes the urban chit funds from their rural predecessors
is
of a group have no direct social ties to each other. Large companies bring thousands
of participants together into these small groups, and the organizers, in exchange for a participation
fee,
are responsible for any defaults that
an auction (often an English auction)
all
the
members
of the
in
may
Moreover, the pot
occur.
each period. The bid amount
group as a "dividend"
.
is
is
now
dispersed through
among
distributed equally
This process continues, with a fresh auction in each
period, until aU the participants have received the pot once - there
is
of course no auction
and no
dividend in the final period.
Although the participants
is still
in
the urban chit funds
a social aspect to the institution.
centuries,
and so
it is
level of trust
and even
in Edison,
While the simple Rosea
similar characteristics, the
The
Participants
can be sustained even
New
is
in the city.
is
chit
is
this
paper
is
mechanism that
played
company that
very
much a non-market
Tamil
institution.
typically brings together individuals with
fund acts as a financial intermediary, matching borrowers and
who wins
generated over the course of the chit fund.
rate that
is
away as Mumbai, on the western coast
the pot early are effectively borrowers, while those
it is
almost
generated endogenously within a group acts as the interest payment.
effectively lenders - the participant
within the group, and
far
Indeed, while the
is
Jersey, such forays are always restricted to the expatriate
a sa\'ings
urban
dividend that
who win
other personally, there
South India, where participants understand how the game
community. The institution that we study in
lenders.
know each
Chit funds have been popular in rural South India for
provided us with the data has organized a few groups as
of India,
not
not surprising that the urban version of this traditional institution
entirely restricted to centers in
and where some
may
last receives his principal in
The dividend thus
consequently not at
all
reflects the
who
wait until the end are
return for
all
the dividends
competitive price of capital
surprising that the chit funds generate an interest
at least 3-4 percentage points higher than
what could be obtained by depositing
capital in
the monopsonistic banking system (James Raj Commission Report 1975).^ Businesses, and borrowers
in general, also benefit
Not
from
this institution, since credit
so severely rationed by the banks.
is
surprisingly, chit funds have captured a substantial share of the credit
market over time.
Starting with almost no registered companies in the 1970s, deposits in registered chit funds were
10%
estimated to be roughly
of the
volume of bank deposits
by 1993 (Bouman 1995), and 15% of the deposits
in the
South Indian state of Tamil Nadu
in the neighboring state of
Kerala (where chit funds
play a more prominent role in the local economy) in 1987 (Shah and Johnson 1989).
report that the
in
amount
of credit
made
Tamil Nadu and 25% of the credit
available
by the
in Kerala.^
chit
The same
sources
fund companies was 12.5% of bank credit
Chit funds clearly provide serious competition to
the banking system, at least in South India, where they are most prevalent.
As
discussed in Section
2,
government regulators and the Reserve Bank of India (RBI) were quick
to notice the emerging popularity of this non-market institution.
RBI
reports from as early as the
1970s explicitly identify chit funds as direct competitors to the banking system, and take note of
the higher interest rates that these institutions could provide.
ultimately led to the passing of the Chit
strict
Efforts to regulate the chit funds
Fund Act by the Indian parliament
in 1982,
which
down
guidehnes uniformly regulating the functioning of this institution throughout the country. For
our purpose, the most significant feature of the Chit Fund Act was the imposition of a
the bids - continuing with our simple example, this says that the
maximum
dollar pot could not exceed thirty dollars. This restriction effectively
chit funds could generate,
were successful
wound
upheld in
The
its
initially,
its
30%
in
we
will exploit in the empirical analysis.
inefficiencies associated
with the chit fund
-
trade
These
is
is
obtained from a single chit fund
restricted within the
inefficiencies are
group and the oppor-
unavoidable since the chit funds
to a precise organizational structure, as specified by law, in order to be allowed to function.
Yet, they
appear to compete very effectively with the banking system; the interest rate calculations that we report later
paper suggest that the difference
Our
the structure of the institution responded to this exogenous change in
tunities for inter-temporal substitution are severely limited.
must adhere
But the case
ceihng in 1993, eleven years after the passing of the Chit Fund Act,
the economic environment. The data that we use for the analysis
There are obvious
in 1983.
They
ceiling.
September 1993.
provides an exogenous institution-specific shock, which
how
30%
and the 1982 Chit Fund Act was ultimately
judicial system,
by the Supreme Court
objective will be to study
on
capped the interest rate that the
winning a stay order from the Madras High Court
imposition of the
ceiling
narrowing their comparative advantage over the banks. Not surprisingly,
way through the Indian
entirety
30%
bid for the one hundred
the chit fund companies went to court, seeking to overturn the imposition of the
slowly
set
in interest rates
in this
between chit funds and the nationalized banks could be as high as 9
percentage points.
Statistics
to
from the references cited above are combined with barrking
compute these numbers. There
non-market institution
along the same
in
lines, in
is
httle
doubt that these
statistics
from Reserve Bank of India documents
statistics substantially
underestimate the importance of this
the local economy, since they do not account for the myriad unregistered chit funds, organized
these states.
company, one
of the largest in the country, with branches in multiple
set provides the value of the bid paid
in the city of
by the winner
Chennai (formerly known
in
each period
the
the groups that
The data
commenced
is
-
one
the business and financial center of the
one company runs as
many
as 20
neighborhood branches
in
city.
The
chit
fund company offers a
for potential participants to
is
this
in all
states.
Madras) from September 1992 to September 1994
as
year before and one year after the policy shock. Chennai
South Indian regional economy, and
South Indian
menu
of groups, with different durations
borrowers and lenders. In this application,
privately records
account
for
average
much
20%
roughly
earlier
is
the chit fund essentially brings together
a "corporate subscriber". These subscribers,
participants, are financial companies
than the "individual subscribers." This
we
net borrowers, and
all
earlier,
easy to single out borrowers, since the organizing
is
it
whether a participant
of
chit values (pot sizes)
choose from. Individual participants join independently, and once a group
formed, the auction occurs every month. As noted
company
and
will therefore treat the
is
who tend
who
to win the auction on
consistent with the view that they are
corporate subscribers as borrowers and the individual
subscribers as lenders in the empirical analysis.
Later in Section 3 we
lenders),
which
is
will present
a simple model of the chit fund with two types (borrowers and
solved in two stages. In the
by choosing from a menu
first
stage, chit fund participants endogenously
of funds of different durations, offered by the chit fund organizer.
match
The
first
stage equihbrium strategy determines the proportion of borrowers and lenders in the different funds
that are offered. In the second stage, the auction
is
executed
in
which the pattern of equilibrium bids
determines the expected payoff, for a given proportion of borrowers and lenders.
Based on the equilibrium expected payoff of the auction, the proportion of borrowers acts
Walrasian "price"
in this institution, adjusting to leave
types of chit funds in equilibrium.
as a
each agent indifferent between the various
Without a participation price
for
each auction to guide them,
individuals use the composition of borrowers and lenders in each type of group to arrive at the decentralized equilibrium. This endogenous matching
and
in addition,
it
is
a novel contribution to the auction literature^,
provides the following main predictions: First, the proportion of borrowers, as a
result of the equilibrium matching, will vary systematically with the duration of the group. Second,
the change in the proportion of borrowers following the policy experiment will depend on the extent
to which bids were capped by the
This
is
precisely
30%
what we observe
in the duration of the
group
in the
ceiling.
in the
data
in
Section
4.
The
proportion of borrowers
is
dechning
unconstrained equilibrium (prior to the bid-cap), across the range of
pot values. The proportion of borrowers also increases disproportionately after the policy experiment
in the long duration groups,
which were capped most
severely, as predicted
by the theory. Remember
that participants join independently, and so do not observe any signals about the attractiveness of
^Endogenous matching has recently received more attention. In an interesting paper, Ackerberg and Botticini (2002)
analyze the impact of matching on contracts.
long or short duration funds ex ante. Their matching decisions are merely based on their beliefs about
other participants' decisions, and
it is
thus quite remarkable that participants respond so sharply to
the change in the economic environment in this non-market institution.
We
chit
complete the empirical analysis in Section 5 by studying the change
the structure of the
in
fund institution over time. The model predicts a re-sorting of borrowers and lenders into groups
30%
of different durations as a consequence of the
One
ceiling.
implication of this re-sorting
is
that the proportion of short duration groups will also shift in response to the policy experiment.
Indeed,
we
will see a
the imposition of the
dramatic increase in the proportion of these groups immediately following
30%
and some overshooting
And even though
ceiling.
initially, this
there does appear to be
some shaking out
new
equilibrium, with
non-market institution
settles into its
a significantly higher fraction of short duration groups, in about two years.
striking
endorsement
for
the view that non-market institutions can be very responsive to changes in
the economic environment that they operate
The paper concludes
This result provides
in
Section 6 with
in.
some
additional
comments on the long-term
institutional
response to the policy experiment and a brief discussion on the regulation of non-market institutions.
The
2
Institutional Setting
This section begins with a brief discussion on the prevalence and the importance of Roscas throughout
the world.
We
pay particular attention to variation
time, since this
tells
us something about
the commercial chit fund, which
events leading
lies
2.1
The
is
up to the imposition
in the structmre of this institution over
its flexibility.
Subsequently we describe the organization of
the focus of this paper, in some detail. Finally,
of the
30%
ceiling,
space and
which
is
we dociunent
the
the exogenous policy experiment that
at the heart of the empirical analysis.
The Prevalence and the Importance
generally accepted definition of a
Rosea
formed upon a core of participants who agree
is
to
of Roscas
provided by Ardener (1964:201):
make
An
association
regular contributions to a fund which is given,
in whole or in part, to each contributor in rotation. Institutions matching this description are found
in
urban and rural areas throughout the developing world (Geertz 1962 and Ardener 1964 provide
comprehensive surveys), and even among migrant groups
instance, describes Roscas organized by
in
West Indian immigrants
throughout sub-Saharan Africa report that 50-80% of adult
and
credit groups,
which include Roscas (Bouman 1995).
participate in Roscas (hut) in a typical year (Levenson
setting for this study, one million subscribers
registered chit funds in 1993
advanced economies (Bonnet 1981,
(8%
in the U.S.).
Numerous
men and women
for
studies from
participate in savings
In Taiwan, at least
and Besley 1996). And
20%
in
of households
Tamil Nadu, the
of the adult urban population) were entered in
(Vaidyanathan and Sriram 2000).
Apart from their popularity, Roscas also play an important
world. Credit granted through Roscas {tontine) in
in the
country (Schrieder and Cuevas 1992) and
role in local
Cameroon was about 27%
in Ethiopia,
we noted
of the credit available in South
in the previous section that credit
credit in the
South Indian states
of
of all loan requirements
the 1968-73 Development Plan estimated
the annual savings volume through Roscas {ekubs) to be 8-10% of
hms provided 20-25%
economies throughout the
GDP
(Begashaw 1978). In Asia,
Vietnam during 1965-75 (Bouman 1995), and
provided by registered chit funds was 12.5-25% of bank
Tamil Nadu and Kerala.
While the Rosea may enjoy a substantial presence throughout the world, the popularity and the
structure of the institution does vary across broad geographical areas. In Africa, for example, Roscas
are concentrated in the
more commercially developed regions
of
West Africa, and are particularly
widespread in Cameroon and Nigeria (Geertz 1962). Similar regional variation
well,
and both informal and registered
Kerala, Tamil
Nadu and Andhra
No
calculated,
interest
is
chit funds are concentrated in the three
Pradesh.
and bidding
is
The
is
observed in India as
South Indian states of
structure of the institution also varies geographically.
absent, throughout Africa (Geertz 1962). In contrast, East
Asian Roscas often use complex procedures to distribute the dividend, and both random and bidding
Roscas are widely prevalent throughout Asia (Ardener 1964).
The
structure of the Rosea also depends on whether
it is
organized in the village or the
Roscas tend to be informal, consisting of members with social
typically
is
institutions in
more as a
The pot
is
social ties to each other are
typically auctioned in each period,
financial intermediary, bringing borrowers
savings institution in which homogeneous individuals
There are two basic explanations
anonymous
In contrast, urban Roscas are usually
which individuals without previous
professional organizer.
match
and
brought together by a
this variant of the
and lenders together, than
Rosea
as a pure
together.
for the observed diversity of the
essentially anthropological, explanation (due to Geertz 1962)
reflects
each other. 10-15 individuals
form a group (Begashaw 1987, Campbell and Ahn 1962, Fernando 1986), and the pot
distributed by drawing lots in each period.
functions
ties to
Rural
city.
is
Rosea
institution.
The
first,
that the structure of the institution
the underlying culture of the participants. Thus urban Roscas differ from rural Roscas because
individuals in the city are
more "commercially"
continue to dominate in the village.
Changes
oriented, whereas
norms
in the institution over
of cooperative behavior
time then
reflect
changes in
underlying individual values and preferences. In contrast, the second, classical economic explanation
for the
observed diversity in the Roscas
is
that the structure of the institution responds to exogenous
changes in the economic environment, while individual preferences remain stable. In this paper, we
provide direct support for the second view by analyzing the institutional response to an exogenous
economic shock, under the plausible assumption that endowments and preferences
remain stable over the short two-year period that we consider.
in the
population
The Organization
2.2
While traditional
commercial
chit funds
fund
chit
is
Commercial Chit Fund
of the
have been widely prevalent
South Indian villages
in
a relatively recent phenomenon.
for centuries, the
Ardener (1964) places the emergence of
commercially organized 'Chit Fund Groups' at the beginning of the twentieth century, mostly
in
Chennai, and to some extent in Travancore and Cochin. But these commercial chit funds appear to
have been quite
fund company
rare,
in
even as late as the 1970s. Anderson (1962)
tells
us that the
registered chit
first
Hyderabad, the capital of Andhra Pradesh and another important center
fund activity today - the S.N. Chit Fund Co. - was founded
in 1951.
Similarly, the
for chit
company that
provided us with the data (Shriram Chits and Investments Pvt. Ltd.), one of the oldest and most
established companies in Chennai, was founded in 1974.
From our
discussions with the founders of
the company, there were only a handful of commercial chit fund companies in Chennai prior to that
date.
The Indian
financial
system was nationalized
in
the early 1970s, after which only specially des-
Non-Bank Financial Companies (NBFCs) were permitted
ignated
aries, in
competition with the government banks.
Companies that operate
were
criteria
first laid
to function as financial intermedi-
One such NBFC was
the commercial chit fund.^
number
as registered chit funds have to satisfy a
of specific criteria.
These
out in Section 2(2) of the Madras Chit Fimds Act, 1961, which regulated
the institution in the state of Tamil Nadu. Subsequently they were adopted in their entirety in the
Miscellaneous Non-Banking Companies Directions, 1973, issued by the Reserve
ultimately in Section 2(b) of the central Chit
Fund Act,
"Chit" means a transaction whether called chit fund,
its
foreman
them
and
[the
Bank
of India,
and
1982, which applies to the entire country:
chit, kuri,
or by any other name, by which
company] enters into an agreement with a number of subscribers that every one of
shall subscribe a certain
sum
or a certain quantity of grain by installments for a definite period
that each subscriber in his turn as determined by lot or by auction or by tender or in such other
manner
as
may
be
provided for in the agreement shall be entitled to a prize amount.
Notice that this legal definition of a chit fund matches closely with Ardener's (1964) general
definition of a
Rosea that we provided
earlier.
As long as the
chit
fund
is
organized precisely along
the lines laid out above, the company can operate as a financial intermediary, regxilated by the
Registrar of Chit Funds in each state, rather than by the Reserve
Chit fund companies organize their subscribers into groups.
month
to auction the pot.
contributes per month, and
reflects
the number of
A
group
its
duration
members
in
is
characterized by the
(in
of India.
Members
amount
of
of a
group meet once a
money that each
months). Since the group meets each month,
the group.
^According to the Reserve Bank's definition,
Bank
NBFCs
subscriber
its
In our data, obtained from one chit fund
duration
company
include equipment leasing companies, hire purchcise financing
companies, loan companies, investment companies, mutual benefit financial companies {nidhis), miscellaneous non-
banking companies
(chit funds), residuary
non-banking companies, and housing finance companies.
^
month ranges from Rs.250
over the 1993-94 period, the contribution per
rate was roughly Rs.25 to the dollar at that time).
to Rs.25,000 (the exchange
The duration ranges from 20 months
to 100
months. The subscriber thus has a menu of groups to choose from. Our chit fund company runs 20
neighborhood branches, spread throughout the
have no social
ties
Chennai. Individual subscribers
city of
with other members of their group. Individuals join independently, and a group
complete when the number of subscribers who have signed on,
company
will typically
Funds
applies to the Registrar of Chit
commence throughout
at that point to
company coordinates
the year, the
campaigns around Pongal, the Tamil
is
New Year
commence the
chit.
The
While groups
participation by organizing enrollment
and the Divali (Ayudha Puja)
in April,
October. 78,000 subscribers joined 2,000 groups
equal to the posted duration.
is
festival in
our chit fund company, in Chennai city alone, in
in
1993-94.
Since participants have no social ties to each other, the social sanctions that prevent default in the
traditional Rosea have no bite in the commercial chit funds.
for defaults in this case.
The company must assume
Most subscribers provide three guarantors, who are respected members
the community, and according to the branch manager's discretion, a subscriber
to pledge property or other assets
when he wins
company
arrears. Default rates are very low - less
5%
than
of the group, organizes the English auction on
for its services,
subsequently receives
As noted
5%
in
is
The company
our data.
first
presumably one way
we discovered
in
be required
a
list
is
facilitates the
formation
responsible for defaults.
pot without competitive bidding, and
of the chit value (the value of the pot) in each
they win the auction. Their promoters are most
also
take him to court to realize the
premises each month, and
its
"finance companies," in the data. These companies
fund, and this
will typically
the company receives the
in the previous section,
may
of
the pot. In the event that a subscriber nevertheless
reneges on his institutional responsibility, the
As compensation
responsibility
number
month.
of corporate subscribers, listed as
no guarantors and provide no security when
likely socially
connected to the organizers of the chit
which high default rates can be avoided while maintaining
a sufficiently high imphcit interest rate to encourage depositors. For the purpose of the statistical
analysis that follows, the presence of the finance companies allows us to conveniently partition each
group into borrowers and lenders.
Consistent with this view
subscribers bid higher and win the pot on average
corporate subscribers account for approximately
feature of the empirical analysis will be to see
the imposition of the
30%
This compensation scheme
much
20%
of
we
earlier
all
will see later that the corporate
than the private subscribers. The
the participants, and one important
how the proportion
of these subscribers responded to
ceifing in 1993.
is
precisely laid
subsequently adopted without modification
down
in
Section 13 of the
in Section 21 of the central
Madras Chit Funds
Chit Funds Act, 1982.
Act, 1961,
and was
^
The
2.3
Policy Experiment
Government
and particularly the Reserve Bank of
regulators,
growth of the
India,
were quick to take note of the
and other NBFCs, following the nationalization
chit funds
of the banking system. Sev-
committees were appointed to study the working of these companies, prominent among them
eral
being the Bhabatosh Datta Commission (1971) and the James Raj Commission (1975). These committees
that while
felt
many NBFCs
frequently resorted to unfair methods, and therefore needed to
be regulated, prohibiting them entirely would adversely
limited access to
bank
economy that had
affect certain sectors of the
credit, or chose not to deposit their
money with
case of the commercial chit fund companies, these study groups
the banks. For the particular
recommended a Model
to be
Bill,
enacted as a Central Act of Parliament, to ensure uniform regulation throughout the country. They
recommended that the administration
also
The Government
The
1982.
of India acted
central chit fund act
of the legislation should be
left
to the state governments.
on these recommendations and passed the Chit Fund Act
in
was modelled to a large extent on the Miscellaneous Non-Banking
Companies Directions, an interim regulatory document issued by the Reserve Bank
in 1973,
which
in
turn was modelled closely on the Madras Chit Funds Act of 1961, which regulated the institution in
the state of Tamil Nadu. Implementation of the Act was
The 1982 Act departed most notably from
state.
The
left
to the Registrar of Chit Funds in each
the 1961 Act by imposing a
30%
ceiling
on the bids.
stated reason for the ceiling was to protect the depositors from defaults that would occur
when
the bids were pushed too high - this would be the standard story with adverse selection or moral
hazard, in which only risky investors participate or only risky projects are chosen
are high.
But
it is
interest rates
very likely that the interest rates were also capped to restrict competition from the
fund companies, since
chit
when
it
was well understood that the higher
interest rates that these
companies
could provide was perhaps their principal comparative advantage over the banks.
Not surprisingly the
were
chit
initially successful,
and the Madras High Court granted a stay order
provisions of the 1982 Chit
work
its
way through the
Supreme Court
in
fund companies went to court over the imposition of the
Funds Act, including the 30%
coinrts,
and
We
will
As
its
it is
it
reasonable to treat the
30%
ceiling
imposed
in
fund company
prior to
1961
from commercial banks
compete with the monetary system and [therefore] there
chit
level,
always difficult to predict
and the numerous appeals that were
is
commencement
is
its
completion.
September 1993, a
the Shah Commission report (1992:20), prepared for the Reserve Bank, put
The
Funds
However, the case did ultimately
legal backlog,
in the Indian judicial system,
differential as a motivating factor for transfers of deposits
NBFCs
1984 on a number of
would only have added to the uncertainty surrounding the timing of
thus find
They
numerous appeals the stay order was vacated by the
September 1993. Given the enormous
when a case will come up for hearing
filed in this case
after
ceiling.®
in
ceiling.
to
it:
full
eleven
The importance of
interest
NBFCs
zs
well recognized
...
The
need to regulate them.
required to deposit a fixed proportion of the value of the pot with the Registrar of Chit
of the group as security.
The
required deposit level was increased in the 1982 Act over
which was another issue that the chit fund companies took to court.
10
j'ears after
the passing of the 1982 Chit Funds Act, as an unpredicted pohry shock.
analysis will
compare the formation
1993, Over a longer period of time,
of chit fund groups, one year before
we
A
3
its
after
empirical
September
study the speed at which the institution was able to
will also
respond to the policy shock, and settle into
and one year
The
new
equilibrium.
Simple Model of Chit Fund Auctions
We now proceed
to formalize the formation of groups
and the pattern
of bids in the chit fund auctions.
In this simple model, there are two types of participants: high types and low types. High types have
superior investment opportunities, and because in equilibrium they collect the pot earlier on average
than the low types, we
will often refer to
two stages. The
them
as the borrowers.
The low types
are the lenders.
the matching stage. Each agent chooses to participate
solve the
model
in a chit
fund of a certain duration, based on the expected future payoff from that chit fund.
in
first
stage
is
We
The
second stage determines the payoff from the auction.
Given a menu of
payoff.
We
chit funds, the participant chooses that
will see that
fund that maximizes her expected future
the proportion of high types acts as a price in this institution, adjusting to
leave each agent indifferent between the various types of chit funds in equihbrium. For example,
exogenous shock increases the payoffs that the high types receive
in
one type of
if
an
chit fund, relative to
the other funds that are available, then this will generate an inflow of high types into that chit fund
(which lowers the payoffs that they receive) until indifference
is
restored once again.
Section 3.1 describes the population and preferences, the matching technology and the auction
technology.
We
solve the
model backwards, starting
in Section 3.2 with the pattern of bids in
the second stage auction, and the payoffs that the participants receive.
derives the
first
stage sorting equilibrium.
The
Subsequently, Section 3.3
analysis concludes in Section 3.4 by studying
the proportion of high types, in groups of different durations, responds to the exogenous
on bids that was put
in place in
September 1993. This
30%
how
ceiling
will later allow' us to empirically identify the
presence of underlying endogenous matching.
Population, Preferences, and the Auction Technology
3.1
3.1.1
Population and Preferences
Let there be a continuum of infinitely lived chit fund participants. Each participant
observable type 7,7 e
is
fj,
-^
7,
7
,
f
where 7 > 7 and where the proportion of high types
and the proportion of low types
is 1
—
fi.
Participants of type 7
access to a deterministic investment opportunity with a retxurn
agents derives from the return on the investment opportunity.
returns from investment,
we
will often refer to
1
who manage
+
7.
The
is
indexed by an
in the
population
to find finance have
heterogeneity amongst
Though both types can
derive positive
the high types 7 as borrowers and the low types
11
This follows from the fact that the high types
7 as lenders.
and are therefore
for funding,
G
Time
[0, 1).
is
organizer of the chit fund offers a
chit
fund auction
menu
Thus, each chit fund group
is
W
(7,
A'^,
p, v)
participate in
is
decision.
So the
is
W
is
determined as the equilibrium
endogenously deter-
menu
only announces
second stage subgame.
in the
as to
maximize
in
W {'y,N,p,v)
subject
each chit fund equals
proportion in the total population). For any interior solution, the proportion p acts as a
make
agents indifferent between different types of chit funds on the menu.
will specify
As a
a p for each auction N,v.
chit
fund {N,p,v)
,
p
is
taken as given in the second stage.
determines the expected payoff for each type W{'y, N, p,
v). In
Now
each period
=
(
the auction technology
1,
..., A'^,
all
group contribute a rupee amount v to the fund, and at the same time, at each
sealed bid auction
is
conducted
in
which the highest bid wins. Each
auction only once, so that participants in the auction are
have not won the auction
and pays the highest
t
[0, 1].
The Auction Technology
Given a
N
p
fund organizer's
chit
and therefore choose N,v from the menu such
an equilibrium matching
3.1.3
—
course,
the group p e
in
instantaneous and without frictions. All agents simultaneously decide which fund to
balancing force to
in a
Of
market clearing condition (that the aggregate number of high types
initial
result,
and the proportion of high types
the normalized expected payoff to an agent of type 7 from participation
a chit auction {N,p,v), where
Matching
v,
Each
N, the contribution that
of participants in the group
characterized by a triple {N,p,v).
mined by each individual's participation
N, V. Denote
of groups for potential participants to choose from.
number
characterized by the
is
each participant must make each period
the
constant discount factor
discrete.
The
to the
common and
at a
All participants are
The Matching Technology
3.1.2
in
have a higher willingness to pay
early in the chit fund auction.
maximizers who discount the future
risk neutral utility
6
move
willing to
will
participants,
The
set
yet.
bid.
i.e.
The winner
The
those
up of the model
is
those A^
fund
—i+
not
is
a
first
price
member can win
1 chit
receives the period's contribution of all
bid paid by the winner
who have
all
chit
t
participants
the
fund members who
A''
participants
Nv
distributed equally amongst the remaining
won the auction
yet.
consistent with the actual organization of the chit fund auction in that
there are no restrictions on the information concerning past bids, or the identity of past winners.
However, the model departs
bidding as a
well
known
guaranteed
first
in
two ways from the actual
chit
fund auction.
First,
we model the
price sealed bid auction instead of the English auction used in practice.
It is
that with private independent values and risk neutral bidders, revenue equivalence
for
both
static auctions.^
In fact, the English auction
Second,
and the second
A^ participants in the group, including the
all
is
most
price auction are strategically equivalent for static independent private
12
While the assumption
recent winner, share the winning bid equally each period in practice.
model does not change the nature of the auction, the advantage
it
we
simplifies the expression for the continuation payoff that
model analytically
It is
of the setup
we have chosen
Nv (1 + 7) +
is
player, in addition to her type
The introduction
ctj.
out tie-breaking bids when there
e
- and as a
7 receives an
result at -
of the
i.i.d.
very small and approaches
is
signal
b
=
(61,62,
...,
0.
i.i.d.
signal at in each period,
67V) indicates
continuation payoff (conditional on not having
]/(
=
We solve
matching
We
6.
won
will use the short
will
consider equilibria where
bt
=
(bt^kt) the bids
all
participants
{^,b;N,p.v) denote the expected
the auction in the past) at time
hand notation
to indicate
Vt
=
t
for player 7,
Vt (7,
6;
N ,p, v)
the model backwards starting in the second stage. For the determination of the equihbrium
in
the
Proposition
first
stage,
1
For
all
We
t
turns out that
it
we only need
to derive the difference
AVi
=
Vf — V^
therefore have the following result:
N
<
AVi{N,p) = 8P^.-'AVn
=
and AVat
A^i; [7
The proof
is
-
7I
reported in the Appendix. In order to get the intuition for this result, we derive the
=
V'/v
investing.
in
period
A'u(l-f 7)
Because
t
< pN
v and a given proportion of high types p
is
the payoff in the last period, which
in equilibrium, bids
types remaining in period
the bid
64.
t.
We
0.
(i.e.
can write the high type's
as
When
With complementary
is
is
1/
[pN —
t
+
1)
,
where
the individual wins, the payoff
probability, the high type loses
value auctions. Further, revenue equivalence
is
strategic equivalence, also between the English
also equal to the return
from
by the high types always dominate those by the low types,
the probability of winning for a high type
less
A'^,
high types in the group) for the case where £ approaches
expected payoff
where
(1)
= Nv A 7-
equilibrium continuation value of a given auction
pN
by
Stage: Strategic Bidding
(and in particular AVi).
with
in
V((7,6;A^,p,i.).
The Second
3.2
profile
we
the strategy profile of
let Vj
,
type 7
for
for technical convenience. It rules
Denote the pair
in a given chit fund. In a given chit fund auction (TV, p, u)
and given a strategy
is
only one high type. Therefore,
is
each of the types. Then the vector
and
that
tractable.
assumed that each
t
is
derive for each type and makes the
with at uniformly distributed over [— £,e]. As a result, the valuation of the investment
period
in the
pN - +
t
is
first
price auctions.
13
the number of high
the return on investment Vyv
and gets the discounted expected
guaranteed between the second and
and
1 is
first
price auctions,
and because
of
payoff in the next period plus her share of the bid
remaining players who have not won
we show that
In the appendix,
to bid
bt
=
—
f^/v
jjl.'[li
that
bt
distributed equally amongst the
is
~
t
yet.
for
t
=
1,
—
...,pN
1,
the equilibrium strategy of the high types
^^t+i)- The intuition behind this
are competing with high types.
N
As a
is
that in
is
those periods, high types
all
bidding makes a player indifferent between winning
result, the
the auction today, and losing and getting the discounted continuation payoff and the share of the bid:
yN — bt =
^^t+i
+ W^i-
This implies that for
=
i
1,
—
...,pN
1,
the equilibrium expected payoff
is
given by
Vt
who
For the low types,
= VN-bt =
+ j^bt.
lose for sure in the early periods, the
Vt
We
6Vt+i
=
^Zt+i
corresponding payoff
AVi =
In period
t
expressed as
+ jj^h.
can now calculate AVt immediately from the equihbrium payoffs above: AVt
recursively,
is
=
6AVt+i. Solving
S^'^-'^AVpN.
= pN, there is only one high type left,
can win the auction
for sure
by offering e above the bid of the low type
the symmetric support of at)- Therefore, for small
are equihbrium bids.
and she now competes with
The low types
bid
up
e, in
period
t
= pN,
all
the low types. She
(recall that e
bt
=
bt
=
is
^_~*^
the bound of
{V_fj
—
6y_t^i)
to the point where they are indifferent between winning
the auction and losing. This implies
Vt
=
VN-h
Vt
=
SVt+^
Differencing the equations above, at
t
+ j;^bt = VN-bt.
= pN, AVpN =
SP^~^AVj\f, giving us the result in Proposition
AV/v.
We
=
can therefore conclude that AVi
1.
Before turning to the determination of the matching equilibrium in the
first stage,
we normalize
the expected payoff from participation in the auction to account for the fact that different funds have
different durations.
For each type 7, the normalized payoff from participation in the chit fund
is
equal to
Hence we can
define
AW{N,p) = W{N,p)-WiN,p) =
I'yy^
=
(2)
J/;v
Next, two comparative statics properties of the expected equilibrium payoff are derived.
basic property of
^
Of
course,
p
is
AW
is
that
it is
first
decreasing in p.^^
not a continuous variable for a finite
the remainder of the discussion we will treat p (and
is
The
N)
easily verified that the properties of the derivatives
N
and given that p
is
the fraction of high types. However, for
as continuous variables. This
is
without
can be replicated using differences.
14
loss of
generahty as
it
Lemma
1.
Consider a
fund and any N,6,v,^,'y. Then
chit
dAW{N.p)
dp
Proof.
First,
—— ="
observe that
d^
—
.^
-r
dp
<0
Then
ji
dp
l-S-"-'
it
immediatelj" follows from equation
that
(1)
dAW
5p^-'^AVn
dp
1-6^
N\n6
= AWN\n6<0
<
since In 6
The
0.
intuition for this result
As p
fairly straightforward.
is
between the
increases, competition
high types increases, pushing up the high types' bids in the early periods. Higher bids imply a higher
revenue
for the
This makes the auction
low types as the gains are distributed amongst the losers.
relatively less attractive to the high types
and more attractive to the low types,
AW(N,p)
i.e.
decreases.
The second
basic property of AH''
Lemma
Consider a
2.
chit
that
is
AW'
is
N
decreasing in
for sufficiently
exists a 6*
fund and any N,6,v^^,'). Then there
low values of
such that for 8
<
6.
6*
dAW{N,p)
dN
Proof. Again, from equations
dAW =
Observe that as
is
positive for
condition for
6
^j^ <
result, there exists
The
3.3
We now
a.
is
6*
1,
(1)
it
^
-jjqit
and as
•
pN +
such that
1
<
0,
6
approaches
<
since ln8
for all 8
^
0.
N8^'
goes to
In s]
— oo.
Thus, even
A
<
6*,
0,
e~^
which impHes 6 <
^^^ <
e
if
-377-
sufficient
[0, 1].
As a
0.
Endogenous Matching
is
characterized by the
number
of participants
belief
about the proportion of high types p that
belief
must be consistent with
utility
alternative chit fund groups will
Suppose that a menu
A',,
6-pN + l){l- 8^) +
must be negative for 6 sufficiently small (close to zero).
that In^
> e"p^
=
[(In
proceed to describe the process by which participants sort themselves into chit fund groups.
Each group
fund
follows that
6^^-^
.
oi 8,
First Stage:
and
vA",
approaches
some values
(2)
A'^,
the chit fund value
will decide to join the
maximizing behavior.
A
fund
A^, v.
is
In equilibrium, this
W of each group.
oifered to potential participants.
there will be associated an equilibrium belief p(7Vi) denoted by
15
and the (common)
potential participant choosing between
compare the normalized continuation value
of chit funds {N,p)^
v,
p,.
An
Then
for
each chit
endogenous matching
.
equilibrium requires every participant to choose that chit fund that maximizes the
function W(7,Af,,pj)
.
different types of chit funds are to coexist, then the utihty
If
requires A^ £ argmax/v
W
solution to this problem
is
(7, A',p(j'V))
In the case of a
.
and implies
interior^^,
immediately that
if
AW {N,p)
normalized value
maximization
symmetric equilibrium with two types, a
W {j,N,,p,) = W {^,Nj,p,) ,y^,\/i^
It follows
normahzed value
condition (3)
will also
is
satisfied for
(3)
J.
both 7 and
7,
then the difference
in the
be equalized across the chit funds:
AW{N^,p^) = AW{Nj,p,),\fij^j.
(4)
In addition, a condition must be satisfied that requires the beliefs pi in each chit fund be consistent
with the proportion n of high types in the entire population. Consider the case of two types 7, 7 with
fractions p..!
be
rii.
—n
Then the
out of a total of n participants. Let the measure of groups of type
total
We can
now
is
J2i
under
n.
endogenous matching equilibrium in the next Propo-
the equilibrium proportion of high types
efficient sorting,
N
=
^iNi
state the characterization of the
systematically related to
Proposition
i
measure of participants
sition. It says that
is
in equilibrium
consistency condition requires
i
where the
i
exists a 6* such that for 5
Proof. From
Lemma
<
6*
2, it
in each fund
For the remainder of the discussion, we use the notation Pi
.
(Endogenous Matching) Consider any two
2
p [N)
chit
funds i,j with Ni
endogenous matching equiUbrium
follows that for 6
<
satisfies p,
>
<
= p {Ni)
Nj. Then there
pj.
6*
AW {N,p) > AW {Nj,p) ,yp
Ni
since
<
Nj. Then, evaluated at p
= p,,
this implies
AW{N^,p^)>AW{N,,p,)
In equilibrium,
AW {Ni,pi) — AW {Nj,pj) from equation
AI^
Consider
same
first
utility as
join the fund.
the case where
=
0.
Then
>
that
AW (iV„p,)
there are no gains from trade to the low types
under autarky), while the high types do benefit from funds where p
On
the other hand, from
the low types are better
always
p
{N,,p,)
(4), so
off).
A
similar
Lemma
1,
=
0.
(i.e.
As a
they
results,
will receive
the
high types will
the high types are relatively worse off as more high types enter (and
argument apphes to the case where p
exists.
16
=
1,
and as a
result,
an
interior solution
Lemma
This implies, from
The
1,
intuition for this result
duration groups, for a given
to equalize
The
3.4
The law
will
>
p-,,
which estabhshes the proof.
We know
very simple.
is
Thus p must be
p.
from
Lemma
2 that
/\W
greater in short
is
Lemma
larger in the short duration groups, from
1,
AW across groups of different duration.
Change
Policy Experiment and the
came
that
now proceed
September 1993 caps the
into force in
Endogenous Matching
in
Vjids at
30%
Nv.
of the auction value
to study the effect of this restriction on the sorting equilibrium.
on the sorting equilibrium are distinguished: the entry
of capping
Of
that p,
effect
Two
We
different effects
and the substitution
effect.
course, empirically only the total (entry plus substitution) effect can be observed, but the theory
allows us to derive separate predictions for each of those effects.
We begin
by showing that
W and decrease
The
VV..
first
for
a given p and
the effect of capping the bids in 1993
TV,
implication of this change
fi
of high types increases after capping the bids.
among
We
the low types. As a result, the
call this
the entry
the sorting equilibrium of an increase in the proportion of high types
p,,
this effect
capping the bids
is
in select
types tend to move into the capped funds.
We
sorting equilibrium of changing
[U^)
=
W
capped groups, where
Then /SW^ =
W
{h'^)
h'^
—
and
2.
the substitution
call this
W^{h'^)
= W^
)
while
'W_{jf).
We
N
show
[\W^
and
let
in
—^
the effect on the
kept fixed.
and low types
the following
Lemma
h^
<
in
the
ht^t.
that the difference in continuation
the high bids be constrained (b^
<
6^
<
AlK
6i), then:
1.
N-bi _
=
> VJ^Tn
777
W
>
W
;
=
~
Vi
1-6^'
is
l-,5^
the low types
given the high bid
"^
effect,
AW > AW.
W=
Now
is
larger than in an unconstrained chit fund
is
w
for
p
as the continuation payoffs for high
Proof. In the unconstrained equilibrium, the payoff to the high types
and
effect:
denotes the vector of constrained equilibrium bids in these groups,
Fix p and
will
into the unconstrained funds while the high
W (increasing W and decreasing W
values in a constrained chit fund
Lemma 3.
W^ < W; 3.
we
funds,
all chit
funds
groups also leads both types to substitute between different chit funds:
now move
W
all chit
(mechanically) larger in the short duration funds. Apart from the entry
payoffs change, and as a result, the low types
Denote
the effect on
effect:
while keeping
unconstrained. While the entry effect increases the proportion of borrowers in
show that
to increase
that more high types decide to participate
is
in all auctions, with a corresponding decline in participation
ratio
is
i_tAf \^y.2
+
in
the
Tv^^i
^
by the period's constraint.
It
Ki
1
1-6'"
1
-
5V, +
d'"
constrained
^6,
-1
l\
L
<
'}
W
first
period
—
t>ecause the low types are not constrained and y_2
'
is
now immediately
(b^
follows that
17
b^
<bi),
AW^ > AW.
^^'
is
Likewise,
not affected
.
By capping
must make them better
The Entry
3.4.1
We now
3
we
the bids,
are exogenously reducing the competition
off relative to
{/\W
the low types
increases), for a given
all
attractive to the high types (for a given
What
will
be the
p and
types, even before a particular auction
shows that when bids are capped, any auction becomes
we expect an
the high types, which
N
on Sorting
Effect
focus on the entry behavior of
In particular,
among
p and N). This
less attractive to
will affect
an increase
in
/i
chosen.
Lemma
the low types and more
the entry decision of
increase in the fraction of high types
effect of
is
all
participants.
ii.^^
on the sorting equilibrium, assuming that
all
funds
continue to be unconstrained? Consider the sorting equilibrium with two types of chit funds offered
Ni,N2, where
A'^i
<
A^2-
Let pi
=
p{Ni) and p2
=
p{N2) and
let
the superscripts
equilibrium values associated with the entry and substitution effect respectively.
E,S
denote the
Then the
following
Proposition follows.
Proposition 3 (Entry
Effect) If n increases
(i.e.
>
ji
while keeping all chit funds unconstrained,
ii)
then the fraction of high types increases more in the short duration chit fund
duration chit fund N2:
Proof.
If
pf —
Pi
>
P2
Ni than
in the long
^ P2-
pi,P2 are equilibriiun values, then the equilibrium conditions
W (pi)
=
W
{p2)
and
W{pi) = W{p2) imply
AW{pi)
= AW{p2)
which, after taking logs of both sides and rearranging, implies
PiNi - P2N2 +
C=
(6)
where
\N2l~5^'
We now
show that
more than
p2-
^^Think of
F(c).
Then
all
as a result of
an increase
Consider any increase in
fi
to
in
sorting equilibrium will imply that pi increases
/i,
n^ >
participation in chit funds
c* satisfies
is
This generates a corresponding increase
jjl.
beneficial as long as IV
W—
c'
=
0.
in pi,
increases, c* will increase
and as a
decreases. It immediately follows that
n
—
c
>
0.
Obviously, there will be a fraction F(c') high
Similarly for the low types, so that
F(c-)
W
,5
types having a private cost c of entering an auction, with c distributed according to the cdf F{c) and
types participating where
If
In
J
+
F(c-)
result so will F{c').
will increeise.
18
The
opposite
is
true,
i.e.
that F_(c*) decreases,
if
W
.
P2 to
pf pfi while the equilibrium
,
for
pf and
po continues to require
pf ^1 - pf A^2 +
This implies
in turn,
from equation
C=
0.
that
(6),
(pf-Pi)A^i-(pf -P2)Af2 =
Since
N-[
<
N2,
The Substitution
3.4.2
Effect
Next consider the substitution
expected payoff
how a change
before,
is
pf -
follows immediately that
it
in
effect
.
pi
> pf —
0.
p2-
on Sorting
on the sorting equilibrium, as a consequence of the change
each of the funds. Keeping the fraction of high types ^ constant, we
in the payofTs in
we assume that there
capped
now
in
consider
chit funds affects the sorting of types into different funds.
are two types of funds, N^ and A^^, where fund A^^
is
the
As
capped while Ni
unconstrained.
Proposition 4 (Substitution
Nj
while keeping
W,W_
Effect) If
for Nt and
^i
W increases and W_ decreases
is
the other hand, Nj
>
W,Wf <
pf —
Pi
< p^ —
W_) for
less in the
Pj
unconstrained,
MV^ip.) =
On
W
unchanged, then the fraction of high types increases
unconstrained chit fund than in the constrained chit fund:
Proof. Since N,
{i.e.
is
constrained, and
W
AW'-(p,).
> W,W_ < W_ which
implies
MV^iPj) > AW{pj).
Equilibrium prior to the capping requires that
AW{p,) = AW{pj),
which implies from the equations above that
AM/^(pO < AW^ipj).
Now
equilibrium after the capping requires,
AW^ipf) = AW^ip^),
so Pi,Pj must shift to restore equilibrium. Since
consistency condition, equation
(-5),
tells
fj,
is
fbced
us that Pi,pj
19
and there are only two types
must
of groups, the
shift in opposite directions.
This follows
immediately from the observation that ^
is
a weighted average oi pi,pj before the capping and pf p^
,
after the capping.
From Lemma
1,
—^
—<
0, pi
must decrease and
pj
must increase to restore equihbrium
after the
capping:
pf -Pi <Pj -Pirn
We know
for a given
from
p and
Lemma
A'^.
3 that the capping exogenously increases
groups to restore equahty in
The
change
entry effect
in
ii.
To
is
simply a mechanical change
From Proposition
short duration groups;
pf —
1,
pi
>
in the sorting
it is
to
show that the substitution
3 the entry effect increases the proportion of high types
P2
~
P2-
From Proposition
—
pi
more
in
4 the substitution effect increases the
< p^ —
Pj.
We
will later verify empirically
the long duration funds that are capped, so the entry and the substitution effects work
in opposite directions.
increases
equihbrium as a consequence of the
match endogenously, we need
proportion of high types more in capped groups; pf
that
that p must increase more in the constrained
AW across different types of groups.
establish that participants
effect is present.
Lemma
This imphes, from
AW in the constrained groups,
more
in the
Thus,
if
we were
to empirically estabhsh that the proportion of high types
capped (long duration) groups, then
this
would
tell
us unambiguously that
participants actively re-sort following the policy experiment.
4
Testing the Theory
We now proceed to test the implications of the model. We begin
with a description of the various data
sources used in the empirical analysis in Section 4.1. Chit fund groups are subsequently partitioned
into aggregate chit value-duration categories in Section 4.2, while individual participants are classified
as low
and high types
in Section 4.3,
which allows us to implement the empirical
tests.
Section 4.4
studies the sorting equihbrium prior to the experiment (Proposition 2), Section 4.5 studies the pattern
of bids before and after the experiment, and Section 4.6 studies the change in sorting from 1993 to 1994
(implied by Proposition 3 and Proposition 4).
The main
p increases much more sharply
in
this particular setting) that the sorting effect
is
of high types
result of this section
is
that the proportion
capped groups, which implies unambiguously
(in
present and hence that participants are matching
endogenously.
4.1
We
The Data
use three sources of data in this paper. First,
in all the gi-oups operated
October
1,
we obtained a complete record
of all winning bids
by Shriram Chits and Investments Pvt. Ltd. that commenced between
1992 and September 30, 1994 in the city of Chennai.
20
The sample period
covers exactly
one year before and one year
refer to the years
1
to
after the imposition of the
1993 and 1994 henceforth in the paper,
September 30 period
and just
just before
South India, and Shriram Chits, which
city in
Nadu, has
30% cap on September
we
after the capping.
is
participated in the chit fund groups that
Our second source
of data provides
be referring to the October
Chennai
is
the largest commercial
the largest chit fund company in the state of Tamil
headquarters, and 20 neighborhood branches,
its
will actually
When we
30, 1993.
commenced
in
the
in the city
income information
In total. 78.000 individuals
city.
during the sample period.
for a limited
number
of subscribers in the
sample. While the winning bids and the group characteristics are computerized and readily available,
can only be obtained from the application forms which are
this additional subscriber information
the time of entry. These application forms are subsequently stacked
filled in at
branch
located
office,
all
over the
obtain income information on
all
We
city.
picked a
random sample
their participants,
in collecting this additional
commenced
and thus there
We
selected.
regressions
And
in 1994,
is
25%
some concern that
finally,
statistics;
our third source of data
is
it is
to the analysis that
we
each
and then attempted to
of the full sample).
We
this
appear to have
this restricted
will
sample may not be randomly
only be used in a few exploratory
not required for the bulk of the analysis.
an aggregate break down of groups, based on the
pot auctioned in each month and the duration,
in
information for individuals belonging to groups that
should emphasize, however, that income data
and to report some basic
back rooms
from the respective branches. Ultimately,
information was collected for 21,906 subscribers (roughly
been more successful
of groups
in
in
size of the
each year over the 1992-2001 period. Extensions
report later in Section 5 will use these aggregate data to study changes in the
structure (duration) of the groups over time.
Classification of
4.2
Groups
Each branch posts a menu of available groups
by the
chit value (the total
amount
at each point in time,
to be auctioned each
participant chooses the group-type that
is
where each group
month) and the duration
appropriate for her, based on
its
(in
commence
company
after the necessary permission
offers
number
months). Each
fills, it is
and the
allowed
from the Registrar of Chit Funds has been obtained. The
a wide range of chit value-duration combinations, and the
analysis will be to classify the groups, along both the chit value
smaller
characterized
characteristics
composition of types that she expects to match with in equilibrium. Once a group
to
is
first
step in the empirical
and duration dimensions,
into a
of aggregate categories.
While new groups form throughout the year, the company helps coordinate the formation of these
groups by organizing two major subscription campaigns each year
April and the
Ayudha Puja
by offering entering
follows,
it
is
gifts
(Divali festival) in October.
when the
-
during the Tamil
The company
New
Year
in
also encourages participation
individual joins a group. For the purpose of the discussion that
important to note that the value of these
21
gifts is
based on the chit value, rather than
The company seems
the individual's monthly contribution.
make the
to
away a constant
individuals save to achieve a target, instead of simply putting
income each month.
The
amount that she expects
the company's lead,
groups
in
we
individual's participation decision
to deposit, rather than the
fraction of their
thus seen to be based on the total
is
payment that she makes each month. Following
will use the chit value, rather
than the monthly contribution, to
classify
the discussion that follows.
Chit values range from Rs. 10,000 to over Rs. 100,000 in our data.
savings target, which
The
implicit assumption that
is
measured by her choice of
chit value,
The
level of the individual's
must naturally be based on her income.
probability that a subscriber will choose a low (high) chit value will most likely be declining
The
(increasing) with income.
empirical relationship between the choice of chit value and income
thus allows us to conveniently partition groups along the chit value dimension.
Table
1
and
presents multinomial logit
The Rs.30,000
chit value
is
linear probability estimates of the chit value regression.
treated as the base category in the multinomial logit regression in Panel A,
while separate regressions are estimated for each chit value to obtain the linear probability estimates
in
Panel B. Even though 16 chit values are observed in the data, we restrict attention to six values
in Table 1
,
which together account
for over
90%
of
Insert Table
As expected, the
as her
income
individual
increases.
and Rs. 100,000
She
1
here.
significantly less likely to choose the lowest Rs. 10,000 chit value
is
is,
the observations in our sample.
all
however, significantly more
chit values as her
income grows. These
likely to
choose the highest Rs.50,000
results are obtained with
both the multino-
mial logit model and the linear probability model. For the intermediate Rs. 15, 000- Rs.30,000 values,
the chit value-income relationship
is
not as clear cut.
It
would thus seem natural to
Rs. 10,000 groups as low value, the Rs.l5,000-Rs.30,000 groups as
and Rs. 100,000 groups as high
The
medium and
high value chits.
is
ambiguous
is
The
trajectory
company made
There
is
a clear visual distinction between
sharply negative for the Rs. 10,000 chit value,
Once more, the
for the intermediate values.
We follow the company's
will see that
is
1.
reversed for the Rs.50,000 and Rs. 100,000 values.
Insert Figure
we
and the Rs.50,000
patterns just described are easy to visualize with the nonparametric kernel regressions, which
while the direction of the trend
pattern
value,
the
value.
correspond to the hnear probability estimates, in Figure
the low,
medium
classify
here.
lead once again, to partition groups along the duration dimension. Later
the long duration (large
efforts to
1
N) groups were
affected
most the 30%
ceiling.
The
organizing
reduce this effect by changing the design of the auction, as of October 2000.
These changes were restricted
to groups with durations 40
22
months
or longer, which are classified by
company
the
as "long duration groups."
We
will use
the same duration classification in the empirical
analysis.
Table 2 describes the different groups that commenced over the 1993-94 period, and shows the
broad classification by chit value and duration that we have adopted. As before, we
to the six major chit values.
There are seven
months, associated with these
diflferent
restrict attention
durations, ranging from 20
months to 100
This leaves us with 42 distinct chit value-month
six chit values.
combinations, which are aggregated into six combinations using the Low, Medium, High classification
on the
chit value dimension,
there are a
number
number
large
and the Short, Long
classification
on the duration dimension.
While
of "gaps" in Table 2, notice that this classification leaves us with a sufficiently
of groups in each aggregate category.
Insert Table 2 here.
Classification of Paiticipants
4.3
When we
classify
groups into
and the target savings
available over time
is
six
level, lock
broad categories we are relying on the idea that income constraints,
The only
the individual into a particular chit value.
whether to join a long or short duration group, which
will allow us to
the sorting and the bidding regressions separately within each category. But this
the individual's participation decision
change
up
in
is
is
estimate
not appropriate
based instead on her monthly contribution. Given the
if
likely
duration over time, individuals with the same endowments and preferences would then end
in different chit values before
We
is
choice that
and
after the
30%
ceiling.
consequently proceed to verify that the characteristics of participants, within each chit value
category, remained the
in that case
same over the 1993-94
period.
The
only change in the economic environment
would be brought about by the 30% bid cap, which allows us to
isolate the effect of the
exogenous institution-specific shock on the matching equihbrium. Looking down the distribution in
Table
3,
Panel A, separately
similar in 1993
and 1994
for low,
medium, and high
chit values,
we
see that incomes are remarkably
at all quantile levels, except at the very top of the
indicates that the underlying income distribution of participants
income distribution. This
was unchanged and that the choice
of chit values was unaffected by the capping of the bids in 1994.^^
Insert Table 3 here.
The
stability of the
income distribution
in
Table
3,
Panel A, for
all chit
support the use of the chit value to partition groups. But as an additional
that
all
values,
would seem to
we
will also verify
test,
our regression results are robust to an alternative classification scheme, in which groups are
partitioned into low,
medium, high monthly
'^We ignore the knife-edge case
in
which changes
contributions, with the cut-offs set at Rs.500
in the
income distribution and changes
just cancel each other.
23
and Rs.lOOO
in the choice of chit value
per month. While not reported here, these cut-offs are constructed using the same approach described
earher in Table
The
1
and Figure
up
discussion
We
short two-year period that
need to
number
to this point has allowed us to partition the groups into a small
aggregate categories.
still
1.
of
have also verified that the income distribution was unchanged over the
we
consider, allowing us to isolate the effect of the
classify participants as
30%
cap. However,
we
low types and high types.
Recall that high types receive a higher return on their outside investments and so will bid higher
and win
earlier in equilibrium.
this institution
is
we can
that
As noted
in
the Introduction, a particularly convenient feature of
identify ex ante borrowers; there
that flags "finance companies." As seen in Table
approximately
20%
of
all
3,
a separate
is
field in
the records
Panel B, these corporate subscribers account
the observations in our data.
The
appear to be trusted by the chit fund organizers, and most
for
proprietors of these select companies
likely
have social
ties to
them. While the
individual subscribers must provide information on their income, assets, and occupation to the chit
fund organizers, and also furnish the names and addresses of three guarantors, the corporate subscribers face
none of these requirements. The money collected from the auction
is
invested elsewhere
by these companies, who clearly have access to superior investment opportunities than the individual
subscribers
To
who
are for the most part salaried employees.
verify that this classification of types, based
we compare the timing
timing variable
is
of
winning bids
defined as the
month
on ex ante characteristics,
for corporate
in
The
companies, zero otherwise.
regression, so the constant
and individual subscribers
The corporate
linear probability
term measures the average timing
corporate subscriber variable megisures
would expect high types to win
early,
how much
and
indeed appropriate,
in
Table
4.
The
which the individual wins the auction divided by the total
duration of the group, and so ranges from zero to one.
for finance
is
model
subscriber variable equals one
is
used to estimate the Timing
for the individual subscribers, while the
companies win on average.
earlier the finance
as expected the corporate subscriber coefficient
absolute magnitude and very precisely estimated.
The same
1993 and 1994, for low, medium, and high value groups.
result
We
will
is
is
We
large in
obtained, without exception, in
consequently treat the corporate
subscribers as high types and the individual subscribers as low types in the empirical analysis that
follows.
The proportion
of high types p,
which helps us study changes
in the sorting equilibrium,
can
then be computed accordingly.
Insert Table 4 here.
4.4
We
Sorting Before the Experiment
noted
p{N) and
in
Proposition 2 that the equilibrium relationship between the proportion of high types
the duration of the group A^ depends on the discount factor
a 6* such that for 6
<
6*
an increase
in
A'^
lowers p{N).
24
S.
In particular, there exists
The
preliminary sorting regression uses data from 1993 only, prior to the policy shock, with a
dummy
corporate subscriber
participant
is
5,
dependent variable. This variable takes on the value of one
one of the finance companies, zero otherwise. The single regressor
dummy, which
Table
as the
takes on a value of one
the
a short duration
the group runs for less than 40 months, zero otherwise.
if
Panel A, begins by partitioning groups into low, medium, and high chit values, and
then estimating the sorting regression separately
B
is
if
in
each aggregate category.
Subsequently, Panel
repeats this exercise with an alternative classification of groups by monthly contribution.
Short
duration groups have a greater proportion of corporate subscribers, without exception, in Panel
and Panel B. Notice
also that the coefficient
Medium, and
across from Low, to
on the short duration
dummy
A
grows larger as we move
particularly to High chit values.
Insert Table 5 here.
Table
5,
Panel C, continues with the exercise reported above, reporting regressions for each of
the six disaggregate chit values discussed earlier in Table
and Table 2 (with the exception of the
1
Rs. 15,000 chit value which has no long duration groups). Looking across columns in Panel
that the coefficient on the short duration
as
we move
The
dummy
is
always positive, and that
negative p
—
will subsequently
N
relationship that
we
systematically observe in Table 5
for the presence of
study changes in p over time, at different values of
of the
30% cap on
4.5
Bids Before and After the Experiment
and durations), before and
really the
bids over time.
is
consistent with
such endogenous matching,
A'^,
following the imposition
groups with different characteristics (chit values
is
The
What we
normalized bid. This bid value
into five equal time periods,
of these time periods
in
after the policy experiment.
to provide us with a normalized bid amount.
is
increasing steadily
the bids.
This section studies the pattern of bids over time
follows,
see
across from low chit values to high chit values.-'^
endogenous matching. To provide additional support
we
it is
C we
and a
dummy
is
is
bid in Rupees
is
divided by the chit value
refer to as the "bid" in all the discussion that
capped
at 0.3 in 1994.
The group
is
divided
included for each period in the bid regression.
Each
interacted with a 1994 year-dummy, to capture the change in the pattern of
The uninteracted Period
unconstrained 1993 bids, prior to the
1-Period 5 estimates in Table 6 thus describe the pattern of
30%
cap. Separate regressions are estimated for long
and short
duration groups, within each aggregate chit value.
""One outlying group-type
Table
5,
and
later in
-
Rs. 30,000 chits running for 60
months
-
is
dropped from the regressions reported
Table 7 where we study changes in sorting over time. The coefficient on the short duration
actually reverses sign in Table
-5,
Column
the sorting that we report in Table 7
is
3
when
in
dummy
the outlying groups are included. Note, however, that the change in
completely unaffected by the inclusion or the omi-ssion of these outlying groups.
25
Insert Table 6 here.
Concentrating on the
strained 1993 bidding pattern,
(particularly in the early
rows of Table
first five
we
months)
6,
Period
1
Period
-
which describe the uncon-
5,
see that higher bids are generated in the long duration groups
in each chit value.
This pattern
is
not at
all
surprising.
bids reflect the fact that the interest rate implicitly faced by borrowers and lenders
over a longer period in the long duration groups. Therefore, even
is
the same in both groups,
we would
duration groups. This point will be
interest rate
and the
still
made
clear in section 5.2,
compounded
initial
periods for long
where we analytically derive the implicit
and short duration groups.
same duration, we
chit values with the
higher
the implicit annual interest rate
expect to see higher bids in the
difference in initial bids between long
Looking next across
if
is
The
see that the normalized bids are
increasing in the chit value, particularly for the long duration groups.
at all surprising,' since the subscribers (particularly the low types)
Once
again, this pattern
must be compensated
not
is
for tying
up
a large amount of capital with the chit fund.
The preceding
in 1994.
description of the unconstrained bids
us
what change we would expect to see
Bids must adjust to the 0.30 cap that was imposed in 1994, and this
in rows 6-10 of Table 6,
which describe the change
which highhght bids above 0.3
(Rows
tells
6-10).
in each case.
The
in
Within a
is
chit value, the
To help
is
change
see
down
to 0.3
always greater in the long duration groups, precisely
is
initial
bids
when unconstrained. And
controlling for
increasing with chit value (especially for the long duration groups).
we present nonparametric
visualize the changes just described,
regression, separately for low,
medium, and high
chit values,
tion groups within each chit value, in Figures 2-4.
bids in 1993 are capped
what we
the bids. Focus on the bold-face coefficients,
that the change in the bid just brings the 1994 bid
because the long duration groups have higher
duration, the change
exactly
1993 (Rows 1-5) and the corresponding change in these bids in 1994
point to note
first
in
is
more
than short duration groups,
severely in 1994.
kernel estimates of the bid
and separately
for short
and long
As noted above, groups with higher unconstrained
Thus long duration groups are capped more
in each chit value.
drura-
For the same duration,
it
is
severely
easy to see across the
Figures that the capping increases with chit value.
Insert Figures 2-4 here.
Looking across Figures 2-4 notice that the 1994 bids always
lie
below the 1993
the bids leads to an increase in the proportion of high types (from Proposition
subsequently verify).
And
4,
bids.
Capping
which we
will
while the 1994 bids in the early periods would certainly have been below
the corresponding 1993 levels in capped funds, the 1994 bid schedule could in principle have crossed
to the right of the 1993 schedule
level, 0.3) in
the
if
the
new equilibrium was
number
of high types (bidding at or below the constrained
sufficiently large.
26
But we
see instead that the 1994 bids start to
drop below the constrained
the 1993 bids reach that level in
(0.3) level long before
Notice also that the 1993 and 1994 bids coincide in the later periods
The explanation
for this observation
and only low types remain to compete
(0.3)
must be the same
chit fund
Changes
4.6
We now study
in
below the constrained
level
Equilibrium
in the Sorting
the change in the proportion of high types p as a consequence of the policy experiment,
in
p
effect (Proposition 3) predicts
a greater increase
the short duration groups following the capping, while the substitution effect (Proposition 4)
predicts a gieater increase in groups that are capped.
capping
We
saw
in
Table
particularly severe in the long duration groups, although
is
duration groups with
more
increase
in the long
To study changes
Table
values and durations.
in all chit
fall
^'^
1993 and 1994.
in
groups with different characteristics. The entry
shoi't
bids
the Figures.
the auction, then the continuation payoff in a given
in
in
Once the
very simple.
is
all
medium and high
duration groups
in sorting
we
if
and Figures
we do
2-4, that the
see mild capping in the
we would expect p
to
company dummy on the 1994 year dummy
in
chit values
Jis
well.
In general,
the substitution effect
regress the finance
6,
is
present.
Separate regressions are run for each aggregate chit value, and for long and short duration
7.
groups within each value. To verify the robustness of the results to alternative partitions of the data,
groups are partitioned by chit value {Nv) in Panel
Taking expectations across
on the 1994 year
dummy
all
A
and by the monthly contribution
subscribers in these regressions,
it is
[v) in
Panel B.
easy to verify that the coefficient
measures the change in p from 1993 to 1994.
Insert Table 7 here.
The
on the 1994
coefficient
dummy
is
significantly larger for the long duration groups, in each
of the three aggregate categories in Table 7, Panel
A
and Panel B. The proportion of high types
in
long duration groups increases from 0.18 to 0.24 in the low chit value groups, from 0.13 to 0.19 in the
medium
chit value groups,
and from 0.12 to 0.25
in the high chit value groups.
The composition
of
the chit funds clearly changes dramatically, particularly in the long duration groups, from one year to
the next. Since the entry and the substitution effects work in opposite directions, the greater increase
in
p
in the
capped long duration groups unambiguously
identifies the substitution effect,
which
tells
us in turn that participants match endogenously in this institution.
Intuitively,
we would
also expect the
duration constant, since the capping
what we
see,
is
although the change in p
change
in
more severe
is
monthly duration
chit values,
in
and short duration
in higher categories,
in higher chit values.
Once
again, this
holding the
is
precisely
not significantly different across successive categories in a
We verified that the same patterns were obtained when
of the aggregated long
p to be greater
we
restricted attention to a single
categories, within each chit value. For this exercise
monthly duration, instead
we used
the most popular
each case; 20 months and 50 months for low chit values, 20 months and 40 months for
and 25 months and 50 months
for
high chit values.
27
medium
couple of cases. '^ Overall, the changes in p that
respond, as
we observe suggest that the
sorting equilibrium does
should, to exogenous changes in the economic environment.
it
Extensions to the Model
5
We now
proceed beyond the model. First, we study changes
in the
term structure, measured by the
proportion of short duration groups, in this institution. Section 5.1 compares the term structure in
1993 and 1994, where we see a substantial increase
the capping of the bids. Second,
its
new
we
proportion of short duration groups following
in the
investigate whether the institution has settled immediately into
(post-cap) equilibrium. While the analysis in Section 4 provides
unambiguous evidence that
the institution has drastically changed in the direction predicted by the theory,
comparing behavior
at
two points
in time,
and short duration groups have equalized
we cannot
whether the unobservable normalized payoffs
in 1994.
of different funds for both years in Section 5.2.
We therefore calculate the
We find that while implicit
different duration funds are roughly equal in 1993, they are not in 1994.
The
tell,
W
by
in long
implicit interest rate
interest rates across
analysis in Section 5.3
confirms that adjustment was not fully completed in 1994. Using aggregate group level data over a
longer 1992-2001 period,
we
find that the basic shift
from the pre-cap to the post-cap equilibrium
is
completed in about two years.
Term Structure Before and After
5.1
The
the Experiment
empirical results described in the previous section provide strong support for the view that the
low types and the high types re-sort themselves following the policy experiment. In the discussion
that follows
we
will
study
how
the term structure in this institution, measured by the proportion of
short duration groups, responded in turn to the policy experiment.
Continuing with the simple case with two types of groups, of duration
condition requires that p\niNi
-I-
p2'^2-^2
(number) of funds of each type. Denote
r]
=
/^
— ^,
('^i-^i
+ '^2-^2)1
A'^i
where nj,
<
71.2
N2, the consistency
denote the measure
then
N2H-P2
NipiAs before we
will
decompose the impact of the capping
Start with the entry effect, which increases
Proposition 2 and Table
the increase in
p. is
12
5.
Further,
to increase
77,
pf —
pi
/u
to fj^
> P2 — P2
.
into
an entry and a substitution
Prior to the capping, pi
from Proposition
3.
>
Thus the
fj.
>
effect.
p2 from
direct effect of
while the indirect effect through the change in p goes in the opposite
direction.
Turning to the substitution
capped more
^
severely.
The constant term
in
effect, fixing p,
With two types
pf — pi < pf
— P2,
since the long duration groups are
of groups, pi actually declines while p2 increases (to preserve
Table 7 measures p in 1993 and so matches the point estimates that we presented in Table
28
5.
the constant
the decHne in pi
If
fj).
is
sufficiently large, relative to the increase in P2,
then
r/
could
increase as a consequence of the substitution effect. But in general, the effect of changes in p on
due
to the entry
and the substitution
Starting with Table
8.
Panel A, we see that the number of individual subscribers (low types)
all
types) does increase, in the
medium and
values,
and the
decline). It
total
ambiguous.
effects, are
declines substantially across
decline in participation
chit values.
among
number
While participation by the corporate subscribers (high
high chit values, this increase never compensates for the
the ordinary subscribers.
Overall participation declines in
all
chit
of participants declined from 43,267 in 1993 to 34,797 in 1994 (a
20%
also evident from these statistics that the overall proportion of high types
is
ry,
16%
substantially over this period (from
(^;)
increases
to 22%), as expected.
Insert Table 8 here.
Turning to the proportion of short duration groups
proportion increases significantly
we noted
earlier
the change in
we proceed
unambiguously leads to an increase
p,
which could go
in
the
first
three rows,
The
B
is
complete.
The
To
reported in Panel A, which
8,
verify the robustness of this result,
Panel C. Starting with durations
in
rows
4-7,
we
see a decline in popularity, once
all
group durations
and After the Experiment
fund institution
by studying behavior at two points
in time
is
making
whether
equilibrium conditions are derived in terms of the normalized payoff
out of equilibrium by comparing the interest rate that
is
no exphcit price
on the actual bids we can
D=
jTjiT—
G
[0, 1]
must
N
still
money
-
interest rate
is
this
-
in
its
change
W, which
months (the duration
t.
The
in this
non-market
is
institution.
But based
the monthly interest rate) and
participant contributes an
of the group).
is
in or
is
calculate the interest rate implicit in a given chit fund auction.
period
way
generated in groups of different types.
be the monthly interest factor (where r^
denote the funds received
period of
for
we
in the data.
unobserved by the econometrician. But we can gain a rough sense of whether this institution
There
less
see an increase in popularity over time, almost without
results presented this far suggest that the chit
tell
f-i
Panel B, we see that this
ni/n2, presumably dominates any effects of
driven by underlying changes across
new equihbrium, we cannot
in
increase in the proportion of short duration groups that
Implicit Interest Rates Before
While the empirical
is
we
Turning to the long duration groups,
observed above in Panel
to a
in
+ no))
increase in
in the opposite direction.
again with almost no exceptions.
5.2
The
to disaggregate the group durations in Table
than 40 months,
exception.
in all chit values.
(t7i/ (ni
Let
let ct
amount v each month over a
Hence, the budget constraint for any participant
satisfy the condition
f2D'-'{ct-v)=0.
t=i
29
(7)
The
net present value of monthly contributions must equal the net present value of funds received.
The
inflow of funds in any period
Cj
=
in
which case she
jjbt'-
collects c^
We
= Nv —
br
+
jjbr,
i-e.
the total pot minus her bid
can now rewrite the budget constraint
the auction in period r
given by
in
equation
Nv —
hr in addition
(7) for a participant
as:
D^-' (Nv -
It
is
she gets her equal share of the bid. In one period, say r, the participant wins the chit fund,
to her share of the bid.
who wins
which a participant does not win the auction
in
t
br)
+ El?*-^ {^^h -
I')
=
0.
follows immediately from this expression that the budget constraints of different agents only differ
in the first term.
constraints,
i.e.
Therefore,
agents
we can
who win
calculate the interest factor
D
from any two agents' budget
the bids in two different periods r and
r'
as
\Nv-br'
Using the relationship between
rm
D
and the monthly
to the corresponding annual rate,
In practice
and the
last
we
we compute the annual
period
value, duration,
(r'
= N)
and year
in
r^ provided
earlier,
and converting
obtain:
interest rate using the
in each group. ^^
Table
interest rate
These
winning bid
in the
second period (r
interest rates are reported separately
=
by
2)
chit
9.
Insert Table 9 here
The 1989 Report on Urban Informal
interest rate paid
by non-banking finance companies, which include chit funds, was 18%. The un-
constrained interest rates that
14%
to 24%.
Credit Markets in India (Dasgupta 1989) tells us that the
we compute
The same Report
tells
1993 match very well with this
for
statistic,
ranging from
us that the interest rate paid by nationalized banks on term
deposits was 9%, so the popularity of the chit funds
is
easy to understand.
Subsequently the capping brought the interest rates down dramatically, and they range from
to
17%
in 1994,
which
is
much
individual subscribers that
closer to the
we saw
in
Table
bank
8,
rate.
Panel A,
is
The sharp
decline in participation by the
once more easy to understand.
Recall from the discussion in Section 2 that the chit fund organizer collects the
and so competitive bidding only commences
in
treated as a pure borrower, while the individual
period
2.
who wins
The
individual
who wins
in the last period
30
8%
is
first
in
pot without bidding,
bi
=
0,
the second period can thus be
a pure lender.
Notice also, from Table
chit value are roughly
that interest rates for short and long duration groups within a given
9,
comparable. ^^ In contrast, we see that the interest rates on the long duration
groups are significantly lower than the corresponding rates
same
and the calculation
of the nnplicit interest rate can
and N2 with Ni <
A'^i
zero: 5/v
=
0.
Then, from equation
(8),
we
Define the
A^2-
P{N) =
normalized by the chit value (as plotted in Figures 2-4) as
is
now
why
also clarify
the
bids in the long duration chit funds are higher than the initial bids in the short duration funds.
Consider any two funds of duration
bid
the short duration gioups, within the
chit value, in 1994.
Finally, Table 9
initial
in
first
competitive bid,
j^. Recall that the
last period's
get
Nv{l~p{N))
12
1-(3{N)) N~2
Since rates in funds A^i and
A''2
are roughly ecjual in 1993, from Table
(l-/3(7Vi))"^>-^
Taking
logs
follows that
^^2-2.
={l-P{N2))
and collecting terms,
ln(l-/?(iV2))
ln(l-/?(iVi))
Since (3{N) e
5.3
9, it
[0, 1]
<
and Ni
map
N2-2
iVi-2-
N2, this imphes that 9{N2)
Long Term Changes
While we cannot
^
in the
>
/3(iVi).^^
Term Structure
the computed interest rates directly into normalized payoffs
W
,
the wide
discrepancy in these interest rates in 1994, for long and short duration groups within the same chit
'^The short duration groups tend to generate a
computation assumes a constant interest factor
why
this
is
unlikely to be the case.
The
first is
D
-slightly
higher interest rate, but this
"tcix"
that
is
be the same
and without
imposed on the participants by virtue of the fact that the
without competitive bidding (this
in each period,
we
is
most
likely
because our
that one would expect the interest rate to differ depending on the interest
rate term structure. Second, the implied markets are clearly not perfect
the
is
(an hence r) in each period of time. In reality, there are two reasons
frictions. In particular,
chit fund organizer
wins the
we
first
ignore
auction
a legally stipulated feature of the institution). By setting the discount factor
are implicitly assuming that there
Eire
no such
frictions within the group.
D to
But once we
introduce the tax, then the discount factor will vary over time, and the famiUar spread between the borrowing and the
lending interest rates will emerge.
Each participant
in
The
interest rates that
The
the spread will be greater in those groups.
lie
below the corresponding rate
in the long
Consider a hypothetical example with
verified that
are
(30)
we report
in
Table 9 thus
lie
somewhere within
this spread.
a short duration group must bear a greater tax burden, for a given chit value, which implies that
=
compounded over
0.29.
actual lending rate in short diu-ation groups could then equal or even
duration groups.
A'l
=
20 and
^2 = 30 and suppose
Long duration funds have higher
longer periods.
31
initial
that
(5
(20)
=
0.20,
then
it is
immediately
bids because they reflect the fact that interest rates
value, suggests very strongly that the chit fund institution
is
yet to reach the post-cap equilibrium.
Additional support for this view can also be obtained from Figure
for the
in
The
low chit value groups.
2,
which describes the bid pattern
bid schedule for the short duration groups
is
essentially the
same
1993 and 1994. In contrast, the 1994 bids are substantially lower than the 1993 bids for the long
duration groups in that Figure. Participants
who were
indifferent
between the long and short duration
low chit value groups in 1993 evidently would not remain that way in 1994. While the proportion of
high types might have adjusted in the right direction to
this institutional
We
move the
conclude the empirical analysis by using aggregate group level data to study the change in
commenced
values.
equilibrium,
change does not appear to have been completed by 1994.
The proportion
the composition of groups over a ten-year period 1992-2001.
that
new
institution to the
in
each year over this period
is
computed, separately
These proportions are plotted, without smoothing,
in
Figure
of short duration groups
for low,
medium, and high
chit
5.
Insert Figure 5 here.
The proportion
and high
of short duration groups increases sharply
chit values, just as
we saw
in
Table
8.
in
The proportion
this increase continues for
of short duration groups in low
1993 to over 0.4 by 1995.
The medium
medium,
for low,
one more year, 1994-
which the proportion of short duration groups flattens
95, consistent with the discussion above, after
out.
But
from 1993 to 1994,
and high
chit values begin
from about 0.2
chit values increases
with a much higher proportion of short
duration groups, above 0.5 in 1993, yet this proportion increases even further to 0.7 by 1995.
term structure
in this institution clearly
responds quite dramatically to the change
in the
The
economic
environment.
There seems to be some overshooting
minor
oscillations in the Figure,
in 1995,
but the basic
and some shaking out thereafter, judging from the
shift
from the pre-cap to the post-cap equilibrium
completed in two years. The institutional response to this exogenous shock
that this
is
a decentralized equilibrium.
which makes the rapid response
6
in this
fresh set of individuals joins the chit fund each period,
non-market institution even more remarkable.
we study
-
paper provide strong support
the chit fund
economic environment.
will
extremely rapid, given
Conclusion
The results
that
in this
A
is
is
-
for the
view that the particular non-market institution
responds swiftly and appropriately to an exogenous change in the
The theory
predicts that groups in which bids are capped
be associated with a larger increase
in
more
severely
the proportion of high types (p) following the policy
experiment. This proportion does increase more sharply in long duration groups (and in higher chit
values) providing striking endorsement for the view that participants in the chit fund are matching
endogenously.
32
An
alternative explanation for the observed changes
changed as a consequence of the
is
that the composition of the participants
bid-ceiling, or that other
economic environment are responsible
what we
for
see.
We
unobserved exogenous changes
have already verified
income distribution of the individual subscribers, within aggregate
time.
It is also
not obvious
how
We
in
Table 3 that the
is
very stable over
chit values,
these alternative arguments would explain the precise change in
we observe, along both the duration and the
that
in the
have seen that the participants
chit value dimension, in the data.
the chit funds responded immediately to the policy shock
in
by re-sorting themselves. The endogenous institutional view that we take
that the structure of the institution
p
itself
in this
paper would predict
should also respond to the policy shock.
And
indeed we
see that the term structure, measured by the proportion of short duration groups, does respond
quite dramatically to the change in the economic environment.
specifies that the
Further, while the Chit
winning bid should be distributed among the members of the group,
stipulate that the bid should be distributed equally
been adopted historically by the
which those subscribers who won the auction
for the
this
is
does not
it
just a convention that has
fund companies. Starting from October 2000, Shriram Chits
chit
introduced the Extra Dividend Scheme (EDS), in
normal dividend thereafter,
among them;
Fund Act
all
groups with durations 40 months or longer, in
in the initial
duration of the group.
months received only one percent
'^'^
of the
This effectively increases the amount
that these early winners pay out, moving the interest rates in the long duration groups closer to their
unconstrained
levels.
Such changes
in the rules of the
with numerous alternative schemes,
described above.
in response to
It is
game
are difficult to implement,
and the Company experimented
a limited number of groups, before
in
it
settled
on the
EDS scheme
nevertheless very encouraging to see the very structure of the institution change,
an exogenous change
in
the economic environment, within a relatively short period of
seven years.
It is
not obvious that capping the bids generated any efficiency gains in this institution. Default
rates were low to begin with,
and continued to remain that way
rates
moved down even
some
of the (potential) subscribers
decline in the overall
after the policy experiment. Interest
further from the competitive level, and while the banks
volume
who stopped
participating, there
of capital entering the system.
The
was most
may have
picked up
likely a substantial
participants in the chit funds did
respond to the policy shock by re-sorting themselves, and the company did respond by altering the
structure of the institution, but these are only second-best responses.
this case
most hkely exacerbated the
inefficiencies that
This restriction on the dividend apphes to those subscribers
of 40
months duration, and the
fir.st
were already present
who win
in
in the financial system.
the auction in the
20 months for groups of longer duration.
33
Government intervention
first
10 months
for
groups
.
Appendix
7
Proposition
For
1.
all
t
N
<
AVi{N,p) = 6p^-^AVn
and AVpi {N,p)
= Nvlj-j] = Nv A 7.
Proof. While
Vj
is
the expected continuation payoff, denote the expected continuation payoff
after realization of the private signal at as vt
pN
There are
high types in the group, so
remains among the bidders,
t
=
...,pN
1,
—
first
1.
more than one high type
consider periods in which
The
payoff to the high type with signal a] can then be
written as
Vt
=
Pr
> max {V'}} {Vn +
{Vt
a\
-
Vt)
+ [\ -
Pr {^j
> max {C}})
(^^Vt+i
=
(^w —
Consider a (type-contingent) symmetric bidding function
^f
=
i^-N
N^-~t+i
"
^Y-t+i)
+
/
("^f)
(where / {a\)
is
6^
j^^^i
j^^ max {V'})
+
^V^t+i
)
+
/
an increasing function that approaches
(o"f)
and
as e -
the bound of the symmetric support of at - goes to zero).
We are interested in the
h = N^t+i i^N ~ ^^t+i) is
when e = 0) is
+
<^
6^
we
verify
whether
an equilibrium strategy. The expected payoff
Vt
for £
(which
=
is
0,
bidding
equal to
vt
= Pr{6;>max{6r}}(y;v-^^/^^(F;v-5F,+ i))
Vt
where Pr
case where e goes to zero, so
(1
- Pr
> max Ibt
+
bidding - say
bt
strictly lower:
Vn -
weakly dominated.
\\
{bl
=
> max {1;'}}) {sVt,, +
[^j^t+i
-
Note that there
is
no incentive to deviate either way. Over-
d - implies winning the auction with certainty; however the expected
jfz^^ [Vn - 6Vt+ij - d < pf^t+i (^^
It is
is
+ [N -
t)
utility is
SVt+i), and underbidding
is
easy to verify that this bidding strategy leaves the high types indifferent
between winning and losing the current auction: Vt
Similarly, there
J^^j/^, (^- - ^^*+0)
no incentive to deviate
Vt
=
6Vt+i
+
for the
— Vn
—bt
=
5Vt+i
jfzi^t-
low type, whose payoff
j^bt
= 6yM + j^_\^-^ iVN-svt+i)34
+
is
Now
In period
t
=
AVi
calculating
= pN,
—
Vt
is
y_f
straightforward:
only one high type
Now
is left.
bution shift (see Maskin and Riley (2000, proposition
Maskin and Riley
^
Q-pN
(2000):
^ = jr^i
The low type
bpN-
highest draw
g_pj^
—
e will
higher than
hpiM
zero,
is
ctJ
bpisi
<
e
is
AVi =
a high bid auction with a distri-
Consider the following bids as derived
^ = jf^^,
if
(liw
in
" 6VpN + i) +
the low type gets the
she have the same bid). As a result, the high type always wins the auction
She has no incentive to deviate provided e
Bidding lower
is
is
sufficiently small.
weakly dominated, while bidding
implies a payoff
=
^-N
+ ^( -
^pN
the other hand, bidding the equilibrium bid
Since
the auction
4.3).
Solving recursively,
(SAVi+i-
- 6VpN+i)+^ and
incentive to deviate either.
V-pN
On
=
never bid higher than the high type (only
will
for sure at the lowest price possible.
The low type has no
(Z/v
AVt
and
£
>
approaches
0,
there
bpj^.
is
As a
assures a payoff
h^
no incentive to deviate.
Now
for e
(and as a result a) approaching
the payoffs VpN are equal to VpN
result,
(i.e.
the expected payoff).
It
easy to verify that this bidding strategy leaves the low type indifferent between winning and losing
the current auction, giving us
As a
result,
AVpiv
=
-
VpN
=
VpN
= ^VpN+l +
AVJv-
Vj^
From the
bpiM
j^ -rjJSl ^T^
fact that
=y-N -
bpN-
AVi = S'^^'^AVpN.
it
now
follows that
AVj
=
F^-iAV/v = 8^^-^NA-^.
Note that
-
all
for
any subsequent period
the high types have already
Vt
t
= pA^+l, ...,iV, thebids
won and no
=
8Vt+i
(fore
=
0) are6j
longer bid - and as a result
+ j;^—bt = VN-bt
35
=
jJl^Ii {Y_;^
—
iSV^j+i)
References
[1]
ACKERBERG, DANIEL
A.,
AND Maristella BoTTiClNl,
2002. "Endogenous Matching and
the Empirical Determinants of Contract Form", Journal of Political Economy. Vol. 110, No. 3,
564-591.
[2]
[3]
Anderson, Robert
T.. 1966. "Rotating Credit Associations in India",
and Cultural Change,
14,:
Ardener, Shirley.
1964.
Economic Development
334-339.
"The comparative Study
of Rotating credit Associations", Journal
of the Royal Anthropological Institute of Great Britain and Ireland, 94(2): 201-229.
[4]
Banerjee, Abhijit V., Timothy Besley, and Timothy W. Guinnane.
bor's Keeper:
The Design
of a Credit Cooperative with
1994.
"Thy Neigh-
Theory and a Test". The Quarterly
Journal of Economics 109(2): 491-515.
[5]
Banerjee Abhijit
V., Dilip
"Inequality, Control Rights
Political
[6]
Economy.
[7]
1978.
"The Economic Role
Savings and Development
4:
249-263.
and
credit Associations.",
American Economic Review, vol.83
BONNETT, Audrey W..
Bouman,
Economic Studies
61: 701-719.
F.J. a.. 1995. "Rotating and Accumulating Savings and credit Associations:
Dasgupta,
New
a.,
1962.
"Kyes and Mujins
Korea". Economic Development and Cultural Change
Nayar, C.P.S. and Associates.
1989.
Delhi: National Institute of Public Finance
Fernando, Edgar.
A
De-
vol.23, no. 3: 371-384.
Campbell, Colin D. and Chang Shick Ahn.
India
[13]
no. 4: 792-810.
Analysis of Rotating Credit Associations Washington: University Press of America, Inc.
diaries in south
[12]
of Rotating Sav-
1981. Institutional Adaptation of West Indian Immigrants to America:
velopment Perspective", World Development
[11]
and Credit Institutions
Besley, Timothy, Stephen Coate, and Glenn Loury, "Rotating Savings and Credit
An
[10]
Maharashtra". Journal of
of Traditional Savings
Associations, Credit Markets and Efficiency", Review of
[9]
in
Besley, Timothy, Stephen Coate, and Glenn Loury, "The Economics
ings
[8]
and Rent Seeking: Sugar Cooperatives
Vol. 109, No.l.
Begashaw, Girma.
in Ethiopia",
Mookherjee, Kaivan Munshi, and Debraj Ray. 2001.
and
-
Financial Interme-
11: 55-68.
Urban Informal Credit Markets in
Policy.
1986. "Informal credit and Savings Organizations in Sri Lanka:
System", Savings and Development 3:253-263.
36
The Cheetu
[14]
Geertz, Clifford.
1962.
"The
rotating credit Association:
Economic Development and Cultural Change
[15]
A
"Middle Rung"
in
Development".
10(3): 241-263.
Levenson, Alec R. and Timothy Besley.
1996.
"The Anatomy
of an Informal Financial
Market: Rosea Participation in Taiwan". Journal of Development Economics 51: 45-68.
[16]
Maskin, Eric, and John Riley.
2000.
"Asymmetric Auctions", Review of Economic
Studies,
67, 413-438.
[17]
MUNSHI, Kaivan and Jacques Myaux. 2002. "Development
An
[18]
Change:
Application to the Fertility Transition". University of Pennsylvania, mimeo.
Schrieder,
Gertrud R, Carlos
E.
Cuevas.
Cameroon". In Adams, Dale, W. Fitchett, Delbert
countn.es.
[19]
as a Process of Social
1992.
"Informal
Financial
Groups
in
A., eds. Informal finance in loiu-income
Boulder and Oxford: Westview Press.
Shah, T. and M. Johnson,
1992. "Informal institutions of financial intermediation:
value of Vishis, Chit Funds and self help groups", Institute of Rural
Social
Management, Anand.
mimeo.
[20]
Townsend, Robert M..
1994. "Risk
and Insurance
in Village India".
Econometrica 62(3):
539-591.
[21]
Udry, Christopher.
1994. "Risk and Insurance in a Rural Credit Market:
Investigation in Northern Nigeria". The Review of
[22]
Vaidyanathan, R. and K. Sriram,
of
2000.
Economic Studies
The Non-Banking
Management, Bangalore, mimeo.
37
An
Empirical
61(3): 495-526.
Financial Sector. Indian Institute
—
Figure
0.7
1
;
Choice of
Ciiit
Value
i
0.6
10
•
\
:
\
0.5 0)
;
N
;
\
:
ni
>
o
O) 0.4
c
10
o
o
°
X
0.3
X
X
~"^^
^
25^
50
-^.^^
15
re
xi
o
i_
CL
':--.-.-;.~;-:~:^..^.
0.2
:
^
-^^^^^
0.1
100
____^
——
y-
---^^
'
^
15
"^
30
1
4
6
Income (thousands of
8
Rs.):
bw=2.5
10
12
Figure 2: Bids
0.4
Long 19 93
0.35
Low
Chit
Values
1
\v
Long 19 94
0.3
^
n
£u
-
1
v.
"S,
N
0.25
Short 1994
NX
o
Io
\ X
\^
-
V-.-i,
0.2
\\ X X
\ X
\^ X
Short
CO
1
993
\^
X
K
"XX
0.15
-
^
Vx.
X
0.1
" ^ - -"-~~-~-l — __
1
0.05
1
0.1
0.2
0.3
1
0.4
0.5
0.6
0.7
Timing (proportion of group duration): bw=0.075
0.8
0.9
Figure 3: Bids
0.5
1
1
-
Medium
1
1
Chit
Values
1
1
1
0.45
0.4
\^
Short 1993
.0.35
0)
>
0.3 _
___I^^
Short 1994
c
o
o0.25
Q.
O
^\^
^"''^^-cV'-^
\^Long
-~-<^
1993
':
\.
^^^
1994""^
Long
T3
S
0.2
^v
:
^\
;
0.15
0.1
\
-
'
0\^
0.05
i
0.1
i
0.2
i
0.3
0.4
1
1
1
0.5
0.6
0.7
Timing (proportion of group duration): bw=0.075
"^-^-J "^^^
0.8
0.9
-
Figure 4: Bids
0.7
1
-
High Chit Values
1
0.6
--X
;
0.5
ra
io.4
o
-
Short 1993
Long
1
99 3
2
lo3
o
Short 1994
~~^-.„^^
.
Long 199
CO
0.2
\^
^^^C^;_v
^-^
0.1
0\
^^"^^-^
\
^"^^
^..___
1
0.1
1
0.2
0.3
0.4
0.5
0.6
0.7
Timing (proportion of group duration): bw=0.075
0.8
0.9
Figure 5: Proportion of Sliort Duration Groups
0.8
1
1
y
0.7
,.-
1
'.^
/
/
(A
/
0.6
a.
/
o
Medium
m
/
\
0.5 -
\
\
o
N
:
/
z:^^^^-
o0.4
o
eo
o
-/
-
;
'J"
/
—
-
.^.^^^
_
;
// /
/
0.3 -
//
//
//
Higli
//
//
0.2
Low
1992
1993
1994
1995
i
i
i
0.1
1997
1996
Year
1998
1999
2000
2001
Table
Dependent
1:
Chit Value-Income Relationship
chit value
variable:
Chit value (thousands of Rs):
A. Multinomial
logit
10
15
25
30
50
100
(1)
(2)
(3)
(4)
(5)
(6)
model
Income
-0.156
0.009
0.030
0.058
0.071
(0.010)
(0.012)
(0.009)
(0.008)
(0.009)
1.574
-0.528
0.147
-0.040
-1.345
(0.041)
(0.051)
(0.041)
(0.040)
(0.050)
Constant
B. Linear probability model
Income
-0.003
-0.0001
0.00006
-0.0003
0.001
0.003
(0.0003)
(0.0002)
(0.0003)
(0.0002)
(0.0003)
(0.0001)
0.409
0.083
0.175
0.137
0.158
0.038
(0.004)
(0.002)
(0.003)
(0.003)
(0.003)
(0.002)
Constant
Note: chit value
is
the product of the
Chit value and income are measured
Muhinomial
logit
model
Linear probability model
Number of observations
is
is
monthly contribution and the duration.
in
thousands of Rs.
estimated with chit value=30 as the base
\
alue.
estimated independently for each chit value.
in all regressions is 20,885.
Standard errors in parentheses.
Table
2:
Group Level
Descriptive Statistics
Breakdown of total groups
m
each
chit
value (%)
Chit value (thousands
ofRs):
10
15
25
30
50
100
(1)
(2)
(3)
(4)
(5)
(6)
Duration
LOW
20 months
HIGH
17.75
3.41
1.72
4.42
3.59
11.30
8.40
-
25.77
--
23.08
10.43
30 months
--
96.59
--
30.94
--
11.30
40 months
73.56
-
71.82
5.52
12.31
41.74
0.28
~
0.69
--
61.03
13.91
60 months
-
~
-
59.12
--
1.74
100 months
—
—
—
—
—
9.57
100.00
100.00
100.00
100.00
100.00
100.00
1059
381
291
181
195
115
SHORT
25 months
LONG
50 months
Total
Total
MEDIUM
number of groups
Note: Chit value
is
the product of the monthly contribution and the the
Number of participants
Groups
is
number of participants
in the group.
equal to the duration of the group in months.
are divided into three aggregate chit values (low,
medium, high) and two aggregate durations
(short, long).
Table
3:
Individual Level Descriptive Statistics
Low
Chit value:
Medium
High
9Q3
1994
1993
1994
1993
1994
(1)
(2)
(3)
(4)
(5)
(6)
2.90
2.98
3.66
3.66
4.84
7,59
(2.70)
(3.06)
(4.79)
(3.00)
(9.12)
(35.94)
0.01 quantile
0.65
0.65
0.90
0.90
1.00
1.00
0.05 quantile
1.00
1.00
L25
1.19
1.50
1.50
0.10 quantile
1.14
1.12
L52
1.55
1.86
1.94
0.25 quantile
1.63
1.70
2.23
2.24
2.58
2.71
0.50 quantile
2.47
2.50
3.00
3.03
3.55
3.83
0.75 quantile
3.50
3.50
4.10
4.33
5.00
5.25
0.90 quantile
4.90
5.00
5.79
6.00
7.35
8.00
0.95 quantile
5.99
6.25
7.48
7.40
10.00
10.00
0.99 quantile
9.24
10.00
12.45
12.50
33.33
60 00
0.17
0.23
0.15
0.20
0.12
0.24
Year:
1
A. Income Distribution (individual subscribers)
Mean
(standard deviation)
B. Proportion of corporate subscribers
Note: Income
Aggregate
is
measured
chit value:
Low
in
thousands of Rs.
if chit
value=IOOOO,
Medium
if
10000<chit value<50000. High
if chit
value>=50000.
Table
Dependent
Timing
variable:
Low
Chit value:
Medium
1994
1993
Year:
Corporate subscriber
Number of observations
Note: Timing
is
Low
measured
if chit
as the
Standard errors
in parentheses.
1994
1993
1994
(1)
(2)
(3)
(4)
(5)
(6)
-0.124
-0.105
-0.144
-0.151
-0.118
(0.005)
(0.006)
(0.007)
(0.006)
(0.010)
(0.008)
0.535
0.543
0.530
0.543
0.529
0.541
(0.002)
(0.003)
(0.003)
(0.003)
(0.003)
(0.004)
21,400
14,635
14,300
13,411
7,555
6,750
winning month divided by the
value=10000.
Corporate subscriber equals one
1993
High
-0.124
Constant
Chit value:
Timing of Winning Bids
4:
if
Medium
if
total
duration of the group.
10000<chit value<50000. High
finance company, zero otherwise.
if chit
value>=50000.
Table
Dependent
5:
Preliminar>' Sorting Regressions (1993)
Corporate subscriber
variable:
(1)
(2)
Low
A. Coarse Partition of chit value (Nv)
(4)
Medium
(5)
High
0.012
0.016
0.095
(0.008)
(0.007)
(0.012)
Short duration
0.177
0.130
0.115
(0.003)
(0.005)
(0.004)
20,806
10,723
7,394
Low
Medium
High
Constant
Number of observations
(3)
B. Coarse partition of contribution (v)
0.022
0.023
0.061
(0.012)
(0.007)
(0.008)
Short duration
0.176
0.129
0.115
(0.003)
(0.005)
(0.004)
Number of observations
19,398
10,727
8,798
C. Fine partition of chit value (Nv)
10,000
Constant
Short duration
dummy
measured
50,000
0.034
0.056
0.085
0.150
(0.013)
(0.026)
(0.015)
(0.026)
0.180
0.130
0.090
0.087
0.149
(0.003)
(0.006)
(0.022)
(0.005)
(0.009)
17725
4696
784
3683
2063
m
Rs.
Low if chit value= 10000, Medium if chit value 10000-50000, High if chit value>=50000.
Contribution: Low if contribution<500/month. Medium if contribution 500-1000, High if contribution>1000.
Chit value:
Corporate subscriber equals one
if
finance company, zero otherwise.
Short duration equals one if the group
Regressions use 1993 data only.
Standard errors
in parentheses.
is
100,000
0.009
Number of observations
is
30,000
(0.008)
Constant
Note: Chit value and Contribution
25.000
of less than 40 months duration.
Table
Dependent
Bid
variable:
Low
Chit value:
Medium
Long
Short
Duration:
(1)
Period
1
Period 2
Period 3
Period 4
Period 5
Period
Period
1
*
1994
dummy
2* 1994 dummy
Periods
*
1994
Period 4 * 1994
Periods
*
1994
dummy
dummy
dummy
is
Chit value:
if chit
Each group
is
0.345
0.466
0.357
0.527
(0.002)
(0.002)
(0.004)
(0.002)
0.202
0.310
0.262
0.371
0.263
0.418
(0.002)
(0.001)
(0.001)
(0.002)
(0.003)
(0.002)
0.137
0.220
0.173
0.275
0.173
0.304
(0.002)
(0.001)
(0.001)
(0.002)
(0.003)
(0.002)
0.090
0.117
0.101
0.181
O.IIO
0.197
(0.002)
(0.001)
(0.001)
(0.002)
(0.003)
(0.002)
0.062
0.065
0.064
0.076
0.064
0.085
(0.002)
(0.001)
(0.001)
(0.002)
(0.003)
(0.002)
0.002
-0.074
-0.051
-0.169
-0.064
-0.224
(0.003)
(0.001)
(0.002)
(0.003)
(0.005)
(0.003)
0.008
-0.039
-0.004
-0.084
-0.001
-0.123
(0.003)
(0.001)
(0.002)
(0.003)
(0.004)
(0.003)
-0.003
-0.001
-0.006
-0.017
0.005
-0.031
(0.003)
(0.001)
(0.002)
(0.003)
(0.004)
(0.003)
-0.013
-0.005
-0.006
-0.002
-0.003
-0.009
(0.003)
(0.001)
(0.002)
(0.003)
(0.004)
(0.003)
-0.010
-0.009
-0.010
-0.009
-0.006
-0.014
(0.002)
(0.001)
(0.002)
(0.002)
(0.004)
(0.003)
5470
29543
13204
13732
2286
11697
Medium
if chit
than 40 months.
divided into 5 equal periods: Period
in parentheses.
(6)
0.368
chit value.
value 10000-50000, High
Long
1-
if chit
value>=50000.
duration groups last for 40 months or more.
Period
coefficients highlight bids greater than 0.3 in
Standard errors
(5)
(0.001)
value=10000.
last for less
(4)
(3)
Long
Short
0.258
measured as the bid amount divided by the
Low
Short duration groups
Bold face
(2)
High
Long
Short
(0.002)
Number of observations
Note; Bid
Bid Regressions
6:
5,
Rows
covering
1-5
its
entire duration in sequence.
and the change
in those bids in
Rows
6-10.
Table
Dependent
7:
Sorting Regressions (1993 versus 1994)
Corporate subscriber
variable:
Low
Chit value/Contribution:
Medium
Long
Short
Duration:
(1)
A. Partition bv
1
994
(3)
(2)
High
Long
Short
Long
Short
(4)
(5)
(6)
chit value (Nv")
dummy
Constant
Number of observations
0.004
0.066
0.030
0.063
0.045
0.133
(0.011)
(0.005)
(0.006)
(0.008)
(0.019)
(0.007)
0.189
0.177
0.145
0.130
0.210
0.115
(0.008)
(0.003)
(0.005)
(0.005)
(0.015)
(0.005)
5,470
29,543
13,204
7,832
2,280
11,697
B. Partition by contribution (v)
1994
dummy
Constant
Number of obsep.'ations
Note: Corporate subscriber equals one
if
-0.010
0.066
0.023
0.063
0.044
0.133
(0.017)
(0.005)
(0.006)
(0.008)
(0.011)
(0.007)
0.198
0.176
0.152
0.129
0.176
0.115
(0.012)
(0.003)
(0.005)
(0.006)
(0.009)
(0.005)
2.088
29.788
13,344
7.587
5.522
11.697
finance company, zero otherwise.
Low if chit value= 10000, Medium if chit value 10000-50000. High if chit value>=50000.
Contribution: Low if contnbution<500/month. Medium if contribution 500-1000, High if contribution>1000.
Chit value:
Short duration groups
last for less
Standard errors in parentheses.
than 40 months.
Long
duration groups last for 40 months or more.
Table
8:
Change
Term
in
Structure and Participation
Low
Chit value;
Medium
High
1993
1994
1993
1994
1993
1994
(1)
(2)
(3)
(4)
(5)
(6)
Private subscribers
7,688
11,331
12,133
10,772
6,637
5,108
Corporate subscribers
3,713
3,304
2,167
2,639
929
1,643
Year:
Panel
Panel
Panel
A
B
C
:
:
:
Subscriber participation
Proportion of short duration groups
Distribution of group durations
0.217
0.318
0.573
0.656
0.217
0.359
(0.017)
(0.023)
(0.025)
(0.024)
(0.033)
(0.037)
14.65
21.26
2.05
4,69
6.83
4.79
7.07
10.51
8.70
8.85
11.80
22.75
(%)
Duration:
20 months
SHORT
25 months
30 months
—
-
46.55
52.08
3.11
8.38
40 months
78.11
67.99
27.11
22.40
16.77
20.96
0.17
0.23
LONG
50 months
60 months
..
100 months
—
~
—
100
100
Total
Note: Chit value:
Low
Short duration groups
if chit
value=10000.
last for less
Medium
than 40 months.
if chit
Long
44.10
32.34
11.18
10.18
—
—
6.21
0.60
100
100
100
100
value 10000-50000, High
A reports number of participants in each chit value in each year.
Panel
B measures proportion of short
if chit
value>=50000.
duration groups in each chit value in each year using group level data.
Proportion of short duration groups in 1994
C
—
11.98
duration groups last for 40 months or more.
Panel
Panel
1.79
13.81
is
significantly higher, at the 5 percent level, for
all
values.
reports distribution of group durations in each chit value in each year (measured as percentage of all groups).
Standard errors in parentheses.
Table
Low
Chit value:
Interest rate
1994
Note: Short duration groups
Low
Long
Short
(1)
(2)
(3)
(4)
(5)
16.48
14.15
18.92
18.17
24.18
20,88
(0.36)
(0.12)
(0.32)
(0.63)
(1.02)
(0.56)
17.00
9.95
14.52
8.77
16.58
8.38
(0.42)
(0.04)
(0.15)
(0.16)
(0.37)
(0.13)
(6)
if chit
last for less
value=10000.
than 40 months.
Medium
if chit
Long
duration groups
value 10000-50000, High
last for
if chit
40 months or more.
value>=50000.
interest rate (in percentage) with standard errors in parentheses.
Interest rates are
All
High
Long
Short
(%)
1993
Mean
Rates
Medium
Long
Short
Duration:
Chit value:
9: Implicit Interest
means
computed
for short
at the
group
level.
and long duration are different
at
the
5%
significance level except
Columns 3-4
(1993).
3837 038
Date Due
MIT LIBRARIES
3 9080 02618 4579
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