Group Identity and Social Mobility in India∗
Rajiv Sethi†and Rohini Somanathan‡
June 23, 2010
Abstract
Wage and skill inequalities across social groups in many parts of the world narrowed
during twentieth century. This was a result of both changes in labor markets accompanying modernization processes and redistributive policies that accompanied the spread of
democracy. In India, the period following political independence witnessed a systematic
expansion of local public goods and a compression of basic educational outcomes. One of
the puzzling patterns within this overall picture of greater social equality is the asymmetry in the gains made by different social groups. The Scheduled Castes and the Scheduled
Tribes were equally disadvantaged in the pre-independence period and there was much
more overt discrimination against the castes. Yet the castes experienced greater mobility
on average than the tribes. We document these changes and explain them using a model
in which individuals have social identities which determine the nature of competition for
public goods from the state. We argue that many of the observed empirical patterns can
be explained by the relative geographical isolation of the tribes and the co-habitation of
the castes with politically active groups.
1
Introduction
Contemporaneous inequalities across social groups in many parts of the world are small by historical standards. The spread of public education, economic expansion and specifically targeted
∗
We thank André Béteille, Meghnad Desai, Amitava Dutt, Joan Esteban, Hemanshu Kumar, Thomas Piketty
and Debraj Ray and E. Somanathan for helpful discussions
†
Department of Economics, Barnard College, Columbia University and the Santa Fe Institute
(rs328@columbia.edu).
‡
Department of Economics, Delhi School of Economics (rohini@econdse.org).
affirmative action policies are all important contributors to the narrower skill and wage gaps
experienced by disadvantaged groups over the course of the twentieth century. These changes
are particularly well documented for large countries, such as the United States and India, where
economic and social divides overlap and race, caste or ethnicity is the main axis of disadvantage. Unlike much of Western Europe and more recently China and East Asia, the emergence of
nation states in these cases did not weaken, and perhaps even accentuated, pre-existing social
identities.
A simple but typical characterization of the process of growth and equalization could be as
follows: The growth of modern industry creates both a demand for educated workers and
a surplus with which to educate them and provide local public goods. The growth of skilled
workers eventually leads to compression in the wage structure. If the economic and social divides
largely concur, then this process may also reduce group disparities. In addition, constitutional
provisions and democratic policy making may accelerate equalization through the introduction
of policies for preferential treatment and the targeting of spending in poor areas.
What remains unexplained by this narrative is the differential mobility among the disadvantaged. India is an interesting setting in which to study these disparities because of the continued
existence of a caste hierarchy with multiple groups and a long tradition of using caste to articulate and understand inequality. Colonial administrators routinely recorded caste in census
operations and affirmative action programs in India since the first half of the twentieth century
have been based on caste identities. In the absence of well-accepted racial or ethnic markers,
caste enumerations have been largely based on self-reported identities and, over the years, these
reports have included thousands of distinct groups. The specific position of some of these groups
has been intensely debated but the broad contours of the hierarchy are widely accepted.1
1
The effect of colonialism on caste hierarchies is controversial. Dirks (2001) argues persuasively that the
colonial power did not simply record caste, they reinvented it to help establish its undisputed superiority over
former Indian rulers:
What Orientalist knowledge did most successfully in the Indian context was to assert the precolonial
authority of a specifically colonial form of power and representation...Caste had been political all
along, but under colonialism was anchored to the service of a colonial interest in maintaining social
order, justifying colonial power, and sustaining a very particular form of indirect rule...By the time
of the first decennial census of 1872, caste had become the primary subject of social classification
and knowledge (Dirks 2001; Chapter 1, pp. 14-15).
2
In the 1950s, soon after political independence, the several thousand castes and tribes that
had previously been enumerated in the Indian census were classified into one of four categories:
Scheduled Castes (SCs), Scheduled Tribes (STs), Other Backward Classes (OBCs) and a residual
category often referred to as the General or Forward Castes (FCs). In 1961, SCs and STs
were 15% and 7% of the population respectively2 and became the recipients of a range of
affirmative action policies leading to their greater representation in politics, state employment
and publicly funded education. The Other Backward Classes was a category designed to include
poor and socially backward individuals, irrespective of caste, but the only official lists of these
communities are based only on caste and the terms Other Backward Classes and Other Backward
Castes are now used interchangeably. The census has never enumerated the OBCs and they
are believed to be between 30-50% of the population.3 The OBCs first began to received castebased preference in public employment in the nineties and affirmative action towards them has
recently been extended to higher education. Castes not included among the STs, SCs and
OBCs are defined as General based on the absence of any legally institutionalized preferential
treatment by the state.
The combination of massive programs of public good construction in Indian villages, caste-based
reservations in political bodies and preferential selection in education and employment resulted
in considerable convergence in educational and occupational outcomes across social groups 4
The gaps observed today are, as a result, small in historical perspective. In 1931, although 17%
of Indian males were literate, male literacy rates varied from 60% among the Kayasthas, who
were employed in large numbers in the colonial administration, to less that 1% among many
of the groups that later formed the Scheduled Castes and Scheduled Tribes. By 1961, male
literacy was 34%, overall literacy was 24% and literacy rates for SCs and STs were 10 and 8.5
percent respectively. In 2001, literacy rates were, respectively, 54%, 45% and 38% for the these
three groups5
2
3
(Census of India 1961 1966; p. XLIV )
The National Sample Survey of 2004-2005, a nationally representative household survey of over 1,00,000
households across the country reports the current shares of the four groups to be roughly 9%, 20%, 41% and
30% respectively. The shares for the SCs and STs reported in the 2001 census are 16.2% and 8.2% respectively,
so the discrepancy in the two sources for the SCs is considerable (http://censusindia.gov.in and National Sample
Survey Organisation (2007).)
4
An excellent discussion of the range of affirmative action programs and their likely effects on mobility can
be found in (Galanter 1984; chapters 3 and 4 ).
5
All literacy rates have been computed as total literates in the group divided by the total population of the
group. These may be lower than literacy rates typically reported because the latter exclude the population
below 6 years of age. An age-wise break up is not available by caste for the colonial period and we have therefore
3
Gaps at higher levels of education also narrowed, but more slowly: only 11% (SCs) and 7.7%
(STs) of the relevant age group completed 8 years of school in the mid-seventies as compared
with over a fifth of comparable children in other social groups. In 1927 out of 55,000 college
students in India only 82 or less than one-sixth of 1 per cent were from these groups, this
number had gone up to between 1 and 2 per cent by 1961 (Galanter 1984; p. 60-61) Both SCs
and STs also occupied a higher fraction of rapidly expanding public employment in the postindependence period. Between 1953-1975 the SC share of jobs in central government in higher
administration went from .3 to 3.4 per cent (or from 20 to 1,201 employees) and for STs from .1
to .6 per cent. The share of clerical jobs went from 4.5% to 11% for SCs and from .47 to 2.3%
for STs.
One of the puzzling patterns within this overall picture of greater social equality in India is the
asymmetry in the performance of the disadvantaged castes and tribes. As seen in the above
figures, the castes gained more than the tribes in both education and employment. This is in
spite of very similar levels of literacy in the 1930s and far greater overt discrimination against
the castes who were commonly referred to even in official colonial documents as the Exterior
Castes and Untouchables (Hutton 1933; p. 471, 502). Atrocities against these groups have
occurred and, in some places, continue to occur over their access to water, inter-caste marriage
and their refusal to perform their traditional tasks (Mendelsohn and Vicziany 2002; chapter 2).
Accompanying the mobility gains of the disadvantaged castes is their greater political visibility.
The Bahujan Samaj Party (BSP), a major political party under Scheduled Caste leadership,
was formed in the mid-1980s, and in 2007 came to power in India’s most populous state, Uttar
Pradesh. In contrast, parties explicitly representing tribal interests have had limited political
success until very recently, even in constituencies where various tribes form a majority of the
population. The Scheduled Castes have succeeded in forming political alliances with many of
the upper castes but there appears to be little solidarity among the different tribes inhabiting
even the largely tribal states such as Jharkhand (Guha (2007) Chandra (2004) Pai (1999)). This
asymmetry also appears in a study of voting behavior of the two groups. In the early seventies,
the Congress party dominated Indian politics and won two-thirds of SC seats and three-quarters
of ST seats. By the early nineties it had lost many of the SC seats but retained two-thirds of
the ST seats. This changing balance of political power was reflected in the distribution of public
spending by the state and parliamentary constituencies with high concentrations of Scheduled
Castes received a disproportionate share of public amenities constructed during the 1971-1991
period, while those inhabited by the Scheduled Tribes received systematically less than the
included all ages to make rates comparable across years.
4
average constituency (Banerjee and Somanathan 2007).
This paper seeks to explain the contrasting fortunes and the political behavior of the different
caste groups in India using a model in which social groups collectively determine the political
effort of their members in obtaining public goods. Since the location of pubic amenities is
village-based, the share of total public goods received by a village depends on the total effort
of various groups within the village relative to those outside. That is, public good allocations
by the state depend on the intensity of collective action by geographical units. Individual
contributions to collective action depend, however, on the social group to which they belong.
We assume that social groups can impose on their members the level of effort that maximizes
the expected gains for the group as a whole, and use this framework to argue that many of the
observed empirical patterns can be explained by the relative geographical isolation of the tribes
and the co-habitation of the disadvantaged castes with other politically active groups.
The detailed structure of the model is as follows. There are a finite number of social groups
(castes), the members of which are distributed across a finite number of locations (villages).
Access to local public goods is determined by the aggregate collective action efforts at the village
level. Such efforts are individually costly, and are determined with the aggregate welfare of the
group in mind. In other words, groups (either through their leaders or other collective decisionmaking mechanisms) choose the levels of effort made by their members at different locations,
which in turn determines aggregate efforts at those locations and hence the distribution across
space of local public goods.
Under these conditions, the levels of effort chosen by groups depend in complex ways on the
manner in which they are distributed across locations and the characteristics of those with
whom they share space. In general, there are two important effects that arise. First, there are
positive inter-group spillovers at any given location: high efforts by one group result in greater
public goods access for all those with whom they reside. This creates advantages for those who
share space with high benefit (and hence high effort) groups. In addition, those residing in
large villages put in lower levels of effort, but will benefit from the efforts of a larger number of
individuals, and have greater access to public goods as a result.
Second, there are negative intragroup spillovers across locations: high efforts by a group at one
location reduce public goods availability to their own members at other locations. There is a
sense in which each group is competing against itself for local public goods. This tends to lower
effort, especially in groups with high levels of fractionalization.
5
We calibrate this model using data on the size and demographic composition of villages in
India. This is done by first classifying villages into seven possible demographic types, and using
the size, composition and frequency of occurrence of each type. We find that if the benefits
of public goods access are equal for scheduled castes and scheduled tribes, and lower for these
groups relative to the other classes, then the scheduled castes are the beneficiaries of substantial
intergroup spillovers and have considerably greater access to public goods than scheduled tribes.
However, they also put in less effort, since they share space with a high effort group. The result
is lower levels of access among scheduled tribes (relative to scheduled castes) as well as lower
levels of intragroup inequality in access.
We then extend the model to consider some of the dynamic effects of access. In the case of
educational goods, greater access increases one’s ability to compete for modern sector jobs
that pay a wage premium over unskilled employment. This increases the marginal returns to
access for groups that are initially very low in the skill distribution, and induces such groups to
increase their levels of effort. Over time, however, the skill premium itself declines as a result of
an increasingly skilled population, lowering the marginal returns to effort for all groups. This
gives rise to a first-mover advantage: groups that raise their skill levels early, either through
their own efforts or through the efforts of those with whom they reside, will end up at higher
skill levels than those who make a slower start. We show how this process can give rise to a
surge of effort among scheduled castes (relative to scheduled tribes).
More generally, as development occurs through time, groups shift their allocations away from
villages which have achieved high skill levels and towards those that have been previously
neglected. This causes others groups to reallocate their own effort levels in response, picking
up slack at some locations and lowering effort intensity at others. The calibrated dynamics
reveal scheduled castes separating themselves from scheduled tribes and narrowing the gap
between their skill levels and those of the initially more advantaged group. It is important
to note that this occurs despite our assumption that scheduled castes and tribes are ex ante
identical with respect to skill levels, and face the same benefits of access to public goods. That
is, the divergence in the fortunes of the two disadvantaged groups arises in this model only as
a consequence of differences in their distribution across space, and the size and demographic
composition of the villages that they inhabit.
There is a large literature that relates demographic composition to collective action and public
goods and examines the role of measures of fractionalization on collective action.6 The results
6
This is surveyed in Banerjee et al. (2008).
6
on fractionalization are mixed. The basic framework used in these studies is one in which the
demographic composition of the village or unit receiving the good determines collective action
within the village. We depart from this assumption by allowing social identities to extend beyond
the village. We believe this is a more realistic approach, certainly for the Indian case where
established links between similar castes in different villages has been crucial to the successful
mobilization of the scheduled castes.
The next section documents patterns of historical disadvantage and village demography in
India. It also discusses mobility differences across the Scheduled Castes and Tribes. Section 3
presents a static model and characterizes equilibrium. In Section 4, we use a calibrated example
to compute within group inequality in public good access in the static models. Section ??
introduces some simple dynamics and traces the time path of collective action, public good
access and group mobility over multiple periods.
2
Historical Trends
Two features of the traditional caste system, hierarchy and endogamy, have tightly linked caste
identities to social mobility7 . Although the several thousands of castes into which the Indian
population is divided are not all placed in a well-accepted hierarchy, the notion of such a
hierarchy is an essential part of the caste system, and mobility is seen as a result of actions
taken collectively by the caste groups rather than individually by its members. 8
Inter-caste differences in social standing in the early part of the twentieth century were staggering. Many of the Scheduled Castes were considered Untouchables and barred from public
utilities such as roads and water sources, from shrines and from trade with other groups. J. H.
Hutton, a well known anthropologist and the Census Commissioner for 1931, comments on the
limited access to public facilities by exterior castes: (Hutton 1933; p. 483)
Generally speaking, if the exterior castes have succeeded in asserting their right to
7
8
Srinivas (1969), p.5
As Béteille points out in his study of a south Indian village in the 1960s, “..there are significant differences
between social mobility in the caste system and social mobility in the class system. In the latter, it is the
individual who moves up and down, whereas in the former, entire communities change their position.”(Béteille
(1996) p. 190)
7
use public wells, the higher castes have given them up...The same applies to the use
of dharamshalas and of public burning ghats and the burial grounds.
and on the enormous social divide between upper and lower castes:
...a caste has been found in Tamilnad, the very sight of which is polluting, so that its
unfortunate members are compelled to follow nocturnal habits, leaving their dens
after dark and scuttling home at the false dawn like the badger, hyaena or aard-vark.
The tribes were less subject to explicit atrocities but were typically too geographically isolated to
effectively use public facilities and also suffered on account of being offered a primary education
in a language that was not their own. Nomadic tribes and those that migrated seasonally also
found it difficult to combine regular schooling with their migratory lifestyle.9
Table 1 lists literacy rates at the time of the 1931 census for some major castes from each of
these categories. Male literacy rates varied from 60% among the Kayasthas who were employed
in large numbers in the colonial administration, to less that 1% among most of the Scheduled
Castes. Interestingly, the Iluvans (the only backward caste with literacy rates comparable to
the upper castes) were concentrated in Kerala which has historically had very good access
to public schools. This inequality in educational outcomes was accompanied by occupational
stratification. Professional jobs went almost entirely to the upper castes and the lower castes
and tribes were primarily engaged in agricultural labor or their traditional occupations.
Table 2 shows the proportion of these two groups in the rural and urban areas of each of the
major Indian states in 1961. The table includes only those states where the populations of both
of these groups was not insignificant. We see that both SCs and STs were more rural than
the rest of the population. This is especially true of the tribes, who were 7% of the Indian
population, but only 1% of its urban population. We also see that the distribution of the castes
was more even across the states while the tribes were concentrated in a handful of states in
central and eastern India.
It is not only the case that the tribes are regionally concentrated, they are also concentrated
in particular villages within a region.Figure 1 shows this concentration of Scheduled Tribes at
9
(Hutton 1933; p. 331) and (Sharma 1988; Chapter 4)
8
Table 1: Literacy by Caste, 1931
Caste
Occupation
Category
Kayastha
Administration
FC
60.7
1.61
Brahman
Priests
FC
43.7
8.9
Iluvan
Palm Growers
OBC
42.8
.71
Rajput
Warriors
FC
15.3
5.99
Teli
Oilmen
OBC
11.4
4.35
Mahar
Village Servants
SC
4.4
2.18
Yadava
Herdsmen
OBC
3.9
8.41
Bhangi
Scavengers
SC
1.9
.43
Gond
Agriculture
ST
1.6
1.49
Santal
Agriculture
ST
1.2
1.52
Bhil
Agriculture
ST
1.1
.43
Chamar
Tanners
SC
1
7.17
Source: Census of India, 1931
9
Literacy (M)
Share
Table 2: The Distribution of SCs and STs, 1961
State
%SC-rural
%SC-urban
India
16
9
8
1
Andhra Pradesh
15
9
4
1
Assam
6
7
18
7
Bihar
14
9
10
3
Gujarat
7
6
17
3
Kerala
9
5
1
0
Madhya Pradesh
14
10
24
2
Madras
21
10
1
0
Maharashtra
6
4
8
1
Mysore
14
10
1
0
Orissa
16
11
25
8
Rajasthan
17
13
14
1
West Bengal
24
8
8
1
Source: Census of India, 1961: V(a) and V(b)
10
%ST-rural
%ST-urban
Fraction of Vilages
.4
.2
0
0
.1
.2
.3
Fraction of Vilages
.4
.6
.8
Figure 1: The Fraction of SCs and STs in Indian Villages, 2001
0
.2
.4
.6
.8
Scheduled Caste Fraction
1
0
.2
.4
.6
.8
Scheduled Tribe Fraction
1
a more disaggregated level. The histograms in this figure use village level shares of the two
groups in 2001. There were roughly half a million villages in the major Indian states in 2001.
Of these, the ST population was less than 5% in over two-thirds of these villages and 7% of all
villages had ST shares of more than 95%. In contrast, about 40% of all villages had SC shares of
between 5% and 25% and there were very few villages with high concentrations of these castes.
Table 3 relates village demographic to the access to primary and high schools. Two interesting
pattens emerge from this table. The first emphasize a finding that we have already discussed;
villages that are homogeneous in STs and SCs do worse in terms of both literacy and school
access than the 18% of Indian villages where there are neither SCs nor STs. The second is
that both groups, but especially the tribes do much better when they are combined with the
higher castes. Mixed villages, defined as those with all three categories, do well, but they are
also significantly larger than the homogeneous villages and since size is an important factor in
public good allocation rules, it is hard to know the relative importance of demographics and
size in determining outcomes for these villages.
11
Table 3: Village Demographics and Access to Education
Village Composition
% Villages
Population
%Literate
% Primary Sch
% High Sch
ST
7
417
28
64
2
SC
1
329
41
43
2
Other Castes
18
815
50
65
7
SC and ST
1
392
30
61
1
ST and Other
7
573
41
73
4
SC and Other
42
1633
49
84
13
SC, ST and Other
25
1575
48
91
18
Source: Census of India, 2001: Village Directories
Intergenerational Mobility
While possible, it is not straightforward to examine relative changes in educational attainment
for each of these caste categories over time because of changes in definitions of both caste
status and educational categories. The lists of SCs and STs that were drawn up in the 1950s
were specific to particular states of the country and to particular districts within each state
where the caste was believed to be socially disadvantaged. In 1976, many of these geographical
limitations within states disappeared and SC or ST status was typically extended to a caste or
tribe throughout a state if it had previously applied to the group in any part of the state. This
makes it difficult to use the data on SC and ST outcomes across census years to arrive at their
rates of mobility.
Figure 2 examines intergenerational mobility among the SCs and STs though figures for the
educational attainment of different age cohorts in the 2001 census. We consider two coarse and
extreme measures of attainment; literacy and college graduation. We find that for older agegroups outcomes for STs are similar to those for SCs, but this is not true for younger cohorts
suggesting a divergence between these two categories over time. This is especially stark for
college graduation rates. In each case, we compute attainment for only those age cohorts which
were old enough in 2001 to complete the required level. This leads us to include those above 13
years of age in our literacy computations, and those above 20 for graduation rates.
12
.03
Fraction completing a graduate degree, 2001
.01
.02
.8
.6
Fraction literate, 2001
.4
0
.2
13-17
18-19 20-29 30-39 40-49 50-59
age cohort
SC
60-69
ST
20-29
30-39
40-49
age cohort
SC
50-59
60-69
ST
Figure 2: Educational Attainment by Age Cohorts, 2001
We now turn to a model which tries to explain these patterns. In the following section we
use a model that relates village demographics, collective action and public good access. Our
model shows that, starting from similar levels of disadvantage, groups sharing villages with
those who have incentives to invest in collective action can experience greater mobility than
similarly disadvantaged groups that are isolated. This challenges much of the fractionalization
literature which does not explicitly allow for groups to be part of established social hierarchies.
3
A Model of Public Action
A population of size n is distributed across geographical units which we call villages. Each
individual is identified by his caste or social group i and his village k. The set of castes is
C = {1, . . . , c} and the set of villages is V = {1, . . . , v} . We shall use subscripts i and j to refer
to castes, and k and l to refer to villages.
Let ni denote the number of individuals who belong to caste i, and nik the number who are
13
both in caste i and reside in village k. That is,
X
nik = ni
k∈V
We begin with a static (single period) model and subsequently extend it to allow for multiple
periods. Suppose that there is a (possibly endogenous) measure of public goods that could be
allocated to one or more of the villages. The public good allocation secured by a village depends
on the political effort invested by the village, as well as the efforts made by the residents of
other villages.
Effort decisions are taken by each caste collectively in a manner that maximizes total expected
benefits for the group. Here we depart from the hypothesis, standard in economic models, that
individuals decide on actions based on their own private costs and benefits. We consider this to
be reasonable departure in the present context. Strong identification with one’s identity group
implies some degree of altruism towards fellow group members. More generally, we might want
this level of altruism to be limited, in the sense that the weights on the material payoffs of others
is smaller than that on one’s own; we view or more extreme assumption of equal weights as
a first approximation. A somewhat different context in which identity based preferences make
sense is that of voting in elections with a small number of well differentiated political parties.
In fact, group based objective functions have recently been used to explain both the levels and
comparative statics of voter turnout in precisely this case (Federson and Sandroni, 2006).
Let eik denote the effort level undertaken by individuals belonging to caste i in village k. Then
the effort level in village k is given by
X
µk =
nik eik
(1)
i∈C
Define the aggregate effort level ē at any effort profile as follows:
X
ē =
µl .
l∈V
Let pk denote the allocation of public goods to village k at time t, given by the function
pk = f (µk , µ−k ),
where f is assumed to be increasing in µk , and decreasing in µl for l 6= k. We assume that public
goods are perfectly divisible, and are allocated deterministically. A special case of this is
pk =
µk
.
ē1−α
14
(2)
for some parameter α ∈ [0, 1). This may be interpreted as follows: the total amount of public
good distributed across villages is ēα , and each village get a share of this that corresponds to
the share of village effort in total effort. If α > 0 then the aggregate supply of the public good
is increasing in effort; if α = 0 then there is a total of one (inelastic) unit of the public good to
be divided across villages.
Let bik denote the benefits of access per unit of the public good for each member of case i in
village j. For the moment we take these to be exogenous, and consider their determinants and
evolution over time below.
The cost to each individual from investing effort into the political process is given by an increasing and convex function c(eik ) satisfying c(0) = c0 (0) = 0. Although this cost is borne at
the level of the individual, the levels of effort eik across villages is determined collectively by
all caste members and maximizes expected welfare of the group, which is simply the expected
return from the public good minus aggregate costs.
The expected payoff to an individual in caste i and village k after public goods assignments
have been made is
πik = bik pk − c(eik ).
(3)
The expected payoff to caste i, aggregating across all villages, is therefore
πi =
X
nil (bil pl − c(eil ))
(4)
l∈V
This depends on the entire profile of effort levels e through the effect of these on the village
levels effort levels and public goods assignments.
Our main departure from the standard analysis of public action lies in our specification of the
determinants of effort. It is generally assumed that such choices are individualistic: each person
maximizes their own payoff given the effort choices of all others. Identity does not play a direct
role in effort choice, although aggregate efforts and access to public goods will vary across groups
and villages. We explore, instead, the case in which identity matters directly for effort choices:
group leaders set effort levels in such a manner as to maximize aggregate payoffs for the group,
given the decisions made by leaders of other groups, and allowing for variations in within group
effort across villages.
15
3.1
Identity and Effort
We consider identity based choices that are flexible in the sense that within-group efforts may
vary by location. An equilibrium profile of effort levels is such that no group i can gain from a
unilateral change in eik for any k. First order conditions for such an equilibrium are, for each
caste i and village k,
X ∂pl
∂c(eil )
nil bil
−
= 0.
∂eik
∂eik
l∈V
For the special case if assignments given by (2), we have, for l 6= k,
∂pl
nik µl (1 − α) ē−α
nik µl (1 − α)
=−
=−
2−2α
∂eik
ē
ē2−α
(5)
and
nik (ē − (1 − α) µk )
nik ē1−α − nik µk (1 − α) ē−α
∂pk
=
(6)
=
2−2α
∂eik
ē
ē2−α
where ē is the aggregate effort level as before. Using (5-6), the equilibrium conditions may be
written
X
nil bil µl = ē2−α nik c0 (eik )
n2ik bik (ē − (1 − α) µk ) − (1 − α) nik
l6=k
or, equivalently,
nik bik ē − (1 − α)
X
nil bil µl = ē2−α c0 (eik ).
(7)
l∈V
For future reference, let Vi denote the set of villages in which those belonging to group i reside:
Vi = {k ∈ V | nik > 0} ,
and let vi = |Vi | denote the number of villages in which group i has a presence. For any given
effort profile, define the locational advantage of group i as
X
X
λi =
nil bil
njl ejl .
(8)
l∈Vi
j6=i
This is a measure of the extent to which group i benefits from the efforts of those with whom
its members share space. Then the equilibrium conditions (7) may be written:
!
X
2
nil bil eil = ē2−α c0 (eik )
(9)
nik bik ē − (1 − α) λi +
l∈Vi
Note that λi is endogenous and depends on equilibrium effort levels of all groups other than i.
A few comparative statics results can be deduced immediately.
16
Proposition 1. At any equilibrium (i) effort is (weakly) monotonic in aggregate village benefit
for any group: nik bik > nil bil ⇔ eik ≥ eil for all i, with strict inequality if eik > 0, and (ii) if
nik bik is sufficiently small, then eik = 0.
Proof. If eik > 0 then the first order condition (9) must be satisfied. Note that the second term
on the left side of this condition is group but not location dependent, and hence is the same for
all villages. If nik bik > nil bil then the left side of (9) is higher for village k than village l, so the
right side must also be higher if the equation holds. By convexity of c, this implies eik > eil
since eik > 0 and eil either satisfies (9) or is zero. Hence eik > eil fails only if both eik = eil = 0,
proving the claim. To prove the second claim, note that if eil > 0 for any l then the second
term on the left side of (9) is strictly negative, so (9) cannot hold for nik bik sufficiently small.
In this case we must have eik = 0.
Hence equilibrium effort is zero in villages were aggregate benefits are sufficiently low (either
because a group’s presence there is very small, or the benefits are very low). More generally,
small villages will have low (or zero) effort levels, especially if the population is heterogeneous
with respect to identity at such locations. This means that highly fragmented groups spread
thinly across space will have low effort levels on the whole. Furthermore, groups with an
uneven population distribution, with high concentrations in some areas and low concentrations
in others, will have high levels of within group effort inequality. This will imply high within group
inequality in access to public goods, unless the fragmented populations happen systematically
to share space with high benefit and high effort groups.
3.2
Intragroup Symmetry
There are a large number of effects operating simultaneously in the determination of equilibrium
collective action and public goods access: village and group sizes, isolation and agglomeration,
locational advantage, and benefit differentials. It is useful to consider a special case of the model
to help us examine these mechanisms in isolation.
17
Suppose that members of the same group are symmetrically placed: they have the same benefits
and live in villages with the same size and demographic composition. In this case it is clear
from (9) that all individuals belonging to the same group will choose the same effort level in
equilibrium. This follows from the fact that the second term on the left side of this condition
is group but not location dependent, intragroup symmetry implies nik bik = nil bil for all villages
k and l, and c is convex. For simplicity we also assume that α = 0, so there is a single unit of
the public good that is allocated in proportion to village efforts.
Letting bi and ei denote the (common) benefit and effort levels in group i, condition (7) reduces
to:
ni bi ē − ni bi
X
µl = vi ē2 c0 (ei ).
(10)
l∈Vi
An immediate consequence is that any group that is evenly distributed across all villages (Vi =
V ) must choose zero effort. To see this, note that If Vi = V, then
X
µl =
l∈Vi
X
µl = ē
l∈V
and the left side of (10) is zero, implying ei = 0. Hence if all villages are identical in size
and composition (nik = n/cv for all i and k) then all efforts are zero. This is simply because
the supply of the public good is inelastic, and groups are completely indifferent regarding the
manner in which this is allocated across villages.
Under intragroup symmetry, (9) reduces to:
ni bi (ē − ni ei ) = vi λi + ē2 c0 (ei ) .
(11)
This allows us to identify the effects of benefit heterogeneity, locational advantage and fractionalization. First consider benefits:
Proposition 2. Consider two groups i and j such that (ni , vi , λi ) = (nj , vj , λj ). If bi > bj then
ei > ej in equilibrium.
18
Proof. Suppose that bi > bj and suppose (by way of contradiction) that ei ≤ ej . Then, since
vi = vj and c is convex, we have
vi λi + ē2 c0 (ei ) < vj λj + ē2 c0 (ej ) .
Also, since bi > bj and ei ≤ ej , we have
ni bi (ē − ni ei ) > nj bj (ē − nj ej ) .
These two inequalities are inconsistent with the requirement that (11) holds for both i and j.
Hence ei > ej .
Hence if two groups have the same size and locational advantage, and are spread across the
same number of villages, then the group with greater benefits will choose higher levels of effort.
Next consider locational advantage.
Proposition 3. Consider two groups i and j such that (ni , vi , bi ) = (nj , vj , bj ). If λi < λj then
ei > ej in equilibrium.
Proof. Suppose that λi < λj and suppose (by way of contradiction) that ei ≤ ej . Then, since
vi = vj and c is convex, we have
vi λi + ē2 c0 (ei ) < vj λj + ē2 c0 (ej ) .
From (11), we therefore obtain
ni bi (ē − ni ei ) < nj bj (ē − nj ej ) .
Since (ni , bi ) = (nj , bj ), this implies ei > ej , a contradiction.
So the group with smaller locational advantage chooses higher levels of effort. This does not
mean that this group has greater access to public goods, of course.
19
Finally, consider fractionalization, holding constant group size. For two groups of equal size,
the one that if more dispersed across villages has the greater fractionalization index.
Proposition 4. Consider two groups i and j such that (ni , λi , bi ) = (nj , λj , bj ). If vi < vj then
ei > ej in equilibrium.
Proof. Suppose that vi < vj and suppose (by way of contradiction) that ei ≤ ej . Then, since
λi = λj and c is convex, we have
vi λi + ē2 c0 (ei ) < vj λj + ē2 c0 (ej ) .
From (11), we therefore obtain
ni bi (ē − ni ei ) < nj bj (ē − nj ej ) .
Since (ni , bi ) = (nj , bj ), this implies ei > ej , a contradiction.
Groups that are more dispersed across space put in less effort and (holding constant locational
advantage) also have lower access to public goods. The effect of group size is ambiguous.
4
A Calibrated Example
Some of the properties of the static model may be explored numerically, based on a calibration
using the data in Table 3. This table identifies seven distinct village ”types” based on the set
of groups that are residents. Using data on the mean population composition in each village
type, we obtain the following:
20
Village Type
1
2
3
4
5
417
329
815
392
573
Number
7
1
18
1
7
42
24
ST share
100
0
0
76
53
0
18
SC share
0
100
0
24
0
23
18
OC share
0
0
100
0
47
77
64
ST population
24%
−
−
2%
18%
−
56%
SC population
−
1%
−
0%
−
69%
30%
OC population
−
−
16%
−
2%
56%
26%
Size
6
7
1633 1575
The most frequently occurring village type is also the largest, and contains a mixture of SC and
OC residents with the latter constituting a significant majority. Larger villages in general occur
more frequently and have significant OC populations. Villages without OC populations are small
and rare. The populations shares of the three groups are 9, 18 and 73 percent respectively.
The last three rows of the table show how individuals in each group are distributed across
village types. A majority of scheduled castes and other castes are found in villages of type 6,
which are large and contain no members of scheduled tribes. On the other hand, a majority of
scheduled tribes are in villages of type 7, which contain all three groups. Scheduled castes are
seldom isolated from other groups, while scheduled tribes and other castes are often found in
homogeneous villages.
Consider the case of 100 villages and assume that the benefits of access to the public good
satisfy b1k = b2k = 7 and b3k = 105 for all villages k. That is, there is within-group homogeneity
in benefits, and the two disadvantaged groups are symmetrically placed. Assume also that
c(eik ) = e2ik /2 and α = 1/2.Using the conditions (9) we can obtain equilibrium effort levels in
all village types numerically for each of the three specifications. These efforts determine access
to public goods by village, and hence inequality both within and among groups with respect to
access.
The following table shows the equilibrium effort levels by each group, and the public good
21
assignment to each village type in equilibrium, as well as mean effort levels by group (all
numbers have been multiplied by 104 ):
1
2
3
ST effort
0.0082
−
−
0.0057 0.0058
SC effort
−
0.0000
−
0.0000
OC effort
−
−
0.0000
−
Village Type
PG Access
4
5
−
6
−
7
Mean
0.0054 0.0062
0.0004 0.0000 0.0002
0.0000 0.0176 0.0000 0.0099
0.1077 0.0000 0.0000 0.0536 0.0559 0.7003 0.0485
It is clear from the table that although SC and ST benefits per unit of access are identical,
and they share the same effort cost function, their equilibrium behavior and payoffs are quite
different as a result of the difference in the manner in which they are distributed across space,
and the extent to which they reside of other groups. ST access to public goods is considerably
greater, despite the fact that they put in much less effort than SC individuals. This is because
two-thirds of their population resides in villages of type 6, which have the highest public good
access. These are the largest villages, and a majority of the SC and OC population lives in
them. All OC and SC effort is concentrated in villages of this type, with all other village types
being neglected. OC efforts are large, which is why such villages end up with superior access.
STs on the other hand, spread their efforts more evenly across village types and receive no
positive spillover from the efforts of other groups. In fact, positive intergroup externalities flow
from ST groups to each of the other two groups (in villages of type 4, 5 and 7).
Even though groups have been assumed here to be homogeneous, within group inequality
emerges endogenously from the process of assignment. Not only do the SC and OC groups
gain greater access, they end up with greater levels of within group inequality. The distributions of access are shown below:
ST access is very low compared to other groups. SC and OBC access is comparable, with SC
access being slightly greater. Although the village type with greatest access has a minority SC
presence, it happens to be that case that two-thirds of SCs actually reside in such villages. They
benefit greatly from OC effort.
The static model (with exogenous benefits) provides a snapshot of the process of collective action
and public good assignment, but a fuller account requires us to consider how access increases
22
75
ST
0
0
0.75
75
SC
0
0
0.75
75
OC
0
0
0.75
Figure 3: Inequality in Public Good Access within Castes
skills and changes the benefits of further access over time. We do this next.
5
Dynamics
We now consider the dynamics of benefits over time, as access to public goods alters levels of
human capital and hence the gains from further increases in access. Benefits depend on existing
levels of human capital for a variety of reasons. For instance, the wage implications of increased
access to schooling depend on the human capital level one begins with - too low a starting point
will not allow an individual to be competitive in the market for modern sector jobs.
Along these lines, consider a sequence of periods 1, 2... with collective action decisions and
public good allocations being made in each period. Let sik (t) denote the skill level of members
of caste i in village k in period t. We are assuming intragroup homogeneity at any given location,
although differences within groups across locations will arise endogenously as public goods are
23
assigned. The aggregate skill level in the economy is then
XX
s̄(t) =
nik sik (t).
k∈V i∈C
Higher skill levels allow individuals to compete for modern sector jobs: the likelihood of getting
a modern sector job is an increasing function q(sik ) of an individual’s skill level. Such jobs
pay a wage w(s̄) > 0, that is a decreasing function of the aggregate economy-wide skill share.
The alternative to a modern sector job is a job in the traditional sector, which pays a wage
normalized to equal 0. That is, w is the wage premium for a modern sector job, and depends
on the relative scarcity of skilled labor in the economy.
Access to public goods yield benefits because they increase the ability to compete for modern
sector jobs. Suppose that the increases in human capital depend on access as follows:
sik (t + 1) = sik (t) + γpk ,
(12)
where γ > 0 is a parameter. That is, access to each unit of a public good raises human capital
by a constant amount, independent of initial skill level.
Since q 0 (sik ) is the increase in the probability of modern sector work resulting from a small
increase in public good access, and benefits in period t are given by
bik (t) = γw(s̄(t))q 0 (sik (t)).
These benefits, previously taken to be exogenous, now depend on one’s own skill share and the
entire distribution of skills in the population. They determine levels of collective action and
hence public goods assignments as before, resulting in a new village and caste dependent skill
hierarchy from one period to the next.
As before, we may explore the properties of this process numerically using the distribution of
individuals across space described in Table 3. To do so we need to specify the functions q and
w. Suppose that
q(s) =
e(s−a)
1 + e(s−a)
where a is a parameter. Then
es−a
e2(s−a)
q (s) = s−a
−
.
e
+ 1 (es−a + 1)2
0
24
Mean Collective Action Levels by Caste
0.014
OC
SC
ST
0
0
300
Period
Figure 4: The Evolution of Collective Action by Caste
The wage premium is given by
w(s̄) = eω(1−s̄/s̄0 ) ,
where s̄0 is the initial mean skill level in the economy and ω is a parameter. The initial wage
premium is therefore equal to 1, and declines over time (as the aggregate skill level rise) at a
rate that is increasing in ω.
We set parameters ω = 2, γ = 0.1 and a = 5, with initial skill levels s1k = s2k = 0 and s3k = 3.
It is easily verified that initial benefits are then exactly as in the static example above. The
dynamics of efforts are depicted in the figure below.
Note that although SC efforts are initially very low, the rise sharply for a period of time as OC
efforts decline. The reason for the decline in OC efforts is that they reach skill levels at which
25
0.02
SC Effort by Village Type
6
0
7
0
300
Period
0.02
OC Effort by Village Type
6
7
3
0
0
300
Period
Figure 5: Effort by Village Type for the Scheduled Castes and Other Castes
the likelihood of modern sector employment is not appreciably increased by additional access
to public goods. A disaggregated look at the allocation of effort by SC and OC individuals
helps explain why the allocation of effort changes quite erratically over time as groups shift the
concentration effort from one village type to another.
Initially OC efforts are concentrated in village type 6, but as skill levels here rise, the marginal
returns to further increases fall. OC efforts (shown in the lower panel of the figure) then switch
to village type 7 (in which all groups are present), and subsequently to village type 3 (in which
OCs are isolated). As OC efforts drop off in specific village types, SC efforts pick up some of
the slack.
The dynamics of ST effort are very different. Unlike the other groups, ST effort is initially
26
ST Efort by Village Type
0.01
1
7
5
4
0
0
300
Period
Figure 6: Effort by Village Type for the Scheduled Tribes
spread across all villages in which they have a presence, but declines steadily over time. Only
when OC effort in village 7 declines does ST effort there pick up again. But ST effort never
reaches the heights that OC and SC efforts reach (figure below).
The resulting evolution of skills is depicted in the figure below. All groups experience increases
in skill through cumulative access to public goods, but a gap opens up between SC and ST
groups (which begin at the same skill level). This gap persists over time, due both the spillovers
from OC to SC groups, and the increase over time in SC collective action efforts. This seems
roughly consistent with the historical record.
6
Discussion
We see this paper as contributing to the literature that relates the demographic compositions
of geographical units to their ability to extract resources from the state and therefore generate
avenues for greater mobility. We have yet to explore many of the implications of this model,
generalize it to allow for both forward-looking behavior and endogenous wage setting and fit it
more carefully to Indian data.
27
10
Mean Skill Levels by Caste
OC
SC
ST
0
0
300
Period
Figure 7: The Evolution of Skills by Caste
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29