Core or Swing? The Role of Electoral Context in Shaping
Pork Barrel
Milan Vaishnav and Neelanjan Sircar∗
March 3, 2012
Abstract
For the past two decades, the framework of core and swing voters has been the analytical workhorse for
the comparative literature on distributive politics. While many studies have treated "core" and "swing" as
essentially static concepts, we argue that it is incorrect to assume a single, "true" pattern of distribution
over time. To the contrary, we put forward a framework and formal model for conceptualizing variations
in core and swing outcomes over time within the same distributive good, by considering the impact
electoral context may have on a party’s targeting calculus. We demonstrate these insights using a unique
dataset on the patterns of public school construction in the southern Indian state of Tamil Nadu from
1977-2007. Using multilevel modeling (MLM) statistical techniques with geo-coded time-series data,
we find that while there is a general pattern of rewarding core voters, there are heterogeneous effects
across elections. We find that the ruling party targets schools in "swing" constituencies when there are
a disproportionately large number of close races in the state. Thus, while ruling party politicians might
prefer to reward their most ardent supporters, they are constrained by electoral realities. The theoretical
framework and methodological tools highlighted in this paper have significant implications for the study
of distributive politics.
∗ Milan Vaishnav (mv2191@columbia.edu) and Neelanjan Sircar (ns2303@columbia.edu), Department of Political Science,
Columbia University, New York, NY 10027. A previous version of this paper was circulated under the title, "The Politics of Pork:
Building Schools and Rewarding Voters in Tamil Nadu." We would like to thank Jeremiah Trinidad for his assistance with the GIS
mapping and Sandip Sukhtankar for providing us with the assembly constituency maps. We would also like to thank Alessandra Casella, Lucy Goodhart, Sebastian Karcher, Massimo Morelli, Maria Victoria Murillo, Phil Oldenburg, Virginia Oliveros, Susan
Stokes, Pavithra Suryanaryan, Matt Winters, and seminar participants at the 2009 Midwest Political Science Association Conference
and Columbia University for comments and conversations that shaped this paper. All errors are our own.
1
1
Introduction
For the past two decades, the debate over whether parties reward core or swing voters has shaped the
comparative politics literature on distributive politics. Political parties wield enormous influence in settings in which clientelism, patronage, pork and other forms of particularlism thrive. The core-swing
framework was developed to try and get a handle on what strategies parties use when it comes to the task
of wielding particularism in an effort to maximize electoral support. This body of work has provided two
distinct explanations for how politicians direct rewards to their constituents; some argue that politicians
will prioritize redistribution to their "core" base of supporters, while other scholars posit that resources
will be targeted towards "swing" or "pivotal" voters. While many studies treat "core" and "swing" as
static concepts, we believe that it is incorrect to assume a single "true" pattern of targeting, as parties may
target core or swing voters based upon shifting electoral realities. The primary goal of this paper is to
explain variations, empirically and formally, in core and swing outcomes by considering the impact that
competitiveness of elections may have on a party’s targeting calculus.
To empirically demonstrate our insights, we analyze patterns of public school construction in the southern
Indian state of Tamil Nadu as a function of the margin of victory within assembly constituencies (ACs).
We compile a unique dataset that combines information on public education with electoral data to study
patterns of school construction from 1977-2007. We find that there is no one "true" pattern of targeting
consistent over time and space. While there is a general pattern of rewarding core constituencies, this
effect varies by election. We find that the ruling party targets schools to more "swing" constituencies when
there are a disproportionately large number of close races in the state. Thus, while ruling party politicians
might prefer to reward their most ardent supporters, they are constrained by electoral realities.
The relationship between core-swing targeting and electoral context is more complicated than it seems at
first blush. First, the term "competitive election" is difficult to define precisely. We argue that competitiveness should be divided along two dimensions. On a polity-wide level, we define competitiveness as a
function of the expected percentage of constituencies in which a party is victorious, or the expected seat
share. On a constituency level, we define competitiveness as a function of the extent to which all parties
battle over a large number of voters, i.e. the extent to which a constituency is a "swing constituency."
Second, the expected seat share and transfers to constituencies are necessarily endogenous since transfers
affect the number of supporters in a constituency, and parties base transfers upon support within the
constituency. By contrast, parties have a priori core preferences for particular constituencies, as well as
a priori information about which constituencies are swing constituencies. We derive a formal model to
address each of these complications to provide a precise logic about how the expected seat share and
the underlying distribution of core and swing constituencies affects core-swing targeting outcomes in
equilibrium.
Methodologically, this paper makes two novel contributions. First, to estimate our model we marry multilevel modeling (MLM) statistical techniques with time series cross-section (TSCS) data. Multilevel modeling allows us to vary the slopes on our coefficients of interest so that we are not forced to assume one
"true" relationship between our variables of interest and the outcome variable. Because our coefficients
are allowed to vary over time and space, we are able to easily identify heterogeneous effects in our data.
Second, we rely on GIS mapping to overcome difficulties posed by the mismatch between administrative
and political boundaries in India. Because administrative and political boundaries are not neatly nested,
we use GIS mapping to link state legislative constituencies to administrative sub-district units (known as
blocks).
Formally, this paper extends the core-swing model of Dixit and Londregan (1996), from which the core
model of Cox and McCubbins (1986) and the swing model of Lindbeck and Weibull (1987) emerge as
special cases, in two important ways. First, each of the models above assume that parties are competing in
a single constituency, attempting to maximize vote share. We model electoral competition over multiple
constituencies, as well as the tradeoffs between awarding transfers to each constituency, where the maxi-
1
mization of expected seat share, not expected vote share, is the goal of electoral-seeking party. Second, we
include party preferences for core distribution into the utility function for each party, so at all times the
party assesses tradeoffs between expected seat share and core preferences.
Our findings provide strong support for three new insights into the study of pork. First, we find strong
empirical support for the effects of the electoral context on core-swing outcomes. Second, we provide
an eplicit formal logic for the effect of electoral context upon core-swing outcomes, appealing to two
distinctive dimensions to political competition. Finally, our findings support explicitly modeling the hierarchical nature of electoral data, for not doing so–as is evident from our data–could lead to inaccurate
inferences.
2
Theory and Background
In most countries at most times, political parties play an influential role in allocating some portion of
goods, private and public, in a way that maximizes their future electoral prospects. This influence may
be explicit or implicit, but it is a truism that the use of political criteria for targeting scarce goods is a
feature of most political systems in which elections play a pivotal role. The debate in comparative politics
is usually not over whether such targeting exists, but the manner in which targeting is calibrated.
In the comparative literature on distributive politics, there have been two, opposing models put forward
to explain the nature of such targeting. Both models begin with the premise that there are two parties
competing in an election and each promises to deliver certain goods to various groups in exchange for
votes. In these studies, there is an affinity between the party and a base of supporters; these are "core"
voters. On the opposite end of the spectrum, there are "opposition" voters who are firmly in the camp of
the opponent. It is assumed that this faction’s support is out of reach for the other party, and thus, it is not
worth attempting to wrest their votes away from their preferred party. The third relevant group, which
sits in between these two extremes, are the "swing" voters. Swing voters are up for grabs and will vote for
the party they believe will benefit them the most.
While the two models share the same broad set of underlying assumptions, they diverge in their theoretical
predictions of targeting distributive goods. One set of studies predicts that politicians will prioritize
redistribution to their core base of supporters (Cox and McCubbins, 1986). Proponents of this view believe
that parties will reward their most ardent supporters–those who share its ideological inclinations and/or
those who believe it will be a credible and effective agent in distributing goods. These models suggest
some faithful base of core supporters, where parties can allocate to their core more efficiently through local
networks. Ansolabehere and Snyder (2003) discuss theories that are more consistent with our electoral
logic. In particular, parties may allocate to areas with greatest support simply because they prefer to target
their own supporters or because they attempt to mobilize voters in areas of strongest support.
Another group of studies argues that resources will be targeted towards "swing" or "pivotal" districts
(Lindbeck and Weibull (1987); Dixit and Londregan (1996)). Proponents of the "swing" voter bias argue
that parties need not waste precious resources on rewarding core supporters who (it is assumed) will vote
for them anyway due to an underlying ideological motivation. Rather, parties will narrow their sights on
those "swing" voters who can make or break an election, although Dixit and Londregan (1996) argue that
this effect might be mitigated somewhat by the so-called "leaky bucket."1 On the other hand, the weakness
of the "swing" thesis is that a party that consistently favors swing over core voters faces the prospect of
alienating the party faithful.
The empirical evidence regarding "core-swing" is inconclusive. Some studies find support for the "swing"
hypothesis (Stein and Bickers (1994); Dahlberg and Johansson (2002); Denemark (2000); Stokes (2005)),
1 The "leaky bucket" phenomenon refers to the idea that parties may have less control over delivery mechanisms in swing areas,
so, holding all else even, they can more efficiently target voters in core areas as opposed to swing areas.
2
while others report findings supportive of the "core" model (Ansolabehere and Snyder (2003); Chen
(2008)).2
2.1
Developing the Theory
In this paper, we study the selective or biased targeting of local public goods (e.g. schools, roads or health
clinics), what is often, in the United States, referred to as "pork." Stokes (2009) provides a useful typology to
understand the difference between pork and other forms of selective benefits (e.g. clientelism). While both
pork and clientelism entail the biased, material, and non-programmatic exchange, pork is differentiated
by the fact that it does not involve a quid pro quo exchange with the voter. If the government builds a public
school, it represents a relatively fixed investment that benefits both supporters and opponents alike. By
contrast, clientelism entails a targeted benefit that can be used directly in exchange for government support
from the voter. Since the government cannot directly target supporters with pork, it makes sense to target
those constituencies with the greatest amount of "core support," in order to minimize the amount of
opposition receiving access to the local public good.
Parties have an incentive to deliver pork after, not before, elections. Without effective monitoring, it is
not clear why parties would deliver public goods prior to an election. Defection is a serious concern
because if voters can secure the good ahead of time, they are free to vote their preferences in the voting
booth due to the secret ballot. This differs from logic of vote-buying and clientelism in Stokes (2005), where
parties hold voters accountable by promising targeted benefits in exchange for votes that can be monitored
by the party.3 We argue, following Diaz-Cayeros, Estevez and Magaloni (2009), public infrastructure
is qualitatively different from private goods. Some intrinsic characteristics (i.e. lack of reversibility or
excludability) of public goods render them blunt instruments for attracting or mobilizing voters, implying
that we are likely to see new investments made post-election. In the words of Cox (2006), these are
"outcome contingent" transfers.
Public works (one of the most common manifestations of pork) cannot be built overnight. Even when
the ruling party controls the distribution process, there is a process of approvals, site determination,
contracting and construction that takes time. Thus, it may not be feasible for politicians to influence
construction prior to an election because of the investments that are required. They may speed up school
construction already in the works or inaugurate new sites, but the completion of new construction is more
difficult. Rather, it makes some intuitive sense that we would see an increase in construction following
elections. This also coincides with the fact that most new social programs are announced shortly after
elections when a new government seeks to convey the sense that it is "delivering" for its citizens. In a
context of anti-incumbency, what lingering effect do outgoing governments (elected out of office) have on
overall targeting patterns if school construction is started–but not finished–under their aegis? We believe
very little; new governments have very little incentive to follow through on the promises of the previous
government and prefer to execute their own schemes. This gives us confidence that the post-election
construction of schools is largely initiated by the new government.
Finally, the targeting calculus of parties is contingent on overall levels of political competition in the
state. Here, it is important to distinguish between two dimensions of competition. While the overall
distribution of seats in the assembly might indicate a landslide, parties must also take into account the
level of competition within constituencies across the state. In equilibrium, the ruling party is likely to
prefer directing pork to those areas which the largest core support. When there is a high degree of
2 A number of related studies find support for a modified version of the core voter hypothesis. See Golden and Picci (2008), and
Miguel and Zaidi (2003).
3 She provides evidence of this from the Peronist party in Argentina. In her model, parties favor swing voters in the distribution of
particularistic benefits. Nichter (2008) argues, contra Stokes, that parties may engage in "turnout buying" rather than "vote buying."
This provides an alternative solution to the problem of monitoring and the secret ballot. Re-analyzing Stokes’ data from Argentina,
Nichter finds that the Peronist party invested in passive or unmobilized "core" constituencies rather than swing voters with the goal
of increasing voter turnout. Both Stokes and Nichter focus on private handouts rather than public goods.
3
competition and elections are close, individual candidates are likely to make even more promises in
marginal constituencies that could swing either way. This follows from the standard logic of political
competition: in swing constituencies where the margin of victory is slim, politicians must make desperate
promises to sweeten the pot. Wilkinson (2006), for instance, argues that competition and volatility have
an unambiguous effect on the number of "pork" promises that are made during election season. Swing
constituencies are fickle and pork represents a low-cost (yet high-risk) investment in potential voters
who may swing against you–and with your opposition–in the next election. In this regard, public goods
simultaneously represent a commitment problem as well as a unique opportunity to reach a wider pool of
voters than targeted transfers. Furthermore, private transfers also imply a working baseline of networks,
information, and relationships that are less likely to exist in swing areas.
3
3.1
Pork Barrel in India and Tamil Nadu
Pork Barrel in India
In India, access to pork barrel resources rests with the ruling party and it is crucial to understand the nexus
between ministers of legislative assembly (MLAs) and the party leadership and its role in the delivery of
pork. That is, an individual legislator’s ability to deliver on his promises of pork pivot on his party’s
success in coming to power (or joining the coalition in power). Party leaders are subject to countless
demands on the part of legislators (not to mention national-level legislators and other political bosses)
to provide jobs to cronies, transfer troublesome bureaucrats, or provide funds for infrastructure projects
in their constituencies. While state legislators themselves might have resources and channels through
which to achieve some of these aims, much of this power is a function of ties to the party leadership.
Thus, we view parties as strategic actors who are cognizant of the larger political landscape in the state
when making distributive decisions. As we document below, this is especially likely to be true in Tamil
Nadu, where the leaders of the two opposing political formations (who have personally alternated in
the Chief Minister’s chair for the past 20 years) run top-down party organizations with little intra-party
democracy.
We assume throughout that India is what Chandra (2004) calls a "patronage democracy." Because patronage is the currency of Indian politics, state-level politicians face incentives to accumulate projects in their
constituencies since projects can be exchanged for votes. As Wilkinson (2006) writes, "politicians, well
aware of the direct link between delivering goods and getting votes, make sure that they control as many
infrastructure and social programs as possible." MLAs are consumed not by their representative or legislative functions, but by their role as reliable intermediary. The subject of this paper is public works projects,
specifically public primary schools. A government can build schools at any time during its tenure, yet
the literature on patronage politics (in India and elsewhere) offers evidence that many new public works
projects are contingent on voter behavior. According to the standard narrative, MLAs typically campaign
on promises of bringing development to their constituency in exchange for being voted into office. For
instance, the study by Puri (1978) of the Rajasthan assembly shows that assurances regarding new local development works were among the most popular pledges made by candidates prior to the election. When
asked "what the voters expected them to do," most MLAs indicated that voters desired new public works
projects. Wilkinson (2006) also describes the incentives for MLAs to make promises of new infrastructure
during the campaign (or to even authorize initial construction) with the implicit understanding that they
will deliver on such promises only if voters uphold their half of the bargain. 4 As Bailey (1963, p. 25)
writes:
4 Both voters and MLAs themselves view the role of a state legislator as an intervener or fixer in the process of policy administration and implementation. There are numerous historical case studies of India’s state assemblies which support this conception.
These include: Chopra (1996); Forrester (1969); Jha (1977); and Puri (1978), among others.
4
"[Their] MLA is not the representative of a party with a policy which commends itself to them,
not even a representative who will watch over their interests when policies are being framed,
but rather a man who will intervene in the implementation of policy, and in the ordinary dayto-day administration. He is there to divert the benefits in the direction of his constituents."
When it comes to large infrastructure initiatives, the role of the ruling party–particularly party leaders–is
central to understanding the distribution of pork. Most education and other large public goods initiatives
emerge from centrally sponsored schemes and projects (and are often bolstered by state-level matching
funds) where the states have broad discretionary authority. For example, this is the framework for India’s
most recent flagship primary education program, Sarva Shiksha Abhiyan (SSA). The implementation of
these plans is done at the state level with state-level line departments playing a key role in decisionmaking. The heads of these agencies are typically members of the state legislative assembly. This reality
underscores the importance of co-partisanship and party hierarchy in understanding the allocation of
pork. MLAs affiliated with the ruling party (coalition) have significant advantages in accessing and directing state resources for both public and private goods.5 The value of co-partisanship, combined with party
hierarchy, has also been shown to be influential in other contexts studied by political scientists, such as the
allocation of intergovernmental grants in the United States (see Ansolabehere and Snyder (2003)).
One might argue that the narrative presented here overlooks the importance of decentralization and local
government. We believe that state-local government interaction is important, not because of the strength
of panchayats (local governments) but due to cycles of dependency. As Singh et al. (2003) document in
their study of Madhya Pradesh, because elected panchayat members do not have significant resources or
autonomy, their election frequently pivots on whether they can promise close ties to higher ups in the
political food chain. The interdependence between tiers of government means that the politicization of
public goods not only brings direct rewards to MLAs but also has numerous positive externalities: namely,
the consolidation of patronage networks and cycles of dependence. Indeed, Yadav (2008) argues that the
principal function of the panchayat raj institutions is to supply a cadre of lower-level functionaries (or
"brokers") to political parties operating at higher levels.
3.2
The Politics of Tamil Nadu
Tamil Nadu is a state of over 70 million people located on the southernmost peninsula of the Indian
subcontinent, occupying a land area of roughly 130,000 square kilometers. It is densely populated (at
roughly 480 people per square kilometer, as opposed to the all-India average of 325) and nearly 44 percent
of the state population lives in urban areas. Although it may seem odd to base an analysis around a
single Indian state, there are several reasons it makes sense to treat our analysis on par with country-level
studies. First, taken by itself, Tamil Nadu would be one of the twenty most populous countries in the
world. Second, the borders of Indian states are based upon linguistic integrity. As such, Tamilians have
a unique history and culture to themselves. Furthermore, the linguistic basis for statehood implies that
the vast majority of Tamilians cannot communicate with the rest of India in their mother tongue, which is
different than the component states of the US or even the majority of countries in Latin America. Third,
as we will discuss, political parties are a function of state-specific concerns, so the two major parties are
uniquely Tamilian parties. In fact a number of Indian states display competitive state-specific parties. This
is quite different than the US where the same two parties are competitive in each state, or even Europe,
where politics is often played on a similar left-right economic dimension.
5 Numerous anecdotes from the literature can be cited in support of this claim. For example, Jayalakshmi et al. (N.d., p. 76) discuss
health sector reform in Andhra Pradesh when the state was ruled by the Telugu Desam Party (TDP). Describing a local project, the
authors write: "The area is a TDP stronghold, and because the TDP MLA from this area was denied a Cabinet post, he was in
compensation given powers over a number of services in the area, including the decision about where to locate the PHC [Primary
Health Centre], which was placed in his home constituency, where a friend, an ex-sarpanch [village headman], donated land for the
construction of the PHC.
5
There are four reasons why, of all the states in the Indian union, Tamil Nadu make an interesting empirical
case for our study: 1) regular bipolar competition; 2) persistent electoral volatility; 3) ideologically devoid
politics; and 4) partisan populism.
For over three decades Tamil politics has revolved around fierce bipolar competition between two coalitions led by opposing regional Dravidian partiesâ the DMK and ADMK (later renamed AIADMK). After
the Congress Party’s defeat in 1967, one of the two fronts has governed the state. The DMK front prevailed in the elections of 1967, 1971, 1989, 1996, and 2006; and the AIADMK alliance won in 1977, 1980,
1984, 1991, and 2001 6 For the purpose of this analysis, this oscillation between the two Dravidian fronts
provides us with sufficient alteration in power to test for targeting effects across both parties and a range
of governments, as well as isolate the effects of margin of victory on the construction of schools.
Another main feature of the two main parties is the dominance of charismatic leaders, which has led
to a triumph of pragmatism over ideology. Thus, we can be confident that ideology or party-specific
characteristics are largely irrelevant to the patterns of school construction we observe. Since their inception
each party has been directed by a omnipresent larger than life cult figure: for decades the DMK has been
fronted by octogenarian (and former screenwriter) M. Karunanidhi while AIADMK has been led by chief
rival and former film star Jayalalitha. The fact that many of Tamil Nadu’s past and present political leaders
emerged from South Indian cinema plays no small role in perpetuating "cult"-like dynamics (see Dickey
1993 for a review). The presence of such charismatic figures atop the party hierarchies has also contributed
to a centralization of power. Widlund (2000, p. 122) argues that both Karunanidhi and Jayalalitha are
intimately involved in all crucial aspects of party decision-making, from selecting candidates to choosing
ministers and deciding which MLA demands are fulfilled. When in power, ruling party MLAs draw their
power from their relative proximity to ministers.
Tamil Nadu’s electoral dynamics have contributed to a perpetuation of competitive populism, and the
two dueling fronts have made no secret of viewing development resources through an electoral-political
lens. Resting primarily on the informal mechanisms described above, the ruling party has wide latitude
to tap state coffers to allocate pork on political grounds. The centrality (some observers of Tamil politics
have called it an obsession) of partisan labels is useful insofar as it supports our contention that partisan
politics is a critical determinant of targeting.7
3.3
The object: school construction in India
In this paper we examine pork barrel dynamics by studying patterns of school construction in Tamil Nadu.
Before describing the local political context, we begin by explaining why focusing on schools makes sense
for the purposes of this study.
First, the Indian system of public education is underdeveloped. Universal access to public primary education has not yet been achieved, and so public schools represent a scarce resource. The historical expansion
of services has been uneven, with strong evidence that lower castes, minorities, and areas with feudal
histories have been underserved (Betancourt and Gleason (2000); Banerjee and Iyer (2005); Banerjee and
6 Ananth (2006, pp. 1232-1233) argues that there have been four stages of post-Independence politics in Tamil Nadu. From
Independence in 1947 to 1967, Congress was the dominant power. The second stage began with DMK’s watershed upset victory
in 1967, persisting until the onset of the Emergency in 1975. This was followed by the decade-long rule of former film star-turned
AIADMK leader M.G. Ramachandran from 1977-1987 and the consolidation of a two-and-a-half party system (AIADMK versus
DMK, with Congress as an important alliance partner). The final stage, which began in 1998 and continues to the present, is marked
by an increasing fragmentation of party politics, the rise of smaller caste-based parties, and the enervation of the two main Dravidan
parties.
7 A recent editorial published in the lead up to the 2009 national elections issued a damning indictment of partisan politics in
Tamil Nadu: "The political discourse during campaigning has centred not so much on the performance of the ruling/oppositional
parties as on the ability of the two main parties (and others) to use their money power and patronage networks...Even issues of
development...are debated through personalised vitriolic attacks" (Shifting Allegiances, 2009).
6
Somanathan (2007)). And it is widely accepted that the influence of politics in public education is pervasive. Politics influences the hiring of teachers (Chin, 2005); the governance of education (Kingdon and
Muzammil 2000); and the location of investments (Wilkinson, 2007).
Thus, access to, and the placement of, public schools is an issue that retains popular salience. This has
been particularly true in Tamil Nadu, where social movements have historically coalesced around the
idea of improving human capital for the general populace. Singh (2007) has argued that generations of
Tamils have rallied around a common subnationalist "Tamil" identity to promote human development and
progressive social policies.
Second, the central and state governments of India are devoting record sums to expanding the system
of primary and secondary education. Banerji and Mukherjee (2008) report that since 2001-02 alone, the
Indian government’s flagship primary education program has financed the construction of nearly 160,000
new primary and upper-primary public schools across India. With increasing budgetary outlays comes
expanded opportunity for political interference.
Third, public education is a responsibility of India’s states where regional politicians retain discretionary
authority. According to India’s constitutional framework, states exercise primary responsibility for a range
of core governmental functions including: law and order, public health, education, agriculture, irrigation,
some forms of taxation, and land rights (Rao and Singh, 2005, p. 364). Furthermore, India’s system of fiscal
federalism is highly vertically unbalanced. While states incur almost 90% of social service expenditures,
the central government finances roughly 55% of the states’ overall spending (McCarten, 2003, pp. 250251). Once federal monies are transferred to the states, regional authorities have considerable discretion
in utilizing funds.
One reason public works projects are attractive to politicians is that they are visible (Mani and Mukand,
2007). With visibility comes an opportunity for credit claimingâ with the corresponding news coverage,
groundbreaking, opening ceremonies, and local prestige. As Bailey (1963) recognized, where building a
school is involved, two groups stand to benefit: local citizens and political cronies. The desire for an MLA
to use infrastructure contracts to enrich his friends, local contractors, and suppliers coincides with his
interest to influence the location of projects.8
4
4.1
Data, model specifications, and empirical results
Data
We utilize two datasets–one on schools and the other on electoral politics–in this paper, integrating them
using GIS techniques. For education, we rely on a unique dataset compiled by the District Information
System for Education initiative of the National University of Educational Planning and Administration.
This initiative collects comprehensive school-level data on facilities, school grants, infrastructural quality,
enrollment, and education outcomes–in an effort to assess (through a "school report card") India’s 1.25
million primary and upper primary schools across all districts. Two unique features of this data stand out.
One is that the data contain information on the year of school construction, which allows us to examine
patterns of school building over time and space. Secondly, each school is coded by the block (sub-district),
district, and state of its location.
Courtesy of the Election Commission of India, we compile assembly constituency-level electoral data
for Tamil Nadu over the period 1977-2007. We focus on this period because boundaries of assembly
constituencies (ACs) are held constant during these thirty years, allowing us to track trends over time
8 As Wilkinson (2006, p. 5) argues, corruption in infrastructure projects often has political roots. "Capital infrastructure projects
which can generate kickbacks are one of the main means through which incumbent politicians and parties can raise money and pay
off party supporters."
7
across consistent units. Our election data contain information on candidates, turnout, votes polled, party
identification, sex, and the caste reservation of constituencies.
In India, the primary administrative unit of analysis within states is the district (analogous to counties
in the United States). Unfortunately, political constituencies do not map perfectly to districts. Thus,
there is no easy way to merge administrative and electoral data. Scholars have previously dealt with this
mismatch in two ways, both less than ideal. Some scholars focus on national parliamentary constituencies
(PCs), which can be roughly mapped to districts (Banerjee and Somanathan, 2007). While focusing on
PCs is computationally convenient, Members of Parliament (MPs) are the wrong actors to analyze if one
is interested in local-level dynamics. The second course pursued is to exploit the fact that ACs are neatly
nested within PCs, and thus can be linked to districts. Cole (2009) and Ravishankar (2007) follow this
path. The problem is that the median district consists of 7.5 ACs, so one has to take crude averages across
constituencies in order to map political variables to district-level administrative data.
This paper improves on extant approaches by using GIS software to map political boundaries to administrative ones. Yet rather than focusing at the district-level, we look one layer below at the sub-district
or block-level.9 Blocks are smaller units of aggregation and thus easier to compare with assembly constituenciesâ providing for more accurate inferences. Furthermore, our data on schools can be aggregated
easily up to the block. While not perfect, there is a significant degree of nesting between block and AC
boundaries in Tamil Nadu. We rely on electronic block-level maps created by the Tamil Nadu unit of the
National Informatics Centre (http://www.tnmaps.tn.nic.in) and use ArcGIS 8.0 to overlay them with AC
maps, including resolving inconsistencies by hand.10
There are 385 administrative blocks and 234 assembly constituencies. We were successfully able to implement the mapping routine for 210 constituencies. Many of the large urban centers of Tamil Nadu have
relatively small constituencies for which we require more detailed city-level maps. Thus we omit the urban
centers of Chennai, Coimbatore, Madurai, and Tiruchirapalli (Trichy). The result is a constituency-level
panel dataset of 210 constituencies over 8 electoral cycles with information on school building from 1977
to 2007.
4.2
Framing the Empirical Question
We may divide electoral competition along two dimensions: 1) the percentage of constituencies won by a
particular party or coalition; and 2) the degree of competitiveness within each constituency.11 As in Tamil
Nadu, the "disproportionality" associated with a first past the post single-member district system implies
that there can be a fair amount of divergence between the two dimensions (Lijphart, 1994).
In this paper, we argue that governments award schools to constituencies based upon each of these dimensions of electoral competitiveness. In order to test these mechanisms, we operationalize the electoral
competitiveness by measuring the percentage of close races in a particular electoral year across 8 elections.
More precisely, we label an electoral year a "competitive" year when more than 50% of the constituencies
have less than a 10% margin of victory.12
9 While there are a multitude of sub-district administrative entities, we utilize data on entities known as "blocks." Each district
is comprised of a number of blocks, which are the sub-district structures used to manage development schemes. They differ from
"taluks," another larger sub-district entity, which primarily deal with revenue issues. The boundaries of the two sub-district entities
bear no systematic relation.
10 We gratefully acknowledge Sandip Sukhtankar of Harvard for making these maps available. Although the Election Commission
provides GIS maps of constituencies, they are not made using any known system of geo-coordinates. For more information, see:
http://www.dartmouth.edu/ sandip/data.html.
11 In the first dimension, one may think about the percentage of constituencies won by a particular coalition. However, electoral
competition may also be framed in terms of the degree of competitiveness at the constituency level. For instance, in a particular
election the AIADMK may win every constituency, but they may win each seat with a small margin of victory. In this case, the election
is not competitive along the first dimension but is competitive along the second dimension. The second dimension, competition at
the constituency level, is crucial for understanding the core-swing behavior of political parties in Tamil Nadu.
12 We discuss the connection of our margin of victory measure to the theory in the following section.
8
Figure 1: Distribution of Schools in Tamil Nadu
The data is broken into quintiles with a low of 30 schools and a high of 638 schools. The darker colors indicate a greater
number of schools.
As we will discuss below, the typical election in Tamil Nadu is not particularly competitive (along either
dimension), and thus, in general, we expect core targeting effects, i.e., a positive relationship between
margin of victory and subsequent school construction. However, in years where the election is competitive, parties spend disproportionately more on swing constituencies because both parties are actively
competing for the swing constituencies in order to win the election. Thus, elections with many close races
mitigate these core effects, i.e. we expect to see much smalleer (perhaps negative) effects of margin of
victory upon subsequent school construction. We write our hypotheses precisely below:
(i) Since most elections are not competitive, we expect that there will be, on average, a positive relationship between
margin of victory and subsequent school construction.
(ii) In years where more than 50% of the constituencies have less than a 10% margin of victory, we expect that
there will be smaller effects of margin of victory upon subsequent school construction.
Tamil Nadu exhibits a strong political business cycle with 95.4% all schools being built within two years
after a new government is elected. This provides evidence that governments award schools based upon
elections. At the same time, Tamil Nadu has experienced extreme party alternation, with perfect alternation in party coalitions across elections since 1984. The alternation in parties provides us with a clean test
of our theories because parties are forced to respond to the recent elections, as parties have little incentive
to award schools with an eye to the future if they are likely to lose in the next election. This feature of
Tamilian politics makes it easier, empirically and theoretically, to isolate the effect of MoV on subsequent
school construction with confidence.
9
1000
300
Figure 2: Patterns of School Building and Party Alternation in Tamil Nadu
1980
1984
1989 1991
1996
2001
2006
800
250
1977
225
600
196
●
●
162
150
144
●
●
400
Majority=118
100
New Schools
200
●
195
200
69
50
●
30
●
0
4
●
0
1975
1980
1985
1990
1995
2000
1977
2005
1980
1984
1989
1991
1996
2001
2006
Year
(a) Political Business Cycle in Tamil Nadu
(b) Number of Seats for AIADMK Alliance
In figure 2(a), the solid line represents the number of schools built over time. The vertical dotted lines delineate years a
new government is formed. In our data, 95.4% of all schools are built in the first two years after a government is formed.
2(b) exhibits the number of seats won by the AIADMK alliance in Tamil Nadu, where an alliance needs to win 118 (out of
the 234 possible seats) to control the government. The data exhibits perfect alternation from 1984 onwards. Taken together,
these data suggest that the margin of victory primarily has an effect on subsequent school construction.
Figure 3 displays the within-constituency MoVs for the winning coalition in each election, starting from
1977. As a crude measure, a swing constituency (the dark bars in the histograms below) is defined as any
constituency where the MoV is less than 10%.13
Figure 3: Core-Swing Constituencies By Government
p=0.22
25
20
15
Frequency
10
20
Frequency
10
20
Frequency
10
0.4
0.0
0.1
0.2
0.3
0.4
0
5
0.3
Margin
0.0
0.1
Margin
Margin of Victory in 1991
0.4
0.5
0.0
0.1
0.2
0.3
0.4
Margin
Margin of Victory in 2001
Margin of Victory in 2006
p=0.35
p=0.66
0.0
0.1
0.2
0.3
Margin
0.4
0.5
0.6
0.0
0.1
0.2
0.3
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40
30
Frequency
0.0
Margin
20
0
0
10
10
20
Frequency
20
10
0
0
10
20
Frequency
30
30
p=0.09
30
0.3
Margin
Margin of Victory in 1996
p=0.03
0.2
50
0.2
40
0.1
0
0
0
0.0
Frequency
p=0.37
30
p=0.51
30
40
30
20
10
Frequency
Margin of Victory in 1989
30
p=0.56
Margin of Victory in 1984
35
Margin of Victory in 1980
40
50
Margin of Victory in 1977
0.1
0.2
Margin
0.3
0.4
0.0
0.1
0.2
0.3
0.4
Margin
The histograms are restricted to constituencies where the future ruling coalition was victorious. The darker bars represent
frequencies of constituencies with a MoV of less than 10%, which we identify as swing constituencies. The gray bars
are, thus, the core constituencies. The values in the upper right corner of each histogram are the percentage of swing
constituencies among those won by the future ruling coalition.
Figure 3 exhibits a large degree of variation across constituency-level competitiveness, with a high of 66%
13 These
graphs are purely for illustrative purposes. Since the statistical models measure the effect of within-constituency margin
of victory on subsequent school constructions, our empirical results are not sensitive to the choice of cutoff in these graphs.
10
swing constituencies for the government starting in 2006, and a low of just 3% swing constituencies for
the government taking power in 1991. On the other hand, there is not much variation along the dimension
of seat share. Each ruling coalition in the study period won at least 70% of the seats in the Assembly,
so we can isolate the effect of within-constituency competitiveness upon subsequent school construction.
Now that we have identified 1977, 1980, and 2006 as competitive election years, we want to demonstrate
that the pattern of school awarding is different in these years as compared to less competitive election
years.
4.3
Model Selection
Our dataset has 210 constituencies over 8 time periods. This sort of data, generally referred to as time
series cross-section (TSCS) data, has been the focus of intense debate in the methodological literature. In
order to properly estimate models with TSCS data, we must always be aware of constituency-level effects,
contemporaneous time effects, and serial correlation in the data. One can control for constituency-level
and contemporaneous time effects by using fixed effects (FE), or dummy variable, regression. However,
there are several drawbacks to FE models. In addition to using up degrees of freedom, the FE approach
does not allow for the inclusion of constituency-level or time-level variables. For instance, our final model
includes a control for the number of schools built before 1977 (a constituency-level variable), which could
not be included under a FE approach. One possible solution to this problem is to use random errors in
modeling the data, where constituency-level and contemporaneous effects are assumed to be normally
distributed with some common mean and variance.
In order to analyze our TSCS data, we use a multilevel modeling (MLM) regression framework.14 All
models were coded to run in the program jags, which uses Markov chain Monte Carlo (MCMC) methods,
to estimate multilevel models.15
In an MLM framework, we view TSCS data as a "non-nested" hierarchical structure. That is, constituencyelectoral year observations (lower level) are nested in the constituency and electoral year levels (higher
levels), but neither constituency nor electoral year are nested within each other. The constituency and
electoral year errors still enter into the model as random errors. However, MLM allows us to explicitly
model intercept and slope coefficients as a function of predictors (fixed) and higher level errors (random).
There are several benefits to this modeling approach. We are able to vary slope coefficients of constituencyelectoral year predictors by higher level groups, and we can explicitly model correlation between these
slopes and the random error in the higher level group.
MLM balances between "pooled" and "unpooled" estimates based one the sample size in each cluster (e.g.
constituency x or time y), what Gelman and Hill (2007) call "partial pooling."16 Pooled estimates refer to a
scenario where the random error is fixed at 0 for each unit, whereas unpooled estimates refer to a scenario
where the random errors are not drawn from a common distribution, as in FE models. As the sample size
grows in each cluster, random errors converge to the fixed effects. Thus, FE can be seen as a special case
of the MLM framework. On the other hand, as the sample size in each cluster goes to zero, the random
errors also converge to 0. Although the social sciences have not used MLM methods for TSCS very often,
Shor et al. (2007) shows superior model performance17 in Monte Carlo tests against OLS and FE models,
14 For
a good introduction to models of this type, please see Gelman and Hill (2007).
Jackman (2009) for a good introduction to fitting multilevel models in jags. All models were run via the program R, using
the package R2jags developed by Yu-Sung Su and Masanao Yajima.
16 The overall goal of multilevel modeling is to account for variance in an outcome variable that is measured at the lowest level of
analysis by considering information from all levels. Steenbergen and Jones (2002) posit three benefits to multilevel analysis. First,
multilevel data allows researchers to combine multiple levels of analysis in a single comprehensive model. Second, multilevel analysis
allows researchers to explore causal heterogeneity: is the effect of lower-level predictors conditioned by higher-level variables? Third,
multilevel analysis can provide a test of the generalizability of one’s findings. Do the findings obtained in one geographic location
apply to other contexts?
17 The paper uses both root mean square error (RMSE) and optimism as measures. In their paper, the model takes a standard OLS
model with cluster-level effects and contemporaneous time shocks.
15 See
11
even when using panel corrected standard errors and robust FE standard errors (Arellano, 1987).
4.4
Specification of Models and Data
The dependent variable in each of the analyses is school building in a particular constituency in the two
years subsequent to an electoral year (yit ).18 Throughout the analysis, we employ an overdispersed Poisson
model to predict school construction as function of voting for the ruling coalition (RC), and the interaction
between the margin of victory (MoV) and RC, as well as a constituency level predictor for the number
of schools built before 1977 (early). In order to model serial correlation in the data, a lag term is always
included in the regression.19
In the data, "MoV" is coded as a non-negative variable between 0 and 1 that measures the vote share
difference between 1st and 2nd place candidates in the specific constituency for the electoral year. The
variable "RC" simply measures whether the winning is a member of the incoming ruling coalition, and
the variable "early" measures the aggregate number of schools that were constructed by 1977.
We run two models, a varying-intercept model, where only the intercepts vary by electoral year and
constituency, and a more complicated intercept-varying and slope-varying model, where we vary the
slopes on voting for the ruling coalition (RC), and the interaction of RC with the margin of victory (MoV).20
Model 1, the varying-intercept model, is written formally below:
yit ∼ Poisson (αit + δyi,t−1 + β 1 RC + β 2 ((1-RC)×MoV) + β 3 (RC×MoV), ω )
αit = α + γ1 early + ε i + ηt ; ε i ∼ (0, σε ) ; ηt ∼ 0, ση
(4.1)
A few features of (4.1) require explanation. First, since we want to account for overdispersion or underdispersion in the data, we explicitly model a dispersion parameter ω (in the classical Poisson model, the
dispersion parameter is assumed to be 1).21 Second, the MoV variable enters into the regression as interacted with RC or (1-RC). Essentially, the model estimates two coefficients for the effect of MoV on school
building, β 2 and β 3 , based upon whether the constituency failed to support the new ruling coalition or
supported the new ruling coalition, respectively.
Our second hypothesis in this paper addresses the conditions under which one is likely to observe a larger
core or swing effect. In particular, we hypothesize that in years with more competitive elections (1977,
1980, 2006), where the many constituencies are swing constituencies, we will observe a greater swing effect
as compared to other years. Since all our models include a lagged dependent variable, we are unable to
18 This
only excludes less than 5% of the total number of schools in the dataset, so it makes little difference to the estimates.
Nevertheless, the restriction to schools built in the subsequent two years guarantees that the model is measuring those schools that
are built as a response to the result of the recent elections.
19 We choose to run a model with lags and schools built before 1977 to control for constituency-level need. This is all the more
important since there is no annual demographic information available at the constituency level. Less than 7% of the observations have
no schools built, suggesting no concern for zero inflation. Finally, we experimented with models controlling for those constituencies
that explicitly supported DMK or AIADMK (as opposed to coalition partners), as well as those controlling for turnout and eligible
voters. None of these predictors seem to matter much for the basic results.
20 All models are calculated using the jags and called with the package R2jags in R, with an overdispersed Poisson specification
21 The estimate of the dispersion parameter models the data-level error as normally distributed. In a negative binomial model the
data level error is assumed to come from an extreme value distribution; the choice of model has little bearing on the results. We
define the data level residual for observation i, where ŷi is the fitted value for observation i, as:
zi =
yi − ŷi
sd(ŷi )
The overdispersion parameter, ω is then defined from the zi terms:
ω=
1
n−k
12
∑ z2i
get a measurement for our coefficients corresponding to the electoral year of 1977 (the first year in the
dataset). This requires a model that allows coefficients estimates to vary by electoral year. Model 2, a
varying-slopes model, is written formally below:
yit ∼ Poisson (αit + δyi,t−1 + β 1,t RC + β 2,t ((1-RC)×MoV) + β 3,t (RC×MoV), ω )
(4.2)
αit = α + γ1 early + ε i + ηt ; β i,t = β i + ηi,t


ηt
 η1,t 

ε i ∼ (0, σε ) ; 
 η2,t  ∼ N (0, V )
η3,t
The equation in (4.2) is identical to (4.1) in that it estimates a varying intercept αit , but now it adds slopevarying coefficients. For instance, the term β 1,t is composed of a pooled estimate β 1 and a random error
that varies at the electoral year level, ηi,t , where t corresponds to the electoral year in question. The random
errors at time level (ηt , η1,t , η2,t , η3,t ) are all taken to be in a multivariate normal with a zero mean and a
common variance-covariance matrix V (i.e. the model allows for correlation between coefficients at both
the electoral year and lower levels). Now, we are able to state our hypotheses in terms of parameters of
the two statistical models:
(i) In general, we expect a core effect. Thus, in model 1, we expect β 3 > 0
(ii) We expect that competitive election years will exhibit a smaller effect of margin of victory upon subsequent
schools construction. Thus, in model 2, we expect β 3,C < β 3,NC , where C and NC correspond to competitive
and non-competitive years, respectively.
4.5
Results
We begin with the results of Model 1, the varying intercept model. Figure 4 shows the estimated coefficients on the (fixed) predictors in Model 1.
The model in Figure 4 suggests a core effect in Tamil Nadu as the coefficients on RC and RC×MoV
are both positive and quite significant.22 This suggests that in "normal" times there is a preference for
parties to reward their core constituents and supporters. However, the coefficient on (1-RC)×MoV is
not significant. Part of the reason for this might be that over the study period, very few constituencies
(less than 18%) actually voted against the ruling constituency, and certain electoral years had virtually all
constituencies voting for the ruling coalition (e.g. out of 210 constituencies, 202 constituencies in 1991 and
196 constituencies in 1996 supported the ruling coalition).
Our second hypothesis claims that there is a stronger swing effect in electoral years where there are
a majority of close races. This demands understanding the variance in core-swing effects over many
electoral periods. In order to address this issue, the second model allows the the effects of RC, MoV, and
their interactions, on school construction to vary over electoral periods. Figure 5 plots the varying slope
estimates for RC × MoV over time, resulting from model 2. In particular, we want to test consistency of
the core effect over time.
The main test of the theory is the magnitude (and direction) of the coefficients on RC×MoV over time. In
particular, we argue that the coefficients in 1980 and 2006 should smaller (or even negative) as compared
to coefficients in the other electoral years due to the presence of many swing constituencies. In order to do
this analysis, we simulate 1000 values of the coefficient on RC×MoV for each electoral year. Based on our
simulations-based approach, we find that there is significant variation in the effect of MoV on the number
of schools constructed based on schools constructed during the first two years of a government period. We
22 RC×MoV
is also significant at the 95% level, and RC is almost significant at the 95% level (p-value of .054).
13
Figure 4: Fixed Effects from Model 1
Lag 10
●
early 100
●
RC
●
(1 − RC) × MoV
●
RC × MoV
●
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
Coefficients
The horizontal bars in figure 4 represent 80% confidence intervals on the estimates. The intervals are drawn from 1000
simulations of coefficient estimates in the model. These simulations account for the fact that these coefficients may be
correlated with each other.
Figure 5: Varying Slope Estimates of Margin of Victory Across Electoral Years
2
%=0.35
●
%=0.03
1.78
%=0.09
1
%=0.22
●
●
0.83
●
0.88
●
0.8
0.51
%=0.66
%=0.51
0
Coefficient on RC × MoV
%=0.37
−0.67
●
−0.69
−2
−1
●
1980
1984
1989
1991
1996
2001
2006
Year
This table shows the random coefficients on RC×MoV over time, plotted with 80% confidence intervals. Thus, this
represents differences in the margin of victory effect among constituencies that voted for the ruling coalition. The terms
beginning "%=" represent the percentage of swing districts among those won by the ruling party, as in Figure 3. The small
numbers to the right of the interval estimates correspond to the coefficient point estimates.
see what looks like marginally like a swing effect (MoV has a negative impact on the number of schools
constructed) in 1980 and 2006, with 75%-80% of the simulated values being less than zero. However, for
14
all other years there is a slight core effect and a fairly significant one in 2001. We are interested in testing
the effect of electoral competitiveness on the estimates of MoV, and we want to test whether the estimates
for the coefficients in swing constituency-heavy electoral years (1980 and 2006) are systematically smaller
than the estimates from other years. Figure 6 compares coefficients on MoV in 1980 and 2006 with other
Figure 6: Comparing Government By Government Swing-Core Effects
1
2
3
4
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2
3
4
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0
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0
50 100
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Difference in Coefficients
Difference in Coefficients
2006 vs. 1984
2006 vs. 1989
2006 vs. 1991
2006 vs. 1996
2006 vs. 2001
−1
1
2
3
4
Difference in Coefficients
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−1 0
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4
Difference in Coefficients
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150
q=0.001
0
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Frequency
50
0
50
0
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Difference in Coefficients
q=0.027
100
Frequency
q=0.026
100
Frequency
200
Frequency
0
50 100
q=0.041
50 100
200
q=0.066
200
Difference in Coefficients
200
Difference in Coefficients
200
Difference in Coefficients
0
Frequency
q=0.029
50 100
q=0.044
1980 vs. 1991
150
200
1980 vs. 1989
0
Frequency
200
1980 vs. 1984
−1 0
1
2
3
4
Difference in Coefficients
0
1
2
3
4
5
Difference in Coefficients
The top row looks at the MoV estimates from 1980 among those where the constituency voted for the ruling coalition
against similar estimates from the years where we observe more of a core effect (1984-2001). The bottom row makes the
same comparison for 2006. The histograms are over 1000 simulations. The value "q" represents the percentage of the time
the coefficient estimate from a core year is smaller than that of the swing year (either 1980 or 2006). This is an empirical
equivalent to a one-tailed t-test.
years in our sample. It suggests that we have greater than 90% certainty that the swing effect among
constituencies that voted for the ruling coalition in 1980 and 2006 was larger than in the other years. The
histograms look at the difference between the estimated coefficient on MoV when the constituency voted
for the ruling coalition. The histogram looks at 1000 simulations and is the empirical equivalent of a onetailed t-test. A skeptic might contend that our statistic of reaching some threshold of swing constituencies
matched up with the years of 1980 and 2006 by random chance. We can test this by using permutation
tests (a common non-parametric technique). The probability that our statistic (at the 10% level) lines up
with the above-mentioned years, assuming that any number of years may be labeled as "swing" years,
1
is 128
= 0.8%. The probability our statistic lines up with the above-mentioned years, assuming that two
1
years are chosen at random to be "swing" years, is 21
= 4.8%. We believe that, taken together, the evidence
suggests that 1) there is a stronger swing effect in 1980 and 2006, years with a disproportionately large
number of swing constituencies, and 2) this result is unlikely to have occurred by random chance.
4.6
Model Fit and Prediction
We conclude the data section by plotting our estimated effect on school construction and assessing model
fit. In figure 7, we assess how well model 2, the varying slopes model, fits the data. In particular, we
model the expected number of schools, and 80% confidence bounds around the estimates. One needs to
remember that in Poisson-type models, the variance increases as the expected number of schools increases.
15
However, it seems that model 2 does a relatively good job of fitting the data.
Figure 7: Fit Quality of Model 2
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Fit for 1984
Fit for 1989
Fit for 1991
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0
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Expected # of Schools
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10
10
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Expected # of Schools
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15
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Expected # of Schools
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0.4
0.6
0.8
1.0
●
Quantile of Estimate
Quantile of Estimate
●
Quantile of Estimate
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Quantile of Estimate
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●
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Fit for 2001
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20
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Quantile of Estimate
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Quantile of Estimate
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Expected # of Schools
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5
15
●
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0
Expected # of Schools
●
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10
● ●
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Expected # of Schools
20
●●
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20
●
Fit for 2006
●
5
Fit for 1996
●
0.2
0.4
0.6
0.8
1.0
Quantile of Estimate
In figure 7, the black dots represent the expected number of schools, as predicted by the model 2, the varying slopes model.
The graph displays 80% confidence bounds around the point estimates. The gray dots represent the actual distribution of
schools.
Figure 8 plots the effect of MoV upon the number of school awarded to a constituency, assuming that the
constituency voted for the ruling coalition. The dotted curves in Figure 8 are the estimated models from
the pooled estimates from model 1. The solid curves correspond to the partially pooled slope estimates
from model 2. Figure 8 shows that there are stark differences in predicted number of schools based on
MoV in 1980, 2001, and 2006, justifying the varying slopes approach.23
5
A Simple Model
We describe the game-theoretic logic for a political party to distribute pork as a function of electoral competition. In section 3, we discussed that electoral competitiveness is a murky concept. In particular, the
term may relate to the number of constituencies the party is expected to win in the polity or may refer to
23 In 2006, approximately 24% of constituencies have a margin of victory of at least 20%, and model 2, compared to model 1,
predicts at least 8% more schools built in expectation for these constituencies. In 1980 and 2006, approximately 30% and 40% of the
constituencies, respectively, have less than a 5% margin of victory, and model 2, compared to 1, predicts at least 4% (1980) and 10%
(2006) more schools built in expectation for these constituencies.
16
Figure 8: The Fitted Model By Government
Predictions for 1989
Predictions for 1991
6
Predictions for 1984
4
3
1
0
0
1
0
0
2
Expected # of Schools
6
4
2
Expected # of Schools
5
4
3
2
Expected # of Schools
3
2
Expected # of Schools
1
5
4
6
Predictions for 1980
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.0 0.1 0.2 0.3 0.4 0.5 0.6
MoV
MoV
MoV
MoV
Predictions for 1996
Predictions for 2001
Predictions for 2006
2.0
1.5
0.5
1.0
Expected # of Schools
15
10
Expected # of Schools
5
5
4
3
2
0.0
0
0
1
Expected # of Schools
6
20
7
2.5
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.0 0.1 0.2 0.3 0.4 0.5 0.6
MoV
MoV
MoV
The dotted line corresponds to the completely pooled estimates for MoV in model 1, and the solid line corresponds to the
partially pooled slope varying estimates for MoV, in model 2, when the constituency votes for the ruling coalition. For the
predicted values, the lag is estimated at the electoral year mean and the value of schools built before 1977 is estimated at
the grand mean.
the relative probability of winning each constituency in a polity. Thus, while we can convincingly demonstrate the differential effect of margin of victory upon core-swing targeting over years with more or less
constituencies with close elections, the interpretation of the result requires more work. In this section, we
develop a model that addresses the precise relationship between within and across constituency competition and core-swing targeting outcomes, as well as a clear description of how the theory maps to our
measure of margin of victory and years with many or few close elections.
Our focus is on the interplay between two, often conflicting, incentives for the party: 1) to maximize
the share of constituencies won; and 2) to ensure that beneficiaries include as high a percentage of supporters as possible in each constituency (i.e. pork is well-targeted). We extend upon the model of Dixit
and Londregan (1996), from which the models of Lindbeck and Weibull (1987) and Cox and McCubbins
(1986) emerge as special cases, in two ways: 1) simultaneously assessing multiple constituencies, and the
dependence between them, instead of a single constituency; and 2) introducing a new objective function
that incorporates party preferences in addition to vote maximization.
First, each of the models cited above focus on targeting within a single constituency; that is, they focus on
maximizing vote share by targeting core and swing groups within one constituency. However, maximizing
the vote share does not map cleanly on to maximizing the share of seats won in a legislative elections
since it is theoretically possible to have a large number of votes clustered in a few constituencies. Parties
generally try to maximize the number of constituencies subject to certain constraints in which they will
win, not the aggregate vote share. This not only admits a different maximization logic, but it requires
the analyst to address tradeoffs and dependency across constituencies. Our focus is on winning elections
by targeting core and swing constituencies over an entire electorate with many constituencies. Cox (1999)
points out that logic of targeting swing or core constituencies over an entire elections admits a different
formal logic than targeting swing and core groups and remains under-theorized in the literature. Thus,
17
by addressing the swing-core logic over entire elections, we fill a gap in the formal literature.
Second, we allow parties to have a preference, ideological or otherwise, for distributing benefits to their
supporters, rather than a narrow focus on maximizing vote share. In this conception, the raison d’etre of
parties is to redistribute benefits to their supporters, but they can only do so if they win the election.
This requires the party to evaluate a tradeoff between targeting supporters with pork or targeting those
who will maximize the seat share for the party. This is further complicated by the fact that maximizing
vote share and seat share are two different things. For this reason, we modify the vote-maximizing objective function of the Dixit-Londregan model to an objective function that represents the tradeoff between
maximizing the expected seat share and a preference for targeting supporters.
In order to understand the logic we undertake in this model, consider a polity with 3 constituencies, A,
B, and C. In one scenario, let probability of winning constituencies A, B, and C be 20%, 50% and 100%,
respectively. Assume further that the marginal impact of transfers on vote share is highest in B because
it is a swing constituency. In this scenario, the party will invest heavily B and relatively less in C because
it’s a safe seat and because the party needs to win B in order to win the election. Now, consider a scenario
in which everything is the same except that the probability of winning in A is 95%. In this scenario, since
the party is all but ensured of winning the election, the party will direct more resources to C relative to
B because B is no longer pivotal, despite its marginal impact on vote share, and because the party prefers
to reward its supporters. This example shows how our simple setup induces dependency across the
constituencies because the change in support in A induces differences in the strategy of targeting between
B and C. In this model, we endeavor to generalize this logic.
5.1
Setup
Our model has the following sequence of play:
1. Two parties, Q and R, make promises about transfers to each constituency, where the aggregate
amount promised for transfer over the polity is fixed.
2. The election takes place, and voters select one of the two parties.
3. The party that wins the election fulfills its promises.
Here, we analyze the decision-theoretic logic for Q, with the understanding that we could undertake
an identical analysis for R. Consider a polity, P, endowed with N constituencies and let tiP ≥ 0 with
P ∈ { Q, R} denote the transfer to constituency i, with tP = (tiP ). We let Q’s probability of winning in
constituency i be distributed according to the distribution function, Fi . We define the "cutpoint" in some
constituency i as a function of an initial cutpoint, xi , and transfers from each party, where Ui denotes the
movement in the cutpoint as a function of the transfer from each party:
Xi = xi + Ui (tiQ ) − Ui (tiR )
The probability that Q wins i is given by Fi ( Xi (tiQ , tiR | xi )). We will define the before transfer probability
of winning constituency i as pi = Fi ( xi − Ui (tiR )) ∈ (0, 1). Finally, we assume that parties make promises
over a fixed budget, B, and fulfill those promises if they win the election.24
We envision the election as a set of "Poisson trials" where each constituency i is distributed as an independent Bernoulli variable (0=Q loses, 1=Q wins) with parameter Fi .25 The expected seat share for Q is given
by N1 ∑ Fi , and we will let Z be an increasing log-concave function of the expected share, and a concave
24 Thus, parties may end up targeting constituencies in which they lose. The unmodeled assumption is that parties will face serious
consequences if they shirk from their promises, and it is thus costly to do so. One could, potentially, extend our model, according
to standard accountability models, to an infinite period game where voters play trigger strategies against a shirking party to ensure
implementation of promises.
25 This assumption implies there are no spillovers in the impact of pork upon vote share in constituencies.
18
function of the transfer. Intuitively, Q should be more able to implement its core preferences with higher
seat shares since this minimizes gridlock in allocation decisions. For instance, if Q holds a bare majority
the opposition party may be able to block allocation to some constituencies by convincing a few wavering
legislators, or winning candidates of Q from pivotal constituencies may attempt to skew distribution of
transfers. Thus, we allow the utility of Q to increase as the expected seat share increases through Z. At
the same time, Q prefers to target its core constituencies, and prefers to win larger vote shares in those
constituencies through larger transfers. Thus, given a core constituency, C, and a swing constituency, S,
∂g
∂g
we will choose a log-concave function g such that ∂F > ∂F . Putting all of this information together, Q’s
C
S
best response function can be described by a simple constrained maximization problem:
!
N
1 N
∗
tQ = arg max Z
Fi (tiQ ) × g( F1 , . . . , Fn ) subject to ∑ tiQ = B
(5.1)
∑
tQ
N i =1
i =1
To build some intuition about the utility function, consider the case where g is a constant. In this case,
Q maximizes its expected share of constituencies, N1 ∑ Fi . By allowing g to vary as a function of core
support, the desire to maximize the the expected share of constituencies is mitigated by a preference for
targeting core constituencies. Thus, the maximization problem expresses a tradeoff between targeting
those constituencies with: 1) the largest amount of core preference; and 2) the largest electoral benefit in
terms of maximizing the expected seat share. Using standard techniques, it is easy to show that a Nash
equilibrium always exists.
Theorem 5.1. A Nash equilibrium exists.
5.2
Assumptions on Fi , gi , and Z
Although the model lends itself to fairly general functional forms, we will find it convenient to explicitly
define our functions in order to develop some intuition for the effects. For notational simplicity, since we
are always talking about party Q, we will drop the subscript corresponding to the party.
As usual, we will assume that Fi is increasing and concave in ti .26 We will assume Fi takes the following
functional form:
Fi = (ti | x0 ) = pi + θi ∗ log (ti + 1)
(5.2)
While our results hold more generally, this particular functional form makes an assumption by holding
the θi parameter constant in the function, which will make the results easier to interpret. The natural
intuition for this functional form is that a 1 percent increase in ti∗ + 1 yields a θi marginal increase in the
probability of winning the constituency. The higher the value of θi , the higher the marginal impact of a
transfer upon Fi . Thus, θi is a measure of the extent to which i is a swing constituency.
At the same time, parties aim to skew benefits to those constituencies corresponding to their core preferences, so the marginal benefit of a transfer to core constituencies exceeds the marginal benefit to swing or
opposition constituencies. We will assume g, the part of the function corresponding to core preferences,
takes the following functional form:
gi (ti ) = wi Fi ; wi ≥ 0
(5.3)
g = exp ∑ gi
The function g, increasing in ∑ gi , is maximized when the distribution of benefits is skewed towards
core constituencies. Intuitively, the marginal impact on g is higher as Q targets benefits to constituencies
26 As
Dixit and Londregan (1996) note, Fi is often not a concave function of Xi ; thus, this assumption is akin to stating that Xi is
sufficiently concave in ti to ensure that Fi is a concave function of ti .
19
x0 + ∆x
θB∆x = θBlog(tiQ + 1)
θA∆x = θAlog(tiQ + 1)
Fi
x0
x~0
x~0 + ∆x
Figure 5.2 gives a graphical representation of a general Fi and the notion of a rectangular representation of effects. In
particular, for a small shift in the cutpoint ∆x, we estimate the change in F as θi ∆x.
shift in cutpoints comes from
This
0 , under which circumstances θ ∆x = θ ∗ log
increasing the transfer from tiQ to tiQ
i
i
0 +1
tiQ
tiQ +1
. Finally we show two regions
where the cutpoint shifts ∆x, where the height of each rectangle is θi . As we see, θ A > θ B , implying that a shift in cutpoint
in the region around the left rectangle induces a greater electoral benefit. Thus, θi is a measure of the extent to which i is
a swing constituency.
Figure 9: Understanding F
(thereby increasing Fi ) with higher values of wi . Thus, wi is measure of the extent of core preference for
constituency i.
Finally, we will assume that Z is an increasing log-concave function of its argument, the expected share
of constituencies.27 We will make the intuitive assumption that Z is an increasing concave function when
the constituency share is at least 50%. For instance, Q benefits more from an increase in (expected) seat
share from 50% to 60% as opposed to one from 80% to 90% since we expect most gridlock to occur when
parties have smaller majorities. Note, however, Z is likely to be convex when the constituency share is less
then or equal to 50% since we would naturally expect Q to benefit more from an increase in constituency
share from 40% to 50% as opposed to one from 10% to 20%.28
5.3
Defining Opposition, Swing, and Core Constituencies
In section 2, we discussed that the core-swing literature differentiates between opposition, swing, and
core constituencies. Intuitively, opposition constituencies are those constituencies where the party is not
particularly attached in terms of preferences and has little opportunity to make an impact on the vote
share. Swing constituencies are those constituencies where the party has marginal attachment but has
opportunities to make large impacts on the vote share through transfers. Finally, core constituencies are
those constituencies where party is strongly attached in terms of preferences but where transfers have little
impact upon vote share.29 Our typology deviates slightly from these definitions, since we define
Opposition (O), swing (S), and core (C) constituencies can be easily described in terms of w and θ. In
particular, wO < wS < wC and θS > θC , θO . In other words, w and θ are directly related when going
from opposition to swing constituencies, and they are inversely related when going from swing to core
constituencies. In order to create a natural divisions between opposition, swing, and core constituencies,
27 A
function f is said to be log-concave if log f is concave.
B discusses a particularly intuitive function form for Z. Nonetheless our results only require log-concavity of Z.
29 Note that this is different than the logic used in Cox and McCubbins (1986) where core "groups" are precisely the populations
where transfers have the largest effect upon vote share.
28 Appendix
20
we define: (1) opposition constituencies as those where the party prefers the to give marginal transfers to
the constituencies with the highest value of θ; (2) swing constituencies as those with a sufficiently high
value of θ, between which the party needs to evaluate a tradeoff between θ and w, and prefers to give
marginal transfers to the constituencies with the highest value of θ; and (3) core constituencies as those
where the party needs to evaluate a tradeoff between θ and w but prefers to give marginal transfers to the
constituency with the highest value of w.
Definition 5.2. Let opposition (O), swing (S), and core (C) constituencies be such that wO < wS < wC , and let
θi ∈ [ θ , θ ]
(i) Given two opposition constituencies, O1 and O2 , θO1 > θO2 implies:
wO1 > wO2
(ii) Given two swing constituencies, S1 and S2 , θS1 > θS2 ≥ θ S , where θ S ∈ [ θ , θ ], implies:
w S1 θ S1 > w S2 θ S2
(iii) Given two core constituencies, C1 and C2 , θC1 > θC2 implies:
wC1 θC1 < wC2 θC2
θ
θ
Opposition
θ
Swing
Core
w
0
1
Figure 10: Hypothetical Relationship Between w and θ
Finally, we divide the swing constituency category into two sub-categories to make the analysis easier to
follow. A swing constituency will be called core-leaning if θi > θ j implies wi < w j , and it will be called
opposition-leaning if θi > θ j implies wi > w j .
5.4
Equilibrium Analysis
The fundamental goal of this section is to analyze the relationship between two endogenous variables
in the model: 1) electoral competitiveness as measured by ∑ Fi∗ ; and 2) difference in transfer between
∗ − t∗ . This subsection clarifies the relationship between these two variswing and core constituencies, tC
S
ables, and how this relationship is conditioned by exogenous parameters in the model. In other words,
21
the endogenous variable of interest in our analysis is the relationship between transfers and electoral
competitiveness.30
We begin by solving for the first order conditions (assuming no corner solutions) resulting from the
∗ , we get:
logarithm of the function in (5.1), for each i, and equilibrium transfer tiQ
∂ log( Z × g)
=
∂tiQ
Z 0 (∑ Fi )
+ wi
Z (∑ Fi )
Fi0 =
θi
ti∗ + 1
Z 0 (∑ Fi )
+ wi
Z (∑ Fi )
=λ
(5.4)
Assuming that the constraint in (5.4) binds, then we can easily solve for the equilibrium transfer to constituency i, as a function of expect seat share.
Theorem 5.3. Assume the constraint in (5.4) binds. For B sufficiently large:
θi Z 0 ∑ Fi∗ + θi wi Z ∑ Fi∗
−1
ti∗ = ( B + K )
∑ θi Z 0 ∑ Fi∗ + ∑ θi wi Z ∑ Fi∗
(θi − θ j ) Z 0 ∑ Fi∗ + (θi wi − θ j w j ) Z ∑ Fi∗
∗
∗
ti − t j = ( B + K )
∑ θi Z 0 ∑ Fi∗ + ∑ θi wi Z ∑ Fi∗
where K denotes the number of constituencies receiving non-zero transfer.
The equations in theorem 5.3 establishes the fundamental relationship between t∗ and Fi∗ . Certain features
of the expression on the right side of the first equation are worth noting. First, the expression includes
∑ Fi∗ , so the equilibrium transfer in any constituency is always related to entire electoral context through
the expected seat share, and this introduces the dependence structure between constituencies. Second, the
transfer is growing in the size of the budget B, and we can guarantee that t∗ is positive for a large enough
value of B.
We define the targeting between two constituencies, i, j ∈ N, to exhibit a swing effect between i and j when
ti∗ − t∗j > 0 for θi > θ j and a core effect when ti∗ − t∗j > 0 for wi > w j . Looking at the second equation, we
see that there is likely to be a swing effect when Z 0 is relatively large as compared to Z (i.e. as Z vanishes)
since the first term in the numerator is large and growing in size of θi − θ j . Thus, when parties are likely
to be on the losing end of the election, we expect swing targeting.
When the value of Z is relatively large as compared to Z 0 (i.e. when the party has all but won the election),
the second term in the numerator is large and growing the size of θi wi − θ j w j . This yields two cases. If
θi > θ j implies wi θi < w j θ j , as it is for two core constituencies, then this yields a core effect between i and
j. If, however, θi > θ j implies wi θi > w j θ j , we still have a swing effect. This shows that movement from a
swing effect to a core effect as an election gets less competitive is not a trivial matter, but depends on the
relative scale of w and θ. The following corollary gives simple sufficient conditions for universal swing or
core effects.
Corollary 5.4. The following conditions are sufficient for universal swing and core effects:
(i) Assume there are no core constituencies receiving positive transfers in equilibrium. Then, ti∗ − t∗j > 0 for
θi > θ j for all i, j ∈ N.
(ii) Assume there are no constituencies such that θi > θ j implies wi < w j and wi θi > w j θ j . Then, ti∗ − t∗j > 0 for
wi > w j for all i, j ∈ N for Z > Z with Z ∈ (0, 1).
In essence, this corollary captures the fact that there are two sets of constituencies upon which the analysis
turns. There are core-leaning swing constituencies, which will always exhibit more swing constituency
targeting. There are also core constituencies where θi > θ j implies wi θi < w j θ j which will exhibit core
30 A
more complicated analysis, which we do not do here, would also analyze how each endogenous variable explicitly changes
(as opposed to in relation to each other) as a function of exogenous parameters.
22
targeting. For all other constituencies, core and swing targeting are coincident. Universal conditions for
swing or core targeting outcomes hinge upon ruling out one or the other set of constituencies.
Our key comparative static of discerning the core and swing effect for years with more than or less
than 50% constituencies with at most 10% margin of victory measures the claims of corollary 5.4. In
years with very few low margin of victory constituencies, the expected seat share should be quite high
and those receiving positive transfers are almost entirely core constituencies. By contrast, in years with
many low margin of victory constituencies, the expected seat share should be lower and there should be
relatively few core constituencies. At the same time, the persistence of some number of core constituencies
may explain why we don’t see aggregate swing effects in those years, but rather a mitigation of core
effects.
5.4.1
Marginal Effect of Competition
∂ ti∗ −t∗j
We now establish the marginal effect of competition on core-swing outcomes, i.e. we investigate ∂ ∑ F∗ .
k
We might feel that the conditions for a universal core and swing effect are too strong and prefer focus on
whether the marginal effects of an increase in ∑ Fk∗ are identical for any pair of constituencies, i.e. does
an increase in ∑ Fi∗ induce greater swing and core effects between any pair of constituencies. Theorem 5.5
investigates how a change in the equilibrium level competitiveness (through initial cutpoints), holding all
of the other exogenous variables constant, affects equilibrium transfers.
Theorem 5.5. Consider two constituencies, i and j, such that θi < θ j and wi > w j . The change in core effect as a
function of increasing seat share,
∂ ti∗ −t∗j
∂ ∑ Fk∗
, is positive if and only if:
θ i wi ∑ θ k − ∑ w k θ k − θ j w j ∑ θ k − ∑ w k θ k > 0
The next couple of corollaries attempt to understand the implications of the expression in theorem 5.5 over
the parameter space of w and θ. First, we consider a simple condition to guarantee a universal marginal
core effect.
Corollary 5.6. Consider two constituencies, i, j ∈ N, such that θi < θ j and wi > w j . Let w j ∑ θk < ∑ wk θk . Then,
∂ ti∗ −t∗j
∂ F∗
∑ k ∂ ti∗ −t∗j
∂ ∑ Fk∗
> 0. Furthermore, if for each swing constituency, S, we have wS ∑ θk < ∑ wk θk , then for all i, j ∈ N,
> 0.
The corollary is a straightforward implication of theorem 5.5, but it gives an intuitive feel for marginal
core effects. The term ∑ wk θk is a weighted sum of thetas, where the greater the core preference for a
constituency, the greater the weight. Thus, if wS ∑ θk < ∑ wk θk for any swing constituency S, it means
that the data are strongly skewed towards core constituencies. As this skew lessens, we expect less
of a marginal impact of an increase in ∑ Fi∗ . This describes another reason why our key comparative
static revolves around testing if there are a majority of core or swing constituencies in the particular
electoral year. When the data strongly skewed towards core constituencies, combined with corollary 5.4,
we arrive at the fact that movement towards a less competitive election predicts stronger core effects for
all constituencies.
Finally, we investigate the conditions for a universal marginal swing effect.
23
Corollary 5.7. Assume there are no core constituencies and θi < θ j .
θ
w j < i wi +
θj
θi
−1
θj
!
∂ ti∗ −t∗j
∂ ∑ Fk∗
< 0 for all i, j ∈ N if:
∑ wk θk
∑ θk
There is never a marginal swing effect between two core constituencies, so corollary 5.7 rules out such
constituencies. There is always a marginal swing effect between two opposition constituencies or an
opposition and a swing constituency. Thus, corollary 5.7 boils down to putting conditions on swing
constituencies in order to guarantee a marginal swing effect. Corollary 5.7 explains that we are much
more likely to see marginal swing effects when there are a lot of opposition-leaning swing constituencies
as opposed to core-leaning constituencies because this implies that ∑ wk θk is lower for a fixed ∑ θk . In
other words, we are likely swing effects when the party is more likely to lose the election.
5.5
Discussion
In section 3, we pointed out that electoral competitiveness is a murky concept. It may refer to the number
constituencies a party is expected to win, ∑ Fi∗ , or it may refer to the underlying distribution of swing
and core constituencies in the electorate, the distribution of w and θ in the electorate. The underlying
distribution of swing and core constituencies is an a priori concept, i.e. parameters that exists before the
election begins, whereas expected constituency share is an ex post concept, i.e. a variable defined as a
function of how each party plays in equilibrium.
Our analysis shows that both of these elements are important for us to discern swing and core targeting
effects in equilibrium. In particular, the party is likely to employ a core targeting strategy when the election
is all but won (i.e. when ∑ Fi∗ is high) and the underlying distribution of constituencies only includes
opposition and core constituencies. We can soften these requirements somewhat by restricting the analysis
to the marginal effect of ∑ Fi∗ on core-swing targeting. Here, we only need that the underlying distribution
of constituencies is skewed towards core constituencies to guarantee a marginal core effect for each pair
of constituencies. A larger share of swing constituencies mitigates this marginal core effect.
This frames the empirical test in the previous section. We operationalized the logic of the model through
the margin of victory in each constituency. In particular, constituencies that won with a low (< 10%)
margin of victory were identified as constituencies with a high value of θ, whereas constituencies won
with a high margin of victory were identified as constituencies with a high value of w (because these
constituencies have a larger percentage of supporters). At the same time, the margin of victory is an
ex post measurement, so it gives us a sense of equilibrium expected constituency share. We chose to
compare electoral years that had at least 50% constituencies with a low margin of victory with those
electoral years that had at 50% of the constituencies with a high margin of victory. This comparison of
years many constituencies with a margin of victory simultaneously addresses both notions of electoral
competitiveness. In addition to measuring the underlying distribution of constituencies, years with many
core constituencies are likely to have higher expected seat share for the winning party.
6
Conclusion
This paper proposes and tests hypotheses relating to variations in core and swing outcomes over time
and the construction of new public schools in Tamil Nadu, India. Following recent developments in the
"core-swing" literature, we do not assume that parties always prioritize core (swing) voters over time. Yet,
unlike recent studies that examine differences in targeting by type of good that is distributed, we explore
how electoral context affects the distribution of the same good (schools) over time.
24
We divide electoral competitiveness along two dimensions, across and within constituencies. We show that
core-swing targeting is sensitive to both the expected share and the underlying distribution of core and
swing constituencies for each party. We also argue that the expected seat share is necessarily endogenous
to transfers, while the underlying distribution of swing and core constituencies are known to all parties.
Section 5 presents a formal model to synthesize these ideas in order to show how (and when) increases in
the expected seat share and greater skews towards swing or core constituencies affect core-swing targeting
outcomes.
A multi-level modeling regression framework allows us to disaggregate targeting strategies across time
and space, and the use of GIS allows us to link administrative and political data. Our analysis of school
construction in Tamil Nadu between 1977 and 2007 demonstrates that electoral context strongly influences
the ruling party’s targeting calculus. We believe that our findings demonstrate that, as a baseline, parties
do rewards core constituencies with schools following the election and formation of a new government.
Yet, there are deviations from the "core" targeting strategy in those years with exceptionally high levels of
electoral competition within constituencies. When more than half the ruling coalition’s victories come in
closely-fought ("swing") constituencies, the ruling party alters its post-election targeting strategy to reward
pivotal swing areas. We interpret this as the constraining effect of electoral competition: while there may
be a bias of rewarding their most ardent supporters, politicians must abide by electoral realities. In swing
constituencies where the margin of victory is slim, politicians must make desperate promises to sweeten
the pot.
In conclusion, we believe that this research can contribute to our understanding of tactical redistribution
in four ways. The first two are theoretical. First, we extend the core-swing framework to multiple constituencies and conceptualize the idea of a core and swing constituency, as opposed to core and swing
groups. Cox (2006) points out that the standard core-swing models only apply to a single constituency
and core and swing groups, whereas most of the empirical tests in the literature address core and swing
constituencies. Thus, by defining and modeling core and swing constituencies, and the structure of dependence between them, we address a major lacuna in the literature.
Second, we create framework to understand the relationship between electoral competitiveness and transfers. In particular, we show that electoral competition is best understood as divided along two dimensions,
across and within constituencies. Furthermore, we address the fact that electoral outcomes and transfers
are necessarily endogenous since election outcomes tend to be measured ex post. At the same time, parties
have a priori information on which constituencies are swing constituencies and a priori core constituency
preferences. Our model shows how these moving parts fit together to create comprehensible comparative
statics.
The third and fourth contributions are methodological. Rather than relying on crude measures of spending, we use micro-level data on school construction. This provides a more accurate picture of actual pork
barrel effort. The real innovation though is using GIS mapping to estimate the effect of pork barreling at
the level of the assembly constituency. This requires us to take block-level data on schools and overlay this
with assembly constituency boundaries. Previous work on distributive politics in India takes shortcuts in
measurementâ primarily by relying on district-level analysisâ that could bias estimates.
Finally, we demonstrate the utility of integrating multi-level modeling (MLM) with time-series, crosssectional (TSCS) data. MLM balances between "pooled" and "unpooled" estimates based one the sample
size in each cluster (e.g. constituency x or time y), what Gelman and Hill (2007) call "partial pooling."
Thus, we can relax the assumption that there is one "true" relationship between our dependent variable
on predictors of interest. Rather, we can vary both intercepts and slopes to obtain disaggregated estimates
across time and space. This modeling strategy allows us to take a nuanced view of the vagaries of tactical
redistribution as electoral conditions change.
25
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A
Proofs
Proof of Theorem 5.1
Note that the only strategic element of the game is the interaction between Q and R in the first stage. The
strategy set for each party tiP for P ∈ { Q, R} is compact and convex since it is just the set tiP ≤ B. We
argue that the objective function for the party,
!
!
N
N
Z
∑ Fi (tiP )
× exp
∑ gi ( t i P )
i =1
i =1
is log-concave in tP .
The concavity of Fi implies that ∑ Fi is concave, and a log concave function with a concave argument,
Z (∑ Fi ) is also log concave in tP . Our chosen
form is clearly log concave since the log of the
functional
1
convex part of the function has the form log 2 + α (log 2 + log (∑ Fi )). Since Fi is positive and concave,
and wi is positive, gi is also positive and concave, and thus function g = exp (∑ gi ) is log-concave. The
product of two log-concave functions is also log-concave, so the objective function is quasiconcave.
Since the objective function for the party is quasiconcave, continuous in the strategy of each party and because the strategy space for each party is compact and convex, we apply the Debreu-Fan-Glicksberg theorem (Debreu (1952), Fan (1952), Glicksberg (1952)) to ascertain the existence of a Nash equilibrium.
One task involves being more precise about which constituencies receive transfers in equilibrium and how
this is related to the type constituency.core and swing constituencies based upon whether the constraint
in (5.4) binds. In particular, there will there will be certain constituencies that will never receive benefits
because the marginal benefit of a transfer is always higher in other constituencies, where the constraint
does not bind. Intuitively, these excluded constituencies have low θ and w values in the function, i.e.
there is little electoral or preference benefit from targeting these constituencies. Since we expect w to be
monotonically increasing in the core vote, these are what we earlier termed opposition constituencies. In
other words, the following lemma formally describes why parties promise nothing to many opposition
constituencies.
Lemma A.1. Consider constituencies i, j ∈ N such that wi > w j . The constraint in (5.4) fails to bind for constituency j and t∗j = 0 if, in equilibrium,
θi
ti∗ +1
> θj.
Thus, for i, j ∈ N as defined above, Bθi+w1i > θ j guarantees that j will never receive a transfer in equilibrium,
irrespective of initial parameters. The immediate corollary defines a sufficient condition for binding constraints, i.e. no corner solutions:
Lemma A.2. Define I ∈ N such that t∗I > 0. There is no corner solution, i.e. (5.4) binds, if
w I > w j for some j ∈ N.
θI wI
B +1
< θ j w j and
The condition in lemma A.2 only fails when θ I or w I is large (relative to B). We introduced θ as a measure
of the electoral responsiveness to a transfer, i.e. swing constituencies were likely to have high values
of θ. We also introduced w as measure of the strength of preference for a particular constituency. Our
fundamental interest is in polity-wide parties that face a tradeoff in targeting swing or core constituencies.
Intuitively, the condition in (A.2) may be violated for a constituency-specific party for constituency i that
would have wi significantly higher than the values for w of any other constituency. Alternatively, the
condition may be violated if w I > w j implies θ I >> θ j , which would occur when parties are extremely
uncompetitive. Our model, thus, works well for polity-wide parties that face a tradeoff between swing
and core constituencies.
29
Proofs of Lemmata A.1 and A.2
The marginal benefit of a transfer to i is greater than any transfer to j in equilibrium if:
0
0
Z (∑ Fi )
Z (∑ Fi )
θi
+ wi > θ j
+ wj
ti∗ + 1 Z (∑ Fi )
Z (∑ Fi )
0
Z (∑ Fi )
θ i wi
θi
− θj
+ ∗
− θj wj > 0
⇒ ∗
ti + 1
Z (∑ Fi )
ti + 1
θi
ti∗ +1
If we assume wi > w j , this condition is guaranteed by
> θj.
On the other hand, the first order conditions bind if there are at least two constituencies that satisfy a
"crossing condition." In particular, let us fix a constituency I that receives a positive transfer in equilibrium,
i.e. t∗I > 0. In order to avoid a corner solution, it must be the case that there are better alternatives than
promising the entire B of the budget to constituency I. In other words, there must be some constituency j ∈
N where the marginal benefit of contributing something to j exceeds the marginal benefit of contributing
to I. Thus,
0
0
Z (∑ Fi )
Z (∑ Fi )
θI
+ wI < θj
+ wj
B + 1 Z (∑ Fi )
Z (∑ Fi )
0
θI
Z (∑ Fi )
θi w I
⇒
− θj
+
− θj wj < 0
B+1
Z (∑ Fi )
B+1
If we assume w I > w j , then the condition is satisfied as long as
θi w I
B +1
< θj wj .
Proof of Theorem 5.3
If the first order conditions bind, then taking the derivative of the Lagrangian yields:
∂ log( Z × g)
=
∂tiQ
Z 0 (∑ Fi )
+ wi
Z (∑ Fi )
⇒ ti∗ + 1 = θi
Fi0
θ
= ∗ i
ti + 1
Z 0 (∑ Fi )
+ wi
Z (∑ Fi )
=λ
( Z 0 (∑ Fi ) + wi Z (∑ Fi ))
λZ (∑ Fi )
Now assume that the first order conditions bind for K constituencies, for which there are non-zero transfers. Then summing across all K conditions, we get:
K
K
i =1
i =1
∑ ti∗ + K = B + K = ∑ θi
⇒λ=
( Z 0 (∑ Fi ) + wi Z (∑ Fi ))
λZ (∑ Fi )
∑ θi Z 0 (∑ Fi ) + ∑ θi wi Z (∑ Fi )
( B + K ) Z (∑ Fi )
Plugging back into the expression for ti∗ and solving yields:
θi Z 0 ∑ Fi∗ + θi wi Z ∑ Fi∗
∗
−1
t = (B + K)
∑ θi Z 0 ∑ Fi∗ + ∑ θi wi Z ∑ Fi∗
For B sufficiently large, the above expression is always positive.
30
Proof of Theorem 5.5:
ti∗
− t∗j
θi Z 0 ∑ Fk∗ + θi wi Z ∑ Fk∗ − θ j Z 0 ∑ Fk∗ − θ j w j Z ∑ Fk∗
= (B + K)
∑ θk Z 0 ∑ Fk∗ + ∑ θk wk Z ∑ Fk∗
Since we are only interested in the direction of the derivative, we can analyze the following expression,
with the following simplification:
!
∂ ti∗ − t∗j
(θi − θ j ) Z 00 + (θi wi − θ j w j ) Z 0
(θi − θ j ) Z 0 + (θi wi − θ j w j ) Z ∗ (∑ θk Z 00 + ∑ θk wk Z 0 )
= (B + K)
−
∂ ∑ Fk∗
∑ θk Z 0 + ∑ θk wk Z
( ∑ θ k Z 0 + ∑ θ k w k Z )2
sign
(θi − θ j ) Z 00 + (θi wi − θ j w j ) Z 0 ∗ ∑ θk Z 0 + ∑ θk wk Z −
(θi − θ j ) Z 0 + (θi wi − θ j w j ) Z ∗ ∑ θk Z 00 + ∑ θk wk Z 0
= (B + K)
Simplifying and canceling out appropriate terms, we get:
(
((
((((
((
((
( B + K ) ( θ(
−(θ (
)∑
θk (
Z 00 ∗ Z 0 + (θi wi − θ j w j ) ∑ θk Z 02 + (θi − θ j ) ∑ θk wk Z ∗ Z 00 + (θi w(
−(θ(
w(
)∑
θk wk Z ∗ Z 0
i
j
i
j
j
(
((
(
(
((((0
(
00( 0
00
02
(
(
(
(
(
(
θ
w
−
θ
w
)
θ
w
Z
∗
Z
−
θ
)
θ
Z
∗
Z
−
(
θ
w
−
θ
w
)
θ
Z
∗
Z
−
(
θ
−
θ
)
θ
w
Z
−
− ( θ(
(
(
i (
i (j j ∑ k k
i i
j j ∑ k
i
j ∑ k k
(i ( j ∑ k
(
(
= ( B + K ) (θi wi − θ j w j ) ∑ θk Z 02 − Z ∗ Z 00 + (θi − θ j ) ∑ θk wk Z ∗ Z 00 − Z 02
(A.1)
θ i wi − θ j w j ∑ θ k + θ j − θ i ∑ θ k w k
= ( B + K ) Z 02 − Z ∗ Z 00
Log concavity of Z implies Z 02 − Z 00 ∗ Z > 0. Combining this with the fact that θi < θ j , we arrive at the
result that (A.1) is positive (and non-positive otherwise) when:
θ i wi ∑ θ k − ∑ w k θ k − θ j w j ∑ θ k − ∑ w k θ k > 0
B
A Functional Form for Z
We define α ≥ 1 as a measure of how much Q only cares about winning the election, as opposed to
weighing each seat equally, where a higher α implies that Q has a greater tendency to only care about
winning the election (in expectation). Consider the following function, which is consistent with our
assumptions:31

 1 (2x )α
if 0 ≤ x < 0.5
2
Z(x) =
where α ≥ 1
(B.1)
 1 − 1 (2(1 − x ))α if 0.5 ≤ x ≤ 1
2
As α tends to ∞, Q solely cares about winning the election (in expectation), and as ν × α tends to 1, Q
cares equally about each constituency it wins, i.e. Z = ∑ Fi . Typically, we expect α to be fairly large since
parties are more likely to care about those seats that mean the difference between controlling government
or being the opposition, as opposed to those seats that add on to an already large supermajority. Figure 11
shows Z changes as a function of α. It should be noted that basing a utility function on the probability of
winning an election, as opposed to the expected share of constituencies won as we have here, is a different
mathematical problem. Using vote share or constituency share (as also in Cox and McCubbins (1986) and
Dixit and Londregan (1996)) tends to have more tractable properties from a game-theoretic perspective.
For some discussion of the difficulties of modeling the probability of winning perspective, see Duggan
(2000) and Patty (2005). Nonetheless, as figure 11 shows, we can get arbitrarily close to modeling a party
only wants win the election in expectation.
expression 1 − 12 (2(1 − x ))α is just the expression 12 (2x )α reflected across the lines x =
is continuous and differentiable (even at x = 12 ).
31 The
31
1
2
and y = 12 . One can check that Z
1
=
0.0
0.2
0.4
Z
0.6
α
α=
0.8
5
α=∞
1.0
Figure 11: Understanding Z as a function of α
0.0
0.2
0.4
0.6
∑ Fi
32
0.8
1.0