leader survival and government spending in democracies and
TRANSCRIPT
Leader Survival and Government Spending
in Democracies and Dictatorships∗
Jeff CarterDepartment of Political ScienceThe University of Mississippi
March 20, 2014
Word Count: 11,301
Abstract
How do government spending and leader survival affect one another when leaders are motivatedby survival and policy concerns? A formal model developed to address this question indicatesvariation across regime type in winning coalitions’ spending preferences and the cost of leaderreplacement results in democrats and dictators securing their survival with different spendingdistributions and varying in their responsiveness to their constituents’ preferences. Consistentwith expectations, I find that proportionately higher military spending increases the probabilitya dictator remains in power but decreases the probability a democratic leader retains office,mean spending patterns vary across regime type, and greater variance in spending exists indictatorships than in democracies.
∗An earlier version of this manuscript received the Stuart A. Bremer Award for Best Graduate Paper presented atthe 2009 annual meeting of the Peace Science Society (International). Previous drafts were also presented at the 2010annual meetings of the International Studies Association and Midwest Political Science Association, and the 2010Empirical Implications of Theoretical Models Summer Institute. Susan Allen, Phil Arena, Scott Bennett, MichaelBernhard, David Carter, Matt DiGiuseppe, Ben Fordham, Ben Jones, Douglas Lemke, Amanda Licht, Burt Monroe,Tim Nordstrom, Glenn Palmer, Jim Shortle, Laron Williams, Chris Zorn, and, in particular, Heather Ondercin arethanked for helpful comments and discussions at various stages of this project. All remaining errors are my own.
Beginning in the spring of 2010, daily life in Greece frequently ground to a halt as workers
went on strike and citizens protested the austerity programs enacted by the government of
Prime Minister George Papandreou, head of the Panhellenic Socialist Movement party (BBC
2010). Papandreou’s government had substantially reduced government spending on public-
sector salaries, farm subsidies, pensions, and other programs in exchange for bailouts and debt
relief from the European Union, European Central Bank, International Monetary Fund, and
private investors. Not wanting the political blame for further, more severe austerity policies,
Papandreou announced on October 31, 2011 that a national referendum would be held regarding
the latest bailout. This plan was scrapped on November 3rd when he realized the referendum
would likely fail, which would prevent Greece from receiving the funds it needed to avoid default
(BBC 2011). Papandreou agreed to step down on November 6th and officially resigned as Prime
Minister on November 11, 2011, only two years into his government’s four year term (Smith and
Klington 2011, Telegraph 2011). Reflecting on his tenure during the spring of 2012, Papandreou
stood by his decision to pursue austerity despite the political consequences: “I knew that these
(policies) would not be popular. And I knew, sooner or later, I would be very much the target”
(Kakissis 2012).
A fundamental task of government is to finance state policies and programs through the allo-
cation of scarce economic resources. Considerable variation exists in how governments distribute
the resources they possess, particularly across regime type. Explanations for why democracies
and non-democracies allocate their resources differently often argue leaders are motivated by
their own political survival and democratic incumbents are politically accountable and respon-
sive to larger constituencies than are autocratic leaders (e.g., Bueno de Mesquita et al. 2003).1
Rather than being motivated exclusively by their political survival, though, most political in-
cumbents also have preferences over policy outcomes (for example, Fenno 1978, Strøm 1990).
As the example of former Prime Minister Papandreou suggests, some leaders are willing to pur-
sue spending policies that go against their constituents’ preferences, even at the cost of their
political survival.
This article examines the relationship between leader survival and government spending
when both an incumbent and her constituents hold preferences over how a government allocates
its economic resources and leaders can be motivated by survival and policy concerns. I develop
1The terms non-democracy, autocracy, dictatorship, and their respective derivatives are used interchangeablythroughout this article.
1
a game-theoretic model to analyze this situation. In equilibrium, a leader’s optimal play is a
function of each player’s spending preferences, an incumbent’s motivation for implementing pol-
icy, and the structural costs of leader replacement to a winning coalition. The model indicates
that a leader will rationally allocate spending distributions other than those preferred by her
key constituents when she is not exclusively motivated by her political survival. However, a
leader that deviates from the spending distribution preferred by her winning coalition faces a
higher probability of losing office than a responsive leader. Variation in the spending preferences
of democratic and non-democratic winning coalitions implies different optimal spending distri-
butions for survival-motivated leaders across regime type. The model also suggests variation
in the cost of replacement results in dictators allocating spending distributions closer to their
ideal points than democrats. Statistical analyses of the period from 1950 to 2001 are consistent
with the model’s expectations. I find the spending distribution that maximizes the probability
a dictator remains in office contains more military spending and less social spending than the
distribution that maximizes a democratic incumbent’s survival. I also find that dictators allo-
cate more of their state’s total spending to the military, on average, and have greater variance
in their spending distributions than do democrats.
This article makes three significant contributions to our understanding of the relationship
between political leaders and government policy. First, the formal and empirical results il-
lustrate the utility of allowing variation in leaders’ motivation for enacting policy and actors’
policy preferences. Doing so allows for more specific predictions about political behavior than
approaches that assume citizens do not vary in their policy preferences. Further, allowing a
leader to vary in the extent to which she is motivated by policy or survival concerns provides
a useful framework for considering how policies vary with dynamic constraints on a leader’s
behavior (Clark and Nordstrom 2005). Second, my findings indicate that the degree to which
an incumbent is responsive to her constituents’ preferences is a function of her motivation for
implementing policy. This qualifies the common claim that policy responsiveness is a defining
characteristic of democracy (e.g., Dahl 1971, Putnam 1993). Third, the statistical analyses are
the first to empirically demonstrate government spending influences leader survival and have
important implications for a number of topics. For example, my finding that a democratic
leader’s probability of survival is maximized with proportionately less military spending than a
dictator’s probability of survival provides micro-foundations for the claim that democracies are
less likely than non-democracies to fight relatively strong opponents (Reiter and Stam 2002).
2
The idea that leader survival and government spending are related is not novel. Most
notably, selectorate theory argues that leaders spend the resources available to them on pub-
lic goods and private benefits in the way that most efficiently ensures their political survival
(Bueno de Mesquita et al. 1999, 2003). The theoretical argument, formal model, and empirics
presented here differ from selectorate theory in a number of important ways. Theoretically, in
contrast to selectorate theory I do not assume that all leaders seek to maximize their probability
of survival or all citizens have the same preferences. With respect to the formal analysis, the
model developed here indicates that in equilibrium leaders will pursue policies that lower their
chances of remaining in power and, accordingly, that they will occasionally be removed from
office by their winning coalitions. Because selectorate theory assumes leaders are exclusively
survival-motivated, equilibrium behavior in the selectorate model of politics sees incumbents
always providing a mix of public goods and private benefits at least as good as the package
of benefits offered by their domestic challengers and, therefore, never being replaced by their
winning coalitions (Bueno de Mesquita et al. 2003, pg. 120). Finally, the empirical analyses pre-
sented here offer insights into the relationship between leader survival and government spending
not explored or predicted by the research associated with selectorate theory. I demonstrate that
the distribution of government spending influences patterns of leader survival and exhibits sig-
nificantly more variance in non-democracies than is the case in democracies. Selectorate theory
argues that spending on public and private benefits will influence a leader’s political survival
but never tests this expectation.2 Further, while Bueno de Mesquita et al. (2003) offer evidence
that mean levels of government spending differ as a function of regime type, they have no ex-
pectations about and therefore do not examine the variance of spending patterns in democracies
and dictatorships. Thus, the theoretical and empirical results presented here contribute to what
we know about the relationship between leaders and government policy and differ in important
ways from the most prominent research on the topic.
The remainder of the article proceeds as follows. The first section outlines the basic moti-
vations all leaders have for enacting policy: securing their survival and pursuing their personal
preferences. I then develop a simple model of the relationship between leader survival and
government spending that allows an incumbent and her winning coalition to have preferences
over the spending distribution and leaders to be motivated by policy outcomes and remain-
2Bueno de Mesquita et al. (2003) test the influence of public goods and private benefits on leader survival byestimating the effects of GDP growth (public good) and black market exchange rate premiums (private benefit) onthe probability an incumbent loses office (pgs. 302-310).
3
ing in power. The model identifies the general dynamics underlying the relationship between
government spending and leader survival that hold for all incumbents and their winning coali-
tions. The third section incorporates into the model systematic variation across regime type in
the spending preferences of incumbents’ winning coalitions and the cost of leader replacement.
This allows us to see how two institutional characteristics of democracies and dictatorships lead
to variation across regime type in the equilibrium behavior of leaders and winning coalitions.
The fourth empirically assesses a set of the model’s expectations. The article concludes with a
discussion of the larger implications of my findings for existing scholarship and future research.
1 Leader Motivations for Policy Decisions
Political incumbents have two basic motivations for enacting policies. Their first is to secure
their political survival, which is done by maintaining the support of their winning coalition
(Riker 1962, Bueno de Mesquita et al. 2003). An incumbent retains the support of her winning
coalition by enacting their preferred policies, a process known as policy responsiveness (inter
alia, Erikson, MacKuen and Stimson 2002, Burstein 2003). One of the most important ways
in which an incumbent is responsive to her key constituents is by allocating scarce resources to
their preferred policies and programs (Smith and Bueno de Mesquita 2011, Arena and Nicoletti
Forthcoming). Consistent with this claim, scholars have demonstrated that patterns of military
spending and social spending in democracies vary with public preferences across countries and
over time (among others, Wlezien 1996, Soroka and Wlezien 2005, Brooks and Manza 2007).
Much of the explicit theorizing and empirical work on policy responsiveness has focused on
democracies. This is unsurprising as it reflects the intuition that democratic politicians are
accountable for their actions while dictators rarely have to answer for their behavior.3 How-
ever, autocrats also secure their political survival through policy responsiveness. Key notes that
even “the least democratic regime ... needs the ungrudging support of substantial numbers of its
people. If that support does not arise spontaneously, measures will be taken to stimulate by tac-
tical concessions to public opinion” (1961, pg. 3). More recently, Gandhi and Przeworski (2006,
2007) argue that autocratic leaders maintain their hold on political power partially through
policy concessions. Similarly, a dictator keeps his ruling coalition satisfied and retains office
through power sharing agreements and policy concessions in Svolik’s (2009) model of authori-
3For example, Dahl argues “a key characteristic of a democracy is the continuing responsiveness of the governmentto the preferences of its citizens” (1971, pg. 1; see also Putnam 1993).
4
tarian politics. All leaders interested in remaining in power therefore have an incentive to enact
their constituents’ preferred policies.
Most political incumbents, though, are not solely motivated by retaining office. Politi-
cians also have personal preferences that influence the policies they pursue (e.g., Fenno 1978,
Wittman 1977, Strøm 1990).4 As both leaders and their constituents hold policy preferences,
incumbents can face a trade-off between enacting their preferred policy and the policy that best
ensures they remain in power (Strøm 1990, Bender and Lott 1996).5 The concept of “shirk-
ing” nicely captures this dynamic. Shirking occurs when an incumbent’s policy preferences
differ from her constituents’ preferences and she pursues her preferred policy (e.g., Kalt and
Zupan 1984, Bender and Lott 1996, Rothenberg and Sanders 2000). As the logic underlying
policy responsiveness would predict, incumbents are more likely to lose office when they deviate
from their constituents’ preferences (Canes-Wrone, Brady and Cogan 2002).
Two factors significantly increase a leader’s incentive to ignore her constituents’ preferences.
The first is when an incumbent no longer cares about her political survival. Consistent with
this idea, scholars have found that shirking is greatest when an incumbent cannot be re-elected
due to term limits, lame-duck status, or retirement (Persson and Svensson 1989, Carey, Niemi
and Powell 1998, Rothenberg and Sanders 2000). Second, a leader is more likely to deviate
from her constituents’ preferred policy as the institutional or structural cost to her winning
coalition of replacing her increases. For example, McGillivray and Smith (2008) demonstrate
that rulers whom are difficult to remove are more likely to defect from interstate cooperation
agreements that benefit the public than leaders whom are easily replaced by their winning
coalitions. Institutional explanations of the democratic peace often rely on a similar logic.
Claims that democratic incumbents are constrained by electoral accountability implicitly argue
that dictators are able to deviate from the public’s preferences due to the relative difficulty of
removing a dictator from power (e.g., Huth and Allee 2002). Incumbents therefore are more
likely to ignore constituent preferences and pursue their preferred policies as they become less
motivated by survival concerns or the structural cost of leader replacement increases.6
4A leader’s policy preferences are related to his or her political ideology or partisanship, but are also inherentlyidiosyncratic (Clark and Nordstrom 2005, Clark, Nordstrom and Reed 2008, Arena and Palmer 2009).
5This trade-off only obtains if a leader and her constituents prefer different policy outcomes. When a leader andher constituents have the same ideal point, there is no tension between an incumbent pursuing her preferred policyversus her constituents’ preferred policy.
6The political accountability literature offers a related explanation for why an incumbent would pursue policiesdifferent from those preferred by her constituents. This approach argues politicians have greater information aboutthe state of the world and the likely effect of policies than do their constituents, whom possess preferences over policy
5
The next section develops a general model of leader survival and government spending that
incorporates insights from the above discussion. Before moving on, though, it should be noted
that the idea leader survival and government spending are related is not novel. Most promi-
nently, selectorate theory argues the mix of spending on public goods and private benefits that
most efficiently secures an incumbent’s political survival is a function of the size of her win-
ning coalition (Bueno de Mesquita et al. 2003). Thus, it is worth highlighting three differences
between the argument and model developed here and selectorate theory. First, the model pre-
sented below allows citizens to vary in their preferences over government spending. In contrast,
selectorate theory assumes all citizens hold the same four policy preferences: more public goods,
more private benefits, more leisure time, and lower taxes (Bueno de Mesquita et al. 2003, pgs.
78-79, 108).7 As everyone wants the same things from their government, selectorate theory
implies that it does not matter who in society gets into a leader’s winning coalition. Second, the
decision to focus on the abstract concepts of public goods and private benefits allows selectorate
theory to speak to a wider range of state behaviors than the argument developed here. However,
the cost of this abstraction is that it prevents selectorate theory from making precise predictions
concerning government spending on particular policies. In the words of Bueno de Mesquita et al.
(2003), selectorate theory cannot “predict which specific bundle of public or private goods will
be emphasized in different societies” (pg. 104). This is particularly relevant for policies that
do not strictly fit the definition of public or private goods, such as government spending (see
Lake and Baum (2001) on the difficulties of treating spending as a public good). By allowing
citizens to vary in their preferences over how a leader distributes resources, the model devel-
oped here can make predictions about how specific “bundles” of government spending influence
leader survival while avoiding the conceptual and empirical issues of treating spending as either
a public or private good. Third, the model developed here allows leaders to be motivated by
their personal preferences over policy outcomes. This means that, in equilibrium, a leader might
choose a policy unpopular with her winning coalition that results in her removal from power. In
contrast, incumbent leaders always retain office in the selectorate model of politics (Bueno de
options and a politician’s competence (e.g., Canes-Wrone, Herron and Shotts 2001, Woon 2012). An incumbent politi-cian can be either a delegate or a trustee to her constituents (Fox and Shotts 2009). A delegate will ignore her ownexpertise and pursue the policies preferred by her constituents. A trustee is willing to ignore her constituents’ prefer-ences and enact welfare maximizing policies. Within the framework discussed above, then, delegates are responsiveto their constituents’ preferences while trustees enact their personally preferred policy.
7Selectorate theory does allow variation in actors’ personal preferences through the concept of “affinity.” Affinity,however, does not refer to policy preferences but “is simply a preference for one individual over another, independentof the policies of the individuals” (Bueno de Mesquita et al. 2003, pg. 61, emphasis added).
6
Mesquita et al. 2003, pg. 120). This result follows from selectorate theory’s assumption that all
leaders are motivated by securing their political survival. Accordingly, in equilibrium leaders
propose a mix of public and private goods that ensures members of their winning coalitions
will not defect to a domestic challenger. I view it as a strength of the model developed here
that it can account for cases in which an incumbent’s tenure is shortened because she made
a rational decision to pursue a policy counter to the preferences of her constituents; as in the
case of former Greek Prime Minister Papandreou. In sum, while selectorate theory speaks to
similar issues, the model developed here differs in important ways and allows for more specific
predictions regarding the relationship between leader survival and government spending.
2 A Simple Model of Leader Survival and Spending
I model the relationship between leader survival and government spending as a game between
country i’s incumbent leader (Li) and her winning coalition (Wi). The model is informally
outlined here and fully characterized in the appendix. The incumbent controls the distribution
of government spending (xi). Let xi ∈ [0, 1] be a one-dimensional policy space that represents
the proportion of total government spending dedicated to the military. I assume the incumbent
and members of her winning coalition hold symmetric, single-peaked preferences over xi. The
functions z(xi) and v(xi) represent the incumbent’s and winning coalition’s respective valuations
of xi. These functions are maximized, respectively, at the incumbent’s preferred distribution
of spending (xL) and the distribution of spending preferred by the median member of the
incumbent’s winning coalition (xW ). I assume incumbents prefer to remain in office (Ii) over
being ousted (Oi) by their winning coalitions. The term αi ∈ [0, 1] identifies the degree to
which a leader obtains utility from the spending distribution directly relative to whether she
remains in office. I define αi as a function of a leader’s motivation for implementing policy
(mi ∈ [0, 1], where zero represents a purely survival-motivated incumbent and one represents a
purely policy-motivated incumbent) and the structural cost of removing her from power to her
winning coalition (si ∈ (0, 1]). The influence of the cost of leader replacement on α, though,
is a function of the degree to which an incumbent cares about retaining office. That is, the
cost of removal does not enter into the decision calculus of a leader motivated exclusively by
securing her personally preferred policy or remaining in power, but will influence an incumbent
motivated by policy and survival concerns. To capture this relationship, αi(mi, si) is defined as
7
follows:
αi(mi, si) =
0 if mi = 0
mi + (1−mi)(si) if 0 < mi < 1
1 if mi = 1
(1)
The model assumes replacing an incumbent imposes a cost (ci > 0) on a winning coalition.
This cost is a function of two factors. First, the cost of leader replacement is assumed to be
an increasing function of how pleased the winning coalition is with the distribution of spending
(v(xi)). This captures the idea that it is costlier to remove a leader when the winning coalition
is relatively happy with the incumbent than when it is comparatively displeased. Second, and as
discussed above, there are structural costs (si ∈ (0, 1]) to removing any ruler (e.g., McGillivray
and Smith 2008, Debs and Goemans 2010). We can think of these structural costs as the a priori
costs of replacing a leader to a winning coalition regardless of how they value the distribution of
spending (e.g., voting in an election is costly regardless of an incumbent’s popularity). Replacing
a leader brings a benefit (bi) to a winning coalition. In substantive terms, bi can be thought of
as the winning coalition’s relative preference for a domestic political challenger compared to the
incumbent leader. More formally, bi is an exogenous shock to the model revealed after a leader
has distributed xi. Upon receiving xi and the uncertainty over bi being revealed, a winning
coalition decides whether to replace (ri) or keep (ki) the incumbent leader.8 The variable p
takes on a value of one if the winning coalition replaces the incumbent leader and zero if it
keeps the incumbent. The utility functions for a leader and her winning coalition are written as
follows:
ULi = αi(mi, si)z(xi) + (1− αi(mi, si))[p(bi, ci(v(xi), si))Oi + (1− p(bi, ci(v(xi), si)))Ii] (2)
UWi =
v(xi) if ki
v(xi) + (bi − ci(v(xi), si)) if ri
(3)
8See Debs and Goemans (2010) for an analogous approach to modeling a domestic population’s decision to removean incumbent.
8
The game is solved for pure strategy subgame perfect equilibria using backwards induction.
From Mas-Colell, Whinston and Green (1995, pg. 276), there exists a unique equilibrium in
pure strategies for any distribution of a model’s parameters in dynamic games of complete and
perfect information. Beginning with the winning coalition’s decision, it keeps the incumbent if
and only if the cost of replacing her is greater than the benefit of installing a new leader:
Wi plays ki iff bi < ci(v(xi), si) and ri otherwise. (4)
Equation 4 indicates that whether an incumbent is removed from office depends on the
relative cost and benefit of replacement to her winning coalition. An incumbent therefore
influences the probability she retains office through the distribution of government spending.
As the cost of leader replacement is increasing in how much her winning coalition values the
spending distribution, a leader minimizes the probability she is removed from office by allocating
her winning coalition’s preferred mix of spending (xW ). Her personal valuation of xi, though,
also influences her utility. We can see this by examining the partial derivative of Equation 2
with respect to αi:
∂UL
∂α(mi, si)= z(xi)− [p(bi, ci(v(xi), si))Oi + (1− p(bi, ci(v(xi), si)))Ii] (5)
Equation 5 implies that as a leader’s utility is increasingly drawn from the value she places
on the distribution of spending, she obtains more utility from a distribution closer to her ideal
allocation (the first term is positive) and less from whether or not she remains in power (the
second term is negative). The optimal xi for an incumbent therefore is a function of her preferred
distribution of spending (xL), the distribution of spending that maximizes her chances of survival
(xW ), and the extent to which she derives utility from the spending distribution directly and/or
her political survival (αi(mi, si)). Specifically,
x∗i = αi(mi, si)(xL) + (1− αi(mi, si))(xW ) (6)
It is worth providing the intuition behind Equation 6. An incumbent can derive utility from
the distribution of social and military spending directly as a function of her personal valuation
and/or indirectly based on how the spending distribution influences whether she stays in power.
If she derives utility exclusively from the distribution of government spending (α(mi, si) = 1),
9
then she will allocate her preferred spending mix (xL). If a leader derives utility exclusively
from retaining office (α(mi, si) = 0), then she will allocate the distribution of spending that
maximizes her likelihood of staying in power (xW ). If an incumbent derives utility from both
the enacted spending distribution and whether she remains in power (0 < α(mi, si) < 1), then
her optimal allocation is a function of her preferred spending distribution and the mix of guns
and butter that maximizes her probability of retaining office, weighted by α(mi, si).
To demonstrate how x∗i varies with αi(mi, si), xL, and xW , Figure 1 presents x∗
i across all
possible combinations of mi and si given that the leader’s personal preference is to allocate
eighty percent of government spending to the military (xL = 0.8) and the median member
of her winning coalition prefers that twenty percent of spending be dedicated to the military
(xW = 0.2). The optimal distribution of spending is increasing in the surface plot’s location
on the z-axis and is represented by progressively darker colors. The structural costs of leader
replacement to a winning coalition and the incumbent’s motivation for enacting a particular
spending distribution are located on the x-axis and y-axis, respectively.
Figure 1 nicely illustrates three characteristics of equilibrium spending distributions. First,
increasing the degree to which an incumbent is policy-motivated moves the optimal spending
distribution closer to her ideal policy. We can see this in Figure 1 by holding the structural
cost of removal constant at any value and noting the height and color of the surface plot as
the extent to which she is policy-motivated increases. Second, unless an incumbent is purely
motivated by survival or policy concerns, x∗ gets closer to her ideal spending distribution as
the structural costs of leader replacement increases.9 Holding her motivation for implementing
policy constant, increasing the structural cost of removal is associated with x∗ moving away
from the distribution preferred by the winning coalition and closer to the incumbent’s preferred
allocation of government spending. Substantively, this implies that the harder it is for a winning
coalition to remove a leader, the more likely she is to deviate from her constituents’ policy
preferences. Third, Figure 1 nicely highlights that an incumbent not exclusively motivated by
her political survival will pursue policies in equilibrium that increase the probability she will be
removed from office (i.e., all x∗ = xW ). Thus, the model captures the behavior of leaders who
knowingly pursue policies that damage their prospects for remaining in power.
The model developed here captures the general relationship between leader survival and
9Recall that the costs of removal do not influence αi(mi, si), and thus x∗, when an incumbent is exclusivelysurvival-motivated or policy-motivated (Equations 1 and 6).
10
Policy Motivated (m
)
0.0
0.5
1.0
Structural Costs (s) 0.0
0.5
1.0
0.0
0.5
1.0
x*
Figure 1: x∗ as a function of xL, xW , and α(m, s). Calculations assume xL = 0.80 and xW = 0.20.Darker colors represent higher values of x∗.
government spending when a leader and her winning coalition hold policy preferences and an
incumbent can be motivated by her political survival and/or personal preferences. One cost of
the model’s generality is that it abstracts away from the influence of regime type. The next
section addresses this issue.
3 The Influence of Regime Type
Two differences between democracies and dictatorships are of particular importance to the
relationship between leader survival and government spending: the spending preferences of the
members of democratic and non-democratic winning coalitions and the relative cost of removing
11
democratic and non-democratic incumbents. These respective differences and their implications
for the formal model are discussed in turn.
3.1 Spending Preferences of Winning Coalitions
The winning coalitions of autocratic and democratic incumbents systematically differ in
their size and socio-economic composition. The relationship between the size of a leader’s win-
ning coalition and regime type is well understood: democratic incumbents have larger winning
coalitions, in both absolute terms and relative to the size of a country’s selectorate, than au-
tocratic incumbents (Bueno de Mesquita et al. 1999, 2003).10 Less appreciated, though, is
the relationship between regime type and who gets into a leader’s winning coalition. The win-
ning coalitions of democratic leaders consist of proportionately more members of the general
public and fewer civilian elites and members of the military than do the winning coalitions
of autocratic incumbents. The comparatively small winning coalitions of autocratic leaders are
made-up almost exclusively by members of the civilian elite and/or military (Bueno de Mesquita
et al. 2003), with the relative influence of the civilian elite and military varying across types of
non-democracies (e.g., civilian dictatorship vs. military junta).11 The political institutions of
contemporary democracies make it impossible for a democratic incumbent to retain office with
only the support of her country’s civilian elite and/or military. The relatively high levels of
political participation and contestation associated with democracy result in democratic leaders
requiring the support of a large portion of the general public to remain in power (among others,
Dahl 1971, Boix 2003). It therefore follows that democratic winning coalitions are composed of
proportionately more members of the general public and fewer members of a society’s civilian
and military elite than are autocratic winning coalitions. This implies that the median voter
in a democratic leader’s winning coalition is a member of the general public while the median
“voter” in a dictator’s winning coalition is a member of the civilian elite or military.
This variation in the composition of autocratic and democratic winning coalitions has im-
plications for the model developed above because, in general, a society’s elite and public hold
different preferences over patterns of government spending. Compared to the elite, members
10Bueno de Mesquita et al. (2003) are clear that “a large selectorate and a large winning coalition do not inthemselves define a democracy” (pg. 72). However, a large winning coalition is viewed as a necessary condition fordemocratic government: “democracies require larger coalitions than autocracies or monarchies” (pg. 72).
11Space considerations prevent me from adequately investigating variation in the relationship between governmentspending and leader survival among types of non-democracies. I briefly return to this issue in the concluding section.
12
of the public should prefer relatively more resources be allocated to social spending and fewer
resources be allocated to military spending. 12 This claim follows from four observations. The
first two concern the preferences of the public and civilian elite over social spending. First, the
general public derives more direct benefits from social spending than do the wealthy civilian
elite, whom can provide themselves with the services that the public receives via the welfare
state.13 It should be highlighted that this is the case with all means-tested social welfare pro-
grams by definition. Second, spending on social programs typically is financed through taxes
on the wealth of the civilian elite (Przeworski et al. 2000, Boix 2003). Thus, the civilian elite
bear the brunt of the costs of the social welfare state while deriving relatively fewer benefits
than members of the public. It then follows that the general public should prefer its government
allocate more of its resources to social spending than the civilian elite. This claim is consistent
with the overall negative relationship between income and support for the welfare state in the
United States and Europe (Cook and Barrett 1992, Jæger 2006) and research on the respective
preferences of the general public and the wealthy in the United States. Gilens (2009, 2012) finds
that the U.S. public is more supportive of social welfare programs than the affluent, defined as
the top 20% in terms of income. Focusing on the preferences of the very wealthy, defined as
the top 1% of income earners, Page, Bartels and Seawright (2013) find that the general public
prefers increases in spending on health care, food stamps, and social security while the very
wealthy prefer reductions in social spending.
The third and fourth observations concern the preferences of the public and military over
military spending. The third is that military training socializes members of a state’s armed forces
to value a stronger military and favor higher military spending than the civilian population
(Huntington 1957, Nordlinger 1977, Geddes 2003). Fourth, the public and members of the
military have reasons to assess military spending beyond what is required for national security
differently. All citizens benefit from the military expenditures needed to provide the public good
of national security (Samuelson 1954, Olson 1965). Military spending beyond this level can crowd
out consumption spending popular among the public (Sprout and Sprout 1968, Fordham and
12To be clear, I am not claiming that all members of the general public prefer higher social spending and lowermilitary spending than all members of the civilian elite and military. Instead, drawing on existing research, I arguethat, in general, members of the public prefer more social spending and less military spending than the wealthy eliteand members of the armed forces.
13Members of the elite do derive some benefits from social spending. In particular, the elite would benefit fromsome of the long-term consequences of increased social spending, such as an educated and healthier workforce. Thatsaid, it is members of the public, and not the elite, that would be better educated, healthier and have a longerlife-expectancy due to government spending on social programs.
13
Walker 2005). However, military expenditures over and above what is necessary for national
security finances private benefits and club goods for members of the military.14 These private
and club goods include, but are not limited to, higher salaries for members of the military, the
ability to purchase goods and services at reduced prices at base exchanges, and free or subsidized
housing.
Public opinion research supports the claim that the public and members of the military have
different preferences over military spending. Bachman, Blair and Segal (1977) find that members
of the military prefer higher military spending than do members of the public. Addressing a
guns-versus-butter trade-off, Holsti (1998, 2001) and Szayna et al. (2007) find that members of
the public are more likely than members of the military to think that military spending should
be decreased in order to increase education spending. The variation in the spending preferences
of the military and public is consistent with the greater weight members of the military place
on military superiority (Szayna et al. 2007) and is driven by a combination of self-selection
and socialization (Bachman et al. 2000). Considered jointly, these observations imply that, in
general, members of the public should prefer lower military spending and higher social spending
than members of the military and/or the wealthy civilian elite.
Due to variation in the political representation of the elite and public across regime type and
their spending preferences, the median member of a democratic winning coalition prefers his
government allocate fewer resources to military spending and more resources to social spending
than the median member of a dictator’s winning coalition. It is straightforward to incorporate
this insight into the model. Define a state’s form of government as gi ∈ {A,D}, where A
represents an autocracy andD represents a democracy. As the distribution of spending preferred
by the median member of an incumbent’s winning coalition is defined as xW , variation in the
preferred spending distribution of the median members of autocratic and democratic leaders’
winning coalitions is represented by the inequality xDW < xA
W .
3.2 The Cost of Leader Removal
The relative cost of removing an incumbent leader from power varies as a function of regime
type. Namely, it is much harder for a domestic population to replace a dictator than a democrat
(among others, Lake and Baum 2001, McGillivray and Smith 2008, Debs and Goemans 2010).
14See Buchanan (1965) on club goods generally and Smith and Bueno de Mesquita (2011) and Arena and Nicoletti(Forthcoming) on the relationship between club goods and leader survival.
14
Replacing a democratic leader with a domestic challenger requires that the incumbent be de-
feated in her re-election bid. Voting for the opposition in an election is a relatively costless act
of political participation in a democracy (Lake and Baum 2001). Non-democratic incumbents
generally are removed from power through irregular events like a coup or revolution (Chiozza
and Goemans 2011). Participation in such events is much riskier and, especially if they fail,
costlier than voting for a domestic challenger in a democracy (McGillivray and Smith 2008).
Thus, the structural cost of leader replacement is lower for democratic winning coalitions than
it is for the winning coalitions of non-democratic leaders.
The importance of this variation in the cost of removing a leader is hard to overstate. Debs
and Goemans (2010) argue that the “costliness of replacing rulers is a significant, if not the
most significant, difference between dictatorship and democracy” (pg. 435). This fundamental
difference in autocratic and democratic politics is overlooked in the model presented in the
previous section. However, it can be incorporated into the model by constraining the structural
cost of leader replacement to a winning coalition for a given valuation of xi to be higher in
non-democracies than in democracies: sDi < sAi ∀ v(xi).
3.3 Formal Results
Accounting for variation in the spending preferences of winning coalitions and the relative
cost of removing an incumbent across regime type yields a number of insights concerning the
relationship between leader survival and government spending. For expositional purposes, I
present the intuition behind the proofs here and provide formal details in the appendix. Fol-
lowing the logic of backwards induction, I begin with the winning coalition’s decision to remove
a leader.
Proposition 1 argminx
F (ci(v(xi), si)) | gi = D < argminx
F (ci(v(xi), si)) | gi = A
Proof. See appendix.
Proposition 1 indicates the distribution of spending that minimizes the probability a demo-
cratic leader is removed from power contains relatively more social spending and relatively less
military spending than the distribution of spending that minimizes the probability a dictator is
removed from office. While she might rationally allocate a different mix of military and social
spending (see Equation 6 and Figure 1), a leader minimizes her probability of being replaced by
15
providing her winning coalition with their preferred distribution of government spending. Mem-
bers of the public generally prefer more social spending and less military spending than do the
civilian elite or military and the median member of democratic winning coalitions is drawn from
the general public while the median member in an autocratic winning coalition hails from the
military or civilian elite. Accordingly, the spending distribution that maximizes the probability
a democratic leader remains in power contains more social spending and less military spending
than the analogous combination of spending for a dictator. The optimal spending distribution
for survival-motivated democrats and dictators follows from this result.
Corollary 1 If mi = 0, then (x∗i | gi = D) < (x∗
i | gi = A).
Proof. See appendix.
Corollary 1 claims that a survival-motivated democratic incumbent will allocate more re-
sources to social spending and fewer resources to military spending than a survival-motivated
dictator in equilibrium. This follows directly from the spending distributions that minimize the
probability of removal for democratic and non-democratic leaders (Proposition 1). Substan-
tively, Corollary 1 provides a rational explanation for the empirical observations that, compared
to autocracies, democracies generally spend less on the military and more on social spending
(among others, Brown and Hunter (1999), Fordham and Walker (2005), and Huber, Mustillo
and Stephens (2008); although see Mulligan, Gil and Sala-i-Martin (2004)).
Proposition 1 and Corollary 1 follow closely from the assumption that the median member of
a democratic leader’s winning coalition prefers less military spending and more social spending
than the median member of an autocrat’s winning coalition. It is instructive to consider what
happens if this assumption is changed. If we assume the median members of autocratic and
democratic winning coalitions do not vary in their spending preferences, then the model implies
no variation across regime type in the mix of spending that maximizes an incumbent’s probability
of survival or the spending distribution allocated by survival-motivated leaders. Alternatively,
we could assume the public prefers lower social spending and higher military spending than the
civilian elite and military. The model implies two things given this assumption. One, the mix
of spending that maximizes the probability a democratic leader retains office contains relatively
less social spending and more military spending than the corresponding spending distribution
for an autocratic leader. Two, survival-motivated dictators should allocate more resources to
social spending and fewer resources to military spending than survival-motivated democrats,
16
an expectation that runs counter to the empirical research cited above (e.g., Fordham and
Walker 2005, Huber, Mustillo and Stephens 2008). Thus, the model is consistent with a set of
known empirical regularities given the assumption that the public prefers more social and less
military spending than the civilian elite or military, but not when this assumption is changed.
Where Corollary 1 pertains to incumbents driven exclusively by the desire to retain office,
Proposition 2 addresses the behavior of leaders motivated by policy and survival concerns.
Proposition 2 (|x∗ − xL| |gi = A) < (|x∗ − xL| |gi = D) ∀ 0 < mi < 1
Proof. See appendix.
Proposition 2 indicates that a dictator will allocate a distribution of government spending
closer to her ideal spending mix than will a democratic leader when both are motivated by policy
and survival concerns. This result is driven by how the structural costs of leader replacement
and an incumbent’s motivation for enacting policy influence equilibrium behavior. A leader
driven by policy and survival considerations is constrained by her winning coalition’s preferences
to the extent they can easily remove her from power. Accordingly, the equilibrium spending
distribution will be closer to a leader’s ideal point as the structural cost of replacement increases.
The cost of removing an incumbent across regime type therefore implies that dictators will
allocate spending distributions closer to their ideal points than democrats when leaders are
motivated by survival and policy outcomes.
4 Empirical Analyses
The formal model has several implications for the relationship between leader survival and
government spending. I find empirical support for a set of the model’s expectations during the
period from 1950 to 2001. I first present results on how the distribution of government spending
influences the survival of democratic and non-democratic leaders before reporting my findings
regarding patterns of government spending in democracies and dictatorships.15
15The data and code needed to replicate all of the analyses associated with this manuscript will be made availableupon publication.
17
4.1 Leader Survival
The model predicts the spending distribution that best secures a democratic leader’s survival
contains less military spending and more social spending than the distribution that minimizes the
probability a dictator loses office. I test this expectation using data on the universe of political
executives from 1950 to 2001. With the exception of variables measuring the distribution of
government spending, all data were taken from the replication materials associated with Debs
and Goemans (2010).16 The dependent variable is the number of days a leader has been in
power and is drawn from the Archigos project (Goemans, Gleditsch and Chiozza 2009).17
Testing the formal model’s expectation requires five explanatory variables. Spending Distri-
bution is operationalized as the portion of a government’s total expenditures that are allocated
to the military in year t, which precisely mirrors xi from the formal model. Total government
expenditures and military spending data are drawn from the Penn World Tables, version 7.1,
(Heston, Summers and Aten 2012) and Correlates of War (COW) National Material Capabili-
ties, version 3.02 (Singer, Bremer and Stuckey 1972) data sets, respectively. The formal model
assumes that a leader’s winning coalition holds single-peaked, symmetric preferences over the
spending distribution. This implies that spending distributions the same degree less than or
more than xW should increase the probability a winning coalition removes an incumbent to the
same degree. The empirical model captures the formal model’s assumption with the variable
Spending Distribution2.18 The formal model’s dichotomous treatment of regime type is prox-
ied with the variable Democracy, coded one in year t if a leader’s government has a value of
+7 on the 21-point Polity2 index (Marshall and Jaggers 2005) and zero otherwise. The inter-
action terms Spending Distribution*Democracy and Spending Distribution2*Democracy allow
the model to identify the effect of government spending on leader survival in democracies and
dictatorships.
I control for a number of factors thought to influence leader survival. Interstate War takes on
16Available at http://www.rochester.edu/college/faculty/hgoemans/research.htm.17I code leader failure as occurring when an incumbent is removed by a domestic audience. Leader turnover due to
an incumbent being replaced by a foreign power or dying from natural causes reflects fundamentally different datagenerating processes.
18Additionally, following Keele’s (2010) suggestions, diagnostics indicate that Spending Distribution has a non-linear effect on leader tenure in democracies and dictatorships and that including Spending Distribution2 is method-ologically appropriate. More specifically, Spending Distribution and Spending Distribution*Democracy violate thenon-proportional hazards assumption when included alone in the duration models but not when I also includeSpendingDistribution2 and Spending Distribution2*Democracy in the models. These diagnostic results hold whenI use splines to assess the linearity of the effects of Spending Distribution and Spending Distribution*Democracy onleader tenure.
18
a value of one if a leader’s country is involved in a war in year t and zero otherwise. I account for
whether the leader’s country was victorious (War Win), vanquished (War Loss), or obtained a
draw (War Draw) in an interstate war during her tenure. Each war outcome variable is modeled
as a decay function of the number of years since a given outcome was achieved.19 Interstate war
participation and outcome variables are based on data from Brecher and Wilkenfeld (1997). I
control for a state’s involvement in a Civil War in year t with a dichotomous indicator based on
the UCDP/PRIO Armed Conflict Database (Gleditsch et al. 2002). The model also accounts for
four aspects of a state’s economy: its (logged) GDP per capita (Maddison 2008), GDP growth
(Maddison 2008), Trade Openness (International Monetary Fund 2008), and Change in Trade
Openness (International Monetary Fund 2008). A state’s (logged) Population (Singer, Bremer
and Stuckey 1972) also is included as a control variable. The models include three leader-level
characteristics argued to influence an incumbent’s tenure: a leader’s Age when he or she entered
office, the number of previous Times in Office he or she served, and whether he or she came
to power via an Irregular Entry. These three variables are drawn from the Archigos project
(Goemans, Gleditsch and Chiozza 2009). Finally, the models capture region-specific variation
in leader survival with a set of variables that identify whether a state is located in Africa, the
Americas, Asia, or the Middle East (Europe serves as the baseline category).
I estimate leader survival using semi-parametric Cox models. The Cox model is preferable to
parametric event history models when the phenomenon of theoretical interest is the relationship
between a set of covariates and the likelihood of a subject failing and not the distributional
form of subject failure (Box-Steffensmeier and Jones 2004). The models estimated here account
for non-proportional hazards between covariates and leader survival. Analysis of the Schoenfeld
residuals was used to determine whether the influence of an explanatory variable on the hazard
of a subject failing was constant over time (Box-Steffensmeier and Jones 2004). Following
Box-Steffensmeier and Zorn (2001), any offending variable was interacted with the natural log
of a leader’s tenure in office up to time t. I also extend the standard Cox model to capture
shared frailty among leaders of the same state. Shared frailty event history models account
for unobserved heterogeneity across sub-groups that makes subjects within group j more or
less likely to fail than subjects in group j (Box-Steffensmeier and Jones 2004). Formally, the
frailty term ν is a random variable with a mean of one and variance of Θ and is drawn from
19For example, if a leader oversaw a winning war effort in year t, War Win takes on a value of 1 in year t, 0.5 int+ 1, 0.333 in t+ 2, etc.
19
the Gamma distribution. Previously, Chiozza and Goemans (2004), Goemans (2008), and Debs
and Goemans (2010) have used Cox estimators with shared frailty to model leader survival.
Amelia II was used to address concerns about missing data (Honaker, King and Blackwell
2007).20 Multiple imputation of missing observations helps avoid the inefficiency and selection
bias associated with listwise deletion and is more accurate than single imputation (King et al.
2001, Honaker, King and Blackwell 2007). For the data analyzed here, Amelia II is preferable
to other imputation programs as it explicitly takes into account the time-series, cross-sectional
nature of the data (Honaker, King and Blackwell 2007, Honaker and King 2010). The multiple
imputation model was specified with one-year lags, one-year leads, and logical or empirical
upper and lower bounds of variables with missing observations.21 Including the lags, leads,
and bounds improves the predictive performance of the imputation model (Honaker, King and
Blackwell 2007, Honaker and King 2010). Further details about the imputation process are
available in the appendix. The multiple imputation model produced five data sets of 7,935
leader-year observations (1,431 leaders from 162 countries).
The estimates presented in Table 1 reflect the mean coefficients and corrected standard
errors yielded by the estimation of identically specified Cox models on each of the five Amelia
II -generated data sets.22 Three points are worth noting before discussing the theoretically
interesting results. First, positive (negative) coefficients indicate higher values of an explanatory
variable are associated with a leader facing a greater (lower) hazard of losing office.23 Second,
the statistically significant Θ in Table 1 indicates non-trivial variation exists in the likelihood of
a leader being removed from power across states and that accounting for shared frailty among
leaders of the same country is methodologically appropriate. Third, the statistically significant
regional indicators imply the presence of regional variation in leader tenure.
Unfortunately, the use of multiplicative interaction terms greatly limits the possible infer-
ences one can draw from Table 1 for two reasons. First, the coefficient associated with any
20I imputed missing values for the constituent terms of the interaction terms and then created the interactionterms based on variables without missing observations. This ensures that the values the interaction terms take onaccurately reflect the values of the constituent terms.
21Variables that have a lower and upper bound by definition were assumed to fall within those bounds whilevariables without a logical range were bounded by the minimum and maximum values observed in the data set.
22Using code from Goemans (2008), the standard errors are computed by taking the square root of T = U+(1+ 1m)B,
where T is the total variance associate with the mean coefficient estimate, U is the within-imputation variance of theestimated coefficient [U = 1
m
∑mi=1 Ui], B is the between-imputation variance [B = 1
m−1
∑mi=1(Q− Q)2], and 1 + 1
m
is a correction factor to account for simulation error in Q (Rubin 1987, Schafer and Olsen 1998).23An interaction with ln(t) signed in the opposite direction of the constituent term indicates a decay in the original
effect over a leader’s tenure.
20
Table 1: Leader Survival, Government Spending, and Regime Type, 1950-2001
β s.e.
Democracy 0.19 0.47Democracy*ln(t) -0.01 0.07Spending Distribution -0.43 0.31Spending Distribution*Democracy 0.78 0.69Spending Distribution2 -0.03 0.13Spending Distribution2*Democracy 0.26 0.62Interstate War -0.72 0.30∗Win War -1.54 0.85†Draw War -0.51 0.61Lose War 1.69 0.48∗∗Civil War 0.81 0.37∗Civil War*ln(t) -0.06 0.06GDP per capita 2.26 0.19∗∗GDP per capita*ln(t) -0.36 0.03∗∗Growth -2.64 0.41∗∗Trade Openness 0.04 0.16∆ Trade Openness -0.13 0.10Population 0.03 0.04Age 0.01 0.00∗∗Times in Office -0.09 0.06Irregular Entry 4.03 0.38∗∗Irregular Entry*ln(t) -0.61 0.06∗∗Africa 7.35 0.57∗∗Africa*ln(t) -1.20 0.08∗∗Americas 5.27 0.52∗∗Americas*ln(t) -0.78 0.07∗∗Asia 6.52 0.51∗∗Asia*ln(t) -1.04 0.07∗∗Middle East 6.20 0.65∗∗Middle East*ln(t) -0.98 0.09∗∗Observations 7935Leaders 1431Failures 1145Log-likelihood -6648.19Wald-test 25.49 ∗∗θ 0.26 6.70∗∗Two-tailed: †: p ≤ 0.1; ∗: p ≤ 0.05; ∗∗ : p ≤ 0.01
variable tells us the impact of an increase in that variable when all of the other constituent
terms are equal to zero (Braumoeller 2004). Second, and related to the first point, the stan-
dard error associated with a coefficient reflects the uncertainty around the estimated effect of a
21
variable when all of the other constituent terms are equal to zero and does not take into con-
sideration the covariance among that variable, the other constituent terms, and the interaction
terms (Brambor, Clark and Golder 2006). This implies the statistical significance of the inter-
action terms and their constituent terms cannot be assessed using Table 1 alone. I therefore
used a set of simulations to calculate how the distribution of government spending influences
the probability of leader survival in democracies and non-democracies. I took 1,000 draws from
a multivariate normal distribution based on the coefficient and variance-covariance matrices of
each model estimated on each of the five imputed data sets using the MSBVAR package in R
(Brandt 2012). I then used the simulated coefficients to calculate the probability of a democratic
leader and a dictator surviving up to time t over a five-year period as Spending Distribution
ranged from 0 to 1 by intervals of 0.1 via the respective cumulative survival functions. Contin-
uous control variables were set to their mean values while nominal and ordinal control variables
were set to their median values for the simulations.
The results of these simulations are reported graphically in Figure 2.24 Panel A presents
the mean predicted probability a democratic leader will remain in office over a five-year period
(x-axis) as a function of Spending Distribution (y-axis). Higher probabilities of survival are
represented by the surface plot’s height on the z-axis and progressively darker colors. Panel A
indicates the probability a democratic leader remains in power is decreasing in the proportion of
government spending dedicated to the military. This result holds throughout a leader’s tenure,
but is most easily seen by examining how the probability a democratic leader will remain in
office for five years changes as the proportion of government spending dedicated to the military
increases. Focusing on the far end of the x-axis, the height of the surface plot decreases along
the z-axis and becomes lighter in color as the spending distribution contains more military
spending (i.e., moves from 0 to 1 on the y-axis). The probability a democratic incumbent will
be in power for five years given no military spending is 0.25 (medium gray), drops to 0.17 if half
of government spending is dedicated to the military (light gray), and reaches a low of 0.09 if
all government spending is allocated to the military (white). Framed differently, a democratic
leader’s probability of serving five years decreases by 32% if she moves from spending no money
on the military to allocating half of the budget to the military and by 64% if she moves to
24The Supplementary Appendix includes a set of graphs of the probability of leader survival in a democracy and anon-democracy over a five-year period at each value of Spending Distribution. These figures include both the meanpredictions and 95% confidence intervals. Figure 2 does not include confidence intervals because their inclusion makesthe graphs overly busy and difficult to interpret.
22
distributing all government spending to the military.
Days in Office
0
1000Spending Distribution
0.0
0.5
1.0
0.0
0.5
1.0
Pro
ba
bili
ty o
f S
urv
iva
l
Panel A: Democratic Leader
Days in Office
0
1000Spending Distribution
0.0
0.5
1.0
0.0
0.5
1.0
Pro
ba
bili
ty o
f S
urv
iva
l
Panel B: Autocratic Leader
Figure 2: The Probability of Leader Survival and the Distribution of Government Spending inDemocracies and Dictatorships, 1950-2001. Darker colors represent higher probabilities of leadersurvival.
A different relationship exists between government spending and leader survival in non-
democracies. Panel B in Figure 2 reports that the probability a dictator remains in power is
increasing in the proportion of government spending dedicated to the military. Again, it is
easiest to see this result by focusing on how the probability an autocrat will remain in power for
five years changes as his government dedicates more resources to the military. Starting at the
far end of the x-axis, the height of the surface plot increases along the z-axis and becomes darker
in color as more of a government’s total spending is dedicated to the military. The probability a
dictator will rule for five years given he spends nothing on the military is 0.29 (white), increases
to 0.38 if half of expenditures are allocated to military spending (light gray), and reaches 0.46
if all government spending is distributed to the military (medium gray). Thus, moving from
allocating no government spending to the military to half of spending to the military increases
the probability a dictator will rule for five years by 27% while the move from no military spending
to all military spending increases his probability of survival by 53%.
23
Figure 2 indicates the effect of government spending on leader survival is conditional on
regime type. As the proportion of spending dedicated to the military increases, the proba-
bility a democratic leader retains office decreases while the probability a dictator remains in
power increases. These results are consistent with the model’s prediction that a democratic
leader’s probability of removal is minimized with a spending distribution that consists of less
military spending and more social spending than the distribution of spending that minimizes
the probability a dictator will lose power.
The results for the control variables generally match expectations. On average, a leader is
less likely to lose office if she is currently involved in an interstate war or wins an interstate
war (at the 0.1 level) and more likely to be removed from power if she oversees a losing war
effort. Obtaining a draw in an interstate war has no significant influence on a leader’s tenure.
Leaders whose states are embroiled in a civil war face a higher hazard of losing office early
in their tenure, but this relationship weakens over time. Higher levels of GDP per capita are
associated with a greater risk of leader removal early in an executive’s tenure, although this
diminishes the longer she has been in office. An incumbent’s hazard of removal is decreasing
in her state’s economic growth. Trade openness, the annual change in trade openness, a state’s
population, and the previous number of times a leader has been in power have no influence on
an incumbent’s tenure. Older leaders and leaders that rose to power in an irregular manner face
a higher hazard of removal, though the latter relationship weakens over time.
I conducted a set of additional analyses of the relationship between government spending
and leader survival. Using the post-estimation simulations from the model reported in Table 1,
I analyzed the differences in the probability of leader survival as Spending Distribution changes
for a democratic leader and a dictator and whether the effects of Spending Distribution on
leader survival are significantly different across regime type. I also estimated models that omit
outliers and with a more parsimonious specification. Consistent with the results presented
here, these analyses imply that increasing military spending and decreasing social spending
increases the probability a dictator remains in power but decreases the probability a democratic
incumbent retains office. These results are reported in the Supplementary Appendix due to
space considerations.
24
4.2 Government Spending
The formal model has several implications regarding empirical patterns of government spend-
ing. Ideal tests of these expectations require systematic data across countries and over time on
leaders’ motivations for implementing policies and relative preferences for military and social
spending. Unfortunately, these data do not exist. However, we can leverage variation in the
spending preferences of winning coalitions and the cost of leader replacement across regime type
and the implications of leaders pursuing their preferred policies to assess the model’s expecta-
tions for government spending.
Equilibrium spending distributions reflect the preferences of a leader’s winning coalition as
long as she is not exclusively driven by the desire to implement her preferred policy. For all
incumbents that are at least marginally concerned with remaining in power, the spending dis-
tributions allocated by democratic leaders will be biased towards lower military spending and
higher social spending than the mix of spending provided by non-democratic leaders. There-
fore, we should observe proportionately higher military spending and lower social spending in
democracies than in dictatorships, on average.
If we consider scholarship on foreign policy substitutability and intra-democratic conflict
variation, the model implies that we should observe greater variance in spending distributions
allocated by dictators than those provided by democratic leaders. Researchers in these tra-
ditions demonstrate that there exists greater variation in policy outcomes as a leader faces
fewer constraints on her behavior and is better able to pursue her personal preferences. Clark
and Nordstrom (2005) argue that idiosyncratic leader preferences explain why increased po-
litical participation in democracies is associated with significant variance in the probability of
democratic conflict initiation. Clark, Nordstrom and Reed (2008) find that leaders of states
with substantial resources pursue cooperative and conflictual foreign policies with greater vari-
ance than those leaders whom are constrained by their states’ lack of resources. Arena and
Palmer (2009) argue that leaders of right governments are less constrained by their constituents
in the decision to use force than are left leaders and therefore should initiate conflicts with
greater variance than left leaders.25 Consistent with this argument, they find greater variance
around the probability democracies with right governments initiate interstate conflicts than is
25As Arena and Palmer (2009) put it, “While leaders who lack constraints preventing them from using force aremore likely to engage in disputes than leaders who are more heavily constrained (as the latter are universally unlikelyto engage in disputes), being free to take risks does not necessarily mean that one desires to do so” (pg. 962).
25
the case with democracies with left governments. In sum, Clark and Nordstrom (2005), Clark,
Nordstrom and Reed (2008), and Arena and Palmer (2009) all find that the variance in policy
outcomes increases as the constraints on a leader’s behavior decrease and she is able to pursue
her personally preferred policies. The formal model indicates that variation in the structural
costs of replacement allows autocratic leaders to enact their personal preferences to a greater
extent than democratic leaders, except for when leaders are motivated exclusively by survival
or policy concerns. This implies we should observe greater variance in non-democratic spending
distributions than in democratic spending distributions.
A quick examination of the means and interquartile ranges of Spending Distribution among
democracies and non-democracies reveals spending patterns that match the model’s expecta-
tions. Democracies have a mean Spending Distribution of 0.24 and an interquartile range that
spans from 0.09 to 0.33 while dictatorships have a mean Spending Distribution of 0.36 and an
interquartile range of 0.09 to 0.49. Framed differently, dictatorships allocate approximately
51% more of their total spending to the military, on average, and have an interquartile range
approximately 63% greater than do democracies. To offer a more rigorous assessment of demo-
cratic and non-democratic spending distributions, I estimated a set of regression models that
account for multiplicative heteroscedasticity. Estimators with multiplicative heteroscedasticity
allow analysts to model the error variance as a function of a vector of explanatory variables
(Harvey 1976, Alvarez and Brehm 1995). The models were estimated on state-year versions of
the five imputed leader-year data sets described above. I converted the data sets to a state-year
unit-of-analysis in order to model temporal dependence in the Spending Distribution series (see
the next paragraph for more details). The state-year data sets have 6,684 observations.
Time-series cross-sectional data present multiple methodological challenges concerning tem-
poral dynamics and unit heterogeneity (Beck 2008). I focus first on issues related to modeling
dynamics. The dependent variable in my analyses of government spending is a state’s Spending
Distribution. Panel unit root tests indicate that Spending Distribution is not integrated; how-
ever, its value at time t is correlated with its value at t−1 at 0.89. Modeling this autocorrelation
is not feasible using the leader-year data sets because the average number of observations per
panel is 6.6. Moving to a state-year unit-of-analysis increases the mean number of observations
per panel to 41.3, allowing me to better model the temporal dependence present in the de-
pendent variable. Diagnostics indicate that statistically significant autocorrelation exists even
after including a one-year lag of the dependent variable in the models. However, after including
26
both a one-year lag and a two-year lag of the dependent variable no significant autocorrelation
remains among the errors.26 The statistical models therefore include SpendingDistributiont−1
and SpendingDistributiont−2 as explanatory variables.
Concerning cross-sectional issues, failure to account for unmodeled unit heterogeneity in the
dependent variable can lead to faulty inferences. Scholars commonly model unit heterogeneity
with fixed-effects or random effects models (among many others, Cameron and Trivedi 2005,
Beck 2008). These estimators are not ideal for testing the model’s implications for two reasons.
First, the model’s expectations concern variation in spending patterns between democracies
and non-democracies. As fixed effects models rely exclusively on within-panel variation (e.g.,
Cameron and Trivedi 2005), they are inappropriate for theoretical questions related to between-
panel variation. Second, random effects models are not particularly well-suited for time-series
cross-sectional analyses because they rely on the assumptions that unit effects are uncorrelated
with the explanatory variables and are independently and identically distributed, both of which
are violated by time series cross-sectional data (e.g., Cameron and Trivedi 2005, Beck 2008). I
attempted to mitigate the threats to inference that follow from unmodeled unit heterogeneity
in two ways. First, all of the models include the dichotomous indicators Africa, Americas, Asia,
and the Middle East. These variables capture regional variation in Spending Distribution while
allowing for inferences about the between-panel effect of regime type on patterns of spending.
Second, the models use robust standard errors clustered by country in order to account for
within-panel correlation among the errors.
The key explanatory variable in the models of government spending is Democracy. In ad-
dition to the explanatory variables discussed above, a state’s mean Spending Distribution is
modeled as a set of factors argued to influence government spending. Involvement in an Inter-
state War or a Civil War has been shown to increase military spending (Goldsmith 2003). As
social spending is a type of luxury good, it is generally increasing in a state’s GDP per capita
(Palmer 1990). Trade Openness is typically associated with expansive social welfare states,
as governments purchase liberal economic policies with large safety nets (Hays, Ehrlich and
Peinhardt 2005). The variance in annual spending distributions is modeled as a function of
Democracy, GDP per capita, and Interstate War. Democracy is included to test the theoreti-
cal expectation that variation in the structural cost of leader removal should result in greater
26More specifically, errors at t − 1 are a statistically significant predictor of the errors at t when onlySpendingDistributiont−1 is included in the models but are a statistically insignificant predictor of the errors att when SpendingDistributiont−1 and SpendingDistributiont−2 are included in the models.
27
variance in the spending patterns of dictatorships than in democracies. Interstate War should
increase the variance in Spending Distribution as leaders are unlikely to uniformly alter how
they allocate resources as a function their state’s involvement in an interstate war. GDP per
capita is included in the variance equation as states with greater resources have been shown
to exhibit greater variance in policy outcomes (e.g., Clark, Nordstrom and Reed 2008).27 The
primary regression results are reported in Table 2.
Table 2: Spending Distribution and Regime Type, 1950-2001
β s.e.
Spending DistributionDemocracy -0.01 0.00∗∗Interstate War 0.05 0.003∗∗Civil War 0.01 0.001∗∗GDP per capita 0.007 0.001∗Trade Openness 0.001 0.001Africa -0.001 0.001Americas -0.01 0.001∗∗Asia -0.002 0.002Middle East 0.03 0.001∗∗Spending Distributiont−1 0.69 0.01∗∗Spending Distributiont−2 0.19 0.01∗∗Constant 0.03 0.001∗∗VarianceDemocracy -1.77 0.23∗∗Interstate War 1.24 0.16∗∗GDP per capita 0.11 0.06Constant -3.43 0.07∗∗Observations 6360Log-likelihood 3079.45
Two-tailed: †: p ≤ 0.1; ∗: p ≤ 0.05; ∗∗ : p ≤ 0.01
Robust standard errors clustered on country.
The estimates presented in Table 2 reflect the mean coefficients and corrected standard
errors yielded by the estimation of identically specified models on each of the five imputed
data sets.28 Unfortunately, we cannot accurately assess the effect of Democracy on Spending
Distribution using Table 2 because the standard error of a variable included in the mean and
27I useGDP per capita to proxy a state’s resources instead of the more common CINC score (Correlates of War 2001)because the numerator of Spending Distribution (annual military expenditures) is part of the CINC index. Using astate’s CINC score to proxy resources therefore could result in a spurious relationship as increases in a state’s militaryspending would necessarily result in increases in both the dependent variable and a state’s CINC score.
28See Footnote 22 for the equation used to correct the standard errors.
28
variance equations of a model with multiplicative heteroscedasticity varies as a function of the
values of that variable (Harvey 1976, Alvarez and Brehm 1995). I therefore conducted a set
of post-estimation simulations from the model’s coefficient and variance-covariance matrices
to test whether the mean and/or variance of Spending Distribution is significantly different in
democracies and non-democracies. Continuous control variables were set to their mean values
while nominal and ordinal control variables were set to their median values for the simulations.
Figure 3 presents these results.
Panel A in Figure 3 reports the mean spending distributions of autocracies (red square) and
democracies (blue diamond) with 95% confidence intervals (solid black lines) yielded by the
simulations. On average, autocracies dedicate 0.35 of their total government spending to the
military while democracies allocate 0.23 of government spending to the military. Framed differ-
ently, the results indicate that autocracies allocate approximately 52% more of total spending
to the military than do democracies. To assess the significance of this finding, Panel C reports
the mean difference in democratic and non-democratic spending distributions (black circle with
the 95% confidence interval again denoted by the solid black line). The difference across regime
type in the average proportion of total government spending dedicated to the military is sta-
tistically significant if the confidence interval does not contain the zero-line. Panel C therefore
indicates that, on average, democracies allocate significantly less of their total spending to the
military than do non-democracies. This result is consistent with the expectation that spending
distributions allocated by democratic leaders will be biased towards lower military spending and
higher social spending than the spending distributions provided by dictators.
The relatively wider confidence intervals associated with autocratic spending distributions
in Panel A of Figure 3 suggest that there is greater variance around non-democratic patterns
of spending than is the case with democratic spending. To more explicitly assess this rela-
tionship, Panel B presents the mean variance of autocratic (red square) and democratic (blue
diamond) spending distributions yielded by the post-estimation simulations. The mean vari-
ance around autocratic spending distributions is 0.01 while the mean variance surrounding
democratic distributions is 0.001. Panel D reports the difference between these two quantities
(black circle). As the 95% confidence interval lies entirely below the zero-line, Panel D indicates
that there is significantly less variance surrounding democratic spending distributions than is
the case with non-democratic distributions. This is consistent with the claim that dictators are
less constrained by the preferences of their winning coalitions and, thus, vary in the spending
29
Pro
port
ion
to M
ilita
ry S
pend
ing
Autocracy Democracy
0.0
0.5
1.0
Panel A: Mean Spending Distributions
Autocracy Democracy
0.00
0.01
0.02
Panel B: Variance in Spending Distributions
Var
ianc
e
−0.
2−
0.1
0.0
Panel C: Difference in Mean
Dem
ocra
cy−
Aut
ocra
cy
−0.
2−
0.1
0.0
Panel D: Difference in Variance
Dem
ocra
cy−
Aut
ocra
cy
Autocracy
Democracy
Democracy−Autocracy
95% Confidence Interval
Figure 3: Spending Distributions of Democracies and Dictatorships, 1950-2001.
distributions they allocate to a greater degree than relatively constrained democratic leaders.
Turning to the control variables, involvement in an interstate war increases the proportion
of spending dedicated to the military and the variance around a state’s annual spending dis-
30
tribution. Civil war participation is associated with proportionately higher military spending.
Contrary to expectations, increases in GDP per capita are associated with proportionately more
military spending but do not influence the variance in states’ spending distributions. I find no
relationship between spending and a state’s trade openness. Compared to European states,
Middle Eastern countries spend proportionately more on the military while American states
spend proportionately less. The spending distributions of African and Asian states do not differ
significantly from those of European countries.
I conducted a set of robustness checks to ensure the findings reported here hold given alterna-
tive specifications. I estimated models on data sets without outliers and models with different
specifications of the variance equation. I also transformed the data to explicitly analyze the
between panel effect of regime type on patterns of government spending. These models all indi-
cate that, on average, democracies spend less on the military and more on social spending than
dictatorships and that there is more variance in patterns of non-democratic spending. These
results are available in the Supplementary Appendix.
5 Conclusion
Arguably the most salient trend in the contemporary study of international relations and
comparative politics has been the increased theoretical and empirical focus on political leaders
and the choices they make. Some of the most important decisions facing a leader concern
choosing which government programs and policies to finance with the scarce economic resources
available to her. I developed a model of the relationship between leader survival and government
spending when both the incumbent and her winning coalition hold preferences over how a
government allocates resources and a leader can be motivated by securing her political survival
and/or the distribution of government spending. The model indicates that whether a leader
will rationally deviate from her constituents’ policy preferences is a function of her motivation
for enacting policy and the structural costs her winning coalition must pay to remove her from
power. Variation across regime type in the preferences of winning coalitions and the structural
costs of leader replacement result in different equilibrium behavior for democratic and non-
democratic leaders and winning coalitions. I found statistical support for a set of the model’s
empirical implications during the period from 1950 to 2001. I close with a brief discussion of
three of the biggest implications of the findings presented here and avenues for future research.
31
First, the article demonstrates the fruitfulness of allowing variation in citizens’ policy pref-
erences and leaders’ motivation for enacting policy. Selectorate theory assumes that all citi-
zens hold the same policy preferences and winning coalitions vary only in their size (Bueno de
Mesquita et al. 2003). These assumptions imply that the citizens whom can determine whether
an incumbent remains in power are perfectly substitutable. In contrast, I argue socio-economic
status influences policy preferences, which implies the policies that best secure a leader’s politi-
cal survival vary as a function of the composition of her winning coalition. If incumbents are at
least partially motivated by their political survival and retain office through policy responsive-
ness, allowing for variation in their constituents’ policy preferences provides substantial leverage
in predicting political behavior.
One natural extension to the argument presented here is to consider the relationship between
government spending and leader survival among types of non-democracies. It is straightforward
to differentiate non-democracies by whether the civilian elite or military have greater influence
in determining whether a dictator remains in power. Weeks (2012) argues that current and
former members of the armed forces place a higher value on having a strong military than the
civilian elite. Given these respective spending preferences and the equilibrium results reported
here, we would expect military dictatorships to allocate proportionately more resources to the
military than civilian-led dictatorships, on average. We also would expect that lower levels of
military spending should be more likely to threaten the survival of military dictatorships than
civilian-led dictatorships. Further analysis of the relationship between government spending and
leader survival among non-democracies must be left to future research.
The idea that equilibrium policy outcomes are a function of a leader’s preferences and her mo-
tivation for implementing policy has implications beyond patterns of government spending. For
example, a growing literature is beginning to investigate how lame ducks differ from democratic
leaders constrained by the prospects of re-election (e.g., Zeigler, Pierskalla and Mazumder 2013).
Electoral accountability therefore represents a dynamic constraint on democratic leaders’ be-
havior (Clark and Nordstrom 2005). The approach taken here suggests that removing electoral
accountability should reduce the extent to which a leader is concerned with survival and allow
her to pursue her preferred policies. This implies that the effect of term limits on policy should
be conditional on a leader’s preferences. Accordingly, we might expect conservative and liberals
to behave differently with respect to patterns of taxation and spending, protectionists and free
traders to behave differently with respect to trade behavior, and isolationists and international-
32
ists to behave differently with respect to honoring interstate agreements when they are no longer
constrained by the desire to be re-elected. More generally, the results presented here suggest
considering variation in preferences and a leader’s motivation for enacting policy is useful for
understanding political behavior within and across leaders, governments, and regime type.
Second, and related to the previous point, the formal model indicates that policy respon-
siveness is a function of an incumbent’s motivation for implementing policies and the structural
cost of replacement. Leaders motivated by retaining office and those leaders whose winning
coalitions can easily remove them from power will be more responsive to their constituents’
preferences. Given variation in the cost of leader replacement across regime type, this implies
that democratic leaders should be more responsive than dictators, a finding consistent with
most people’s intuition. However, this result only holds when a leader cares about retaining
office. A leader unconcerned with her political survival will ignore her constituents and imple-
ment her preferred policies regardless of the cost of removal. This implies that a dictator who
wants to remain in power will be more responsive to her constituents’ preferences than a demo-
cratic incumbent unconcerned with her survival. While this claim might seem unreasonable
at first blush, I would argue that a lame duck democrat has less of an incentive to enact her
constituents’ preferred policies than a dictator who likely will be killed or jailed if his winning
coalition decides to remove him from power (see Debs and Goemans (2010) on the perils of
being an ex-dictator). Thus, the model’s equilibrium results call into question scholarship that
argues policy responsiveness is a defining feature of democracy (e.g., Dahl 1971, Putnam 1993).
Last, despite the growing focus on the relationship between leaders and policy decisions, this
article is the first to empirically analyze the effect of patterns of government spending on leader
survival in democracies and non-democracies. Duration analysis of all leaders from 1950 to 2001
is consistent with the formal model’s prediction that the distribution of government spending
that best secures a democratic leader’s tenure contains less military spending and more social
spending than the spending distribution that best ensures a dictator remains in power.
The relationship between government spending and leader survival identified here has a
number of implications for existing scholarship and future research. For example, one conse-
quence of interstate war is that it leads governments to allocate relatively more resources to
military spending (Goldsmith 2003). My results indicate that a democratic incumbent would
face a relatively higher hazard of losing office than a dictator given this shift in the spending
distribution. This implies we should observe survival-motivated democrats behaving differently
33
than survival-motivated dictators in at least two ways. First, it suggests that dictators should
be willing to increase the proportion of total spending dedicated to the military during a war
to a greater degree than democrats, especially given the findings that interstate war outcomes
have a larger influence on the survival of dictators (Chiozza and Goemans 2004, Debs and
Goemans 2010, Chiozza and Goemans 2011). This implication is consistent with the findings of
Carter and Palmer (Forthcoming). Second, a survival-motivated democrat has a greater incen-
tive than a survival-motivated autocrat to avoid interstate wars that require substantial increases
in military spending. Consequently, the analyses reported above provide micro-foundations for
the observations that democracies are significantly less likely than non-democracies to initi-
ate interstate conflicts against stronger opponents and the “selection effects” explanation of
democratic success in interstate wars (Reiter and Stam 2002).
The relationship between political survival and government spending is complex. This article
demonstrates how patterns of spending and leader survival affect one another when an incumbent
and her constituents have preferences over how a government spends its resources and leaders
are not exclusively motivated by remaining in power. The theoretical and empirical findings
presented here have implications for how we interpret existing scholarship and suggest several
avenues for future research.
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Appendix
This appendix presents the formal model. The robustness checks discussed in the main text
are available in the Supplementary Appendix.
A Model
The model is a one-shot game between a state’s incumbent leader (Li) and her winning
coalition (Wi). Li’s strategy set is xi ∈ [0, 1], where xi represents the proportion of government
spending dedicated to military spending. Wi’s strategy set is di ∈ {r, k}, where ri replaces Li
and ki keeps Li. The indicator variable pi takes on a value of 1 if Wi plays ri and 0 if Wi plays
ki. Li prefers to remain an incumbent in office (Ii) over being ousted (Oi); Ii > Oi.
Li and Wi hold single-peaked, symmetric preference profiles over xi. The valuations of xi
for Li and Wi are defined as the strictly concave functions z(xi) and v(xi), respectively. I define
xL as Li’s ideal xi ⇒ argmaxx
z(xi) = xL ∀ Li. The ideal policy of the member of Wi holding
the median preference over xi is defined as xw ⇒ argmaxx
v(xi) = xw ∀ Wi.
αi(mi, si) ∈ [0, 1], where mi ∈ [0, 1] represents Li’s motivation for implementing policy and
si ∈ (0, 1] represents the structural cost of leader replacement to Wi. αi(mi, si) is defined as
follows:
α(mi, si) =
0 if mi = 0
mi + (1−mi)(si) if 0 < mi < 1
1 if mi = 1
(A-1)
Replacing Li brings a benefit (bi) to Wi, where bi is an exogenous preference shock to the
model unknown at the beginning of the game that follows the uniform distribution U [l, h], where
l ≤ 0 and h > 0 and arbitrarily large. The cumulative distribution function of bi is written as
F. Removing Li imposes cost ci(v(xi), si)) > 0 upon Wi, where ci is increasing in v(xi) and si:
∂ci(v(xi), si))
∂v(xi)≥ 0 ∀ si (A-2)
∂ci(v(xi), si))
∂si≥ 0 ∀ v(xi) (A-3)
The timing of the game is as follows:
42
1. Incumbent leader Li distributes xi.
2. Uncertainty over bi is lifted.
3. Winning coalition Wi decides to replace (ri) or keep (ki) Li.
As noted in the main text, utility functions for Li and Wi are written as follows:
ULi = αi(mi, si)z(xi) + (1− αi(mi, si))[p(bi, ci(v(xi), si))Oi + (1− p(bi, ci(v(xi), si)))Ii] (A-4)
UWi =
v(xi) if ki
v(xi) + (bi − ci(v(xi), si)) if ri
(A-5)
B Solution
The model is a dynamic game of perfect information with exogenous uncertainty and there-
fore is solved for pure strategy subgame perfect equilibria using backwards induction (Osborne
2004, pg. 226). From Mas-Colell, Whinston and Green (1995), in dynamic games of complete
and perfect information there exists a unique equilibrium in pure strategies for any distribution
of the model’s parameters (pg. 276). Upon receiving xi and observing bi, Wi’s decision rule is
as follows:
Wi plays ki iff bi < ci(v(xi), si) and ri otherwise. (A-6)
As F is the cumulative distribution function of bi, F (ci(v(xi), si)) identifies the probability
with which Wi plays ri and Li loses office.
Li then distributes xi. The first partial derivative of Equation A-4 with respect to αi(mi, si)
identifies how UL changes with αi(mi, si).
∂UL
∂αi(mi, si)= z(xi)− [p(bi, ci(v(xi), si))Oi + (1− p(bi, ci(v(xi), si)))Ii] (A-7)
Note that the first term of Equation A-7 is positive and the second term is negative. The
xi that maximizes Li’s utility then is a function of the values of αi(mi, si), xL, and xw. As
argmaxx
z(xi) = xL ∀ Li and argmaxx
v(xi) = xw ∀ Wi, x∗i ,
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x∗i = αi(mi, si)(xL) + (1− αi(mi, si))(xW ) (A-8)
C Propositions
Define a state’s type of government as gi ∈ {D,A}. The following inequalities define the
conditions placed on winning coalitions’ preferred spending distributions and structural costs of
leader replacement:
xDW < xA
W (A-9)
sDi < sAi ∀ v(xi) (A-10)
Proposition 1 argminx
F (ci(v(xi), si)) | gi = D < argminx
F (ci(v(xi), si)) | gi = A.
Proof. Li minimizes F (ci(v(xi), si)) with the xi that maximizes ci(v(xi), si). From Equation
A-2, ci(v(xi), si) is increasing in v(xi) ∀ si. As argmaxx
v(xi) = xw, then argmaxx
ci(v(xi), si) =
xw ∀ si ⇒ argminx
F (ci(v(xi), si)) ∀ si. Given Equation A-9, argmaxx
v(xi)| gi = D < argmaxx
v(xi)| gi = A ⇒ argminx
F (ci(v(xi), si)) | gi = D < argminx
F (ci(v(xi), si)) | gi = A .
Corollary 1 If mi = 0, then (x∗i | gi = D) < (x∗
i | gi = A).
Proof. From Equation A-8, x∗i = αi(mi, si)(xL) + (1 − αi(mi, si))(xW ) ⇒ x∗
i = xw ∀ Li if
αi(mi, si) = 0. Equation A-1 defines αi(mi, si) = 0 if mi = 0. The proof of Proposition 1
therefore implies that if mi = 0, then (x∗i | gi = D) < (x∗
i | gi = A).
Proposition 2 (|x∗i − xL| |gi = A) < (|x∗
i − xL| |gi = D) ∀ 0 < mi < 1
Proof. From Equation A-1, αi(mi, si) = mi+(1−mi)si if 0 < mi < 1 ⇒ ∂αi(mi,si)∂si
≥ 0 ∀ 0 <
mi < 1. From Equation A-10, sDi < sAi ⇒ αi(mi, sDi ) < αi(mi, s
Di ) ∀ 0 < mi < 1. Given
Equation A-8, it follows that (|x∗i − xL| |gi = A) < (|x∗
i − xL| |gi = D) ∀ 0 < mi < 1.
44