Download Dictatorship, Interest Groups and Government Predation: The Case

Dictatorship, Interest Groups and Government
Predation: The Case of Zimbabwe
Johnson Gwatipedza & Thorsten Janus1
Abstract
This paper studies the dictatorship and economic decline of Zimbabwe since the late 1990s. We
build a model with a ruler and two interest groups, the militia and the general citizens. The ruler
provides a public good and a surplus to both militia and citizens to stay in power. Only the
citizens pay taxes, but both the militia and citizens benefit from the public good. We show that in
“normal” times the ruler provides a surplus to both militia and citizens, output is relatively high
and the country is politically stable. However, an exogenous productivity shock can push the
economy into a predatory-state equilibrium where public goods provision and output decline, the
regime redistributes output from citizens to the militia, and the citizens try to replace the regime,
causing political instability. These predictions are consistent with the decline of Zimbabwe‟s
economy since the late 1990s following several negative weather and terms-of-trade shocks in
the early 1990s.
1
The authors would like to thank Professor Avinash Dixit whose discussions inspired this paper to be written while
he was visiting the University of Wyoming on a seminar at held on the November 2007.
1
1. Introduction
This paper studies the dictatorship and economic decline of Zimbabwe since the late 1990s. We
build a model with a ruler and two interest groups, the militia and the general citizens. The ruler
provides a public good and a surplus to both militia and citizens to stay in power. Only the
citizens pay taxes, but both the militia and citizens benefit from the public good. We show that in
“normal” times the ruler provides a surplus to both militia and citizens, output is relatively high
and the country is politically stable. However, an exogenous productivity shock can push the
economy into a predatory-state equilibrium where public goods provision and output decline, the
regime redistributes output from citizens to the militia, and the citizens try to replace the regime,
causing political instability. These predictions are consistent with the decline of Zimbabwe‟s
economy since the late 1990s following several negative weather and terms-of-trade shocks in
the early 1990s.
Several other papers study rent extraction from the private sector by a self-interested
government. For instance Dixit (2004, 2010) studies the optimal contract an autocratic ruler will
offer its bureaucrats and Myerson (2010) studies how a government‟s temptation to expropriate
affects investment incentives. Unlike these papers we abstract from bureaucracy and private
investment.
Olson (1993) and McGuire and Olson (1996) argue that a single dictator or
“stationary bandit” who expects to remain in power decreases rent extraction compared to a
sequence of myopic dictators or “roving bandits.” Intuitively, only a stationary bandit
internalizes the fact that economic growth today increases tomorrow‟s tax base. Our model
differs since the cause of government predation is a low value of holding office instead of
myopia. Besley and Kudamatsu (2008) note that autocrats typically rely on party structures,
economic elites or other interest groups that can in principle depose the leader. We share this
view by assuming the ruler must satisfy both a militia and the general citizens to guarantee
staying in power. Acemoglu et al (2006a,b) explain that many of Africa‟s recent democracies
have only weak checks on the exercise of political power. We similarly emphasize government
discretion as a source of abuse of power, slow growth and political instability.
2
The remainder of the paper proceeds as follows. Section 2 provides an overview of Zimbabwe‟s
economy since independence. Section 3 presents the model, the first-best and the actual outcome.
Section 4 considers extensions. Section 5 concludes the paper. All proofs are in the appendix.
2. Zimbabwe’s Economy since Independence
Zimbabwe‟s post-independence economic performance can be broken into three periods; rapid
economic growth followed by economic stagnation and then rapid economic decline.
1980-1990
Zimbabwe began as a prosperous country. It was coined “the jewel of Africa” and “breadbasket‟
of central and southern Africa” (Potts 2006). In the first elections ZANU-PF, the liberation
movement led by Robert Mugabe, won a clear majority (Eriksen 2011). Economic growth was
10.7 per cent in 1980 and 9.7 per cent in 1981 (Makina 2010). The average growth rate of 4.3%
in the 1980s was one of the highest in Sub-Saharan Africa (Makina 2010, Chavunduka and
Bromley 2010). The ZANU-PF regime sought to satisfy rural expectations by providing social
services and subsidized inputs for agriculture. This led to increased agricultural production and
consolidated rural support (Eriksen 2011). There was also significant industrial expansion behind
tariff walls and exchange rate controls, and an expansion of social services, health, and education
(Barry et al 2009). The economy became dominated by industry and mining, rather than
agriculture, and was among the most mature, sophisticated and integrated in sub-Saharan Africa
(Potts 2006). Most formal employment was urban-based and non-agricultural (Potts 2006). By
the early 1990s the unemployment rate was 10% (Chang 2008), an impressive figure for a
middle income country.
The ZANU-PF regime was a broad cross-class alliance held together by opposition to minority
rule and mobilized on a national-democratic basis. Although it was dominated by the former
liberation movement, it was also supported by urban professionals, the labour movement, and
peasants (Eriksen 2011). The regime‟s opponents included white capitalist farmers and
entrepreneurs, who had been closely tied to the old regime (Eriksen 2011). Since ZANU-PF
controlled the state, but whites remained economically dominant, a separation between economic
and political power emerged (Eriksen 2011).
3
1990-1997
Growth declined in the early 1990s (Barry et al. 2009, Chavunduka and Bromely 2010, Makina
2010). There was major drought in 1992 - described as the worst in more than a century - and a
more localized second drought in 1995. Unfavourable global commodity prices distressed the
agricultural sector (Chavunduka and Bromley 2010). During 1991-95 economic growth averaged
less than one per cent (Barry et al 2009).
Zimbabwe also underwent a major enhanced structural adjustment program (ESAP) from 199196. The program was promoted by the World Bank, IMF, and other aid donors (Chavunduka and
Bromely 2010, Potts 2006, Eriksen 2011). Unlike most other ESAP countries, when Zimbabwe
began its program its foreign debt was manageable, its debt commitments were being honoured,
and growth had been positive in preceding years (Eriksen 2011). The program was linked to
worse performance regarding poverty reduction, diversification, growth, employment, and wages
than during the 1980s (Eriksen 2011). Per capita incomes stagnated, social conditions worsened,
and the number of people living in extreme poverty increased (Chavunduka and Bromley 2010).
The index of manufacturing output, which had gone from 100 in 1980 to 143 in 1991, declined
to 109 in 1996. The share of manufacturing in GDP fell from 25–27% in the 1980s to 17% in
1998. There were rapid inflation, cutbacks in education and health, and declines in subsidies and
real urban incomes. Minimum industrial wages and food subsidies, including for the staple
mealie-meal, were reduced. Controls on many other basic products were also removed, import
controls were dropped and the currency was devalued. The private sector was encouraged to take
over provision of services even in sectors such as low-income housing. Real annual earnings per
employee fell by an estimated 26.5% from 1991 to 1995 (Potts 2006) and urban employment
became increasingly informal. There was also pressure to reduce public sector wages.
Not surprisingly, there was a large increase in urban poverty during the program period.
Although ESAPs have had similar effects in other African countries (Potts 2006), due to the
prosperous 1980s, and because the program was not implemented during a crisis, urban people‟s
aspirations in Zimbabwe may have been significantly higher than elsewhere (Potts 2006). Rural
areas were hit via cuts in health and education as well as the removal of subsidies on fertilizer
and other agricultural inputs. More competition in crop pricing may have helped those who were
4
well-located relative to markets, but tended to disadvantage those who were not. Most of
Zimbabwe‟s smallholders were also net food purchasers. Urban remittances, which were of
central significance to many rural families, declined (Potts 2006). Structural adjustment also
weakened state capacity due to the decline in economic resources and cuts in public
administration.
1997-present
By 1996 the government had returned to unsustainable fiscal expansion and effectively
abandoned the liberalization regime (Makina 2010). Policies became increasingly interventionist
as authorities sought to reverse the economic decline. Although the central bank (the Reserve
Bank of Zimbabwe) lent to the private sector at negative real interest rates, the private sector
faced an overvalued exchange rate, a shortage of foreign exchange, a shrinking domestic market,
and a variety of supply-side bottlenecks including fuel, electric power, imported inputs, and
skills (Makina 2010). Poor relations with creditors and donors, and deteriorating economic and
social conditions, prevented access to external financing (Coorey et al. 2007).
The economic decline since the early 1990s led to urban discontent and support for the
opposition Movement for Democratic Change (MDC). In the absence of political violence the
MDC might have won the 2000 parliamentary elections. The labour movement, which had been
loyal supporters of ZANU-PF, become more critical of the regime (Eriksen 2011). The regime‟s
support shrank to include primarily the peasantry and communal areas apart from the party elite
and groups linked to it. As social services and agricultural subsidies were reduced, even rural
support weakened (Eriksen 2011).
In August 1997, thousands of veterans who had been
demobilised in the early 1980s rose up demanding land and factories as compensation for their
role in the war of liberation (Potts 2006, Barry et al 2009, Chavunduka and Bromely 2010,
Makina 2010). Zimbabwe‟s president, Robert Mugabe, trying to solidify his position, seized the
property of farmers to distribute to the ruling elite and his political supporters (Besley and
Ghatak 2010). Redistribution of land had been a key demand in the independence struggle, and
while progress in this area had been limited in the 1990s, the demand for land was never in doubt
(Eriksen 2011).
1471 commercial farms were designated for expropriation without
compensation, although few were effectively transferred (Potts 2006). The veterans also received
5
large one-off payments and on-going pensions (Chavunduka and Bromley 2010, Eriksen 2011),
which further destabilized the government budget. On “Black Friday,” 14 November 1997, the
Zimbabwe dollar crashed due to a combination of contagion from the Asian crisis (via South
Africa) and fiscal imbalances. The deficit further grew with Zimbabwe‟s 1998 participation in
the conflict in the Democratic Republic of the Congo (Makina 2010).
As the state became increasingly weak and politicised after 2000 (Eriksen 2011), tenure security
declined. The creation of a youth militia unleashed violence during the government‟s chaotic and
partisan Fast Track Land Resettlement Programme (FTLRP). The FTLRP was supposedly
completed in 2002, but farm occupations continued amidst intensified contestation over land
claims (Chavunduka and Bromley 2010). There was also a very poor agricultural season in much
of Southern Africa , including Zimbabwe, in [year] (Potts 2006). The collapse of the rule of law
combined with electoral malpractice and human rights violations to cause an unprecedented
socio-economic meltdown (Robinson and Torvik 2009, Makina 2010). After Mugabe and his
allies seized and redistributed commercial and financial institutions in 2002, investment ceased
and capital and labour fled the formal economy (Azam et al 2009).2 The government was deeply
suspicious of private business transactions and acquired large stakes in private firms. Credit
extended by the central bank was effectively subsidies. The state also reduced investment in
education, health, housing, and other public services (Makina 2010). Real GDP growth declined
from 0 percent in 1998 to –7.4 per cent in 2000 and –10.4 per cent in 2003. It averaged –5.92
percent from 2005-07 (Makina 2010). The cumulative decline between 1998 and 2006 was 37
per cent, while there was a cumulative gain of over 40 per cent elsewhere in Africa (Makina
2010). In 2004 manufacturing output was at its lowest level in 30 years and 45.6% lower than in
1998 (Potts 2006). There were a number of bank failures and company closures. Gross fixed
capital formation declined from an average of 23 per cent 1995 -99 to only 6 percent 2000–06.
The savings–GDP ratio declined from 28 per cent in 1995 to 5 per cent in 2001 and 14 percent in
2005 (Makina 2010). Urban households turned to informal activities (Potts 2006).
2
This was not the first time that civilians had suffered from state-sponsored violence. During Gukurahundi, the
1980s civil war in Matabeleland, over 20 000 people were killed by five Brigade. It seems that whenever the state‟s
legitimacy is questioned, land is used dispel these doubts (Chavunduka and Bromley 2010).
6
As the economy, tax base and export earnings declined, the government found it impossible to
balance the budget. Due to the crisis and the regime‟s instability, it could not borrow externally.
It then turned to the central bank‟s printing press (Barry et al 2009). Inflation soared from about
20 percent in December 1997 to 623 percent in January 2004 (Munoz 2006). The last officially
recorded hyperinflation figure is 231 million per cent by July 2008 and it was estimated that
hyperinflation peaked at about 500 billion per cent by September 2008. The currency was
virtually replaced by foreign currency by October 2008 (Makina 2010) and private savings were
extinguished (Chavunduka and Bromley 2010). The adjusted overall fiscal deficit, including
government and central bank interest payments, was estimated at 80 percent of GDP in 2006
(Coorey et al 2007). By 2008 the central bank was broke (Buiter 2008) with more than US$1.2
billion in debt.
The human costs of the crisis were huge. Around two-thirds of the rural population and over half
of the urban population, totalling over 7 million out of a total population of 12 million, could not
meet basic food and non-food requirements and depended on food aid (Chavunduka and
Bromley 2010, Makina 2010). Life expectancy became the lowest in the world, falling to 37
years for men and 34 for women. By the end of 2008, unemployment was estimated to be over
90 per cent. Over 3 million Zimbabweans had migrated to neighbouring countries, South Africa,
the UK, USA, Canada, Australia, New Zealand, and other destinations (Makina 2010). In 2003
72 percent of the population was estimated to be living below the poverty line compared to 55
per cent in 1995.
Faced by a situation where its position was under threat, Zimbabwe‟s regime chose policies to
strengthen its grip on power in the short term. As a result, the regime found itself in a downward
spiral, in which both the welfare of the population and the power of the state were undermined
(Eriksen 2011). Zimbabwe‟s state was “captured‟ by the ruling party and the standard separation
of powers between government, bureaucracy, and political parties became blurry. It became not
only a captured state, but a predatory state, as illustrated by the fast track land reform
programme.
7
3. A Model of Economic Decline in Zimbabwe
We build a model in which a ruler provides a public good to a country‟s citizens. The citizens
produce
, where
is the public good and
is a productivity parameter. For simplicity capital
depreciates fully. The ruler‟s capital provision cost is
and for simplicity we ignore labour
3
and private investment inputs to production. The citizens pay taxes
transfers
to the militia. If the citizens face a tax rate
and the ruler pays
they produce in the formal
sector and otherwise they more production to the non-taxable informal sector. Transfers to the
militia carry a deadweight loss
≥0 per unit and taxation carries a loss
also gets an expected value V>0 is she stays in office, where
≥0 per unit. The ruler
is the ruler‟s discount
factor. For example, she may collect taxes in the future or borrow against the revenues of future
governments (Jayachandran and Kremer 2006). In the latter case
, where
the international interest rate. For simplicity the citizens‟ discount factor is always
is
.
The surplus to the ruler, citizens and militia are
S R  ak /(1  C )  k 2 / 2  (1  R ) R +
(1)
SC  (1   )ak
(2)
S M  k  R ,
(3)
where k captures any militia benefit from the public good. For example, in Zimbabwe military
officers own or manage a number of production and trade facilities (Jenkins and Knight 2002).
3
Alternatively, suppose that the ruler owns the capital stock and hires citizens at a wage equal to the income they
can earn in the informal sector. Normalizing this income to zero the ruler‟s only expenditure is capital.
8
To guarantee staying in power, the ruler must provide a surplus to citizens, S C0 , as well as a
surplus to the militia, S M0 .4 If she does not satisfy the citizens they try to replace her. The
likelihood that the replacement attempt succeeds is (1  p)  (0,1) . If the does not satisfy the
militia, on the other hand, the militia overthrows her with certainty. The fact that the militia
represents a more severe threat seems consistent with Zimbabwe‟s experience. Once the ruler is
overthrown her payoff is zero. Finally, to focus the analysis we assume that


arg max p  ak /(1  C )  k 2 / 2  (1  R )(S M0  k )  V  0 .
(A1)
k
Assumption (A1) states that the ruler can achieve a non-negative payoff by choosing the
maximum tax rate,  , and paying the militia the minimum transfer to avoid a militia uprising
( S M  S C0 ). The timing is that first the ruler provides capital k and decides tax and transfer
policies  , R . Then the militia rises against the ruler if its incentive constraint is not satisfied.
Finally if the militia did not rebel the citizens decide whether to do so. The citizens cannot rebel
against the militia.
First-best solution
Since transfers are distortionary, efficiency implies zero transfers. Since capital depreciates fully,
the efficient capital stock simply maximizes the current-period social surplus with zero transfers,
. This implies the first-best public capital stock
(4)
4
Endogenizing these reservation values may require an understanding of collective action and group organization
within the populace and military. We leave documentation and modelling of these microeconomic processes to
future work.
9
Political economy solution
Due to (A1) the ruler prefers satisfying the militia to being replaced and earning zero. However,
she may or may not satisfy the citizens. To explore this question we compare the ruler‟s
equilibrium payoff if she only satisfies the militia to her payoff if also she satisfies the citizens.
Proposition 1 (i) If the ruler only satisfies the militia the solution is
 a

k p  
  (1  R )   , S Cp  (1   )ak p , S Mp  S M0 ,  p   , R  S M0  k p
 1  C

(5)
and the ruler’s indirect utility is


V ,
(6)
where the superscript p denotes that the government preys on the private sector.
(ii) If the ruler satisfies both the citizens and the militia the solution is
 a

k np  
  (1  R )   , S Cnp  S C0 , S Mnp  S M0 ,  np  1  SC0 / ak np , R np  S M0  k np (7)
 1  C

and the ruler‟s indirect utility is


V ,
where the superscript np denotes that the government does not prey on the private sector.
(iii) The ruler satisfies both the citizens and the militia (only the militia) if
10
(8)
2
2
 a

 a
 

  (1   R )   p
  (1   R ) 
2
  1  C

1  C






(9)

S0
 1  p  (1   R ) S M0  V  C  ()0,
1  R
The intuition for Proposition 1 is that satisfying not only the militia, but also the citizens, costs
the ruler an extra
. However, it increases her probability of surviving in office from
p  1 to one. She satisfies both interest groups if and only if the gain exceeds the loss. The
capital stock is greater in the non-predatory equilibrium because it plays the dual role of
providing a tax base and satisfying the citizens‟ incentive constraint. In the predatory equilibrium
it only plays the former role. As expected citizens‟ surplus, SC  (1   )ak , is bigger under nonpredation:  is lower and k is higher. Since k is higher, the transfer to the militia, R  S M0  k ,
and the deadweight loss of this transfer, R R , are also less under non-predation.
Corollary 1 The ruler is more likely to satisfy both interest groups when productivity,
, the
militia’s marginal benefit from public goods, , the future office value, V , or the risk of
overthrow if the citizens are dissatisfied,
are high. She also tends to favour both groups
when the public good provision cost parameter, , the demands of either militia or citizens,
, the tax distortions,
or
or
,and the maximum feasible tax rate under predation,  , are low.
The intuition for the corollary is that high values of productivity,
, and militia public good
benefit, , respectively, increase the ruler‟s tax base and decrease the transfer she must pay the
militia. Her value of office holding therefore increases and she is more willing to pay the citizens
to avoid an uprising. That incentive also strengthens if unhappy citizens pose a more severe
threat, so (
is high, or the value of future office, V , is high.5 Conversely, costly public
goods provision (high
5
, high surplus demands
and
, or large tax and transfer distortions,
In Zimbabwe, President Mugabe‟s ageing and possibly illness may have decreased , thus promoting predation.
11
C and  R , decrease the value of office and makes the ruler more tempted to gamble on nonreplacement by extracting surplus from the citizens. Finally, predation is also less tempting if
citizens can easily move to the informal sector and therefore the maximum tax rate,  , is low.
We now turn to the paper‟s main result concerning the effects of a productivity shock.6
Proposition 2 A small decline in citizens’ productivity can lead to government
predation
and large declines in the public capital stock, output, and citizens’ welfare, as well as a large
increase in transfers to the militia. The effects are bigger the larger the productivity decline.
Proposition 2 offers a theory of Zimbabwe‟s economic decline: if the droughts and declining
terms of trade in the early 1990s decreased productivity enough to change the left hand side of
(9) from positive to negative, then their direct effects on output and the citizens‟ surplus would
have been greatly magnified as the regime switched from moderate rent extraction to predation:
going from moderation to predation sharply decreases the capital stock and output, while the tax
rate increases. Thus, citizens‟ welfare falls sharply. Since the militia‟s payoff from capital, k ,
fall with the capital stock, a large transfer increase is needed to keep its payoff (3) constant.
4. Extensions
Endogenous ruler survival under a citizen uprising
A larger stock of physical or human capital, or infrastructure, could potentially help an uprising
by the citizens succeed. We therefore now assume that the ruler‟s likelihood of surviving the
uprising is p  p(k ) , p' 0 , with a non-decreasing hazard rate (that is,  p' (k ) / p(k ) is nondecreasing, as is true for the normal, uniform, exponential, and many other distributions).
6
The militia‟s marginal public good benefit may also have dropped,   0 , since as noted Zimbabwe‟s militia
owns substantial productive assets. We ignore this drop for simplicity but note that it would exacerbate the output
loss and cause a further rise in transfers required to satisfy the militia in (3).
12
Proposition 3
Assume that public capital increases the likelihood that a citizen uprising
against the ruler succeeds. Then the non-predation outcome does not change, but capital, output
and citizens’ surplus in the predation equilibrium are smaller than if the uprising success
probability did not depend on capital. However, the predation equilibrium may be less likely.
The intuition for proposition 3 is simply that the ruler has less incentive to provide capital when
she knows that capital erodes her power in case of an uprising due to predation. With less capital,
output and the citizens‟ welfare decline. However, if the ruler‟s predation payoff is smaller than
in the original model (e.g. the rent-maximizing capital stock and therefore the tax base may be
smaller) she is less likely than before to choose predation. This helps the citizens.
Constraints on borrowing
The imperfections of sovereign lending markets (Panizza et al. 2009) may prevent the regime
from borrowing. To why this can be important, assume for simplicity that the both the ruler‟s
and the citizens‟ discount rate equal the international interest rate.
Proposition 4
International credit access can help to avoid government predation and
increase the public capital stock, output and citizens’ welfare.
The intuition for Proposition 4 is that the ruler may prefer non-predation because (9) is nonnegative. However, her current-period maximized income when satisfying both the citizens and
the militia (see (8)) can still be negative:


< 0. In
this case, without credit the regime cannot satisfy both interest groups and is forced to predate. In
contrast, with credit access it could borrow enough (since (9) is positive) to satisfy both groups.
The citizens would gain from the switch to non-predation as described in Proposition 2.
Zimbabwe’s Structural Adjustment Program
Most countries begin their structural adjustment programs during times of economic distress and
out of necessity. When Zimbabwe began its program in 1991, however, neither the economy nor
13
the government were distressed. Given that reform programs tend to be painful – which seems to
have been true for Zimbabwe as well – it is worth asking what might have motivated the
Zimbabwe program decision. Although we leave a careful analysis and formal modelling to
future work, one explanation may be that the regime hoped the program would increase
productivity a . As noted, however, it seems more likely that the program decreased at least
short-run productivity, thus encouraging predation. Another explanation may be that, since
growth was already declining, the regime may have used the adjustment program to legitimize
predation it was planning to do anyway. After all, the adjustment program sought to (i) diminish
public goods provision, (ii) increase net taxation (taxation net of transfers and subsidies) and (iii)
increase public savings or, equivalently, the ruler‟s surplus in equation (1). This is also what the
predatory equilibrium achieves. The program years 1991-96 may then have shown the regime a
relatively efficient and legitimate way to increase rent extraction. More extreme and costly
means of rent extraction, such as expropriations and inflation taxation, were only after the
program ended in 1996. Finally, Zimbabwe‟s program decision could also reflect that the regime
could not borrow on the international private credit market. A promise to adjust was then the
price of overcoming a credit constraint, such as studied above (Proposition 3). In that case the
loan aspect of the adjustment program may have helped to hinder predation, while the
adjustment aspect may have promoted moderate predation by decreasing productivity and/or
legitimizing predation.
5. Conclusions
In this paper we have studied the fragile political economy of Zimbabwe. We argue that the
Mugabe regime has had to operate under the twin constraints of satisfying both its citizens and
the country‟s powerful militia. When negative shocks to productivity associated with droughts
and term-of-trade declines hit in the early 1990s, however, the regime found it either optimal or
necessary to prey on its citizens. The result was economic decline and political instability as the
citizens rose against the regime. Additionally, the regime had to increase transfers to the militia
to avoid militia disaffection as well. Further research might explore how an option for the regime
to punish social uprisings and invest in repressive capacity affects the different outcomes. If
building repressive capacity means empowering the militia, then it could be a double-edgedd
sword: the price of keeping the citizens under control may be losing control over the militia.
14
Another extension is to study Zimbabwe‟s structural adjustment program and its relation to the
economy‟s decline and subsequent collapse. A third area involves distinguishing the mining,
agricultural and industrial sectors, or urban and rural areas, as both sector and geographical
distinctions seem relevant to understand the country‟s political economy.
15
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Appendix: proofs
Proof of Proposition 1
(i) If the ruler ignores the citizens, she pays the militia
k  R  S M and the optimal capital stock maximizes the left hand side of (A1). Straightforward
computation gives (5). Using (A1) and (5) the ruler‟s indirect utility is (6):


=


.
(ii) If the ruler satisfies both the militia and the citizens she chooses F , R, k to maximize (1)
subject to S C  S C0 and S M  S M0 . Assigning Lagrange multipliers

first-order conditions,
(1 
;
and
1
((1   )ak  S C0  0 ;
;
2
to (3) and (4), the

( k  R  S M0 )  0 , imply (7). Combining (1) and

(7) gives (8):


=

.
(iii) The ruler prefers to satisfy both interest groups if and only if the payoff (8) exceeds the
payoff (6). This is true if and only if (9) is non-negative 
Proof of Corollary 1 The results follow from inspecting (9) and noting that p ,
19
 1. 
Proof of Proposition 2 Consider a small productivity decline ( a  0 ) which changes
the left hand side of (9) from non-negative to negative and recall that   1 . Comparing (7) to
  (a  a)  a 
   0 , in output
(5) the change in public goods provision is k  k p  k np  
1  C


 (a  a   ) 2   (a   ) 2

  (1  R )a    0 ,
((a   )k )  (a   )k p  (a  a   )k np  
1  C


and in citizens‟ welfare SC  SCp  SCnp  (1   )(a  a)k p  (1   np )ak np  0 except if  np   .
  (a  a)  a 
   0 .
The change in militia transfers is R  R p  R np    (k p  k p )    
1


C


All of these changes are larger when the productivity decline, a , is larger. 
Proof of Proposition 3
The non-predation outcome does not change since it does not
involve a citizen uprising. In the predation equilibrium, since taxation does not affect the ruler‟s
survival probability she still sets  . She also still pays the militia R  S M0  k p . The only
difference is therefore that the capital stock now solves, not the left hand side of (A1), but


max p(k )  ak /(1  C )  k 2 / 2  (1  R )(S M0  k )  V ,
k
(A1‟)
implying
 a /(1  C )  k  (1  R ) 
 p' (k )

2
0
ak /(1  C )  k / 2  (1  R )(S M  k )  V  p(k )
or u' (k ) / u(k )   p' (k ) / p(k ) , where u is the ruler‟s payoff (the denominator on the left hand
side). If p' 0 , so the capital stock has no effect on the ruler‟s ability to retain office, then the
solution for k p is the same as in (5). If  p' / p  0 , however, then the left hand side requires a
lower value of k compared to the original model. Thus, the public capital, k p , output, ak p , and
20
the citizens‟ payoff if the ruler stays in power, (1   )ak p , are less than in the original predation
equilibrium. However, if the ruler‟s predation payoff (6) declines due to a low value of k p and
potentially a low survival probability, p , she is less likely to prefer predation ((9) is less likely to
hold). 
Proof of Proposition 4 From Proposition 1 the regime prefers non-predation (predation)
if and only if
2
2
 a

 a
 

  (1  R )   p
  (1   R ) 
2
  1  C

1  C







S C0
 1  p  (1   R ) S  V / R 
 ()0.
1  R
0
M
/
Assume now that this expression is non-negative, but the ruler‟s current-period maximized
income when satisfying both the citizens and the militia (see (8)) is negative:


< 0. Without foreign credit access the regime must choose the
predatory equilibrium. With credit access it could borrow enough to choose non-predation,
implying a higher capital stock and output. The citizens would gain by switching to nonpredation as described in Proposition 2. 
21