How a Corrupt Oﬃcial Can Increase His Budget
Kimiko TeraiaaAmihai Glazerb

Faculty of Economics, Keio University, 2-15-45 Mita, Minato-ku, Tokyo 108-8345, Japan
E-mail: kterai@econ.keio.ac.jpbDepartment of Economics, University of California–Irvine, Irvine, California 92697, U.S.A.
E-mail: aglazer@uci.edu

May 6, 2017

Abstract
A principal aware that an agent will steal will nevertheless fund the agent, because theprincipal values the output the agent produces. The agent in turn will decide how much tosteal on period 1 by anticipating how his behavior in period 1 aﬀects the budget the principal
will give him in period 2. Under some conditions, the agent can increase the budget he getsby engaging in greater corruption. A budget constraint imposed for the ﬁnal period can limit
corruption in each period, and induce eﬃcient investment.

Keywords: political economics; public investment; corruption; budget allocation; ﬁscal cap
JEL classiﬁcation: D72, D73, D92, H54, H611

1

Introduction

Governmental projects often suﬀer from cost overruns. Cantarelli et al. (2010) summarize some ofthe evidence for transportation projects. The Government Accountability Oﬃce found that 77%
of highway projects in the United States experienced cost escalation. Another estimate is that the
average overrun of infrastructure projects is about 50%. A review of 3,500 projects found that
overruns are the norm, generally ranging between 40% and 200%.
A major example of cost overruns, caused in part by corruption and incompetence, appeared in
the Big Dig project in Boston, Massachusetts. In 2006 a concrete ceiling panel and debris weighing
24,000 kg fell on a car, killing a passenger. Investigation and repair of the collapse caused a sectionof the Big Dig project to be closed for almost a full year, causing chronic traﬃc backups.1 The
project suﬀered from faulty epoxy, light ﬁxtures dropping, sea water leaks. The cost ballooned
from $2.6 billion to nearly $15 billion, and was eight years behind schedule. Cost overruns ofmore than $1 billion at the Veterans Aﬀairs hospital in Colorado arose in large part because of
a design that often sacriﬁced aﬀordability in the name of aesthetics.2 The theft of funds can bemassive: a study of grants to schools in Uganda ﬁnds that the schools, on average, received only
13 percent of the grants. Most schools received nothing, with most of a grant captured by local
oﬃcials (and politicians).3 Such behavior often has the characteristic of “throwing good money
after bad.” Consider the following example from Kenya:
Kenyans need to be informed now that even today the government is perpetuating
further actions of corruption, no doubt related to the need to raise money for elections.
Speciﬁcally it has committed Ksh. 840 Million by a contract of February 2007 tooverhaul four second-hand junk helicopters which were fraudulently purchased throughAnglo Leasing type procedures in 1998. Provision has been made in the current budget1

https://www.bostonglobe.com/magazine/2015/12/29/years-later-did-big-dig-deliver/tSb8PIMS4QJUETsMpA7SpI/story.html
http://www.denverpost.com/2016/09/21/aurora-va-oﬃcials-warned-repeatedly/
3
Reinikka and Svensson 2004.
2

2

estimates to pay for overhauling the junk helicopters, thus throwing good money after
bad. It would be better to cancel the fraudulent deals and instead buy new, functional
equipment transparently...The purchase of faulty equipment on whose rehabilitation andmaintenance ever greater sums must be spent provides a cover for continued theft of
public resources.4
Sometimes, however, corruption or excessive spending reduces spending in future periods, or evencancellation of a program. Following is an example:
The Sesame Workshop was “dismayed” to ﬁnd out today that a $20 million U.S. program
to beam Elmo and his pals in Pakistan has been halted because of allegations of fraud
and abuse. “We had what we believed were credible allegation...Rather than continue
to throw good money after bad, we thought it was prudent …to cut oﬀ this program
and wait for the results of the investigation.”5
A model of corruption should allow for both types of behavior, explaining when each pattern willappear. Our paper does.
An agent who gets money from a principal may steal some of it. The agent’s incentives to steal
depend on the consequences. One consequence, studied here, is how theft in one period aﬀects
opportunities in later periods. A standard approach has theft in one period reduce opportunities
for theft in future periods—the agent may be penalized or apprehended, other people may havelearned of the theft and so take greater precautions in the future, or the victims may be poorer
from the theft, reducing the amount that can be stolen in the future. But there is another eﬀect.
Consider a principal who gives money to an agent, which the agent can use to produce a good
the principal values. Theft by the agent reduces, other things equal, production of the good. A
principal who highly values the good may then compensate by increasing the resources he gives
the agent in future periods, so that at least some minimal level of the good is provided. This
4
5

http://humanrightshouse.org/noop/page.php?p=Articles/8146.html&d=1
http://abcnews.go.com/International/sesame-street-dismayed-corruption-charge-pakistan-loss-us/story?id=16497

3paper explores such eﬀects. In doing so, we shall show conditions under which the agent can gainfrom stealing, and conditions under which he cannot. Two eﬀects will be seen as important. First,
if small investment in period 1 makes the marginal product of investment in period 2 small, theprincipal gains little from investing in period 2. Second, if the principal’s marginal utility from
output is high, then a small investment in period 1 would call for a large investment in period 2
because otherwise output would be low. Depending on the strength of these eﬀects, and on whether
the agent will continue in oﬃce, the agent may gain or lose from stealing in period 1.
We shall also explore how a principal who commits to the level of spending in future periods
can limit the incentives to steal, showing conditions under which a ﬁscal constraint imposed upon
the principal can limit stealing by agents. The credibility of such a commitment can depend on thenumber of agents, and on whether the ﬁscal cap is imposed on each agent individually, or insteadon aggregate spending.

2

Literature

We consider an agent who can steal more the larger the budget he receives. The argument thatgovernment budgets are excessive has a long history, perhaps beginning with Hume’s view that government is a Leviathan aiming to enlarge itself. The view was formalized by Niskanen (1971) who
supposed that a government agency aims to maximize its budget. Besley and Smart (2007) model
political agents, who are unknown to maximize voter welfare or to maximize rents extracted fromthe government. They ﬁnd that a ﬁscal constraint imposed upon the budget size is desirable only
when political agents are suﬃciently likely to be self-interested. Somewhat related are Alesina andTabellini (1988) and Tabellini and Alesina (1990) who show that voters may favor budget deﬁcits
which constrain future public policy. These papers, however, do not capture, as we do, a dynamic
feature of a principal-agent relationship, that is, how an agent distorts his behavior to aﬀect the
principal’s behavior in the next period. Besfamille and Lockwood (2008) point out an ineﬃciency
of a hard budget constraint, which may give an agent excessive incentives for high eﬀort and may
4discourage investment by this agent anticipating it. Natvik (2013) analyzes governmental production, which requires both labor and predetermined capital, examining how input complementarityand political turnover make capital a tool for incumbents to aﬀect future policy. These models,
however, do not treat corruption. Our analysis also relates to Gersbach and Glazer (2009) who
consider the ratchet eﬀect of a worker’s action aﬀecting a ﬁrm’s payment in the future. The more
the ﬁrm pays in one period, the wealthier is the worker in the following periods, and so the morehe must be paid for a given eﬀort. This wealth eﬀect can induce an employer to pay little initiallyand more later on, while the worker may work harder than the employer prefers. The incentive
contracts ﬁrms oﬀer may therefore cap the worker’s earnings.
Much empirical work ﬁnds a negative correlation between corrupt environments and ﬁrm productivity (see, for example, Yan and Oum 2014, and Dal Bo and Rossi 2007). Similar eﬀects arefound in European airports (Randrianarisoa 2015), where strong evidence shows that corruption
reduces airport operating eﬃciency. A study of a large antipoverty program in Indonesia that distributed subsidized rice to poor households estimated that at least 18% of the rice disappeared due
to corruption (Olken 2006). A study of road construction in rural Indonesia suggests that about
24% of the spending was wasted or stolen (Olken 2007). Looking at spending by U.S. states, Liu
and Mikesell (2014) claim that increased corruption by public oﬃcials increases state spending.
We look instead at how expected productivity can aﬀect the opportunities for corruption. Some
evidence for such causality is given by Kyriacou, Muinelo-Gallo, and Roca-Sagales (2015), who
examine the cross-country connection between the size of the construction sector and the public’s
perceptions of corruption.
Relatedly, competition among local governments has been viewed as limiting corruption. Montinola and Jackman (2002) examine how political or economic competition aﬀects levels of corruption,ﬁnding that corruption is lower in dictatorships than in partially democratized countries; but once
past a threshold, democratic practices inhibit corruption. With respect to economic competition,
their analysis show that membership of the Oil Producing and Exporting Countries (OPEC) increases corruption. Laﬀont and N’Guessan (1999) empirically explored the relationship between
5competitiveness and corruption, measuring competitiveness by the openness of African economies.
Their results are ambiguous, indicating that the sign of the relationship depends on the level of corruption. Brennan and Buchanan (1980), followed by Edwards and Keen (1996) and Arikan (2004),
see competition as allowing ﬁrms or residents to move to localities with low corruption, reducing
the incentives of any one local government to be corrupt. Menes (1999, 2003) attributes much of
the decline in municipal corruption in the United States to the expansion of the American frontierand development of railroads, which raised the elasticity of the local revenue base available to pay
bribes or taxes.6

3

Assumptions

3.1

The principal and the agent

The principal delegates production to an agent, giving the agent a budget Bt in period t (t = 1, 2).
The agent spends some of that budget on investment, Kt , and can spend some of that budget on
himself, engaging in corrupt stealing.
Investment in each period is a factor of production, generating output in period 2, which the
2

∂F
∂ F
principal values, according to the technology Q = F (K1 , K2 ), with ∂K> 0, ∂K
2 ≤ 0, t = 1, 2, andtt∂2F∂K1 ∂K2≥ 0, meaning that investment in period 1 can increase the productivity of investment inperiod 2, and hence, aﬀect the principal’s action in this period.
The agent’s choice of stealing is binary. He can steal nothing, or he can steal a fraction S(0 < S < 1) of the budget in any period. The agent’s action is observable and veriﬁable. Stealing
costs the agent CS > 0; the agent’s beneﬁt from stealing is UA (SBt ), with limSBt →0 UA (SBt ) = 0,
UA′ > 0, and UA′′ < 0. The values of S and CS are exogenously ﬁxed. The agent gets no utility from6

Our summary of Brennan and Buchanan (1980), Edwards and Keen (1996), Arikan (2004), and Menes (1999,

2003) relies on Mookherjee (2015).

6

the output. In summary the agent’s utility in period t is
 UA (SBt ) − CS , if the agent steals in period t; 0,otherwise.
The principal’s utility is
UP (Q) − B1 − B2 ,(1)

where UP′ > 0 and UP′′ < 0. The agent’s beneﬁt does not matter to the principal, but the resourcestolen by the agent, not spent on production, is a loss for him.
Note that K1 can be interpreted as investment in capital, and K2 as spending on operating
costs, say labor. All we need is that the same agent gets the budgets in the two periods. If theagent responsible for spending in period 2 diﬀers from the agent responsible for spending in period
1, then the agent in period 1 has no incentive to limit theft in that period. So the principal may
prefer to commit to having the agent responsible for spending in both periods.

3.2

Timing

The timing of the game is summarized as follows. In period 1:
1. The principal gives the agent a budget B1 .
2. The agent steals or not from B1 , spending the resources left on investment. The agent obtains
a beneﬁt UA (SB1 ) from his theft.
3. The principal observes the agent’s action, and the agent incurs a cost CS if he stole.
In period 2:
1. The principal gives the agent a budget B2 .
2. The agent steals or not from B2 , spending the resources left on investment. Production iscarried out. The agent obtains a beneﬁt UA (SB2 ) from his theft.
73. The principal observes the agent’s action, and the agent incurs a cost CS if he stole. The
principal’s utility is determined.
To determine the behavior of the principal and the agent, we work backwards to solve for thesubgame perfect equilibrium, ﬁrst looking at the actions of the principal and the agent in period 2
for a given investment in period 1. We then examine the behavior of the principal and the agent
in period 1, each anticipating behavior in period 2.
First, as a benchmark, we derive the budgets and investments in each period, ((B1∗ , B2∗ ), (K1∗ , K2∗ ))that maximize the principal’s utility. We call this combination of the budgets and the investments
the ﬁrst-best solution for the principal. Let this solution be internal. Then for t = 1, 2,
Kt∗ = Bt∗ ;∂UP ∂F(K ∗ , K ∗ ) = 1.
∂Q ∂Kt 1 2(2)

That is, maximizing the principal’s utility, represented by (2), requires no stealing in each period
and the equalization of the principal’s marginal beneﬁt and marginal cost of giving money to theagent.

4

Optimal budget allocation by principal given agent’s behavior

4.1

Choices in period 2

For a given budget in period 2, B2 , the agent steals in period 2 if and only if UA (SB2 ) ≥ CS . The
principal chooses B2 that maximizes his utility, given the amount the agent invested in period 1,
K1 , and anticipating whether the agent steals. Hereafter Bts denotes the budget in period t which
induces the agent to steal in period t. Then rationally expecting the agent to steal in period 2 theprincipal chooses Bts to maximize
UP (F (K1 , K2 (B2s ))) − B2s = UP (F (K1 , (1 − S)B2s )) − B2s ,8(3)subject to UA (SB2s ) ≥ CS . The solution satisﬁes the condition7∂UP ∂F(1 − S) ≤ 1.
∂Q ∂K2(4)

Relation (4) implicitly gives the principal’s best response to the agent’s action in the previous
period. For intuition, suppose for the moment that with this solution the constraint for the agent
does not bind, so that (4) holds with equality. Then an increase in K1 has two eﬀects on theprincipal’s utility, and therefore, on his choice of B2s :8
∂UP

∂2F

∂ 2 UP ∂F∂F∂B2s∂B2s ∂K2
1∂Q ∂K1 ∂K2 + ∂Q2 ∂K1 ∂K2
=
=−
(
)2 .
∂K1
∂K2 ∂K1
1 − S ∂UP ∂ 2 F∂ 2 UP
∂F
+
2
2
∂Q ∂K
∂K2
∂Q

(5)

2

2

F
First, an increase in K1 may increase the marginal product of K2 ( ∂K∂1 ∂K≥ 0 in the ﬁrst term2on the numerator of (5)). That would induce the principal to increase K2 , and hence B2s . Second,2

because output Q increases with K1 , the marginal utility of output declines ( ∂∂QU2P < 0 in the second
term on the numerator of (5)). Thus, in general, an increase in K1 can induce the principal toeither increase or reduce B2s , depending on the production function and on the utility function. If( 2)
the principal is almost risk-neutral ∂∂QU2P → 0 , then increased theft (i.e., a smaller investment)in period 1 induces the principal to reduce B2s . If the investments in the two periods are perfect( 2)
F
substitutes ∂K∂1 ∂K=
0, increased theft in period 1 induces the principal to increase the budget2
in period 2.
For illustration, see Figure 1, which displays how the agent’s budget in period 2 (B2s ) decreases
with theft in period 1. The curve at the bottom shows output Q when the agent, given B1 , stolein period 1, so that Q = F ((1 − S)B1 , (1 − S)B2s ) which is tangent to the principal’s indiﬀerent
curve UD at point D. The curve showing output Q when the agent did not steal in period 1,
Q = F (B1 , (1 − S)B2s ), is located above it and is tangent to the principal’s indiﬀerent curve UE at
7

The assumptions on UP (·) and F (·, ·) imply that the principal’s utility function is strictly concave (see thedenominator in (5)).
8∂B s

In (5) K2 = (1 − S)B2s , so that ∂K22 = 1/(1 − S).

9point E. Thus the agent gets a smaller budget when he stole in period 1 than when he did not.
The opposite outcome is illustrated in Figure 2. The point D lies to the right of point E, meaningthat the agent’s theft in period 1 has the principal increase the budget in period 2.
Example 1. Consider an extreme case, where K1 and K2 are perfect substitutes, or Q = K1 + K2 .
Let the principal desire output Q. That output is obtained if and only if total investment over thetwo periods is Q.
Because K1 and K2 are perfect substitutes, the budget the principal gives the agent in period
2 declines with the amount the agent invested in period 1. In other words, the principal’s choice ofthe budget in period 2 is a strategic substitute of the agent’s choice of investment in period 1. The
more is stolen in period 1, the larger the budget the principal must give in period 2 in response to1
it, namely B2s = Q−K
1−S , which decreases with K1 . Thus, anticipating such behavior in period 2, theagent will want to steal in period 1 and in period 2.
Example 2. At the other extreme, let Q = min(K1 , f K2 ), with f < 1. Let the marginal beneﬁtof output to the principal be greater than the worst possible marginal cost in period 2 (namely,
1/(f (1 − S))). The principal values increased output, but spending for the agent costs him. Thismeans that the smaller is K1 , the smaller is K2 ; that is, the more the agent steals in period 1, thesmaller the budget he gets in period 2.
Moreover, if f < 1, then the agent prefers to steal in period 2 than in period 1, because(1 − S)B1 = f K2 = f (1 − S)B2s < (1 − S)B2s . That is, if the agent steals in period 1 then thebudget the principal gives the agent in period 2, B2s = Bf1 , is greater than B1 .
If instead the agent does not steal in period 1, then the budget the principal gives the agent in
B1
period 2, in anticipation of the agent’s theft then, satisﬁes B1 = f (1−S)B2s , and hence, B2s = f (1−S),

which is greater than the budget the agent would be given after stealing in period 1.
In a similar manner, denote by Btn the budget in period t which induces the agent not to steal10

in that period. Then the principal maximizes
UP (F (K1 , K2 (B2n ))) − B2n = UP (F (K1 , B2n )) − B2n ,(6)subject to UA (SB2n ) ≤ CS . The solution for this problem satisﬁes∂UP ∂F≥ 1.
∂Q ∂K2(7)

Consequently, given K1 , the principal’s optimal choice of B2 is derived by comparing his indirect
utility under B2s and under B2n . Comparison of (4) and (7) indicates that without the constraint for
the agent, the budget size maximizing (6) exceeds that maximizing (3) and brings a higher utility
to the principal. However, the incentive constraints for the agent require B2n ≤ B2s , so that it is notevident which makes the principal better oﬀ.

4.2

Choices in period 1

In period 1 the agent either steals or not. Let B2 (K1 ) be the principal’s utility-maximizing budget
in period 2 given K1 , with B2 (K1 ) either B2s (K1 ) or B2n (K1 ). If the agent steals in period 1, theagent’s utility over the two periods is9
UA (SB1 ) − CS + max [UA (SB2 ((1 − S)B1 )) − CS , 0] .

(8)

If he does not steal, his utility over the two periods is
max [UA (SB2 (B1 )) − CS , 0] .

(9)Thus, the agent will not steal in period 1 if and only if his utility without theft is at least as greatas his utility with theft, which gives
UA (SB1 ) − CS + max [UA (SB2 ((1 − S)B1 )) − CS , 0]
≤ max [UA (SB2 (B1 )) − CS , 0] .
9

(10)

If UA (SB2 (K1 )) − CS > 0, then B2 (K1 ) = B2s (K1 ). If B2 (K1 ) = B2n (K1 ), then UA (SB2 (K1 )) − CS ≤ 0 bycontradiction. Even if UA (SB2s (K1 )) − CS > 0, B2 (K1 ) = B2n (K1 ) may hold; then UA (SB2 (K1 )) − CS ≤ 0.

11

When the principal expects the agent not to steal in period 1, the principal chooses B1n to
maximize
UP (F (B1n , K2 (B2 (B1n )))) − B1n − B2 (B1n ),(11)subject to (10), in which B1 is replaced by B1n . If the solution does not make the constraints bindfor the agent in period 1 and in period 2, then using the envelope theorem (so that B2 is unchanged
as B1n changes), it is implicitly given by∂UP ∂F= 1.
∂Q ∂K1(12)

The following proposition is derived immediately from (2), (7), and (12).
Proposition 1 The principal can attain the first-best outcome, by allocating the budgets (B1∗ , B2∗ ),if and only if
UA (SB2∗ ) − CS ≤ 0;
UA (SB1∗ ) − CS + max [UA (SB2 ((1 − S)B1∗ )) − CS , 0] ≤ 0.

(13)

For proof, see Appendix A.
Proposition 1 describes when the principal has his preferred outcome in equilibrium. If theinvestments are suﬃciently complementary (so that investment in one period greatly increases themarginal product of investment in the other period), as implied in (5), theft in period 1 will leadto a smaller budget in period 2, so that the conditions in Proposition 1 can apply. Contrary to
the assertion in Proposition 1, if UA (SB1∗ ) ≤ CS , but if investments in the two periods are strong
substitutes and B2 ((1 − S)B1∗ ) = B2s ((1 − S)B1∗ ) is suﬃciently greater than B2 (B1∗ ) = B2n (B1∗ ) (i.e.,
stealing in period 1 gives the agent a larger budget in period 2) to induce the agent to steal inperiod 2, the agent, given B1∗ , steals in period 1. If the principal expects the agent to steal in period
1, the principal’s utility is
UP (F ((1 − S)B1s , K2 (B2 ((1 − S)B1s )))) − B1s − B2 ((1 − S)B1s ).
12

(14)

If the constraints for the agent are not binding in each period, then using the envelope theorem
shows that the principal’s best choice of B1s satisﬁes∂UP ∂F(1 − S) = 1,
∂Q ∂K1(15)

suggesting that the principal cannot attain the ﬁrst-best outcome.
The agent is assumed to beneﬁt from corrupt stealing. Instead, we can suppose that the agent
does not beneﬁt directly from theft, but rather wants to maximize the budgets he gets, as inNiskanen’s (1971) model of the budget-maximizing bureaucracy. Then subject to slight revisionof our model, the results we derived above continue to hold: the agent will steal in period 1 if
he can thereby increase his budget in period 2. The model can be interpreted in additional ways.
The agent may not steal directly, but instead use the funding he gets for services or projects thatﬁt his preferences more than the principal’s. For example, a building may be designed to gainarchitectural awards rather than to best serve residents, or a local oﬃcial may want to hire many
local workers rather than to construct a highway in the most eﬃcient way.

5

Fiscal constraints on the principal

This section examines whether a ﬁscal constraint on the principal’s spending in either period, oron his total spending, can beneﬁt him and induce the ﬁrst-best outcome with the allocation in (2),i.e., ((B1∗ , B2∗ ), (K1∗ , K2∗ )). We suppose in this section that the principal can commit to the ﬁscal
constraint. We will discuss the time-consistency of the ﬁscal constraint later. The following Lemma
relates to Proposition 1.
Lemma 1 Suppose UA (SB1∗ ) ≤ CS and UA (SB2∗ ) ≤ CS . Let the principal face the fiscal constraint
B1 ≤ B1∗ on the budget in period 1. Then the outcome is inferior to the first-best for the principal
if
UA (SB1∗ ) − CS + max [UA (SB2 ((1 − S)B1∗ )) − CS , 0] ≥ 0.
13

(16)

The ﬁrst-best solution requires a budget in period 1 of B1∗ , as stated in Proposition 1. However, if(16) holds, the agent, given B1∗ , will then steal in period 1. From (5), when investments are strong
substitutes, and hence, B2 ((1 − S)B1∗ ) = B2s ((1 − S)B1∗ ) is suﬃciently large, then the agent may still
steal in period 1, expecting that he will be able to steal much in the future even if UA (SB1∗ ) ≤ CS .
Then B2∗ is no longer the principal’s best response. In contrast, the principal can induce the agent
not to steal in period 1 by committing to the ﬁscal constraint in period 2.
Proposition 2 Suppose UA (SB1∗ ) ≤ CS and UA (SB2∗ ) ≤ CS . Let the principal face the fiscal
constraint B2 ≤ B2∗ on the budget in period 2. Then the principal attains the first-best outcome
with the allocation ((B1∗ , B2∗ ), (K1∗ , K2∗ )), with the agent never stealing in any period.

For proof, see Appendix B.
If the principal commits to the ﬁscal constraint on the total budget which just allows him toattain the ﬁrst-best outcome, namely, B1 +B2 ≤ B1∗ +B2∗ , the principal achieves the same allocation
as with the ﬁscal constraint only on the budget in period 2: after choosing B1∗ , he is inevitably
subject to the ﬁscal constraint B2 ≤ B2∗ .
Corollary 1 Suppose UA (SB1∗ ) ≤ CS and UA (SB2∗ ) ≤ CS . Let the principal face the fiscal constraint B1 + B2 ≤ B1∗ + B2∗ . Then the principal attains the first-best outcome with the allocation((B1∗ , B2∗ ), (K1∗ , K2∗ )), with the agent not stealing in any period.
Thus, the ﬁscal cap which constrains the principal’s behavior after observing investment in the ﬁrst
period is crucial.

6

Multiple agents

We can ask how the ﬁscal constraint works with multiple agents who compete with each other forbudgets. Consider two agents. Subscript i represents agent i = 1, 2. Let the utility function and14

the production function be common among agents. The agent’s incentive is given analogously tothe deﬁnition in Section 3. The production function is
Qi = F (K1i , K2i ).
Let the principal’s utility be
UP

(
∑
i

)
Qi

−

∑
i

B1i −

(17)

∑

B2i .

(18)

i

Aggregate output is the sum of the output by each agent, and hence,∂UP∂UP∂ 2 UP∂ 2 UP=> 0,=< 0, i = 1, 2.
∂Q1∂Q2∂Q1 ∂Q2∂Q2i(19)

The ﬁrst-best outcome for the principal who faces multiple agents has the allocation ((B1∗ , B2∗ ), (K1∗ , K2∗ ))for i = 1, 2, such that for t = 1, 2,
Kt∗ = Bt∗ ;∂UP ∂F(K ∗ , K ∗ ) = 1.
∂Qi ∂Kti 1 2(20)

So far we considered the ﬁscal constraint which sets limits on the principal’s spending. The
results presented in Section 5 for a single agent also apply to any individual agent among multiple
agents, because these results are associated with the ﬁscal constraint placed on an individual budget.
Then we will examine another way to control the principal. Suppose that in period 2, given(K11 , K12 ), the principal is committed to the total budget B21 + B22 = 2B2∗ he allocates between
the two agents. Will agents then steal? The following proposition states that this ﬁscal constraint
imposed on the principal’s total expenditure in the ﬁnal period eﬀectively controls the agents’behavior in the ﬁrst period.
∂ F∗∗
Proposition 3 Let ∂K
2 < 0 for i = 1, 2. Suppose UA (SB1 ) ≤ CS and UA (SB2 ) ≤ CS for i = 1, 2.
22i

Let the principal commit to spend the total budget B21 + B22 = 2B2∗ for period 2. Then the principal
attains the first-best outcome with the allocations ((B1∗ , B2∗ ), (K1∗ , K2∗ )) for i = 1, 2, with no agent
stealing in any period.
15

For proof, see Appendix C.
The assumption with regard to the strictly decreasing marginal product of investment assuresthat the optimal budget allocation between agents in period 2 is an internal solution. Competition
among agents for budgets in the ﬁnal period reduces the budget an agent who steals gets in that
period, thereby aﬀecting agents’ incentives for stealing in the previous period, seeking to steal
more later, though K1i and K2i are strong substitutes. Thus we have a conclusion resembling theconclusion with a single agent: a ﬁscal constraint for the ﬁnal period is crucial. Moreover, bothconstraints imposed individually and totally induce equilibrium outcomes which are most preferredby the principal.

7

Time consistency of a fiscal constraint

So far we assumed that the principal can commit not to spend more than a ﬁxed amount. Is thisﬁscal device time-consistent? When the principal faces only one agent, a ﬁscal constraint in period2, B2 ≤ B2∗ , would not be time-consistent if given B1∗ , the agent would steal in period 1 without
it. Because then, without the ﬁscal constraint of B2 ≤ B2∗ , (16) in Lemma 1 holds. Keeping theassumption that UA (SB2∗ ) ≤ CS in Lemma 1, if UA (SB1∗ ) < CS and the beneﬁt of stealing from
B1∗ is strictly lower than its cost, (16) means that
UA (SB2 ((1 − S)B1∗ )) − CS > 0 ≥ UA (SB2∗ ) − CS .

(21)

Hence, B2 ((1 − S)B1∗ ) = B2s ((1 − S)B1∗ ) > B2∗ with UA′ > 0. Thus the principal’s best choice inperiod 2, after observing the agent stealing in period 1, and expecting the agent to steal in period
2, is greater than B2∗ . Therefore the principal’s commitment to B2 ≤ B2∗ is not time-consistent;
he may violate this constraint after observing investment in period 1. The agent, who steals in
the current period, anticipating that the principal will violate the ﬁscal constraint in a following
period, may make the ﬁscal constraint moot. Therefore, when investments are strong substitutes,

16

an additional device for enforcement, which makes the ﬁscal constraint binding, is necessary.10
This conclusion on time inconsistency of the ﬁscal constraint on an individual budget holds for
multiple agents. If, however, the principal is constrained to allocate a ﬁxed amount among agentsin the ﬁnal period, agents’ outputs are substitutes, so that the principal can give a larger budget tothe agent who spent more on investment, while reducing the budget to an agent who stole. Thus,
the ﬁscal constraint on the aggregate budget for period 2 is time-consistent. Having multiple agents
beneﬁts the principal. It makes the ﬁscal constraint not only eﬃcient but also credible. A separateﬁscal cap imposed on spending by each agent may appear rigid, but will not credibly discipline anagent who steals in period 1 and anticipates that the principal would beneﬁt from giving him alarge budget in period 2. In contrast, a ﬁscal cap on aggregate spending in period 2 alone, though
it may appear loose, credibly controls agents, .

8

When will corruption be prevalent

Our analysis suggests that it matters whether the same agent will continue in the following period;a principal’s ability to switch agents will aﬀect an agent’s incentives to steal in period 1. If increased
K1 increases K2 , then an agent who can serve only one term has more incentive to steal than anagent in his ﬁrst term who can increase his budget in the second term by not stealing in the ﬁrst
term. If increased K1 reduces K2 that the same agent would receive, then the opposite holds. So it is
not clear whether corruption will increase with an agent’s tenure. But the analysis does suggest that
corruption will vary, in some direction, with tenure. The empirical evidence is consistent with thisview. Ferraz and Finan (2011), in a study of Brazilian mayors, ﬁnd signiﬁcantly less corruption inmunicipalities where mayors can get reelected: in municipalities where mayors are in their ﬁrst term,
the share of stolen resources is, on average, 27 percent lower than in municipalities with second-term
10

If the agent would not steal in period 1 even with no ﬁscal constraint, the ﬁscal constraint B2 ≤ B2∗ would betime-consistent, because without this ﬁscal constraint B2 (B1∗ ) = B2n (B1∗ ) = B2∗ , meaning that the principal’s best
response after observing the agent not stealing in period 1 does not exceed B2∗ .

17

mayors (who cannot run for re-election). Similarly, in a study of Italian municipalities, Coviello andGagliarducci (2010) ﬁnd that an increase in tenure is associated with worse procurement outcomes.
Some governments have therefore tried to limit corruption by limiting the length of time anoﬃcial stays in oﬃce. For example,
The Malaysian government has enforced that it will rotate its civil servants every three
years, in an attempt to tackle corruption within ministries. Once oﬃcers hit a three year
mark, they will be evaluated, and transferred to another ministry, a spokesperson fromthe Prime Minister’s Oﬃce told GovInsider. “This is certainly not a one-oﬀ aﬀair but
will be done continuously and will also involve oﬃcers managing grants, funds, permits,
licences and law enforcement,” said Dr Ali Hamsa, Chief Secretary to the Government.
“For the ﬁrst phase, 80 oﬃcers holding sensitive posts in ﬁnance, development andprocurement divisions were transferred eﬀective April 18,” he added. The regulation
to rotate oﬃcers has always been in place, but it was enforced after a ﬁnance oﬃcer
allegedly embezzled some US $24 million (RM100 million) from the Youth and Sports
Ministry fund over a period of six years, The Star Online reported.11
Our analysis shows, however, that rotation of agents can, under some circumstances, increase
corruption: an agent who serves only in period 1 does not care if his theft reduces the budget
allocated in future periods.
We would expect corruption to be greatest for projects which must be completed, almost regardless of cost. A good example is construction for the Olympics games—host governments face aﬁxed deadline, they had publicly committed to building stadiums and sports facilities, and failure
leads to widespread negative publicity. Corruption in such construction is notorious. For example,
The Guardian reported that...Rio has not been able to avoid the other pathologies of stadium and infrastructure
construction: large scale corruption and forced removals. Again, historical comparisons11

https://govinsider.asia/inclusive-gov/malaysia-rotates-civil-servants-to-tackle-corruption/18

are kind. Sochi was bedevilled by allegations of corruption...when it comes to using
the Olympics as a cover for entirely unrelated but fabulously proﬁtable real estatedevelopment Rio is a contender. Considered in all promotional literature to be a central
Olympic project, the Porto Marvilha redevelopment of the city’s historic dock district isonly home to the media village and a small technical-operations centre. Not much, but
enough for the programme to acquire the urgency of Olympic projects and a gigantic
public-private partnership, in which the city government handed over the planningand governance of the city’s largest ever development to a consortium of three private
construction companies.12
Large-scale corruption also appeared in the Sochi Winter Olympics:
Whatever happens on the ice and snow of Sochi in the next couple of weeks, one thingis certain: this Winter Olympics is the greatest ﬁnancial boondoggle in the history of
the Games. Back in 2007, Vladimir Putin said that Russia would spend twelve billion
dollars on the Games. The actual amount is more than ﬁfty billion. (By comparison,
Vancouver’s Games, in 2010, cost seven billion dollars.) Exhaustive investigations by
the opposition ﬁgures Boris Nemtsov, Leonid Martynyuk, and Alexei Navalny reveal
dubious cost overruns and outright embezzlement.13
The literature review above mentioned corruption in road construction. Our analysis would
suggest high corruption in that activity, because it is characterized by a high marginal product ofspending if too little was invested earlier—completing a road which has a missing midsection canbe highly attractive. That is, the marginal beneﬁt of completing the road is very high, and so
the principal will fund construction in period 2 even if corruption was rampant in period 1. That
generates an incentive for contractors or agents to steal in period 1. So, not surprisingly, “the link
12David Goldblatt, “Rio 2016 buildup part of the chaotic and corrupt tradition of Olympic hosts.” The Guardian,

July 26, 2016.
13
James Surowiecki, “The Sochi eﬀect.” New Yorker, February 10, 2014.

19

between corruption and construction is a problem across the globe. Transparency International
has long cited the construction industry as the world’s most corrupt, pointing to the prevalence ofbribery, bid rigging, and bill padding.”14
In contrast, maintenance, unlike construction, can often be postponed, or not completed, or done
piece meal—repair only a section of the road. We would expect less corruption in that activity.

9

Conclusion

This paper extends analyses of corruption by considering how both a principal and a dishonest
agent behave when each realizes that actions taken in one period can aﬀect the opportunities forcorruption in a later period. Some of the interesting eﬀects appear when an agent who steals inperiod 1 thereby increases his opportunities for stealing in period 2. That can make corruption
self-perpetuating: much corruption in period 1 allows even greater corruption in the next period.
But it can also mean that corruption in period 1 will be small if corruption in period 1 reduces, in atime-consistent way, the budget in period 2. The eﬀect can be ameliorated if the principal commits
to giving the agent a small budget in period 2, thereby oﬀering one explanation for the eﬃciency
of ﬁscal caps. Our analysis also shows that competition among multiple agents makes commitment
binding, thereby reducing corruption.
Much work on corruption examines how culture, political institutions, education, incomes, andso on aﬀect corruption. But surprisingly little work examines, as we do, the dynamics of corruption,
how theft in one period aﬀects theft in future periods. And little work has examined how corruption
will vary with the type of activity, say why corruption is especially prevalent in construction. Our
analysis oﬀers a start.

14

James Surowiecki, “The Sochi eﬀect.” New Yorker, February 10, 2014.

20

Appendix A: Proof of Proposition 1
If UA (SB2∗ ) − CS ≤ 0, given K1 = B1∗ , the principal’s optimal choice in period 2 is B2 (B1∗ ) =B2n (B1∗ ) = B2∗ . Therefore,max[UA (SB2 (B1∗ )) − CS , 0] = max[UA (SB2∗ ) − CS , 0] = 0.

(A.1)

If UA (SB1∗ )−CS +max[UA (SB2 ((1−S)B1∗ ))−CS , 0] ≤ 0 = max[UA (SB2 (B1∗ ))−CS , 0], the principal,
anticipating that the agent does not steal in period 1, can optimally set B1 = B1n = B1∗ . Thus
there exists an equilibrium in which the principal allocates (B1∗ , B2∗ ) and the agent never steals.
This equilibrium is unique because the principal’s utility is at the maximum. Thus Proposition 1
is proven.

Appendix B: Proof of Proposition 2
The ﬁrst-best solution for the principal requires him to set (B1∗ , B2∗ ), and to induce the agent tospend all the budget on investment.
In period 2, given B2 , the agent steals if and only if UA (SB2 ) ≥ CS . Then given any K1 ,under the ﬁscal constraint B2 ≤ B2∗ , and under the assumption that UA (SB2∗ ) ≤ CS , the principal’s
optimal choice of the budget for period 2 induces the agent not to steal in that period, because
the principal’s utility-maximizing choice of the budget in period 2, B2 (K1 ), is subject to the ﬁscal
constraint, and therefore, the following should hold:
UA (SB2 (K1 )) − CS ≤ UA (SB2∗ ) − CS ≤ 0.

(B.1)

Therefore, given K1 , the principal’s best choice of the budget in period 2, without theft by theagent in that period, is B2 (K1 ) = min[B2n (K1 ), B2∗ ].
In period 1, the principal chooses an internal solution B1n = B1∗ , because given that UA (SB1∗ ) ≤CS , and noting that UA (SB2 ((1 − S)B1∗ )) − CS = UA (S min[B2n ((1 − S)B1∗ ), B2∗ ]) − CS ≤ 0, theagent, given B1∗ , does not steal in period 1. Then B2 (B1∗ ) = min[B2n (B1∗ ), B2∗ ] = B2∗ . Thus, there
21

exists a unique equilibrium in which the principal sets the budgets (B1∗ , B2∗ ), inducing the agent
not to steal in each period. Thus Proposition 2 holds.

Appendix C: Proof of Proposition 3
We will show that under the ﬁscal constraint B21 + B22 = 2B2∗ , there exists an equilibrium in which
the principal gives each agent (B1∗ , B2∗ ) and the agent spends all the budget on investment.
In period 2, given B2i , agent i (i = 1, 2) does not steal if and only if UA (SB2i ) ≤ CS .
Anticipating the agent’s reaction, given K1i and K1j (j ̸= i, j = 1, 2), the principal allocatesthe budget in period 2 between the two agents, to maximize
UP (F (K1i , K2i (B2i )) + F (K1j , K2j (B2j ))),

(C.1)

B2i + B2j = 2B2∗ .

(C.2)

subject to

The necessary condition for the principal’s optimal allocation is∂UP ∂F∂UP ∂F(1 − Si ) =(1 − Sj ),∂Qi ∂K2i∂Qj ∂K2j(C.3)

where Si = S when the principal expects agent i to steal (then (K2i (B2i ) = (1 − S)B2i ); Si = 0
when he is expected not to steal (then (K2i (B2i ) = B2i ). In a similar manner Sj is deﬁned. The
values of Si and Sj have to be consistent with the agents’ behavior in period 2. This equation
indicates that the marginal products are equalized between agents.
For the moment suppose that Si can take any value within the interval [0, 1). Then
∂B2i
∂B2i ∂K2i=∂Si∂K2i ∂Si1= −1 − Si=[(1 − Si )

∂F
1
∂K2i
(1 − Si )2 ∂ 2 F2
∂K2i

∂ 2 UP
∂Q2i

(

∂F
∂K2i

)2

P ∂F
− ∂U
∂Qi ∂K2i
]
2

P ∂ F
+ ∂U
∂Qi ∂K 2

2i

< 0,

2

∂ UP
∂F ∂F
− (1 − Sj ) ∂Q
i ∂Qj ∂K2i ∂K2j

(C.4)

22

where we used (19) and∂F∂F(1 − Si ) =(1 − Sj ),
∂K2i
∂K2j

(C.5)

which is also derived from (19) and (C.3). We can interpret this result as showing that ﬁxing agent
j’s behavior, the budget the principal wants to give agent i when the agent is expected to steal as , is smaller than the budget hefraction S of the budget in period 2 (Si = S), which we call B̃2in.
prefers to give the agent i when the agent is expected to steal nothing (Si = 0), which we call B̃2i

In period 1, given B1 , agent i can choose whether to steal or not. From (C.3) agent i calculates∂B2i∂B2i ∂K2i=∂K1i∂K2i ∂K1i[ 2]∂ UP ∂F ∂F∂UP∂ 2 UP
∂2F
∂F ∂F
(1
−
S
)
+
i
∂Qi ∂K1i ∂K2i − (1 − Sj ) ∂Qi ∂Qj ∂K1i ∂K2j
1
∂Q2i ∂K1i ∂K2i
[
]
= −
(
)2
1 − Si∂ 2 UP∂ 2 UP∂UP ∂ 2 F∂F
∂F ∂F
(1 − Si ) ∂Q2 ∂K2i + ∂Qi ∂K 2 − (1 − Sj ) ∂Q
i ∂Qj ∂K2i ∂K2j
i

2i

∂2F

= −

1 ∂K1i ∂K2i
≥ 0.
1 − Si ∂ 2 F2

(C.6)

∂K2i

Thus, when agent i steals in period 1, he anticipates that the principal may reduce his budget inperiod 2, because the marginal product of investment in period 2 is aﬀected by investment in period1.
In period 1, the principal wants to give each agent B1∗ , because under the assumption that
UA (SB1∗ ) ≤ CS , given B1∗ , agent i does not steal in period 1:
UA (SB1∗ ) − CS + max [UA (SB2i ((1 − S)B1∗ , K1j )) − CS , 0]
≤ max [UA (SB2i (B1∗ , K1j )) − CS , 0] ,(C.7)

where we use
max [UA (SB2i (B1∗ , K1j )) − CS , 0] ≥ max [UA (SB2i ((1 − S)B1∗ , K1j )) − CS , 0] ,(C.8)

because from (C.4) and (C.6):
n (B ∗ , K )) − C > U (S B̃ s (B ∗ , K )) − C , the principal’s expectation that(i) If 0 ≥ UA (S B̃2i
1j
1j
S
A
S
1
1
2i

23

n (B ∗ , K )) − C ≥ U (S B̃ n ((1 −Si = 0 is consistent with agent i’s actual behavior. Then UA (S B̃2i
1j
S
A
1
2i
s ((1 − S)B ∗ , K )) − C , so that agent i would not steal after stealingS)B1∗ , K1j )) − CS > UA (S B̃2i
1j
S
1

in period 1. Thus (C.8) holds.
n (B ∗ , K )) − C > U (S B̃ s (B ∗ , K )) − C ≥ 0, the principal’s expectation that(ii) If UA (S B̃2i
1j
1j
S
A
S
1
1
2i
n ((1 −
Si = S is consistent with agent i’s actual behavior. Then whether B2i ((1 − S)B1∗ , K1j ) = B̃2is ((1 − S)B ∗ , K ), (C.8) holds.
S)B1∗ , K1j ) or B2i ((1 − S)B1∗ , K1j ) = B̃2i
1j
1Then in period 2, the principal gives each agent the optimal budget B̃2n (B1∗ , B1∗ ) = B2∗ underthe ﬁscal constraint B21 + B22 = 2B2∗ , expecting no agent to steal. Indeed, UA (SB2∗ ) ≤ CS byassumption, so that this expectation is consistent with the agents’ behavior. Thus, there exists a
unique equilibrium in which the principal can set the budgets (B1∗ , B2∗ ) for agents 1 and 2, inducing
the agents not to steal in each period. Thus Proposition 3 holds.

24

Notation
Bt Budget principal allocates in period t
Bt∗ Budget principal allocates in period t in ﬁrst-best solution for principal
Btn Budget principal allocates in period t when he anticipates agent will not steal in that period
Bts Budget principal allocates in period t when he anticipates agent will steal in that period
CS Cost to agent of stealing
F (K1 , K2 ) Production function
Kt Investment in period t
Kt∗ Investment in period t in ﬁrst-best solution for principal
Q Output
S Fraction of budget that can be stolen
UA Utility of agent
UP Utility of principal

25

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28

Q

UE

F (B1 , (1 − S)B2s )UDE
F ((1 − S)B1 , (1 − S)B2s )

D

B2s

0

Figure 1: Theft in period 1 reduces the budget in period 2

29

Q

UE

F (B1 , (1 − S)B2s )UDE
F ((1 − S)B1 , (1 − S)B2s )

D

B2s

0

Figure 2: Theft in period 1 increases the budget in period 230