Bribery, Extortion, and Citizen Complaints∗

-Preliminary, please do not circulate-

Charles Angelucci

Columbia Business School

ca2630@columbia.edu

Antonio Russo

ETH Zurich and CESIfo

russo@kof.ethz.ch

April 7, 2015

April 7, 2015

Abstract

This paper investigates the issue of petty corruption in public administration and

proposes a simple mechanism to help deter it. We consider a situation whereby private

citizens have to comply with some regulation upon undertaking a socially risky activity.

Public o�cials are charged with verifying compliance and have full discretion: they may

take bribes from non compliant citizens, or extort money from compliant ones. If the

government only observes reports of noncompliance, it is forced to provide low powered

incentives to o�cials, which results in bribery in equilibrium. We show that by allowing

citizens to complain when sanctioned�and by rewarding those who do�the government

is able to deter both forms of corruption, even if the truthfulness of complaints cannot be

veri�ed. We then consider bureaucracy intermediaries, who often assist citizens in dealing

with, and eventually bribing, o�cials. We show that low powered incentives to o�cials

are a key reason why intermediaries are so pervasive. Hence, the social desirability of

exploiting entrepreneur complaints is even stronger when intermediaries are involved in

corruption.

JEL Classi�cation: H11, H83, O17, D82

Keywords: corruption, extortion, bribery, complaints, bureaucracy intermediaries

∗We thank Yossi Spiegel for useful comments. Opinions and errors are ours.

1 Introduction

Corruption is a bane to public administration in many countries, especially in the developing

world (Olken and Pande (2012), Svensson (2005)). One of its worst consequences is arguably

that it dampens the e�ectiveness of rules and regulations designed to protect society from risks

and hazards. Take for instance environmental rules. Firms are commonly required to abide

by rules meant to protect the environment, but compliance is sometimes di�cult to achieve

without active enforcement by public o�cials. When o�cials are opportunistic, incentives to

comply with regulations are distorted, and harm may occur as a consequence.

We consider a situation whereby entrepreneurs must obtain permits before undertaking a

valuable but socially risky activity. Public o�cials are in charge of verifying whether rules

have been respected, and have full discretion as to grant or deny permits. Respecting the

regulation is costly to entrepreneurs. Moreover, public o�cials may engage in two types of

corrupt behavior: they may take bribes from non-compliant entrepreneurs (in exchange for

granting the permit), or extort money from compliant entrepreneurs (by threatening to deny

the permit). While bribery bene�ts both the bribe-taker and the bribe-giver, extortion only

hurts those who are forced to pay. Our objective is to investigate the properties o�cials'

compensation schemes should possess when these two types of corrupt behavior are at play.

Previous literature (see below) has shown that there is a tension that arises when trying to

deter both bribery and extortion. In fact, when o�cials have full discretion over the decision

to be made, the tension may have so much bite that a welfare-maximizing government may

deliberately choose to tolerate bribery so as to deter extortion (Hindriks et al. (1999), Khalil

et al. (2010)).

We propose a simple mechanism to help ease this tension: increasing the o�cials'

accountability by allowing for and exploiting complaints by entrepreneurs. This mechanism

is in the spirit of recent whistleblowing programs around the world; for instance Ghana's

Whistleblower Act, Pakistan's Punjab Citizen Feedback Model1, and �I paid a bribe� websites

introduced in Kenya, India and Buthan. In contrast to traditional appeals courts�which

are often expensive, ine�cient and also prone to corruption�these mechanisms are easily

accessible to citizens. A natural concern that arises is whether individuals will use these

schemes in a way that accurately describes o�cials' behavior. This concern is even more

salient when rewards are promised to incentivize reporting o�cial misconduct. We incorporate

this dimension in our model and show that complaints can be useful even when the validity

1For a description of this system, see The Economist (September 24, 2009)

2

of claims cannot be veri�ed. In particular, we show that introducing a reporting mechanism

allows the government to deter both extortion and bribery, thereby raising the e�ectiveness

of regulation.

We model a continuum of agents (e.g., entrepreneurs), di�ering in the private cost of

complying with some regulation. Noncompliance produces some harm on third parties, but is

not directly observable. O�cials observe a signal correlated with the agent's noncompliance

and decide whether to report it to the government. Information is fully manipulable in the

sense that the o�cial can report noncompliance regardless of the signal's realization. O�cials

and agents can hiddenly engage in side transfers. In this environment, tackling both bribery

and extortion using monetary incentives alone is di�cult. To deter bribery, the o�cial must

be rewarded for uncovering (and reporting) noncompliance. However, this makes it harder

to deter extortion since the threat of a negative assessment becomes more credible, thereby

leaving the agent at the o�cal's mercy. Our model applies to several examples of petty

corruption in public administration. In many countries, especially in the developing world,

bribes are routinely paid to o�cials charged with, e.g., enforcing tra�c law, issuing business

permits or driving licenses, collecting taxes and enforcing tari�s at customs. In these examples,

the o�cial's primary task is to verify compliance with regulation designed, in principle, to align

private incentives with social welfare. Corruption greatly undermines this purpose. 2

We show that a simple mechanism in which the government communicates with the agent

allows to deter extortion without making deterrence of bribery suboptimal. In this mechanism,

the agent is asked to consent or dissent with the o�cial's report of noncompliance (e.g. �le a

complaint or not), and the o�cial receives a reward only if noncompliance is reported and the

agent assents. The agent receives a reward from the government for disagreeing (the reward is

small but higher than the cost of �ling a complaint). Interestingly, the mechanism we propose

rests on agent and o�cial playing cooperatively in equilibrium, despite information being

2Let us make a couple of concrete examples. Trucking �rms are generally required to respect ceilings on truckweight, which raise shipping costs. Violating ceileings produces social harm because overweight trucks stronglyincrease the wear and tear of roads, as well as the risk of accidents. Governments therefore set up weighingstations along the main commercial routes, requiring, in case of noncompliance, unloading of excessive cargo.However, o�cials manning these stations are often corruptible, making enforcement problematic. Moreover,corruption increases the cost of using roads for compliant �rms, distorting production decisions and tradepatterns (see, e.g., Barron and Olken (2009) for the case of Indonesia and Foltz and Bromley (2014) forWest Africa). A second example is shipping of goods through ports. Export duties, an important sourceof government revenue, are to be paid proportionally to the quantity and type of goods shipped. Customso�cials are charged with inspecting cargo, to ensure actual quantities match declared ones. The fact that theyoften engage in corruption is well-documented (Sequeira and Djankov (2013) present evidence from ports inSouthern Africa). Corruption not only hinders the government's ability to collect revenue, but also raises thecost of shipping goods for �rms.

3

reported truthfully. If they do not, the agent systematically complains when noncompliance is

reported (even if the report is truthful), so the o�cial loses any incentive in making such

report. This neutralizes the threat of extortion/framing, but agents found in breach of

regulation are always rewarded for unjustifed complaints. Moreover, bribery is still a pro�table

option. However, if the government promises the o�cial a large enough reward, the latter

has an incentive to reach a cooperative agreement with the agent, �convincing� him not to

complain when in breach of regulation. To do that, the o�cial compensates the agent for the

foregone bene�t of disagreeing and pockets the di�erence. Rewarding the o�cial for reporting

noncompliance (conditionally on the agent agreeing) therefore avoids bribery without opening

the door to extortion.

This mechanism can be implemented in practice without the o�cial having to make any

payment to the individual. It is for instance common that individuals applying for a permit

must pay an application fee, directly pocketed by the administration in charge of issuing the

permit. The government may allow o�cials to grant a small reduction in the fee whenever

individuals who were denied a permit renounce the opportunity to later complain.

We propose several extensions of the baseline model, showing that our results are robust

to several generalizations of the basic setup. The most important extension studies the role

of bureaucracy intermediaries, who may assist the entrepreneurs in bureaucratic procedures.

Such intermediaries are ubiquitous in reality, particularly in developing countries.3 Yet, few

formal models exist that study their role. Intermediaries provide several services, which,

many contend, are not always socially desirable. On the one hand, intermediaries reduce

the transaction cost of dealing with the bureaucracy. For example, they possess a superior

technology for handling paperwork and, by serving several applicants at the same time, can

exploit economies of scale and scope. However, intermediaries can also facilitate corruption:

by developing stable relationships with o�cials they guarantee a preferential treatment to

their customers, thereby weakening regulatory controls. We focus on two questions. First,

why is the involvement of intermediaries so pervasive (especially in developing countries)?

Our model suggests that this is a by-product of low powered incentives provided to o�cials,

which are, in turn, an optimal response to the o�cials' lack of accountability. We also

show that intermediaries unambiguosly reduce the quantity of entrepreneurs that complies

with regulation. Second, can exploiting entrepreneur complaints help the government make

intermediaries less pervasive? We show that the government can implement an incentive

3For example, Bertrand et al. (2007) document their role in the context of driving licenses in India. Usingintermediaries, they argue, strongly reduces the incentives to learn how to drive for applicants. See Frederiksson(2014) for a comprehensive account of the role of intermediaries in many developing countries.

4

scheme such that o�cials do not rely on intermediaries and, as a result, incentives to

enforce regulation are strenghtened. Therefore, if properly exploited, communication with

entrpreneurs reduces intermediaries' ability to facilitate corruption and, under reasonable

conditions, enhances social welfare.

Related Literature. There is a vast literature dealing with the issue of corruption in public

adminisitrations, an endemic problem in developing countries (Aidt [2003, 2009], Banerjee et

al. [2012], Olken and Pande (2012)). In particular, much attention has been devoted to the

design of incentives for public o�cials in environments where the latter have large discretionary

power and little accountability (for instance because of a weak judicial system).4 It is well-

recognized that a tension exists between providing o�cials with incentives to enforce rules and

preventing extortion (or framing) of agents (Mookherjee 1997, Hindriks et al. (1999), Polinsky

and Shavell (2000)). A recurrent �nding is that extortion is more socially harmful than bribery.

The intuition is that extortion primarily hurts those who respect the rules and has therefore the

most detrimental impact on incentives to comply. The logical consequence is that bribery is

a necessary evil, providing justi�cation for o�ering low-powered incentive schemes to o�cials.

Arguably, though, this �nding rests on some arbitrary restrictions on the set of tools at the

government's disposal. In particular, it is obtained assuming the government cannot make

use of information reported by individuals who are subject to o�cial scrutiny.5 However, the

examples mentioned above show that, albeit nonveri�able, this information may be available

at a low cost. Our paper departs from previous literature by allowing the government to

rely on the agent's nonveri�able report on the o�cial's behavior. Dufwenberg and Spagnolo

[2014] have looked at the interaction between a civil servant in charge of issuing licenses and

a citizen, examining the well-known proposal by Basu (2011) to "legalize bribe giving". They

show that it is optimal to grant amnesty to the citizen reporting the illegal transaction. Their

main focus is nevertheless on "harassment bribes", which individuals pay to obtain services

they are (by assumption) legally entitled to. They therefore ignore the interaction between

incentives to enforce rules and the threat of harassment by o�cials.6

4This has been studied in several settings, such as law-enforcement (Polinsky and Shavell [2001], Mishraand Mookherjee [2013]) and tax collection (Marjit and Mukherjee (1996), Mookherjee [1997], Hindriks, et al[1999]).

5The only protection against framing (if any) for individuals is a costly appeals process. Nonetheless, incases of petty corruption (especially in developing countries), going to court is hardly a viable option forvictims of extortion (Court et al. (2003)). Mishra and Mookherjee (2013) propose a solution to the problemwhich involves optimizing rewards and �nes for both agents and o�cials.

6See Olken (2007) and Bjorkman and Svensson (2009) for some empirical evidence on grass-roots monitoringof o�cials. Atsu Amegashie (2013) studies consumer complaints as a remedy to corruption. His focus is on

5

Extortion is also a prominent issue in the literature on collusion within organizations.

When the supervisor's information is hard, Kessler [2000] has shown that both bribery and

extortion are costless to deter. Also in an envrionment of hard information, Vafai [2012] shows

that it is costly but optimal to deter both forms of corruption when supervisors credibly commit

to execute their threats. In an environment of (almost) soft information, Khalil et al [2010]

show (i) that extortion is much more detrimental than bribery, and (ii) that preventing both

forms of corruption is so costly that it may be optimal to tolerate bribery (but not extortion).7

This follows a line of reasoning �rst proposed by Tirole [1992]. He argues that collusion-proof

organizations may be suboptimal in presence of "non-separablities" between constraints that

have to be satis�ed in order to avoid di�erent types of misreporting. In Khalil et al [2010],

as in our setting, such non separability stems from the fact that incentives to prevent bribery

make framing a credible threat. As we show, communication with the agent is key in resolving

this tension.

Still within the literature on collusion in organizations, communicating with the agent has

been shown to be useful in deterring collusion. Celik [2009] �nds that supervision is useful

only if the principal maintains the communication channel with the agent open, as it allows

the former to manipulate the latter's outside option when bargaining with the supervisor.

His result hinges on information asymmetries between the two collusive parties and is not

related to extortion. Felli and Hortala-Vallve [2014] explore, in a di�erent setup than ours,

how whistle-blowing can be used to deter bribery and extortion (or blackmail, as they refer

to it). In their model, the principal also relies on communication with the agent to �ght

blackmail. However, the threat of blackmail is relevant only assuming that the supervisor

learns the agent's type during side-contracting and that collusive agreements can be reneged.

Furthermore, blackmail (and collusion) can be costlessly prevented by the principal, as no side

contracting takes place in equilibrium if the optimal contract is implemented. By contrast,

in our model, while bribery and extortion do not take place in equilibrium, they impose a

cost on the government. Moreover, the mechanism we propose relies on side contracting in

equilibrium, though cooperation among supervisor and agent is bene�cial. More generally,

our paper is also related to a vast literature that investigates the impact of whistleblowing

on antitrust and corporate crime (see Miceli, Near, and Dworkin [2008], Spagnolo [2008] and

the e�ectiveness of complaints in presence of negligent supervisors.7Assuming both manipulating information and making side-transfers are costly, Yun [2012] shows that it

may be optimal to tolerate bribery, extortion and framing. Angelucci and Russo [2012] show that extortioncan be prevented by letting supervisor and agent reach side agreements before the latter has chosen the levelof e�ort. In a three-tier hierarchy model with an adverse selection problem, Scott [2014] �nds conditions underwhich the principal may let either or both extortion and bribery occur in equilibrium.

6

Gambetta and Reuter [1995] for surveys).8

Finally, our paper relates to the growing literature on bureaucracy intermediaries. Bertrand

et al. (2007) empirically document the role of intermediaries in obtaining driving licenses in

Delhi. Drugov et al. (2014) examine how intermediaries a�ect the moral costs of corruption.

From a theoretical standpoint, Hasker and Okten (2008), Bose and Gangopadhyay (2009) and,

more recently, Frederiksson (2014) study bureaucracy intermediaries. Although a common

�nding is that intermediaries increase the ine�ciencies generated by corruption, their focus is

on di�erent issues than that considered in the present paper.

The rest of the paper is organized as follows. Section 2 presents the model. Section 3

solves the game �rst allowing supervisor and agent to side-contract only once the latter has

chosen his action, and then introducing the possibility of side contracting also before that.

It ends by deriving implications for the delegation of payroll authority to the supervisor and

for the optimal organization of internal audits. Section 4 presents the extensions. Section 5

concludes.

8See for instance Søreide [2008], Heyes and Kapur [2009], and Beim, et al [2014] for recent contributions.

7

2 The Setup

Consider a welfare-maximizing government and a continuum of entrepreneur/o�cial pairs of

mass one. All players are risk neutral. Entrepreneurs wish to engage in a productive activity

that generates private bene�t G, assumed constant across entrepreneurs. The activity is

socially risky in that it may lead to some harm H being inposed onto third-parties (e.g. cause

injury or pollute the environment), and the government wants to regulate it.

An entrepreneur can either comply with regulation designed to prevent damage (A = C),

or not (A = N). We assume there is no private cost of engaging in the activity without

compliance. Entrepreneurs are heterogeneous in their cost of complying with the regulation.

There is an individual-speci�c compliance cost ψ distributed across entrepreneurs according to

an atomless cumulative distribution function F (·), with support [0, ψ(, where ψ <∞. If the

activity is carried out without compliance (and without being sanctioned by the authorities)

harm H is produced on third parties.9 We suppose that G ≤ ψ < H. It is socially optimal

for entrepreneurs to comply with safety regulations, but not necessarily privately optimal.10

We assume A is observable only to the entrepreneur. In order to enforce regulation,

the government employs o�cials with the task of uncovering noncompliance and administer

sanctions if necessary. If the entrepreneur did not comply with regulation, the o�cial observes

a (perfectly informative) signal of noncompliance σ = n with probability ρ. With probability

1 − ρ, the o�cial observes no such evidence, i.e. σ = c. If the entrepreneur complied with

regulation, the o�cial never �nds evidence to the contrary, i.e. σ = c with probability one. The

parameter ρ is common knowledge and exogenous.11 There is a mass of unit size of identical

o�cials. We assume that, conditionally on undertaking the activity, an entrepreneur always

interacts with an o�cial and the two are paired randomly. Note that, even if entrepreneurs

could choose which o�cial to deal with, since the latter are all identical entrepreneurs would

be indi�erent as to whom to choose in equilibrium.

9We however suppose that the government is unable to detect who is responsible. For example, it is notalways possible to establish who is responsible for polluting a river when many �rms exploit it. Tra�c accidentsmay be caused by unsafe driving but it may be di�cult to establish the drivers' responsibility, especially whenmany drive violating rules. An alternative assumption, yielding similar results, is that the extent to whichthose responsible can be made liable once harm has occurred is limited. Hence, they can internalize the costthey impose on society only to a limited extent.

10If the government did not regulate the activity (i.e. D = g always), no entrepreneur would �nd it bene�cialto comply and the associated �no regulation� level of welfare would be W = G−H < 0.

11It should be interpreted as the e�ectiveness of the detection technology o�cials are endowed with. Thisdepends, for instance, on the amount of resources allocated to enforcement (which is generally limited indeveloping countries). Of course, in reality the e�ectiveness of inspections depends also on the o�cial's e�ort.We ignore this dimension for simplicity.

8

Upon observing σ, the o�cial decides whether to impose a sanction on the entrepreneur

(D = d) or not (D = g). The purpose of the sanction is both to punish non-compliers and

protect the public from potential harm. For concreteness, we will refer to d as �denying a

permit to carry out the activity� and to g as �granting the permit� (examples being business

permits or driving licenses). However, one may also interpret d as ordering some measures be

taken to amend noncompliance before the activity can continue, possibly in combination with

�nes. We assume that, when D = d, the entrepreneur gets a private surplus equal to zero and

H is avoided. When D = g, the entrepreneur obtains G and, if A = n, harm H is produced.12

We assume that before undergoing an inspection, entrepreneurs are required to pay a small

adminstrative fee k. This may for instance cover the cost of producing the paperwork that

certi�es the outcome of the inspection. We assume k is collected directly by the o�cial and

independently of her decision. Thus, if he undertakes the activity, the entrepreneur pays k

irrespectively of complying with regulation.

It is assumed that σ is observable to both the o�cial and the entrepreneur, but not veri�able

by third-parties (including the government): it is �soft information�. Hence, o�cials have full

discretion in their decision as to grant the permit. Since σ is a perfectly informative signal of

noncompliance, if the government could directly observe it, it would impose a sanction on the

entrepreneur only if σ = n. However, o�cials act according to their interest, possibly engaging

in corruption. We distinguish between two types of corrupt behavior, depending on whether

it is to the entrepreneur's bene�t (bribery) or his detriment (extortion). Bribery occurs when

the o�cial accepts a payment from an entrepreneur found not compliant (i.e., when σ = n),

in return for granting the permit. Extortion occurs when the o�cial obtains a payment from

an entrepreneur found compliant (i.e., when σ = c), under the threat of denying the permit.

Both forms of corruption involve the entrepreneur making a monetary payment to the o�cial,

which we denote t. In the baseline model, we assume (for ease of exposition) that the payment

is determined as a take-it-or-leave it o�er made by the o�cial. In other words, the o�cial

simply sets the price for her services.13

Because o�cials are corruptible, the government has to provide them with incentives to

loyally perform their duty. Of course, these can only be conditional on what the government

observes. As mentioned, the government cannot observe σ, but it observes whether the

12It would be fairly simple to generalize the model to the case where the entrepreneur obtains a prvivategain x ∈ (−∞;G) when D = d and only part of the harm H is avoided. This would complicate the analysiswithout adding further insight.

13This is in line with many previous models of corruption, e.g. Shleifer and Vishny (1993), Banerjee (1997)and, more recently, Frederiksson (2014). We consider a more general case where t and associated payo�s aredetermined by the Nash bargaining solution in an extension. See Section 4.

9

permit is granted.14 Furthermore, the government can ask the entrepreneur to evaluate the

o�cial's decision, reporting, in particular, whether he has been treated fairly. For concreteness

(and without loss of generality), we assume that only entrepreneurs whose application was

unsuccessful are asked to submit a report. Entrepreneurs can then indicate to the government

whether they agree (e = 1) or disagree (e = 0) with the o�cial's decision. We will refer to the

former as a "complaint" and the latter as "no complaint". Accordingly, o�cials are o�ered

a wage schedule{wg, wd,0, wd,1} , where wg is paid in case the permit is granted, wd,1 is paid

in case a permit is denied and the entrepreneur does not complain, and wd,0 paid in case the

entrepreneur disagrees/complains. Finally, o�cials face an (arbitrarily small) expected cost

0 < s < G2when deceiving the government. For instance, with a small probability the o�cial's

work is audited by a higher o�cial. If s ≥ G2, it can be shown that the government can

costlessly deter all types of corruption.

We assume the entrepreneur sustains a private cost γ ≥ 0 when �ling a complaint. There is

no cost of agreeing with the o�cial's decision (indeed, e = 1 does not require any further action

on the entrepreneur's part). We assume there is no appeals process following a complaint: the

o�cial's decision is never overturned (i.e. signal σ remains unobservable for the government).

Thus, if the government wants a complaint to be �led, it has to promise a compensation b > γ

to the entrepreneur. 15

As a �nal remark, note that we refer to agents as entrepreneurs since our model naturally

applies to regulation concerning �rms (e.g. safety or environmental regulation). Nevertheless,

our analysis also applies to activities that are not strictly business-related. Consider, for

instance, driving motorized vehicles. This is a risky activity that may generate harm on

third parties (e.g., road accidents). Such risk depends on the driver's training, which is

costly to acquire and not directly observable by the government. Governments thus require

would-be drivers to undergo some tests before being issued a licence. There is abundant

evidence suggesting that corruption signi�cantly weakens the e�ectiveness of such tests (see,

e.g., Bertrand et al., 2007).

Timing. We summarize the model by presenting the timing of moves:

1. The government chooses the o�cials' wage schedule {wg, wd,0, wd,1} and, when

14We assume that whether harm on third-parties is imposed is not contractible, for instance because it isnot easily observable.

15This is not necessarily a handout: it may come, for instance, in the form of a rebate of the applicationfee k. Note also that a complaint is never an informative signal regarding the entrepreneur's compliance:conditionally on being denied the permit, either all entrepreneurs �le a complaint or none does (regardless ofA). We will return on this point below.

10

applicable, the rebate b to complaining entrepreneurs;

2. Entrepreneurs decide whether to engage in the productive activity and, if so, the level

of compliance with regulation (A);

3. Conditionally on undertaking the activity, the entrepreneur interacts with an o�cial and

signal σ is realized;

4. Entrepreneur and o�cial possibly engage in corruption. The o�cial decides whether to

grant the permit (D);

5. If denied a permit, the entrepreneur decides whether to �le a complaint (e);

6. The o�cial's wage is paid, the entrepreneur receives his private payo� and harm

eventually occurs.

Entrepreneur payo�s. Consider the ex-post payo� of an entrepreneur of type ψ. This is

denoted U (ψ,A, σ, e), and is conditional on (i) the entrepreneur's type, (ii) the action chosen,

(iii) the realization of σ and (iv) the report e following the o�cial's decision. Denoting Dσ

the o�cial's decision conditional on σ, and by tσ the corresponding bribe, we have

U (ψ,C, σ, e) = GIDσ − tσ−ψ− k+ (b− γ) Ie,Dσ , U (N, σ, e) = GIDσ − tσ− k+ (b− γ) Ie,Dσ ,

U (∅) = 0, σ = {c, n}

where IDσ = 1 if Dσ = g and IDσ = 0 if Dσ = n, and where Ie,Dσ = 0 if e = 1 in response to

the o�cial's decision Dσ and Ie,Dσ = 1 if e = 0. In words, the entrepreneur obtains G only

if the permit is granted and b − γ when making a complaint of o�cial misbehavior. Recall

that the government accepts complaints only if the premit is denied. Hence, e = 1 when

Dσ = g. Observe also that, when Dσ = n, the entrepreneur will choose e = 0 if and only if

b > γ. This means that e is never an informative signal of (non)compliance for the government.

Finally, to simplify notation, we drop the argument ψ from U (.) when A = {N, ∅}, since theentrepreneur's payo� depends on ψ only if he complies with regulation.

The interim payo� of the entrepreneur (that is, before the realization of σ) is therefore

EU (ψ,C) = GIDc − tc − ψ − k + (b− γ) Ie,Dc ,

EU (N) = ρ (GIDn − tn + (b− γ) Ie,Dn)+(1− ρ) (GIDc − tc + (b− γ) IeDc)−k, EU (∅) = 0.

11

The entrepreneur will choose A = {C,N, ∅} maximizing his ex ante utility. Denote ψ the type

of entrepreneur indi�erent between complying with regulation and not, i.e.

EU(ψ, C

)= max [EU (N) ; 0] .

Since EU (ψ,C) is decreasing in ψ, a quantity of entrepreneurs F(ψ)choose A = C, while

1− F(ψ)choose A = N if EU (N) > 0 and A = ∅ otherwise.

O�cial payo�s. Consider the ex-post payo� of an o�cial. This is denoted V (σ), as it

depends on the realization of σ. We have

V (c) = wDc,e − sIDc + tc, V (n) = wDn,e − sIDn + tn,

where IDc = 1 if Dc = d and IDc = 0 if Dc = g, while IDn = 1 if Dn = g and IDc = 0 if Dn = d.

In words, the o�cial receives a punishment s when denying (resp. granting) a permit without

(resp. in presence of) evidence of noncompliance. We denote by wDσ ,e (resp. wDn,e) the wage

paid to the o�cial conditionally on Dc and the report e by the entrepreneur. Although the ex

post payo� of an o�cial does not depend on the type of the entrepreneur she is paired with,

ψ determines the entrepreneur's action. Therefore, the o�cial's interim payo� (i.e. before the

realization of σ) does depend on ψ. It is denoted EV (ψ). We have

EV (ψ) = wDc,e − sIDc + tc, if ψ ≤ ψ.

EV (ψ) = ρ(wDn,e − sIDn + tn

)+ (1− ρ)

(wDc,e − sIDc + tc

)− k if ψ > ψ.

We assume the o�cial cannot commit to Dσ and tσ before observing σ. She will therefore

choose Dσ and tσ maximizing V (σ) (anticipating the report by the entrepreneur).

Third parties. Recall that harm on third parties H is produced if and only if A = N and

D = g. Denoting the ex ante payo� of third parties as T , and recalling that 1− F(ψ)is the

12

quantity of entrepreneurs that does not comply with regulation, we have

T =

−H(

1− F(ψ))

if D = g ∀σ

−ρH(

1− F(ψ))

if D = g when σ = n

− (1− ρ)H(

1− F(ψ))

if D = g when σ = c

0 if D = n ∀σ.

Welfare. The objective of the government is to maximize social welfare. The welfare

function speci�es equal weight to all entrepreneur/o�cial pairs, as well as third parties. We

also assume that there is a cost λ ≥ 1 to society of making transfers to o�cials (i.e. the cost of

public funds). We denote by w the total wage bill paid by the government. The social-welfare

function is thus

W =

ˆ ψ

0

(EU (ψ,C) + EV (ψ)) dF (ψ)+

ˆ ψ

ψ

(EU (N) + EV (ψ)) dF (ψ)+T−λw when EU (N) > 0,

and W =

ˆ ψ

0

(EU (ψ,C) + EV (ψ)) dF (ψ)− λw when EU (N) ≤ 0.

3 Solving the Model

We now turn to the solution of the model. We begin from the benchmark situation in which

o�cials are uncorruptible. Next, we introduce corruption and consider the optimal incentive

scheme when, by assumption, entrepreneurs are not allowed to evaluate the o�cial's behavior.

Finally, we consider the possibility of letting entrepreneurs �le complaints when sanctioned by

o�cials.

3.1 Uncorruptible o�cials

Consider a situation in which o�cials are uncorruptible or, equivalently, suppose hidden

payments are unfeasible. That is, t = 0 for any σ. Since o�cials do not collect payments

from entrepreneurs, it is enough to set the o�cial's wages to zero to have them act in the

socially optimal manner. Furthermore, the government can set b = 0 as it is not necessary to

rely on citizen complaints to discipline o�cials. As a result, we have

EU (ψ,C) = G− ψ − k, EU (N) = (1− ρ)G− k.

13

Hence, an entrepreneur complies with safety regulations if and only if

G− k − ψ ≥ max [(1− ρ)G− k, 0] , (1)

Throughout the analysis, we will assume that

k < (1− ρ)G. (2)

That is, even in the absence of bribery, the expected private bene�t of undertaking the activity

without compliance is positive. Consequently, a fraction F (ρG) of entrepreneurs applies for a

permit and complies with safety regulations. The remainder does not comply but nevertheless

applies. Thus, the benchmark level of welfare is:

W ∗ =

ˆ ρG

0

(G− ψ) dF (ψ)− (1− ρ)

ˆ ψ

ρG

(H −G) dF (ψ) . (3)

The reader can immediately see that if k ≥ (1− ρ)G, and if corruption is ruled out,

entrepreneurs undertake the activity only if they comply with regulation. While this outcome

is theoretically conceivable, we deliberately focus on situations in which, even if o�cials are

perfectly honest, the government cannot ensure that only compliant entrepreneurs operate

on the market. There are several reasons for this choice. First of all, in reality resources

allocated to enforcement of regulation are quite small, particularly in developing countries.

Thus, entrepreneurs who are unwilling to comply can still expect a substantial private gain

(since ρ is below one). It seems therefore unlikely that, even if o�cials were perfectly honest,

governments could ensure full compliance simply by rasing taxes all active �rms. Furthermore,

in reality, the size of fees required to achieve such an outcome is probably large enough that

also compliant entrepreneurs would be discouraged from production (for instance, if they are

credit constrained).16 Finally, welfare-maximizing governments should design policy with the

objective of not only ensuring compliance, but also of minimizing business costs: imposing

high fees on all entrepreneurs (irrespectively of compliance) could easily achieve the opposite

result. This could be formally captured by assuming that an entrepreneur staying out of the

market produces a social cost (on top of the foregone private gain G), potentially greater

than the net harm from noncompliance H − G. Raising k to the point that only compliant

16Our baseline model does not distinguish between individuals' willingness and ability to pay for a permit(see Banerjee (1997)). However, we explicitly consider this in an extension (see Section 4 below). We showthat, unless the government can set k so large that entrepreneurs are unable to make side payments to o�cials,if the government does not condition o�cial wages on complaints it is never optimal to raise k to the pointthat (13) does not hold.

14

entrepreneurs are active would then be suboptimal.17

3.2 Corruptible O�cials

We now consider the case of corruption. That is, o�cials decide whether to grant permits

purely according to their interest, possibly demanding side-payments from entrpreneurs.

3.2.1 Absence of Communication with Entrepreneurs

Assume o�cials are corruptible but requesting entrepreneurs to either agree or disagree with

o�cials' decisions is not feasible. This means that wd1 = wd0 = wd and e = 1 always. To gain

intuition regarding the tension that arises when trying to deter both bribery and extortion, it

is useful to consider separately the case in which an entrepreneur is found not compliant with

regulation, and then the reverse situation.

Bribery. Suppose the o�cial discovers that the entrepreneur did not comply with regulation

(i.e., σ = n). If D = d, the o�cial obtains wd, while the entrepreneur's ex-post payo� is −k.If instead D = g, the o�cial receives wg − s. On top of this, the o�cial can also pocket a

bribe tn = G (we assume that, when indi�erent, the entrepreneur always chooses to obtain

the permit).18 Assuming that the o�cial reports information truthfully when indi�erent, the

government must therefore set

wd ≥ wg − s+G (4)

in order to deter bribery.

Extortion. Consider now a situation in which the o�cial �nds no evidence of noncompliance

(i.e. σ = c). In case wg ≥ wd − s, even absent a bribe from the entrepreneur, it is in the

o�cial's interest to grant the permit. This means that the threat of framing is not credible.

Hence, D = g with tc = 0. Thus, the entrepreneur's ex post payo� is G− ψ − k if a = c and

G−k otherwise. However, if wd− s > wg, the o�cial would strictly prefer denying the permit

in the absence of bribes. Thus, the threat of framing is credible. Hence, the entrepreneur

17For instance, the entrepreneur may decide to remain in the informal sector, thereby not only losing theprivate gain from operating in the formal economy but also generating less surplus for other stakeholders (e.g.employees).

18Formally, the ex post payo� of the entrepreneur if D = g is G− tn. Hence, he will accept to pay tn ≤ Gin order to obtain the permit. The o�cial will therefore set tn = G.

15

is willing to pay tc = G to obtain the permit. As a consequence, we have D = g but the

entrepreneur's ex post payo� equals −k − ψ if a = c and −k otherwise.19 It follows that, for

the government to deter extortion, it must set

wg ≥ wd − s. (5)

Rearranging (4) and (5) leads to the following chain of inequalities: s ≥ wd −wg ≥ G− s,which cannot hold since G

2> s by assumption.20 In words, the government is unable to deter

bribery and make the threat of framing not credible at the same time. This means that a

choice has to be made between preventing bribery, preventing extortion or allowing both: the

government has to pick the "lesser evil". Which is more detrimental for social welfare? To �nd

the answer, it is useful to consider the maximization problem of the entrepreneur. Suppose (4)

holds: bribery is deterred but extortion is not. Then, an entrepreneur complies with regulation

if and only if

−k − ψ ≥ max [−k; 0] = 0.

Clearly, this inequality cannot hold. This implies that no entrepreneur complies with

regulation. In fact, none even undertakes the activity. Suppose now (5) holds. Then an

entrepreneur chooses to comply with regulation if and only if

G− k − ψ ≥ (1− ρ)G− k.

Hence, the quantity of entrepreneurs that comply with regulation is F (ρG). Those who do

not comply obtain the permit, thereby producing harm on third parties, with probability ρ.

Proposition 1. There exists a threshold H ≡ G−´ ρG0 ψdF (ψ)

1−F (ρG)such that when H ≤ H, the optimal

incentive scheme is such that wd = 0 and wg = 0: extortion is avoided, but bribery takes place

in equilibrium. If H > H, the optimal incentive scheme is such that wd = G− s and wg = 0:

the government deters bribery.

Proof. See Appendix.�

We noted above that it is not possible to deter extortion and bribery jointly. Proposition

19This is true except if wd − s > wg + G, in which case the o�cial is better o� framing the entrepreneurregardless of the bribe.

20Note that, in case G2 < s, the government could deter both bribery and extortion by setting all wages

equal to zero.

16

1 suggests that the government should focus on deterring extortion only if the harm produced

by noncompliance is large enough. To grasp the intuition, recall that we are assuming that (i)

active entrepreneurs always interact with an o�cial and (ii) the latter has strong bargaining

power in determining bribes. In such an environment, if the government does not deter

extortion, all compliant entrepreneurs face the prospect of paying a large extortionary bribe.

Hence, none chooses to comply. Consequently, at least as long as harm on third parties is not

too large (i.e. H < H), the government tolerates bribery. O�cials get no reward for denying

permits and, thus, cannot make a credible threat of framing. The drawback is of course that

there are insu�cient incentives to report and sanction noncompliance when uncovering it.

Allowing bribery is socially costly for two reasons: the �rst is that the expected cost of

breaking the law is reduced. Secondly, bribery means that noncompliant entrepreneurs are

allowed to carry on with their activity, producing harm on society. Given the large bargaining

power of the o�cial, the �rst of such consequences is of limited relevance: bribing one's way

into unduly obtaining the permit is very expensive. However, when harm produced on third

parties is signi�cant (i.e. H ≥ H) bribery is highly detrimental for society. Hence, the

government should deter it, at the cost of allowing extortion.

The fact that bribery is less harmful than extortion, and may thus be tolerated in

equilibrium, is not a novel result (see, e.g., Hindriks et al. (1999), Khalil et al. (2010)).

However, in line with previous literature, this has been obtained assuming that the government

is unable to communicate with entrepreneurs. In particular, there is no possibilty for the latter

to claim they have been victims of framing. This possibility is explored in the next section.

We will see that, under reasonable conditions, the optimal incentive scheme looks radically

di�erent from the one we described so far.

A remark may be in order before moving forward. Assumption (2) postulates that the

fee k is small enough that, even if o�cials are perfectly honest, only compliant entrepreneurs

are active on the market. Suppose this assumption were relaxed: corruption would not be a

problem for the government in this simple model. Indeed, a zero salary (i.e. not conditional on

D) to o�cials, letting them collect bribes from noncompliant entrepreneurs, would be enough

to achieve compliance and make the threat of extortion void. Nonetheless, as explained above,

the focus of our analysis is on situations in which the government cannot simply rely on high

fees or taxes to make corruption irrelevant.

17

3.2.2 Communicating with Entrepreneurs

Suppose now that the government o�ers entrepreneurs who were denied a permit the ability to

claim they su�ered from unfair behavior on the part of the o�cial. Speci�cally, the government

commits to rewarding any entrepreneur �ling a complaint, by paying them a (small) amount

b > γ, where b−γ < G−2s. Note that under such a scheme, it is rational for any entrepreneur

whose permit was denied to �le a complaint, regarldess of whether the o�cial they interacted

with behaved opportunistically. As we will now argue, it is possible (and, under conditions

outlined below, optimal) to deter both forms of corruption.

To gain intuition, let us revisit the incentives to engage in bribery and extortion. Consider

extortion �rst. Suppose σ = c. Given that b > γ, if the o�cial threatens to deny the permit,

she knows that the entrepreneur will eventually �le a complaint. Therefore, if there is no

reward for denying a permit when a complaint follows, doing so is not sequentially rational

for the o�cial. Hence, to make the threat of extortion void, the government has to set

wg ≥ wd,0 − s.

Turn now to bribery. When σ = n, and if the entrepreneur complains after being denied a

permit, the o�cial chooses not to engage in bribery if and only if

wd,0 ≥ wg − s+G. (6)

holds. However, assuming the government wants to deter extortion, (6) cannot hold. Does

this mean that bribery cannot be deterred? Not necessarily. In principle the government can

set the o�cial's reward in the absence of complaints high enough to deter bribery, without

opening the door to extortion. Suppose the government gives no reward to o�cials who denied

a permit if entrepreneurs subsequently �le a complaint, setting wd,0 = wg = 0. Suppose also

that an o�cial who denies a permit without triggering a complaint can be rewarded with a

large payment wd,1 = G − s. Of course, the fact that b > γ means that, if entrepreneur and

o�cial do not reach an agreement, D = d will always result in a complaint. Yet, reaching an

agreement such that the permit is duly denied and no complaint is made is bene�cial for both

o�cial and entrepreneur. Consequently, this is an instance where cooperation between the

two parties becomes bene�cial for the government. The o�cial can �bribe� the entrepreneur

into not complaining, by promising a compensation equal to b − γ + ε, where ε > 0 and

18

arbitrarily small.21 If the entrepreneur refuses, the o�cial rationally denies the permit (since

wd,0 > wg − s). As a result, facing the prospect of being denied a permit either way, the

entrepreneur is better o� accepting the o�cial's o�er and forego his right to complain.

We have therefore established that, by actively incentivizing entrepreneurs to �le

complaints, and by tying the o�cial's compensation to them, the government is able to

eliminate the tension that otherwise arises when trying to deter both types of corruption.

The next question is whether doing so is socially desirable. The answer is a�rmative as long

as the potential harm to the economy produced by noncompliance is large. To grasp the

intuition, recall that one of the social costs of bribery is that noncompliant entrepreneurs are

allowed to remain on the market. Nevertheless, deterring both forms of corrupt behavior is

not without cost. This is because a high wage must be paid to o�cials who deny permits. Not

surprisingly, therefore, we �nd that when externalities produced by noncompliance are small

enough, the government lets bribery occur, and sets o�cial wages equal to zero. These results

are summarized in the following.

Proposition 2. There exists a threshold H ≡ λ (G− s) such that when H ≤ H, the

optimal incentive scheme is such that wg = wd,1 = wd,0 = 0: extortion is avoided, but

bribery is tolerated in equilibrium. If H > H, the optimal incentive scheme is such that

wg = wd,0 = 0 < wd,1 = G− s: both extortion and bribery are avoided in equilibrium.

Proof. See Appendix.�

A direct consequence of Proposition 2 is that establishing communication with

entrepreneurs is never harmful, but is not always useful. In particular, when H ≤ H,

the optimal incentive scheme is such that the o�cial is paid a �at wage and bribery is

not discouraged in equilibrium. Such scheme can be implemented without conditioning the

o�cial's wage on the entrepreneur's reports. Hence, in that case communication with the

entrepreneur is redundant. We can therefore state the following

Corollary. Relying on entrepreneurs' complaints to discipline o�cials is strictly optimal if

and only if H > H. Otherwise, it is unnecessary.

3.2.3 Implementation of the optimal incentive scheme

The mechanism we have proposed relies on o�cials making �payments� to entrepreneurs to

have them not complain. There are various alternative institutional arrangements that can

21To minimize the payo� of entrepreneurs who decide to break the law, the government optimally sets b− γclose to zero.

19

be designed to avoid having o�cials actually make payments to individuals. Take for instance

the application fee k. The government could give discretion to o�cials to grant a small

reduction in the fee (equal to b − c + ε) to entrepreneurs willing to forego their right to

subsequently complain. Rather intuitively, this mechanism would achieve the same result and

enjoy legitimacy as well.

4 Extensions

4.1 Bargaining power of entrepreneurs

The above results have been derived assuming that the o�cials have all bargaining power

when engaging in illegal transactions with entrepreneurs. In reality, though, o�cials may not

be fully able to set the price for their services. For instance, in some situations entrepreneurs

could be able to choose which o�cial they interact with, leading to some competition between

o�cials. Reassuringly, while the assumption of full bargaining power to o�cials simpli�es

exposition, it is by no means crucial for our results. Suppose δ ∈ [0, 1]. In the absence of

communication with entrepreneurs, the optimal incentive scheme is still such that bribery is

tolerated, but extortion is not, if and only if the harm produced by breaching the law is not

too large. Furthermore, the larger is δ , the less entrepreneurs su�er from extortion, and the

more they bene�t from bribery. Not surprisignly, therefore, we also �nd that, all else given,

greater bargaining power of the entrepreneur makes tolerating bribery more costly for society.

Indeed, the greater the bargaining power of agents, the lower the threshold value of H above

which it is optimal to tolerate bribery and deter extortion.

Suppose now communication with entrepreneurs is possible. As in the baseline model, we

�nd the optimal incentive scheme is such that both extortion and bribery are deterred, except

if the cost of public funds λ is very large and harm produced by noncompliance is very small.

Again, the social cost of allowing bribery in equilibrium increases with the entrepreneur's

bargaining power. Hence, the larger it is, the more desirable it is to exploit entrepreneurs'

complaints We provide the proof of these results in the Appendix.

4.2 Intermediaries

We now extend the model to study the role of intermediaries, who may assist the entrepreneurs

in bureaucratic procedures. This extension is motivated by the fact that such intermediaries

are ubiquitous in reality, particularly in developing countries (Bertrand et al. 2007, Fredriksson

20

2014). Intermediaries provide several services, which are not always welfare-enhancing. On

the one hand, intermediaries reduce the transaction cost of dealing with the bureaucracy. For

example, they possess a superior technology for handling paperwork and, by serving several

applicants at the same time, can exploit economies of scale and scope. Moreover, in situations

where o�ces have to be visited several times in order to comply with rules, intermediaries

can act as �one stop shops�. However, intermediaries also facilitate corruption: by developing

stable relationships with o�cials they guarantee a preferential treatment to their customers,

thereby weakening regulatory controls.

Of course, given that they perform several functions, it is hard to capture all the

implications of the role played by intermediaries in a single model. The objective of this

section is therefore necessarily limited in scope. We will focus on two questions. First, why

is the involvement of intermediaries so pervasive (especially in developing countries)? Our

model suggests that this may be a by-product of the low powered incentives provided to

o�cials, which are, in turn, an optimal response to their high discretionary power and lack of

accountability. We will establish that, when communication with the entrepreneurs is ruled

out, despite the fact that intermediaries weaken the incentives for o�cials to enforce regulation,

the optimal incentive scheme is such that all entrepreneurs that do not comply with regulation

make use of intermediaries. In other words, much like direct bribery, intermediaries are a

�necessary evil�. Second, can exploiting entrepreneur complaints help the government make

the role of intermediaries less pervasive? We will show that the government can implement an

incentive scheme such that o�cials do not rely on intermediaries and, as a result, incentives to

enforce regulation are strenghtened. Therefore, if exploited correctly, communication with

entrpreneurs reduces intermediaries' ability to facilitate corruption and, under reasonable

conditions, enhances social welfare.

Modi�ed setup. The baseline setup is modi�ed as follows. The action space of

entrepreneurs is expanded by allowing them to choose, instead of dealing directly with an

o�cial, to acquire the permit via an intermediary. Hence, we have A = {C,N, I, ∅}, where Idenotes �going through an intermediary�. The intermediary guarantees issuance of a permit

by means of his connections with o�cials. Hence, if A = I the o�cial chooses D = g.

Intermediaries charge a fee ϕ for their services and pay a price p to the o�cial issuing

the permit. The price p is common knowledge. It set by the o�cial with the objective of

maximizing her (ex ante) expected payo�. Note that since all o�cials are identical, they all

set the same p. This will be explained in detail below. We assume that the government

21

cannot observe whether an entrepreneur uses an intermediary to obtain the permit. Using the

intermediary does not require any compliance e�ort on the entrepreneur's part (we assume

the intermediary cannot observe the entrepreneur's type nor his action).

We assume that, on top of obtaining the permit with probability one, the intermediary

also possesses a �superior technology� for dealing with the bureaucracy compared to a simple

entrepreneur. In particular, we assume that, if the entrepreneur deals directly with an o�cial

(A = C,N), he has to sustain an extra cost denoted r. This captures costs like red tape,

transportation costs to visit bureaucrats, etc. 22 When A = I, instead, cost r is avoided.

This captures the fact that the intermediary can help the entrepreneur bypass red tape, avoid

traveling to di�erent o�ces, etc. We assume that, on top of the money paid to the o�cial p,

the intermediary sustains no cost for carrying out the application procedure on behalf of the

entrepreneur. We also assume, for simplicity, that competition among intermediaries drives

their fees to marginal cost. Hence, ϕ = p.

We assume an o�cial announces p before interacting with any entrepreneur (or

intermediary) and cannot modify it afterwards. However, the o�cial cannot commit to a

bribe t before interacting with an entrepreneur and, in particular, observing signal σ. This is

consistent with the fact that if an entrepreneur has chosen to deal with the o�cial directly, after

σ has been observed the entrepreneur cannot revise its decision and switch to an intermediary.23

Hence, if A = C,N or ∅ are chosen, the continuation game is exactly as in our basic setup.

To abstract from competition among o�cials, which would complicate the analysis without

adding much insight, we retain the assumption that an entrepreneur is paired exogenously

with an o�cial.

Finally, to simplify the analysis, we will focus on a speci�c on a speci�c distribution of

entrepreneur types. We assume that ψ ∼ U[0, ψ

]. Hence, F (ψ) = ψ

ψand f(ψ) = 1

ψ.

Timing. The timing of the game is as follows:

1. The government chooses the o�cials' wage schedule {wg, wd,0, wd,1} and, when

applicable, the rebate b to complaining entrepreneurs;

2. O�cials set the price p charged to intermediaries. Intermediaries set ϕ.

22For simplicity, r is not under the control of the o�cial. If this were endogenized, it would be easy to showthat the o�cial has an incentive to raise r above the socially optimal level.

23Suppose that, after having examined the entrepreneur's �le, the o�cial requests a bribe in order to grantthe permit. Our assumption means that if the entrepreneur refuses, he cannot simply withdraw the application.Consequently, he will be denied the permit.

22

3. Entrepreneurs decide A = {C,N, I, ∅}; Conditionally on undertaking the activity, the

entrepreneur interacts either directly with an o�cial or with an intermediary.

4. If A = I, the entrepreneur pays ϕ to an intermediary, who transfers p to the o�cial.

The o�cial grants the permit, D = g.

5. If A = C,N , the entrepreneur sustains cost r and signal σ is realized. The game then

proceeds as in the baseline model.

Entrepreneurs' incentives. Consider the choice of an entrepreneur of type ψ. If the

entrepreneur chooses A = C,N , or ∅, he obtains the same payo�s EU(.) as in Section 3.

When A = I, the payo� of entrepreneur is EU(I) = G− p− k. As a result, the entrepreneur

will choose A = c if and only if

GIc − tc − r − k − ψ ≥ max [0; ρ (GIn − tn) + (1− ρ) (GIc − tC)− r − k;G− p− k] .

We can therefore identify the marginal entrepreneur, indi�erent between A = C and the most

pro�table of the other three actions. Denote ψ the type of entrepreneur indi�erent between

complying with regulation and not, i.e.

EU(ψ, C

)= max [EU (N) ;EU(I); 0] . (7)

Therefore, a quantity F (ψ) of entrepreneurs will choose A = C in equilibrium, while 1−F (ψ)

choose either A = N , A = I or A = ∅, depending on conditions.

O�cial incentives. Consider �rst the case where an o�cial interacts with an entrepreneur

directly (i.e. A = C,N). The interim payo� EV (ψ) is as described in Section 3. Suppose now

A = I. The interim payo� of the o�cial is EV (ψ) = wg + p − s. This allows us to describe

the ex ante payo� of an o�cial. This is de�ned as her expected payo� before interacting with

entrepreneurs or intermediaries. This is the expectation of EV (ψ) computed over ψ, using

(7), which writes as follows:

Eψ (V ) =

F (ψ) · (wcD + tc − sIcD) +

(1− F (ψ)

)· (wg + p− s) if EU(I) < EU (N) ,

F (ψ) · (wcD + tc − sIcD) +

+(

1− F (ψ))· (ρ (wnD + tn − InDs) + (1− ρ) (wcD + tc − sIcD)) if EU(I) ≥ EU (N) .

23

No communication with entrepreneurs. Let us begin from the benchmark case in which

the government does not make use of communication with entrepreneurs. This implies that

wd0 = wd1 = wd and b = 0. Consider the direct interaction between an o�cial and an

entrepreneur. The game played by the two parties is exactly as in the baseline model. Hence,

constraint (4) has to hold in order to avoid bribery, while (5) has to hold to avoid extortion.

As argued above, the constraints cannot hold jointly. In light of this, the optimal incentive

scheme designed by the government has to be such that extortion is deterred, but no bribery.24It follows that the optimal incentive scheme has to be such that (5) holds, while (4) does

not. As a result, we have tc = 0 and tn = G, and D = g for any σ. Thus, an entrepreneur

chooses A = C if and only if

G− r − k − ψ ≥

(1− ρ)G− r − k if p ≥ ρG+ r,

G− p− k if ρG+ r > p.(8)

As a result, denoting as usual the entrepreneur indi�erent between complying and not to

regulation as ψ, we have

ψ =

ρG if p ≥ ρG+ r,

p− r if ρG+ r > p > r,

0 if p ≤ r.

Let us interpret the above expressions. Given that extortion is ruled out, an entrepreneur

that complies with regulation obtains the permit with certainty. Entrepreneurs who choose

not to comply will either bribe directly o�cials (if found noncompliant) or acquire the permit

through an intermediary. In the former case, the expected cost of obtaining the permit is

the expected bribeρG, plus the red tape cost r. In the latter, the cost is p. Hence, when

p ≥ ρG + r, even entrepreneurs who do not comply with regulation prefer to deal directly

with o�cials: a quantity F (ρG) chooses A = C, while the rest choose A = N . When

ρG+ r > p > r, entrepreneurs who do not comply prefer to deal with intermediaries. Hence,

F (p − r) entrepreneurs choose A = C, while the rest choose A = I. Finally, if p ≤ r, even

entrepreneurs who could comply with regulation at zero private cost prefer to obtain the

permit via an intermediary. Hence, ψ = 0. As one would expect, the fraction of entrepreneurs

24A formal proof is provided in the Appendix and we here provide an informal argument. Suppose thegovernment did not deter extortion. Any entrepreneur complying with regulation would, with certainty, haveto pay a large bribe tc = G in order to obtain the permit. Hence, from the ICA above, it is immediately seenthat the payo� of complying cannot be positive. Anticipating this, o�cials would set p low enough to makesure all entrepreneurs choose to obtain the permit by means of an intermediary, resulting in ψ = 0. Quiteclearly, this cannot be a socially desirable outcome.

24

that uses intermediaries is nonincreasing in p.

Consider now the ex ante payo� of an o�cial. From the above discussion, we can write it

as

Eψ (V ) = wg +

(1− F (ρG)) · (ρ (G− s)) if p ≥ ρG+ r,

(1− F (p− r)) · (p− s) if ρG+ r > p > r,

p− s if r ≥ p.

This is explained as follows. When p ≥ ρG + r, the o�cial knows that no entrepreneur

uses intermediaries and anticipates that the probability of dealing with a noncompliant

entrepreneur is (1− F (ρG)). The expected bribe from such entrepreneur (after accounting

for lying cost s) is ρ (G− s). When ρG + r > p > r, the proability of receiveing a request

for a permit from an intermediary is (1− F (p− r)), and the net payment pocketed is p − s.Finally, when r ≥ p, the o�cial knows that the entrepreneur will surely use an intermediary,

hence the expected payment is p− s. Note that, since bribery is not deterred, the o�cial will

always grant the permit and pocket wg.

How will an o�cial set p? We assume that the o�cial's objective is to maximize Eψ (V )

(recall that p has to be announced before interaction with intermediaries or entrepreneurs

takes place). Observe from Eψ (V ) above that the choice of p does not depend on wg. By

maximizing Eψ (V ) with respect to p, we obtain the following result (proved in the Appendix):

Lemma 1. Suppose the government does not rely on communication with entrepreneurs to

discipline o�cials. The optimal incentive scheme is such that wg = wd = 0 and

- if r > ψ − 2ρG + s, o�cials set p = ψ+s+r2

, such that ρG + r > p > r. A quantity

F ( ψ+s−r2

) of entrepreneurs complies with regulation, while the remainder uses intermediaries

to unduly obtain the permit.

- if r ≤ ψ− 2ρG+ s, o�cials set p ≥ ρG+ r. A fraction F (ρG) of entrepreneurs complies

with regulation , while the remainder does not comply, but none use intermediaries.

The intuition is as follows: since extortion is ruled out, there are two ways for the o�cial

to exploit her discretionary power. The �rst is to directly collect bribes from entrepreneurs

found in breach of regulation. The second is to sell permits to intermediaries. Of course, these

are substitutes, in the sense that an entrepreneur that decides not to comply with regulation

will either call upon an intermediary or directly bribe o�cials, but not both. Given that

entrepreneurs save r when going through an intermediary, the larger this cost the larger the

price an entrepreneur is willing to pay to use an intermediary. As a result, for a given price

25

p, the quantity of entrepreneurs willing to use intermediaries increases with r. Consequently,

when r is large enough, the o�cial �nds it optimal to have some entrepreneurs go through

intermediaries. However, doing so implies that no bribes will be directly collected. As a result,

when r ≤ ψ− 2ρG+ s, the o�cial prefers to avoid intermediaries and deal with noncompliant

entrepreneurs directly.25

Lemma 1 makes an important point: when communciation with entrepreneurs is not

exploited by the government, it is optimal to provide o�cials with low powered incentives,

leaving the door open to either a direct or an indirect form of bribery, i.e. through the

presence of intermediaries. A natural question is whether the involvement of intermediaries in

corruption is welfare-diminishing. Would society be better o� they did not exist? The answer

is not obvious since intermediaries play an ambivalent role. On the one hand, they reduce the

di�erential cost noncompliant entrepreneurs have to sustain to obtain a permit (compared,

that is, to those who respect regulations). Indeed, we have

r > ψ − 2ρG+ s⇔ F (ρG) > F (ψ + s− r

2),

which means that, when the optimal incentive scheme is such that o�cials deal with

intermediaries, the share of compliant entrepreneurs in equilibrium is strictly smaller than

if intermediaries were ruled out. On the other hand, intermediaries reduce the ine�ciencies

produced by red tape. The following proposition provides the answer

Proposition 3. Suppose the government does not make use of communication with

entrepreneurs to discipline o�cials

- The optimal incentive scheme is such that wg = wd = 0.

- When r > ψ− 2ρG+ s, there exists a threshold H such that if and only if H > H, social

welfare would be strictly higher if intermediaries were unavailable. H threshold is increasing

in r.

It follows from Proposition 4 that, if it cannot ask reports from entrepreneurs and when the

external harm produced by noncompliance is large, a welfare maximizing government would

want to forbid o�cials from dealing with intermediaries. However, in reality intermediaries

are �paralegals� who operate outside the boundary of government control. Hence, it is hard to

crack down on them. Since the threat of extortion constrains the government to providing low-

powered incentives to o�cials, we �nd that the government cannot design an incentive scheme

25It turns out that it is never optimal to set p ≤ r, so that all entrepreneurs rely on intermediaries. This ispartly due to the speci�c distribution of types adopted in this section.

26

that induces entrepreneurs and o�cials not to make use of intermediaries. Can communicating

with entrepreneurs help? We turn to this question in the next paragraph.

Communication with entrepreneurs. We now allow the government to exploit

communication with entrepreneurs. For the sake of brevity, we will not fully characterize the

optimal incentive scheme. We will only establish that it is possible to �nd an incentive contract

that conditions o�cial compensation to entrepreneurial complaints and, without opening the

door to extortion, provides o�cials with enough incentives to not only avoid direct bribes, but

also not to sell permits through intermediaries. This contract allows to strictly increase social

welfare with respect to the case in which communication with entrepreneurs is shut down.

The contract we propose is very similar to the one we derived in Proposition 2. It involves

providing a bonus to the o�cial for denying a permit, though only on condition that the

entrepreneur does not complain about the decision. That is, wd0 > wd1 = wg = 0. If

wd0 ≥ G−s, direct bribery (as well as extortion) can be avoided. The logic is exactly the same

as for the baseline model (we refer the reader to the commentary following Proposition 2 for

the intuition). The key di�erence with respect to the baseline model is that the o�cial can also

choose to sell permits to intermediaries. As we argued above, the larger the bureaucratic cost

r, the larger the rents that the o�cial can extract by dealing with them. However, contrary to

the case where no communication is possible, the government can now raise the compensation

for denying permits to undeserving applicants, wd0. Intuitively, when the expected gain from

catching non-compliant entrepreneurs is large enough, o�cials will choose not only to reject

bribes from entrepreneurs, but also not to deal with intermediaries.

Proposition 4. Suppose the government makes use of communication with entrepreneurs. By

setting wd0 = max

[(ψ+r

2

)2− s2

4

ρ(ψ−ρG+ε)+ ε;G− s

]> wd1 = wg = 0, the government avoids all forms

of corruption in equilibrium, including the use of intermediaries. There exists a thresholdH

such that when H >H, this contract strictly increases social welfare with respect to the optimal

incentive scheme with no communication described in Proposition 4.

Proof. In Appendix.

This �nding strengthens our baseline results: by introducing intermediaries in the model,

we have shown that communciation with entrepreneurs can not only allow to �ght direct

corruption of o�cials, but also indirect corruption through intermediaries. When the external

27

costs produced by noncompliance are strong, it is thus strictly optimal to make use of

communication.

We conclude with a brief discussion of two important assumptions we made in this section.

The �rst is that o�cials do not control the size of red tape r. Suppose we relaxed this

assumption. Since, as we have shown, o�cials payo�s tend to increase with r, we would

obtain that o�cials have an incentive to raise this cost in order to extract more rents from

entrepreneurs. As a result, we would expect o�cials to set this cost above the socially optimal

level. Nonetheless, this would not change the main conclusions of our analysis. Secondly, we

have assumed that entrepreneurs and o�cials are paired exogenously. Hence, o�cials do not

compete to attract entrepreneurs. While this assumption is irrelevant for the way in which

o�cials set direct bribes, it has some relevance for the way o�cials choose the price charged

to intermediaries. If o�cials competed for intermediaries, they may have an incentive to set p

below the equilibrium levels we identi�ed above. This would complicate the analysis, without

changing the qualitative �ndings: if the harm produced by noncompliance is large, it would

still be optimal to discourage the use of intermediaries. Furthermore, if o�cials collude when

setting p, the analysis of this section would be unchanged.

5 Conclusion

Corruption is endemic to the developing world, and tends to reduce the e�ectiveness of

regulation aiming at reducing the risks and hazards associated with certain types of economic

activity. In line with previous literature, we have stressed the di�erence between two forms

of corrupt behavior: bribery and extortion. We have shown that it is impossible for the

government to deter both forms of corruption when relying exclusively on the structure of

public o�cials' wages. We have then made the case that governments can use a simple

mechanism to deter both forms of corruption. This mechanism allows for individuals to �le

for complains, and ties the o�cials' compensation to these complaints. One virtue of our

mechanism is its simplicity, which does not rely on the government being able to discern fair

complaints from opportunistic ones. We have extended the analysis in several directions. One

of them is to include corruption intermediaries and shown that, despite their ambivalent role,

in many circumstances their involvement in corruption makes the problem worse. As a result,

we have found, it is even more desirable to exploit communication with entrepreneurs. The

reason is that the pervasive role of intermediaries is at least in part due to the low powered

incentives that have to be provided to o�cials in order to avoid extortion.

28

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31

Appendix

Proof of Proposition 1

We divide the proof in two cases, depending on whether bribery is deterred by the government.

Case 1: wd ≥ wg+G−s. From (4) and (5), bribery is deterred but extortion is not. Suppose

wg + G + s ≥ wd ≥ wg + G− s. When σ = c, t = G and D = g. The entrepreneur's ex post

payo� is −k − ψ if A = C and −k if A = N . Suppose σ = n, since wg + G − s ≤ wd, the

o�cial will not choose D = g unless t > G, which the entrepreneur cannot accept. Hence,

D = d. Thus, irrespectively of A, it can never be pro�table to participate for entrepreneurs.

Suppose now wd > wg +G+ s. Even if σ = c, the o�cial will not choose D = g unless t > G.

Hence, when wd ≥ wg + G − s, no entrepreneur would undertake the activity. As a result,

social welfare can never be positive.

Case 2: wd < wg + G− s. From (4) and (5), bribery is not deterred. When σ = n, D = g

is obtained only by paying a bribe t = G. Hence, the entrepreneur's ex post payo� is −k.Suppose extortion is deterred, i.e., wg ≥ wd − s. Then, an entrepreneur found compliant

with regulation (σ = c) obtains the permit without a bribe. As a result, an entrepreneur

complies with regulation if and only if G − k − ψ ≥ (1− ρ)G − k. Note that k < (1− ρ)G

by assumption. A quantity F (ρG) of entrepreneurs chooses A = C, while the rest chooses

A = N . We have D = g for any σ, so wd is never paid. It is therefore optimal to have

wd = wg = 0. Social welfare is equal to:

W =

ˆ ρG

0

G− ψdF (ψ)−ˆ ψ

ρG

(H −G) dF (ψ) . (9)

Suppose now extortion is not deterred, i.e., if wg < wd−s. As in Case 1 above, if σ = c the

entrepreneur's ex post payo� −k−ψ (−k) if A = C (A = N). On the other hand, when σ = n,

the entrepreneur's payo� is −k since t = G in order to have D = g. Hence, no entrepreneur

undertakes the activity. As a result, social welfare can never be positive.

32

Optimal incentive scheme

W can be strictly positive only if wd =wg = 0. Assuming social welfare is zero when no

entrepreneur participates and rearranging, (9) we obtain that this is optimal if and only if

H ≤ H ≡G−´ ρG

0ψdF (ψ)

1− F (ρG).

Otherwise, the government sets wg = 0 and wd = G− s.

Derivation of the results of Section 4.1: Nash bargaining

No communication with entrepreneur

Assume communicating with the entrepreneur is not feasible. This implies that, when D = d,

we have wd1 = wd0 = wd.

Bribery. Suppose σ = n. If D = d, the o�cial obtains wd, while the entrepreneur's obtains

0. If D = g, the o�cial obtains wg − s and the entrepreneur G. By the Nash bargaining

solution concept, entrepreneur and o�cial play cooperatively and choose D = g if and only if

wd < wg − s + G (we assume that bribery takes place only if the net gain is positive). The

resulting entrepreneur's payo� is δ (wg − s+G− wd). Otherwise, the o�cial chooses D = d

and no bribe is exchanged. Hence, bribery is deterred if and only if

wd ≥ wg − s+G. (10)

Extortion. Suppose σ = c. If wg ≥ wd − s, the threat of framing is not credible. Thus, no

bribe is paid and the entrepreneur's payo� is G−ψ if a = c and G otherwise. If wd− s > wg,

the threat of framing is credible and extortion will take place in equilibrium.26 It follows that,

for the government to avoid extortion, condition

wg ≥ wd − s (11)

must hold.

26If wd− s ≥ wg +G, in which case the o�cial is better o� just reporting D = d, as this yields higher payo�than asking for a bribe.

33

Derivation of the optimal incentive scheme with no communication with

entrepreneur

We divide the proof in two cases, depending on whether bribery is deterred by the government.

Case 1: wd ≥ wg + G − s. From (10) and (11), bribery is deterred but extortion is not.

Suppose wg + G + s ≥ wd ≥ wg + G − s. When σ = c, the entrepreneur-o�cial coalition

chooses D = g and the entrepreneur's ex post payo� is δ (wg +G+ s− wd)− ψ if a = c and

δ (wg +G+ s− wd) otherwise. When σ = n, the o�cial cannot be better o� by cooperating

with the entrepreneur than by choosing D = d. Thus, the entrepreneur has payo� zero. As a

result, an entrepreneur chooses a = c if and only if

δ (wg +G+ s− wd)− k − ψ ≥ max [(1− ρ) δ (wg +G+ s− wd)− k, 0] .

Suppose k < (1− ρ) δ (wg +G+ s− wd): a quantity F (ρδ (wg +G+ s− wd)) of

entrepreneurs chooses a = c; the remainder chooses a = n. Social welfare is therefore

W =

ˆ A

0

G−ψdF (ψ)−(1− ρ)

ˆ ψ

A

(H −G) dF (ψ)−(λ− 1) [wdρ (1− F (A)) + wg [F (A) + (1− ρ) (1− F (A))]]

where A = ρδ (wg +G+ s− wd). It is optimal to set wd = wg + G − s since this raises the

fraction of compliant entrepreneurs and decreases the government's salary costs. Hence,

W =

ˆ ρδ2s

0

G−ψdF (ψ)−(1− ρ)

ˆ ψ

ρδ2s

(H −G) dF (ψ)−(λ− 1) (wg +G− s) ρ (1− F (δρ2s)) +

− (λ− 1)wg [F (ρδ2s) + (1− ρ) (1− F (ρδ2s))] ,

It is then immediately seen that setting wd = G−s and wg = 0 is locally optimal. As a result,

if k < (1− ρ) δ2s, we get

W =

ˆ ρδ2s

0

G− ψdF (ψ)− (1− ρ)

ˆ ψ

ρδ2s

(H −G) dF (ψ)− (λ− 1) (G− s) ρ (1− F (δρ2s)) .

(12)

Suppose now that k ≥ (1− ρ) δ (wg +G+ s− wd). A proportion

F (δ (wg +G+ s− wd)− k) of entrepreneurs chooses a = c; the remainder undertake the

34

activity at all. Social welfare is

W =

ˆ ρδ(wg+G+s−wd)−k

0

G− ψdF (ψ)− (λ− 1)wg [F (ρδ (wg +G+ s− wd − k))] .

Again, it is optimal to set wd = G − s and wg = 0. As a result, if k ≥ (1− ρ) δ2s, only

entrepreneurs whose disutility ψ is weakly below ρδ2s are active (and comply). So

W =

ˆ δ2s−k

0

G− ψdF (ψ) . (13)

It remains to consider the case where wd > wg + G + s. If σ = c, the net payo� of the

o�cial when choosing D = g cannot exceed wg +G− s−wd, which is negative by assumption.

The same holds when σ = n. Therefore, the quantity of active entrepreneurs is zero.

Case 2: wd < wg +G− s. From (10), bribery is not deterred. When σ = n, we have D = g

and the payo� of an entrepreneur (after paying a bribe to the o�cial) is δ (wg +G− s− wd).Suppose extortion is deterred, i.e., wg ≥ wd − s. Then, if σ = c, we have D = g and no bribe

is paid. As a result, an entrepreneur complies if and only if

G− k − ψ ≥ ρδ (wg +G− s− wd) + (1− ρ)G− k

Note that k < ρδ (wg +G− s− wd) + (1− ρ)G holds by assumption. Therefore, a quantity

F ((1− δ) ρG− ρδ (wg − s− wd)) of entrepreneurs chooses a = c, while the rest chooses a = n.

Thus, increasing wd raises the quantity of compliant entrepreneurs. The opposite applies to

wg. Noting that wd is never paid in equilibrium, it is optimal to have wd = s and wg = 0 so

the quantity of compliant entrepreneurs is F ((1− δ) ρG+ 2ρδs). We get

W =

ˆ (1−δ)ρG+2δρs

0

G− ψdF (ψ)−ˆ ψ

(1−δ)ρG+2ρδs

(H −G) dF (ψ) . (14)

Suppose now wg < wd − s. If σ = c, as in Case 1 above, the entrepreneur obtains ex post

a payo� δ (wg +G+ s− wd)− ψ if a = c and δ (wg +G+ s− wd) otherwise. Hence, a = c is

chosen if and only if

δ (wg +G+ s− wd)− k − ψ ≥ max [δ (wg +G− wd)− (2ρ− 1) δs− k, 0] .

If k < δ (wg +G− wd) − (2ρ− 1) δs, a quantity F (2ρδs) chooses a = c and the remainder

chooses a = n. As a consequence, it is locally optimal to set wg = 0 and wd = s + ε, where

35

ε > 0 and arbitrarily close to zero. Social welfare is equal to:

W =

ˆ 2ρδs+ε

0

G− ψdF (ψ) +

ˆ ψ

2ρδs+ε

(G−H) dF (ψ) . (15)

If k ≥ δ (wg +G− wd) − (2ρ− 1) δs, the quantity of compliant entrepreneurs

F (δ (wg +G+ s− wd)− k). The remainder does not participate. Given that wg + s < wd, it

is socially optimal to set wg = 0 and wd = s+ ε, so social welfare is equal to:

W =

ˆ δG−k

0

G− ψdF (ψ) (16)

Optimal incentive scheme

We have up to now identi�ed several local optima. To �nd the optimal incentive scheme, we

need to compare the value function W in expressions (12) - (16) above. Simple comparison

suggests that (14) dominates (15). Hence, the latter can be ignored. Comparing (12) and

(13) to (15) and (16), it can easily be seen that social welfare W is weakly higher in the �rst

couple of expressions than in the second one, except if the cost of public funds λ is large. We

will assume that λ is close enough to one that (12) and (13) dominate (15) and (16). Thus,

the optimal incentive scheme is found comparing (12) to (14) when k < (1− ρ) δ2s, and (13)

to (14) otherwise.

Suppose that k < (1− ρ) δ2s. It is optimal to allow bribery but prevent extortion, i.e. set

wd = s and wg = 0 if and only if

ˆ (1−δ)ρG+2δρs

0

G− ψdF (ψ)−ˆ ψ

(1−δ)ρG+2ρδs

(H −G) dF (ψ) ≥

ˆ ρδ2s

0

G− ψdF (ψ)− (1− ρ)

ˆ ψ

ρδ2s

(H −G) dF (ψ)− (λ− 1) (G− s) ρ (1− F (δρ2s)) ,

which we can rearrange to obtain

ˆ ψ

ρδ2s

G−ψdF (ψ)+(λ− 1) (G− s) ρ (1− F (δρ2s)) ≥ H

(ˆ ψ

(1−δ)ρG+2ρδs

dF (ψ)− (1− ρ)

ˆ ψ

ρδ2s

dF (ψ)

).

The left hand side of the above expression is strictly positive. As for the right hand side, it is

positive if and only if

ρ ≥ F ((1− δ)ρG+ δρ2s)− F (δρ2s)

1− F (δρ2s).

36

Thus, if the above holds, there exists a threshold ¯H such that when H ≤ ¯H, allowing birbery

but �ghting extortion is optimal. Summing up, if k < (1− ρ) δ2s, wd = s and wg = 0 (�ght

extortion, allow bribery) is optimal if and only if H ≤ ¯H when ρ ≥ F ((1−δ)ρG+δρ2s)−F (δρ2s)1−F (δρ2s)

, or

if ρ < F ((1−δ)ρG+δρ2s)−F (δρ2s)1−F (δρ2s)

.

Suppose now that k ≥ (1− ρ) δ2s. To �nd the optimal incentive scheme, we need to

compare (13) to (14). We have thus that wd = s and wg = 0 (allow bribery, �ght extortion)

is optimal if

ˆ (1−δ)ρG+2δρs

0

G− ψdF (ψ)−ˆ ψ

(1−δ)ρG+2ρδs

(H −G) dF (ψ) ≥ˆ 2δρs

0

G− ψdF (ψ)

which can be rearranged to get

G (1− F (2δρs))−´ (1−δ)ρG+2δρs

2ρδsψdF (ψ)

(1− F ((1− δ) ρG+ 2δρs))≥ H.

Hence, it is optimal to have wd = s and wg = 0 ifG(1−F (2δρs))−

´ (1−δ)ρG+2δρs2ρδs ψdF (ψ)

(1−F ((1−δ)ρG+2δρs))≡ ¯H ≥ H.

Communication with entrepreneur

Noncooperative Game. We begin by stating the outcome of the noncooperative game so

as to compute status-quo payo�s. Since b > c, entrepreneurs complain when their requests

are denied. Thhus, if σ = C, o�cials grant permits if and only if wg ≥ wd0 − s. If σ = N ,

o�cials deny permits if and only if wd0 ≥ wg − s. This gives rise to three possible outcomes:

1. Case I: wg > wd0 + s. O�cials grant permits ∀σ.

2. Case II: wd0 + s > wg > wd0 − s. O�cials grant permits if and only if σ = C.

3. Case III: wd0 − s > wg. O�cials deny permits ∀σ.

Cooperative Game. A given entrepreneur/o�cial pair's aggregate payo� is given by:

U + V =

wg +G− l (σ, a) s if a = g,

wd0 + b− c− l (σ, a) s if a = d & e = 0

wd1 − l (σ, a) s if a = d & e = 1,

,

where l (σ, a) = 1 if either �σ = c and a = d� or �σ = n and a = g�.

37

We consider in turn all 3 possible outcomes of the noncooperative game. We ignore cases

in which schedules of transfers lead to permits being systematically denied in equilibrium.

The associated level of welfare is bounded from above by zero, which is lower than what is

achieved under the derived optimal policy. Also, it can be shown that no schedule of wages

can lead to permits being granted when σ = N and denied when σ = C. We are therefore left

with three cases to consider:

1: wg +G > max [wd0 + b− c+ s, wd1 + s] =⇒ The coalition plays a = g for all σ.

2: wd1 − s < wg + G < wd1 + s & wd1 > wd0 + b − c =⇒ The coalition plays a = g if σ = C

and �a = d & e = 1� if σ = N .

3: wd0 − s + b − c < wg + G < wd0 + b − c + s & wd0 + b − c > wd1=⇒ The coalition plays

a = g if σ = C and �a = d & e = 1� if σ = N .

5.1 Case I: wg > wd0 + s

The outcome of the noncooperative game is such that o�cials grant permits ∀σ.Entrepreneurs' status-quo payo�s are then equal to G, while o�cials' is equal to wg− l (σ, g) s.

Suppose �rst that the government sets wages so that wg +G > max [wd0 + b− c+ s, wd1 + s].

No entrepreneur complies with safety regulations since:

G+ δ (wg +G− (G+ wg))− k − ψ ≥

ρ (G+ δ (wg +G− s− (G+ wg − s))) + (1− ρ) (G+ δ (wg +G− (G+ wg)))− k,

which simpli�es to −ψ ≥ 0. The associated level of social welfare is W = G − H −(λ− 1)wg − ρs, which is lower than zero since H > G.

Suppose now that the government sets wages so that wd1 − s < wg + G < wd1 + s and

wd1 ≥ wd0 + b− c. Again, no entrepreneur complies with safety regulations (and social welfare

is negative) since:

G− k − ψ ≥ ρ (G+ δ (wd1 − (wg +G− s))) + (1− ρ)G− k,

which simpli�es to −ψ ≥ ρδ (wd1 − (wg +G− s)) . Again, since H > G, this schedule of

wages cannot be socially optimal.

38

Finally, suppose the government sets wages so that wd0 +b−c−s < wg+G < wd0 +b−c+s

and wd1 < wd0 + b − c. Again, no entrepreneur complies with safety regulations (and social

welfare is negative) since:

G− k − ψ ≥ ρ (G+ δ (wd0 + b− c− (wg +G− s))) + (1− ρ)G− k,

which simpli�es to −ψ ≥ ρδ (wd0 + b− c− (wg +G− s)) .

5.2 Case II: wd0 + s ≥ wg ≥ wd0 − s

Here, in the noncooperative game, o�cials grant permits if and only if σ = C. The

entrepreneurs' status-quo payo� is then either equal to G or b− c depending on σ. Similarly,

the o�cials' status quo payo� is either wg or wd0 depending on σ.

5.2.1 wg +G > max [wd0 + b− c+ s, wd1 + s]

The government designs the schedule of wages so that, in equilibrium, permits aresystematically granted, even when σ = N . An entrepreneur complies with safety regulationsif and only if:

G− ψ ≥ ρ (b− c+ δ (wg +G− s− (wd0 + b− c))) + (1− ρ)G,

which simpli�es to: A ≡ ρ ((1− δ)G− (1− δ) (b− c)− δ (wg − s− wd0)) ≥ ψ. The

government chooses {wg, wd0, wd1} to maximize:

W =

ˆ A

0

(G− ψ) dF (ψ) +

ˆ ψ

A

(G−H) dF (ψ)− (λ− 1)wg − (1− F (A)) ρs s. t. (17)

wg − s < wd0 < wg + s, (18)

wd0 < wg +G− (b− c+ s), (19)

wd1 + s < wg +G. (20)

Note that (17) is increasing in wd0. We proceed by assuming that only the second inequality

in expression (18) is binding, and verify later that the other constraints hold. Substituting

wd0 = wg + s− ε into (17), where ε > 0, yields:

39

W =

ˆ A

0

(G− ψ) dF (ψ) +

ˆ ψ

A

(G−H) dF (ψ)− (λ− 1)wg − (1− F (A)) ρs (21)

where A = ρ ((1− δ) (G− (b− c)) + δ2s− δε). It is then strictly optimal to set wg = 0

and weakly optimal to set wd1 = 0. One can verify that all constraints hold as long as

b− c < G− 2s.

5.2.2 wd1 − s < wg +G < wd1 + s & wd1 ≥ wd0 + b− c

Under this schedule of wages, the government induces, in equilibrium, permits to be granted

when σ = C, and denied when σ = N . In addition, entrepreneurs do not complain when their

request for a permit is unsuccessful. An entrepreneur complies with safety regulations if and

only if:

G− ψ − k ≥ ρ (b− c+ δ (wd1 − (wd0 + b− c))) + (1− ρ)G− k,

which simpli�es to A ≡ ρ (G− (1− δ) (b− c)− δ (wd1 − wd0)) ≥ ψ. The government

chooses {wg, wd0, wd1} to maximize:

W =

ˆ A

0

(G− ψ) dF (ψ) +

ˆ ψ

A

(1− ρ) (G−H) dF (ψ) (22)

− [F (A) + (1− F (A)) (1− ρ)] (λ− 1)wg − (1− F (A)) ρ (λ− 1)wd1 s.t.

wd1 − s < wg +G < wd1 + s, (23)

wd1 > wd0 + b− c, (24)

wd0 − s < wg < wd0 + s. (25)

First, one immediately derives that ∂W∂wg

< 0 since A is independent of wg. Also,

∂W

∂wd1

= [G− A− (1− ρ) (G−H) + ρ (λ− 1)wg + ρ (λ− 1)wd1] f(A)∂A

∂wd1

− (1− F (A)) ρ (λ− 1) .

40

Using the fact that G− A = (1− ρ)G+ ρ ((1− δ) (b− c) + δ (wd1 − wd0)) , we have

∂W

∂wd1

= [(1− ρ)H + ρ ((1− δ) (b− c) + δ (wd1 − wd0)) + ρ (λ− 1) (wg + wd1)] f(A)∂A

∂wd1

− (1− F (A)) ρ (λ− 1) .

Since (i) ∂A∂wd1

< 0 and (ii) all terms within the bracket are positive, it follows that ∂W∂wd1

< 0.

Expression (22) is decreasing in wg and wd1. We anticipate that the �rst inequality in

expression (25) and the second inequality in expression (23) bind, and verify later that the other

constraints hold. Since G−2s > b−c, and since wg > wd0−s, we have wg+G−s > wd0 +b−cnecessarily. Now, suppose that wd0 − s < 0, so that wg = 0. Welfare is then equal to:

W =

ˆ A

0

(G− ψ) dF (ψ) +

ˆ ψ

A

(1− ρ) (G−H) dF (ψ)− (1− F (A)) ρ (λ− 1) (G− s) , (26)

where A = ρ ((1− δ)G− (1− δ) (b− c) + δ (s+ wd0)). Since A is increasing in wd0, expression

(22) is also increasing in wd0. Hence, it is optimal to have wd0 = s− ε, as well as wg = 0 and

wd1 = G− s+ ε.

Suppose instead that wd0 − s > 0. Hence, wg = wd0 − s. The objective function becomes:

W =

ˆ A

0

(G− ψ) dF (ψ)+

ˆ ψ

A

(1− ρ) (G−H) dF (ψ)−[F (A) + (1− F (A)) ρ] (λ− 1) (wd0 − s)

(27)

− (1− F (A)) ρ (λ− 1) (G− 2s+ wd0)

with A = ρ ((1− δ)G− (1− δ) (b− c) + δ2s), which is independent of wd0. Therefore,

expression (27) is strictly decreasing in wd0 and the government optimally sets wd0 = s + ε.

Finally, it follows that wg = 0 and wd1 = G− s. It is therefore optimal for the government to

set wd0 = s, wg = 0, and wd1 = G− s, and the achieved level of social welfare is identical (up

to an epsilon) to (26).

5.2.3 wd0 + b− c− s < wg +G < wd0 + b− c+ s and wd1 < wd0 + b− c

The government cannot induce this behavior as it cannot jointly satisfy inequality wg + G <

wd0 + b− c+ s and inequality wg ≥ wd0 − s.

41

5.3 Case III: wd0 − s > wg

When wd0 − s > wg, the entrepreneurs' status-quo payo� is equal to b − c, while the

o�cials' is equal to wd0. To begin with, suppose the government sets wages so that

wg+G > max [wd0 + b− c+ s, wd1 + s], i.e., in equilibrium permits are systematically granted.

An entrepreneur complies with safety regulations if and only if:

b− c+ δ (G+ wg − (wd0 − s+ b− c))− ψ ≥

ρ (b− c+ δ (G+ wg − s− (wd0 − s+ b− c))) + (1− ρ) (b− c+ δ (G+ wg − (wd0 − s+ b− c))) ,

which simpli�es to ρδs ≥ ψ. The proportion of entrepreneurs who comply with safety

regulations is independent of wages, so that it optimal to set wd0 = s + ε, wg = wd1 = 0, and

the associated level of Welfare is:

W =

ˆ ρδs

0

(G− ψ) dF (ψ) +

ˆ ψ

ρδs

(G−H) dF (ψ)− (1− F (ρδs)) ρs

Suppose now that the government sets wages so that wd1 − s < wg + G < wd1 + s and

wd1 ≥ wd0 + b − c. Permits are granted when σ = C, and denied when σ = N . In addition,

entrepreneurs do not complain when their request is unsuccessful. Here, an entrepreneur

complies with safety regulations if and only if:

b− c+ δ (wg +G− (wd0 + b− c− s))− ψ ≥

ρ (b− c+ δ (wd1 − (wd0 + b− c))) + (1− ρ) (b− c+ δ (wg +G− (wd0 + b− c− s))),

which simpli�es to: A = ρδ (wg +G+ s− wd1) ≥ ψ. Welfare is equal to:

W− =

ˆ A

0

(G− ψ) dF (ψ) +

ˆ ψ

A

(G−H) dF (ψ) (F (A) + (1− FA) (1− ρ)) (λ− 1)wg

− (1− F (A)) ρ (λ− 1)wd1.

The government �nds it optimal to set wd0 = s + ε ,wd1 = wg + G − s and wg = 0. All

constraints are satis�ed and welfare is equal to:

42

W =

ˆ ρδ2s

0

(G− ψ) dF (ψ) +

ˆ ψ

ρδ2s

(G−H) dF (ψ)− (1− F (ρδ2s)) ρ (λ− 1) (G− s)

Finally, suppose the government chooses wages so that wd0+b−c−s < wg+G < wd0+b−c+sand wd1 < wd0 + b − c. Permits are granted when σ = C, and denied when σ = N .

Entrepreneurs complain when their request is denied. Here, an entrepreneur complies with

safety regulations if and only if:

b− c+ δ (wg +G− (wd0 + b− c− s))− ψ ≥

ρ (b− c+ δ (wd0 + b− c− (wd0 + b− c))) + (1− ρ) (b− c+ δ (wg +G− (wd0 + b− c− s))),

which simpli�es to A = ρδ (wg +G− (wd0 + b− c− s)) ≥ ψ. Social Welfare is given by:

W =

ˆ A

0

(G− ψ) dF (ψ) +

ˆ ψ

A

(G−H) dF (ψ)− (F (A) + (1− F (A)) (1− ρ)) (λ− 1)wg

− (1− F (A)) ρ (λ− 1)wd0

The highest possible level of compliance that can be achieved is equal to ρδ2s (since

wg + G ∈ [wd0 + b− c− s, wd0 + b− c+ s]). Suppose this level of compliance is achieved. It

is then optimal to set wg = 0 and wd0 = G − (b− c) − s + ε. One can then verify that all

constraints hold, and that compliance is indeed equal to ρδ2s. Since the payment b − c is

made in equilibrium, Social Welfare is given by:

W =

ˆ ρδ2s

0

(G− ψ) dF (ψ) +

ˆ ψ

ρδ2s

(G−H) dF (ψ)− (1− F (ρδ2s)) ρ (λ− 1) (G− s+ ε)

The last step of the proof involves comparing welfare levels. It turns out that only two

policies are relevant: those of case II.1 and case II.2. One derives that the wage schedule

associated with case II.2 is optimal if and only if H ≥ λ (G− s).

43

Proof of Lemma 1

Let us maximize Eψ (V ), as described in equation..., with respect to p. We will begin by

proceeding piecewise. If r ≥ p, it is optimal to set p = r. If ρG + r > p > r, the optimal

p maximizes (1− F (p− r)) · (p− s), so p = ψ+s+r2

. Note that ψ+s+r2

> r since ψ > r − s

by assumption. Hence, p = ψ+s+r2

is a local maximizer only if r > ψ − 2ρG + s. Finally,

ρG+ r ≤ p is also a local maximizer.

We can now proceed to identifying the global maximizer of Eψ (V ). When p = r,

Eψ (V ) = r. When p = ψ+s+r2

, Eψ (V ) =

[(ψ+r

2

)2

− s2

4

]1ψ(but recall that this is feasible

only if r > ψ − 2ρG + s). When ρG + r ≤ p, then Eψ (V ) =(ψ−ρGψ

)· (ρ (G− s)). By

comparing the three local maxima we identi�ed, we obtain that when r > ψ − 2ρG + s,

the global maximizer is p = ψ+s+r2

. Otherwise, the global maximizer is ρG + r ≤ p. As a

result, using (8) we get that if r > ψ − 2ρG + s, the fraction of compliant entrepreneurs is

F ( ψ+s+r2− r) = F ( ψ+s−r

2), while the remainder buys a permit through the intermediary. If

instead r ≤ ψ−2ρG+s, the fraction of compliant entrepreneurs is F (ρG) , while the remainder

does not comply but is active.

Proof of Proposition 3

Using Lemma 1, when r > ψ − 2ρG+ s social welfare is

W =

ˆ ψ+s−r2

0

G− ψdF (ψ)−ˆ ψ

ψ+s−r2

(H −G) dF (ψ)− (λ− 1)wg − r(

1− F(ψ + s− r

2

)).

It is immediately seen that it is optimal to set wg = 0 and, since (5) has to hold, wd = 0 as

well. Hence,

W =

ˆ ψ+s−r2

0

G− ψdF (ψ)−ˆ ψ

ψ+s−r2

(H −G) dF (ψ)− r(

1− F(ψ + s− r

2

)). (28)

Suppose now that R ≤ ψ − 2ρG+ s. Using Lemma 1, social welfare is

W =

ˆ ρG

0

G− ψdF (ψ)−ˆ ψ

ρG

(H −G) dF (ψ)− (λ− 1)wg − r.

44

Again, it is optimal to set wg = wd = 0. Hence,

W =

ˆ ρG

0

G− ψdF (ψ)−ˆ ψ

ρG

(H −G) dF (ψ)− r. (29)

Since r > ψ− 2ρG+ s⇔ ψ+s−r2

< ρG, when r > ψ− 2ρG+ s, there exists a threshold H such

that (28) is strictly smaller than (29) if and only if H > H. Furthermore, it is easily seen that

this threshold increases with r. When instead r ≤ ψ − 2ρG + s, (28) is always strictly larger

than (29).

Proof of Proposition 4

Assume that the government sets wd0 ≥ G − s > wd1 = wg = 0 and b = ε > 0 (arbitrarily

small). We will begin by studying the game played by entrepreneur and o�cial when A = c, n.

Next, we will analyse the game when A = i. Subsequently, we will consider the incentives of

the o�cial when setting p and, ultimately, the decisions made by entrepreneurs in equilibrium

and social welfare. As a �nal step, we will compare the level of social welfare attained with

the case of Proposition 4.

Direct interaction between o�cial and entrepreneur (A = n, c). Suppose the game

is played noncooperatively. When σ = c, the o�cial obtains 0 if D = g and −s otherwise

(as the entrepreneur complains for a denied permit). When σ = n, the o�cial obtains −swhen D = g and 0 otherwise (as the entrepreneur complains for a denied permit). It follows

that the outcome of the noncooperative game is such that when σ = c we have D = g, the

o�cial obtains 0 and the entrepreneur obtains G. When σ = n, the o�cial obtains 0 and the

entrepreneur obtains b = ε.

Consider now the cooperative game between o�cial and entrepreneur. Suppose σ = c.

Given that the entrepreneur obtains G in the noncooperative game, and that t > −G by

assumption, it is easily veri�ed that the o�cial cannot do better than simply propose t = 0

and D = g to the entrepreneur. Hence, when σ = c we have D = g, the entrepreneur obtains

G and the o�cial 0. Suppose now that σ = n. Given that the entrepreneur obtains ε in

the noncooperative game, the o�cial will propose t = −ε and D = d, 0 to the entrepreneur.

Hence, when σ = n we have D = d, 0, the entrepreneur obtains ε and the o�cial wd,0.

Interaction with intermediary (A = i). If the entrepreneur chooses the o�cial sells the

permit to the intermediary at price p. The o�cial therefore obtains p−s and the entrepreneur

45

G− k − p.

Price setting by o�cial. Given the above, we can write the incentive compatibility

constraint of an entrepreneur of type ψ as

G− ψ − r − k ≥ max [(1− ρ)G+ ρε− k − r;G− k − p; 0] .

Making use of this constraint, and recalling that wg = 0, we can write the ex ante payo� of

an o�cial, conditionally on p, as follows

Eψ (V ) =

p− s if r ≥ p

(1− F (p− r)) · (p− s) if ρG+ r > p > r

(1− F (ρG− ε)) · (ρ (wd,0 − ε)) if p ≥ ρG+ r.

Piecewise maximization of Eψ (V ) yields the following result. If r ≥ p, the local maximizer is

p = r. If ρG+ r > p > r, it is p = ψ+s+r2

. Note that ψ+s+r2

> r since ψ > r− s by assumption.

Hence, p = ψ+s+r2

is a local maximizer only if r > ψ − 2ρG + s. Finally, ρG + r ≤ p is also a

local maximizer. We can now proceed to identifying the global maximizer of Eψ (V ). When

p = r, Eψ (V ) = r. When p = ψ+s+r2

, Eψ (V ) =

[(ψ+r

2

)2

− s2

4

]1ψ(but recall that this is

feasible only if r > ψ − 2ρG + s). When ρG + r ≤ p, Eψ (V ) =(ψ−ρG+ε

ψ

)· (ρ (wd,0 − ε)). By

comparing the three local maxima we identi�ed, we obtain the following:

- Suppose r > ψ − 2ρG+ s. If wd,0 <

(ψ+r

2

)2− s2

4

ρ(ψ−ρG+ε)+ ε, the global maximizer is p = ψ+s+r

2. If

wd,0 ≥(ψ+r

2

)2− s2

4

ρ(ψ−ρG+ε)+ ε, the global maximizer is ρG+ r ≤ p.

- Suppose R ≤ ψ − 2ρG+ s, the global maximizer is ρG+ r ≤ p.

Behavior of entrepreneurs in equilibrium and social welfare. From the above

paragraph, we can conclude the following. If r > ψ − 2ρG + s and wd,0 <

(ψ+r

2

)2− s2

4

ρ(ψ−ρG+ε)+ ε,

the fraction of compliant entrepreneurs is F ( ψ+s−r2

) , while the remainder buys a permit

through the intermediary. If r ≤ ψ − 2ρG + s or if wd,0 ≥(ψ+r

2

)2− s2

4

ρ(ψ−ρG+ε)+ ε, the fraction of

compliant entrepreneurs is F (ρG − ε) , while the remainder does not comply but is active.

The noncompliant obtain a permit only if σ = c, which happens with probability 1− ρ.

46

As a result, when r ≤ ψ − 2ρG+ s, social welfare is

W =

ˆ ρG−ε

0

G− ψdF (ψ)− (1− ρ)

ˆ ψ

ρG−ε(H −G) dF (ψ)− (λ− 1)wd,0ρ (1− F (ρG− ε))− r.

Consider now the case where r > ψ − 2ρG+ s , we get that

W =

ˆ ψ+s−r2

0

G− ψdF (ψ)−ˆ ψ

ψ+s−r2

(H −G) dF (ψ)− r(

1− F(ψ + s− r

2

)), (30)

if wd,0 <

(ψ+r

2

)2− s2

4

ρ(ψ−ρG+ε)+ ε and

W =

ˆ ρG−ε

0

G− ψdF (ψ)− (1− ρ)

ˆ ψ

ρG−ε(H −G) dF (ψ)− (λ− 1)wd,0ρ (1− F (ρG− ε))− r

(31)

if wd,0 ≥ max

[(ψ+r

2

)2− s2

4

ρ(ψ−ρG+ε)+ ε;G− s

]. Noting that ε is arbitrarily small, r > ψ − 2ρG + s

implies that the fraction of compliant entrepreneurs is unambiguosly larger in the latter case.

Hence, there must exist a threshold H such that (30) is smaller than (31) if and only if H < H.

Note that (30) is the same as (28). The claim follows.

47