Extortion and Political-Risk Insurance Fr´ed´eric Koessler

†

∗

Ariane Lambert-Mogiliansky

‡

September 9, 2014

Abstract We consider the problem faced by firms operating in a foreign country characterized by weak governance. Our focus is on extortion based on the threat of expropriation and bureaucratic harassment. The bureaucrat’s bargaining power is characterized by a general extortion mechanism adapted from the optimal auction theory in Myerson (1981). This characterization is used to analyze the determinants of the quality of governance and whether and how this is improved by political-risk insurance. This insurance reduces the bureaucrat’s total revenue from corruption, but may also increase the risk of expropriation and extortion bribes. The analysis allows us to derive some policy recommendations with respect to public intervention in the political-risk insurance sector. Keywords: Auctions; corruption; expropriation; extortion; governance; harassment; mechanism design; political-risk insurance. JEL: D44, D73, D82, F21, G22, H23.

1

Introduction

With the advent of the UK Bribery Act 2010, the issue of how corruption can be resisted has become central for firms. Under the new regime there is increased jurisdictional scope and greater criminal exposure for corporate entities. In this context, a number of Multi-National Corporations (MNCs) have complained about “passive bribery”: the request for bribes by public officials. The firms’ claim here is that they are prosecuted when they are actually themselves the victims of extortion. In response to the risks that foreign firms face when operating in countries with weak governance, particular insurance contracts called political-risk insurance (PRI) have been developed and are currently provided by both private and public entities.1 While the issue of extortion has recently become a major concern for MNCs, public international-aid agencies have over the past few decades officially made the fight against corruption a central priority. One question of interest ∗

We are grateful to Jean-Edouard Colliard, Philippe Jehiel, Vasiliki Skreta, Daniel Villar, and especially Kai Konrad, Laurent Lamy and the anonymous referees for useful comments and suggestions. Financial support from MIGA (World Bank Group) is gratefully acknowledged. † Paris School of Economics – CNRS, [email protected] ‡ Paris School of Economics, [email protected] 1 In most developed countries, public agencies have programs providing guarantees to protect national firms’ investments through political-risk insurance as part of their development aid policy. The World Bank’s Mutual Investment Guarantee Agency (MIGA) complements government-sponsored and private guarantee programs.

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is then whether there is any rationale for public intervention in the PRI sector. In this article we set out a general theoretical model which allows us to consider extortion mechanisms and understand the impact of political-risk insurance on the quality of governance in the country where the investment is based. In a series of surveys of corporate officials commissioned by MIGA (the Multilateral Investment Guarantee Agency, World Bank Group), businessmen say that they are very concerned by political risks. Among those risks two stand out: the breach of contractual obligations by the state and expropriation (regulatory takings, creeping expropriation and outright nationalization; see MIGA 2011).2 In MIGA’s 2009 political risk survey, nearly 45% of respondents mention political risk as the greatest constraint on their business in emerging markets. When asked about the ways in which firms attempt to mitigate the risks, nearly 70% of respondents in Russia reply “engagement with the government”, 65% in India and 55% in China.3 The expression “engagement with the government” is an euphemism for all kinds of influence and corrupt activities. The firms thus report being forced into corruption in order to mitigate some risks, and in particular to avoid expropriation and bureaucratic harassment.4 Although this issue thus represents a serious concern for business and a challenge for development aid, it has received only little attention in the economic literature. Most often the knowledge and understanding of extortion has remained at the level of anecdotes and case studies. This article proposes a framework for the better understanding of the mechanisms at play in the extortion of foreign firms operating in countries with weak governance. We develop a model where public officials can threaten to abuse their power by extracting rents from a number of privately-informed firms. This latter number of firms is typically greater than the number of firms that the public official will actually be able to harm. We are interested here in how the official exploits their limited nuisance power via competition between the potential victims. The first motivation for this approach is empirical. In the surveys mentioned above, extortion affects significantly more firms than could actually suffer from expropriation (we hereafter will use the term “expropriation” to refer to both expropriation and harassment). As such, the expropriation of all firms is not a credible option for the host country. The second rationale is that by setting firms in competition with each other, the gains to the bureaucrat from a given nuisance power are typically larger than when focusing exclusively on the firms that he can actually harm. We capture this feature by distinguishing between the number of foreign firms operating in the country and the number of firms the bureaucrat can expropriate via a “political” constraint on the bureaucrat. There are a number of ways of motivating this political constraint. One, in the spirit of racketeering, is that the bureaucrat has only limited time and resources to expropriate or harass firms, so that the threat of expropriating them all is not credible. A second is that the degree of expropri2

Political risk also includes the risks due to war and terrorism. The alternatives were joint-ventures, risk analysis, and third-party intermediation. 4 Bureaucratic harassment includes arbitrary changes in contract conditions or the creation of obstacles to the firm’s activity by various means (e.g., blocking access to electricity or water, requesting numerous permits, delaying authorizations, and so on). 3

2

ation is perceived as a signal of the extortionary pressure in the country, i.e., of the size of bribes. Greater extortionary expectations (analogously to tax pressure) will deter firms from investing in the country. Finally, the political constraint is a convenient and tractable way of introducing competition between firms and limiting the bargaining power of the bureaucrat. We closely follow Myerson (1981) in the characterization of the optimal extortion mechanism. The underlying idea is that the situation is analogous to an auction. The bureaucrat sells promises to “leave the firm alone” in exchange for a bribe. At first sight, this setting differs from that in Myerson (1981) in a number of respects. First, the bureaucrat can sell as many promises as he wants. Second, he may be forced to sell at least a certain number of these promises via the political constraint. Third, the bureaucrat’s valuation of these promises depends on the characteristics of the firms which do not receive it, i.e., which are expropriated. Last, the firm’s outside option may dependent on its private information. Nevertheless, we show that Myerson’s general model is almost directly applicable. This model covers very general situations in which the value (or cost) of expropriation for the bureaucrat varies across firms, and firms may be heterogeneous regarding their profits and insurance compensation. An optimal extortion mechanism is characterized by thresholds for non-expropriation and the size of the bribes firms pay to avoid expropriation. The optimal mechanism when firms are ex-ante symmetric is implemented by a simple auction-bribing game. Our first result is that the value to the bureaucrat of the expropriated assets (in the case of harassment, we are dealing with a cost) is, unsurprisingly, an important determinant of the quality of governance. We capture the latter via three indicators: expropriation risk, the bribe to avoid expropriation, and extortion revenue. We find that the greater the expropriation values the higher the reserve prices below which the bureaucrat will expropriate the firms and therefore the greater the risk of expropriation. When the political constraint does not bind, all firms that are not expropriated pay a reserve price (which is the same in the case of ex-ante symmetric firms, and firm-specific otherwise). Greater expropriation values then yield higher requested extortion bribes to avoid expropriation. Last, the bureaucrat’s revenue rises with the expropriation values both directly and indirectly through higher bribes. The second determinant of the quality of governance is the political constraint. By definition the political constraint limits the number of firms that can be expropriated, and therefore the risk of expropriation. However, we also show that this reduces the size of the bribes demanded to avoid being expropriated. The fewer firms there are that the bureaucrat can expropriate, the lower his revenue from corruption. The second part of the article introduces political-risk insurance. This is a guarantee of compensation for firms incurring losses due to an abuse of power by the bureaucrat. In line with common practice, this compensation is calculated as a weighted sum of a (possibly common-knowledge) investment and a (private-knowledge) random profit.5 The insurance contract is exogenous and 5

The main rule for MIGA is to insure the financial instruments, i.e. the equity investment or loans and loan guarantees. Financial instruments can be insured up to a value of 95 percent. In addition the revenue attributable

3

firms pay no premia. We hence leave the analysis of the market for PRI for future research. We instead consider both symmetric situations and general situations in which firms may have customized insurance contracts, and analyze the best reply to the whole range of (linear) contracts. We establish that the impact of a rise in the firm’s fixed insurance compensation on the overall risk of expropriation is always positive, but the impact of the marginal insurance compensation depends critically on the sign of the firm-specific value to the bureaucrat of abusing power. When the bureaucrat gains from exerting a threat, higher marginal insurance compensation always increases the risk.6 Otherwise, when expropriation is relatively costly for the bureaucrat, the risk falls with the marginal insurance compensation. Since our model covers situations with asymmetric firms, it also allows us to establish interesting results regarding the individual and cross effects of insurance. Higher insurance compensation for a given firm leads to a reallocation of risk between different firms. A greater fixed insurance compensation for a firm always increases the expropriation risk for that firm and, when the political constraint binds, reduces the expropriation risk for other firms. When the value to the bureaucrat of abusing power with respect to a certain firm is negative enough, a rise in that firm’s marginal insurance compensation always reduces its expropriation risk and, if the political constraint binds, increases the risk faced by the other firms. On the contrary, when the value to the bureaucrat of abusing power is positive, the impact of a rise in marginal insurance compensation varies across the interval of possible firm profits. It falls for low profits and rises for intermediate profits. This also implies that when the firm increases its marginal insurance compensation, the expropriation risk for other firms may rise or fall depending on the actual profit with the higher marginal insurance compensation. We next address the question of how insurance affects the size of extortion bribes. In a simple leading example the effect of a symmetric increase in the fixed or marginal insurance compensation is unambiguously “virtuous”, i.e., it reduces bribes. But we also show that increased marginal insurance compensation may have the opposite effect. We formulate general conditions under which the own extortion bribe always falls with own insurance. When the political constraint binds, greater insurance in one firm may yield higher bribes for the other firms. Last, we establish that a rise in the fixed or marginal insurance compensation always reduces the bureaucrat’s expected income from corruption, i.e. the optimal combination of expropriation and bribery. Our results yield new insights with respect to the rationale for public intervention in the PRI sector. In particular, subsidies for firm PRI purchase are justified when extortion is characterized by harassment or creeping expropriation. Similarly, we find clear support for public intervention to the investment can be insured for up to five times the value of the investment. Private insurance providers (members of the Bern Union) are known for their lack of transparency regarding contractual arrangements. The same two elements (financial instruments and revenue) are expected to be the basis of the compensation. See, e.g., the Investment Guarantee Guide http://www.miga.org/documents/IGGenglish.pdf. 6 This is consistent with the standard result in the insurance literature that, due to moral hazard, insurance increases risk, as the agent expends less effort to reduce the risk. In our context, the firm’s effort to reduce risk corresponds to paying bribes.

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targeting the recovery of expropriated assets from the host government. Other more nuanced implications are discussed in the concluding section. Related Literature.

There is currently a large economic literature on corruption.7 Extortion

has been addressed in the economics of organized crime, where a central concern has been the credibility of the threat. One example is Konrad and Skaperdas (1997, 1998), who emphasize the role of up-front investments in destructive capacity by criminal gangs in racketeering, and show that the game’s perfect equilibrium is characterized by both extortion and inefficient violence. Despite pervasive bureaucratic harassment of firms and citizens to extract rents in most developing and transition economies (with very significant social economic consequences: see, e.g., Klitgaard, 1988), there has been only little theoretical work on the microeconomics of extortion by public officials. An early contribution is McChesney (1987), who investigates the social economic cost of extortion in the context of a Stiglerian model of regulation where politicians can extract rents by threatening new legislation (the so-called “milk bills”). Few articles have addressed extortion based on the abuse of administrative power. One example is Hindriks et al. (1999), who consider the optimal tax-collection mechanism when officials can threaten to over-report income in order to extort bribes. Choi and Thum (2004) analyze extortion of one firm when the bureaucrat who issued the license can return and demand the renewal of the license in the second period. They show that there exists no pure strategy equilibrium in the repeated game, a feature that they interpret as a rationale for arbitrary behavior by bureaucrats. Lambert-Mogiliansky et al. (2007) also address extortion in licensing, but from a different perspective. They consider a track of bureaucrats, each of whom must give their approval in turn. This introduces a bureaucratic hold-up problem, whose socially-efficient and bribe-maximizing equilibria are analyzed. Expropriation is addressed in Thomas and Worrall (1994) via a model of the bilateral relationship between a MNC and a host country. The host country can expropriate the MNC via its sovereignty. The properties of self-enforceable contracts are considered in a multiple-period moral-hazard setting, where the firm provides transfers in return for being allowed to operate. These contracts are characterized by under-investment and delayed payment in an initial period. We here contribute to the literature by providing a general model of how bureaucrats can use competition to extort rents from more firms than can credibly be expropriated. A second contribution is to assess the impact of political-risk insurance on the quality of governance, and derive implications for public intervention in the PRI sector. The remainder of this article is organized as follows. The next section presents the analytical framework. We derive the optimal extortion mechanism, and provide comparative-static results for the quality of governance with respect to the expropriation value and the political constraint. In Section 3 we introduce political-risk insurance and determine the modified optimal extortion mechanism. Section 4 then investigates the impact of greater insurance compensation on the 7

See for example Rose-Ackerman (1999, 2006, 2011) and Mishra (2005).

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quality of governance. Last, the concluding section formulates some policy recommendations. The appendix contains some of the proofs.

2

Optimal Extortion Mechanism

2.1

Basic Model

Consider a set N = {1, . . . , n} of (risk-neutral) firms carrying out some activity in a weakgovernance country, and one (risk-neutral) bureaucrat (government official) who can demand a bribe from firms in exchange for not expropriating them. The term “expropriation” is used to refer to the expropriation of firms’ rents in a broad sense. This covers the expropriation of firm assets in the conventional sense of the divestment of ownership as well as “creeping expropriation” and harassment by means of regulatory and other measures. Let N0 = N ∪ {0} be the set of all players (the n firms and the bureaucrat). We analyze the expropriation risk, extortion bribes and the bureaucrat’s corruption revenue using a mechanism-design approach. This allows us to characterize the bargaining power of the bureaucrat as a function of a number of factors, including the degree of asymmetric information, the total number of firms, the political constraint and the expropriation values. We assume that the bureaucrat is not perfectly informed about the values that firms attach to non-expropriation. Were the bureaucrat to know each firm’s value perfectly, he would be able to fully extort them by threatening any non-obedient firm with expropriation. The optimal extortion mechanism is obtained by adapting the design of an optimal auction in Myerson (1981). The differences between our setting and his auction model are as follows: (i) The seller (bureaucrat) sells several goods (a “good” in our model being a guarantee against expropriation) and each buyer (firm) requires one good at most (each firm needs at most one guarantee not to be expropriated); (ii) The seller has some political constraint (PC) on the minimum number of goods he should sell (i.e. the bureaucrat may not be able to expropriate all firms); (iii) The seller’s valuation of a good depends on the types of the buyers who do not receive the good (i.e. the bureaucrat’s payoff from expropriation may depend on the values of the firms that are expropriated); (iv) With political-risk insurance, a buyer’s outside option may be type-dependent - a firm’s payoff when expropriated may depend on its type when compensation (according to the insurance contract) is type-dependent. Without extortion, each firm i’s profit from operating in the country is given by ti ∈ Ti ≡ [ai , bi ], where 0 ≤ ai < bi < +∞.8 Only firm i knows the true value of its profits or “type” ti . For simplicity we assume, as in Myerson (1981), that firm types are independently distributed. Let fi : Ti → R+ be the continuous density function of the types of i, and Fi the corresponding cumulative distribution 8

Note that we assume that firms always make positive profits. This is not restrictive provided that foreign firms can terminate their activity in the host country. This precludes the pathological cases in which a firm may prefer to be expropriated than to exert its property right over the assets.

6

function.9 When firm i is expropriated its payoff is independent of its type and is normalized to zero. By way of contrast, the expropriation value of firm i to the bureaucrat may depend on firm i’s type, and is denoted by ei (ti ) ∈ R. We allow for negative expropriation values, for example if the bureaucrat incurs a reputation or harassment cost. The function ei (·) is assumed to be continuous, but not necessarily monotonic. A (direct-revelation) mechanism is given by outcome functions p : T → [0, 1]n and x : T → Rn+ . Given a profile of announced types t = (t1 , . . . tn ), pi (t) is the probability of not expropriating firm i and xi (t) is the expected amount of money, or bribes, paid by firm i. As in Myerson (1981), the optimal mechanism will turn out to be deterministic. Given a mechanism (p, x) the (interim) expected utility of firm i when its type is ti ∈ Ti is given by Ui (p, x; ti ) =

Z

(ti pi (t) − xi (t)) f−i (t−i )dt−i ,

(1)

T−i

and the (ex ante) expected utility of the bureaucrat is U0 (p, x) =

Z

T

X

!

(1 − pi (t))ei (ti ) + xi (t) f (t)dt.

i∈N

(2)

A mechanism is feasible if it satisfies both the individual-rationality (IR) constraint Ui (p, x; ti ) ≥ 0,

for all i ∈ N,

and the incentive-compatibility (IC) constraint Z (ti pi (si , t−i ) − xi (si , t−i )) f−i (t−i )dt−i , Ui (p, x; ti ) ≥

(3)

for all i ∈ N, si , ti ∈ Ti .

(4)

T−i

Condition (3) implies that firms cannot be forced to participate in the mechanism: they should receive an (interim) expected payoff which is at least the expected payoff obtained when they are expropriated with probability one (in which case their expected payoff would be zero). Condition (4) implies that firms have no incentive (at the interim stage) to misreport their type to the bureaucrat when they expect that all other firms will truthfully report their type. In addition to these standard constraints, there is also a political constraint: the bureaucrat is required to expropriate at most K ∈ {1, . . . , n} firms, so that X

pi (t) ≥ n − K,

for all t ∈ T.

(5)

i∈N 9

Note that even if the bureaucrat does not exactly know each firm i’s profits, we do not exclude that the bureaucrat receive some signal about firm profits; indeed, the distribution Fi could be interpreted as capturing the residual uncertainty about firm i’s value after the observable components (e.g., the physical capital) have been observed by the bureaucrat.

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The particular case in which there is no political constraint is simply K = n. The political constraint is a key determinant of the bureaucrat’s bargaining power. This reflects that expropriations are both resource- and time-consuming; it also allows us to introduce competition in bribes between firms in a tractable way. We below characterize the bureaucrat’s revenue when he optimally exploits this competition. Main assumptions discussed.

A central assumption that we make is that the firms are captive

in the host country and we adopt a static mechanism design approach. This allows to explicitly characterize the optimal extortion mechanism and to provide comparative statics results on the impact of insurance. We consider that the richness of the extortion issue deserves a truly general treatment. A limit to this approach is that we leave many important issues for further research including firms’ choice of insurance coverage and entry decision, issues that call for a dynamic approach. In the last section, we discuss how we expect dynamic considerations to affect our main results. The assumption about the bureaucrat’s ability to commit to the mechanism is standard in the mechanism design literature. And assuming that illegal deals are enforceable is a standard assumption in the literature on corruption. It is motivated either by appealing to illegal enforcement by criminal groups or to a community enforcement argument, i.e., to the (implicit) repeated character of the interaction.

2.2

Feasible and Optimal Mechanisms

The objective of the bureaucrat is to choose the mechanism (p, x) that maximizes his expected payoff U0 (p, x) under the IR constraint (3), the IC constraint (4) and the PC (5). Following the characterization in Myerson (1981) exactly, the optimal mechanism is given by xi (t) = pi (t)ti − and p : T → [0, 1]n that maximizes Z X T

Z

ti

pi (si , t−i )dsi ,

(6)

ai

 1 − Fi (ti ) ti − ei (ti ) − pi (t)f (t)dt, fi (ti ) i∈N | {z } ci (ti )

subject to the PC (5) and the monotonicity constraint of the interim probability that firm i of type ti is not expropriated. The expression ci (ti ) = ti − ei (ti ) −

R

T−i pi (t)f−i (t−i )dt−i 1−Fi (ti ) fi (ti ) is referred to

as the virtual valuation of firm i. This includes the true type ti minus a term related to the firm’s information rents

1−Fi (ti ) fi (ti )

minus the value of not selling the promise, i.e. of expropriating that firm,

ei (ti ). In the remainder of the article we make the following standard regularity assumption, which guarantees that the state-by-state maximization of the above program implies that pi (ti , t−i ) rises in ti , and thus that the monotonicity condition is satisfied. This assumption requires, in particular, 8

that the bureaucrat’s expropriation value does not rise too fast in the firm’s type.10 Assumption 1 (Regularity) For every i ∈ N the virtual valuation of firm i, ci (ti ) = ti − ei (ti ) −

1 − Fi (ti ) , fi (ti )

(7)

is strictly increasing in ti . Under regularity we immediately obtain the following characterization of the optimal mechanism: Proposition 1 (Optimal Extortion without Insurance) Under regularity, the optimal extortion mechanism (p, x) is such that p : T → [0, 1]n maximizes X

ci (ti )pi (t) subject to n − K ≤

i∈N

X

pi (t) ≤ n for all t ∈ T,

i∈N

where the virtual valuation ci (ti ) of firm i is given by (7): pi (t) = 0 for the firms with the (up to) K lowest virtual valuations below 0, and pi (t) = 1 for the others. The payment of firm i to the bureaucrat is given by the xi (t) defined in (6). For any finite set {x1 , x2 , . . .} of real numbers, denote by minK i xi the Kth-smallest element of this set. That is, if x1 ≤ x2 ≤ · · · ≤ xK ≤ · · · , then minK i xi = xK . Let yi (t−i ) = min{si ∈ Ti : ci (si ) ≥ 0 or ci (si ) ≥ minK cj (tj )}, j6=i

(8)

be the smallest type of firm i such that firm i is not expropriated when other firm types are given by t−i . The optimal mechanism can therefore be reformulated as follows: ( ( yi (t−i ) if ti > yi (t−i ), 1 if ti > yi (t−i ), and xi (t) = pi (t) = 0 if ti < yi (t−i ). 0 if ti < yi (t−i ),

(9)

For each firm i the optimal mechanism involves a (possibly firm-specific) threshold value c−1 i (0) for non-expropriation which is determined so that the virtual valuation of firm i equals zero. This threshold value plays a role similar to that of the reserve price in optimal auction mechanisms, and is chosen by the bureaucrat in order to maximize expected revenue. When the bureaucrat has no political constraint (K = n) he never sells a promise not to expropriate a firm for a bribe below that threshold value. He sells each firm i a promise not to expropriate at price c−1 i (0), and if firm i does not pay it is expropriated. When the bureaucrat cannot expropriate as many firms as he wishes, i.e. when he is forced to sell a promise of non-expropriation to at least n − K firms, he cannot obtain the threshold values from all non-expropriated firms. Instead, he will reduce the bribe for a 10 When the regularity assumption is not satisfied, the optimal mechanism involves some bunching. The same techniques as introduced by Myerson (1981, Section 6) can be used in this case. A case with bunching is illustrated in an example with insurance in Section 3; see also the discussion following Assumption 2.

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non-expropriated firm i to yi (t−i ) as given by Equation (8), i.e. the highest bribe acceptable to the lowest non-expropriated firm i’s type. As a result, the role of the threshold value in the extortion mechanism will become more limited the tighter is the PC (the smaller is K) and the greater the total number of firms. When firms are ex-ante symmetric, i.e. ei (·) = ej (·) and fi (·) = fj (·) for every i, j ∈ N , we denote by t0 = c−1 i (0) the optimal and common threshold value for non-expropriation. In this case, the optimal mechanism is much simpler. When the PC does not bind (i.e. |{i ∈ N : ti < t0 }| < K), every firm i whose type ti is below t0 is expropriated (pi (t) = 0) and pays nothing, and the others are not expropriated and pay the threshold value t0 . When the PC binds (i.e. |{i ∈ N : ti < t0 }| ≥ K), then only the K firms whose types are the K-lowest below t0 are expropriated and pay nothing, and the others are not expropriated and pay the same price: minK j∈N tj , the Kth-lowest type in {t1 , . . . , tn }. Note that, contrary to standard auctions, when the PC binds the effective bribe 0 (minK j∈N tj ) may be strictly lower than the bureaucrat’s “reserve price” (t ).

When firms are ex-ante symmetric, the optimal mechanism can be implemented through a simple bribing game similar to a second-price auction with a reserve price: each firm i ∈ N simultaneously and voluntarily submits a bid bi (ti ) ≥ 0 as a function of its type ti ∈ Ti ; then, up to K firms with the lowest bid below t0 are expropriated, and the others are not expropriated and pay min{t0 , minK j∈N bj (tj )}. Note that, as in second-price auctions, it is a weakly-dominant strategy for each firm i to bid its value: bi (ti ) = ti for every ti ∈ Ti . As in auction mechanisms, if firms are not ex-ante symmetric, then the optimal mechanism takes into account the heterogeneity in observable firm characteristics. Example 1 As an example, assume that for every i ∈ N the type ti of firm i is uniformly distributed on [a, b] with 0 ≤ a < b, and the expropriation value for the bureaucrat is linear in the type of firm i: ei (ti ) = γti , with γ < 1.11 Then, the virtual valuation of firm i is given by ci (ti ) = ti − γti −

1 − (ti − a)/(b − a) = (2 − γ)ti − b, 1/(b − a)

which rises in ti , so that the regularity assumption is satisfied. The (common) threshold value for 0 non-expropriation is c−1 i (0) = t =

b 2−γ .

The political constraint binds when the types of the K

firms with the K-lowest types are below t0 . The optimal mechanism characterized in Proposition 1 is such that up to K firms with the K lowest types below t0 = pay

b 2−γ

are expropriated, and the others

min{t0 , minK j∈N tj }. When firms are not ex-ante symmetric the optimal mechanism discriminates among different

firms according to their type distributions and the bureaucrat’s expropriation values. This can be 11

Note that γ < 2 is sufficient for the example to satisfy our assumptions, but γ > 1 seems unrealistic since this would imply that the bureaucrat is more efficient in the use of assets than is the firm.

10

seen by considering two different firms i and j with the same type y and noting that cj (y) ≥ ci (y) ⇐⇒ ej (y) +

1 − Fi (y) 1 − Fj (y) ≤ ei (y) + . fj (y) fi (y)

Hence, firm j, with a smaller expropriation value ej (·) for the bureaucrat or a higher hazard rate fj (y) 1−Fj (y) ,

will be expropriated less often and pay lower bribes than firm i with the same type y as

firm i.

2.3

The Quality of Governance

In this subsection we consider the impact of the political constraint and the expropriation value for the bureaucrat on the quality of governance. This latter is captured by three indicators: the extent of expropriation, the size of the bribes, and the bureaucrat’s extortion revenue (see below). We focus on a well-defined notion of quality of governance rather than the welfare costs of corruption, as there is no consensus on how to characterize the latter.12 In addition, governance is empirically recognized as a factor producing economic welfare (see, e.g., Mauro (1995)). A fundamental feature of good governance is the respect of property rights. Extortion is precisely the violation of those rights, be it through bribes or expropriation. The first indicator of the quality of governance is the overall risk of expropriation implied by the threshold values for non-expropriation c−1 i (0). The probability of expropriation corresponds to the probability of the complete denial of the firm’s property right over its assets. Recall from −1 Proposition 1 that firm i is never expropriated if ci (ti ) > 0, i.e. ti > c−1 i (0); otherwise, if ti < ci (0),

firm i is expropriated whenever the bureaucrat’s PC does not bind. The second indicator is the magnitude of the bribes that firms pay to avoid being expropriated. The bribe paid by individual firms corresponds to the partial expropriation of the firm’s profit, i.e. a denial of the firm’s property rights over a share of the proceeds from its assets. The third indicator is the revenue of the bureaucrat, which comes both from bribes and expropriation. The total revenue from bribery is an indicator of the profitability of the business of violating property rights. 2.3.1

The Expropriation Value

One determinant of the virtual valuation of firm i, and hence of the threshold value c−1 i (0), is the function ei (·) : Ti → R which shows the value to the bureaucrat of expropriating firm i as a function of firm i’s type ti ∈ Ti . In Example 1 we assumed that ei (ti ) = γti and the threshold value t0 =

b 2−γ

were common to all firms and increasing in γ. When t0 < b, i.e. γ < 1, the

ex-ante probability that any firm be expropriated rises with the value of the firm to the bureaucrat. This also results in higher bribes (equal to t0 ) paid by firms that are not expropriated when the 12

On the one hand, some consider bribes to be like taxes with their own (illegal) transaction costs. Bribes are thus transfers that distort allocations and produce deadweight losses. On the other hand, expropriation implies a less-efficient use of assets. Most would agree that these are unsatisfactory measures of the welfare cost of corruption.

11

PC does not bind (when the PC binds, bribes are constant in γ and equal to the highest firm’s type among the set of expropriated firms). The following proposition shows that this is a general comparative-static property of the optimal mechanism, for arbitrary distributions of types and for values of expropriation that are not necessarily symmetric and linear in firm type. Proposition 2 For each firm i, the expropriation probability, the extortion bribe paid when not expropriated, and the bureaucrat’s revenue rise with the bureaucrat’s expropriation value function ei (·). Proof. Consider an expropriation value e˜i (·) of some firm i ∈ N such that e˜i (ti ) > ei (ti ) for every ti ∈ Ti and such that regularity is satisfied. The virtual valuation of firm i is then given by −1 c˜i (ti ) < ci (ti ) for every ti ∈ Ti , so that the threshold value for non-expropriation is c˜−1 i (0) > ci (0).

The expropriation probability for firm i and the extortion bribe paid when not expropriated are higher with e˜i (·) than with ei (·). To show that the bureaucrat’s revenue is also higher with e˜i (·) than with ei (·), it suffices to note that the optimal extortion mechanism with ei (·) is also feasible with e˜i (·) as the expropriation value does not enter into the firm’s utility, and yields the same bribe revenue but higher expropriation values. The optimal extortion mechanism with e˜i (·) therefore necessarily yields greater total expected revenue for the bureaucrat. The overall expropriation risk and the bureaucrat’s revenue are always lower for smaller values of expropriation of any firm j. But reducing the expropriation value of some firm j may be detrimental to another firm i when the PC binds and i’s type is below its threshold for nonexpropriation (ti < c−1 i (0)). Lower values of ej (·) imply higher values of j’s virtual valuation cj (·), and hence the virtual valuation of every other firm i falls relative to j’s virtual valuation. The resulting bribe and risk of expropriation of firm i may thus rise as yi (t−i ) in Equation (8) increases with cj (·). Our findings are consistent with empirical evidence (Kobrin, 1980) showing that expropriation (in the conventional sense of the seizure of assets) was a concern in capital-intensive sectors such as petroleum and mining; however fewer than 5% of all foreign-owned firms in developing countries were expropriated between 1960 and 1976. The expropriated firms were characterized by relatively highly-valuable physical capital (a large ei (ti )) compared to other firms. Unfortunately, there exists no data on the characteristics of the firms which were victims of “creeping expropriation” or bureaucratic harassment. 2.3.2

The Political Constraint

The political constraint limits the bureaucrat’s ability to expropriate. When he is able to expropriate as many firms as he wants, the optimal mechanism calls for the expropriation of all firms with ci (ti ) < 0, with each remaining firm i that is not expropriated paying a fixed bribe of c−1 i (0), which is independent of the other firms’ types. When the bureaucrat can expropriate at most K 12

firms, the K firms with the K-lowest virtual valuations below 0 are expropriated, with the others paying the value of their smallest possible types allowing them not to be expropriated given the others’ types. In Example 1, the K-lowest types below t0 =

b 2−γ

are expropriated and the others

pay min{t0 , minK j∈N tj }. Hence, the weaker is the PC (the larger is K) the greater the probability of expropriation and the bribes extracted from each firm. Since K is only present as a constraint in the bureaucrat’s optimization program (through Equation (5)), his revenue also rises with K. These results extend to the general case and we have: Proposition 3 The expropriation risk, bribes when not expropriated, and the bureaucrat’s revenue are increasing with the number K of firms the bureaucrat has the power to expropriate. Proof. Directly from Proposition 1 and the observations above. We conclude that the quality of governance is unambiguously decreasing in the value that the bureaucrat can obtain from expropriation and with the total number of firms he can credibly threaten to expropriate. We note that our approach provides an additional explanation of the resource curse. Resource-rich countries attract foreign firms with more physical capital from which a greater amount can be expropriated by the host government. In a context of weak governance this implies more expropriation and extortion, so that resource availability negatively affects the quality of governance.

3

Optimal Extortion Mechanisms with Insurance

This section introduces political-risk insurance which protects firms against various types of expropriation undertaken by the bureaucrat. We do not here consider the firms’ decisions regarding the extent of insurance coverage or any other features of the insurance market. In particular, insurance is costless for firms. This is clearly a simplification but is partly justified by political-risk insurance often being heavily subsidized by national governments, reflecting the World Bank’s policy of encouraging foreign investment in difficult countries. We leave for future research the analysis of the political-risk insurance market, building on the results presented here.13 Our objective is to investigate how the presence of insurance with various degrees of coverage affects the quality of governance. When firm i of type ti is expropriated it receives compensation of Ai (ti ) ≥ 0, where Ai (·) is continuously differentiable.14 We assume that vi (ti ) ≡ ti − Ai (ti ) ≥ 0 for every ti , which means that over-compensation is precluded; this ensures that no firm ever prefers expropriation to staying in business.15 We also assume that vi (ti ) ≡ ti − Ai (ti ) is strictly increasing 13

In a more general model within our framework, firms would choose their insurance coverage before profits are known, and the actual losses would only be learned by the insurance company ex-post. 14 Note that our analysis does not exclude information asymmetries between the firm and the insurance company. When Ai (ti ) depends on ti it is only required that, in the case of expropriation, the firm’s actual type ti be ex-post verifiable by the insurance company so that the appropriate compensation Ai (ti ) is paid out. 15 In the MIGA Investment Guarantee Guide (page 9) it is stated that: “Regardless of the nature of the project,

13

in ti , so that it can be inverted and the optimal mechanism with insurance can be characterized using the same methods as in the previous section, with a change of variable.16 A typical example satisfying these assumptions is when the amount of assets covered by the insurance is linear in the firm’s loss of income: Ai (ti ) = λi ti + A¯i , with λi ∈ [0, 1) and A¯i ≤ (1 − λi )ai . With insurance, the interim expected utility of firm i is given by Z   ti pi (t) + Ai (ti )(1 − pi (t)) − xi (t) f−i (t−i )dt−i .

(10)

T−i

The individual-rationality constraint requires that this expected utility be higher than Ai (ti ) or, equivalently,

Z

(vi (ti )pi (t) − xi (t)) f−i (t−i )dt−i ≥ 0.

T−i

Note that, normalizing firms’ utilities to17 Z Ui (p, x; ti ) = (vi (ti )pi (t) − xi (t)) f−i (t−i )dt−i ,

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T−i

we obtain the same IR and IC constraints as without insurance, except that the value for nonexpropriation for firm i is vi (ti ) = ti −Ai (ti ) instead of ti . Consider the following change of variable: f (v−1 (t˜ )) t˜i = vi (ti ). Let F˜i (t˜i ) = Fi (vi−1 (t˜i )) and f˜i (t˜i ) = i′ i−1 i be the corresponding distribution and vi (vi (t˜i ))

density of t˜i over T˜i = [˜ ai , ˜bi ] ≡ [vi (ai ), vi (bi )]. With this change of variables, and for a mechanism (˜ p, x ˜), where p˜ : T˜ → [0, 1]n and x ˜ : T˜ → R+ , players’ expected utilities (1) and (2) can be rewritten as: ˜i (˜ U p, x ˜; t˜i ) = and ˜0 (˜ U p, x ˜) =

Z

T˜

Z

T˜−i

X


t˜i p˜i (t˜) − x ˜i (t˜) f˜−i (t˜−i )dt˜−i , !

(1 − p˜i (t˜))˜ ei (t˜i ) + x ˜i (t˜) f˜(t˜)dt˜,

i∈N

(12)

(13)

where e˜i (t˜i ) = ei (vi−1 (t˜i )). The optimal mechanism can therefore be characterized exactly as in the previous subsection, which yields the following virtual valuation for each firm i: 1 − F˜i (t˜i ) 1 − Fi (ti ) . ci (ti ) = t˜i − e˜i (t˜i ) − = vi (ti ) − ei (ti ) − vi′ (ti ) ˜ ˜ fi (ti ) fi (ti ) We again make the following regularity assumption. an investor is required to remain at risk for a portion of any loss.” 16 Note that this trick is not possible in some of the other extensions of Myerson (1981) in which the type-dependent outside options only enter the agents’ participation constraints (see, e.g., Figueroa and Skreta, 2009). In our model, the outside option Ai (ti ) applies both when the firm does not participate in the mechanism (in which case it is expropriated for sure) and when it participates but is expropriated. 17 Ai (ti ) is a constant, independent of the mechanism, so it can be subtracted from firm i ’s interim expected utility given by (10) without modifying the incentive-compatibility constraints.

14

Assumption 2 (Regularity with insurance) For every i ∈ N the virtual valuation of firm i with insurance, ci (ti ) = vi (ti ) − ei (ti ) − vi′ (ti )

1 − Fi (ti ) , fi (ti )

(14)

is strictly increasing in ti . Note that this assumption is stronger than without insurance as, when the expropriation value ei (ti ) rises with ti , this requires that both the expropriation value and insurance compensation do not increase too fast in the firm’s type. Otherwise, the optimal mechanism will be characterized by some degree of bunching, so that different types of the same firm will pay the same bribes and face the same probability of expropriation. In the extreme case in which, for every firm i, ci (ti ) is decreasing over the whole interval, we have complete bunching: up to K firms with the highest difference E(ei (ti )) − vi (ai ) above 0 are expropriated, and each non-expropriated firm i pays a fixed bribe of vi (ai ) to the bureaucrat. When, in addition, firms are ex-ante symmetric, the mechanism boils down to a random expropriation lottery. All firms prefer not to be selected for expropriation, and non-expropriated firms pay a fixed bribe to the bureaucrat (see the example below for an illustration). This could help explain the arbitrary nature of bureaucratic expropriatory behavior in some situations. The optimal mechanism (p, x) defined on the original types, p : T → [0, 1]n and x : T → R+ , is such that pi (t) = p˜i (v1 (t1 ), . . . , vn (tn )) and xi (t) = x ˜i (v1 (t1 ), . . . , vn (tn )). We therefore obtain the following characterization of the optimal extortion mechanism with insurance: Proposition 4 (Optimal Extortion with Insurance) Under regularity, the optimal extortion mechanism (p, x) with insurance is such that p : T → [0, 1]n maximizes X X ci (ti )pi (t) subject to n − K ≤ pi (t) ≤ n for all t ∈ T, i∈N

i∈N

where the virtual valuation ci (ti ) of firm i is given by (14). Therefore pi (t) = 0 for the firms with the (up to) K-lowest virtual valuations below 0, and pi (t) = 1 for the other firms. The payment of firm i to the bureaucrat is given by: xi (t) = pi (t)vi (ti ) −

Z

vi (ti )

pi (si , t−i )dsi .

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vi (ai )

The optimal mechanism with insurance can be reformulated in terms of the initial types: if yi (t−i ) = min{si ∈ Ti : ci (si ) ≥ 0 or ci (si ) ≥ minK cj (tj )} j6=i

is the smallest type of firm i that would result in firm i not being expropriated when other firms’ types are given by t−i , the optimal mechanism can be rewritten as: ( ( 1 if ti > yi (t−i ), vi (yi (t−i )) pi (t) = and xi (t) = 0 if ti < yi (t−i ). 0 15

if ti > yi (t−i ), if ti < yi (t−i ).

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Example 1 continued Consider again Example 1, and assume that all firms have the same linear ¯ where λ ∈ [0, 1) is the marginal insurance compensation: vi (ti ) = ti − Ai (ti ) = (1 − λ)ti − A, compensation and A¯ ≤ (1 − λ)a is the fixed compensation from the insurance company. The virtual valuation of firm i as a function of its type ti is then given by: ¯ ci (ti ) = (1 − λ)ti − A¯ − γti − (1 − λ)(b − ti ) = [2(1 − λ) − γ]ti − (1 − λ)b − A. Regularity is satisfied when λ and γ are not too high: 2(1 − λ) − γ > 0, i.e. λ < 1 − γ/2. In this situation, the (common) threshold for non-expropriation is given by: t0 = c−1 i (0) =

(1 − λ)b + A¯ , 2(1 − λ) − γ

and up to K firms with the K-lowest types below t0 are expropriated. The non-expropriated firms ¯ minK (1 − λ)tj − A}; ¯ that is, they pay (1 − λ)t0 − A¯ when the PC does pay min{(1 − λ)t0 − A, j∈N not bind, and minK (1 − λ)tj − A¯ when it does. j∈N

The threshold t0 , and therefore the risk of expropriation, is always increasing in the fixed ¯ it rises with the marginal compensation λ when γ > −2A¯ , but falls with λ when compensation A; b

¯ −2A b .

¯ The bribes paid by firms when the PC binds, minK j∈N (1 − λ)tj − A, obviously always ¯ When the PC does not bind, the payment (1 − λ)t0 − A¯ applies. strictly fall with both λ and A. This is strictly decreasing in A¯ when

γ <

1−λ < 1, i.e., λ < 1 − γ. 2(1 − λ) − γ When the above inequality is not satisfied (i.e. when λ ≥ 1 − γ) we have t0 ≥ b, so the risk of expropriation is constant and the PC always binds. The payment minK (1 − λ)tj − A¯ thus always j∈N

applies for the n − K non-expropriated firms, and the bribes and bureaucrat’s expected revenue ¯ Last, the bribe (1 − λ)t0 − A¯ paid by firm i when the PC does not bind falls in λ if fall with A. ∂ ∂ (1 − λ)b + A¯ (1 − λ)t0 = < 0, γ ∂λ ∂λ 2 − 1−λ ¯ Again, when this inequality is not satisfied we have t0 ≥ b, so the i.e. if 2b(1 − λ)(1 − λ − γ) > Aγ. PC must bind.18 We conclude in this example that bribes are always decreasing (or constant) in both the fixed and marginal compensation of the insurance. In Section 4.2 we will provide general conditions for this result to hold, but also some examples in which bribes increase with the marginal compensation of insurance. If the regularity assumption is not satisfied (i.e. γ > 2(1 − λ)), then non-expropriated firms pay ¯ If E(ei (ti )) − vi (ai ) = γ a+b − (1 − λ)a + A¯ > 0, i.e. γ > a constant bribe equal to (1 − λ)a − A. 2 2(1−λ)a−2A¯ , a+b

then K firms are always expropriated (randomly, or in any arbitrary manner). In this

18 ¯ implies that t0 > b(1 − λ)/γ; whether λ is smaller or larger than 1 − γ We can see that 2b(1 − λ)(1 − λ − γ) < Aγ we have t0 > b.

16

example, the last inequality always holds when the regularity assumption is not satisfied. However, this is not general. If we add, for instance, a fixed cost of expropriation τ (i.e., ei (ti ) = γti − τ ), and if τ is large so that the expected value of expropriation for the bureaucrat is too low compared to the minimum bribe he could ask for, then all n firms are required to pay (1 − λ)a and are never expropriated.

4

The Quality of Governance with Insurance

This section analyzes the quality of governance as a function of firm insurance compensation. Our three indicators of the quality of governance are as defined in Subsection 2.3: (i) the overall and individual risk of expropriation, (ii) the size of the bribes, and (iii) the bureaucrat’s corruption revenue. In order to obtain tractable comparative-static results regarding insurance coverage, we assume here that insurance is linear in firm type, i.e., Ai (ti ) = λi ti + A¯i , where λi ∈ [0, 1) is the marginal compensation and A¯i ≤ (1 − λi )ai the fixed compensation.19 For example, imagine that the firm has invested I dollars in some manufacturing business in the host country, and that it expects a profit of from ΠL to ΠH dollars from this investment. The bureaucrat knows the value of the initial investment, but is not perfectly-informed about the firm’s prospects (which might depend, for example, on the firm’s private information about market conditions or production costs). An insurance contract (or a combination of a number of public or private insurance contracts) might cover a share α ∈ [0, 1] of the firm’s initial investment (which is commonly-known), and a share β ∈ [0, 1) of its losses due to expropriation (which are only evaluated ex-post, or depend on information like purchase orders that are not accessible to the bureaucrat). We can then represent the firm’s type by ti ∈ [ΠL , ΠH ], and write Ai (ti ) = αI + βti , so that in this example λi = β and A¯i = αI.20

4.1

The Risk of Expropriation

In our main symmetric example, the threshold value for non-expropriation, t0 , is common to all firms. A larger threshold implies a greater probability that any firm’s type be below this threshold, and hence a larger risk of expropriation. In the example, this threshold is always rising in the ¯ rises with the (common) marginal compensation λ when the (common) fixed compensation A, value of expropriation to the bureaucrat is positive or not too negative (γ > when the bureaucrat’s expropriation value is otherwise (γ < 19

¯ −2A b ).

¯ −2A b ),

but falls in λ

The comparative-static analysis is very difficult to extend to non-linear insurance coverage; in particular it is not clear what the correct parameters are to reflect this non-linearity. Moreover, in view of the current practice at the MIGA, the linear insurance schedule seems to be an acceptable approximation 20 With (1 − β)ΠL > αI to preclude over-compensation.

17

We show below that these qualitative results regarding the effect of insurance on expropriation risk hold beyond this specific example. By looking at asymmetric firms, we are also able to evaluate the interesting impact of one firm’s insurance coverage on firms’ relative risk of expropriation when the PC of the bureaucrat binds. The individual threshold value for the non-expropriation of firm i comes from the solution to t0i −

A¯i + ei (t0i ) 1 − Fi (t0i ) − = 0. 1 − λi fi (t0i )

The LHS of this equation falls in λi when A¯i + ei (t0i ) > 0, so that when the regularity condition is satisfied (i.e. ci (·) is increasing) greater marginal insurance compensation λi implies a higher threshold value for the LHS of the equation to equal 0. Similarly, when A¯i +ei (t0 ) < 0 the threshold i

value falls in λi , and when A¯i + ei (t0i ) = 0 the threshold value is independent of marginal insurance compensation. Last, the LHS of this equation always falls with the fixed insurance compensation A¯i .21 This yields the following proposition. Proposition 5 Assume that insurance is linear. The impact of firm i’s marginal insurance compensation λi on the threshold value for the nonexpropriation of firm i depends on the sign of A¯i + ei (t0i ): the threshold for non-expropriation rises (falls) with λi when A¯i +ei (t0 ) > 0 (A¯i +ei (t0 ) < 0), and does not depend on λi when A¯i +ei (t0 ) = 0. i

i

i

The impact of firm i’s fixed insurance compensation A¯i on the threshold value for the nonexpropriation of firm i is positive. The threshold values have an impact on the overall risk of expropriation since any type above this threshold is certain not to be expropriated. Unsurprisingly, we learn from this proposition that higher fixed insurance compensation increases the overall risk of expropriation. More interestingly, we also learn that the impact of marginal insurance compensation λi on the overall risk of expropriation depends critically on the value to the bureaucrat of exerting a threat against firm i, i.e. the value of the expropriated assets or the cost of harassment. If the bureaucrat’s extortionary power is based on some ability to seize the assets and benefit from them, the overall probability of expropriation will then always rise with the marginal insurance compensation, as the threshold for non-expropriation is higher. The intuition is that if marginal compensation rises and expropriation is directly valuable to the bureaucrat, then expropriation becomes more attractive relative to extortion as the firm’s willingness to pay bribes is reduced by the insurance compensation. On the contrary, if the bureaucrat’s power is based on an ability to harass the firm, the risk falls if harassment is costly enough for the bureaucrat. The intuition is that, when expropriation is costly for the bureaucrat, the only benefit to the bureaucrat from expropriating low firm types is to extract bribes from the higher types. Since the firm’s willingness to pay bribes falls with insurance, the bureaucrat has less incentive to take such costly actions. 21

Note that this fixed insurance compensation effect does not depend on the linear form of the insurance schedule.

18

When the PC does not bind, the expropriation risk for firm j 6= i is not affected by firm i´s insurance, as the virtual valuation, and therefore the threshold for non-expropriation of firm j, c−1 (0), does not depend on λi and A¯i . In this case the results in the proposition apply immediately j

to the individual expropriation risk: the expropriation risk for firm i rises with the fixed insurance compensation A¯i , and with the marginal insurance compensation λi when the value of expropriation to the bureaucrat is positive or not too negative. When the PC binds there are cross-effects between the different firms. The expropriation risk of a given firm whose type is below its threshold depends on the position of its virtual valuation relative to those of other firms with valuations below zero. We analyze below the impact of insurance on the virtual valuation ci (ti ) of firm i, and hence on the individual expropriation probabilities. Clearly, since ci (ti ) falls in A¯i for every ti , increasing the fixed insurance compensation of firm i reduces the relative position of firm i’s virtual valuation relative to that of any other firm j 6= i. Hence, we have: Proposition 6 If the fixed compensation from firm i’s insurance, A¯i , rises, then the expropriation risk of firm i rises and that of another firm j 6= i falls. The impact of the marginal insurance compensation of firm i on the virtual valuation ci (ti ) of firm i is more complex as it depends on the actual type ti of firm i. We have: ∂ci (ti ) 1 − Fi (ti ) < 0 ⇐⇒ ti > , ∂λi fi (ti ) so that, for relatively high types (ti >

1−Fi (ti ) fi (ti ) ),

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the impact of higher marginal compensation

on the virtual valuation is negative. Conversely, for lower types (ti <

1−Fi (ti ) fi (ti ) )

higher marginal

compensation leads to an increase in the virtual valuation. The intuition is that, as the marginal compensation of firm i rises, the difference in terms of the willingness to bribe between two different types of this firm falls, so it becomes less attractive for the bureaucrat to discriminate between firm types. This translates into a flatter virtual valuation curve of firm i (see Figure 1) and yields the type-dependent impact of insurance on the virtual valuation described above. Denote by t∗i the solution of t∗i − c−1 i (0) −

1−Fi (t∗i ) fi (t∗i )

= 0. Since c−1 i (0) is the solution to

¯ ei (c−1 1 − Fi (c−1 i (0)) + Ai i (0)) − = 0, −1 1 − λi fi (ci (0))

−1 ∗ ¯ we have c−1 i (0) > ti when ei (·) + Ai > 0, in which case ci (0) rises with λi as in Proposition 5. −1 ∗ ¯ We also have c−1 i (0) < ti when ei (·) + Ai < 0, in which case ci (0) falls with λi , so that the

expropriation risk for firm i does not fall whatever its type (it strictly falls when ti < c−1 i (0) and is zero and constant when ti > c−1 i (0)). This is illustrated in Figure 1 with two levels of marginal ¯ i > λ , corresponding virtual valuation functions c¯i (·) ¯ insurance compensation λi and λi , with λ i and ci (·), and threshold values t¯0i = c¯−1 (0) and t0i = ci−1 (0). In the left-hand panel we have i 19

ci (ti ) ci (ti )

Risk of expropriation ր

Risk of expropriation ց

Risk of expropriation ց

c¯i (ti )

c¯i (ti ) t∗i

t∗i

ti t0i

t¯0i

t¯0i

ti

t0i

¯ i > λ when Figure 1: The effect of an increase in marginal insurance compensation from λi to λ i ei (·) + A¯i > 0 (left panel) and ei (·) + A¯i < 0 (right panel) on the virtual valuation of firm i and its expropriation risk. ei (·) + A¯i > 0, and in the right-hand panel ei (·) + A¯i < 0. Note that even when ei (·) + A¯i = 0, the risk of expropriation of firm i falls with λi for ti < t∗i = c−1 i (0) when the PC binds (because ci (ti ) increases for ti < t∗i ), although the threshold value c−1 i (0) does not change with λi (so that the expropriation risk is zero and independent of λi for ti > t∗i = c−1 i (0)). As an example, consider the case of two firms with K = 1, and assume that both firms are initially symmetric, e1 (·) + A¯1 = e2 (·) + A¯2 > 0, t∗1 = t∗2 = t∗ , with low marginal insurance compensation λ and c1 (·) = c2 (·) = c(·). Consider first the case in which firm 1’s type is t1 and firm 2’s type is t2 , with t1 < t2 < t∗ < c−1 (0) as in Figure 2. With the common low marginal compensation, firm 1 is expropriated, but not firm 2, as c(t1 ) < c(t2 ) < 0. But if firm 1 increases its marginal compensation to λ (yielding the virtual valuation function c(·) represented in Figure 2), then the roles are switched: firm 2 is expropriated as c(t2 ) < c(t1 ) < 0. The reverse may pertain for higher types: consider the case in which firm 1’s type is s1 and firm 2’s type is s2 , with s1 > c−1 (0) > s2 . With common low marginal insurance compensation, firm 2 is expropriated as c(s2 ) < 0 < c(s1 ). If firm 1 increases its insurance to λ as before, the roles are reversed: firm 1 is expropriated while firm 2 is not, as c(s2 ) > c(s1 ).

20

c(·)

c¯(·) t1

t2

t∗

s2

s1

ti

Figure 2: Cross effects of marginal insurance compensation with two initially ex-ante symmetric firms, when firm 1’s marginal insurance compensation increases.

21

The following proposition summarizes the observations above with respect to the impact of the firm’s marginal insurance compensation on firms’ individual expropriation risks: Proposition 7 Assume that insurance is linear, and let t∗i be the solution of t∗i −

1−Fi (t∗i ) fi (t∗i )

= 0. If

the marginal insurance compensation of firm i, λi , rises, then ¯ (i) The expropriation risk of firm i falls for low types: for ti < t∗i < c−1 i (0) if ei (·) + Ai > 0, and for ti < c−1 (0) < t∗ if ei (·) + A¯i < 0; i

i

(ii) The expropriation risk of firm i rises only if ei (·) + A¯i > 0 and for intermediate types ti > t∗i below the threshold for non-expropriation. (iii) The expropriation risk of another firm j 6= i rises for low types of firm i (ti < t∗i ) and falls for high types of firm i (ti > t∗i ). We know from Proposition 5 that for ei (·) + A¯i > 0, the expropriation risk of firm i rises with its marginal insurance compensation whenever the political constraint does not bind, as its threshold for non-expropriation increases. However, from Proposition 7(i) we also learn that, even if ei (·) + A¯i > 0, the expropriation risk of firm i falls for low types of firm i, as their virtual valuations increase and may therefore become larger than other firms’ virtual valuations (which might be expropriated in their place). The intuition here is that, when the PC binds, the bureaucrat gains from reallocating expropriation to increase the base level of the bribe so as to counter the reduced willingness to pay due to firm i’s insurance. The change in marginal insurance compensation which affects the order of the virtual valuations may permit such a profitable reallocation. This effect is clearly illustrated in Figure 2 when considering the impact of marginal insurance compensation on bribes (see the next subsection).

4.2

Extortion Bribes

If we consider a simple insurance relationship, there is a standard moral-hazard result that the more insured an agent is the less effort she expends to reduce risk. In the context of extortion, firms pay bribes to reduce the expropriation risk. This suggests that we could expect that the more insured is the firm the less bribes it pays.22 In Example 1, with ex-ante symmetric firms and a uniform distribution of types, we have seen that the bribes paid by firms that are not ¯ The expropriated fall in both the (common) marginal and fixed insurance compensations λ and A. proposition below provides more general sufficient conditions under which bribes falls with own insurance compensation. 22

Note that from a private insurance company’s point of view moral hazard is an issue because as the risk increases the company will have to pay out compensation more often. However, from the point of view of governance, moral hazard is a blessing as the size of the bribe is negatively related to governance.

22

Proposition 8 Assume that insurance is linear. The size of the bribes firm i must pay to avoid being expropriated falls with the fixed insurance compensation A¯i . It falls with marginal insurance compensation λi under the following conditions: (i) The expropriation value is not too high for all types below the threshold for non-expropriation:23 ei (ti ) + A¯i ≤ ti c′i (ti ) − ci (ti ), for every ti ≤ t0i ; (ii) Firm i’s type is not too high: ti <

(18)

1−Fi (ti ) fi (ti ) .

Proof. See the Appendix. Higher fixed insurance compensation A¯i thus always makes the bribes paid by firm i smaller. Higher marginal insurance compensation λi of firm i also makes the bribes paid by firm i smaller, except when the firm’s type is high and the expropriation value of this firm to the bureaucrat is positive and large enough. To see how marginal insurance compensation can produce larger bribes to avoid expropriation, assume as in Example 1 that ei (ti ) = γti for every firm i and type ti , and let A¯i = 0 and Ti = [0, 1] for every i. We therefore have ci (·) = c(·), and c(t0 ) = 0 ⇐⇒ t0 −

1 − F(t0 ) γt0 − = 0. f(t0 ) 1−λ

From the implicit-function theorem, we have: ∂t0 = ∂λ

γt0 /(1 − λ)2 1−

∂ 1−F(t 0

0)

f(t ) ∂t0

−

,

γ 1−λ

which is positive when γ > 0, in accordance with Proposition 5. The extortion bribe when the PC does not bind falls in λ if

∂(1 − λ)t0 < 0, ∂λ

i.e.,



(1 − λ) 1 −

0

) ∂ 1−F(t f(t0 )

∂t0



 > 2γ.24

(19)

With a uniform distribution of types, as in Example 1, we have inequality simplifies to λ < 1 − γ, which always holds when

t0

∂ 1−F(t 0

0)

f(t ) ∂t0

= −1, so the previous

is below the upper bound of the

(uniform) distribution of the firm’s type. For the exponential distribution F(ti ) = 1 − e−hti , which has a constant hazard rate h =

f(t0 ) 1−F(t0 )

> 0, Equation (19) is equivalent to λ < 1 − 2γ . Hence, for

values of the parameters satisfying 1 − 2γ < λ < 1 − γ, 23 ¯i < 0 for every ti ∈ Ti implies (18) under the regularity condition, since in that case we have Note that ei (ti ) + A c′i (ti ) > 0 and ci (ti ) < 0 for every ti ≤ t0i . 24 This expression can also be obtained directly from Equation (18) in Proposition 8 for ti = t0i .

23

and when the PC does not bind, any type above t0 = pays higher bribes, of (1 − λ)t0 =

(1−λ)2 h(1−λ−γ) ,

1−λ , h(1 − λ − γ) as marginal insurance compensation λ rises.

We end this subsection by illustrating some cross effects of insurance coverage on the bribes paid by other firms. Consider again the case analyzed in Figure 2. Here there are two firms, at most K = 1 firm can be expropriated, both firms are ex-ante symmetric, e1 (·) + A¯1 = e2 (·) + A¯2 > 0, t∗1 = t∗2 = t∗ , with a low marginal insurance compensation λ and c1 (·) = c2 (·) = c(·), firm 1’s type is t1 and firm 2’s type is t2 , with t1 < t2 < t∗ < c−1 (0). We have seen that higher marginal insurance compensation of firm 1 (to λ, yielding the virtual valuation function c¯(·)), could reduce its expropriation risk (to zero) at the expense of firm 2 of type t2 . Consider now what happens with a third firm (firm 3) which is ex-ante identical to firm 2 but has a higher type t3 > t2 , so it is not expropriated in this configuration. Before firm 1 increased its insurance coverage, firm 3 paid a bribe of (1 − λ)t1 ; after firm 1 increases its insurance it pays (1 − λ)t2 , which is larger. There is a positive cross effect of firm 1’s insurance coverage on firm 3’s bribe.

4.3

Corruption Revenue

The third governance indicator is the total revenue from corruption (including the proceeds from expropriation and bribes). The next proposition establishes that this always falls with marginal and fixed insurance compensation, i.e. the more insured the firms the lower are the rents that the bureaucrat can extract from them. Proposition 9 Assume that insurance is linear. The bureaucrat’s expected revenue from corruption, including the proceeds from expropriation and bribery, falls with both the fixed insurance compensation A¯i and the marginal insurance compensation λi of any firm i. Proof. See the Appendix. In contrast with the two previous governance indicators (the expropriation risk and the bribe), the impact of insurance on revenue is unambiguous. Even if the optimal mechanism calls for more expropriation and, in some cases, larger bribes for high-type firms, total expected revenue from corruption always falls with insurance coverage. This important result means that changes in the optimal mechanism regarding bribes and expropriation risk in response to higher insurance coverage cannot undo the effect of insurance on the bureaucrat’s ability to extort – this is lower. The intuition is as as follows. Consider some linear insurance schedule and its associated optimal mechanism, and assume that the fixed or marginal compensation falls for some firm, so the firm is willing to pay more to avoid expropriation. As such, the individual rationality constraint of this firm is effectively relaxed. The bureaucrat can therefore retain the same mechanism and just ask 24

the firm for a higher bribe. As insurance is linear, this can be done without violating the firm’s incentive constraints. Hence, with less insurance the initial mechanism is still feasible and permits greater bribe income. As mentioned above (Section 2.3), we have opted for an evaluation in terms of the quality of governance rather than welfare analysis. One reason is that there is no consensus regarding the definition of the welfare costs of extortion. Another is that our model does not allow for meaningful welfare analysis of the value of insurance. There are a number of reasons for this. First, our model does not consider the firms’ decision to take out insurance, and insurance is costless for firms. Second, the static approach allows for an in-depth analysis of the extortion mechanism and the impact of insurance on extortion. It however excludes any issues related to the impact of extortion and insurance on firms’ entry decisions. Any meaningful welfare analysis should account for these, as the welfare value of reducing extortion is to improve the profitability of business in countries with weak governance, thereby unleashing their productive potential.

5

Concluding remarks and policy implications

The analysis provided in this article has overall concluded that the impact of insurance on the quality of governance is somewhat ambiguous. We have chosen to evaluate the quality of governance via three indicators reflecting the costs associated with extortion in countries with weak governance: the expropriation risk, the size of bribes, and the expected revenue from corruption. The expected revenue from corruption always falls in both the fixed and the marginal insurance compensation. The relationship between the size of bribes and insurance is more complex. While the bribes paid by firms fall under a wide range of circumstances (in particular, bribes always fall with the firm’s fixed insurance compensation, and with its marginal insurance compensation whenever the expropriation value to the bureaucrat or the profit of the firm are not too high), we have identified circumstances under which a high type could end up paying more bribes as marginal insurance compensation rises. We also showed that customized insurance induces cross effects between firms: greater insurance coverage in one firm may produce higher bribes in another. Last, unsurprisingly, the effect of insurance on expropriation risk is the most problematic. Insurance does reduce the total amount that can be extorted in bribes, but leaves the value of expropriation unaffected, affecting the trade-off between the two means of rent-extraction (when expropriation is in itself profitable), making expropriation relatively more attractive to the bureaucrat. It is then not surprising that this risk may rise, especially when the value of expropriation to the bureaucrat is positive. The analysis has identified the circumstances under which firm coverage by PRI introduces externalities in terms of the three dimensions of the quality of governance in the host country. This allows us to draw some conclusions regarding the rationale for public intervention in the PRI sector. We discuss two types of interventions: subsidizing firms’ purchase of insurance and enforcing the recovery of expropriated assets from the host government. 25

First, we learned that in a country where the firms’ major concern is harassment or creeping expropriation (i.e. when expropriation is costly to the bureaucrat) PRI brings about a positive externality on the quality of governance, which would justify subsidizing the insurance premium as, for example, MIGA does by providing PRI at low cost. Similarly, in less corrupt countries (where the political constraint is tight and therefore likely to bind), the impact of insurance on the overall quality of governance is positive and again justifies subsidizing PRI.25 In the most corrupt states, where asset seizure is a serious worry for firms (when the value of expropriation to the bureaucrat is positive), we know that insurance always increases the probability of expropriation while the overall revenue from extortion falls. There is no straightforward policy recommendation here. However, suppose that the international community greatly values reducing the income from extortion, then an interesting question could be: Which firms should be subsidized to buy insurance in the first place? Our result suggests that among firms with comparable risks, those with less physical capital should be given priority. As such, MIGA should subsidize telecoms companies rather than oil-drilling companies. We also underline the critical role played by the value of the expropriated assets to the bureaucrat. When this is negative enough, as in the case of pure harassment (but not only in this case), marginal insurance compensation is positively associated with all three indicators. When the expropriation value is positive, the expropriation risk rises with marginal insurance compensation, and when the expropriation value is high enough, the bribes paid by high-type firms may increase. It is therefore of interest to consider ways in which the expropriation value may be reduced. One way of doing so is for insurance companies to seek to recover assets from the bureaucrat responsible. While this will often be difficult and costly, MIGA devotes considerable effort to asset recovery at the central-government level. When the central government can hold the bureaucrat accountable (i.e. when the expropriation value to the bureaucrat is effectively reduced), the end result may be a positive effect of PRI on the quality of governance. As such, we would expect to see better outcomes in terms of PRI’s effect on governance in countries where central government has some control over its bureaucracy (as in many Latin American countries). By way of contrast, the impact of PRI on governance in the weakest-governance countries (e.g., some African failed states) will likely be limited. We end with some conjectures about the impact on our main results of integrating the mechanism design analysis into a dynamic framework. Let us consider the following setting. In each period, a pool of potential entrants decide whether or not to invest (i.e., enter). If they do invest, they face an optimal extortion mechanism with the non-expropriated incumbents. A first point is that in such a dynamic setting, we would expect expropriation to occur less often. There are several reasons for that. First, for each individual firm the value of expropriated assets to the bureaucrat 25 This implicitly assumes that only the global risk of expropriation and bribe burden matters to public entities in developed countries but not its distribution between firms, as the reasoning here does not take into account the cross effects of insurance coverage between firms.

26

must be weighed against the flow of future extortion bribes. Second, the value of expropriation in terms of threat that induces firms to pay a bribe must be weighed against its impact on entry, i.e., on new flows of bribes. Both these two effects reduce the value of expropriation for the bureaucrat. Extortion bribes are likely to be affected as well. On the one hand a lower probability of expropriation (just like a tightening of the political constraint) reduces the magnitude of the bribes. On the other hand the distribution of firms is expected to shift toward higher types thus increasing the level at which the K-lowest firm type (determined by equilibrium expropriation) is indifferent between expropriation and bribe payment. Most of the comparative static results are likely to carry over but in a more complex manner. For instance, the availability of (costless) insurance increases the profitability of the market in the host country which would also increase entry, thus inducing a higher rate of expropriation. The impact of insurance on the level of bribe is likely to be ambiguous. So in particular we may expect a new effect due to increased entry that is expected to push the total amount of bribes up.

Appendix Proof of Proposition 8. (i) From the characterization of the optimal mechanism with insurance (Proposition 4 and below), the extortion bribe paid by firm i when it is not expropriated is (1 − λi )yi (t−i ) − A¯i , where yi (t−i ) = min{si ∈ Ti : ci (si ) ≥ 0 or ci (si ) ≥ minK cj (tj )}. j6=i

Consider a given profile of types t−i of the other firms and let α = min{0, minK cj (tj )}, j6=i

so that the bribe paid by firm i can be rewritten as ¯ (1 − λi )c−1 i (α) − Ai . Clearly, this always falls in the fixed insurance compensation A¯i . It will also fall with the marginal insurance compensation λi if ∂(1 − λi )c−1 i (α) < 0, ∂λi We have ci (θ) = α ⇐⇒ θ −

i.e.,

∂c−1 c−1 (α) i (α) < i . ∂λi 1 − λi

α ei (θ) + A¯i 1 − Fi (θ) − − = 0. 1 − λi fi (θ) 1 − λi

Using the implicit-function theorem, Equation (20) can be rewritten as

1−

¯i +α ei (θ)+A (1−λi )2   1−Fi (θ) ∂ f (θ) e′i (θ) i 1−λi − ∂θ

27

<

θ , 1 − λi

(20)

which simplifies to ei (θ) + A¯i < θc′i (θ) − ci (θ). (ii) We know from Equation (17) that when ti <

1−Fi (ti ) fi (ti ) ,

the virtual valuation ci (ti ) of type

ti rises (see also Figure 1). From the characterization of the optimal mechanism with insurance (Proposition 4 and below) this implies that yi (t−i ) falls with λi , and therefore so does the payment (1 − λi )yi (t−i ) − A¯i for any non-expropriated type. Proof of Proposition 9. Consider the optimal mechanism with the profile of fixed insurance
compensations A¯1 , . . . , A¯n and the profile of marginal insurance compensations (λ1 , . . . , λn ). Un-

der the optimal mechanism with insurance in Proposition 4, the firms with the K-lowest virtual valuations below their threshold t0i are expropriated and each other firm i pays (1 − λi ) yi (t−i )− A¯i .  
Assume now that each firm’s insurance coverage fall to A¯˜1 , . . . , A¯˜n ≤ A¯1 , . . . , A¯n and ˜ < A¯ or λ ˜ , ..., λ ˜ ) ≤ (λ , ..., λ ), with A¯ ˜ < λ for at least one firm i. Consider the mecha(λ 1

1

n

n

i

i

i

i

nism that  was optimal with the original profile of insurance coverage but now let each firm i pay  ˜ i yi (t−i ) − A˜ ¯i instead of (1 − λi ) yi (t−i ) − A¯i when it is not expropriated. While this new 1−λ

mechanism is not optimal under the lower profile of insurance coverage (in particular, any change

in insurance coverage will affect the virtual valuation functions, and thus change the thresholds for non-expropriation) it does increase the bureaucrat’s total expected payoff. This comes about as the bureaucrat’s expropriation revenue is exactly the same as before, but the revenue from bribery rises. It remains to be shown that this mechanism is incentive compatible. To this end, it suffices to observe that:
(i) With the original mechanism and the original profile of insurance coverage A¯1 , . . . , A¯n and

(λ1 , ..., λn ), the (normalized) expected payoff of firm i of type is ti (see Equation (11)) is Z (1 − λi )(ti − yi (t−i ))f−i (t−i )dt−i , Ui (ti ) = {t−i :yi (t−i )
  (ii) With the modified mechanism and the new profile of insurance coverage A˜¯1 , . . . , A˜¯n and   ˜ 1 , ..., λ ˜n , the (normalized) expected payoff of firm i of type is ti is λ ˜i (ti ) = U ˜i (ti ) = Since U

˜i 1−λ 1−λi Ui (ti )

Z

˜ i )(ti − yi (t−i ))f−i (t−i )dt−i . (1 − λ {t−i :yi (t−i )
for every ti ∈ Ti and i ∈ N , the IR and IC constraints in situation (i) imply

the analogous IR and IC constraints in situation (ii). We conclude that lower levels of insurance coverage are associated with greater corruption revenue, so that greater insurance coverage reduces the bureaucrat’s expected corruption revenue.

28

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