Corruption: top down or bottom up?

Waller, Christopher J. ; Verdier, Thierry ; Gardner, Roy 等

I. INTRODUCTION

Corruption takes many forms and can arise at many levels, as pointed out by the classic study of Wade (1985). A large literature has grown up since then, modeling various aspects of corruption; see the surveys by Bardhan (1997), Organisation for Economic Co-operation and Development (OECD) (1997), and Schneider and Enste (2000). One of the questions that this literature has yet to answer concerns the structure of corruption. Borrowing the language of budgeting, we can think of two structures of corruption: top-down and bottom-up, as in Gardner and von Hagen (1996) and Cheung (1998). Top-down corruption refers to a setting in which corruption decisions are centralized in the chief of state, who then monitors lower-level officials in an attempt to collect corruption rents. Bottom-up corruption refers to a setting in which corruption decisions are decentralized at the level of lower officials. In this form of corruption, the chief of state is simply one among many collectors of corruption rents. A similar distin ction, using the same language, is made by Rose-Ackerman (1999), where "bottom-up" refers to low-level officials collecting bribes and sharing them with superiors, while "top-down" refers to corrupt superior officials buying the silence of subordinates by sharing their ill-gotten gains.

There is evidence that both forms of corruption exist in practice, especially in various parts of the Commonwealth of Independent States (CIS). Quantitative evidence of the importance of corruption to macroeconomic performance is also available. In the latest report of the European Bank for Reconstruction and Development (EBRD), the states of the CIS are found to have substantially higher levels of corruption than the states of Central Europe, the Baltic republics, and the Balkans.

In the former, firms report paying 5.7% of all revenues as bribes; in the latter, only 3.3% of revenues (EBRD, 1999). The report finds it no coincidence that economic growth in the latter, less corrupt states, is more than 2% higher on average than growth in the CIS.

It goes without saying that states exhibiting either top-down or bottom-up corruption get low marks from the various international surveys of corruption. For instance, according to Transparency International, the average transparency ranking of ten Central European countries is 46, compared to 86 for ten CIS countries. However, what is unclear is how these different structures affect the economic performance--efficiency and growth--of the economy. Bardhan (1997) suggests that corruption is more acute in Russia today than in the former Soviet Union because it is now decentralized, not under party control as in the old days. He also compares Indonesia with India and raises an important question:

The two countries are equally corrupt and yet the economic performance by most accounts has been much better in Indonesia. Could it be that Indonesian corruption is more centralized and thus somewhat predictable ... whereas in India it is a more fragmented, often anarchic system of bribery? (Bardhan, 1997, 1325)

Bardhan's question is one of second best: Given that corruption exists, to what extent is one structure of corruption to be preferred to another? Informal arguments have been offered to suggest that one or the other structure is to be preferred, as in Shleifer and Vishny (1993) and Acemoglu and Verdier (1998, 2000), but a formal analysis has yet to answer this question. Our objective is to build a principal-agent model of government corruption to determine when and under what conditions centralized corruption is better for the economy than decentralized corruption. As we will show, the answer is not straightforward but depends on a large number of economic fundamentals.

Our metric of preference is allocative efficiency. One of our results is that allocative efficiency is monotonically decreasing in the total amount of corruption in monetary terms. This provides considerable support for allocative efficiency as a metric of preference. Another result characterizes the distribution of corruption payments, although, as might be expected, the relationship between distribution and allocative efficiency is quite complex. This point is made forcefully, albeit in a rather different model, by Bliss and Di Tella (1997).

Our main result is that we can divide the parameter space of the model into three mutually exclusive sets and, using these parameter sets, determine when top-down corruption is the preferred corruption regime and when bottom-up corruption is preferable. Under one set of circumstances (roughly, a government with high monopoly power and lower public sector wages), centralization of corruption increases overall corruption, because it is simply adding an additional layer of corrupt officials at the top. By contrast, when there are high enough public wages to motivate lower-level bureaucrats efficiently (through an efficiency wage kind of reasoning), centralization of corruption solves the double marginalization problem, improving the allocation of resources.

The crucial parameters for dividing the parameter space include the number of lower-level officials, their official wage, and their probability of being monitored. Previous studies have pointed to the importance of these variables. Thus, Mookherjee and Png (1995) give a central role to the official wage and the probability of being monitored, whereas the number of corrupt officials plays a central role in Tirole (1996). In contrast to the latter model, however, all (not just some) lower level officials are corrupt in our decentralized regime.

We also study the comparative statics of total corruption with respect to these parameters within a particular corruption regime as well as across corruption regimes. Here again the relationship between these parameters and allocative efficiency is complex. For instance, increasing the official wage (a popular policy recommendation among international donor organizations) may reduce neither the total amount of corruption, nor the number of corrupt officials. Such a reduction depends on the structure of corruption, as well as other parameters in the model. Results such as this suggest how sensitive empirical studies are to the specification of corruption. They also help explain why empirical results are so often inconclusive concerning the role of variables, such as the official wage of lower level officials.

This article has implications as well for the closely related literatures of crime, rentseeking, endogenous growth, common-pool resources, and the economics of transition. Basu et al. (1992) show that issues arise in complex corrupt settings that go well beyond the standard economic model of crime. Rentseeking, as in Acemoglu (1995) and Olson (1995), is what motivates officials playing in either of the corruption structures studied here. Our officials are rent-seekers, with rents being generated by expected gains from investments made in the economy; the autocrat in our model is likewise a rent-seeker. To the extent that corruption results in allocative efficiency losses--here, lost investments--we also get endogenous growth effects. These growth losses provide a formal explication of the concepts of social capital, as in Putnam (1993), and social breakdown, as in Hirshleifer (1995).

Next, one can interpret the demand for investments in an economy subject to corruption as a common-pool resource, as in Ostrom et al. (1994), where the commons is man-made and those using the commons are the bureaucrats (and possibly autocrat) charging bribes. Absent institutions to prevent tragic outcomes, one can expect such a commons to exhibit serious efficiencies in the presence of a large number of bribe-takers. This connection was first noticed by Shleifer and Vishny (1993).

Finally, because some of the successor states of the former Soviet Union rank among the most corrupt in the world, our results apply to the economics of the transition of those states from planned to market economies. Thus, for instance, we would expect the Tanzi effect--increases in the price level have a negative impact on real taxes collected due to corruption--to be present in the data generated from such countries. Moreover, we would predict considerable transition costs involved in restructuring a corrupt regime into a more transparent and open economic system. The financial crisis of summer 1998, whose effects still linger in the CIS, partly reflects the failure of international aid programs to achieve such a restructuring of these economies. Such is increasingly the view of the EBRD after a decade of aid programs in the CIS.

The article is organized as follows. Section II lays out the basic principal-agent model. Section III contains the results on bottom-up corruption; these turn out to be straightforward compared to those on top-down corruption. Section IV studies top-down corruption under the assumption that the participation constraints for lower-level officials is satisfied. Section V is devoted to a detailed examination of the participation constraint question. Section VI concludes.

II. MODEL

Our model has three players: entrepreneurs, bureaucrats, and an autocrat. Entrepreneurs undertake investment projects but need permits from the government to operate. The autocrat is at the top of the government hierarchy; the bureaucrats occupy the lower level of government responsible for day-to-day operations. Our government hierararchy has only two levels, and our autocrat is not accountable to the electorate, an assumption reasonable for many developing countries. Bag (1997) develops a model in which the public is the principal, monitoring the autocrat who in turn monitors the bureaucrat. We abstract from real-world complications by assuming at most two levels of corruption. Of course, in the real world there may be many layers of corruption. (See Guriev [1999] for an example of a three-tier government.) We assume bureaucrats have power to grant permits that private agents need to carry out business in the formal economy.

Corruption occurs when a bureaucrat demands a bribe from a private agent in return for the permit. The autocrat, if involved in the bribery, either receives a kickback from bureaucrats or chooses a level of bribe for the bureaucrats to demand. In our model, we do not impose any restrictions on the morality of the autocrat, that is, he or she does not oppose corruption on moral grounds, nor do we assume that the people are able to force the autocrat to oppose corruption via electoral competition. Again, we do not impose any restrictions on the morality of the bureaucrats; if taking bribes maximizes their utility, they take bribes.

The basic question in which we are interested is whether having the autocrat involved in the bribe process: (1) simply adds another bribe-taker or (2) reduces some inefficiency that arises from letting the bureaucrats determine bribes on their own.

Entrepreneurs

Individual entrepreneurs are endowed with two possible investment projects: one in the formal sector of the economy and one in the informal sector. The formal projects have idiosyncratic payoffs, and the informal sector projects do not. In short, the informal projects are homogeneous; each project offers the same fixed-return, as opposed to the heterogeneity inherent in formal sector projects. Operating in the formal sector requires the payment of taxes. The value of a formal sector project drawn by entrepreneur i is

(1) [V.sup.L.sub.i] = [V.sup.L] - t + [[alpha].sub.i],

where t is a lump-sum tax paid by each entrepreneur in the formal sector of the economy and [[alpha].sub.i] is the idiosyncratic return on the investment project, uniformly distributed on the interval [0, a]. If all entrepreneurs operate in the formal sector, the size of the formal economy is 1. The assumption that [[alpha].sub.i] is uniformly distributed is made for technical convenience only. Any continuous distribution will lead to the same qualitative results.

The informal project has a payoff

(2) [P.sup.I.sub.i] = [V.sup.I]

for all i. Taxes do not apply to the informal sector.

To undertake investment in the formal sector, entrepreneurs need to acquire a permit from each of n > 1 different bureaucrats in the government. In practice, this can lead to a large number of permits. Even for a small business in Ukraine, n = 10 is a typical number. Consequently, the net payoff to entrepreneur i from investing in the formal sector is given by

(3) [V.sup.L.sub.i] = [V.sup.L] - t + [[alpha].sub.i] - [B.sub.i],

where [B.sub.i] is the total amount of bribes paid by entrepreneur i, the sum of bribes [b.sub.i,j] paid by i to each bureaucrat j. We distinguish between taxes, t, which are determinate and predictable, and bribes B, which even at equilibrium have an element of arbitrariness to them. This interpretation is made forcefully by Wei (1997).

Entrepreneur i will choose to enter the formal sector of the economy when (3) exceeds (2), which implies

(4) [[alpha].sub.i] [greater than or equal to] -([V.sup.L] - t - [V.sup.I] - [B.sub.i]).

We will assume that [V.sup.L] - t - [V.sup.I] > 0. In the absence of corruption, where [B.sub.i] = 0 for all i, there would be no shadow economy, as (4) would hold for all i. This is the first-best benchmark outcome. At this first-best outcome, given our normalization, total taxes collected equal t, a maximum.

Bureaucrats

Each bureaucrat chooses a bribe to charge an entrepreneur who applies for a permit from his office. He also receives a civil servant wage, given by w. We assume w exceeds the bureaucrat's reservation wage from non-governmental employment, which we normalize to zero. This allows us to ignore modeling the bureaucrat's decision to work in the civil service, as in Besley and McClaren (1993).

The bureaucrat chooses a bribe to maximize expected income. The bureaucrat is not able to observe the idiosyncratic part of the entrepreneur's project but does know the distribution of [[alpha].sub.i]. By symmetry, a bureaucrat charges the same bribe to all entrepreneurs who request permits. Furthermore, he is aware that other bureaucrats are also demanding bribes.

Given these assumptions, the demand for permits Q, also the size of the formal sector, is piecewise linear in bribes. Letting X = a + [V.sup.L] - t - [V.sup.I] - [SIGMA][b.sub.j], where the latter sum is taken over all bureaucrats j, one has Q = X/a when X does not exceed a, and Q = 1 otherwise.

We also assume that the autocrat receives a kickback from each bureaucrat, with q denoting the fraction of the bribe income paid to the autocrat. Alternatively, one can think of q as the probability the autocrat detects whether or not the bureaucrat charges a bribe. If the bureaucrat is found to have taken a bribe, the autocrat takes the entire bribe but does not fire the bureaucrat. One could also model the problem as one in which the bureaucrat risks being fired in addition to losing the bribe income. As long as the kickback tax rate does not exceed q, the bureaucrats will be truthful in reporting their bribe income to the autocrat under this scenario also.

Under either of these interpretations, we take q to be exogenous, admittedly an extreme assumption made solely to better focus on the main issue, centralized versus decentralized corruption. For a method of endogenizing q, see Besley and McClaren (1993); our main results are robust to q endogenized in this way.

The bureaucrat's problem is to maximize bribe income, given by

(5) [max.sub.[b.sub.j]] [w + (1 - q)[b.sub.j] [[integral].sub.[X.sup.a]] (1/a)d[[alpha].sub.i]]

= [max.sub.[b.sub.j]] w + (1 - q)[b.sub.j]X/a

Notice that the bureaucrat's problem is degenerate if q = 1.

Autocrat

The autocrat levies taxes on the legal sector, pays civil servants wages out of the budget, monitors bureaucrats, and collects bribe income from those bureaucrats detected taking bribes. The autocrat's income z from the bribe process is z = qn[b.sub.j] X/a. The budget deficit G - T is given by G - T = nw - t X/a. Under our assumptions of a fixed w and n, government expenditures G are constant across all regimes. At the same time, taxes T are proportional to the size of the legal economy. Thus, at the first-best outcome, where the size of the legal economy is 1, one has G - T = nw - t = 0, where the last equality comes from assuming a balanced budget at the first-best outcome. Corruption, which reduces taxes collected, results in a budget deficit. One could impose a balanced budget constraint among the corrupt regimes as well. Because corruption leads to a smaller tax base, the need to cover a budget deficit by taxing other sectors of the economy would only be exacerbated in such a case.

A hallmark of corrupt regimes is the keeping of multiple sets of books. For instance, the autocrat (or his agent) may keep one set of books to satisfy international financial institutions that the budget is balanced, while keeping another set of books (the accurate set) showing the true budget imbalance. Such appears to have been the case at the Central Bank of Ukraine, which in 2000 agreed to pay the International Monetary Fund (IMF) a $100 million fine for bookkeeping and related irregularities in 1997-98.

III. DECENTRALIZED CORRUPTION

Uncoordinated Bribe-Setting

In our decentralized equilibrium, the autocrat specifies q and lets the bureaucrats choose whatever bribes they desire. At this Nash equilibrium, bureaucrats are modeled as players choosing their bribes simultaneously, taking the other bureaucrats' bribes as given. Consequently, the first-order condition from (5), exploiting symmetry, yields the following Nash equilibrium bribe per bureaucrat and total bribes paid by each entrepreneur:

(6) [b.sup.d.sub.j] = k/(1 + n),

where k = a + [V.sup.L] - t - [V.sup.I]

[B.sup.d] = nk/(1 + n),

where the superscript d denotes the decentralized equilibrium. These expressions have a long history in economics, going back to Cournot's (1838; rpt. 1963) treatment of the reverse monopoly problem. Given (6), the size of the legal economy is Q = k/(1 + n), which we assume to be less than 1 for the remainder of the article.

Total bribes paid in the economy are

(7) total bribes = Q[B.sup.d] = [k.sup.2]n/[(1 + n).sup.2],

of which proportion q are paid to the autocrat:

(8) z = q[k.sup.2]n/[(1 + n).sup.2].

Coordinated Bribe-Taking

If the bureaucrats coordinate their bribes and choose a common bribe, b, then the optimal bribe maximizes the representative bureaucrat's income, now given by

(9) [max.sub.b] [w + (1 - q)b [[integral].sub.-[X.sup.a]] (1/a)d[[alpha].sub.i]]

= [max.sub.b] w + (1 - q)bX/a,

where X = [V.sup.L] - t - [V.sup.I] - nb

Maximizing with respect the common bribe b yields

(10) b = k/(2n)

B = nb = k/2.

The size of the formal economy is Q = k/(2a), and total bribes are

(11) total bribes = BQ = [k.sup.2]/(4a).

Comparing (10) and (6) we see that the bribe price per entrepreneur is lower in this case than in the uncoordinated case. Comparing (11) and (7) reveals that total bribe income is larger in the coordinated case. Furthermore, the size of the formal economy is larger when bureaucrats coordinate their bribes. These results are shown in Figure 1.

This result generalizes that of Shleifer and Vishny's (1993) two-bribe-setter model. The reason for the high bribe price per entrepreneur in the uncoordinated case is that each bureaucrat fails to take into consideration how his bribe affects other bureaucrats' bribe choices. When bureaucrat i raises his bribe, on the margin he knows that this will reduce the probability that an entrepreneur will pay the higher bribe. However, he ignores the fact that by reducing the entrepreneur's probability of paying bribes, he reduces expected bribe income for all other bureaucrats. This negative externality results in asking for too large a bribe by all n bureaucrats in the uncoordinated case.

In a sense, the investment demand under decentralized corruption is like a commonpool resource, in which the entrepreneurs are an investment commons being exploited by the bureaucrats. As a result, a typical tragedy of the commons problem arises and the bureaucrats overuse (extract too much rent) the resource. As pointed out by Ostrom et al. (1994), in the absence of institutional arrangements to prevent overuse from occurring, one expects very inefficient outcomes as the number of bureaucrats grows large. Here, as n gets large, investment demand is extinguished--the ultimate inefficiency, as compared to the first-best benchmark.

All bureaucrats would benefit from forming a cartel and acting as a monopoly bribe-setter. In addition, the legal economy would be larger under the cartel arrangement. However, the usual problems with enforcing cooperation apply here. Thus an institutional arrangement that enforces the monopoly bribe-setting outcome is needed. This is where the hierarchical structure of the government comes into play--the autocrat can serve as the institutional enforcement mechanism to maximize total bribe income. It is to this arrangement that we now turn.

IV. CENTRALIZED EQUILIBRIUM

Now consider the case where the autocrat mandates that the bureaucrats charge a bribe of a certain size, which is to be turned over to the autocrat. The autocrat can then redistribute all or part of the bribe income back to the bureaucrats in the form of a lumpsum transfer. However, bureaucrats may decide to disobey orders by charging more than the mandated bribe and keeping the difference. Hence, the autocrat and bureaucrats are involved in a standard principal agent problem. To enforce compliance, the autocrat threatens dismissal if a bureaucrat is caught charging more than the mandated bribe. If the bureaucrat is caught taking an extra bribe, the bribe is confiscated and he is fired from his civil service job. Though the threat of job loss is a standard argument for inducing honest behavior on the part of civil servants, in our model, the threat of job loss is not used as a tool to eliminate corruption. Rather, it is used to ensure that bureaucrats produce the autocrat's desired amount of corruption.

By locating the bribe decision at the top of the hierarchy, we are confronted with a dilemma. Does centralizing the bribe decision at the top increase total corruption by simply adding a layer of corruption to the process? Or, by internalizing the effect of total bribes on legal activity, does centralization at the top reduce total corruption? In the next section, we show that either outcome can be generated, depending on the parameters of the model.

The Bureaucrat's Problem

In the centralized equilibrium, the autocrat tells each bureaucrat to charge b per permit and return the proceeds back to the autocrat. Each bureaucrat must then decide whether or not to charge more than b at the risk of getting fired. If the bureaucrat does not charge an amount above b, his income is simply w plus his lump sum transfer [tau]. If he does charge more than the mandated bribe b his problem is

(12) [max.sub.[b.sub.j]] [(1 - q)(w + [tau]) + (1 - q)[b.sub.j] [[integral].sub.-[X.sup.a]] (1/a) d[[alpha].sub.i]]

= max(1 - q)[w + [tau] + [b.sub.j] X/a],

where X = [V.sup.L] - t - [V.sup.I] - nb - [SIGMA] [b.sub.j], b is the mandated bribe per bureaucrat and [b.sub.j] is the additional bribe demanded by bureaucrat j over and above that mandated by the autocrat. The first-order condition for this problem yields the following Nash solution for [b.sub.j] in the centralized equilibrium

(13) [b.sup.c.sub.j] = (k - nb)/(1 + n)

where the superscript c denotes the centralized equilibrium.

If k - nb < 0, the net value of the project is zero and no entrepreneurs will be in the legal sector, which means no bribe income or tax revenues for the government. Thus, we will only consider solutions for which (13) is positive. The bureaucrats will only choose to demand [b.sup.c.sub.j] if their expected equilibrium income from asking for additional bribes exceeds their civil service salary. Otherwise [b.sup.c.sub.j] = 0. The condition for the bureaucrats to comply with the mandated bribe and set [b.sup.c.sub.j] = 0 is

(14) nb [greater than or equal to] k - (1 + n)[[aq(w + [tau])/(1 - q)].sup.1/2].

Note that (14) is more likely to hold, the larger are q, w, [tau], and b. Intuitively, bureaucrats are more likely to do what the autocrat tells them to do the larger the probability of getting caught and the more costly it is getting fired. Furthermore, the larger the mandated bribe b, the smaller the expected number of entrepreneurs applying for permits. Because this reduces the expected payoff from asking for even more bribes, the bureaucrats are more likely to comply with the autocrat's orders. Because the bureaucrat cares about the sum w + [tau], we set [tau] = 0 and simply rescale the value of w to account for this. As we argue later, the autocrat has strong incentives to reward the bureaucrats in this fashion.

The Autocrat's Problem

The autocrat wants to choose b to maximize his expected bribe income, denoted Y(nb), taking the bureaucrat's bribe decision as given. However, from (14) we see that his choice of b affects the bureaucrat's decision to cheat on the mandated bribe or not.

Let n[b.sub.0] = [B.sub.0] denote the value that makes (14) hold with equality,

(15) [B.sub.0] = k - (1 + n)[[aq(w + [tau])/(1 - q)].sup.1/2].

This is the value of n[b.sub.0] that makes the bureaucrat indifferent between cheating or not. Hence, the bureaucrat's bribe decision is

(16) [b.sub.j] = (k - nb)/(1 + n) when nb < [B.sub.0]

[b.sub.j] = 0 otherwise.

Now, depending on whether bureaucrats ask for bribes or not, the autocrat's expected income can be computed as follows. When bureaucrats comply with the autocrat's bribe orders, [b.sub.j] = 0, the autocrat becomes a monopolist bribe-setter. In this case, his expected income [Y.sub.m](nb) is given by

(17) Y(nb) = [Y.sub.m](nb) = [(k - nb)/a](nb).

The first term in (17) is the measure of entrepreneurs who apply for permits (k - nb)/a and the second term nb is the level of mandated bribes.

When bureaucrats charge more than the mandated bribe, the autocrat merely becomes the n + 1 bribe-setter. Hence his expected income in this case, denoted [Y.sub.2](nb), is the sum of his expected mandated bribe income plus his expected income from confiscating the additional bribes from bureaucrats he catches cheating:

(18) Y(nb) = [Y.sub.2](nb)

= [(k - nb)/(a(1 + n))]

x [(qn[k - nb]/[1 + n]) + nb].

The first bracketed term in (18) is the measure of entrepreneurs who apply for permits, and the second bracketed term is the sum of confiscated bribes and mandated bribes. Figure 2 plots the two functions [Y.sub.2](nb) and [Y.sub.m](nb). The autocrat's expected income with bureaucrats' corruption [Y.sub.2](nb) has a maximum at [B.sup.^] = n[b.sup.^] = [gamma]k/2, where [gamma] = (1 + n - 2qn)/(1 + n - qn) < 1.

His monopolistic expected income [Y.sub.m](nb) has a maximum at [B.sup.*] = n[b.sup.*] = k/2 > [B.sup.^]. Because being a monopolist is clearly better than being an n + 1 bribe setter, one also gets that [Y.sub.m]([B.sup.*]) [greater than or equal to] [Y.sub.2]([B.sup.^]).

Figure 2 plots these two payoff functions for the autocrat. Let [B.sup.~] be the value of B for which the autocrat's income in the monopolistic bribe-setting regime equals his maximum income in the bureaucratic corruption regime. Any value of B in [k/2, [B.sup.~]] yields higher bribe income for the autocrat than the regime with bureaucratic corruption.

The problem of the autocrat is then to maximize his payoff function Y (nb) over B = nb given the incentive constraint for bureaucrats given by (14). Three possible regimes can emerge, depending on where the boundary point of the incentive constraint lies. It turns out that the optimal value of B can be reached at [B.sup.^] = [gamma]k/2, [B.sup.*] = k/2, or the threshold point [B.sub.0]. We consider each regime in turn.

Regime 1: Bribes at Both Levels of Government

This case, represented in Figure 3, occurs when [B.sub.0] > [B.sup.~] > k/2. The autocrat maximizes his expected income at [B.sup.^]. As a result, this is a regime with corruption at both levels of government. Because entrepreneurs pay bribes to both bureaucrats and the autocrat, total bribes per entrepreneur are

(19) total bribes per entrepreneur

= n[b.sup.c] + n[b.sup.^] = (2n + [gamma])k/(2[1 + n]).

Total bribes paid in this regime equal

(20) total bribes = (n[k.sup.2])/(a[[1 + n].sup.2])

- [gamma][k.sup.2](n - 1 + [gamma]/2)

/(2a[[1 + n].sup.2]),

and the autocrat's bribe income in this regime is [Y.sub.2]([B.sup.^]) = [k.sup.2]/(4a[1+n(1-q)]).

Comparing (19) to (6) we see that total bribes per entrepreneur is higher than in the decentralized corruption case. However, the total amount of bribes paid to the government in this regime is lower than in the decentralized corruption equilibrium. The reason is that the total number of entrepreneurs applying for permits falls enough to more than offset the increase in bribe payments per entrepreneur, that is, the demand for permits is bribe-elastic at this level of equilibrium bribes per entrepreneur. This is a result of the distributional assumption on [[alpha].sub.i], permit demand is elastic for B > k/2. Thus, the formal economy is smaller in this regime than in the decentralized regime. Adding a layer of government to the corruption problem leads to a worse outcome than in the uncoordinated decentralized equilibrium.

Regime 2: Monopolistic Bribe-Setting by the Autocrat

Figure 4 shows this regime, which occurs when [B.sup.*] = k/2 [greater than or equal to][B.sub.0]. The autocrat has a maximum income at the point: [B.sup.*] = n[b.sup.*] = k/2, which is also the total bribe per entrepreneur, as this is the regime with monopoly corruption.

The autocrat sets a higher mandated bribe if he is a monopolist bribe-setter than he does in the regime in which bureaucrats cheat and charge additional bribes. However, despite the fact that the autocrat mandates a higher bribe in regime 2 than regime 1, comparing [B.sup.*] to (10) and (20) shows that total bribes actually paid per entrepreneur are lower in this case than in regime 1 or the decentralized corruption equilibrium. Nevertheless, equilibrium bribe income is highest in this regime. By centralizing the bribe process and becoming a monopolist bribe-setter, the autocrat internalizes the externality associated with uncoordinated decentralized bribe-setting into account. As a result, total bribes per entrepreneur are reduced.

Regime 3: The Constrained Monopolist Bribe-Setter

This is the regime that reflects the fact that the autocrat is constrained in his maximization of monopolist bribes and is shown in Figure 5. This regime occurs when [B.sup.~] > [B.sub.0] > k/2. The autocrat cannot choose the monopolist bribe because it is not high enough to deter the bureaucrats from charging an additional bribe. However, by choosing [B.sup.*] = [B.sub.0] in this case, the autocrat makes the mandated bribe high enough to deter additional bribes and still earn more income as a monopolist bribe-setter that reverting to being the n + 1 bribe-setter. Consequently, in the regime the autocrat is at a corner. Total bribes paid per entrepreneur are higher than in the case where [B.sup.*] = k/2. The total bribes paid per enterpreneur will be lower than in the decentralized case when 2(1+n)[(aqw/[1 - q]).sup.1/2] < k < [(1 + n).sup.2] [(aqw/[1 - q]).sup.1/2].

Figure 6 summarizes the ordinal ranking of each regime compared to the decentralized Nash bribe-setting regime. We see that the two-level bribe equilibrium is the worst outcome, followed by the decentralized Nash equilibrium, the constrained equilibrium and the monopoly bribe-setter equilibrium.

Discussion of the Three Regimes

It is useful to investigate the parameters' conditions under which the different regimes prevail. To do this, let y = [(aqw/[1 - q]).sup.1/2] and thus [B.sub.0] = k - (1 + n)y.

The conditions for regime 1 are [B.sub.0] > k/2 and (k - [B.sub.0])[B.sub.0]/a < [k.sup.2]/(4a[1 + n - qn]). These can be rewritten as k > 2(1 + n)y and k > 2(1 + n)A(q, n)y, where A(q, n) = 1/[1 - [[n(1 - q)/(1 + n[1 - q])].sup.1/2]] > 1. Hence the two-level bribe regime will prevail under the condition

(A) k > 2(1 + n)A(q, n)y.

Similarly, the condition for the monopolistic centralized bribe regime (regime 2) is given by [B.sub.0] < k/2, which can be rewritten as

(B) k < 2(1 + n)y.

Finally the constrained monopolist regime (regime 3) occurs when

(C) 2(1 + n)y < k < 2(1 + n)A(q, n)y.

The three regions (A), (B), and (C) are represented in Figure 7 in the plane (y, k). The value of k represents the measure of how many high return investment projects there are in the economy. When this number is large, asking for a bribe has a small effect on driving entrepreneurs into the informal sector. The value of y reflects the expected cost of getting fired. The monopolist bribe regime is more likely to prevail when y is large relative to k, which is likely to be satisfied when the cost of getting fired is relatively high. In this region, the autocrat is able to implement the monopolist bribe because he is able to efficiently monitor his bureaucrats through the stick (the probability of control q) or the carrot (the wage rate w).

On the other hand, the regime with bribes at both levels is more likely to occur when k is large--namely, when the after-tax relative return of the legal sector as compared to the informal sector is high or there are many high-value investment projects in the economy (a large value of a). In this region, the temptation for bureaucrats to ask for an additional bribe is quite high, making it difficult for the autocrat to fight corruption at that level of the bureaucracy. Hence his optimal response is to choose the two-level corruption regime. Finally, for intermediate values of k and y, the constrained monopolist bribe regime prevails. The autocrat would ideally want to be a monopolist briber but, given the fundamentals of the economy, his monopolistic bribe level is not high enough to deter bribe-taking at the lower level of the bureaucracy. Therefore he prefers to choose a constrained monopolistic bribe level.

An increase in the size of the bureaucracy n shifts counterclockwise the two rays k = 2(1 + n)y and k = 2(1 + n)A(q, n)y in Figure 7. This has the effect of enlarging the monopolistic bribe region and reducing the two-level bribe region. The effect on the constrained monopolist bribe region is ambiguous. The reason is that as n increases, bribing becomes less profitable for bureaucrats, as fewer entrepreneurs choose to enter the formal sector by paying bribes. Hence it is easier for the autocrat to sustain the monopolistic bribe regime or the constrained monopolistic regime.

The previous discussion provides also some cross-country predictions on the implications of having an additional layer of corrupt administration on corruption and its efficiency costs. In particular, it suggests that an additional layer of corrupt bureaucracy is more likely to have corruption efficiency costs on output for rich economies, which presumably are also the ones with large corporate opportunities for business in the formal sector. On the other hand, poor economies in this second-best world may be better off in terms of production with a corrupt autocratic government hierarchy able to capture monopolistic rents and deter lower-level corruption.

Interestingly, this also suggests that any liberalization or economic reform, which increases the profitability of the private legal sector, should be accompanied by intensive administrative reforms against corruption. Otherwise, liberalization without reform at the top level of the bureaucracy may well move the corruption equilibrium from a monopolistic bribe region (B) to a two-level bribe situation (A), increasing corruption-induced inefficiencies and thereby stripping away the potential economic gains of the liberalization process.

The Correlation of Corruption with Economic Activity

Which of the bribe equilibria has the lowest level of corruption? To answer this question, we must construct a metric of corruption. However, such a construction is problematic given the above results. If we measure corruption as the bribes paid per entrepreneur (or investment project), then corruption is highest in the centralized regime 2 and lowest in the centralized regime 1. On the other hand, if we measure corruption as total bribe income, then corruption is lowest in regime 1 and highest in regime 2. Hence, depending on how one wants to measure corruption, the monopoly bribe-setting equilibrium may be viewed as the lowest- or the highest-corruption equilibrium. But regardless of how corruption is measured, the legal sector of the economy is largest in this regime, as is per capita income.

This result is interesting because it ties into a long-standing debate regarding the efficiency implications of corruption. On the one hand, it is argued that corruption reduces private market efficiency by creating frictions that inhibit private sector investment. Hence, corruption is sand in the wheels. On the other hand, it is also argued that corruption is often the only way to get things accomplished; without it, nothing gets done. According to this line or argument, corruption greases the wheels.

Our results show that whether or not corruption is correlated with private sector investment depends to some extent on how one measures corruption. In the monopoly bribe-setting equilibrium, bribes per investment project are the lowest, hence there is more private sector investment. But because more entrepreneurs choose to operate in the legal sector and acquire permits from the government, total bribe payments in the economy are high. Hence, by the first measure, corruption exhibits a negative correlation with private sector activity; by the second measure, corruption is positively correlated with private sector activity. This suggests that empirical studies purporting to estimate the correlation between corruption and private sector activity must be very careful in how they measure corruption.

For our purposes, because the regime with the lowest bribe per entrepreneur has the largest legal sector and, thus, the largest level of per capita income, we believe this is the most relevant measure of corruption. Consequently, in regime 1 we find that adding a layer of government to the bribe process simply leads to more corruption, whereas in regime 2 we find that adding a layer of government actually lowers the amount of corruption.

Welfare Analysis of the Different Regimes

Clearly the regime with corruption at both levels is the worst equilibrium possible for all involved, except the bureaucrats. In this equilibrium, bribes per entrepreneur and the shadow economy are at their highest values and tax revenues and the autocrat's bribe income are at their lowest values. Adding the autocrat into the bribe process simply adds a layer of corruption that worsens economic efficiency. On the other hand, the monopolist regime may be welfare-improving compared to the decentralized (one-layer) corruption equilibrium. As we already noticed, in a second-best world in which corruption is unavoidable, centralized corruption internalizes the negative externality of corruption by other bureaucrats on investment decisions in the formal economy. This tends to improve the efficiency of allocation of resources in the economy. On the other hand, a monopolist in corruption has more monopoly power to set bribes, hence asking for a larger bribe per project. Whether the centralized monopolist corruption e quilibrium is more efficient than the decentralized corruption equilibrium depends on which effect is stronger. Here the externality effect is stronger than the monopolization effect, as total bribes per project in the decentralized equilibrium nk/(1 + n) is larger than total bribes per project under monopolization. Hence, from an efficiency point of view, centralized regime 2 provides the best corruption equilibrium.

The third corruption regime can be analyzed similarly. Total bribe per project is [B.sub.0], which is smaller than the bribe with centralized corruption, nk/(1 + n), as long as k < [(1 + n).sup.2]y holds. In this case, this regime provides a larger legal economy than does decentralized corruption and so leads to a more efficient allocation of resources.

V. ENSURING BUREAUCRATIC COMPLIANCE

Up until now we have assumed that the parameters affecting the bureaucrats' compliance with the bribe mandate, q, w, n, and k, were constant. However, all four of these parameters are under the control of the autocrat to some extent. The parameter q is a function of the autocrat's monitoring technology and effort. The civil servant's salary, w, can be set by the autocrat. The size of the bureaucracy, n, is also under the control of the autocrat. Finally, k is affected by the taxes imposed on entrepreneurs by the autocrat.

Because the autocrat's most preferred bribe equilibrium is the interior monopolist bribe-setting solution, he has a strong interest in ensuring that bureaucrats comply with the mandated bribes. Combining the equilibrium bribe under monopoly [B.sup.*] with the incentive compatibility constraint (14) yields

(21) k [less than or equal to] 2(1 + n)y.

Because he has control of the parameter values of k, q, n, and w, the autocrat can adjust these four parameters to ensure that (21) always holds. He can do this by

1. raising tax rates to lower k (the net value of legal projects);

2. increasing the bureaucrats' salary;

3. increased monitoring of bureaucrats (increase q); or

4. increasing the size of the bureaucracy (increase n).

Although the autocrat can ensure that (21) holds using any one of these instruments, he will not be indifferent to which of these parameters is used. In the sections that follow we discuss the attractiveness of using each of these variables to ensure the bureaucrats' compliance with the mandated bribes.

Raising Taxes

Increasing taxes on firms will lower the value of all projects and the demand for legal projects. By lowering the expected bribe income for bureaucrats, the autocrat ensures that they are less willing to ask for bribes and risk being fired. Unfortunately, lowering k also reduces the autocrat's bribe income. Sacrificing income to induce bureaucrats to behave seems to us to be an unattractive method for inducing cooperation.

Raising Civil Servant Salaries

By raising civil servant salaries, the autocrat increases the penalty of getting caught taking an additional bribe. Because civil servant salaries are paid for out of the public budget rather than the autocrat's bribe income, this is essentially a free tool for the autocrat to ensure compliance with his bribe orders. In a sense, this is a key difference between an autocrat and a mafia chieftain. Mafia chieftains are the residual claimants to enterprise profits whereas autocrats are not typically the residual claimants on government tax surpluses. Increasing the pay of underlings reduces the residual profits of the mafia enterprise and thus the income of the chieftain, but paying higher salaries to civil servants out of public revenues does not reduce the autocrat's income. So unless the autocrat is able to use tax revenue surpluses for his own use, raising civil servant salaries to induce compliance with his demands seems to be a relatively costless method for maximizing his bribe income.

Of course, if the autocrat gets utility from public spending projects, such as more education, highways, or monuments glorifying him, then the reallocation of tax revenues from these types of projects to civil servant salaries will impose a cost on the autocrat. The form of corruption and preventive measures may affect the allocation of government revenues on public goods. Mauro (1998) finds that corruption is negatively correlated with government spending on education. Thus, the question becomes, Which is more important, his personal bribe income or the warm glow he gets from improving the government capital stock? Our suspicion, based on casual observation of autocratic governments around the world, is that the former is more important to autocrats than the latter.

Increased Monitoring

The autocrat can also undertake more intensive monitoring of the bureaucrats to ensure that they abide by his bribe mandate. But if this requires expending utility reducing effort by the autocrat, he may opt for another method of enforcement, as in Bac (1996a, 1996b). On the other hand, if the autocrat can use public funds to increase compliance, then we have the same situation as with raising salaries. For example, if he creates a watchdog group of civil servants responsible for enforcing compliance with the autocrat's demands and pays them with tax revenues, then the autocrat has a free method of increasing monitoring. However, this simply creates another principal-agent problem for the autocrat because the bureaucrats may pay bribes to the internal police to avoid dismissal. In short, who monitors the monitors?

Increasing the Size of the Civil Service

By increasing the size of the bureaucracy, the total amount of bribes increases, thereby reducing the demand for permits and the expected bribe income of an individual bureaucrat. Hence, as an individual bureaucrat becomes a smaller part of the government bureaucracy, he is less likely to risk being fired to receive a small amount of bribe income. Once again, the bureaucracy is paid for out of public funds, so this is a free method for the autocrat to ensure compliance with his orders. However, this assumes that the probability of detection remains the same as the number of bureaucrats increases. In general, this is not true; as the size of the bureaucracy increases, detection of additional bribe-taking is reduced. Hence, increasing n will typically be associated with a reduction in detection, which increases the payoff from asking for an additional bribe. As a result, increasing the size of the bureaucracy may actually backfire and lead to a greater likelihood of an individual bureaucrat asking for additional bribes.

VI. CONCLUSION

In summary, it appears that increasing civil servant salaries is the best option for the autocrat to ensure that bureaucrats ask only for the bribes they are told to collect. All of the other methods appear to impose nontrivial costs on the autocrat.

If the economically optimal amount of corruption is not zero, then an interesting question is where should the corruption be allocated--at the top of the government hierarchy or the bottom? Having built a hierarchical model of government, we explored the question of whether centralizing corruption at the top simply increases the total amount of corruption in an economy or reduces it by generating an organizational efficiency gain (via a principal-agent relationship between levels of government). We have argued that if corruption is measured by the amount of bribes paid per investment project, then centralizing corruption at the top of the government may lead to a more efficient allocation of corruption. Furthermore, the top level of governmental hierarchy has many tools at its disposal to ensure that this outcome prevails. However, if corruption is measured as the total volume of bribes paid in the economy, then centralizing bribe decisions at the top of the hierarchy leads to more corruption in the economy, even though there is a larger private sector in this corruption regime. Thus, our theoretical results provide an important caveat for doing empirical work on the effects of corruption on private sector activity. In either event, the EBRD's concern with the amount of corruption in the CIS is well founded. Indeed, the CIS would seem to be an area where centralizing corruption does not seem to yield good economic results.

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RELATED ARTICLE: ABBREVIATIONS

CIS: Commonwealth of Independent States

EBRD: European Bank for Reconstruction and Development

OECD: Organisation for Economic Co-operation and Development

ROY GARDNER *

* We would like to thank Krister Andersson, Kaushik Basu, Steve Lewarne, Rob Masson, Michael McGinnis, Bruce J. Bueno de Mesquita, Elinor Ostrom, Eric Rasmusen, and an anonymous referee for helpful comments. Any remaining imperfections are the sole responsibility of the authors, who wrote this article as visiting faculty members at Economics Education and Research Consortium, National University of Ukraine, Kyiv-Mohyla Academy.

Waller: Gatton Chair, Department of Economics, University of Kentucky, Lexington, KY 40506-0034. Phone 1-859-257-6226, Fax 859-323-1920, E-mail cjwall@pop.uky.edu

Verdier: Professor, Department and Laboratory of Theoretical and Applied Economics (DELTA), 75014 Paris, France. Phone 33-1-43 13 63 98, Fax 33-1-43 13 63 10, E-mail tv@delta.ens.fr

Gardner: Chancellor's Professor, Departments of Economies and West European Studies, Indiana University, Bloomington, IN 47405. Phone 1-812-855-6383, Fax 1-812-855-3736, E-mail gardner@indiana.edu