Delegation,capture and endogenous information structures

1. Introduction

Policy-making most often takes place in highly complex and uncertain environments. Macroeconomic and fiscal policies, economic, environmental and social regulations to quote a few offer a whole array of examples where the precise contours of optimal public decisions are difficult to assess ex ante and their ex post consequences hard to anticipate at the time of their design by acts of Law. Congress lacks the needed expertise to reach sound policy-making. In response to this informational deficit that spans an ever-expanding set of issues, Congress has chosen to delegate an increasing share of its decision-making to better informed agencies, legislative committees and sub-committees so as to inform and sometimes design better policies. ¹

Following Gilligan and Krehbiel (1987, 1989, 1990), Epstein and O’Halloran (1994, 1999), Huber and Shipan (39), Bendor and Meirowitz (8), and Baron (6) among many others, a large and insightful branch of formal political science has been devoted to study this delegation process in contexts pervaded by asymmetric information. This literature has offered a number of key insights on what should be the optimal degree of discretion left to the bureaucracy, the scope and nature of communication processes between bureaus, committees, regulatory agencies and Congress and the various institutional tools that could help controlling bureaucratic drift if any.

Yet, the extant literature on delegation has also mostly focused on the two-tier simple hierarchical relationships between Congress and the bureaucracy when taken in isolation, treating the environment in which agencies evolve as immune to any outside influence. In particular, a basic tenet of this approach remains to assume that the preferences of bureaucrats over policy outcomes and the informational structure are exogenously given. In practice, non-elected officials do entertain close-knitted relationships with various interest groups. ² Interest groups devote much time and resources to influence government agencies and experts commissions. ³ This influence, in turn, shapes the agencies’ preferences and thus their relationships with Congress. As forcefully argued by Boehmke et al. (12), “Theories of legislative-bureaucratic relations that ignore the role of interest groups and non-governmental actors generate predictions that, while potentially important and informative, are only ‘partial equilibrium’ in nature.” ⁴ Starting from this important observation, this paper aims at reinstalling the Theory of Delegation into a more realistic realm. In this respect, we shall assume that agencies are not only subject to the influence of Congress but also under the pressure of interest groups. We thus study how regulatory capture by interest groups determines the delegation process.

Taking into account the influence of interest groups is all the more relevant that, at least since Lowi (54) and Stigler (74), one of the main concerns raised against the wide recourse to delegation is the threat it poses to the whole democratic process of policy-making. Policy-making is viewed as being at the risk of escaping from the hands of the elected public representatives to end up under the uncontrolled influence of private interest groups. Even when taking this concern very seriously, McCubbins et al. (1987, 1989) took an optimistic stance. Indeed, those authors argued that, with an eye on the environment in which those agencies evolve, Congress is able to design bureaucratic procedures to keep agencies on check. More precisely, Congress can stack the desk so that agencies are monitored by groups which are de facto allied with Congress. This seminal idea, although it stimulated a large body of works in the political science literature, has so far received no formal modeling, at least to the best of our knowledge. This paper aims at filling that gap.

In this respect, it should be first recognized that the ability of interest groups to channel their influence on regulators depends on the information structure that surrounds the bilateral relationship they entertain with those regulators. While some groups share most policy relevant information with the relevant agency, and thus stand on equal feet, others lack relevant information, making the relationship with their agency de facto quite asymmetric. A first step of our analysis thus consists in investing the role and the possible consequences that various degrees of informational asymmetries have on the way interest groups might influence their regulatory agencies.

From there, a second step our analysis, much in the spirit of McCubbins et al. (1987, 1989), consists in observing that Congress might react to this influence of interest groups by shaping the contours of the agency’s mandate and discretion. In more technical parlance, the degree of discretion left to regulatory agencies and the information structure that surrounds their intervention should jointly be determined at equilibrium.

This approach is novel. While asymmetric information between the Congress and agencies has long been recognized as the main justification for both the discretion left to the bureaucracy and the limited scope of regulatory mandates, nothing is known on how the distribution of information between interest groups and agencies impacts those mandates and the afforded discretion. ⁵ Addressing this question helps us to understand which informational structure interest groups would favor, depending on how their preferences differ from those of Congress and the agency. ⁶

Key ingredients of the Model. Congress (referred as it in the sequel) delegates regulatory rights to an informed agency (she) who is herself subject to the influence of an interest group (he). The raison d’être of this delegation is that policy-making takes place in a world of uncertainty. ⁷ Congress has to rely on the agency’s expertise who learns about a policy-relevant state of nature so as to improve decision-making.

When the group exerts no influence. Absent any influence by the interest group, the only flip side of such a delegation is that the agency’s own preferences on which policy should be pursued might differ from Congress’ ideal point. The optimal mandate of the agency then results from a well-known trade-off between rules and discretion. ⁸ Using the workhorse model of the political science literature with quadratic preferences and a uni-dimensional policy, ⁹ it is easy to see that, when the agency has a fixed upward bias with respect to Congress, this mandate takes a simple form. Congress limits the agency’s discretion by putting a cap on the possible policies the agency can choose from. The Ally Principle ¹⁰ then states that a more biased agency should be given less discretion.

The Ally Principle takes the perspective of Congress which acts as a principal in designing regulatory mandates. Taking now the perspective of an interest group with his own preferences somewhat modifies the results, and allows to identify two antagonistic effects. On the one hand, and for a given a level of discretion left to the agency, the interest group would always benefit from an agency having an ideal point close to his own. Indeed such an agency would pick decisions closer to the group’s preferences. This Proximity Effect echoes the Ally Principle but now takes the group’s perspective. On the other hand, when bringing the agency ideologically closer to the group also means moving her away from Congress, Congress’ response is to restrict the agency’s discretion. As rules become more stringent, policies are less sensible to the state of the world, which in fine hurts the group by reducing the agency’s discretion. This Discretion Effect contrasts with the Proximity Effect; an interest group prefers an agency closer to Congress than what he is himself.

Suppose now that the interest group plays a more active role and aims at capturing the agency to promote his own goal. We model such an influence by means of a side-contract in which the group offers transfers to the agency in exchange for more favorable decisions. By modifying which policies would end up being implemented by the agency, this external influence also perturbates the relationship between Congress and the agency, and the extent to which the former is willing to delegate. To see how it can be so, we consider two alternative scenarios.

Capture under symmetric information. Suppose first that the interest group and the agency collude against Congress under symmetric information. Following the vocabulary coined by Hula (41) in another context and later used in Martimort and Semenov (59), we will refer to a strong coalition in that scenario. Since no informational friction prevents efficiency, the interest group and the agency agree on a decision that maximizes their joint surplus provided that it remains feasible, i.e., within the limits of the agency’s mandate. When such a strong coalition realizes, the agency ends up choosing decisions which are optimal for the coalition she forms with the group. This decision corresponds to the ideal point of a fictitious agency whose preferences would average her own and that of the group.

Capture under asymmetric information. Suppose now that the agency has an informational advantage vis-à-vis the interest group. Such asymmetry is likely to be prevalent in any situation where the group’s vision of the ins and outs of policy-making is at best limited in scope. ¹¹

A key building block of our analysis thus consists in developing a theory of capture under asymmetric information. The side-contract proposed by the group now serves a twofold objective. First, it helps the agency to better internalize the group’s preferences. Second, and in sharp contrast with the case of symmetric information, it facilitates screening of the agency’ private information. Under asymmetric information, the side-contract is drafted with an eye on a rent-efficiency trade-off. Implementing a decision rule that would be close to that a strong coalition would choose may require leaving an information rent to the agency. This rent is viewed as costly by the group in terms of extra side-payments needed to induce information revelation. Because of this trade-off between rent extraction and efficiency, the decision rule is now distorted towards the agency’s ideal point. Asymmetric information is akin to a shift in bargaining power towards the informed agency that renders capture more difficult. The outcome of regulatory capture under asymmetric information can be encapsulated into a single parameter: the agency’s virtual bliss point. When a weak coalition forms, everything happens as if the agency’s ideal point was now conflating the influence of the group and its own preferences with some added distortions due to asymmetric information. The loss of bargaining power due to informational asymmetry might sometimes be so severe that the group ends up having no influence at equilibrium. ¹² Most often, the group may still keep some influence but it remains limited in scope. In both cases, it is of crucial importance for our analysis that this virtual bliss point always ends up to be closer to the agency’s ideal point than when collusion takes under symmetric information.

Agency’s mandate and discretion. The impact of capture on the discretion granted by Congress depends on the group’s bias and on whether a weak or strong form of collusion emerges. An extreme group, that is even more biased than the agency, will pressure the bureaucracy to implement more biased actions than in the absence of capture. In response, Congress enacts more stringent mandates and restricts discretion. How severe this response ends up being depends on the group’s ability to influence the agency. Since a strong coalition is closer to the group’s ideal point than a weak one, Congress grants more discretion when facing a weak coalition.

The reverse holds when the group is moderate, i.e., less biased than the agency. Capture by such a group tilts the decision towards Congress’ ideal point. In response, the agency is granted a less stringent mandate. This effect matters all the more that the group has a greater ability to influence the agency. As a consequence, Congress will now grant more discretion when facing a strong coalition.

That, in front of a moderate group, Congress would like to increase this group’s ability to influence the agency because it would better align this agency with its own position is an important take-away from our analysis. This result provides firm foundations for McCubbins et al. (1987)’s insights that the pattern of outside influence on an agency somehow shapes its mandate and may explain some intriguing features of bureaucratic procedures. To illustrate, these authors pointed out the case of the U.S. Consumer Product Safety Commission. This agency was once constrained and funded by Congress in such a way that both its agenda and the writing of safety standards were virtually dictated by the organized groups most interested in consumer safety. This surprising feature is well explained by our theory that argues that Congress should find it profitable to facilitate capture of an agency by a moderate group.

Commitment and Endogenous Information Structures. Suppose that the group and the agency can commit to an information structure before Congress designs the agency’s mandate. By remaining uninformed, an extreme group reduces his own influence. The agency’s virtual ideal point is now further away from the group’s own ideal point. Applying the logic of the Proximity Effect, such commitment is thus costly for the group. Yet, the agency is now also given more discretion in response to the interest group’s limited influence. More discretion means that the decision taken by the agency better reflects information which is relevant for the group. The fact that the decision better reflects state-relevant information somehow provides the group with insurance against uncertainty. In contrast, imposing that the agency should follow more rigid rules means that the group’s payoff may fluctuate a lot which is costly for the group. It turns out that the benefits associated to this Discretion Effect most often dominate. Improving discretion and granting less stringent mandates favors the group’s objectives. With an extreme group, we thus expect a weak coalition to form. Asymmetric information then works as a commitment-device for inefficient capture, that softens Congress’ response and benefits the group.

Instead, a moderate group would always prefer to share information with the agency. The Proximity Effect and the Discretion Effect both entail a benefit for the group if capture takes place under symmetric information. This induces the choice of a less stringent mandate, while allowing for more favorable decisions within the limits of this mandate.

Our model thus yields strong predictions. The distribution of information within the Iron Triangle affects the implicit bias between Congress and the bureaucracy. Moderate groups are more likely to acquire information which is relevant for policy-making. Extreme groups instead have strong incentives to remain poorly informed. Yet, in both cases, the information structure that emerges out of this multi-stage game is the one that fosters the agency’s discretion and calls for less stringent mandates. Interest groups enjoy having an agency which is a Better Ally for Congress. More discretion means that decisions reflect state-relevant information and it provides to the group some insurance against payoff fluctuations. More broadly, there is a strong congruence of interests within society taken as a whole on the regulatory mandate that should emerge.

Limited commitment. All the previous results are obtained when Congress can fully commit ex ante on a decision rule that determines which policy should be implemented in response to the agency’s communication on the relevant state of nature. A key question is whether our findings would still prevail beyond this mechanism-design environment. In this respect, we also entertain the polar assumption that Congress can commit to menus of actions which are ex post optimal conditionally on whatever information is communicated by the agency. The constraints imposed by such renegotiation modifies the form of optimal delegation mechanisms but it does not change the main insights of the analysis. Under limited commitment, the group would always prefer the informational structure that induces a virtual point for the coalition which is as close as possible to Congress’ ideal point. The Discretion Effect unambiguously dominates.

Organization of the paper. Section 2. reviews the relevant literature. Section 3. presents the model. Section 4. considers a familiar benchmark where the interest group is not active. We present there also the key intuition behind the Proximity and the Discretion Effects. Section 5. solves for the optimal regulatory’s mandate in the case of a strong coalition. Section 6. analyzes capture under asymmetric information. We believe that our modelling of a weak coalition is important in its own sake and could be used elsewhere as a building block for other analysis. Equipped with the characterization of collusive deals between the group and the agency under asymmetric information, Section 7. turns to the optimal regulatory mandate in that scenario. Section 8. then points at the role of asymmetric information within the coalition as a commitment device. Section 9. shows that Congress and interest groups share congruent preferences regarding the distribution of information. Section 10. confirms that our results also hold in a context of limited commitment where Congress can ex post overrule the agency. Finally, Section 11. concludes and proposes alleys for future research. All proofs are relegated to an Appendix.

2. Literature Review

The closest paper to ours is certainly Bennedsen and Feldmann (9). These authors also study how Congress grants discretion to an agency, when the latter can be captured by an interest group. They assume that the agency and the interest group, although they might not have the same marginal value of income, always form a strong coalition. Our analysis instead allows for the possibility of a weak coalition. Considering such possibility is a necessary step to derive the equilibrium information structure which might endogenously emerge. It also distinguishes our modeling of capture from earlier work by Laffont and Tirole (1993, Chapter 13). These authors also assume that capture takes place under symmetric information but, in contrast with us, deduce from this assumption that the agency’s discretion should always be restricted in response to capture. Bennedsen and Feldmann (9) demonstrate that capture by a moderate (resp. extreme) group would increase (resp. decrease) the agency’s discretion; a result we confirm below in a context where delegation mechanisms are always optimally designed. Importantly, these authors take as given the existing information structure while, in contrast, we endogenize this information structure from the group and the agency’s joint incentives to share or not information. Finally, Bennedsen and Feldmann (2006)’s main concern, which is orthogonal to ours, consists in investigating the consequences of having a unified (no conflict of interests between Congress and the agency) or a divided government on the amount of discretion left to the agency under the threat of strong capture.

Using a simplified model of delegation, with Congress either keeping full control over the decision or fully delegating regulatory rights to the agency, Boehmke et al. (12) conduct a comparable analysis. Instead, their concern is on the choice of venues, and whether a lobbyist prefers to target Congress or the bureaucracy. These authors focus on the optimal choice of the agency’s bias from Congress’ viewpoint. Again, and in contrast with our analysis that allows for a broader set of information structures, this paper assumes symmetric information between the interest group and the agency. ¹³

Two other related papers are Baron (6) and Krishna and Morgan (46). In sharp contrast with most of the literature on delegation, these authors introduce the possibility of using monetary transfers to control an agent who has also quadratic preferences on the set of feasible policies. ¹⁴ These two papers consider two-tier hierarchical structures, with Congress choosing an incentive mechanism that stipulates not only which policy should be taken but also a set of contingent transfers for the agent. Baron (6) considers the relationship between Congress and an informed committee who might discharge and not communicate at all with Congress. Under those circumstances, Congress then chooses its most preferred decision absent any information. Because this outside option entails a very low payoff for the committee, Congress may actually extract transfers from the committee. In response to what could be seen as an unpalatable result, Krishna and Morgan (46) impose an additional non-negativity constraint on transfer schedules and show that the optimal contract always entails a cap on actions. Since we allow side-transfers in any collusive side-contract, the solution to the principal-agent relationship between the group and the agency bears some ressemblance with those contributions. There are two differences. First, the design of the side-contract takes as given the set of actions made available to the agency by Congress when delegating regulatory rights. Following Laffont and Martimort (1997, 1998), a collusive side-contract is thus reached within the limits of options that have been stipulated through a grand-contract. We thus have to envision a nested mechanism design problem with Congress’ delegation mechanism being designed upfront. In particular, and in contrast with Krishna and Morgan (46) who implicitly assume that the agent cannot take actions outside of those stipulated in the transfer schedule by the principal, this option remains always feasible in our context because an interest group has no such rights. Second, if she refuses the side-contract offered by the group, the agency is still free to choose decisions within the delegation set made available by Congress. It leads to a mechanism design problem with a type-dependent participation constraint that needs to be solved carefully and whose solution depends on whether the group is extreme or moderate.

Finally, Gailmard and Patty (2012) argue that, to adequately describe the administrative relations, the Principal-Agent model must integrate the fact that information acquisition and information sharing are both endogenous. Incentives for interest groups and bureaucrats to do so are a central feature of the institutional problem. Our paper contributes on this important but somewhat underdeveloped front.

3. The Model

Players, information, preferences. Congress designs a policy on behalf of society. To illustrate, this policy may stem for a production subsidy in a regulated firm, an environmental tax or a standard that applies to a whole sector, an import tariff or a quota in a trade context, etc. This policy, thereafter denoted by x lies in some bounded interval X ¯ ⊆ R . This decision affects the payoffs of three players: Congress, the regulatory agency in charge of implementing this policy, and an interest group which has a stake in such implementation. Payoffs not only depend on the policy but also on the current state of the world, θ . In line with the extant delegation literature, we assume that, thanks to her expertise, the agency is better informed on this parameter. Instead, Congress remains uninformed although it holds correct beliefs on the states distribution. To simplify exposition, we also assume that θ is drawn from a uniform distribution on the interval Θ = [ 0 , 1 ] . Information is soft, i.e., the agency might manipulate her report on the state of nature to Congress at no cost. ¹⁵ The information structure is common knowledge to all parties.

The interest group wants to capture the agency to induce implementation of policies that better please his own interests. How easy it is to channel the group’s influence on policy-making depends on how much information is shared between the group and the agency. Whether the interest group also knows θ or not indeed determines the magnitude of bargaining frictions that affect the relationship between the agency and the interest group at the time of colluding against Congress. We will refer to a strong coalition as one where the interest group and the agency both know θ . Capture takes thus place under symmetric information; the interest group and the agency reaching an efficient side-deal. Such capture is more likely to occur when the group has gone through the whole process of learning of the bureaucratic environment, and when the information that determines the agency’s decision is also known by the firm. An example in order could be a cost parameter in the case of economic regulation. Instead, a weak coalition arises when only the agency is informed about θ while the interest group remains ignorant. Capture then takes place under asymmetric information and contracting frictions between those two parties precludes an efficient side-deal. Informational costs then plague the capture relationship. Weak capture is more likely when the group faces an unknown or moving bureaucratic system, and/or when the group himself has only a partial view of what would be the optimal policy. For instance, the agency must aggregate various pieces of information, and some remain unknown to the group, before determining the optimal policy. This will arguably be the case each time the agency is designed to assess the macro impact of some policies, since such assessment requires models and estimations that go beyond the group’s private information. Even when the group can develop his own models, he still does not know precisely on which ground the agency is conducting her own evaluation. A last justification might be that the group himself can be made of heterogenous parties who have failed in solving the Olsonian collective action problem in information gathering. ¹⁶

All parties have preferences over policy that are quadratic and single-peaked loss functions, namely (with subscripts being self-explicit)

u c ( x , θ , T ) = − 1 2 ( x − x c ( θ ) ) 2 , u a ( x , θ , T ) = − 1 2 ( x − x a ( θ ) ) 2 + T , u g ( x , θ , T ) = − 1 2 ( x − x g ( θ ) ) 2 − T .

Following a standard assumption in the political science literature on delegation, monetary transfers between Congress and the agency are banned. In the tradition of McCubbins et al. (1987, 1989), the sole possibility for controlling any bureaucratic drift is by means of a convenient design of the agency’s mandate. A contrario, bribes are possible between the interest group and the agency. We do not impose any restriction on the sign of side-transfers. Nevertheless, the structure of the game will imply that the interest group always offers non-negative bribes at equilibrium. Lastly, we also assume, for simplicity, that transferring bribes entails no deadweight loss. All sources of frictions in side-contracting will come from the information structure. ¹⁸ The side-transfers between the group and the agency can be viewed as any form of monetary contributions, quasi-transfers such as the provision of technical or legal assistance, or as a reduced form for a “revolving door” strategy, ¹⁹ in which the head of an agency which remains compliant with the interest group will be rewarded by a favorable position in the private sector in the future.

The following assumption on biases is maintained throughout:

Assumption 1.

Δ ≡ b g − b a ∈ [ − 2 b a , 1 − 2 b a ] and 0 < b a < 1 2 .

Three cases must be distinguished. When Δ ∈ [ 0 , 1 − 2 b a ] , the agency and the interest group have congruent preferences, both willing higher decisions than Congress. Yet, the group is more extreme, having a greater ideal point. When instead Δ ∈ [ − 2 b a , 0 ] the agency has the most extreme preferences, with the group being possibly opposed to the policy when Δ ∈ [ − 2 b a , − b a ] . In those latter two cases, we will refer to a moderate group.

Finally, the right-hand side upper bound on b a is a technical condition which ensures that communication between the agency and Congress is always valuable when capture is not an issue. This condition rules out situations in which a fixed mandate, independent on the state of nature, would always be optimal. In other words, this condition means that the agency’s expertise and discretion is needed for a sound decision-making process.

Timing, regulatory mandate and capture. The following game form describes how communication takes place within the organization and how decisions are taken in such an environment. It is a sequential contracting game with two principals, Congress and the interest group, taking turns in influencing the agency. ²⁰

Congress acts as a Stackelberg leader in the game and publicly commits to a (deterministic) policy rule contingent on the information reported by the agent. From the Revelation Principle, ²¹ there is no loss of generality in focusing on such a communication mechanism. Following the mechanism design literature on delegation, ²² we might view such a rule as a direct revelation mechanism of the form { x ( θ ^ ) } θ ^ ∈ Θ , that would specify a decision x ( θ ^ ) for each report θ ^ that the agency makes over the state of nature to Congress. Alternatively, and it is sometimes a route that is followed in the sequel, we might rely on the Taxation Principe, ²³ and replace any direct communication mechanism by a delegation set X ⊂ R from which the agency is free to choose her favorite decision with no direct communication with Congress. The agency’s mandate, i.e., the delegation set, actually corresponds to the image range of the direct mechanism, X = x ( Θ ) . ²⁴ Finally, notice that this regulatory mandate is public and thus perfectly known by the interest group at the time of striking a side-deal with the agency. ²⁵

Once Congress has publicly committed to a revelation mechanism, the interest group proposes a collusive side-contract to the agency. The interest group has all bargaining power in designing such side-contract and, accordingly, makes a take-it-or-leave-it offer to the agency. In contrast with the regulatory mandate, this side-deal is only observed by the collusive parties. ²⁶ For any possible delegation set X ⊆ X ¯ that might have been offered upfront by Congress to the agency, the Revelation Principle again applies at this last collusive stage of the game. ²⁷ The side-contract is thus a pair ( x ( θ ~ ) , T ( θ ~ ) ) θ ~ ∈ Θ that stipulates which decision x ( θ ~ ) should be taken by the agency within the available set X together with a bribe T ( θ ~ ) as a function of the agency’s report on the state of nature to the interest group. ²⁸ This agency’s report θ ~ to the interest group can be manipulated in the case of a weak collusion or it cannot be so if the interest group is informed and a strong collusion prevails.

Lastly, if the agency refuses to collude with the interest group, her outside option is obtained as her best choice within the delegation set offered by Congress. If the agency accepts the collusive side-contract, communication flows up towards the interest group and second towards Congress. The compounding of the mechanism offered by Congress and the side-contract leads to a decision which is not necessarily the decision that would prevail if the sole communication were to take place between the agency and Congress.

That Congress acts as a Stackelberg leader and anticipates how the interest group will react to the design of the agency’s mandate illustrates well the idea that any capture of the regulatory process takes place within the contours of the regulatory mandate that Congress has set ex ante.

4. No Capture

Suppose that the interest group is not active. The sole principal-agent relationship under consideration involves Congress and the agency. The outcome of the delegation game in this simple scenario is well known. ²⁹ The objective of the Congress is to find a decision rule x ( θ ) that maximizes its expected payoff subject to the incentive compatibility constraints that ensure that the agency always reports truthfully her information. We now turn to a precise characterization of those constraints.

Incentive compatibility. First, let define U 0 ( θ ) the agency’s payoff when adopting such truthful strategy, namely

U 0 ( θ ) = − 1 2 ( x ( θ ) − x a ( θ ) ) 2 .

(4.1)

Incentive compatibility constraints amounts to

U 0 ( θ ) = max θ ^ ∈ Θ − 1 2 ( x ( θ ^ ) − x a ( θ ) ) 2 .

(4.2)

The following lemma characterizes incentive compatible allocations ( U 0 ( θ ) , x ( θ ) ) .

Lemma 1

The allocation ( U 0 ( θ ) , x ( θ ) ) is incentive compatible if and only if the following conditions are satisfied.

U 0 ( θ ) is Lipschitz continuous, a.e. differentiable, with at any point of differentiability:

U ˙ 0 ( θ ) = x ( θ ) − x a ( θ ) .

(4.3)

x ( θ ) is non-decreasing, a.e. differentiable, with at any point of discontinuity θ 0

x ( θ 0 + ) + x ( θ 0 − ) = 2 x a ( θ 0 ) .

(4.4)

From (4.3) and the definition (4.1), we deduce the following integral representation:

− 1 2 ( x ( θ ) − x a ( θ ) ) 2 = − 1 2 ( x ( 0 ) − a ) 2 + ∫ 0 θ ( x ( θ ~ ) − x a ( θ ~ ) ) d θ ~ , ∀ θ ∈ Θ .

(4.5)

At any point of differentiability of x ( θ ) (i.e., almost everywhere), differentiating the integral representation (4.5) yields

x ˙ ( θ ) ( x ( θ ) − x a ( θ ) ) = 0.

(4.6)

Under those circumstances, an implementable decision is either a flat rule ( x ˙ ( θ ) = 0 over some range with nonempty interior) or it corresponds to the agency’s bliss point ( x ( θ ) = x a ( θ ) over some range); in which case the latter has full discretion to choose the decision within the delegation set.

Interval Delegation. To simplify exposition, we will often take as granted that Congress offers continuous direct mechanisms (or connected delegation sets in the indirect version of the game) to the agency. Results on the continuity of the optimal delegation mechanisms have been derived in Martimort and Semenov (58), Alonso and Matouschek (3) and Gailmard (2009a). In our context, this continuity is equivalent to assuming that the delegation set from which the agency chooses is an interval of the form X = [ x _ , x ¯ ] or alternatively that the range of the direct revelation mechanism { x ( θ ^ ) } θ ^ ∈ Θ is X . This simplification, although made upfront, turns out to be without loss of generality, as it appears that, whatever the nature of the coalition, the (unrestricted) optimal mechanism would indeed be continuous. ³⁰

Given a delegation set X , the corresponding decision rule is thus

x ( θ ) = min { x ¯ , max { x _ , x a ( θ ) } } .

(4.7)

It should be already noticed that Section 10. shows that considering discontinuities as those described in (4.4) is necessary when Congress cannot commit not to overrule the agency ex post .

Optimal Mechanism. Congress’ optimization problem consists in finding a decision rule that maximizes its expected payoff subject to the incentive compatibility constraints (4.7). The optimal mechanism and delegation set can be immediately characterized as follows.

Proposition 1

Optimal mandate; no capture. Suppose that Assumption 1 holds. The optimal mechanism x a ( θ ) entails only a cap x ¯ a on the agency’s discretion:

x a ( θ ) = min { x a ( θ ) , x ¯ a }

(4.8)

where

x ¯ a = 1 − b a .

(4.9)

The intuition for this result is familiar. From Assumption 1, the agency is biased towards choosing decisions that are above those that would be chosen by Congress itself had it been informed on the state of nature. Under asymmetric information, this means that the agency would like to manipulate upwards her report on that state. Those incentives are controlled by setting a cap on the set of decisions that are available within the agency’s mandate. Assumption 1 then ensures that communication is always valuable on the interval θ ∈ [ 0 , 1 − 2 b a ] and that leaving discretion to the agency also always is. Figure 1 illustrates this scenario.

The group’s most preferred agency. Building on Proposition 1, it becomes possible to investigate what are the ex ante preferences of an interest group over the agency’s bias when, as supposed above, this group is unable to directly influence this agency.

OPEN IN VIEWER

Figure 1.

No capture; b a = 0.2 , Δ = 0.4 .

Proposition 2

The agency’s ideal bias b a * ( b g ) from the interest group’s viewpoint is given by:

0 ≤ b a * ( b g ) = b g + 1 4 − b g 2 + 1 16 ≤ b g .

(4.10)

Although somewhat artificial, this exercise already highlights the key trade-off faced by the interest group when willing to influence the agency. The interest group always prefers an agency whose preferences lie in between those of Congress and his own. In other words, the group favors a more moderate agency. Two compounding forces are at play that explain such a choice. On the one hand, for a given cap on the agency’s discretion, the interest group always benefits from choosing an agency with nearby preferences since, when the agency has discretion, her decision is then close to the group’s ideal point, a Proximity Effect. On the other hand, Congress will leave more discretion to the agency when her preferences are closer to its own, a Discretion Effect. The best agency’s bliss point from the group’s viewpoint results from a compromise between those two effects. ³¹ As a result, the interest group always prefers an agency with more moderate preferences, that is, whose bliss point lies in between that of Congress and his own.

In practice, the group might have little or even no influence at all on the agency’s appointment process. The only possibility is thus to capture this agency ex post . Sections 5. and 7. investigate how such capture occurs and its consequences on policy choices depending on whether capture takes place under complete or asymmetric information. Such analysis is a building block to investigate how and under which circumstances deciding to gather or not information acts as a commitment for the interest group to implicitly change the policy chosen by the agency, in a very similar vein but more subtle way, to what he would do by directly choosing her preferences.

When the interest group is active and colludes with the agency, the picture becomes more complex. Once Congress has decided upon a delegation set, the decision chosen within this set by the agency will depend on the collusive side-contract that the agency and the interest group design ex post . In this section, we will first study the case of a strong coalition; the interest group and the agency both know θ .

5.1. Coalitional Efficiency

Assume that Congress has defined a delegation interval of the form X = [ x _ , x ¯ ] . The interest group proposes to the agency a side-contract that stipulates the decision x ∈ X and an associated transfer T . Because the interest group has all bargaining power in designing the collusive side-contract and information is symmetric, the interest group can compensate the agency with a bribe that leaves her always indifferent between colluding or not, in which case, she freely chooses her best decision within X .

Given that utilities are transferable between the agency and the group, the optimal collusive side-contract should thus induce the agency to choose the decision that maximizes the joint welfare of the coalition she forms with the interest group, i.e.,

u g ( x ) + u a ( x ) ≡ − ( x − θ − b a + b g 2 ) 2 − 1 4 ( b g − b a ) 2

which can be reduced as

u g ( x ) + u a ( x ) = − ( x − x s c ( θ ) ) 2 − Δ 2 4 where x s c ( θ ) = x a ( θ ) + Δ 2 .

(5.1)

The coalitionally efficient policy is thus equivalent to that of a fictitious agency having now an ideal point x s c ( θ ) . This fictitious agency has thus a stronger (resp. weaker) bias towards higher decisions than in the absence of capture when the group (resp. the agency) has extreme (resp. moderate) preferences, i.e., Δ ≥ 0 (resp. Δ < 0 ).

For further references, observe that the decision x 0 ( θ ) that the agency would take when free of the interest group’s influence is again given by the familiar expression

x 0 ( θ ) = min { x ¯ , max { x _ , x a ( θ ) } } .

The corresponding reservation payoff of the agency then becomes:

U 0 ( θ ) = − 1 2 ( x 0 ( θ ) − x a ( θ ) ) 2 ≡ { − 1 2 ( x _ − x a ( θ ) ) 2 if \; θ ∈ [ 0 , x _ − b a ] , 0 if \; θ ∈ [ x _ − b a , x ¯ − b a ] , − 1 2 ( x ¯ − x a ( θ ) ) 2 if \; θ ∈ [ x ¯ − b a , 1 ] .

(5.2)

5.2. The Agency’s Mandate

The optimal delegation mechanism with a strong coalition is immediately deduced from Proposition 1 by replacing mutatis mutandis the bias b a with a modified bias b a + b g 2 = b a + Δ 2 .

When choosing the mandate of the agency, Congress anticipates how decision-making is impacted by a strong capture. When the group is more extreme, i.e., Δ ≥ 0 , the agency becomes a bad ally for Congress. In response, the agency’s discretion is even further reduced in comparison with the case of no capture. Instead, with a moderate interest group, i.e., Δ < 0 , preferences are somewhat better aligned with those of Congress. The agency’s incentives to overstate the state of nature are then mitigated.

Proposition 3

Optimal mandate; strong capture. The optimal delegation mechanism x s c ( θ ) is of the form:

x s c ( θ ) = min { x s c ( θ ) , x ¯ s c }

(5.3)

where the cap x ¯ s c ³² is given by

x ¯ s c = 1 − b a − Δ 2 .

(5.4)

The cap is more (resp. less) stringent than without any capture when the interest group is extreme (resp. moderate), i.e., Δ ≥ 0 (resp. Δ < 0 ).

Figure 2 illustrates, in the case of an extreme group, how the discretion of the agency is reduced when a strong coalition forms, and how the reverse happens with a moderate group.

OPEN IN VIEWER

Figure 2.

Strong coalition with an extreme group and with a moderate one.

6. Weak Capture

To address the possibility of capture taking place under asymmetric information, we will borrow the methodology of nested contracting problems that was laid down in Laffont and Martimort (1997, 1998). Given a delegation mechanism first set up by Congress (a grand-contract to use the expression coined in this literature), colluding parties design their own mechanism (a side-contract) to promote their collective goals subject to incentive compatibility constraints within the coalition.

A collusive side-contract stipulates which decision the agency should be taking when influenced by the group for any possible realization of the state of nature θ . Of course, this decision must remain within the agency’s discretion set. The following feasibility constraint must thus hold:

x ( θ ) ∈ X = [ x _ , x ¯ ] , ∀ θ ∈ Θ .

(6.1)

When the interest group remains uninformed about θ , the side-contract must be designed so as to screen this piece of information from the informed agency. Of course, the Revelation Principle again applies at this collusion stage of the game and there is no loss of generality in focusing on incentive compatible side-contracts of the form { T ( θ ~ ) , x ( θ ~ ) } θ ~ ∈ Θ . Those direct mechanisms induce the agency to truthfully reveal her information to the group and, in response, stipulate a bribe and a decision to be implemented. ³³

Incentive compatibility and participation constraints. To describe the set of such incentive-compatible side-contracts, it is useful to define the agency’s information payoff when following a truthful strategy in her communication with the interest group, namely

U ( θ ) ≡ T ( θ ) − 1 2 ( x ( θ ) − x a ( θ ) ) 2 .

By incentive compatibility, we must have:

U ( θ ) = max θ ~ ∈ Θ T ( θ ~ ) − 1 2 ( x ( θ ~ ) − x a ( θ ) ) 2 .

The following lemma characterizes incentive compatibility allocations ( U ( θ ) , x ( θ ) ) .

Lemma 2

The allocation ( U ( θ ) , x ( θ ) ) is incentive compatible if and only if the following conditions are satisfied.

U ( θ ) is Lipschitz continuous, a.e. differentiable, with at any point of differentiability:

U ˙ ( θ ) = x ( θ ) − x a ( θ ) .

(6.2)

x ( θ ) is non-decreasing, and thus a.e. differentiable.

This Lemma echoes Lemma 1. ³⁴ In particular, notice that the slopes of the payoff profiles U ( θ ) and U 0 ( θ ) take a similar expression, although of course the decision rule may differ in response to the influence of side-transfers that channel the interest group’s influence; a fact that receives some attention below.

Expressed in terms of information rent, we can also rewrite the agency’s participation constraint that must be fulfilled so that she accepts the side-contract:

U ( θ ) ≥ U 0 ( θ ) .

(6.3)

The right-hand side is the agency’s payoff U 0 ( θ ) when choosing freely within the delegation set X , i.e., without any influence from the interest group. The expression of this payoff is still given by (5.2). For future reference, we shall denote by Θ * the acceptance set, i.e., the closure of the subset of those types who get strictly more from colluding than from behaving. Let denote by Θ c * , the complementary set. Quite obviously, types belonging to that complementary set get no bribes.

Optimal side-contract. The optimal policy chosen by a weak coalition results from a trade-off between coalitional efficiency and rent extraction. On the one hand, choosing a policy as close as possible to the coalitional efficient decision x s c ( θ ) maximizes the sum of the agency and the group’s payoff. On the other hand, choosing such policy also means leaving too much of the corresponding coalition surplus to the agency under the form of information rent that are conceded by the uninformed interest group.

To illustrate, suppose that the weak coalition wants to implement the same decision as what a strong coalition would choose when constrained by the agency’s mandate, i.e.

x ~ ( θ ) = min { x ¯ , max { x _ , x s c ( θ ) } } ∀ θ ∈ Θ .

Because a strong coalition incorporates the preferences of the interest group, this decision is modified in a direction that reflects the group’s preferences. Formally, we have:

x ~ ( θ ) ≥ x 0 ( θ ) = min { x ¯ , max { x _ , x a ( θ ) ) } } ⇔ Δ ≥ 0.

(6.4)

As we show below, this comparison matters a great deal to evaluate the profile of information rents that a weak coalition must propose to the agency to implement the decision x ~ ( θ ) . This in turn determines for which type realizations the agency becomes a “better ally” of the group.

Extreme interest group, Δ ≥ 0 . In this scenario, we thus have x ~ ( θ ) ≥ x 0 ( θ ) . From the incentive compatibility condition (6.2), the side-contract that implements the decision x ~ ( θ ) must thus leave to the agency a payoff U ~ ( θ ) that has a greater slope than what she gets without capture:

U ~ ˙ ( θ ) = x ~ ( θ ) − x a ( θ ) ≥ x 0 ( θ ) − x a ( θ ) = U 0 ˙ ( θ ) .

(6.5)

Remember that, to accept a collusive side-contract, the agency must get more than her reservation payoff for types θ ∈ Θ * . The inequality (6.5) thus implies that the agency’s participation constraint (6.3) is harder to satisfy for low values of θ if one keeps the decision (6.4). This might be too costly and as a result, the group may want to distort the decision rule and no longer implement (6.4) so as to reduce the agency’s information rent. At the optimal side-contract, a whole interval of types of the form Θ c * = [ 0 , θ * ] possibly receives no bribes. Of course, the lower bound θ * of the acceptance set is determined endogenously by the group.

The precise intuition is as follows. Because he has all bargaining power in designing the side-contract, the extra information rent (i.e., U ( θ ) − U 0 ( θ ) ) that the colluding agency gets beyond her reservation payoff is costly for the interest group. Bribes must be reduced to minimize this extra rent. It is so up to the point where the agency having observed low values of θ (namely θ ≤ θ * ) becomes indifferent between colluding or not. Those low types are “worst allies” from the group’s viewpoint. In contrast, the “best ally” is an agency who has observed θ = 1 . Nearby types get strictly more from colluding than their reservation payoff. Indeed, observe that the agency who has observed a state close to θ = 1 would like to pretend she has actually observed a lower realization of θ . So doing, she appears more difficult to be captured in the eyes of the interest group. To induce the agency to reveal information, the interest group must thus offer large bribes if the agency were to choose a policy close to the coalitionally efficient policy x s c ( θ ) . At the same time, pretending having observed low values of θ is made less attractive if the interest group offers very little bribes and does not require large changes in decision away from x 0 ( θ ) for θ close to θ * from above. At the extreme, the interest group eschews any collusion at all with types below θ * . The optimal side-contract results from this trade-off between coalitional efficiency and rent extraction.

While Section 4. highlighted the agency’s tendency to overstate the state of nature vis-à-vis Congress, leading to a cap on the delegation set, now the agency also faces some countervailing incentives in her relationship with the interest group who has even stronger preferences towards higher decisions although being equally uninformed. In response, we expect that the weak coalition will now choose policies that are less biased towards the interest group’s ideal point as what a strong coalition would do.

Moderate interest group, Δ < 0 . The ranking on decisions and the slopes of the agency’s information rent are now reversed, namely

x ~ ( θ ) ≤ x 0 ( θ ) = min { x ¯ , max { x _ , x a ( θ ) ) } }

(6.6)

and

U ~ ˙ ( θ ) = x ~ ( θ ) − x a ( θ ) ≤ x 0 ( θ ) − x a ( θ ) = U 0 ˙ ( θ ) .

(6.7)

By an argument that is the symmetric to that made above, it immediately follows that the participation constraint (6.3) now necessarily binds at θ = 1 . Again, keeping the decision (6.4) might turn out to be too costly. As a result, the group may want to distort this decision rule and no longer implement (6.4) so as to reduce the agency’s information rent. At the optimal side-contract, types on a whole interval Θ c * = [ θ * , 1 ] for some θ * receive no bribes.

The intuition is the reverse of before. From the moderate interest group’s viewpoint, minimizing the agency’s information rent that she gets beyond her reservation payoff now requires to reduce bribes up to the point where the agency having observed large values of θ is indifferent between colluding or not. At the same time, those types are choosing decisions closer to x 0 ( θ ) . They are the “worst allies” from the moderate group’s viewpoint. In contrast, the moderate interest group’s “best ally” is now an agency who has observed θ = 0 . Types in that neighborood get strictly more when colluding. When dealing with the interest group, an agency having observed a low value of θ wants to pretend the state was higher to appear less corruptible.

Whether the interest group is moderate or extreme, there is a common thrust to our findings. The weak coalition chooses policies which are no longer coalitional efficient and, on top, are always more biased towards the agency than when capture takes place under symmetric information. Next proposition formalizes this intuition and characterizes the decision-process that takes place within a weak coalition under both scenarios.

Proposition 4

Fix a delegation set X = [ x _ , x ¯ ] . The policy picked by a weak coalition is given by

x w c ( θ ) = min { x ¯ , max { x _ , x ~ w c ( θ ) } } .

(6.8)

where the weak coalition’s ideal point x ~ w c ( θ ) satisfies

When the interest group is extreme, i.e., Δ ≥ 0 ,

x ~ w c ( θ ) = max { x a ( θ ) , x s c ( θ ) − 1 2 ( 1 − θ ) } ;

(6.9)

When the interest group is moderate, i.e., Δ < 0 ,

x ~ w c ( θ ) = min { x a ( θ ) , x s c ( θ ) + 1 2 θ } .

(6.10)

When the agency and the interest group form a weak coalition, they still behave like a single player but now with a virtual ideal point which is located at x ~ w c ( θ ) . Private information de facto increases the agency’s bargaining power in the collusion with the interest group and somehow mitigates the influence of the interest group. The rationale is as follows. Because collusion takes place under asymmetric information, the group must give up information rent beyond her reservation payoff to convince the agency to opt for more favorable policies. To limit this information rent, the group designs a collusive side-contract that tilts the decision implemented by a weak coalition towards the agency’s bliss point. It is thus lower (resp. higher) than that of a strong coalition when the group is extreme (resp. moderate).

With an extreme interest group (i.e., Δ ≥ 0 ) and when θ is small enough (more specifically θ ≤ θ * * = 1 − Δ ), the virtual ideal point is significantly shifted downwards in comparison with that of a strong coalition, since it is now identified with the agency’s ideal point. For higher values of θ , the agency remains an ally for the group, but a moderate one. The “best ally” of the interest group is actually an agency who has observed high realizations of θ : ³⁵

x ~ w c ( θ ) ≤ x s c ( θ ) ( with equality at θ = 1 ) .

This downward distortion goes up to the point where the interest group prefers to eschew all influence on the agency, bribes are nil and the agency is freed from any external influence.

With a moderate interest group (i.e., Δ ≤ 0 ) and when θ is now large enough (more specifically θ ≥ θ * * = − Δ ), the virtual ideal point is significantly shifted upwards in comparison with the scenario of a strong coalition, and is now identical to the agency’s ideal point.

x ~ w c ( θ ) ≥ x s c ( θ ) ( with equality at θ = 0 ) .

Again, this upward distortion goes up to the point where the interest group prefers to eschew capture when the agency appears a “bad ally”.

7. Agency’s Mandate: Weak Capture

We can now turn to the characterization of the agency’s mandate. Congress’ optimization problem again consists in finding a decision rule that maximizes its expected payoff, which now takes into account the agency’s decision under weak capture as specified in (6.8). Next proposition summarizes our findings.

Proposition 5

Optimal mandate; weak capture. The optimal delegation mechanism x w c ( θ ) is again of the form

x w c ( θ ) = min { x ~ w c ( θ ) , x ¯ w c }

(7.1)

where the cap x ¯ w c is now given by

x ¯ w c = { x ¯ a if \; 0 ≤ Δ 2 ≤ b a \;or \;if \; b a ≤ 1 + Δ 2 \;and \; Δ < 0 1 − b a 2 − Δ 4 if \; b a ≤ Δ 2 , 1 − b a 2 − 1 + Δ 4 if \; 1 + Δ 2 ≤ b a \;and \; Δ < 0 .

(7.2)

.

Figure 3 illustrates the characterization of the optimal floor for a couple of scenarios depicted in Proposition 5. Let us now describe each of the different possible configurations and explain the nature of the distortion.

Extreme group. When Δ is sufficiently large, the group has enough leverage to influence the agency. Intuitively, the gains from choosing decisions beyond the agency’s ideal point are large enough to compensate for the extra information rent that the agency can grasp. Although the virtual ideal point of the weak coalition remains tilt towards the agency’s bliss point, it also departs from it. As a result, and even if Congress finds the agency a “better ally” than when capture takes place under symmetric information, the dominant force is that the group matters, which in turn determines the degree of discretion left to the agency. In comparison with the case where she is freed of any external influence, the agency ends up being given less discretion even if collusion takes place under asymmetric information:

x ¯ w c = 1 − b a 2 − Δ 4 ≤ 1 − b a = x ¯ a .

Congress fears the influence of the extreme group a lot and reacts by significantly restricting discretion.

OPEN IN VIEWER

Figure 3.

Weak coalition with an extreme group and with a moderate one.

When the group is not so extreme (i.e., b a > Δ 2 ), there are not enough gains from colluding between the group and the agency to cover the information costs in side-contracting. The group has no longer any influence on the agency which behaves as if capture was not even a concern.

Moderate group. When Δ is not too negative, the moderate group has not much influence on the agency if collusion takes place under asymmetric information. Only for a small range of states of the world will he manage to change the agency’s behavior. As a result, Congress again treats the agency as being freed of any influence. Since the group is moderate, the agency is now more constrained and is given less discretion in comparison with the case of symmetric information where the presence of a moderate group in a strong coalition would make the agency a “better ally”.

When Δ is sufficiently negative, the preferences of the moderate group get more strongly represented. The virtual ideal point of the weak coalition is now tilt towards Congress. Even if this effect is not as significant as with a strong coalition, it is sufficient for inducing Congress to react by increasing the level of discretion it grants to the agency. The agency becomes a “better ally” of Congress even under asymmetric information.

More comparative statics. Asymmetric information is akin to an increase in the agency’s bargaining power. Decisions, which are now dictated by the virtual ideal point of the weak coalition, are thus tilt towards the agency’s own bliss point. This choice is more (resp. less) favorable to Congress when the group is extreme (resp. moderate). As a result, Congress expands (resp. reduces) the agency’s discretion by raising (resp. decreasing) the cap on decisions.

Proposition 6

The optimal cap with a weak coalition is less (resp. more) stringent than with a strong coalition when the interest group is extreme (resp. moderate), i.e., Δ ≥ 0 (resp. Δ < 0 ):

x ¯ w c ≥ x ¯ s c ⇔ Δ ≥ 0.

(7.3)

Asymmetric information sometimes acts as a barrier to entry for an extreme interest group. The bureaucracy can even be made immune to the threat of capture. By contrast, an informed interest group would always be able to modify the agency’s decision; which in turn calls for changes in how much discretion she is given.

Proposition 7

Suppose that Δ 2 ≤ b a and the group is extreme ( Δ ≥ 0 ). An uninformed interest group has no influence on the agency, while an informed interest group would always influence the decision:

x ¯ w c = x ¯ a ≠ x ¯ s c .

(7.4)

Notice that (7.4) also holds when 1 + Δ 2 ≥ b a and the group is moderate ( Δ < 0 ). But in this last case, and for low enough values of θ , the coalition chooses x ~ w c ( θ ) < x a ( θ ) , so that the group keeps some influence. On the contrary, an extreme group would only manage to drive the virtual point x ~ w c ( θ ) above x a ( θ ) for decisions that do not belong to the mandate conferred by the Congress. Therefore, while it is always the case that being uninformed hinders the group’s ability to capture the agency, an extreme and a moderate group are not equally impacted. A moderate group keeps some influence at least for some states of the world, while an extreme group may be left totally outside of the policy process.

8. Asymmetric Information as a Commitment Device

Equipped with the characterization of the objectives that pertain to either a weak or a strong coalition, we may now investigate what sort of information structure is likely to emerge and when; i.e., under which circumstances information is shared or not by the agency and the interest group. Of course, and as already noticed by Gailmard and Patty (2012), addressing the question of the endogeneity of information structures requires a close look at the exact timing of the game form. Lessons of such investigation may actually vary with fine details. To illustrate, observe that, at the interim stage, i.e., once Congress has already committed to a mandate for the agency, the interest group will always find it profitable to influence the agency’s choice. In this respect, sharing information with the agency and thereby building a strong coalition is unambiguously the best strategy.

Let us now envision a scenario where the agency was established beforehand. For instance, the head of the agency was appointed earlier on and contacts with the group were already established but the contours of the agency’s mandate have not yet been designed. In this ex ante scenario, the regulatory mandate might be modified in response to the strength of the collusion that prevails between the group and the agency. To describe this scenario, we now append to the game that was so far studied, a prior stage in which the group and the agency decide whether they would share information or not. To simplify the analysis, we assume that there is no direct cost of access to information for the group. Actually, the main thrust of our analysis is to unveil conditions under which the group prefers to have a limited access to the agency. Adding such a cost would just make the case for capture under asymmetric information even stronger. To assess the consequences of information sharing for the coalition, we take the expected payoff of the strong coalition as our welfare criterion. To justify this choice, we might argue that, in the prior stage of the game, the agency and the interest group can bargain over the choice of the best information structure before Congress, knowing whether close ties have been knitted or not, decides of the agency’s mandate and before information is learned. The corresponding benefits could then be shared by the agency and the interest group by means of ex ante lump-sum transfers. In particular, keeping the same allocation of bargaining power ex ante and ex post (i.e., once information is learned by the agency and possibly by the group) amounts to assuming that the group pockets all those benefits.

Comparing the objectives of a weak and a strong coalition unveils the role that information plays in determining the interest group’s influence. By getting informed, the interest group can certainly induce more favorable state-dependent decisions as long as those decisions are not bound by the cap on the agency’s discretion. Sharing information with the agency always fosters the Proximity Effect. Yet, the consequences of such information sharing on the Discretion Effect are ambiguous and depend on the relative magnitudes of the group’s and the agency’s biases as we will see below.

Moderate group. Under those circumstances, a strong coalition implements less biased decisions than what the agency would do on her own. That means that, for a fixed value of the cap, decisions end up being tilt towards Congress’ ideal point. The Proximity Effect mitigates the conflict of interests between the agency and Congress. As a result, the agency is given more discretion and the cap is raised. The Discretion Effect and the Proximity Effect thus go in the same direction and together favor not only the group but also Congress. Instead, asymmetric information would undermine the Proximity Effect. In turn, it would also reduce the magnitude of the Discretion Effect and call for a more stringent mandate for the agency. This simple logic is summarized in the next proposition.

Proposition 8

A moderate group always prefers to form a strong coalition.

Extreme group. In this case, the group’s and the agency’s objectives are again better aligned when capture takes place under complete information. The Proximity Effect bites again. Yet, the ideal point of a strong coalition is shifted further away from Congress’ ideal point which leads Congress to further reduce the agency’s discretion. The Discretion Effect now goes counter the Proximity Effect and up to the point where an agency, part of a strong coalition, is given less discretion than when standing alone.

The welfare comparison between the two modes is thus a priori ambiguous. Although we were not able to provide a complete comparison, next propositions provide some insights on which effect may dominate by looking at the two polar cases where Δ is small (but positive) or large. In both cases, the coalition opts for capture under asymmetric information.

Proposition 9

An extreme group prefers to form a weak coalition when Δ is small enough.

The intuition for this result is straightforward. When the group and the agency are almost congruent (i.e., Δ close to zero), we know from Proposition 7 that a weak coalition has no influence and the agency’s bliss point gets implemented. Yet, this decision remains quite close to the strong coalition’s ideal point. The Proximity Effect thus entails a loss in the expected payoff of the strong coalition which is only of a second order magnitude Δ 2 . Instead, when Congress knows that capture is not a concern, it chooses a mandate for the agency which leaves her with more discretion than under complete information; an illustration of the Discretion Effect. The set of states of nature over which the cap now binds is actually reduced by a term of first-order magnitude in Δ . Overall, colluding under asymmetric information is a way to weaken Congress’ control and induces a soft regulatory mandate that favors the coalition.

For larger values of Δ , the same result obtains.

Proposition 10

An extreme group prefers to form a weak coalition when Δ is large enough.

The logic is somewhat similar to that above but the magnitudes of the Proximity and the Discretion Effects differ. The first one disappears and only remains the impact of an expanded discretion. To understand how it is so, consider indeed the polar case where Δ is so large that, when capture takes place under symmetric information, the cap on decisions is always binding. More specifically, consider the lowest value of such Δ . When capture instead takes place under asymmetric information, the agency would like to choose a decision along her virtual ideal point. Keeping the above cap as fixed, this virtual ideal point happens to be chosen only on the lower tail of the state distribution. The agency has de facto more discretion for a set of such states which has positive measure. In turn, Congress softens the agency’s mandate and increases the cap which allows her to implement decisions that better please the interest group.

9. Optimal Capture from Congress’ viewpoint

Mirroring our approach of Section 8., we now investigate Congress’ preferences regarding the strength of collusion between the agency and the interest group. When designing bureaucratic procedures, Congress might actually play on how efficient a group can be in channelling influence on the agency. For instance, quasi-transfers may be banned more or less severely, or public disclosure requirements may be requested so as to render more or less transparent the objectives and information of the agency.

The Ally Principle, when applied to the coalition between the group and the agency, already conveys all the intuition needed. With a moderate group, Congress will be better off as this group becomes more efficient in capturing the agency, since it contributes to tilt the coalition’s ideal point closer to its own. The reverse holds when Congress faces an extreme group. Reducing the group’s ability to capture the agency will benefit to Congress. As far as transfers are concerned, the result is immediate: Congress would prefer to ban transfers by extreme groups, and allow them by moderate groups. More interesting are the results about the distribution of information:

Proposition 11

Congress prefers to face a strong (resp. weak) coalition when the group is moderate (resp. extreme).

Comparing this result with those in Section 8. shows that a strong congruence prevails between private interests and the rest of society regarding the distribution of information. It follows that we can expect the emergence of a large consensus about the design of bureaucratic procedures, the degree of transparency and the span of regulatory mandates.

10. Limited Commitment

We have so far assumed that Congress could commit to a mechanism upfront, before receiving any information from the agency. Of course, this assumption is somewhat extreme since it implies that, whenever θ gets known - and it is so in equilibrium thanks to the Revelation Principle - the requested decision is generally not ex post optimal from Congress’ point of view. When Congress might overrule the agency’s choice within the delegation set to implement its most preferred action, the agency’s incentives to truthfully reveal information beforehand are in turn perturbed. This point is well known from Crawford and Sobel (16) (who assumed no commitment at all), Bester and Strausz (11) and Krishna and Morgan (46) in related contexts with limited commitment and has reached its full strength in political science following the seminal work of Gilligan and Krehbiel (30).

In this section, we consider the possibility that, once the agency has chosen an action within the delegation set, Congress may overrule this decision. With such limited commitment ability, Congress should offer delegation mechanisms that are still menus of possible decisions with the added property that each action is conditionally optimal from Congress’ point of view given the information inferred by the agency’s choice of such option within the menu. In other words, the delegation mechanism should be not only incentive compatible for the agency but also renegotiation-proof. ³⁶

The requirement of renegotiation-proofness puts lots of structure on implementable menus. An immediate and obvious consequence is that there cannot be any interval with full separation of types. Viewed in terms of delegation set, it means that such set could only entail a countable set of actions. If full separation was possible on a given interval, then Congress would always choose its ideal point on such interval which would violate incentive compatibility on the agency’s side.

More generally, consider a N -item renegotiation-proof mechanism of the form { x 1 j , … , x n j } with x 1 j < ⋯ < x n j . (We index the menu with a superscript j ∈ { s c , w c } to stress that those menus may differ depending on whether a weak or a strong coalition forms.) It is by now routine to show that, because of incentive compatibility, the space of sets of nature can be partitioned into N subsets of the form [ θ i j , θ i + 1 j ] , i ∈ { 0 , … N } , with θ 0 j = 0 and θ N j = 1 . The agency chooses a decision x i + 1 N when θ ∈ [ θ i j , θ i + 1 j ] .

Incentive compatibility implies that the agency should be indifferent between the two consecutive options when she has observed θ j . Of course, this indifference condition writes differently depending on whether the agency is part of a strong or a weak coalition. The coalition’s virtual ideal point is at x j ( θ ) (for j ∈ { s c , w c } ), and should be at equal distance of those two options. We shall write this condition as

x j ( θ i j ) = x i j + x i + 1 j 2 \,for j ∈ { s c , w c } .

(10.1)

On the other hand, renegotiation-proofness implies that decisions are conditionally optimal; a condition that we write as

x i j = E θ ( θ | θ ∈ [ θ i − 1 j , θ i j ] ) = θ i − 1 j + θ i j 2 .

(10.2)

We have the following result.

Lemma 3

For any information structure ( j ∈ { s c , w c } ), there exists at most one N -item renegotiation-proof delegation mechanism { x 1 j , … , x N j } , and a unique associated partition ( θ 0 j = 0 , … , θ i j , … , θ N j = 1 ) .

Moreover, for all N ≥ 1 , such a N -items renegotiation-proof delegation mechanism exists for the information structure j ∈ { s c , w c } if b a + Δ 2 (resp. b a ) is small enough and the group is extreme (resp. moderate).

The fact that there is a unique N -items renegotiation-proof mechanism for both informational structures allows us to easily compare the payoffs of the coalition under those two informational scenarios. This comparison is highly simplified by the fact that conditions for renegotiation-proofness allow to apply the Law of Iterated Expectations. Whatever the N -options menu, the expected decision is constant across information structures, independently on whether a weak or strong coalition is considered. It is the decision that Congress would take ex ante, namely

E θ ( x j ( θ ) ) = ∑ i = 1 N x i j P ( θ ∈ [ θ i − 1 j , θ i j ] ) = ∑ i = 1 N θ i − 1 j + θ i j 2 ( θ i j − θ i − 1 j ) = 1 2 = E θ ( θ )

(10.3)

where x j ( θ ) = x i j if θ ∈ [ θ i − 1 , θ i ] .

Because preferences are quadratic, it follows that the comparison of the coalition’s expected payoffs across different information structures solely depends upon the variance of the distance between the decision and the ideal point of the coalition. Indeed, up to some constant terms, the payoff of the coalition writes as ³⁷

U c o a l j = E θ ( − 1 2 ( x j ( θ ) − x s c ( θ ) ) 2 ) = E θ ( − 1 2 ( x j ( θ ) − θ ) 2 ) − 1 2 ( b a + Δ 2 ) 2 ,

or again

U c o a l j = − 1 2 V θ ( x j ( θ ) − θ ) − 1 2 ( b a + Δ 2 ) 2 .

On the other hand, the ex ante payoff of Congress is, keeping with the same notations,

U c j = E θ ( − 1 2 ( x j ( θ ) − θ ) 2 ) = − 1 2 V θ ( x j ( θ ) − θ ) .

(10.4)

The payoff of the coalition only differ from that of Congress by a constant which depends on the coalition’s bias. It follows from this congruence that the coalition prefers the informational structure that also maximizes Congress’ expected payoff. Since Congress is better off when closer to the agency, both Congress and the coalition prefer an agency whose ideal point is closer to Congress’ bliss point. ³⁸

The expected decision being constant, the coalition favors the information structure that provides the lowest exposure to risk. Such a structure happens to coincide with the one that minimizes the distance between the interest group’s and Congress’ objectives. We summarize these findings in the next proposition.

Proposition 12

Suppose that both a weak and a strong coalition are given a N -options renegotiation-proof delegation mechanism. The variance of payoffs is always lower (resp. higher) with a weak coalition when the group is extreme (resp. moderate). Moreover, the coalition always prefers to face a weak (resp. strong) coalition (resp. symmetric) if the group is extreme (resp. moderate).

Assuming limited commitment on Congress’ side does not modify and even strenghtens the intuitions given in Section 8.. That Congress is now able to pick its favorite decision after the agency’s move decreases the magnitude of the Proximity Effect, while the Discretion Effect remains at play. Any commitment device that better aligns the agency’s objectives with those of Congress will therefore benefit both players. For an extreme group, it is obtained by reducing his ability to influence the agency (thus favoring a weak coalition), while the reverse is true for a moderate group.

Whether a weak or a strong coalition forms, the maximal number of options that Congress can propose in a renegotiation-proof mechanism is increasing as the biases of the agency and the group decrease. When the group is extreme, a N -options mechanism is possible if

N ≤ ⌈ − 1 2 + 1 2 1 + 2 b a + Δ 2 ⌉ .

When the group is moderate, a sufficient condition for a N -option mechanism to exist both for a weak and a strong coalition is

N ≤ ⌈ − 1 2 + 1 2 1 + 2 b a ⌉ .

These conditions become less stringent as b a + Δ 2 (resp b a ) gets smaller.

Turning to the optimal renegotiation-proof mechanism, both Congress and the interest group would prefer the menu with the largest number of options. For technical reasons, Proposition 12 compares menus that entail the same number of options in both informational scenarios. Yet, it is the case that, as the agency’s virtual ideal point gets closer to Congress’ ideal point, the number of options that Congress can credibly offer increases. It implies that, when considering the optimal renegotiation-proof mechanism, both Congress and the interest group will generally prefer the informational structure that better aligns the coalition’s objectives with those of Congress.