A Theory of Policy Expertise

Transcription

1 A Theory of Policy Expertise Steven Callander January 9, 2008 Abstract The canonical model of expertise has two prominent features: expertise is a single piece of information and it is perfectly invertible. In this paper I offer a broader conception of expertise that relaxes both of these features. I define expertise as direct knowledge of the policy process itself. Thus, expertise represents a superior understanding of how policies are transformed into outcomes and does not reduce to the possession of a single piece of information. This formulation allows expertise to be invertible, non-invertible or partially invertible, resonating more closely with how expertise is commonly understood. To demonstrate that this generality matters to political behavior, I develop a simple model of delegation and show that the complexity of expertise provides a solution to the commitment problem of legislative-bureaucratic policy making. The theory predicts that only issues of sufficient complexity can be delegated, consistent with anecdotal evidence. For helpful comments I thank Jonathan Bendor, Chuck Cameron, Olivier Compte, Sven Feldman, Sean Gailmard, Tom Hammond, John Hatfield, John Patty, and the referees and editors of this journal. Managerial Economics and Decision Sciences, Kellogg School of Management, Northwestern University, Evanston, IL 60208; scal@kellogg.northwestern.edu.

2 It is by now well understood that expertise plays a central role in policy making. This gives rise to a fundamental question: what does it mean to be an expert? Over recent decades models of policy have come to rely on a particular conception of expertise, encapsulated in the now-canonical cheap-talk model of Crawford and Sobel (1982). This model, borrowed from economics, provides a parsimonious and tractable theory of policy formation, and has formed the theoretical foundation for numerous influential studies of politics, ranging from Gilligan and Krehbiel s (1987, 1989) seminal work into committee structure and legislative organization, to the enormous literature on Legislative-Executive branch relations, and even political debate (Austen-Smith 1990). Although the canonical formulation of the cheap-talk model is attractively simple, it provides a limited conception of expertise. According to this approach, expertise is equivalent to the possession of a single piece of information. This definition is not only discordant with expertise as commonly understood, but in the policy process it produces several peculiar properties. Most notably, it implies that expertise is perfectly invertible, such that a single statement from an expert can render an intelligent layperson an expert. Simplifications are necessary, of course, in any theoretical enterprise. Yet those inherent in the canonical model are excessive, not only limiting our understanding of expertise but, more substantially, casting doubt on the structural soundness of all research built upon its foundation. My objective in this paper is two-fold: to introduce a broader representation of expertise and to show that this generality matters. I begin by defining expertise directly over the policy process the function that maps policies into outcomes and allow for a broader array of possible processes. In this framework it is possible that a layperson lacks knowledge not only of a shock to policy, as in the canonical model, but also what is the functional form of the policy process itself. Expertise, therefore, need not reduce to a single piece of information. Relaxing how much a layman knows about the true policy process allows me to relax the invertibility of expertise. Rather than a layman learning everything about policy from observing one point in the policy mapping, he may on some issues learn nothing expertise is non-invertible or learn some amount in between such that expertise is partially invertible. Partial invertibility represents the realistic middle ground between two extremes, yet it is itself a vast category and one that leaves subsequent questions unanswered. For instance, if a layman learns neither everything nor nothing from an expert s statement, how much he does learn. To provide traction on this question, I model the policy process as a Brownian motion. I argue that the stochastic generation of a Brownian path captures many realistic properties of real policy making and does so in a highly tractable form. Moreover, the parameters of the motion determine how much a layman learns from a statement by an expert, offering a simple measure of the invertibility or complexity of expertise. 1

3 To demonstrate that a broader view of expertise matters for political behavior, I construct a simple model of policy making and allow the complexity of the underlying issue to vary. Although the ideas are generally applicable, I take as my leading example the legislative-bureaucratic relationship. A central tenet of this relationship is that the delegation of authority although frequent is not irrevocable as Congress always retains the right to pass overriding legislation. This power creates a dilemma: if Congress can learn from the expert recommendations of an agency, what prevents it from using this information toward its own ends? In principle, the canonical model of policy provides no barrier and Congress ability to subvert agency expertise gives rise to a problem of commitment. Congress inability to commit to the delegation of authority implies that agencies cannot protect their expertise from Congressional oversight, undermining the rationale for agency expertise and delegation more generally. The commitment problem provides a theoretical challenge as it places Congress in the position of power over the agency, a conclusion in conflict with how the relationship is generally understood. 1 Thestandardresolutionoffered in the literature is institutional. 2 It is argued that barriers or frictions exist that limit the ability of Congress to override agency recommendations, thereby restoring agency power (for example, a closed rule in the legislative-committee relationship). I offer instead an informational based resolution of the commitment problem. To contrast with the institutional approach, I develop a frictionless model of policy making and show that Congress can productively delegate authority to agencies if and only if policy issues are complex. If an agency s expertise is sufficiently more complex than a single piece of information, the agency can protect its informational advantage over a non-expert Congress and favorably influence policy outcomes. This ability provides the rationale for an agency to invest in expertise, thereby explaining agency power in the face of de jure legislative authority. Moreover, the prediction that only complex issues are delegated resonates with empirical and anecdotal evidence (Ringquist 1995; Epstein and O Halloran 1999). Key to successful delegation is that the agency achieves both an informational and distributive gain from acquiring expertise. In fact, when delegated to, an expert agency is fully empowered and acts as if the threat of oversight did not exist. This allows the agency to achieve with certainty its own ideal policy outcome, maximizing bureaucratic drift. Although such broad informational powers for an agency are novel in a theoretical setting, they resonate with observations of policy making in practice. As Bendor, Taylor, and Van Gaalen (1985, p. 1042) conclude: 1 Under normal conditions, the power position of a fully developed bureaucracy is always overtowering. The political master finds himself in the position of the dilettante who stands opposite the expert. Max Weber (quoted from Gerth and Mills 1958, p. 232). 2 An exception is Diermeier (1995) that offers an overlapping-generations reputational explanation. 2

4 A bureau s influence rests not on it formal authority its ability to manipulate the rules but, as Weber noted, its control of information, its ability to manipulate either the construction of policy alternatives or information about the consequences of different alternatives. My informational explanation of delegation differs from institutional explanations also in the conditions under which delegation occurs. The frictionless model reverses the power of free-riding relative to a model with institutional constraints, allowing the agency to free-ride off legislative expertise and predicting, most notably, a failure of the famous ally principle that says legislatures delegate to ideologically similar agencies. Instead, I find that delegation occurs only because the players differ endogenously in the policy benefits they receive from acquiring expertise, and that this asymmetry is sufficient to induce delegation only when the agency s ideal outcome is distinct from that of the legislator. POLICY PROCESSES AND EXPERTISE Policy outcomes can seldom (if ever) be chosen directly. Rather, policy makers choose policies that, once implemented, deliver outcomes, and it is these outcomes that directly motivate political actors. Policies are transformed into outcomes by a policy process ψ, such that ψ : P O, wherep represents the set of policies and O the set of outcomes. Thetrueprocessψ is chosen from the set of possible processes, Ψ, such that ψ Ψ. The set Ψ defines the policy issue. A policy expert possesses superior knowledge than a non-expert as to how policies are mapped into outcomes. For simplicity and as is standard I suppose an expert knows the true ψ (and understands the policy process perfectly). The difference between anexpertandalayman,therefore,isdeterminednotbyhowmuchanexpertknowsbut by how little a layman knows. The knowledge of a layman depends on the variety and complexity of processes that make up the set Ψ. The Canonical Model: Simple Expertise According to the canonical model, policy follows the simple process: ψ : x = p + θ, (1) where x is the outcome, p the policy instrument chosen, and θ is a shock, or state of the world. 3 Formally, the canonical model restricts the set Ψ of possible mappings to consist entirely of functions of the form of Equation 1, differing only in the value of θ. Figure1 depicts the possible policy processes for various realizations of θ. 3 The original assumptions of Crawford and Sobel (1982) generalize this form in several respects, although the following criticisms apply to their general structure with equal force. 3

5 policy outcome x 6θ =2 θ = 1 θ = 2-0 p policy instrument θ =1 θ =0 Figure 1: The Canonical Model: ψ (p) :x = p + θ The central assumption in this model is that expert and laymen alike know that the policy process is linear and additive in components, with the only difference being that the expert possesses knowledge of θ whereas the layperson does not. Thus, the difference between expert and layperson reduces to a single piece of information. This formulation has several strong implications. First, the policy process and consequently, expertise is perfectly invertible. 4 If a non-expert learns one point in the mapping then the mapping is fully revealed to him. Consequently, it is possible in this model for a single statement from an expert to render alaymananexpert. Second, in knowing that all possible mappings are monotonically increasing, a nonexpert is assumed to know how to order policies according to which deliver more liberal or more conservative outcomes. A non-expert knows, therefore, not only which policies are more likely to deliver liberal outcomes, but which policies do deliver more liberal outcomes. Despite not knowing the true mapping, the non-expert can order the continuum of policies precisely according to the outcome each delivers. Moreover, the linearity of Equation 1 implies a non-expert knows by exactly how much an outcome moves following a change in policy. The simplicity of expertise in the canonical model is perhaps most evident in the type of example that satisfies its strictures. For instance, the canonical model is satisfied 4 Formally, the process is invertible if for each p P and ψ, ψ 0 Ψ, ψ (p) 6= ψ 0 (p); thatis,foranyp thepossibleprocessesdonotintersect. 4

6 by expertise over the days-of-the-week, where a layman does not know the current day but does know how the days are sequenced. Under these circumstances, and only under these circumstances, the difference between a layman and an expert is a single piece of information. In knowing that Monday is followed by Tuesday, the layman can perfectly invert the message that tomorrow is Tuesday to infer today s day. In fact, as the layman knows the distance between days, he is also able to infer that in four days it will be Friday. Such an ordering is well beyond the capabilities of a layman on most issues, however, and a greater gap in knowledge exists between a layman and an expert. It is to modeling this gap that I now turn. The Opposite Extreme: Maximally Complex Expertise Occupying the opposite extreme to the canonical model are non-invertible policy processes. In this class of processes, learning one point in the mapping teaches a non-expert nothing else about other policies. More precisely, learning, say, that ψ (p) =x allows a layman toruleoutanyprocessthatdoesnotpassthroughthispoint,butthisinformationdoes not reduce the set of possible policy processes enough for the layman to infer anything valuable about other policies. 5 From a layman s perspective, a non-invertible policy process is essentially a random function, with the outcome from different policy instruments even those that are close to each other entirely uncorrelated with one another. On such issues a non-expert knows very little about policy. He may be able to order policies according to which deliver in expectation more liberal or conservative outcomes, but does not know if this ordering will be reflected in realized outcomes and knows nothing about how realized outcomes are related (e.g., that nearby policies produce nearby outcomes). Partially Invertible Expertise Reality, most often, lies somewhere between the extremes, and an issue is partially invertible if it is neither invertible nor non-invertible. The set of partially invertible policy processes and issues is enormous, covering every possible case except those of the two extremes. Consequently, it is not difficult to specify a set Ψ of processes that are partially invertible. The challenge is to obtain a tractable family of policy processes that are partially invertible and exhibit additional desirable properties of policy making. One way to do this is to model the policy process as a Brownian motion. In particular, define an issue as the set of Brownian motions with drift μ and variance σ 2. A layman knows that the process is a Brownian motion of parameters μ and σ 2, with the nature of 5 Formally, if a non-expert learns that ψ (p) =y and updates using Bayes rule, non-invertibility requires that his posterior beliefs be identical to his prior beliefs for all policies q 6= p. Non-invertible processes do not submit to a particular functional form or even family of functions and the processes need not be continuous. 5

7 policy outcome x 6»PP ψ (p) ³³» slope = μ y - 0 p policy instrument Figure 2: Partially Invertible Policy Process ψ (p): driftμ, varianceσ 2,andψ (0) = y the issue varying in these parameters, but he does not know the realized path. 6 The Brownian motion is a continuous stochastic process with stationary independent increments. Although the true path is fully realized and observed by an expert the stochastic generation of the path is important for a layman s beliefs. If a layman learns one point in the mapping, say ψ (q) =y, his beliefs over all other policies p R are distributed normally with the following moments: Expected Outcome: Eψ (p) =y + μ (p q), Variance: var (p) = p q σ 2. The drift parameter μ measures the expected rate of change of the path. The variance of beliefs is proportional to σ 2 and increasing linearly in the distance between a policy p and the policy q for which the outcome is known. Figure 2 depicts one possible path of the Brownian motion that passes through ψ (0) = y, with the expected outcome of other policies represented by the dotted line through this point. The Brownian motion is partially invertible: from learning ψ (q) =y a layman infers information about other policies but for no other policy is the outcome known with certainty. The process is also proportionally invertible in that the amount a non-expert learns about a policy p decreases in the distance of that policy from the known point. This property captures the intuition of Lundblom (1959) that greater uncertainty is incurred themorepolicyismovedfromwhatisknown. 6 Although Brownian motions are normally associated with movement through time, time plays no role here. Instead the policy instrument serves as the independent variable, as in the canonical model. 6

8 The appeal of the Brownian motion as a model of the policy process is that, in addition to relaxing invertibility, it relaxes several other pathologies of the canonical model. 7 First is the assumption that laymen can order policies according to the actual outcomes they produce. Instead, for the Brownian motion the drift parameter supposes that a layman can do this only in expectation and not according to the realized outcomes. The path of a Brownian motion can be, therefore, non-monotonic, as depicted in Figure 2. 8 Similarly, the non-monotonicity of the realized path implies that a layman cannot be sure of the rate at which outcomes change for a change in policy, in contrast to the canonical model. Further, the Brownian motion is continuous. Although continuity is not necessary to understand policy, it captures the intuitive idea that policies that are closer to each other produce outcomes that are close. Another feature of the Brownian motion is that, while it is partially invertible, it is never fully inverted. Thus, no matter how many (finite) points in the mapping a layman observes, he will never fully understand the policy process. 9 The parameters of the Brownian motion (μ and σ 2 ) control how much a layman knows about a policy issue and the ratio σ2 provides a measure of issue complexity. Thelarger μ the ratio the less precise are a layman s beliefs upon learning a point in the mapping, and I say the issue is more complex. Issue complexity varies continuously in the parameters, with the limiting case σ2 representing issues of extreme complexity (non-invertible μ expertise), whereas the opposite extreme of σ2 μ (invertible expertise) represents increasingly simple issues ISSUE COMPLEXITY AND DELEGATION In this section I integrate the various policy processes into a model of delegation and policy formation and show that the complexity of expertise has a real effect on political behavior. To focus on the effects of informational complexity, the model I develop is highly stylized and consistent with established models in the literature, differing only in the policy processes allowed. 7 Although properties of the Brownian motion are consistent with observations from the rich history of policy making, it by no means provide an exhaustive account. Additional properties such as non-stationarity or discontinuities are captured by more general stochastic processes, such as a Levy process. 8 One may, of course, rearrange the policies such that the function is monotonic, but this merely transfers the uncertainty to knowledge of which orderings of policy deliver monotonic processes. 9 This feature in particular distinguishes the Brownian motion from other more obvious formulations. For instance, the canonical model can be relaxed by assuming both the slope and the intercept of the policy process is unknown by laymen. Although this representation relaxes invertibility it does so only minimally and is what might be called two-point invertible. 10 The limiting case σ 2 =0corresponds to the canonical model, although a discontinuity exists in the properties of the Brownian motion at this limit. 7

9 The Model The players are a Legislator (L)andanAgency(A). Policy is chosen once and the players can either retain the status quo sq or choose a new policy, where the set of alternative policies is the real line; thus, P = {sq, R}. The outcome space is the real line, O = R. The legislator s ideal outcome is 0 and the agency s ideal outcome is a>0. Both players have quadratic loss utility functions; the utility from outcome x is: u L (x) = x 2, u A (x) = (a x) 2, where the subscript denotes the player. Risk aversion is not necessary for the results to follow but represents the default case in the literature (Bendor and Meirowitz 2004). Policy instruments are mapped into outcomes via the function ψ Ψ. The legislator and agency both begin the game as laypeople with equal knowledge of ψ. Expertiseisa binary variable and, if obtained, the bearer gains perfect knowledge of the policy process (observes the true ψ). The cost of expertise to each player is c L,c A 0. I focus on the case c L = c A = c>0, ensuring that the emergence of agency expertise is due to issue complexity and not cost asymmetries; I consider the asymmetric cost case as an extension in the appendix (including the commonly studied case of c A =0). The sequence of play is given in Table 1. The legislator holds all formal decision power and can override agency recommendations (as it takes the final move of the game). The model is intentionally frictionless, with the legislator costlessly able to override agency recommendations. Thus, any power obtained in equilibrium by the agency is due to an informational advantage rather than some institutional feature. The assumption of frictionless oversight does have an impact on communication between the players as policy recommendations now take the form of costless messages. I restrict the channel of communication to be the proposal of a policy instrument and, by the revelation principle, study equilibria in which policy recommendations reflect the information they convey. 11 The status quo policy provides an outside option to policy makers. If the status quo is known by a layperson to deliver the legislator s ideal point with certainty then there is no need for delegation (nor the acquisition of expertise). I assume the sq policy delivers an uncertain outcome that is distributed uniformly around zero with support [ i, i]. 12 The policy process is varied as follows. For invertible issues, ψ is as specified in the canonical model, with the state-of-the-world θ distributed uniformly on the interval 11 That is, if the agency reveals that ψ (p) =x it is conveyed by a recommendation of instrument p (rather than, for example, recommending p ε with L knowing to adjust upwards). This restriction is without loss of generality and is also efficient if the legislator incurs a cost to override (including to change) the agency s proposal. 12 This uncertainty arises naturally with the evolution of technology or the arrival of an exogenous shock, such as an election that changes the composition of the legislature. An alternative formulation would be to assume the status quo delivers a known outcome that differs from zero. 8

10 Stage 1: The legislator chooses whether to delegate. If not jump to stage 4. Stage 2: Stage 3: Stage 4: Stage 5: Stage 6: The agency decides whether to acquire expertise. The agency proposes a policy instrument & the legislator updates beliefs. The legislator chooses whether to acquire expertise. The legislator decides whether to override the agency proposal; if so it chooses a policy instrument. The selected policy instrument is implemented and mapped into a policy outcome; payoffs are determined. Table 1: Timing of the Delegation Game [ λ, λ], where i 2 +3a 2 λ <. For non-invertible issues, ψ is an onto function (for each y R, ψ (x) =y for some x), and for partially invertible issues ψ is a Brownian motion of drift μ and variance σ 2, which with probability one is an onto function. 13 For non- and partially invertible issues a layman s prior beliefs over policies p R are distributed uniformly over the outcome space. 14 The equilibrium concept is Perfect Bayesian Equilibrium (PBE). I restrict attention to equilibria in which delegation occurs only when it is strictly preferred. That is, the legislator delegates only if the agency acquires expertise and the legislator benefits from this information. Informally, this restriction says that delegation is used only when it is value added. Denote L s utility by u L (y J) when the policy outcome is y and player J {L, A, } has paid the cost of expertise; u A (y J) is analogous. Results I begin by establishing two simple properties that serve as outside options for the players. First, consider the optimal policy choice of either player in the absence of expertise. By construction, it is optimal to retain the status quo rather than choose a policy in R 13 As Brownian motions are stochastic processes, each player may not have a unique most preferred policy, and such a policy maps into their ideal policy with probability one. 14 Formally, a uniform belief over R is known as improper and it is a common asumption in statistics and formal models in the social sciences. It can be constructed by drawing the value ψ (0) uniformly from R and generating ψ as a Brownian motion in either direction. The improper prior corresponds to the limit of the invertible case as λ and is made for analytic convenience. It does not substantively affect the results. 9

11 randomly. The status quo delivers reservation utilities: u L (sq ) = 1 3 i2, u A (sq ) = 1 3 i2 a 2. Observe that these values differ as for the agency the outcome is both uncertain and has an expected value different from its ideal point. The legislator, in contrast, suffers only from uncertainty, which is a public bad. Gilligan and Krehbiel (1987) refer to these as informational and distributional costs, respectively. Second, the value of u L (sq ) implies that the legislator, if acting in isolation, acquires expertise only if the cost is less than the disutility of the status quo; that is, the legislator acquires expertise rather than accept the status quo if and only if c< 1 3 i2.incontrast, the agency prefers acquiring expertise to accepting the status quo for all c< 1 3 i2 + a 2. Delegation With Commitment Before analyzing the full model, I first solve for optimal delegation if the legislator can commit to the delegation of authority. This case is analytically simpler than the full model and, when contrasted to the full model, clearly exposes the role of commitment. The invertibility of expertise is immaterial in this environment as even if the legislator is able to invert the agency s expertise it is unable to benefit from this knowledge. Consequently, if delegated to, the agency acts independently of oversight and implements its own ideal point (conditional on acquiring expertise). Formally, ignoring the commitment problem in delegation is equivalent to the following change to Step 3 of the delegation game: Step 3 alt : Agency selects a policy instrument. Proceed to Step 6. Define the Commitment Game as that produced when Step 3 alt is substituted for Step 3. Lemma 1 characterizes delegation in this environment. Lemma 1 Commitment game. The legislator delegates if and only if: (i) c< i2 and a<a 3 1,where(a ³ 1 ) 2 = c. (ii) i2 2i2 i <c< and a a 3 3 2, 3, where(a 2 ) i2 = c. If delegated to, the agency acquires expertise and implements its own ideal outcome. Proof. The agency acquires expertise only if c<c i A (a), and this delivers: u L (a A) = a 2 and u A (a A) = c. h Comparing i u L (a A) to u L (sq ) and u L (0 L) implies L delegates only if a 2 < min c, i2, and the result follows by algebra. 3 If granted authority the agency acquires expertise and, without the threat of oversight, chooses its ideal policy. Anticipating this response, the legislator is left with a stark 10

12 choice: determine policy independently or receive the agency s ideal outcome. These incentives lead to delegation of two types. In the domain of case (i) both the legislator and agency would acquire expertise. Theagency sidealpointissufficiently close to 0, however, that the legislator prefers to delegate and free-ride off the agency s investment in expertise. Delegation in this case satisfies the famous ally principle (Bendor, Glazer, and Hammond, 2000). The delegation of case (ii) is somewhat different. The legislator delegates to more extremeagenciesasitisnotpreparedtoacquire expertise itself. In this situation, the legislator s point of comparison is the status quo, rendering attractive any agency up to a = i 3. Of course, the legislator would like to delegate to any agency more centrist than this bound, but it is only the more extreme agencies in this set that are prepared to acquire expertise. If c> 2i2 both conditions cannot be satisfied simultaneously and 3 no delegation occurs. Delegation of type (ii) exploits the different willingness to pay of the players (and that the agency s willingness to pay is an increasing function of a), and fails the ally principle. Delegation and Oversight In the absence of commitment the agency operates in the shadow of legislative oversight. In this setting the invertibility of an issue matters and I demarcate results accordingly. Invertible Policy Processes: A useful starting point is to ask: does the equilibriumbehaviorinlemma1holdupin the absence of commitment? For invertible policy processes, the answer is no. If the agency acquires expertise and reveals the policy that delivers outcome a, the legislator can invert the agency s expertise and use its power of override to implement its own ideal point. The nature of delegation necessarily changes, therefore, in the absence of commitment. Proposition 1 shows that, in fact, it is entirely undermined. Proposition 1 Delegation does not occur in equilibrium if the policy process is invertible. Proof. Conditional on the agency acquiring expertise, communication must be via partitions and for any realization of θ the distribution of policy outcomes has mean 0 (Crawford and Sobel 1982). The agency s willingness to pay for expertise is less than 1 3 i2, but for c< 1 3 i2 the legislator would itself acquire expertise and deliver u A (0 L) = a 2. The agency prefers to free-ride rather than acquire expertise and the result follows. The logic of why delegation fails has two steps. The first step turns on the nature of communication between the players should the agency acquire expertise. Invertibility implies that the legislator can appropriate all information built into the agency s recommendation and use it for its own ends, obtaining the entire distributional benefit of expertise. This ability is rather obvious should the agency use a fully-revealing message. 11

13 Less obviously, it is also true if the agency inserts noise into its message, such as by recommending only whether the legislator choose a high or a low policy. Although such partitional messages prevent the legislator from acquiring full expertise, the expertise not reflected in the message cannot affect policy and is wasted. The second step in the logic is what the nature of communication implies for the agency s willingness to acquire expertise. With the legislator obtaining the distributional benefit of expertise, the agency receives only the informational benefit. But as the legislator also receives the informational benefit, the legislator s willingness to pay for expertise must be at least as great as that of the agency. Whereas in the commitment gamethelegislatorisabletofree-rideoff the agency, the absence of commitment reverses these roles and now the agency prefers to remain a non-expert and free-ride off the legislator, undermining the rationale for delegation. Delegation fails in this environment because the legislator is too powerful. Its first source of power is that, in holding all formal decision making authority, it lacks the leverage to induce the agency to acquire expertise, thereby allowing the agency to freeride. The second source of power is that the gap between an expert and non-expert is not large enough to allow an expert agency to protect any expertise it acquires. To explain delegation in this context, the literature has focused on relaxing the first source, exploring how a legislator could tie-its-own-hands in some way to allow for successful delegation. In contrast, I explore the second source of legislator power and I turn now to more complex forms of expertise. Non-Invertible Policy Processes: Suppose again that upon being delegated to, the agency acquires expertise and recommends a policy that maps into its ideal outcome. Whereas such an announcement fully reveals the mapping when an issue is invertible, it reveals nothing about other policies for non-invertible issues. In evaluating policies with which to override, the legislator then has only its prior beliefs as a guide. This leaves the legislator with a stark choice: accept the agency s ideal point or decide policy independently. This is the same choice as the legislator faced in the commitment game and, not surprisingly, equilibrium behavior is closely related but subtly different to that in Lemma 1. Proposition 2 Non-invertible policy. An equilibrium in which the legislator delegates, the agency acquires expertise, recommends its ideal ³ policy, and is not overridden by the legislator, exists if and only if i2 2i2 i <c< and a a 3 3 2, 3. Proof. I proceed by backward induction. (a) If A recommends policy p, L s beliefs over all q 6= p are unchanged and these policies h i remain dominated by sq. L accepts the agency recommendation iff a 2 < min c, i2. (b) Conditional on L accepting its 3 recommendation, A can do no better than its ideal policy. (c) A acquires expertise iff 12

14 a>a 2 and c> i2,asl otherwise acquires expertise if c< i2 3 ³ and A prefers to free-ride. 3 (d) Delegation is value added iff i2 2i2 i <c< and a a 3 3 2, 3. The complexity of non-invertible expertise changes the nature of communication between the players. In contrast to the invertible case, here an expert agency need not resort to partitional messages. Instead, the agency is able to communicate one piece of its expertise precisely, removing all informational costs of policy making and obtaining the entire distributional benefit for itself. To be sure, the legislator would like to override the agency and move the outcome closer to its ideal point, but its hands are tied by its own ignorance. Note, however, that although the legislator s ignorance is ex-post restraining, it is ex-ante beneficial as its virtual commitment to not override an agency recommendation is what induces the agency to pay the cost of expertise. Proposition 2 is notable also for what is missing. Delegation occurs here only when the legislator prefers the status quo to paying for expertise itself (c > i2 ). Thus, type 3 (ii) delegation from Lemma 1 survives whereas type (i) delegation does not. Type (i) delegation fails as relaxing commitment changes who can free-ride off whom. That the agency can free-ride in the absence of commitment leads to the failure of the ally principle, showing that it is largely the product of how decision rights are allocated between the players and not due to some ideological meeting-of-the-minds. 15 The delegation that does occur exploits the different willingness of the players to pay for expertise. In acquiring expertise the legislator can obtain either an informational benefit(iftheagencyisnotexpert)oradistributionalbenefit(iftheagencyisexpert),but not both. In contrast, the agency receives both an informational and a distributive benefit from expertise as for a 2 < i2 <cthe legislator is credibly committed to not acquiring 3 expertise itself, regardless of the agency s choice. As the agency s distributional benefitis increasing in a, delegation to legislative allies is not possible and the ally principle fails. Proposition 2 provides only a possibility result and does not characterize the full set of equilibria. The equilibrium identified is Pareto efficient and the optimal equilibrium for the agency conditional on it paying the cost of expertise. It is also straightforward to establish that this equilibrium is unique among equilibria in which one or more points of the policy mapping are implicitly revealed. Partially Invertible Policy Processes: The preceding results have shown that the legislator overrides when it learns everything from an agency recommendation and does not override when it learns nothing. In this section I turn to the more realistic middle ground and ask: Does the legislator override 15 The timing of legislative-bureaucratic interaction is in practice more fluid than modeled here and some bargaining over the cost of expertise may occur. Regardless of the outcome of any such process, however, the message remains that the legislator s independent incentive to acquire expertise changes the incentives of the agency as well as the practice of delegation. 13

15 if it learns something but not everything from an agency recommendation? The answer to this question depends on whether a little bit of information leads to a little bit of overriding or whether a critical level of invertibility exists such that the legislator does not override. This distinction is important as any amount of overriding can complicate communication between an agency and a legislator and potentially undermine the possibility for successful delegation. Proposition 3 shows that a critical bound does exist such that the legislator does not override and this bound provides the basis for successful delegation. Proposition 3 Partially invertible policy. The equilibrium in which the legislator delegates, the agency acquires expertise, recommends its ideal ³ policy, and is not overridden by the legislator, exists if and only if i2 2i2 <c<, a i a 3 3 2, 3,anda σ2. 2μ Proof. Set μ 0 (μ 0 is analogous). As the agency may have multiple ideal policies, let its recommendation rule be p 0 =max{p ψ (p) =a}, whichexistswithprobability one (otherwise recommend any p = ψ 1 (a) or a policy that delivers the outcome closest to a). For L, anyp>p 0 is dominated by p 0 and the utility from p = p 0, for 0, gives: u L (p) = (a μ) 2 σ 2 du L (p) d = 2μ (a μ) σ 2 d 2 u L (p) d 2 = 2μ 2 < 0. L accepts p 0 iff du L(p) σ2 0 at =0,whichrequiresa. The result then follows from d 2μ the arguments in the proof of Proposition 2. Upon seeing the agency s recommendation the legislator refines its beliefs and knows in which direction it must move policy to move the expected value toward its own ideal outcome. In fact, it knows by exactly how much policy should be adjusted ( a)sothat μ the expected outcome is equal to its ideal outcome. This ability is only in expectation, however, and the benefit itoffers must be weighed up again the possibility of moving the outcome in the wrong direction or moving in the right direction but overshooting. The critical value a σ2 ensures that the legislator prefers the agency recommendation to the 2μ uncertainty of all other policies, thereby providing the foundation for agency expertise and successful delegation. DISCUSSION Propositions 1-3 establish that delegation is possible for sufficient issue complexity and not possible for maximally simple expertise, but they are silent as to behavior for intermediate levels of complexity. Driving successful delegation on complex issues is the 14

16 agency s ability to obtain a distributional as well as informational benefit, a benefit that is not attainable when expertise is invertible. Whether delegation is possible for intermediate complexity turns, therefore, on whether the agency can obtain a distributional benefit from obtaining expertise. Proposition 3 establishes that the agency cannot obtain the full distributional benefit for intermediate complexity but leaves the exact nature of communication in equilibrium as an open question. Insight into behavior under intermediate complexity can be gleaned from how the legislator would override the agency recommendation should the agency reveal its ideal policy. In this case the legislator would not move the expected outcome all the way to its own ideal outcome, but rather it would move it to an intermediate value that trades off lower uncertainty for remaining divergence. Although such a partial override cannot support equilibrium (as in anticipation the agency would adjust its recommendation), it does suggest the opportunity for mutual gain and a role for political institutions. For instance, if an institution existed that enabled points in the policy mapping to be verified (Congressional hearings, say), delegation could be supported in equilibrium by identifying a sharing of distributional benefits acceptable to both players. The model is extendable in a variety of directions, such as partial or incomplete learning of the policy mapping or repeated interaction. Perhaps the most interesting extension is to endogenize issue complexity. A straightforward implication of the model is that, to protect its expertise, an agency would increase issue complexity, even at the cost of resources or policy making efficiency. This incentive suggests an endogenous explanation for the often lamented inefficiency and complexity of modern bureaucracies, and resonates with Fiorina s famously cynical theory that the labyrinthine federal bureaucracy is the product of intentional design. Finally, the generalization of expertise offered here remains informational. Although this formulation is open to broad interpretation, it does not capture expertise in its full breadth. An alternative perspective is to view expertise as an ability (or a strategy) rather than a difference in knowledge (Page 2007). Expert skills may also have varying degrees of invertibility and integrating the two approaches is of obvious interest. Such a task is beyond the scope of this paper, however, and is left for another time. APPENDIX: ASYMMETRIC COSTS OF EXPERTISE The legislative-bureaucratic relationship is dynamic, and expertise obtained on one issue maybeusefullyappliedtothesameordifferent issues in the future. As such, many policy making situations are more accurately modeled under the condition c A <c L.Ibriefly consider this extension here and present two results, one for each extreme of invertibility. Corollary 1 considers non-invertible expertise and shows that the ally principle is restored only in the limit case of c A =0. The proof is a simple generalization of that for Proposition 2 and is omitted; Note that a 0 1, a 00 1, anda 0 2 are analogues of a 1 and a 2 defined 15

17 in Lemma 1. Corollary 1 Non-invertible hpolicy. For c A <c L, the legislator delegates if and only if: (i) c A < ³a i2 and a 0 3 1, min a 00 i 1, 3 i, where(a 0 1) 2 = c A and (a 00 1) 2 = i2. 3 ³ (ii) i2 <c 3 A < 2i2 and a a 0 i 3 2, 3, where(a 0 2) i2 = c A. Delegation of type (ii) is a continuous generalization of that in the equal cost case, whereas type (i) is new. The agency is willing to develop expertise in this case despite knowing the legislator otherwise would as the cost is sufficiently small to warrant moving the outcome from 0 to a. The legislator does not override as its cost exceeds the reverse benefit ofmovingtheoutcomefroma to 0. The more interesting case of asymmetric costs arises when expertise is invertible. Proposition 1 continues to hold for c A <c L as long as the asymmetry is not too great, although it breaks down for c A sufficiently small. In this case the agency is prepared to acquire expertise as it prefers having the legislator appropriate the expertise than the legislator remaining uninformed. Communication in this game must be partitional and policy outcomes possess the following properties. Krehbiel (1991, page 93) reports a similar result, referring to it as the Procedural Commitment Principle. Remark 1 If delegation occurs for an invertible policy process when c A <c L, the distribution of realized outcomes has mean zero and strictly positive variance for all realizations of θ. Policy outcomes in this situation are Pareto inefficient. The agency receives no distributional benefit from its expertise (no bureaucratic drift) and would strictly prefer to give all of its expertise to the legislator but is unable to do so. These properties are inconsistent with the Weberian view of bureaucratic power, reinforcing the conclusion that an informational explanation of agency power and bureaucratic drift requires the underlying policy issue to be complex. References [1] Austen-Smith, David Information Transmission in Debate. American Journal of Political Science 34 (February): [2] Bendor, Jonathan, Serge Taylor, and Roland Van Gaalen Bureaucratic Expertise versus Legislative Authority: A Model of Deception and Monitoring in Budgeting. American Political Science Review 79 (December): [3] Bendor, J., A. Glazer, and T. Hammond Theories of Delegation. Annual Review of Political Science 4:

18 [4] Bendor, Jonathan, and Adam Meirowitz Spatial Models of Delegation. American Political Science Review 98 (May): [5] Crawford, Vincent P. and Joel Sobel Strategic Information Transmission. Econometrica 50 (November): [6] Diermeier, Daniel Commitment, Deference, and Legislative Institutions. American Political Science Review 89 (June): [7] Epstein, David and Sharyn O Halloran Delegating Powers. New York: Cambridge University Press. [8] Fiorina, Morris P Congress: Keystone of the Washington Establishment. New Haven: Yale University Press. [9] Gerth, H.H. and C.W. Mills (Eds. and trans.) From Max Weber: Essays in Sociology. New York: Oxford University Press. [10] Gilligan, Thomas, and Keith Krehbiel Collective Decision Making and Standing Committees: An Informational Rationale for Restrictive Amendment Procedures. Journal of Law, Economics, and Organization 3 (2): [11] Gilligan, Thomas, and Keith Krehbiel Asymmetric Information and Legislative Rules With a Heterogeneous Committee. American Journal of Political Science 33 (May): [12] Krehbiel, Keith Information and Legislative Organization. AnnArbor, MI: University of Michigan Press. [13] Lundblom, Charles The Science of Muddling Through. Public Administration Review 19: [14] Page, Scott E The Difference: How the Power of Diversity Creates Better Groups, Firms, Schools, and Societies. Princeton NJ: Princeton University Press. [15] Ringquist, Evan J Political Control and Policy Impact in EPA s Office of Water Quality. American Journal of Political Science 39 (May):