Stovepiping

1. A strategic model of stovepiping

In this section, we develop a strategic model of information transmission within a simple policy-making hierarchy. While this model is game theoretic, we omit some aspects of a full description of the game for purposes of clarifying the presentation of the interesting results.

Intuitively, the model captures a process in which a line agent A is formally charged with assembling information about the value of altering policy from a status quo, and can decide at its discretion to forward its information to the principal P who will make the final decision about whether to make policy, denoted by a_P = 1, or not, denoted by a_P = 0. We assume that A is more conservative than P in the sense that there are some reports on which P would want to act but are deemed unworthy of action by A. This is not particularly restrictive given P’s power to choose a_P: if A were less conservative, i.e. there are reports on which A would act but P would find unpersuasive as the basis of making new policy, then P could simply ignore them. ⁷

With positive probability, an Outsider O also observes the same information observed by the agent about the value of making new policy (i.e. choosing a_P = 1). If O observes this information, it can choose to forward it to P regardless of A’s action. The Outsider is, for the time being, assumed to be less conservative (i.e. more likely to favor making new policy, a_p = 1) than both P and A in the sense that if either P or A believes that a report warrants making new policy, then O necessarily finds this information persuasive as well. In addition, A has substantive capacity to implement policy that brings it systematically closer to P’s desired outcome, but only if A involves itself by recommending a policy change; otherwise, P must pursue policy change without A’s substantive capacity. One way to think of this is that policy can result in a Type I error, taking action when it is inappropriate, and actors are ordered in terms of the cost they attach to Type I errors. ⁸ While A attaches the greatest cost to Type I error, all actors also know that, given that policy change will take place, the probability of Type I error is minimized when A applies its substantive capacity to implementing the new policy.

For instance, A could represent a field agent in the FBI who observes untoward activity among suspected terrorist organizations, but is concerned that intervening against the suspects prematurely could undermine a more intricate case he or she is working on. On the other hand, P is less concerned about line agents’ painstaking case development, and more concerned to ‘do something’ in the public eye about terrorism and ensure that no attacks happen on her watch; besides, if new action is taken inappropriately, P can always blame it on overzealous field agents. The outside informant O in this example could represent agents from another unit (e.g. another division of the FBI, the CIA, or local law enforcement) who believe the agents A are excessively lax or timid. Numerous other examples are also possible, e.g. with A representing the National Security Agency, P the president, and O a military commander in the field.

Alternatively, A could represent drug reviewers at the Food and Drug Administration who observe the quality of scientific protocols used to evaluate the efficacy and safety of new drugs proposed by industry, while P represents a hierarchical principal in the FDA with formal authority to approve new drugs for marketing. Due to their acute concern for the scientific reputation of their agency (Carpenter, 2010), drug reviewers may be inclined against approving new drugs for marketing if they are supported by lax protocols. On the other hand, P may be more attuned to political pressure to break the ‘drug lag’ and bring new drugs to market. The outsider O could then represent other informed groups such as pharmaceutical research associations, patient advocacy groups, or government health researchers (e.g. the National Cancer Institute) who are more interested than FDA drug reviewers in seeing new drugs approved for marketing. While these outside groups have information about drug safety and efficacy to present to the principal, P still benefits from A’s involvement; e.g. A may have specific expertise in crafting a drug label to convey intricate dosage information and side effects to physicians.

Structure of play. The line agent A observes the report r with probability π _A  ∈ (0, 1] and the Outsider O observes the report r with probability π _O  ∈ (0, 1]. Whether A or O observes the report is independent of whether the other player observes the report, and neither player observes whether the other player observes the report. The probabilities π _A and π _O are common knowledge. Upon observing r, player i ∈ {A, O} chooses whether to forward the report to the Principal: a_i = 1 if the report is forwarded by i and a_i = 0 otherwise. After A and O have made their decisions the Principal decides whether to promulgate a new policy (a_P = 1) or not (a_P = 0).

When π _A  < 1, standard bureaucratic redundancy arguments ⁹ imply that the Outsider’s presence is beneficial for the principal, P. Specifically, the Outsider’s presence raises the probability that at least one agent observes the report. As will become clear below, however, this is not the primary value of O to P; rather O is valuable because of the changes it induces in A’s reporting behavior. Note that we formally model A’s and O’s decisions to submit the report to P as simultaneous.

It may seem that stovepiping would be more naturally captured in a sequential game in which O observes A’s report a_A, and then chooses its report a_O. However, it can be shown that the sequential move version when O follows A will generate the same subgame perfect Nash equilibria. In particular, O would report exactly the same set of reports in both versions of the game and, more importantly, O’s decision is independent of A’s action (and, hence, strategy) in both game forms. ¹⁰

Information. The report r consists of one number, q_r > 1, which represents the quality of policy implementation based upon the report. ¹¹ Report quality q_r is observed by the Principal if and only if the report is forwarded by either the Agency or the Outsider, and the Agency and/or Outsider can forward the report only if they observe it. Information is ‘hard’ in the sense that if either A or O forwards the report, they must do so truthfully; they cannot lie about its content. This is a straightforward way to represent either relational/reputational costs, or formal legal sanctions (as might apply to A), associated with lying about q_r; essentially we are assuming that these costs are high enough to deter lying even if it is caught with very small probability. While A and O must tell the truth, they need not tell the ‘whole truth’: they may send no signal at all. This captures a situation in which information submitted to the agency comes with a paper trail; agents have some discretion to decide what information (if any) to pass up the hierarchy, but passing up false information is formally prohibited.

Note that our model is not a ‘cheap-talk’ signaling model, in that the report r can be revealed credibly. A better description of the model is as one of ‘informational gatekeeping’ with multiple gatekeepers. The state of nature is r revealed with some positive probability to the agents who then independently decide whether to also reveal it to the principal. The agents have divergent preferences, in this case over the minimal quality of information required for the agent in question to prefer that the Principal make new policy, and divergent abilities. As we discuss below, the conservative informational gatekeeper (in this case the Agency, A) is also more effective at utilizing the information contained in any given report. Accordingly, one can conceive of the Agency as inherently possessing ‘more information’ than the Outsider.

The ‘policy-setting’ process. If a_P = 0, an exogenous status quo with known utilities remains in effect. If a_P = 1, P makes new policy with precision (or quality) equal to q_r. ‘Precision’ is assumed here to be a commonly valued characteristic of policy-making: high precision is preferred, ceteris paribus, by all three agents. ¹² The precision of the report r is drawn from a commonly known distribution with cumulative distribution function (CDF) F. We assume that the observation of the report by the Agent and the Outsider (occurring with probabilities of π _A and π _O , respectively) are each independent of q_r. ¹³

Payoffs. The Principal’s payoff function, u_P, is based on a_O, a_P, and q_r as follows:

u P ( a O , a P , q r ) = { b P − 1 q r if a P = 1 and a A = 1 , b P − τ q r if a P = 1 , a O = 1 , and a A = 0 − x P if a P = 0 .

Thus, the first line covers cases where P makes new policy with A’s input, the second line where P makes new policy with O’s input but not A’s, and the third where P keeps the status quo. The parameter b_P ≥ 0 measures the Principal’s desire to promulgate new policies, ceteris paribus. For instance, the principal may desire to ‘leave her mark’ on policy or show some degree of activity to yet a higher-level (unmodeled) principal. The parameter x_P ∈ (0, 1) represents the Principal’s payoff loss from the status quo policy. In our framework, the cost of promulgating a new policy (a_P = 1) stems from uncertainty about policy outcomes (which is inversely proportional to q_r). This could be described as the potential for blame for policy outcomes that would be (perhaps unfairly) attributed to the new regulation. Alternatively it could simply be standard spatial distance between a desired target outcome and the realized outcome. ¹⁴ The parameter τ > 1 is an exogenous and commonly known value that measures the increased uncertainty (i.e. lack of precision) resulting from policymaking without the guidance of the Agency. We assume that q_r and the observations of the report by the Agency and Outsider are all independently distributed. ¹⁵

The Outsider’s payoff function, u_O, is similarly based on a_O, a_P, and q_r:

u O ( a O , a P , q r ) = { σ b P − 1 q r if a P = 1 and a A = 1 , σ b P − τ q r if a P = 1 , a O = 1 , and a A = 0 − x O if a P = 0 .

The parameter σ measures the alignment between the Outsider’s and Principal’s direct preferences for ‘new policy making’ and x_O ∈ (0, 1) represents the Outsider’s payoff loss from the status quo policy. The Outsider and the Principal effectively have identical preferences over policy outcomes and, if σ ≥ 1, the Outsider’s preference for new policymaking are at least as strong as the Principal’s. Conversely, when σ ∈ (0, 1), the Outsider has a ceteris paribus preference for new policy making, but this preference is weaker than the Principal’s.

Finally, the Agency’s payoff function, u_A, is based on a_O, a_P, and q_r as follows:

u A ( a P , q r ) = { − 1 q r if a P = 1 and a A = 1 , − τ q r if a P = 1 , a O = 1 , and a A = 0 − x A if a P = 0 .

where x_A ∈ (0, 1) represents the Agency’s payoff loss from the status quo policy.

Several features of the payoffs are worth mentioning due to the role they play in our results. First, all players share preferences over implementation quality: higher values of q_r uniformly make the players better off conditional on the Principal making policy (a_P = 1). This holds regardless of whether the Agency, Outsider, or both forward the report to the Principal. This assumption is critical for our analysis, and while credible in many applications, it probably does not hold universally. For example, if q_r represents a sort of reduced form variance over policy outcomes, an actor might prefer greater variance if it makes it more likely for policy to exceed some desired threshold. That is, some actors might have conventional preferences for lower variance, while others might prefer greater variance because it raises the chance of policy exceeding a critical threshold, thus increasing the option value of enacting a policy change. In that case, players would not have common preferences over q_r, and the subsequent analysis would generally not hold.

Second, note that the model appears to represent divergence in the players’ preferences in two ways: they may have different preferences over whether to make new policy at all (i.e. σb_P > 0) and/or they may receive different relative payoffs from the status quo (for example, b_P = 0 but x_A ≠ 0). This difference is one in appearance only, as the action space is particularly coarse. In instrumental terms, policy is either changed or it is not. Accordingly, there is a duality built into the model’s parameterization: increasing x_P is equivalent to increasing b_P. ¹⁶ However, the representation allows us to frame the comparative statics in direct terms so that the presentation of the results is clearer.

Third, no player cares about the quality of the report, q_r, unless the Principal chooses to make new policy (a_P = 1). This assumption creates an incentive for all players to defer to the status quo policy unless the report has high enough quality. Thus, although the players agree that precision in policy implementation (i.e. a high-quality report) is desirable, there is important heterogeneity in their motivations through the fact that they will disagree over the cost of Type I errors or, in other words, what level of quality is sufficiently high to justify changing the status quo policy.

Fourth, and finally, we assume throughout that for each player i ∈ {A, O, P}, there is a sufficiently high level of quality such that player i would be made strictly better off by new policy being made (i.e. such that a_P = 1 is strictly preferred by player i to a_P = 0). Thus, Type II errors (failing to change policy when it is beneficial relative to the status quo) are a potential concern to all players, as are Type I errors (changing policy when it is not beneficial). Furthermore, we assume that there are sufficiently low-quality reports that the Agency would prefer not to make new policy.

2. Analysis

With the payoff functions in hand, it is simple to define the following sequentially rational policy making strategy for the Principal. Along with the content of the report r, q_r, there are essentially three cases to consider (one of which is invariant to the content of the report because the Principal does not observe it). These are described below.

Policy making with ‘everyone in the room.’ Given a report r with quality q forwarded by the Agency (a_A = 1), the Principal’s optimal policy choice is

a P * ( q | a A = 1 , a O = 0 ) = a P * ( q | a A = 1 , a O = 1 ) = { 1 if b P + x P ≥ 1 / q , 0 otherwise .

Policy making with the agency absent. Given a report r with quality q not forwarded by the Agency (a_A = 0) but forwarded by the Outsider (a_O = 1), the Principal’s optimal policy choice is

a P * ( q | a A = 0 , a O = 1 ) = { 1 if b P + x P ≥ τ / q , 0 otherwise .

Policy making with no report. Given a report r with quality q not forwarded by either the Agency or by the Outsider (a_A = a_O = 0), the Principal’s optimal policy choice is

a P * ( q | a A = 0 , a O = 0 ) = { 1 if b P + x P > 1 0 otherwise .

Before continuing, it is useful to note the nature of the Principal’s possible responses to a report: he either ‘pulls the trigger’ and makes new policy or he effectively ignores the report. This stark approach is useful because it allows us to focus on the interesting aspects of the informational structure. ¹⁷ Specifically, the analysis here is of information handling within the bureaucracy.

Combined with the binary nature of policy making and the fact that reports can be well ordered in terms of their quality, q(r), this initial analysis of the Prinicipal’s incentives allows us to describe any player’s ex ante preferences about policy making in relation to any other’s. Accordingly, and throughout, we use the terms ‘conservative’ and ‘aggressive’ to describe a player’s policy making preferences in relation to the principal’s preferences.

Definition 1. A player i is conservative (relative to P) if the set of reports that i prefers a_P = 1 to a_P = 0 is a strict subset of the set of reports such that a P * ( q | a A = 1 , a_O = 1) = 1. Conversely, a player i is aggressive (relative to P) if the set of reports that i prefers a_P = 1 to a_P = 0 is a strict superset of the set of reports such that a P * ( q | a A = 1 , a O = 1 ) = 1 .

It is straightforward to verify the following facts:

The responsive principal assumption. The following assumption is a useful baseline to rule out uninteresting cases.

Assumption 1. The Principal prefers leaving policy unchanged in the absence of a report: b_P + x_P ≤ 1.

Without this assumption, there is never a reason (presuming sequential rationality by the Principal) for either the Agent or the Outsider to withhold a report. Even more specifically, when this assumption is violated the only reason for P to listen to a stovepipe is essentially to insure against the possibility that the Agency does not receive a report (which occurs with probability 1 − π _A ). In such cases, the stovepipe benefits both the Principal and the Agency in a standard redundancy fashion. While this is of course an empirically relevant consideration in real-world organizations, note that its effects are not the result of any interesting strategic interaction between any of the players. ¹⁸

Note that the Outsider’s expected payoff is independent of his or her choice to report (a_O) if the Agency reports. Thus, the Outsider’s expected payoff from a_O = 1, conditional on a_A = 0, q_r, and the Principal’s optimal strategy as described above, is ¹⁹

V O ( a O = 1 ; q ) = { σ b P − τ / q if b P + x P ≥ τ / q , − x O otherwise .

(1)

It is without loss of generality to presume that the Outsider reports only if the Principal would act upon the report (this is always known by the Outsider conditional on observing r, since τ, b_P, and x_P are all common knowledge and the Outsider knows q_r). This strategy is written formally as

a O * ( q ) = { 1 if min [ b P + x P , σ b P + x O ] ≥ τ / q 0 otherwise .

(2)

In equilibrium, then, the Agency’s strategic incentives are derived using (2), which leads to the following expected payoff function for the Agency: ²⁰

V A ( a A | q , π O ) = { − 1 / q if b P + x P ≥ 1 / q and a A = 1 − π O τ q − ( 1 − π O ) x A if min [ b P + x P , σ b P + x O ] ≥ τ / q and a A = 0 − x A otherwise .

(3)

Utilizing Equation (3), the following straightforward derivations yield the optimal strategy for the Agency.

If min[b_P + x_P, σb_P + x_O] ≥ τ/q, then the Agency should report whenever

− 1 / q ≥ − π O τ q − ( 1 − π O ) x A , q ≥ 1 − π O τ ( 1 − π O ) x A ,

and if b_P + x_P ≥ 1/q, the Agency should report whenever q ≥ 1/x_A. Indeed, a_A = 1 is a dominant action for any report with q ≥ 1/x_A. ²¹ Accordingly, the Agency’s optimal strategy can be written as follows:

a A * = { 1 if q ≥ 1 / x A , 1 if q ≥ max [ τ / min [ b P + x P , σ b P + x O ] , 1 − π O τ ( 1 − π O ) x A ] , 0 otherwise .

(4)

We are now in a position to examine the comparative statics of the Agency’s optimal behavior. There are two cases of interest, depending on whether the Outsider is more or less conservative than the Principal. If b_P + x_P < σ b_P + x_O, then the Principal is more conservative than the Outsider and, conversely, if b_P + x_P > σ b_P + x_O, then the Outsider is more conservative than the Principal. We label these two cases ‘Aggressive Outsider’ and ‘Conservative Outsider,’ respectively.

To make the presentation of the remaining results parsimonious, we assume throughout what follows that q_r is drawn from a continuously differentiable CDF F(q) (with probability density function f) possessing positive support for all q > 1.

Assumption 2 (Higher-quality reports always possible). For all q > 1, f(q) > 0.

With Assumption 2 in hand, we can now proceed to answer several questions within the model. First, under what circumstances does the presence of the Outsider affect the Agency’s behavior? Second, what are the determinants of the proportion of reports that are forwarded by the Agency in response to the presence of the Outsider?

When does stovepiping alter the agency’s behavior?. Equation (4) clearly indicates a necessary condition for the Outsider’s presence to have any effect on the number of reports forwarded by the Agency. Specifically, since 1 / x A > 1 − π O τ ( 1 − π O ) x A for all τ > 1, π _O  > 0, and x_A > 0, the following must hold for the Agency to forward reports in the presence of the Outsider that would not be forwarded if the Outsider were not present:

1 / x A > τ / min [ b P + x P , σ b P + x O ] .

(5)

The following proposition summarizes the implications of Inequality (5). ²²

Proposition 1. The Outsider has an effect on the optimal reporting behavior of the Agency if:

The first conclusion of Proposition 1 is intuitive: when the agency is sufficiently satisfied with the status quo policy, the presence of a stovepipe will lead to an increase in the number of reports that are forwarded to the Principal simply because the choice of not forwarding the report to the Principal is no longer sufficient to guarantee that the status quo policy will remain in effect. So long as the Outsider is less efficient at policy implementation than the Agency (i.e. τ > 1), the installation of a stovepipe will lead to direct reduction in the Agency’s expected payoff from withholding reports from the Principal.

The second and third conclusions of Proposition 1 are similar to the first conclusion but rely on a slightly different foundation. Specifically, as the Principal and the Outsider both become increasingly displeased with the status quo and/or the Principal is sufficiently interested in making new policy for the sake of making new policy, the Agency realizes that the minimal quality level that the Principal and Outsider will find sufficient cause to make new policy is decreasing as well. Since the Agency has an incentive to be ‘in the room’ whenever it knows that a new policy is being made, the increasing willingness of the Principal to make policy increases the willingness of the Agency to forward reports to the Principal.

Proposition 1 compares the frequency of reporting under two starkly different institutional structures (i.e. in the presence of versus the absence of any Outsider). We now turn to the question of comparing institutional structures that, in general, differ on the margin: holding the presence of the stovepipe constant, we can examine the effect of changes in the preference and technology parameters of the model.

Comparative statics of the Agency’s behavior. In order for the comparative statics of the Agency’s behavior to depend on the structure of the Outsider’s involvement, the Outsider need be sufficiently competent (i.e. that τ not be too large). Otherwise, the minimum level of quality that the Agency need worry about depends solely on the Principal’s preferences. ²³ The maximum level of relative inefficiency of implementation in the absence of the Agency is given by the following inequality:

0 < 1 − π O τ ( 1 − π O ) x A − τ / ( b P + x P ) , τ < b P + x P π O ( b P + x P ) + ( 1 − π O ) x A .

(6)

Aggressive Outsider. Supposing that b_P + x_P < σ b_P + x_O and that Inequality (6) is satisfied, the reports of interest are those for which

q ∈ ( 1 − π O τ ( 1 − π O ) x A , 1 x A ) .

(7)

This is the set of reports that, in equilibrium, the Outsider’s presence causes the Agency to forward to the Principal when the Outsider is sufficiently competent that Inequality (6) is satisfied. This set is no-empty for all π _O  > 0 and vanishes when π _O  = 0. Invoking Assumption 2 then yields the following comparative static.

Proposition 2. When the Outsider is more aggressive than the Principal and the Outsider is not too incompetent (i.e. inequality (6) is satisfied), the ex ante probability that the Agency forwards a report to the Principal is:

Supposing that b_P + x_P < σ b_P + x_O and that inequality (6) is not satisfied, the reports of interest are those for which

q ∈ ( τ b P + x P , 1 x A ) .

(8)

As above, this is the set of reports that, in equilibrium, the Outsider’s presence causes the Agency to forward to the Principal when the Outsider is sufficiently incompetent that inequality (6) is not satisfied. This set is clearly empty for sufficiently large values of τ: in such cases the Outsider’s presence has no effect on the Agency’s reporting behavior. Invoking Assumption 2 then yields the following comparative static.

Proposition 3. When the Outsider is more aggressive than the Principal and the Outsider is sufficiently incompetent (i.e. inequality (6) is not satisfied), the ex ante probability that the Agency forwards a report to the Principal is decreasing with respect to the Outsider’s relative incompetence, τ.

The effect of the Outsider’s relative inefficiency (τ) is displayed in Figure 1. The figures graphs the minimal quality level that the Agency would forward to the Principal as a function of τ. All three possible regions are illustrated. When τ is low (i.e. close to 1), the effect of increasing τ is to decrease the minimal quality level (increasing the frequency of reports being forwarded), as described in Proposition 2. For intermediate values of τ, increasing τ increases the minimal quality level that is forwarded (decreasing the frequency of reports being forwarded), as described in Proposition 3. Finally, for sufficiently large values of τ, the Agency’s behavior is insensitive to further increases in τ because the Principal will never act upon a report unless it is forwarded by the Agency.

OPEN IN VIEWER

Fig. 1.

The effect of outsider policy making efficiency on agency reporting.

Before continuing to the case of a conservative Outsider, note that, regardless of the competence of the Outsider (i.e. the value of τ), the set of reports that the Agency will forward to the Principal is, quite intuitively, increasing in the Agency’s dissatisfaction with the status quo (i.e. x_A).

Conservative Outsider. When b_P + x_P > σ b_P + x_O, the analog to inequality (6) is

τ < σ b P + x O π O ( σ b P + x O ) + ( 1 − π O ) x A .

(9)

Also, when b_P + x_P > σ b_P + x_O, inequality (9) also identifies when the agency’s behavior is affected directly by the preferences of the Outsider. Thus, the following Propositions are immediate.

Proposition 4. When the Outsider is more conservative than the Principal and the Outsider is not too incompetent (i.e. inequality (9) is satisfied), the ex ante probability that the Agency forwards a report to the Principal is:

The intuition behind Proposition 4 can be understood as follows. When the Outsider is not ‘too incompetent,’ there is a positive probability that the Principal will receive and act upon a report forwarded only by the Outsider, O. Thus, in this region, increases in the likelihood of the report being received by the Outsider commensurately increase the downside risk the Agency incurs by withholding a report and accepting that policy might be made without the Agency in the room by increasing the probability of such an event. Analogously, in this region, decreases in the Outsider’s competence increase the downside risk for the Agency of withholding a report by increasing the ex post cost of such an occurrence. The next proposition deals with situations in which the Outsider is sufficiently incompetent that inequality (9) is not satisfied.

Proposition 5. When the Outsider is more conservative than the Principal and the Outsider is sufficiently incompetent (i.e. inequality (9) is not satisfied), the ex ante probability that the Agency forwards a report to the Principal is:

The conclusions of Proposition 5 can be understood in the following way. When the Outsider is sufficiently incompetent, there will exist reports of low quality that the Agency would forward if the Agency believed that the Principal would act upon them in the Agency’s, but the Principal would not be rational to act upon them if the Agency is not in the room (because the Outsider is too incompetent to justify action over inaction in the Agency’s absence). The first conclusion of the proposition follows from the fact that this set of reports grows as τ increases (i.e. as the Outsider becomes less competent). As for the second conclusion, we are considering the case of a conservative Outsider: there are some reports that the Outsider will not forward to the Principal that the Principal would act upon even if the Outsider were the only one to forward them. Accordingly, this set of reports decreases, implying that the probability that the Outsider forwards a report to the Principal increases, as σ increases, as this makes the Outsider less conservative (i.e. more aggressive). Thus, the Agency’s downside risk from withholding a report is increasing as σ increases.

Implications for institutional design. Before continuing on to extend the model so as to incorporate endogenous information collection, consider the implications of the model so far for the ‘institutional design’ problem faced by the Principal if he or she is allowed to select an Outsider. Specifically and for simplicity, presume that the Principal can choose τ. That is, suppose that the Principal has a set of possible outsiders to select from, each with different levels of implementation ability (i.e. competence). Furthermore, and in line with one of the two endogenous information extensions we consider later in the article, modify the game above so that the Outsider obtains the report only if the Agency also obtains the report. ²⁴

The combination of Propositions 4 and 5 suggests that the Principal has an interior, optimal level of incompetence. Specifically, given the presumption that the Outsider receives the report only if the Agency also receives it and that the probability of the Agency receiving the report is independent of the chosen level of τ, ²⁵ the level of incompetence of the Outsider that maximizes the Principal’s equilibrium expected payoff is strictly greater than τ = 1 (i.e. less competent than the Agency). In this extension/modification of the model, the Principal has an incentive to leverage his or her the ability to commit himself to inefficient implementation, which the Agency does not like, as a mechanism to force the Agency’s hand on reports of marginal quality that the Agency would not forward if it did not fear the cost of ‘not being in the room.’ This cost is increasing in τ, and Proposition 5 indicates that any optimal level of τ from the Principal’s (ex ante) perspective must satisfy inequality (9).

3. Stovepipes and endogenous information collection

The fundamental strategic effect of stovepiping is to increase the Agent’s incentive to report what it knows. It may therefore seem that P is uniformly better off with a stovepipe than without. However, this intuition ignores the effects of stovepiping on the Agent’s incentives to acquire information in the first place. In this subsection we consider two extensions that partially endogenize the information conditions in the game. Both of these extensions show that the simple intuition that stovepipes are beneficial for the Principal is misguided when information is endogenous. ²⁶

Throughout this section we make the simplifying normalization that x_P = x_O = 0: the Principal and Outsider’s interests in making new policy are measured completely by b_P. ²⁷

3.1. Costly information processing in the agency

The first extension relates to information acquisition by the Agent when the Outsider’s information is given. Just as the stovepipe can induce the Agency to forward reports that it would not otherwise forward, the stovepipe can induce the Agency to acquire more information in the first place. At the same time, if the stovepipe does not impose too large a cost on the Agency when it does not report, the stovepipe can actually reduce the Agency’s incentive to acquire information about q.

Specifically, we suppose now that the Agency can choose whether to discover the report r’s quality, q_r. As above, the Agency believes that the distribution of the quality is characterized by a cumulative distribution function, F. If the Agency chooses to discover the quality q_r, then it incurs an opportunity cost denoted by k > 0. The Agency can then decide whether to forward the report to the Principal as in the analysis reported in the previous section. If the Agency choose not to discover the quality, then it cannot forward the report to the Principal. ²⁸ Regardless of the Agency’s decision, the Outsider learns q with probability π _O , as in the earlier analysis. This assumption removes any strategic effects of the Agency’s decision on the likelihood that the Outsider will forward the information to the Principal.

Let q*(τ,b_P, σ, π _O ,x_A) denote the minimal quality level of the set of reports that the Agency would forward to the Principal. Recalling Equation (4) and substituting our assumption that x_P = x_O = 0, this threshold is given by

q * ( τ , b P , σ , π O , x A ) ≡ max [ τ min [ b P , σ b P ] , 1 − π O τ ( 1 − π O ) x A ] ,

(10)

which, whenever the context is clear, we will denote simply by q*.

Aggressive Outsider: σ ≥ 1. If the Outsider is at least as aggressive as the Principal in pursuit of policy change, then the reporting threshold presented in Equation (10) can be rewritten as

q * ≡ max [ τ b P , 1 − π O τ ( 1 − π O ) x A ] .

Applying sequential rationality on the part of the Agency implies that the Agency’s expected payoff from discovering the report’s quality is

v ¯ A 1 = − [ ∫ 1 τ / b P x A d F + ∫ τ / b P q * ( π O τ q + ( 1 − π O ) x A ) d F + ∫ q * ∞ 1 q d F ] − k ,

and the Agency’s expected payoff from not discovering the report’s quality is

v ¯ A 0 = − [ ∫ 1 τ / b P x A d F + ∫ τ / b P ∞ ( π O τ q + ( 1 − π O ) x A ) d F ] .

Thus, the Agency’s net expected payoff from processing the report and discovering q_r can be written as

Δ A ( τ , b P , σ , π O , x A , k ) ≡ ∫ q * ∞ ( π O τ − 1 q + ( 1 − π O ) x A ) d F − k .

(11)

Conservative Outsider: σ < 1. If the Outsider is no more aggressive than the Principal in pursuit of policy change, then the reporting threshold presented in Equation (10) can be rewritten as

q * ≡ max [ τ σ b P , 1 − π O τ ( 1 − π O ) x A ] .

Note, however, that duplicating the derivations for the case of an aggressive Outsider results in the following expression of the Agency’s net expected payoff from processing the report and discovering q_r:

Δ A ( τ , b P , σ , π O , x A , k ) ≡ ∫ q * ∞ ( π O τ − 1 q + ( 1 − π O ) x A ) d F − k ,

which is identical to Equation (11). All differences between the Agency’s optimal behavior when the Outsider is aggressive and that when the Outsider is conservative are conveyed through the differences between q* in the two cases (i.e. the differences due to the change in which constraint binds: τ/b_P or τ/(σb_P)) and, accordingly, we can omit the distinction between the two cases in the analysis that follows.

To be clear, note that if Δ _A is positive, the Agency’s optimal response is to incur the cost k to discover q_r while, if Δ _A is negative, the Agency’s optimal choice is to decline to process the report. Note that while the comparative statics of Δ _A depend crucially and unsurprisingly on those of q*, there are now direct effects of π _O and x_A as well in the sense that these parameters affect the Agency’s decision to acquire information even if they have no effect on the frequency with which the Agency would forward an already-processed report to the Principal. Let k*(τ,b_P, σ, π _O ,x_A) be defined as the opportunity cost that leaves the Agency indifferent with respect to whether it processes the report or not:

k * ≡ ∫ q * ∞ ( π O τ − 1 q + ( 1 − π O ) x A ) d F .

We can now directly describe the effect of various parameters on the Agency’s willingness to gather and process information for potential forwarding to the Principal. That is the subject of the following proposition.

Proposition 6. Suppose that π _O  < 1. Then, the maximum cost the Agency should incur to discover the quality of the report, k*, is

non-increasing in the minimal report quality the Agency would forward to the Principal (q*);

increasing in the Agency’s dissatisfaction with the status quo (x_A);

may be increasing or decreasing in the probability that the Outsider observes the report (π_O).

Proof. The first conclusion requires a straightforward application of Leibniz’s rule:

∂ k * ∂ q * = ∂ ∂ q * ∫ q * ∞ ( π O τ − 1 q + ( 1 − π O ) x A ) d F , = − ( π O τ − 1 q * + ( 1 − π O ) x A ) f ( q * ) , = { 0 if τ min [ b P , σ b P ] < 1 − π O τ ( 1 − π O ) x A ( min [ b P , σ b P ] 1 − π O τ τ − ( 1 − π O ) x A ) f ( q * ) ≤ 0 if τ min [ b P , σ b P ] ≥ 1 − π O τ ( 1 − π O ) x A

(12)

where inequality (12) is implied by the following derivation:

1 − π O τ ( 1 − π O ) x A ≤ τ min [ b P , σ b P ] , ( min [ b P , σ b P ] 1 − π O τ τ − ( 1 − π O ) x A ) ≤ 0 , ( min [ b P , σ b P ] 1 − π O τ τ − ( 1 − π O ) x A ) f ( q * ) ≤ 0 .

The second conclusion follows from a more involved application of Leibniz’s rule:

∂ k * ∂ x A = ∂ ∂ x A ∫ q * ∞ ( π O τ − 1 q + ( 1 − π O ) x A ) d F , = ∫ q * ∞ ∂ ∂ x A ( π O τ − 1 q + ( 1 − π O ) x A ) d F − ∂ q * ∂ x A · ( π O τ − 1 q * + ( 1 − π O ) x A ) f ( q * ) , = ( 1 − π O ) ( 1 − F ( q * ) ) > 0 .

(13)

The third conclusion follows from a similar application of Leibniz’s rule: letting

G F ( q * ) ≡ ∫ q * ∞ q − 1 d F ,

partial differentiation of k* with respect to π _O yields the following:

∂ k * ∂ π O = ∂ ∂ π O ∫ q * ∞ ( π O τ − 1 q + ( 1 − π O ) x A ) d F , = ∫ q * ∞ ( τ q − x A ) d F − ∂ q * ∂ π O · ( π O τ − 1 q * + ( 1 − π O ) x A ) f ( q * ) , = τ G F ( q * ) − x A ( 1 − F ( q * ) ) .

(14)

To establish the relevant conclusion of the proposition, note that G_F(q*) ∈ (0, 1/q*) and G F ′ ≤ 0 , but more importantly, note that q* is independent of F, since q* is based on an interim calculation after q is realized. Thus, for any ε > 0 and q* > 1, there exists a CDF F⁺ satisfying our assumptions such that min[F⁺(q*), G_F⁺(q*)] > 1 − ε and there exists a CDF F⁻ satisfying our assumptions such that max[F⁻(q*),G_F⁻(q*)] < ε. These facts imply that, fixing x_A ∈ (0, 1) and τ > 1, one can find a CDF F⁺ such that the right-hand side of Equation (14) is positive, and a CDF F⁻ such that the right-hand side of Equation (14) is negative, as was to be shown.

Proposition 6 can be interpreted in the following way. The first conclusion, that the Agency is less willing to pay for reports when those forwarded by the Agency have higher expected quality is interesting and somewhat counterintuitive. Accordingly, it is illustrative to understand its basis. As the proof of the proposition lays out, the Agency’s willingness to pay for information is invariant to q* when q* is determined ‘by the Agency,’ which is the case when τ min [ b P , σ b P ] < 1 − π O τ ( 1 − π O ) x A .

The second conclusion is unsurprising: as the Agency’s disutility from the status quo policy increases, both the net payoff from forwarding any given report to the Principal, and the probability of observing a report of sufficiently high quality to warrant forwarding, increase as well. The complementary effects directly translate into an increased willingness on the Agency’s part to pay to acquire information in the hopes of generating an actionable report.

Finally, the third conclusion is closer in spirit to an existence result than it is to a positive characterization: the effect of increased involvement by the Outsider (higher values of π _O ) on the Agency’s willingness to acquire information is ambiguous from an ex ante perspective. This ambiguity follows from the range of possible distributions of q. If few reports are of very high quality (i.e. a higher proportion of the mass of F is just less than x A − 1 ), then increasing the probability that the Outsider gets the report will increase the Agency’s incentive to screen the report as well. If, on the other hand, many reports were of very high quality (i.e. greater than x A − 1 ), then the Outsider’s involvement is, with a very high probability, a substitute for that of the Agency from the Agency’s perspective. Accordingly, in such a case increasing the probability that the Outsider gets the report will decrease the Agency’s incentive to invest in information acquisition.

3.2. Agency sabotage

In the previous extension we considered an institutional environment in which the stovepipe’s access to the information was beyond the Agency’s control. A closely related institutional possibility would allow the Agency to preclude both itself and the Outsider from the report. For instance, the Agency might choose to ‘sabotage’ the report by destroying the evidence before it can be processed. Specifically, we suppose now that before the game laid out in Section 1 is played, the Agency has a chance to permanently destroy the report (which is equivalent to imposing c_A = c_O = 0 in the formulation of Section 1). If the Agency chooses not to sabotage, then the game proceeds as in Section 1 whereas, if the Agency does sabotage, then neither the Agency nor the Outsider observes the report. We maintain our other assumptions about players’ information and payoffs, so that the choice by the Agency to sabotage and destroy the report implies that the status quo policy will be retained, resulting in a payoff of −x_A for the Agency.

Aggressive Outsider: σ ≥ 1. If the Outsider is at least as aggressive as the Principal in pursuit of policy change, then we can utilize sequential rationality and the arguments Section 3.1 to write the Agency’s expected payoff from not sabotaging the report’s quality as

v ¯ A 1 = − [ ∫ 1 τ / b P x A d F + ∫ τ / b P q * ( π O τ q + ( 1 − π O ) x A ) d F + ∫ q * ∞ 1 q d F ] ,

and the Agency’s expected payoff from sabotaging the report as

v ¯ A 0 = − x A .

Continuing with the logic of Section 3.1, we can define the net payoff from sabotage as

Σ = v ¯ A 0 − v ¯ A 1 = π O ∫ τ / b P q * ( τ q − x A ) d F + ∫ q * ∞ ( 1 q − x A ) d F

The first result is perhaps the most informative about the nature of the Agency’s strategic calculation: the Agency will sabotage only if it is the most conservative player (i.e. q* > τ/b_P). This is because, in essence, the Agency need fear the Outsider’s involvement only when there are reports such that the Outsider would forward them to the Principal, the Principal would act upon them with only the Outsider in the room, and the Agency would not forward them to the Principal in the Outsider’s absence.

Proposition 7. The Agency will sabotage the information collection process only if it is more conservative than both the Principal and the Outsider. That is, sabotage is the optimal choice for the Agency only if q* ≥ max[τ/min[b_P, σb_P]].

Proposition 7 additionally provides a useful baseline in terms of deriving the comparative statics of the benefit from sabotage. ²⁹ In particular, noting that

∂ q * ∂ π O = { 1 − τ ( 1 − π O ) 2 x A < 0 if τ min [ b P , σ b P ] < 1 − π O τ ( 1 − π O ) x A , 0 if τ min [ b P , σ b P ] ≥ 1 − π O τ ( 1 − π O ) x A ,

direct and repeated applications of Leibniz’s rule yield the following:

∂ Σ ∂ π O = { ∫ τ / b P q * ( τ q − x A ) d F + 1 − τ ( 1 − π O ) 2 x A π O f ( q * ) ( τ − 1 q * ) if τ min [ b P , σ b P ] < 1 − π O τ ( 1 − π O ) x A , ∫ τ / b P q * ( τ q − x A ) d F > 0 if τ min [ b P , σ b P ] ≥ 1 − π O τ ( 1 − π O ) x A , ∂ Σ ∂ τ = { π O ( ∫ τ / b P q * q − 1 d F + ( x A − b P ) f ( τ / b P ) ) if τ / b P < q * , π O ( x A − b P ) f ( τ / b P ) < 0 if τ / b P ≥ q * , ∂ Σ ∂ b P = π O τ b P 2 ( b P − x A ) f ( τ / b P ) > 0 , ∂ Σ ∂ x A = − π O ( 1 − F ( τ / b P ) ) < 0 .

These derivations are the basis of the following proposition.

Proposition 8. If q* > max[τ/min[b_P, σb_P]], the Agency’s incentive to sabotage the information collection process:

is increasing with respect to the Principal’s desire to promulgate a new policy (b_P);

is decreasing with respect to the Agent’s dissatisfaction with the status quo policy (x_A);

is for some parameter values increasing, and for others decreasing, with respect to the probability that the Outsider will observe an unsabotaged report (π_O); and

is for some parameter values increasing, and for others decreasing, with respect to the Outsider’s competence (τ).

The first and second conclusions of Proposition 8 are intuitive: each simply says that the Agency’s desire to destroy information (and ensure that Principal is not allowed to make new policy by choosing a_P = 1) declines as the Agency and Principal’s preferences become more similar. Accordingly, the third and fourth conclusions are the most interesting. Each of these illustrates an ambiguity that is particularly relevant if one considers the implicit institutional design problem for the Principal as described earlier (see ‘Implications for institutional design’ in Section 2). In a nutshell, both the third and fourth conclusion indicate that, if information collection is endogenous, a policy-seeking Principal should consider the details of the informational environment (i.e. the distribution of qualities, F) and the players’ preferences (i.e. b_P, x_P, and x_A) when considering both how aggressively the Principal wants the Outsider to be (this is analogous to π _O ) and how competent the Outsider should be with respect to policy implementation (i.e. τ).

Taken together, the results on endogenous information show that the welfare effects of stovepiping for the Principal are more subtle than they first appear. The results of Section 2 demonstrate that the ‘first-order’ effects of stovepiping is to increase P’s information, both directly through the stovepipe’s reporting and indirectly through the altered incentives of the agent to transmit its information. But stovepiping also has ‘second-order’ effects when information in the Agency is endogenous. Stovepiping can in some cases (depending on the effectiveness of the stovepipe when the Agency remains ignorant) decrease the Agency’s incentive to incur costs to obtain information, and stovepiping can increase the Agency’s incentive to sabotage available information to ensure that no policy change can be made. These ‘second-order’ effects work against the ‘first-order’ effects of stovepiping by decreasing the aggregate information available in the policy-making process, to the detriment of the Principal.

4. Conclusion

When bureaucrats have the first cut at decision-relevant information and can censor it, they exercise agenda-setting power with respect to hierarchical principals. Principals, for their part, can employ several alternative channels to obtain the requisite information despite this agenda setting. Stovepipes and other outside providers of information provide such a channel. While these alternative information sources may be less ‘conservative’ (status quo inclined) than line bureaucrats, they typically do not have the substantive expertise or organizational resources that line bureaucrats have to formulate or implement a decision. Thus, while stovepipes may be more willing than line agents to provide information to a decision-making principal, their information may not be as high in quality as the line agents’.

The model in this article captures this dynamic, and its effect on the information available to principals in policy making. The model reveals two effects whereby stovepipes can lead to greater provision of information to a decision maker. First, the stovepipe provides information to the principal in situations where the line agent does not, because the line agent considers the information too weak to be actionable. Second, the stovepipe induces the line agent to report information to the principal in situations where the line agent would not report if there were no stovepipe. This is precisely because the stovepipe’s information is of lower quality than the line agent’s, and given that policy will be changed in such instances, the line agent would rather its higher-quality information be used as the basis for it. The line agent would rather not change policy at all in these cases, but with a more aggressive (inclined to change the status quo) stovepipe and principal, this is not an option. Thus, the model reveals that in these senses, stovepipes and kitchen cabinets increase the information available to the principal to make a decision, and therefore the principal’s utility.

At the same time, these effects assume that the information available to both the line agent and the outsider is given. When this information is endogenous, the effects of stovepipes and kitchen cabinets on the principal’s utility are more subtle. First, if the stovepipe’s information, although of lower quality than the line agent’s, is reasonably good, the line agent may have less incentive to incur any costs to process the information the principal needs. In such cases, the stovepipe creates a redundant channel of information, and the line agent has an incentive to free ride on its provision of information to the principal. Ironically, to avoid such perverse incentives on the agent, the principal prefers a relatively incompetent stovepipe or kitchen cabinet. Second, the line agent may have an opportunity to ‘sabotage’ the decision-relevant information, or destroy it before either the agent itself or the stovepipe can act on it. The agent has an incentive to sabotage the information when it is sufficiently conservative. In such cases the principal is better off with no stovepipe at all; in that case, the agent passes at least some information to the principal, rather than censoring it entirely.