The Policy Choice

At the last stage of the lobbying game, the policymaker has a posterior λ ^P and chooses whether to keep the status quo or to implement a reform. Reform is costly and, therefore, is only chosen when its expected payoff exceeds that of the status quo. We define the policymaker’s reform implementation threshold λ* as the probability the policymaker attaches to the state being “reform” such that they are indifferent between reform and status quo. Hence, they choose reform if

(3.1)$${\lambda ^P} \ge {1 \over 2} + {c \over {2\alpha }} \equiv \,{\lambda ^*}.$$

We see that the higher the policymaker’s reform implementation threshold the more costly is the reform or the lower is the policy salience.

The Policymaker’s Information Choice

The policymaker knows that they will implement reform in the final round if (3.1) is satisfied and also the expected payoffs they will experience based on this choice. Their information choice then depends on its cost and the potential impact of that information on their beliefs. This in turn depends on the likelihoods and accuracy of the signals they may receive and their beliefs at this stage. These beliefs depend on the initial prior updated using Bayes’ rule according to any informational signals that have been generated by the lobby.

The policymaker’s options are to (i) never gather information and never reform, (ii) never gather information but always reform, or (iii) gather information and decide based on the signal. Consider first the case when the policymaker would neither gather information nor reform. In this case, the policymaker is termed negatively convinced, and his/her prior is such that they view reform as undesirable and the policy issue not worth further costly investigation. In the second case, the policymaker is termed positively convinced because their prior is such that they will always reform and view further information as unnecessary. The third case describes the range of beliefs for which the policymaker is not convinced and would be willing to gather costly information. This range is further divided into subintervals dependent on the policy choice the policymaker would make based only on their prior. If they would choose reform in the absence of new information, then we term them optimistic; on the other hand, if they would choose status quo in the absence of new information, we term them pessimistic. Let $\underline \lambda$ and $\bar{\lambda }$ denote the upper and lower thresholds of the range of priors for which the policymaker investigates. Formally, we have

(3.2)$$\underline \lambda = {{\left( {1 - \mu } \right)\left( {\alpha + c} \right) + e} \over {\alpha + c\left( {1 - 2\mu } \right)}}\;{\rm{and}}\;\overline \lambda = {{\mu \left( {\alpha + c} \right) - e} \over {\alpha + c\left( {2\mu - 1} \right)}}.$$

The lower threshold $\underline \lambda$ is defined as the belief for which the policymaker is indifferent between cases (iii) and (i). Similarly, the upper threshold $\bar{\lambda }$ is defined as the belief for which the policymaker is indifferent between the cases (iii) and (ii). We illustrate the four ranges with their respective thresholds and the policymaker’s policy criterion in Figure 3.

FIGURE 3.

Policymaker’s Beliefs and Information Choice

For the analysis to be of interest requires the following.

Lemma 1. The policymaker gathers information if $\underline \lambda \lt \min \left\{ {\bar{\lambda },1} \right\}$, which is equivalent to (α ² − c ²)(2μ − 1) − 2αe > 0.

That this interval exists requires that; the information signals, μ, are sufficiently accurate, policy salience compared with the reform cost is sufficiently high, α > c, and that the cost of information, e, is sufficiently low. The comparative statics of changes in the model’s parameters on the threshold values for gathering information can be summarized as follows:

(3.3)$$\underline \lambda = \lambda \left( {\mathop \alpha \limits_{\left( - \right)} ,\mathop c\limits_{\left( + \right)} ,\mathop e\limits_{\left( + \right)} ,\mathop \mu \limits_{\left( - \right)} } \right)\;{\rm{and}}\;\bar{\lambda } = \lambda \left( {\mathop \alpha \limits_{\left( {{ + / - }} \right)} ,\mathop c\limits_{\left( + \right)} ,\mathop e\limits_{\left( - \right)} ,\mathop \mu \limits_{\left( + \right)} } \right).$$

Further, if we define $\Lambda \,\equiv \,\bar{\lambda } - \underline \lambda$, then we may obtain

(3.4)$$\Lambda = \Lambda \left( {\mathop \alpha \limits_{\left( + \right)} ,\mathop c\limits_{\left( - \right)} ,\mathop e\limits_{\left( - \right)} ,\mathop \mu \limits_{\left( + \right)} } \right).$$

The signs under the variables indicate the direction of the comparative statics.^{Footnote 24} A greater salience makes a policymaker who is indifferent between choosing the status quo and gathering information more likely to gather information as getting the policy right becomes more important to him/her. More interesting is that a policymaker—just indifferent between gathering information and choosing reform immediately—responds ambiguously to a change in the policy salience. A greater salience implies that a policymaker gains more from the right policy, which would increase the threshold, $\bar{\lambda }$ but also raises the payoff of reform relative to the status quo, making the choice more attractive, hence tending to reduce the threshold. However, we can state clearly that an increase in policy salience increases the range of beliefs for which the policymaker gathers information.

The effect of an increase in the reform cost is to shift the range of beliefs for gathering information to the right and to decrease this range, making the policymaker both more conservative and less informed in his/her policy choice. This is because the expected net benefit from reform is lower but the expected benefit from the status quo remains the same, so the belief for which the policymaker is indifferent between the status quo and gathering information that can lead to reform must be higher; similarly, the belief for which he/she is indifferent between gathering information and reform must also be higher such that the whole range of beliefs for gathering information shifts, although it also shrinks because of greater policy costs. If the information cost increases, then the policymaker gathers information for a narrower range of initial beliefs. This is simply because the net expected benefits of gathering information decline for all beliefs.

An increase in signal accuracy, μ, causes the policymaker to engage in information gathering for a wider range of priors. This follows because an increase in signal accuracy increases the expected value of a signal at all priors.

Because we know that the policymaker will not choose reform for $\lambda > \underline \lambda$, always chooses reform for $\lambda > \bar{\lambda }$, and will choose according to the signal he/she receives for $\underline \lambda \,\le \,\lambda \,\le \,\bar{\lambda }$, we can illustrate the probability of reform as in Figure 4.

FIGURE 4.

Policymaker’s Thresholds and Probability of Reform

Given that the lobby understands how information affects the likelihood of reform, and given the initial priors, we may now examine how the lobby makes its information gathering decision.

The Lobby’s Information Choice

We now turn to the lobby’s decision whether or not to engage in costly informational lobbying. The lobby correctly anticipates the policymaker’s strategies and considers the following questions: Can they induce the policymaker to change their information gathering and policy choices, and do they want to given the cost?^{Footnote 25} Recall that the lobby’s expected payoffs are increasing in the probability that the policymaker will implement a reform. There are two basic ways the lobby might accomplish this: First, it might gather costly information which, if it is a reform signal, induces the policymaker to update their prior to a value above the threshold $\bar{\lambda }$, guaranteeing that the policymaker will not gather any additional information and will implement reform with probability one (persuasion motive). Second, the lobby might gather information which, if it is a reform signal, raises the policymaker’s prior above $\underline \lambda$ but below $\bar{\lambda }$ which induces the policymaker to gather more information which, if it is also a reform signal, will induce them to implement the reform policy (salience motive). Hereafter, we only consider the interesting cases, where the lobby’s choices can change the probability of reform, these are illustrated in Figure 5.

FIGURE 5.

Lobby’s Information Choices

For the case denoted C1, the policymakers’ prior is sufficiently low such that unless they receive information from the lobby, they will not gather information and will keep the status quo. If the lobby receives a status quo signal, then clearly the policymaker keeps the status quo. If, however, the lobby receives a reform signal, then the policymaker updates and their prior moves into the range over which they will gather information themselves, as indicated by the arrow on the diagram pointing rightwards from C1, their policy is then determined by this second signal.

Cases C2–C4 can be interpreted similarly. In case C2, a reform signal gathered by the lobby is sufficient to make the policymaker “positively convinced” and triggers a reform. In case C3, a status quo signal generated by the lobby will not prevent the policymaker gathering information and basing their policy that signal, but a reform signal has the same effect as in case C2, immediate reform. Information gathering by the lobby is a form of insurance in this case because a single reform signal drawn by either the lobby or policymaker leads to a reform policy, but two status quo signals are required for the status quo policy to be chosen (insurance motive). Finally, in case C4, if the lobby decides to gather information the signal, either status quo or reform, causes the policymaker to choose not to gather information, and is alone sufficient to determine the policymaker’s policy (substitution motive). However, should the lobby decline to gather information, the policymaker does so with the same expected outcome. It follows that the lobby will leave the cost of information to the policymaker, and there will be no lobbying in equilibrium. Notice that the lobby will never choose to gather information when neither signal will shift the policymaker’s priors out of the unconvinced region as this signal would be redundant with the policy determined by the subsequent policymaker’s signal.

Proposition 1. For the homogeneous case, the lobby may engage in informational lobbying only when the policymaker is initially negatively convinced or optimistic, that is, if,

1. (i) C1; $\lambda \,\le \,\underline \lambda \,\le \,\lambda \left( {{x^r}} \right) \,\le \,\bar{\lambda }$ and (1 − μ)² + λ(2μ − 1) ≥ e,

2. (ii) C2; $\lambda \,\le \,\underline \lambda \,\le \,\bar{\lambda } \,\le \,\lambda \left( {{x^r}} \right)$ and 1 − μ + λ(2μ − 1) ≥ e, or

3. (iii) C3; $\underline \lambda \,\lt \,\lambda \left( {{x^s}} \right) \lt \,{\lambda ^*} \lt \,\lambda \lt \,\bar{\lambda } \lt \,\lambda \left( {{x^r}} \right)$ and μ − μ ² ≥ e.

The second part of each of the statements (i)–(iii) in Proposition 1 simply tells us when the expected benefits from informational lobbying exceed the costs. Cases C1 and C2 are where there is a pure persuasion motive for informational lobbying, whereas C3 involves an insurance motive. We may now turn our attention to the further possibilities introduced when resource constraints bind.

Policy Choice and Implementation Subsidy

To understand the implications of a binding policymaker resource constraint, it is necessary to consider the policy choice and the resource transfer that flows to them from the lobby. Policymakers wish to choose reform if their belief at the last stage is above the policy implementation threshold as described in (3.1). The lobby correctly anticipates the policymakers’ preferred policy, and, in the case where they prefer reform, knows whether or not the policymaker has the required resources. The lobby thus knows the transfer that would be just sufficient to allow the policymaker to implement reform, hence this involves

(4.1)$${\tau ^*} = \left\{ \openup+4pt{\matrix{ {e + c - {y^P}} \hfill & {{\rm{iff}}\;z = {z^r}\;{\rm{and}}\;1 \,\ge \,e + c - {y^P}} \hfill \cr 0 \hfill & {{\rm{otherwise}}} \hfill \cr} .} \right.$$

If the policymaker has not spent resources on information gathering or does not want to reform, then the lobby has no incentive to relax the policymaker’s constraint and the transfer is zero. The lobby only contributes when the policymaker has gathered information—leaving them requiring a subsidy to implement a reform—and when the signal received indicates that the state is reform. Notice that a policy subsidy is then more likely the greater is the likelihood that the policymaker will receive a reform signal and the smaller is the transfer needed to subsidize a reform.

The Policymaker’s Information Choice

Given that a policymaker knows that they will receive a subsidy from the lobby if they receive a reform signal but cannot afford to implement reform, they are de facto unconstrained and face a similar problem to that analyzed before. However, there is one key difference, the policymaker now has a strategic incentive to gather information because this increases the expected implementation subsidy from the lobby. This impacts the policymaker’s updating choice.

Proposition 2. The resource constrained policymaker’s updating thresholds $\left( {\underline \lambda \prime ,\bar{\lambda }\prime } \right)$ lie outside those of an unconstrained policymaker $\left( {\underline \lambda ,\bar{\lambda }} \right)$—that is., $\,\,\underline {\lambda '} \,\lt \,\underline \lambda$ and $\bar{\lambda }\prime > \bar{\lambda }$, which implies Λ′ > Λ.

This is perhaps somewhat counter-intuitive, a resource-constrained policymaker engages in costly information gathering for a wider set of beliefs than an unconstrained one. The reason is that the constrained policymaker has a strategic incentive to spend on information so as to extract an expected subsidy from the lobby.^{Footnote 26} Unconstrained policymakers who gather information and implement reform face the full cost of policy implementation. However, if they are constrained, they can anticipate an implementation subsidy from the lobby in the same circumstances. Hence, the expected cost of reform is lower when the policymaker is constrained, and hence the incentive to gather information greater.^{Footnote 27}

Clearly, there is also an impact on the probability of reform. Figure 6 illustrates the likelihood that a resource-constrained policymaker will enact a reform and compares this to the unconstrained case.

FIGURE 6.

Policymaker’s Thresholds and Probability of Reform

The thresholds $\underline {\lambda '}$ and $\bar{\lambda }'$ are for a constrained policymaker, whereas the thresholds $\underline \lambda$ and $\bar{\lambda }$ are for the unconstrained policymaker as in Figure 4. The likelihood of reform is zero for priors ${\lambda ^L} \,\lt \,\,\underline {\lambda '}$, one for priors ${\lambda ^L} > \bar{\lambda }\prime$, and follows the probability of receiving a reform signal for all other beliefs. Hence, we see that the resource constraint makes reform more likely over the interval $\left[ {\underline {\lambda '} ,\underline \lambda } \right]$ and less likely over the interval $\left[ {\bar{\lambda },\bar{\lambda }\prime } \right]$. The intuition, here, is quite simple; the expected subsidy makes the policymaker more willing to expend resources on information as this will not reduce their ability to implement a reform. The range of initial priors for which they gather information, thus, increases.

We now consider the comparative static effects of changes in the models’ parameters on the range of beliefs for gathering information. We may write

(4.2)$$\underline \lambda \prime =\,\, \lambda \left( {\mathop \alpha \limits_{\left( - \right)} ,\mathop c\limits_{\left( 0 \right)} ,\mathop e\limits_{\left( \pm \right)} ,\mathop \mu \limits_{\left( - \right)} ,{{\mathop y\limits_{\left( + \right)} }^P}} \right)\;{\rm{and}}\;\bar{\lambda }\prime = \lambda \left( {\mathop \alpha \limits_{\left( \pm \right)} ,\mathop c\limits_{\left( + \right)} ,\mathop e\limits_{\left( - \right)} ,\mathop \mu \limits_{\left( + \right)} ,{{\mathop y\limits_{\left( - \right)} }^P}} \right).$$

The signs under the variables again indicate the comparative static effects.^{Footnote 28} For the upper bound, $\bar{\lambda }\prime$, these are the same as in the unconstrained case and follow from the same intuition. However, for the lower bound, $\underline {\lambda '}$, there are some differences reflecting the constrained policymaker’s extra strategic incentives. First, an increase in reform costs has no effect on the constrained policymaker’s lower bound. This is because an increase in the cost is matched dollar-for-dollar by an increase in the policy implementation subsidy. Second, an increase in the policymaker’s information cost unambiguously reduces the range of beliefs for which there is information gathering in the unconstrained case, but has an ambiguous effect on the range here. This reflects that an increase in the information cost is partially offset by the anticipated subsidy.

Next, we turn to the lobby’s information choice. In deciding whether or not to gather information, the lobby is aware of the consequences for the policymaker’s information gathering, the potential need for a policy implementation subsidy, and the subsequent likelihood of reform.

The Lobby’s Information Choice

As before, the lobby’s incentives to gather information come from the effect information has on the probability that the policymaker will implement a reform. Here, there is the additional complication that in equilibrium, this may also trigger the need for the lobby to pay a subsidy to the policymaker. As established previously, and illustrated in Figure 6, the existence of a possible subsidy increases the range of beliefs for which the policymaker gathers information. This feeds back and affects the lobby’s choices. Applying the same logic as in the unconstrained case, we may state the following:

Proposition 3. For the homogeneous case with a constrained policymaker, informational lobbying arises for the same cases as for the unconstrained policymaker, although the thresholds $\left( {\underline \lambda \prime ,\bar{\lambda }\prime } \right)$ differ. If

1. (i) $\lambda \,\le \,\underline \lambda \prime \,\le \,\lambda \left( {{x^r}} \right) \,\le \,\bar{\lambda }\prime$ and ${{\left( {{\mu ^2}\lambda + {{\left( {1 - \mu } \right)}^2}\left( {1 - \lambda } \right)} \right)\left( {1 - c + {y^P}} \right)} \over {\left( {{\mu ^2}\lambda + {{\left( {1 - \mu } \right)}^2}\left( {1 - \lambda } \right) + 1} \right)}} \,\ge \,e$, then informational lobbying occurs, and there are implementation subsidies if z = z ^r;

2. (ii) $\lambda \,\le \,\underline \lambda \prime \,\le \,\bar{\lambda }\prime \,\le \,\lambda \left( {{x^r}} \right)$ and 1 − μ − λ(1 − 2μ) ≥ e, then there is only informational lobbying;

3. (iii) λ(x ^s) ≤ $\underline {\lambda '}$ < λ < λ* ≤ λ(x ^r) and 1 − e − c + y ^P > 0; then there is no informational lobbying but there are implementation subsidies if z = z ^r;

4. (iv) $\lambda \left( {{x^s}} \right) \,\le \,\underline \lambda \prime \,\le \,\lambda \,\le \bar{\,\lambda }\prime \,\le \,\lambda \left( {{x^r}} \right)$ and 1 − e − c + y ^P > 0, then there is no informational lobbying, but there are implementation subsidies if z = z ^r;

5. (v) $\underline \lambda \prime \,\lt \,\lambda \left( {{x^s}} \right) \,\lt \,{\lambda ^*} \,\lt \,\lambda \,\le \,\bar{\lambda }\prime \,\le \,\lambda \left( {{x^r}} \right)$ and ${{2\left( {\lambda - 1} \right)\mu \left( {c - {y^P}} \right) + {\mu ^2}\left( {c - {y^P} - 1} \right) - \left( {{y^P} - c} \right)\left( {1 - \lambda } \right) + \mu } \over {\lambda - {\mu ^2} - 2\left( {\lambda - 1} \right)\mu }} \,\ge \,\,e$, then both informational lobbying, and implementation subsidies occur.

The three cases where informational lobbying occurs in Proposition 3 are essentially the same as the cases C1–C3 in Proposition 1 of the unconstrained case and follow for the same strategic considerations. The obvious difference, of course, is the presence of implementation subsidies in the constrained case. The need for implementation subsidies has two interesting effects: first, as already noted, the range of priors for which the policymaker would choose to gather information expands; second, the conditions under which the lobby would find lobbying economically worthwhile change. This second effect arises both because implementation subsidies are costly and because the change in the policymaker’s information-gathering behavior changes the circumstances under which these costs are incurred.

There are two cases where there are only policy implementation subsidies. Part (iii) of Proposition 3 follows by comparing the likelihood of reform with and without the lobby gathering information. If they gather information and receive the signal x ^s, then the status quo policy is immediately chosen. If they receive the signal x ^r, then the policymaker gathers information, and this determines the policy triggering an implementation subsidy if z = z ^r. Hence, both signals x ^r and z ^r are required to give a reform policy. If the lobby does not gather information the policymaker does, and there is reform if z ^r is received. The lobby then supplies an implementation subsidy. It follows that in this case, information gathering by the lobby is expensive and lowers the probability of reform. Hence, they only supply an implementation subsidy when required. In part (iv), a single signal determines the policy choice, as both a reform or status quo signals push beliefs into one of the “convinced” ranges. The lobby, thus, chooses between gathering information or supplying an implementation subsidy. In expected terms, the latter is cheaper. Hence part (iv).

Part (v) of the proposition is, perhaps, the most interesting because it is observationally equivalent to “damage control” as discussed by Bennedsen and Feldmann (Reference Bennedsen and Feldmann2006) and Dahm and Porteiro (Reference Dahm and Porteiro2008a, Reference Dahm and Porteiro2008b). Here too, the lobby makes a financial contribution to the policymaker after the arrival of unfavorable information, x ^s, but the role of the implementation subsidy is to relax the policymakers’ resource constraint such that they can afford to both gather information and enact a reform if they so choose. This second round of information gathering by the policymaker acts as insurance to the lobby against an initially negative signal because λ* < λ(x ^s, z ^r). Here, damage control is an implementation subsidy that effectively purchases the lobby who tries receiving a decisive reform signal.

Our results in this section yield some novel insights into implementation subsidies; first, there is no ex ante relationship between the policymaker’s prior and implementation subsidies; however, after information gathering, subsidies are offered to policymakers who shifted their policy choice to reform after receiving a reform signal, ex post the lobbyist’s friends.

A Comparison of Lobbying of a Constrained and Unconstrained Policymaker

A comparison between the constrained and unconstrained cases provides some insights into both which policymakers are lobbied and when lobbying occurs at all. We know from Propositions 1 and 3 that the lobby gathers information so as to influence either negatively convinced or optimistic policymakers. They supply information to policymakers with priors in the former group so as to get them to consider reform and to the latter group as they are relatively easy to persuade. The tightening of resource constraints changes the range of priors that define these two lobbied groups. As the policymaker’s resource constraint binds, the lobby stops supplying information to policymakers just below the margin between being negatively convinced and pessimistic. The range of negatively convinced policymakers being supplied by the lobby with information shrinks. However, the reverse is true for the optimistic group. As the policymaker’s resource constraint binds, the lobby starts supplying information to policymakers with priors just above the margin between being optimistic and positively convinced. Hence, this range expands.

Now, we consider the extensive margin where the lobby decides whether to lobby or not. Employing the cost benefit conditions from Propositions 1 and 3, we have the following:

Proposition 4. The lobby will engage in informational lobbying.

1. (i) In the case C1; of both unconstrained and constrained policymakers if e < [μ ²λ + (1 − μ)²(1 − λ)](1 + y ^P − c − e) < [μ ²λ + (1 − μ)²(1 − λ)], and of only the unconstrained policymakers if [μ ²λ + (1 − μ)²(1 − λ)](1 + y ^P − c − e) < e < μ ²λ + (1 − μ)²(1 − λ)];

2. (ii) In the case C2; of both unconstrained and constrained policymakers if 1 − c + y ^P > e;

3. (iii) In the case C3; of both unconstrained and constrained policymakers if e < μ(1 − μ) − μ(1 − μ)(e + c − y ^P) < μ(1 − μ), and of only the unconstrained one if μ(1 − μ) − μ(1 − μ)(e + c − y ^P) < e < μ(1 − μ).

In simple terms, proposition 4 tells us that the cost of policy implementation subsidies when policymakers are resource constrained reduces the information gathering cost at which the lobby is just indifferent between lobbying or not. Taken together, Propositions 1, 3, and 4 allow us to broadly conclude that as policymaker’s resource constraints bind, the lobby switches some of their persuasion activities from their ex ante enemies to their ex ante friends, but engages in informational lobbying for a narrower range of parameters.

Tightening the Policymaker’s Constraint Further

Now, suppose that we tighten the policymaker’s constraint further such that they can afford to gather information but cannot afford to implement policy.^{Footnote 29} Deriving the lower and upper information thresholds for this case, as we did for Proposition 2, and denoting the resulting bounds $\underline {\lambda ''}$ and $\!\!\!\bar{\lambda ''}$, we can state the following:

Lemma 2. If c > y ^P > e and y ^L > e + c, then $\underline {\lambda ''} = \underline {\lambda '}$ and $\underline {\lambda ''} = \bar{\lambda '}$, which implies Λ″ > Λ′.

The intuition behind this is very similar to the previous case except that a policymaker who gathers information may now anticipate full rather than partially support for their implementation costs. Hence, there is an incentive to gather information for a wider range of beliefs. The policymaker’s choices are, of course, anticipated by the lobby, which now provides reform subsidies for a wider range of initial priors and makes these subsidies larger. Clearly, then, the range of parameter values for which the lobby finds lobbying optimal decreases.

Tightening the Lobby’s Constraint

Finally, suppose the lobby’s resource constraint is binding such that the lobby can either afford to gather information or pay a policy subsidy but not both. Further, the combined resources of the lobby and policymaker are insufficient to pay for two information signals and implement a reform—that is, e + c > y ^L ≥ max{e ^L, c + e − y ^P} and 2e + c > y ^P + y ^L. Clearly, then, there will never be two rounds of information gathering. However, the policymaker’s updating thresholds are unaffected by the tightening of the lobby’s resource constraint and depend only on the policymaker’s constraint as before. The implications are that, given that two signals cannot be gathered in equilibrium, a lobby faced by a negatively convinced policymaker will only choose to gather information if signal accuracy is sufficient to shift the policymaker’s priors into the positively convinced range. Further, the lobby no longer has the option of gathering information as insurance against a status quo signal and, thus, does not lobby optimistic policymakers.

It is interesting to note, however, that the likelihood of lobbying a negatively convinced policymaker and of a reform outcome in this case actually increases. The reason is that a lobby can induce an immediate reform with a less precise information signal as the policymaker’s threshold for immediate reform is no longer the upper threshold when the policymaker can gather information $\left( {\bar{\lambda },\bar{\lambda }\prime ,\;\!{\rm{or}}\;\!\!\bar{\lambda ''}} \right)$, but rather the policymaker’s policy implementation threshold (λ*) which is lower. In other words, being resource constrained yields a lobby a strategic advantage in lobbying a constrained negatively convinced policymaker. If the lobby generates a reform signal, the policymaker will give them the “benefit of the doubt,” although they would prefer more information. We will discuss further strategic considerations arising from the lobby facing a binding resource constraint when we introduce heterogeneously accurate signals in the following paragraphs.

The Commitment Motive

In almost all equilibria with homogeneous signals and an unconvinced resource-constrained policymaker, information gathering is performed by the policymaker and the lobby supplies an implementation subsidy.^{Footnote 40} If signal accuracies are heterogeneous, there can also be a commitment motive that leads to information gathering by the lobby. The idea is that by depleting their own resources on information gathering, the lobby is unable to fund an implementation subsidy to the policymaker. The policymaker then has no incentive to engage in information gathering as they could not then afford to implement the policy. The commitment motive operates when the policymaker would choose reform, in the absence of further information, being optimistic, and the lobby’s signals are sufficiently uninformative. The strategic incentive to waste resources in this scenario is then different to the traditional notion of “burning money” in signaling and access models where a lobby is trying to enhance its credibility with costly signals (Potters and van Winden Reference Potters and van Winden1992; Austen-Smith and Banks Reference Austen-Smith and Banks2000, Reference Austen-Smith and Banks2002) or trying to get the policymaker’s attention with contributions (Austen-Smith Reference Austen-Smith1995, Reference Austen-Smith1998; Lohmann Reference Lohmann1995; Cotton Reference Cotton2009, Reference Cotton2012; Cotton and Dellis Reference Cotton and Dellis2016).

Who is Lobbied and When?

Consider first, the question of which policymakers get lobbied. Our results indicate that ex ante there is relatively little that can be said about which policymaker will get lobbied simply on the basis of their prior policy positions. Clearly, policymakers with priors sufficiently extreme such that no available information signal will change their policy choice are not subject to informational lobbying. However, extremist “friends”, our positively convinced policymakers, are given implementation subsidies if they require them. The reason why sweeping ex ante statements cannot be made is because the lobby’s decision of whether or not to lobby depends on the policymaker’s priors, the availability and location of resources in the lobbying process, and the relative accuracy and costs of information gathering. However, if we provide a more nuanced answer to this question, we are able to conclude that lobbies lobby policymakers that they expect to become or confirm as their friends ex post. Broadly, they engage in informational lobbying with policymakers whose probability of choosing reform is increased by being lobbied and supply implementation subsidies to those who would choose reform were their resource constraints loosened.

In an informational environment where the lobby and policymaker receive similar homogeneous signals, perhaps, from a given “expert” source (such as an expert body or think tank), we know that negatively convinced and optimistic policymakers will be subject to informational lobbying. If informational signals are sufficiently accurate such that the insurance motive is in operation, we predict a discontinuity in informational lobbying. There will be a range of intermediate unconvinced pessimistic policymaker priors for which the lobby will offer no information. However, only ex post friends, those that support reform, are given policy implementation subsidies.

In a heterogeneous informational and/or cost environment, one for example where the lobby and policymaker have their own separate information sources, there will tend to be more informational lobbying than in a homogeneous environment. In such an environment, both the commitment, substitution, and insurance motives for informational lobbying operate. Most noticeable are the insurance and substitution motives which induce the lobby to engage in informational lobbying of pessimistic policymakers.

De Figueiredo and Richter (Reference de Figueiredo and Richter2014) review empirical studies on lobbying activities and show that many conclude that lobbies mostly lobby policymakers who favor their preferred policy. However, they also note that there are empirical studies that show that lobbies approach opposing policymakers in an attempt to change their initial positions (Austen-Smith and Wright Reference Austen-Smith and Wright1994, Reference Austen-Smith and Wright1996; de Figueiredo and Cameron Reference de Figueiredo and Cameron2009), this is, generally consistent with our analysis of both informational lobbying and implementation subsidies. In our analysis, a lobby engages in informational lobbying with an opposing policymaker to gain their support or to induce them to gather further information. If the policymaker is also resource constrained and does not have sufficient resources for a policy change, then the lobby, if its resources are sufficient, would also provide an implementation subsidy and actually support the policymaker throughout the political process. This is also consistent with Mello, Abiola, and James (Reference Mello, Abiola and James2012)’s case study of Merck discussed in the Introduction.

Other empirical studies document that undecided, or moderate, policymakers are lobbied (Hojnacki and Kimball Reference Hojnacki and Kimball1999, Reference Hojnacki and Kimball2001; Mian, Sufi, and Trebbi Reference Mian, Sufi and Trebbi2010). In our analysis, a lobby approaches these policymakers when informational lobbying is relatively inexpensive and persuasive enough to determine their policy choice. Implementation subsidies, as a sole lobbying strategy, would be provided if a moderate policymaker has, from the lobby’s perspective, an accurate information technology but not sufficient resources to implement reform. Finally, there is also the evidence that lobbies support friendly policymakers (Kollman Reference Kollman1997; Hojnacki and Kimball Reference Hojnacki and Kimball1998; Eggers and Hainmueller Reference Eggers and Hainmueller2009; Mian, Sufi, and Trebbi Reference Mian, Sufi and Trebbi2013; Igan and Mishra Reference Igan and Mishra2014; Schnakenberg Reference Schnakenberg2017). In our analysis, friendly policymakers are lobbied via policy subsidies when they have insufficient resources to implement a policy, which is similar to Hall and Deardorff (Reference Hall and Deardorff2006).

Resource-Constrained Lobby: A Strategic Disadvantage?

Tullock (Reference Tullock1972) famously asked, “why is there so little money in politics?;” this is a question that has been frequently repeated both in the context of campaign contributions and lobbying expenditures.^{Footnote 41} In the context of our model of lobbying, the answer is that having limited resources can be a strategic advantage. Most obviously, an unconstrained policymaker never receives an implementation subsidy from a lobby but a constrained one does. From the perspective of a lobby, when faced with an optimistic policymaker, resources, either their own or the policymakers, are undesirable. In the absence of more information, a policymaker would choose reform, but resources buy more information. The only context where more resources in the lobbying process are desirable from the lobby’s perspective is when they allow the purchase of a second signal that acts as insurance and induces information gathering by an initially negatively convinced policymaker.

The answer to the question whether the lobby gains or loses a strategic advantage when it is resource constrained is, “it depends.” It depends specifically on the policymaker’s prior and the accuracy of information signals. When the policymaker is negatively convinced and the information technology is not very effective (Case C1), then a constrained lobby is worse off as a potential reform is no longer feasible with given resources. However, when the policymaker is negatively convinced and the information technology is at least intermediate (case C2), then the constrained lobby gains as the necessary threshold to induce a reform is λ* instead of $\bar{\lambda }\prime$. Furthermore, when the insurance motive is in play (case C3), then the resource-constrained lobby is worse off as a second information signal is no longer feasible; but when the substitution and commitment motives are in play (case C4 and case C4′), then the resource-constrained lobby again gains from the lower threshold to induce reform of λ* instead of $\bar{\lambda }\prime$.

Relationships between Information and Implementation Subsidies

We have identified persuasion, commitment, insurance, and substitution motives for informational lobbying. Whereas an implementation subsidy is made whenever the policymaker has the ex post will but not resources to enact reform. These different motives arise with different combinations of resource constraints, signal accuracies, and signal costs, implying different predicted relationships between the lobby’s lobbying instruments and policymaker’s information gathering. These can be thought of as substitutes, complements, or independent in the sense that the choice of information gathering by the lobby influences information gathering by the policymaker and both influence implementation subsidies.

We can state that information gathering by the lobby and policymaker are complements whenever the insurance or persuasion motives are in operation; they are substitutes whenever the commitment or substitution motives are in operation; and they are independent otherwise.^{Footnote 42} The details may be found in Table 1. Cases C1–C4 are exactly as introduced in Figure 5; case C4′ is the situation where the commitment motive is in operation.^{Footnote 43}

TABLE 1.

Relationships Between Policymaker’s and Lobby’s Information Gathering

Compl, complements; Subs, substitutes; Ind, independent; ⁺, persuasion motive; * insurance motive.

** Substitution motive; *** commitment motive; n/a, not applicable; λ ∈ {λ, λ′} as defined for each case.

In a similar vein, the details of the circumstances when the lobby supplies an implementation subsidy may be found in Table 2. Table 2 allows us to describe when a policymaker is lobbied and how. First, consider when a lobby uses both lobbying instruments. These are represented by the gray-shaded cells in the table with checkmarks (✓) within them. This occurs in two circumstances, in both of which the lobby is resource-rich and the policymaker constrained. In the case C1, the lobby faces an initially negatively convinced policymaker and gathers information to try to persuade them to consider reform. If they receive a reform signal, this induces the policymaker to gather information; and if they two receive a reform signal, enact a reform policy financed by an implementation subsidy; in the case C3, the lobby faces an unconvinced policymaker and gathers information because of the insurance motive; if they receive a status quo signal, then the policymaker gathers information; and if this signal is reform, enacts a reform policy financed by an implementation subsidy. Next, consider when the lobby employs only informational lobbying; these are represented by the green-shaded cells in the table. We can see that for ten of the seventeen subcases analyzed, there is only informational lobbying. Whenever the lobby gathers information that gives a signal leading to the policymaker being either positively or negatively convinced; loosely when the lobby’s signal is very persuasive, then no implementation subsidy is required. Alternatively, if the lobby’s signal leaves the policymaker unconvinced but they themselves generate a status quo signal, then there will be no implementation subsidy and there will be no reform policy. The only other case is C4′ where a lobby deliberately gathers poor quality information as a commitment device so as to not supply an implementation subsidy. Here, an optimistic policymaker adopts a reform policy essentially on the basis of his/her original prior.

TABLE 2.

Relationships Between Information Gathering and Implementation Subsidies

Legend: n/a, not applicable; * when λ(x ^r) > λ; * λ ∈ {λ, λ′} as defined appropriately for each case.

There are several cases where a lobby only provides an implementation subsidy. These are represented by the orange-shaded cells in the table with checkmarks (✓) within them. These are cases where policymakers are initially unconvinced and will gather information themselves if the lobby does not provide any. If either policymakers are more likely than the lobby to generate a reform signal and/or the cost of their information gathering is lower, then the lobby will prefer to supply an implementation subsidy rather than information to a constrained policymaker.