We assume that the voter cannot separate the effect of the external shock from the effect of the policy choice. When 𝑢 < 𝜖 < 𝑢¯ (Region 5𝐴in Figure 2.5), voters always re-elected the incumbent party if the state was matched, regardless of the policy choice (1+ 𝜖 > 𝑢𝐵 > 𝑢¯). The voter can infer the behavior of the low-ranking incumbent from perceived utility and policy choice.
In general, despite some similarities in the voter's and the politician's motives (matching the state), the equilibrium expected welfare of the voter decreases when the incumbent government can anticipate an external shock. In the baseline model, the voter evaluates the candidate's competence by observing which policy he or she chooses. If the voter is willing to pay attention to 𝐵given truthfulness (𝑐 < 𝜙𝐵(0)), then in equilibrium the incumbent president is truthful and the voter pays full attention to 𝐵(𝜌𝐵 =1).
If the voter does not want to pay attention to given veracity (𝑐 > 𝜙𝐵(0)), then the incumbent panders are balanced (𝜎∗. If the voter is willing to pay attention to 𝐴 given veracity (𝑐 < 𝜙𝐴(0)) , then the incumbent in equilibrium is fair and the voter pays full attention after 𝐴(𝜌𝐴 =1).
Introduction
We need to show the same for the low-type incumbent with the unpopular signal𝑠= 𝐵. We have already shown that this re-election probability makes the low-type incumbent true in Region 3𝐵. In Region 4𝐵, the voter never re-elects the incumbent regardless of the policy choice to a mismatched state.
We now prove why low-type IC is mandatory for optimal effort levels.
External Shocks and Anticipatory Pandering
Introduction
We make a wealth comparison between the equilibria of the base model and the main model, to show the effect that the politician's anticipation of the external shock has on the voter's wealth. In certain realizations of the external shock, the politician's anticipation of external shocks benefits the voter by eliminating it.
The Model
The voter can see her own utility 𝑢𝑣, but does not know the realization of the external shock 𝜖. In this paper we look at forms of external shocks that are completely beyond the control of the incumbent politician.
Baseline Model: Incumbent does Not Observe 𝜖
We have already established three facts about the current president's equilibrium strategy: (1) the incumbent in the second period always follows his signal; (2) a high-type politician always follows his signal even in the first third; (3) the low-type politician always follows the popular signal 𝑠 = 𝐴 in the first third. 𝐵. The analysis shows that ˜𝜎the level of competence of the lower type employee 𝑞 is strictly decreasing.
The Main Model: Anticipated External Shocks
This is a perfect signal that the incumbent is a low type (only the low-type incumbent mismatches the state, since the high-type politician knows the correct state for sure and always follows his private signal). For these observed utility levels, the voter mixes between voting for the incumbent and the challenger after observing the popular policy choice 𝑦 = 𝐴.
Welfare Analysis
Irrelevantly, for 𝑞 > 𝑞˜ the basic model has a true equilibrium, so the voter's welfare is the same in both models. For other values of 𝜖, the politician's knowledge of the upcoming shock lowers the expected equilibrium level of voter welfare.
Conclusion
To this model, we add an ability for the voter to learn about the consequences of the incumbent's policies by paying costly attention after they are implemented. The first key insight from our analysis is that the disposition of voter attention is not neutral. When the cost of attention is low enough, the voter will pay attention regardless of which policy the incumbent chooses.
Let ¯ In the absence of any ex-ante difference between the two policies, the voter's treatment of the incumbent in equilibrium cannot depend on his policy choice. Similarly, if the voter paid attention only to the unpopular policy 𝐵 (and still conserved immediately after 𝐴) the incumbent would only have an incentive to praise when.
Voter Attention and Electoral Accountability
- Introduction
- Related Literature
- The Model
- Preliminary Analysis
- Preliminary Results
- Equilibrium Characterization
- Voter Welfare
- Conclusion
𝑅 is not constant, strictly increasing in 𝑐 and the overall expected utility difference is trivially strictly decreasing in 𝑐 due to the last term. Unlike the low type case, which is treated as high, the benefit of high type is treated as low 𝐵𝐿. The restriction of the IC agent with a high level is binding, and the restriction of the IC agent with a low level is loose.
𝐿(𝑒1) is decreasing in 𝑒1 and will not violate IC high because the incentive compatibility constraint of agent high is loose.
Formal Requirements on Costly Information
Introduction
The preferences of the agent observing the high private signal coincide with those of the principal. This mechanism encourages the agent to reveal her low private signal by relieving her of some of the burden of acquiring an expensive public signal. In this model, we use the second approach, which links the costly effort with the informativeness of the public signal.
An important feature of the model is the agent's pre-existing private information, which is valuable to the principal.
The Model
Formal proofs as well as the exact values of cutoffs and bounds for the regions in the parameter space are given in the appendix. The agent's strategy is to choose private report based on the realization of her private signal ˜𝑠. For the RUC, meetings are regulated and transparent to ensure that prices are fair.
The principal commits to a mechanism that requires certain effort levels based on private reports from the agent.
Preliminary Analysis: Policy Decision
These policy choices are relevant in balancing equilibria, where the agent chooses different levels of effort depending on the realization of her private signal (and for off-path beliefs in equilibria bundling). Contradictively, imagine that the agent always chooses the effort level, but that the director also trusts her private report. For the same public signal, the client always makes a lower policy choice after observing a low private signal than after observing a high signal: 𝑥0,𝑖 < 𝑥1,𝑖for𝑖 ∈ {0,1}.
Therefore, everyone has an incentive to report a high private signal and the principal must ignore it completely.
Agent Decides Effort
Therefore, when viewed as the high type, the low type prefers the lowest possible stake level for 𝑒1. 1 for the high type that makes the low type indifferent to reporting either private signals. For 𝑐 < 𝑐¯, the low-type mean is strictly better off deviating to any effort level 𝑒 ≠𝑒∗ if it is considered a high-type.
Therefore, off-path beliefs always assuming that the agent is of low type satisfies the Intuitive Criterion.
No Commitment with Formal Requirements
Substituting all these results into 𝐼 𝐶0and solving for Proposition 29 If the principal imposes formal requirements on the effort level of the public signal, splitting is only possible for 𝑐 > 𝑐¯. For sufficiently low costs, both agents exert maximum effort and the principal only follows the public signal.
When the principal brings about a divorce, he must stimulate the low-type agent by lowering the level of effort required for her.
Welfare Comparison
Note that when the agent controls the level of effort, we choose the best scenario for the principal. However, this does not mean that the principal always prefers to differentiate when controlling the level of effort. This is why the expected utility of the principal (solid red line on the graph) is decreasing.
This is why the expected utility of principal (grey dotted line and blue solid line) is increasing.
Conclusion
Given this voter strategy, the low-ranking president with signal 𝑠 = 𝐵 𝐸 𝑈𝐵 gets utility. Since ˜𝜎 is chosen to equalize these two expected utilities, the incumbent has no incentive to deviate. Since its private signal is informative, the original low-type operator is true and has no profitable deviation. We have already shown that this reelection probability makes the inferior candidate true in region 3𝐴.
5A and 5B Similar to the previous case, the reelection shuffle probability causes the low-type incumbent with an unpopular signal to be indifferent between any policy choice and to have no profitable deviation.
Preliminary Analysis
The Voter's Problem When the voter is initially called to play, she has observed the incumbent's first-period policy choice 𝑥, and must choose her probability to pay attention𝜌𝑥 and to keep the𝜈𝑥. Although some sequences of play may be off the path of play given a low-ability incumbent's strategy (for example, failure of a policy 𝑥when a low-ability incumbent always believes to choose¬𝑥), it can be easily verified that sequential consistent beliefs about the incumbent's ability 𝜈𝑥. With these beliefs in hand, it can be easily verified that the voter's expected utility from her expected strategy𝜃𝑥 = (𝜈𝑥.
To investigate the voter's attention decision 𝜌𝑥, recall from the main text that the values of negative and positive attention 𝜙𝑥−, 𝜙𝑥+.
Equilibrium Characterization
To claim that VI𝑧(𝜂𝑧) is decreasing, first observe by Lemma 9 and Corollary 43 that 𝜙𝑧(𝜂𝑧) =min{𝜙𝑧−(𝜂𝑧), 𝜙+𝑝(𝑧)−, 𝜙+𝑧(𝜂𝑧) is strictly increasing in 𝜂and𝜂𝑧. 𝑧( 𝜂𝑧) strictly decreasing in𝜂𝑧. Since 𝜙𝑧−(𝜂𝑧) is strictly increasing in 𝜂𝑧, it is easy to see that {𝜌 : ∃𝜃ˆ𝑧 ∈ Θ¯𝑧 with𝜌 = 𝜌.ˆ𝑧} is an increasing correspondence 𝜈ˆ¬𝑧 = 1, 𝜈ˆ¬𝑧 = 0) −𝜌𝑧Pr(𝜔 ≠ 𝑥|I) is decreasing in 𝜌𝑧 (that is, more attention to 𝑧damages re-election prospects when poll-friendly). It thus immediately follows that V𝑧I(𝜂𝑧) is again decreasing over the interval𝜂𝑧 > 𝜂¯𝑧. c) If 𝜂𝑧 is sufficiently close to ¯𝜂𝑧.
With the previous lemma in hand, we first prove Proposition 10 of the main text, which states that the original owner is always true when 𝜋 = 12 (ie, it is not an ex-ante "popular" . policy).
Main Proofs
Finally, suppose that𝑐 ≥ max{𝜙¯𝐴,𝜙¯𝐵}; then there exists a voter's best response ˆ𝜃 to truthfulness without attention following either policy, and the conditions on the remaining quantities for truthful equilibrium are trivially identical to the conditions in the CHS model. Recall from the main text that there exists a unique level of pandering ˆ𝜎 ∈ (0,1) that makes policy choice uninformative and thus satisfies𝜇𝐴(𝜎ˆ) =𝜇𝐵(𝜎ˆ) = 𝜇. We finally assert that 𝜙+𝐴(𝜎ˆ) < 𝜙+𝐵(𝜎ˆ), which implies the desired property since 𝜙+𝐴(𝜎) is decreasing and 𝜙+𝐵(𝜎) is increasing.
Supporting such an equilibrium requires that a low-ability incumbent who receives signal 𝐵 has a strict electoral incentive to choose 𝐴; it is easy to check that this consequently requires both that 𝜈𝐵 < 1 (so 𝜎∗.
Voter Welfare
We have already shown that these equilibrium quantities are feasible and the low type has no incentive to deviate. Proof We have already shown that this strategy is feasible and that the low-type mean has no profitable deviation. The only possible case left is that when the principal imposes different effort levels depending on the private report, for the optimal effort levels, the IC constraint of the low type is binding and the IC of the high type is lax.
Evidence We have already established that in this case the IC constraint of the low-type agent is binding, the IC constraint of the low-type agent is slack, and 𝑒1 = 1.
