Reference no: EM133709607

Assignment:

The following set-up corresponds exactly to the model of accountability covered in Lecture 3. Here's a summary:

This is a two-period model involving a voter and a set of politicians. The ability of each politician is a random variable that takes two possible values: it is high (H) with probability p ∈ (0,1) and low (L) otherwise. Each politician knows his or her own ability, but the voter does not know it. Each period, the politician in office chooses how much effort to put into public administration. Effort, et, is unobservable to the voter and ranges from (0,1).

The policy outcome can be either good or bad. High-ability politicians al- ways achieve the good outcome; low-ability politicians achieve the good outcome with probability equal to their effort level, et. After the first period, the voters observes the policy outcome and decides whether to replace the incumbent with a random opponent drawn from the population of politicians. The voter only cares about the policy outcomes and prefers good ones to bad ones. Politicians receive a benefit B > 0 (and B < 1) if they win an election. Politicians also e2 dislike effort, with its cost equal to 2t .

(a) How much effort will the winner of the election supply in the second period? Why?

(b) The voter will definitely not re-elect the incumbent if the policy outcome was bad in the first period. Explain the intuition behind this result in 5 lines or less.

(c) Explain why the voter, upon seeing a good outcome, thinks the incumbent is more likely to be high ability than upon seeing a bad outcome.

(d) Write down the utility function for the low-quality incumbent in the first period. Find the level of effort that maximizes the incumbent's utility in the first period.

(e) Explain why the voter, upon seeing a good outcome, thinks the incumbent is more likely to be high ability than before seeing any outcome. You may choose to use Bayes' Rule to illustrate your answer, but you are not required to do so.

(f) Suppose now that the voter is imperfectly informed about the policy out- come. She can perfectly detect if the outcome was bad, but may fail to recognize a good outcome. In particular, with a probability θ ∈ (0,1), the voter fails to recognize a good outcome, and instead thinks it is bad. Re-write the expected utility of the low-quality first-period incumbent and recalculate the equilibrium amount of effort. How does your answer com- pare to the previous one? Explain the intuition behind this result in 5 lines or less.

(g) Do you think that the creation of a government news agency could help to improve government performance in the setting described in part (f)? Discuss.