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BEE3058 Homework Assignment

Please answer all questions. Full work must be shown in your answer. There is no need to reference Pons & Bullet (2025) in your answers, unless you explicitly quote parts of their text. If you do so, you will still need to provide an explanation of the quoted text using your own words. Provide definitions when necessary. If you think you need to make additional assumptions, state them clearly. If you introduce and use additional notation, define it clearly. Please do not exceed 2,000 words in total (see breakdown by question). This does not mean that I expect you to write 2,000 words. Keep your answers concise and on point: this is not an essay, and “less is more”.

Question 1 [12 points]

[Max 300 words]

1. [4 points] What is the research question the authors are trying to answer in this paper?
2. [5 points] What are the identification challenges in estimating the causal effect of turnovers?
3. [3 points] Give one reason why the answer matters for policy debates about democratic accountability.

Question 2 [33 points]

[Max 650 words]

After an election at t = 0, the winner governs for one term and chooses reform effort e ≥ 0 (e.g., anti-corruption effort or governance effort). Effort has cost

C(e) = 1/2 e².

Country performance during the term is

Y = e + ε,     ε ~ U[-1,1].

At the next election, the leader is re-elected if Y ≥ 0. If re-elected, the leader obtains a continuation value B > 0.

A close win can signal a de facto term limit: a narrowly re-elected incumbent expects that, even if performance is good, the probability of winning the next election is scaled down by λ ∈ (0,1]. Formally, assume the probability of re-election is

Pr(re-elect | e) = λ · Pr(Y ≥ 0 | e).

Assume:
(i) a new challenger who just won (a turnover) has λ = 1;
(ii) a narrowly re-elected incumbent has λ < 1.

1. [6 points] Derive Pr(Y ≥ 0 | e) for e ∈ [0,1]. How does the effort impact the probability to be re-elected?
2. [12 points] Write the leader’s objective function U(e) and solve for optimal effort e(B,λ). What drives the optimal effort of the leader?
3. [5 points] Show how e varies with B and λ (signs only).
4. [6 points] Let B = 2. Compute e for (i) λ = 1 and (ii) λ = 0.6. Compute expected performance E[Y] in each case and the gap E[Y]|λ=1 − E[Y]|λ=0.6.
5. [4 points] In 3-4 sentences, explain how this model rationalizes larger turnover effects in close elections.

Question 3 [32 points]

[Max 650 words]

The authors use a Regression Discontinuity Design (RDD) as their main empirical strategy. Column (1) of Table 1 shows one of their main results on which this question focuses.

Figure 1: Main Table

Notes: This table reports RD estimates corresponding to equation (1) for our measures of country performance, expressed in standard deviation terms. We report local linear regression estimates from Calonico et al. (2014), robust standard errors in parentheses, the p-value associated with the robust confidence interval in brackets, the number of observations in the sample and in the bandwidth, and the MSERD-optimal bandwidth. ** p < 0.05, *** p < 0.01.

1. [10 points] For this regression, what is the treatment? What is the running variable? What is the cutoff used for the running variable? What is the outcome? What is the bandwidth used for the running variable?
2. [15 points] If you found strong sorting in the density of the running variable at 0, explain precisely which identifying assumption fails and why that matters for causal interpretation.
3. [7 points] Under Downsian competition with commitment, what turnover effect on economic performance would you expect at the cutoff? Table 1, col. (1) reports a 0.269 SD gain after a turnover. Name one friction from lecture that can reconcile this fact.

Question 4 [23 points]

[Max 400 words]

1. [8 points] Table 1 reports effects in standard deviations (SD). Explain what a 0.269 SD effect means. Explain why the authors report the effect in terms of SD. Give two reasons why the authors use indices.
2. [8 points] Figure 6 reports dynamic effects and includes placebo estimates (τ = −2). Explain what the placebo is testing and how the time profile of effects informs interpretation (e.g., immediate policy change vs. gradual institutional change).
3. [7 points] Close elections may be a selective subset. Explain the external-validity concern and describe one approach used in the paper to speak to effects away from the cutoff.

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