Informativeness and the Incumbency Advantage

Transcription

1 Informativeness and the Incumbency Advantage Scott Ashworth Ethan Bueno de Mesquita Amanda Friedenberg April 22, / 23

2 The Incumbency Advantage Following Erickson (1971), a large literature has studied high incumbent reelection rates The worry is that these rates indicate normative trouble Whenever the resources of public office are used to insulate individual politicians from electoral risk, their accountability to their constituents is weakened.... Thus, insulation from electoral risk of the kind suspected would, at a single stroke, debilitate the two fundamental accountability relationships of a democratic system of government. Cox and Katz (2002) 2 / 23

3 A Picture of the Literature Open Seat Election Electoral Selection Governance Period Office Holding Effect Engage in Public Policy Exercise Perquisites of Office Closed Seat Election High Reelection Rates Recent empirical work tries to isolate office holding effect Argues this is the normatively troubling part 3 / 23

4 Our Intervention in the Argument We emphasize a new mechanism that operates during the governance period Governance outcomes are correlated with Incumbent s type Suppose incumbent and challenger are ex-ante identical Difference in informativeness leads to incumbency effect on reelection Key finding is that incumbency effect and voter welfare can be positively related 4 / 23

5 Related Literature Many, many papers estimate the incumbency advantage Recent empirical wave initiated by Lee (2008) Follow-ups: Linden (2004), Fowler and Hall (2014), Klasnja and Titiunik (2016),... Eggers (2016) critiques the identification Closely related theoretical papers: Caselli, Cunningham, Morelli, and Moreno de Barreda (2013) Ashworth, Bueno de Mesquita, and Friedenberg (2017) 5 / 23

6 An Example 2 candidates: Incumbent and Challenger Each has type θ {θ, θ} Same prior for each: Pr(θ = θ) = π (0, 1) In each of 2 periods, governance outcome depends on type of politician in power and mean-zero normal noise: g t = θ t + ɛ t Between the governance periods, Voter retains Incumbent or replaces with Challenger Observes g 1, but not θ 1 or ɛ 1 Payoff is g 1 + g 2 6 / 23

7 Solving the Example Voter reelects iff Pr(θ I = θ) π Reelect iff g 1 ĝ = (θ+θ) 2 7 / 23

8 Solving the Example Voter reelects iff Pr(θ I = θ) π Reelect iff g 1 ĝ = (θ+θ) 2 ( ) ν ( ω ) ( ) 4 f θ,ω g^ f θ,ω 4 7 / 23

9 Incumbent s Win Probability Hypothesis testing interpretation: H 0 = {θ I = θ} vs. H 1 = {θ I = θ} Rejecting the null = replacing the Incumbent Type I error: replace high type Incumbent (prob α) Type II error: retain low type Incumbent (prob β) Symmetry of Normal pdf α = β 8 / 23

10 Incumbent s Win Probability Hypothesis testing interpretation: H 0 = {θ I = θ} vs. H 1 = {θ I = θ} Rejecting the null = replacing the Incumbent Type I error: replace high type Incumbent (prob α) Type II error: retain low type Incumbent (prob β) Symmetry of Normal pdf α = β Incumbent is reelected if: θ I = θ and no Type I error θ I = θ and Type II error Pr(Reelect Incumbent) = π(1 α) + (1 π)β 8 / 23

11 The Incumbency Effect The incumbency effect is Pr(reelect incumbent) 1 2 Since α = β, incumbency effect is IE = π(1 α) + (1 π)α 1 2 = (π 1 )(1 2α) 2 Positive iff π > 1 2 Decreasing in probability of error 9 / 23

12 A More General Model Now suppose g = f(a, θ) + ɛ where a A, a closed subset of R + with smallest element a f strictly increasing in a and θ ɛ has symmetric density φ whose likelihood ratio is onto R + with strictly positive derivative ( MLRP) Politician in office gets payoff B c(a) c is strictly increasing B > c(a) Symmetric uncertainty about θ 10 / 23

13 Complements vs Substitutes Effort and type are complements if, for any a > a, f(a, θ) f(a, θ) f(a, θ) f(a, θ) eg, f(a, θ) = aθ Effort and type are substitutes if, for any a > a, f(a, θ) f(a, θ) f(a, θ) f(a, θ) eg, f(a, θ) = a + θ 11 / 23

14 Voter Behavior Suppose Voter expects effort a Voter reelects Incumbent iff φ(g θ) φ(g θ) 1, or g ĝ(a ) f(a, θ) + f(a, θ) 2 12 / 23

15 Equilibrium Effort If Incumbent actually chooses effort a, reelection probability is Pr(a a ) = π [ 1 Φ ( ĝ (a ) f ( a, θ ))] + (1 π) [1 Φ (ĝ (a ) f (a, θ))] There is a pure-strategy equilibrium with effort level a iff for all a A. B Pr(a a ) c(a ) B Pr(a a ) c(a) 13 / 23

16 Proposition Suppose that: A = R + ; A Comparative Static f is concave and differentiable in a, with f > 0; and a c is strictly convex and differentiable, with c (0) = 0 and lim a c (a) =. (Plus a technical condition.) Fix B > B. If a H (B) and a H (B ) are the largest equilibrium efforts at B and B, respectively, then a H (B) > a H (B ) 14 / 23

17 Hypothesis Testing Redux Probability of Type I error: ( α(a ) Pr(f(a, θ)+ɛ 1 < ĝ(a )) = Φ f(a ), θ) f(a, θ) 2 Probability of Type II error: ( ) f(a, θ) f(a, θ) β(a ) Pr(f(a, θ)+ɛ 1 ĝ(a )) = 1 Φ 2 Symmetry of φ implies α(a ) = β(a ) 15 / 23

18 Informativeness Both error probabilities are decreasing in ι(a ) f(a, θ) f(a, θ) 2 Interpret by thinking of g as outcome of an experiment informative about θ different actions induce different experiments Proposition (ABF 2017) The experiment induced by a is Blackwell more informative than the experiment induced by a if and only if ι(a ) > ι(a ) 16 / 23

19 The Incumbency Effect The incumbency effect is Pr(reelect incumbent) 1 2 IE(a ) = π(1 α(a )) + (1 π)α(a ) 1 2 = (π 1 2 ) (2Φ(ι(a )) 1) There is an incumbency advantage if π > 1 2 incumbency disadvantage if 1 > π 2 and an The absolute value of the effect is increasing in informativeness 17 / 23

20 Informativeness and the Incumbency Effect Complements Substitutes π > 1 2 IE(a) increasing in a IE(a) decreasing in a π < 1 2 IE(a) decreasing in a IE(a) increasing in a Complements f(a, θ) f(a, θ) increasing in a Substitutes f(a, θ) f(a, θ) decreasing in a IE increasing in ι(a) = f(a,θ) f(a,θ) 2 18 / 23

21 Voter Welfare Fix equilibrium with first-period effort a Expected first-period welfare: VW 1 (a ) = πf(a, θ) + (1 π)f(a, θ) Ex ante expected second-period welfare: VW 2 (a ) = Pr(θ 2 = θ a )f(a, θ) + (1 Pr(θ 2 = θ a ))f(a, θ). Pr(θ 2 = θ a ) = ex ante (equilibrium) probability winner has type θ 19 / 23

22 Comparative Statics of Voter Welfare Proposition (ABF17) VW 1 is increasing in a. VW 2 is increasing in a if effort and type are complements. VW 2 is decreasing in a if effort and type are substitutes. Complements informativeness increasing in a Blackwell Voter second-period payoff higher 20 / 23

23 Comparative Statics of Voter Welfare, II Proposition (ABF17) Fix a > a, and suppose effort and type are substitutes. There exist π[a, a ], π[a, a ] (0, 1) so that the following are equivalent: 1. π (0, π[a, a ]) (π[a, a ], 1). 2. VW 1 (a ) + VW 2 (a ) VW 1 (a ) + VW 2 (a ). Benefit of increased informativeness increasing in ex-ante uncertainty 21 / 23

24 Is the IE a valid measure of VW? 22 / 23

25 Is the IE a valid measure of VW? No Consider complements and π > 1 2 Shift from low effort to high effort Increase in both components of Voter welfare Since π > 1, increase incumbency advantage 2 Opposite of the relationship suggested by the literature 22 / 23

26 Is the IE a valid measure of VW? No Consider substitutes and π > max(, 1/2, π[a, a ]) Shift from low effort to high effort Increase sum of components of Voter welfare Since π > 1, decrease incumbency advantage 2 Opposite of the case of complements 23 / 23