Empirical Results

5.5.1 RDD and Diff-in-disc Estimates

As is standard in the literature, a first assessment of the results is based on graphical evidence on the treatment effects. All graphs are constructed by first dividing the running variable into bins of size one within a bandwidth of [−40,40]. The outcome variables – vote share and probability of winning – are then averaged within each bin for the pre- and post-reform period, i.e. ¯ynpwith the subscriptsnandpindexing bin and period. The RDD graphs display these observations fit by a local polynomial plot of quadratic degree on each side of the threshold, relying on a triangular kernel. To obtain the diff-in-disc graphs it is necessary to first calculate the difference within each bin between the post- and pre-reform period, ∆yn = (¯y_n,1−y¯_n,0), to then plot these differences against the running variable and fit the observations with a polynomial plot in the same fashion as before.

Figure 5.1 provides the RDD and the diff-in-disc graphs depicting the vote share and probability of winning in period t against the vote margin in t −1. All graphs show a

.2.3.4.5.6Vote Share

−.4 −.2 0 .2 .4

Vote Margin (t −1) − RDD

−.2−.10.1.2Vote Share

−.4 −.2 0 .2 .4

Vote Margin (t −1) − Diff−in−disc

0.25.5.751Winning Probability

−.4 −.2 0 .2 .4

Vote Margin (t −1) − RDD

−1−.50.51Winning Probability

−.4 −.2 0 .2 .4

Vote Margin (t −1) − Diff−in−disc

Fig 5.1: Vote Share and Winning Probability. Graphs plot the vote share at timetagainst the vote margin at t−1. Observations in a bandwidth of [-40, 40] are averaged within bins of size 1% and second degree polynomial plots are constructed using a triangular kernel. 95% confidence intervals are indicated in gray.

sizable jump around the zero threshold providing evidence of a significant incumbency effect. For the main outcome variable, the RDD graph suggests a combined personal and partisan incumbency advantage of around 8 to 10 percentage points, while the diff-in-disc graph shows a negative discontinuity amounting to 15 percentage points for municipalities affected by the term limit. The latter plot suggests that in case there exists a partisan effect, it is not as large as the personal one. The graphs depicting the probability of winning at timet against the vote margin att−1 are in line with this assessment.

Coefficient estimates in Table 5.2 support the graphical evidence. Estimates follow a similar pattern across specifications with the ones for the spline polynomial approximation, which were obtained relying on a cubic specification of the running variable in the models in Equations (5.3) and (5.7), suggesting in general larger treatment effects.¹⁷ The choice of which estimates to substitute into the expressions quantifying the personal and partisan incumbency advantages is therefore inconsequential. In the following, results are discussed

17Results are robust to different order polynomials.

Table 5.2: RDD and Diff-in-disc Estimates.

Notes: IK stands for the bandwidth selected as in Imbens and Kalyanaraman (2012). The spline polynomial regression estimates are obtained relying on a third-order approximation. All models include election term fixed effects. Robust standard errors are clustered at the municipal level. Stars indicate significance levels of 10%(*), 5%(**) and 1%(***).

for the specification relying on the bandwidth selected as in Imbens and Kalyanaraman (2012) due its conventional use in the RDD literature.

5.5.2 Partisan and Personal Incumbency Advantages

In addition to the RDD and diff-in-disc estimates, a third input is necessary in order to obtain the personal and partisan incumbency advantages: the probability that an incum-bent reruns. This is obtained by simply regressing a dummy variable indicating whether the incumbent officeholder is running for re-election on a linear function of the running variable.

The first three rows of Table 5.3 show the estimates of the three inputs required to compute the incumbency effects. These are substituted into Equations (5.9) and (5.10) and 95% bias-corrected confidence intervals are obtained relying on a non-parametric bootstrap with replacement clustered at the municipal level. This involves repeatedly re-estimating the three inputs and substituting them into the equations in a simultaneous fashion using different random samples from the original dataset.

The last two rows of the table provide the estimates for the personal and partisan incumbency advantage with and without fixed effects. The personal effect has a positive causal impact on electoral success. A party benefits by up to 17 percentage points from running an incumbent officer. The incumbency status of the party, however, is not

sta-Table 5.3: Personal and Partisan Incumbency Advantage.

Vote Share Winning Probability

RDD 0.090 0.111 0.386 0.227

[0.063, 0.118] [0.084, 0.139] [0.262, 0.503] [0.087, 0.362]

Diff-in-Disc -0.154 -0.184 -1.154 -1.557

[-0.259, -0.043] [-0.295, -0.084] [-1.655, -0.592] [-2.153, -0.888]

Prob. 0.922 0.979 0.830 0.886

[0.627, 1.213] [0.589, 1.381] [0.569, 1.091] [0.515, 1.277]

Incumbency Advantage

Personal 0.167 0.188 1.391 1.758

[0.048, 0.322] [0.076, 0.372] [0.693, 2.348] [0.893, 3.446]

Partisan -0.109 -0.129 -0.961 -1.444

[-0.021, 0.003] [-0.239, 0.026] [-1.456, -0.390] [-2.063, -0.797]

FE No Yes No Yes

Notes: The first three rows provide the inputs for the system of equations relating personal to partisan incumbency advantage.

The last two rows provide the estimates of personal and partisan incumbency advantage. Bias-corrected confidence intervals in brackets. FE indicates whether municipality fixed effects. All models include election term fixed effects.

tistically different from zero thus having no sizable causal impact on the resulting vote share.

The results for the probability of winning, in turn, identify statistically significant personal and partisan effects but of opposite signs. These results are presumably rooted in the high magnitude and significance of the personal incumbency effect on the resulting vote share. Arguably, based on the descriptive evidence in Table 5.1, being the incumbent is a sure win. By ascribing this effect to the candidate rather than the party, it follows that running a new candidate undermines a party’s electoral prospects. The high magnitude of the effect is likely due to the significant loss in vote share that led to a considerable reduction in the party re-election rate in 2013 in term-limited elections.¹⁸ Still, the significantly negative partisan effect should not be interpreted as a partisan incumbency disadvantage but rather as the disadvantage of not running an incumbent candidate.

5.5.3 Explanatory Hypotheses

This section tests two possible explanations for the baseline results. First, whether there exist ruling costs, as suggested by a strand of the literature on the effects of political representation on electoral outcomes (Paldam, 1986). Second, whether the fact that a challenger is rerunning for the election matters. Results are based on re-estimations of the

18Parties were re-elected in around two thirds of the 150 term limited elections compared to an average of above 80% in the pre-reform period.

diff-in-disc models with the dummy variable bit indicating mayors that did not run for re-election after at least three consecutive terms in office in the first case, and municipalities with a binding term limit where no challenger is rerunning for the election in the second.

Table 5.4: Hypotheses Test.

Notes: The outcome variable is the vote share of the baseline party. In Panel A the sample is restricted to the pre-treatment period. IK stands for the bandwidth selected as in Imbens and Kalyanaraman (2012). The spline polynomial regression estimates are obtained relying on a third-order approximation. All models include election term fixed effects. Standard errors are clustered at the municipal level and robust to heteroscedasticity. Stars indicate significance levels of 10%(*), 5%(**) and 1%(***).

Coefficient estimates collected in Table 5.4 suggest no consistently significant ruling costs despite the almost professionalization of the mayor-career that characterized the pre-reform period. On the other hand, incumbent challengers appear to be driving part of the effect. The diff-in-disc estimates remain significantly negative but their magnitude is down by half of the baseline estimates. This result is presumably due to the fact that the major opposition party nominee running as an incumbent challenger is not unknown to the electoral district. In fact, he was most likely part of the municipal council and the closest to the mayor figure in terms of public recognition. Accordingly, in more than half of the 2013 term limited elections where the incumbent challenger or a former mayor reran, they won the mayorship. The relevance of the candidates thus transpires even through the success of rerunning challengers once the incumbent mayor is excluded from the electoral race. This result reinforces the baseline findings and lends increased support to the thesis that incumbency is personal and parties play only a secondary role.