Internal Validity

The validity of an RDD hinges on fulfilling the continuity assumption that implies no sorting around the zero threshold. This assumption is satisfied as long as individuals are not able to precisely manipulate their location relative to the threshold. This is plausible in the context of competitive elections as parties cannot precisely manipulate their vote

shares and even to a lesser extent the resulting vote margin between winner and runner-up. Two methods can be used to validate this assumption: testing for discontinuities in the density of the running variable through a McCrary (2008) plot, and checking for any significant differences in baseline characteristics between the treatment and control groups, i.e. incumbents and non-incumbents. The McCrary (2008) plot on the left side of Figure 5.2 and the graphs collected in Figure 5.3 testing for differences on six pre-determined characteristics – the parties’ vote share and winning probability int−1, whether the party is one of the two major center-left or -right parties, if it is a coalition, whether the candidate is male or female and his or her previous experience – show no significant discontinuities around the zero threshold implying no manipulation and no selection bias.

0.511.52Frequency

−.5 0 .5

Vote Margin (t− 1) − RDD

−30−20−10010Frequency

−.5 0 .5

Vote Margin (t −1) −− Diff−in−disc

Fig 5.2: Manipulation of the Running Variable. The McCrary plot on the left graphs the density of the running variable. The McCrary style plot on the right graphs the change in the density of the running variable from the pre-to the post-treatment period.

The diff-in-disc design, in turn, is superior to the RDD as it captures a second source of variation combining diff-in-diff and RDD methodologies. The diff-in-diff aspect of the approach addresses any concerns with the continuity assumption described above. The RDD aspect controls for differential trends and unobservable municipal characteristics.

Still, one assumption must be fulfilled in order to validate a diff-in-disc design: that the ability or incentives to manipulate the vote margin did not change from the pre- to the post-treatment period. This is tested relying on a variant of the McCrary (2008) plot that depicts the change in the number of observations around the threshold from one period to the other. There is no reason to suspect that parties are now able to manipulate their vote shares as the right hand side graph in Figure 5.2 shows no discontinuity in the change in the number of observations close to the cutoff from pre- to post-treatment period.

In addition, in order to be able to identify the partisan and personal effects relying on the proposed approach, these two effects are assumed unchanged from pre- to post-treatment period. There is no obvious reason why this should not be the case. Still, this assumption can be verified by restricting the analysis to the 2005 and 2009 elections, when the law establishing term limits already exists but is not applied, to compare expiring to

0.2.4.6Vote Share t−1

−.4 −.2 0 .2 .4

Vote Margin (t− 1)

0.2.4.6.8Probability of Winning t−1

−.4 −.2 0 .2 .4

Vote Margin (t− 1)

0.2.4.6.81Party Affiliation

−.4 −.2 0 .2 .4

Vote Margin (t− 1)

−.20.2.4.6Coalition Party

−.4 −.2 0 .2 .4

Vote Margin (t− 1)

−.10.1.2.3Female Candidate

−.4 −.2 0 .2 .4

Vote Margin (t− 1)

0.511.52Experience

−.4 −.2 0 .2 .4

Vote Margin (t− 1)

Fig 5.3: Selection Bias. Graphs test for selection into treatment for six different pre-determined characteristics indicated on the y-axis. 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.

non-expiring mayors.^19,20 This test involves restricting the sample size, therefore inference relies on the three data driven bandwidth selectors suggested in the literature: Ludwig and Miller (2007), Imbens and Kalyanaraman (2012) and Calonico et al. (2014).

Results are collected in Table 5.5 and are obtained relying on a local linear regression as in Equation (5.1) for all bandwidths above including half and two times the bandwidth selected as in Imbens and Kalyanaraman (2012). The RDD estimates suggest a positive and significant combined partisan and personal effect for all incumbents in line with the baseline estimates. The diff-in-disc estimates, obtained by defining bit in Equation (5.6) as to indicate expiring officeholders, provide no evidence of a significantly different incumbency effect between the two groups.

Table 5.5: Diff-in-disc Assumption.

Local Linear Regression

Design CCT 1/2 IK IK 2 IK CV

RDD 0.123*** 0.116*** 0.114*** 0.076*** 0.118***

(0.024) (0.036) (0.022) (0.016) (0.021)

Diff-in-disc 0.039 0.088 0.051 0.029 0.066

(0.066) (0.126) (0.057) (0.035) (0.051)

Obs. 270 149 299 494 332

Notes: The outcome variable is the vote share of the baseline party. CCT, IK and CV stand for the bandwidths selected as in Calonico et al. (2014), Imbens and Kalyanaraman (2012) and Ludwig and Miller (2007), respectively. 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%(***).

Overall, this section validates each of the assumptions underlying the proposed ap-proach. There exists no manipulation at the zero threshold neither in the pre- nor in the post-treatment period, there is no evidence of selection bias and both the personal and partisan incumbency advantage are unchanged by the electoral reform introducing term limits. Baseline results are, therefore, susceptible of causal interpretation.

5.7 Conclusion

The aftermath of a constitutional reform introducing term limits at the local level elections is the perfect laboratory to identify the personal and partisan returns to incumbency. The institutional setting, comprising 278 homogenous municipalities, an exogenous constitu-tional reform, heterogeneity in treatment resulting from the law ruling the application of term limits and the verified comparability between bare winners and bare losers, allows for the implementation of both RDD and diff-in-disc design providing coefficient estimates suitable of causal interpretation.

19The law was voted and approved in Parliament before the 2005 local elections.

20This terminology is borrowed from Fowler and Hall (2014). Expiring mayors are the ones running for their last possible term in office. Non-expiring mayors have no short-term perspectives of being termed-out.

Results show that the original definition of incumbency advantage purposely focuses on the candidate rather than the party. Positive returns accrue to the rerunning officeholder by virtue of his incumbent status independently of the incumbency status of the party. Even though it would be reasonable to assume that parties play a significant role in attracting and retaining votes, particularly in a multi-party context with a PR system of closed lists (Shugart et al., 2005), fact is that the assessed partisan effect is indistinguishable from zero.

The magnitude of the effect conditional on the institutional setting in which it emerges, together with the evidence on the importance of incumbency and personal characteristics in explaining voting behavior at various levels of government motivate the external validity of the results. These reinforce the relevance of candidates vis-a-vis parties in politics at large.

Conceivably both voters and politicians will over time adapt to the new institutional setting. Preliminary assessments show e.g. an increase in candidates’ mobility between municipalities whereas traditionally it followed a bottom-up pattern. This is in line with the theory of political ambition and its interaction with the political structure in shaping incentives and provides an interesting avenue for further research (Schlesinger, 1966; Black, 1972).