Elections at the Departamento Level

The institutional figure of the Intendente (mayor) was created in 1908. It was replaced by the 1918 constitution, which introduced a collegiate executive at the departmental level, and reinstated in 1934. Under this system, elections are decided by simple majority using the double simultaneous vote (DSV) mechanism, whereby both the candidate and the political party are elected jointly. The elected mayor is the most-voted candidate from the most-voted political party, allowing for both intra-party and inter-party competition. Importantly, the 1934 constitution established that mayors could not run for election after two consecutive terms in office. A subsequent constitutional reform in 1952 reinstated collegiate authorities at both regional and national levels, but this was reversed with the approval of a new constitution in 1966 (Breunig and Rocabert Reference Breunig and Rocabert2020).

The 1971 elections are distinctive for several reasons. Prior to this election, the collegiate system prevented the estimation of incumbency effects; the 1971 elections were the first held after the 1966 constitutional reform, and therefore the first suitable for such estimation.Footnote ⁷ These elections were also the last before the 1973 military coup and the ensuing dictatorship, which lasted until 1984. The coup led to the removal of some mayors elected in 1971, who were replaced by “interveners.”Footnote ⁸ Once democracy was restored, the electoral system returned to its prior form.Footnote ⁹

A new constitutional reform in 1997 introduced two important changes to regional elections. First, regional and national elections were separated by time.Footnote ¹⁰ Second, a cap was placed on the number of candidates per party per department (maximum of three), and these candidates must be validated by the party’s internal democratic bodies (Convención). As noted, the first clear effect of the reform was to allow voters to split their support between different political parties at the national and departmental levels. The reform also gave mayors greater visibility, enabling voters to better evaluate individual candidates, while also clearly limiting the number of candidates.

We focus on elections held after 1966, because the Frente Amplio entered the political arena after that year and this was due to the complexities of the 1966 election.Footnote ¹¹ Our analysis includes the elections of 1971, 1984, 1989, 1994, 2000, 2005, 2010, 2015, and 2020.Footnote ¹²

Incumbency Effects in Uruguay and the Latin American Region

The divergence between personal and partisan incumbency effects in Uruguay reflects the particular interaction of institutional, cultural, and electoral factors in the country. However, these dynamics acquire clearer contours when contrasted with patterns observed in other Latin American democracies. First, regarding electoral rules and personalization of politics, Uruguay’s use of the double simultaneous vote (Ley de Lemas) and proportional representation fosters a high level of intra-party competition and candidate-level campaigning, which in turn enhances the salience of individual over partisan brands. This system contrasts with closed-list PR systems in countries like Argentina or Brazil (in Senate elections), where parties exercise stronger control over candidate ranking, often reinforcing the partisan brand over the individual one (Carey and Shugart Reference Carey and Shugart1995).

Nevertheless, Brazil shares some similarities with Uruguay in terms of personalization: its open-list system incentivizes name recognition and direct constituent engagement (Samuels Reference Samuels2001). However, in Brazil, these personal dynamics often coexist with clientelist practices that are less common in Uruguay due to its more institutionalized party system and stronger public administration (Kitschelt and Wilkinson Reference Kitschelt and Wilkinson2007).

Second, regarding candidate selection and internal competition, Uruguay’s open and competitive candidate selection processes—through primaries and multiple internal lists—contrast with more centralized or informal methods in other countries. For example, in Mexico or Argentina, party elites often exert strong control over nominations, limiting internal contestation (Langston Reference Langston2003; de Luca et al. Reference De Luca, Jones and Tula2002). In such contexts, the partisan label often serves as a stronger electoral cue, particularly when voters lack detailed information about individual candidates. By enabling multiple factions to compete within the same party and election, Uruguay allows candidates to build personal followings that transcend the electoral fortunes of the party as a whole. This mechanism is rarer in countries with single-candidate parties or where internal dissent is suppressed.

Third, regarding party system institutionalization and electoral volatility, Uruguay’s highly institutionalized party system—with deep historical roots and stable inter-party competition—sets it apart from much of the region. Countries like Peru and Ecuador have experienced extreme party system volatility and the collapse of traditional party organizations (Levitsky et al. Reference Levitsky, Loxton, Van Dyck and Domínguez2016). In such contexts, both personal and partisan incumbency effects are weakened, but personalization becomes dominant as parties function primarily as electoral vehicles for individual politicians. In contrast, Chile and Costa Rica resemble Uruguay in their degree of institutionalization, yet their electoral rules (especially Chile’s old binominal system) and less factionalized parties tended to reinforce party-level advantages over personal ones until recent reforms (Siavelis Reference Siavelis, Gallagher and Marsh2002; Taylor-Robinson Reference Taylor-Robinson2006).

Fourth, regarding term limits and re-election rules, re-election rules directly shape the space for incumbency effects. In countries with strict term limits—like Mexico, where immediate re-election was only recently allowed—incumbency effects are systematically dampened at both personal and partisan levels (Moreno Reference Moreno2003). By contrast, in countries like Colombia or Brazil, where re-election is permitted, personal incumbency effects tend to be stronger, though they are often accompanied by advantages conferred by partisan control of state resources. Uruguay allows immediate re-election in the legislature and at the subnational level but prohibits presidential re-election. This creates asymmetries in the visibility and accountability of incumbents, with stronger personal effects at lower levels of government where incumbents have more frequent contact with voters and more room for individual political entrepreneurship.

Fifth, regarding political socialization and voter heuristics, Uruguay’s high levels of political information, civic engagement, and democratic culture encourage voters to rely on personal evaluations of candidates, especially in subnational races. This differs markedly from countries where party labels or clientelist networks function as low-information cues for voters. For example, in Honduras or the Dominican Republic, personal ties and patronage remain central to voter decision-making, but in less programmatic and more transactional forms (Desposato Reference Desposato2006; Moreno et al. Reference Moreno, Crisp and Shugart2003). In Chile and Costa Rica, as in Uruguay, voters tend to exhibit higher levels of political sophistication and issue-based voting, but personalization has increased as party identities weaken, particularly among younger voters (Luna Reference Luna2014b; Carlin et al. Reference Carlin, Singer and Zechmeister2015). Sistch, regarding alternation in power and institutional constraints, frequent and peaceful alternation in power is relatively rare in Latin America, where dominant parties or coalitions often maintain long periods of control (e.g., the PRI in Mexico, the MAS in Bolivia, the FSLN in Nicaragua). Uruguay’s recent alternation between the Frente Amplio and the Partido Nacional reflects an equilibrium that promotes electoral accountability and curbs excessive partisan advantage (Altman Reference Altman2019). In contrast, countries with less competitive party systems often see stronger partisan incumbency effects due to control over public resources, media, and the civil service (Mares and Young Reference Mares and Young2016). However, such advantages can backfire under conditions of scandal or crisis, leading to dramatic party collapses—events that Uruguay’s more stable equilibrium has largely avoided.

To sum up, Uruguay’s combination of competitive electoral rules, institutionalized but internally competitive parties, high political engagement, and democratic alternation creates a distinctive environment for incumbency effects. In this context, personal incumbency thrives as a product of voter sophistication, media visibility, and intra-party competition, while partisan incumbency is structurally constrained by democratic norms and institutional checks. Comparatively, Uruguay shares some features with Brazil, Chile, and Costa Rica, particularly in electoral openness and civic culture, but stands out for the degree to which its institutions favor personal over party-level political capital. Conversely, in countries with centralized party systems, dominant coalitions, or weak institutional controls, partisan incumbency remains stronger, often linked to clientelism or asymmetric access to the state. This comparative perspective underscores the need to account for the interaction of rules, culture, and voter behavior in explaining the sources and limits of incumbency advantages across Latin American democracies.

Data

We use the dataset from Schmidt et al. (Reference Schmidt, Cardarello and Lujan2020), which contains information at the department, political party, and candidate levels for national and departmental elections from 1918 onward. We focus on elections held after 1966. The first four in this period took place simultaneously with national elections, while the subsequent ones were held separately and subject to a limit of three candidates per party per department, as established by the 1997 constitutional reform.

The data reveal a marked underrepresentation of women: out of 1,273 individual observations, 68 correspond to women and 752 to men.Footnote ¹³ We restrict the dataset at the political party level to the main parties—Partido Colorado, Partido Nacional (both with liberal and conservative factions), and Frente Amplio, a center-left coalition created in 1971—which had realistic chances of contesting and winning departmental governments.Footnote ¹⁴ After data cleaning, the final dataset includes 513 observations at the party level, exclusively involving candidates from these three main parties.

Table 1 presents basic descriptive statistics, complemented by data from Cardarello (Reference Cardarello2011).Footnote ¹⁵

Table 1. Running and Winning Re-elections: Number and Rates for Incumbents

Source: Schmidt et al. (Reference Schmidt, Cardarello and Lujan2020) and Cardarello (Reference Cardarello2011).

The table shows that, with the exception of 1971, more than half of elected mayors sought re-election in the following electoral cycle. Moreover, the victory rate of incumbent mayors exceeds 50% in all but the first three elections considered.Footnote ¹⁶

While these figures suggest strong individual incumbency advantages, the unconditional re- election rate does not constitute a causal estimate. To make causal claims, we exploit differences in re-election rates between legally open and closed elections. Table A2 in the Appendix classifies each election as “legally open” (25.2%), “de facto open” (25.7%), or “Closed” (50.9%).

Identification and Estimation Strategies

The main goal is to estimate the change in the probability of re-election for a given candidate and political party due to their current incumbency. The individual incumbent effect can be defined as the difference in votes that two candidates from the same incumbent party would obtain, one being the incumbent and the other not, within the same election, department, and year. Similarly, the party incumbent effect can be defined as the difference in votes between two non-incumbent candidates from the same party, where one runs in a district where the party is the incumbent and the other does not.

The Rubin Causal Model

This is a classic case of causal inference with missing counterfactuals, framed within the Rubin Causal Model (Rubin Reference Rubin1974). Theoretically, the model is clear, but in practice, we can only observe a subset of potential outcomes. To address the selection bias that arises when treatment assignment is not random, researchers turn to natural experiments and causal econometric techniques applied to observational data.

Within the Rubin Causal Model (Rubin, Reference Rubin1974), let ${Y_{i,p,d,t}}(I)$ denote the potential electoral outcome (e.g., probability of re-election or vote share) for candidate i from party p in department d at election t, under incumbency status $I \in \{ 0,1\} $ . The overall incumbency effect is defined as

$${\tau ^{{\rm{overall}}}} = \mathbb{E}\left[ {{Y_{i,p,d,t}}(1) - {Y_{i,p,d,t}}(0)} \right],$$

that is, the expected change in electoral success of a given candidate and party if they currently hold office versus if they do not.

We further distinguish between candidate-level and party-level effects. For a candidate i in party p, let ${Y_{i,p,d,t}}({I^{{\rm{cand}}}})$ be the potential outcome when i is the incumbent ( ${I^{{\rm{cand}}}} = 1$ ) and when i is not ( ${I^{{\rm{cand}}}} = 0$ ), holding the party’s status fixed. The individual incumbency effect is

$${\tau ^{{\rm{individual}}}} = \mathbb{E}\,\left[ {{Y_{i,p,d,t}}(1) - {Y_{i,p,d,t}}(0)} \right],$$

the expected difference in electoral support for the same candidate running as incumbent versus as non-incumbent.

Similarly, for a non-incumbent candidate j from party p, let ${Y_{j,p,d,t}}({I^{{\rm{party}}}})$ denote the potential outcome when the party is incumbent ( ${I^{{\rm{party}}}} = 1$ ) and when it is not ( ${I^{{\rm{party}}}} = 0$ ). The party incumbency effect is

$${\tau ^{{\rm{party}}}} = \mathbb{E}\left[ {{Y_{j,p,d,t}}(1) - {Y_{j,p,d,t}}(0)} \right],$$

the expected difference in votes obtained by a non-incumbent candidate depending on whether her party currently holds the office.

In practice, only one of these potential outcomes can be observed for each candidate-party- election unit (the fundamental problem of causal inference). The identification strategy therefore relies on exploiting quasi-random assignment near electoral thresholds and the variation induced by term limits through the Diff-in-Disc design.

Running a simple Ordinary Least Squares (OLS) regression of the probability of being elected on an incumbent/challenger dummy—even when controlling for a broad set of covariates—produces biased estimates if relevant variables (e.g., candidate quality or motivation) are omitted (see Erikson Reference Erikson1971; Jacobson Reference Jacobson1978, and Gelman and King Reference Gelman and King1990).Footnote ¹⁷ Thus, causal identification requires that election to the first term approximates random assignment.

The Differences-in-Differences Approach

While RDD addresses endogeneity concerns by exploiting quasi-random assignment near electoral thresholds, it faces a fundamental limitation in our context: the confusion between individual and party incumbency effects. Since incumbent mayors almost invariably run for re-election under the same party label, standard RDD estimates capture the combined effect of both individual and party incumbency, making it impossible to disentangle these distinct mechanisms.

The Differences-in-Differences (DiD) approach offers a complementary identification strategy that leverages institutional variation in incumbency opportunities. In our setting, this variation arises from Uruguay’s constitutional term limits, which create two distinct electoral contexts: closed elections where incumbent mayors can seek re-election, and legally open elections where term limits prevent incumbents from running again.

Conceptual Framework

The DiD design exploits the fact that in closed elections, the winning party benefits from both individual incumbency (the mayor’s personal advantage) and party incumbency (the party’s institutional advantage), while in legally open elections, only party incumbency operates since no individual can carry forward personal incumbency advantages. By comparing electoral outcomes between these two contexts, DiD can theoretically isolate the individual incumbency component.

Formally, let ${Y_{p,d,t}}$ , denote the electoral outcome for party p in department d at time t. In closed elections, winning parties receive treatment intensity ${T_{closed}} = {\tau _{individual}} + {\tau _{party}}$ , while in open elections, they receive ${T_{open}} = {\tau _{party}}$ . The individual incumbency effect can then be identified as:

(1)

Key Assumptions

The validity of DiD identification rests on several critical assumptions:

Parallel trends: In the absence of incumbency advantages, electoral outcomes for winning and losing parties would follow parallel trajectories in both closed and open elections. This assumption requires that unobserved factors affecting electoral performance evolve similarly across the two contexts. Violations could occur if, for example, voter behavior, campaign dynamics, or candidate selection processes differ systematically between closed and open elections.

Common shocks: Time-varying factors that affect electoral outcomes should impact both closed and open elections similarly. This assumption may be challenged if economic conditions, national political trends, or local shocks have differential effects depending on whether incumbents can seek re-election.

Stable unit treatment value assumption (SUTVA): The incumbency advantage received by one party should not spill over to affect other parties’ electoral prospects. While this assumption is generally reasonable at departmental level, it could be violated if strategic interactions between parties vary across closed and open elections.

No composition effects: The types of candidates and parties competing should not differ systematically between closed and open elections in ways that confound the incumbency effect. For instance, if high-quality challengers are more likely to enter open elections, this could bias the estimated individual incumbency advantage downward.

Validation of the Identification and Estimation Strategy

Note that in our case, spillovers from the treatment group to the control group are not possible, as allocation and participation are equivalent. Moreover, the timing of the reform’s implementation canbe considered quasi-random, and there are no other concurrent treatments beyond those considered. Two additional assumptions are required for the RDD: non-manipulation of the running variable and continuity of observables around the cutoff point. The first must hold at both the candidate and party levels, while the second is tested only at the party level, assessing continuity across departments and parties.

It is worth noting that the identification assumptions required for Diff-in-Disc estimation are a combination of those used in RDD and Diff-in-Diff approaches (Gamalerio Reference Gamalerio2017). Although the literature is still debating the precise assumptions needed for full identification, we follow Gamalerio (Reference Gamalerio2017), who propose three necessary conditions (to be met in both legally and de facto closed and open elections): (i) no manipulation of the running variable around the cutoff; (ii) continuity of observables around the cutoff; and (iii) parallel trends above and below the cutoff. While other authors (de Benedetto Reference De Benedetto2020; Lopes da Fonseca Reference Lopes da Fonseca2017) consider the first two conditions sufficient for unbiased and valid Diff-in-Disc implementation, we test all three.

First, the assumption of no manipulation of the running variable implies that electoral results are not subject to fraud or tampering by candidates or political parties. In Uruguay, where strong insti- tutions have long been responsible for organizing, conducting, and announcing elections—and where there is no history of electoral fraud—it is reasonable to assume this condition holds.Footnote ²³ Nonetheless, we conduct McCrary tests (McCrary Reference McCrary2008) for both closed and de facto open elections. As shown in Table A3 and Table A4, the results provide no evidence of manipulation at conventional significance levels.

The second assumption requires that incumbents and challengers do not differ significantly in observable characteristics around the cutoff in both legally open and closed elections. For instance, the number of people eligible to vote (among other variables) should not vary substantially on either side of the cutoff. As shown in Table 2, we observe a small difference in closed elections at the party level. This suggests that some parties tend to fall more frequently to the left or right of the cutoff when the incumbent runs for re-election.Footnote ²⁴ Nevertheless, the preferred specification includes political party dummies to control for these differences.

Table 2. Test: Continuity of Observables in Closed and Legally Open Elections

Own elaboration based on Boreluy. Robust standard errors.

The third assumption derives from the Diff-in-Diff component of the methodology. It assumes that treated and control groups would have followed similar trends in the absence of treatment—a condition that is inherently untestable. To address this, we assess the presence of non-parallel trends above and below the cutoff in legally open and closed elections using placebo Diff-in-Disc estimations. We create a placebo dummy variable with the same mean and standard deviation as the real treatment indicator but randomly assigned across the sample. We then replicate all estimations from the following section. As shown in Table A10 in the Appendix, results are null.

Estimation

We first estimate two RDD models to identify individual and partisan incumbency effects. Following Gelman and Imbens (Reference Gelman and Imbens2019), we restrict polynomial orders to two or lower, and we employ the optimal bandwidth estimator developed by Calonico et al. (Reference Calonico, Cattaneo and Titiunik2014a, c). For general estimation procedures in RDD, we follow the guidelines set out by Cattaneo et al. (Reference Cattaneo, Idrobo and Titiunik2019).

While the choice of polynomial order balances interpretability and smoothness, it also involves a well-known trade-off: higher-order polynomials increase flexibility but can induce spurious oscil- lations and overfitting near the cutoff, whereas lower-order specifications may fail to capture genuine nonlinearities in the relationship between the forcing variable and the outcome (Gelman and Imbens Reference Gelman and Imbens2019). Regarding bandwidth selection, we employ the mean squared error-optimal bandwidth pro- cedure of Calonico et al. (Reference Calonico, Cattaneo and Titiunik2014b), which minimizes the asymptotic mean squared error of the local polynomial estimator.

Next, we implement a Diff-in-Disc model, as proposed by de Benedetto (Reference De Benedetto2020) and Lopes da Fonseca (Reference Lopes da Fonseca2017). The starting point is equation 2:

(2) $${y_{p,d,t}} = {\alpha _0} + {\alpha _1}MM{V_{p,d,t - 1}} + {\beta _0}{d_{p,d,t - 1}} + {\beta _1}{d_{p,d,t - 1}} \times MM{V_{p,d,t - 1}} + {\epsilon _{p,d,t}.}$$

The outcome variable ${y_{p,d,t}}$ is a binary indicator equal to 1 if political party p won the election in department d during period t, and 0 otherwise. The running variable $MM{V_{p,d,t - 1}}$ denotes the MMV obtained by party p in department d in the previous election ( $t - 1$ ).Footnote ²⁵

The main variable of interest, ${d_{p,d,t - 1}}$ , is a dummy that equals 1 if party p held office in department d in the previous period ( $t - 1$ ), i.e., an indicator for partisan incumbency. An interaction term is also included, and ${\epsilon _{p,d,t}}$ , represents an idiosyncratic error term.

In this specification, ${\alpha _0}$ is the intercept of the regression line to the left of the cutoff and captures the unconditional probability that the challenging party wins the election in period t, given that it lost in $t - 1$ by a single vote. The coefficient ${\alpha _1}$ measures the slope to the left of the cutoff, capturing how the probability of winning in t for the challenger decreases as the margin of loss in $t - 1$ increases.

The coefficient ${\beta _0}$ represents the increase in the probability that the incumbent party wins in t, relative to the challenger, given that it won in $t - 1$ by one vote. The sum ${\alpha _0} + {\beta _0}$ corresponds to the intercept of the regression line to the right of the cutoff. Finally, ${\beta _1}$ reflects the slope of the regression line to the right of the cutoff.

The parameter of interest capturing the partisan incumbency effect is ${\beta _0}$ . However, as shown by Fowler and Hall (Reference Fowler and Hall2014) and Erikson et al. (Reference Erikson and Titiunik2015), ${\beta _0}$ actually estimates twice the partisan incumbency effect, plus a term that reflects the combined effect of individual and partisan incumbency.Footnote ²⁶ This is made explicit in the mapping between coefficients and parameters:

(3) $${\beta _0} = 2 \times Incumbenc{y_{Party}} + 2 \times P(Reru{n_{Candidate}}) \times Incumbenc{y_{Candidate}.}$$

Here, $Incumbenc{y_{Party}}$ captures the pure partisan incumbency advantage; $P(Reru{n_{Candidate}})$ is the probability that the current officeholder runs for re-election; and $Incumbenc{y_{Candidate}}$ represents the pure individual incumbency advantage.

It is worth emphasizing that the adjustment for double counting is not restricted to two-party systems, even though it was first formalized in that context by Erikson et al. (Reference Erikson and Titiunik2015). The intuition behind the correction applies more generally: at the cutoff, the RDD framework compares a just-barely winner with a just-barely loser. By construction, winning by a single vote mechanically implies that another candidate (or party) loses by that same vote. The raw discontinuity therefore reflects both the advantage conferred on the winner by incumbency and the disadvantage imposed on the loser by the lack of incumbency. This symmetric “winner-loser” contrast does not depend on the number of parties but on the fact that electoral competition at the threshold always produces a marginal winner and a marginal loser. Failing to correct for this double counting implicitly assumes that the loser’s counterfactual outcome is unaffected by the winner’s incumbency status—an assumption that is difficult to defend in competitive multiparty environments where holding office carries direct implications for rivals. For this reason, following Fowler and Hall (Reference Fowler and Hall2014) and Lopes da Fonseca (Reference Lopes da Fonseca2017), we apply the correction to obtain estimates that more closely align with the causal parameter of interest: the pure incumbency advantage of winning office.

In Uruguay, constitutional rules prohibit mayors from serving more than two consecutive terms. This restriction provides a natural source of variation to separate the effects of individual and partisan incumbency, which typically co-occur. The Diff-in-Disc methodology exploits this variation by comparing margins of victory around the cutoff between elections with and without eligible incumbents (i.e., open vs. legally closed races).

Following Lopes da Fonseca (Reference Lopes da Fonseca2017), inference is based on two steps. First, a local linear regression is applied, restricting the sample to intervals $MM{V_{p,d,t - 1}} \in [ - h,h]$ , to estimate the model:

(4) $${y_{p,d,t}} = {\gamma _0} + {\gamma _1}M\,\,M{V_{p,d,t - 1}} + {\rho _0}{d_{p,d,t}} + {\rho _1}{d_{p,d,t}} \cdot MM{V_{p,d,t - 1}} + {\epsilon _{p,d,t}.}$$

In a second step, the analysis incorporates the introduction of term limits. As noted by Fowler and Hall (Reference Fowler and Hall2014), partisan and personal incumbency are often jointly and non-randomly assigned. Term limits provide a reliable instrument for disentangling these effects by exogenously breaking the link between the incumbent party and its incumbent candidate. Under term limits, only the party may run again by nominating a different candidate, presumably unknown to the electorate. This setting allows a clean comparison between incumbent parties that re-run elections with the incumbent candidate and those constrained to nominate a new candidate, making it ideal for assessing the partisan incumbency advantage.

For this purpose, inference relies on an extended RDD known as the Diff-in-Disc design (Grembi et al. Reference Grembi, Nannicini and Troiano2012b), which combines elements of difference-in-differences and RDD approaches. It estimates the difference in vote share between incumbent parties that barely won in departaments with and without a binding term limit. Compared to a standard RDD, the Diff-in-Disc design captures a second source of variation and produces coefficient estimates robust to omitted variables, manipulation at the cutoff, and co-treatment effects. As a result, it allows for causal identification of the partisan incumbency advantage.

In the second step, the additional treatment variable ${b_{p,d,t}}$ , bit indicates whether the term limit is binding and ${\beta _0}$ is the Diff-in-Disc estimator and identifies the treatment effect of exogenously opening a seat. The corresponding specification, following Lopes da Fonseca (Reference Lopes da Fonseca2017), is given in equation 5:

(5)

Equation (5) decomposes electoral outcomes into several components that capture baseline effects, individual incumbency, contextual influences, and interactions between these factors. The dependent variable ${y_{p,d,t}}$ represents the electoral outcome for party p in district d at election t, which could be vote share or the probability of winning. The key explanatory variables include the previous election’s minimum margin of victory ( $MM{V_{p,d,t - 1}}$ ), an indicator for whether the candidate was an incumbent in $t - 1$ ( ${d_{p,d,t - 1}}$ ), and an indicator for contextual treatment such as an open election ( ${b_{p,d,t}}$ ).

The first term, ${\alpha _0} + {\alpha _1}MM{V_{p,d,t - 1}}$ , represents the baseline outcome for non-incumbent candidates in standard elections. Here, ${\alpha _0}$ captures the expected outcome when the previous margin of victory is zero, and ${\alpha _1}$ reflects how prior electoral strength conditions the outcome, allowing for momentum or persistence effects from the previous election.

The second term, ${d_{p,d,t - 1}}({\beta _0} + {\beta _1}MM{V_{p,d,t - 1}})$ , captures the effect of individual incumbency in standard elections. The coefficient ${\beta _0}$ represents the direct advantage of being an incumbent when the previous margin is zero, while ${\beta _1}$ allows this effect to vary with the prior margin of victory. This specification recognizes that incumbents who barely won the previous election may enjoy a smaller advantage than those who won by larger margins.

The third component, ${b_{p,d,t}}({\gamma _0} + {\gamma _1}MM{V_{p,d,t - 1}})$ , reflects the impact of contextual factors, such as open elections where incumbents are barred from running. The parameter ${\gamma _0}$ measures the baseline shift in outcomes due to the election context for non-incumbents, and ${\gamma _1}$ captures how this shift varies with the previous margin of victory.

Finally, the interaction term ${b_{p,d,t}}{d_{p,d,t - 1}}({\delta _0} + {\delta _1}MM{V_{p,d,t - 1}})$ isolates the effect of incumbency within the open election context. The coefficient ${\delta _0}$ represents the additional advantage (or disadvan- tage) of being an incumbent in such elections, and ${\delta _1}$ allows this effect to depend on prior electoral strength. Together, these interaction terms enable the Diff-in-Disc design to separate individual incumbency effects from broader party-level incumbency effects.

The error term ${\varepsilon _{p,d,t}}$ , captures unobserved shocks or idiosyncratic influences on electoral out- comes. Overall, equation (5) provides a flexible framework to disentangle how past performance, individual incumbency, and election context jointly shape electoral success.

Note that (5) is a special case of (6). To prove it, we start from equation (4):

If we impose the following assumptions (the conditions under which equation (2) simplifies to the form of equation (1)):

1. 1. ${b_{p,d,t}}$ = 1 for the relevant observations (i.e., the personal incumbency term is always active in period t),

2. 2. ${d_{p,d,t - 1}}$ = d _p,d,t (the lagged incumbency indicator coincides with the contemporaneous one used in equation (1)).

Then, substituting ${b_{p,d,t}} = 1$ and renaming ${d_{p,d,t - 1}}$ as ${d_{p,d,t}}$ , equation (2) becomes:

We can then define the “reduced-form” parameters:

$${\tilde \gamma _0} \equiv {\alpha _0} + {\gamma _0},\quad \quad {\tilde \gamma _1} \equiv {\alpha _1} + {\gamma _1},$$

$${\tilde \rho _0} \equiv {\beta _0} + {\delta _0},\quad \quad {\tilde \rho _1} \equiv {\beta _1} + {\delta _1}.$$

With these definitions, we obtain exactly the form of equation (2):

$${y_{p,d,t}} = {\tilde \gamma _0} + {\tilde \gamma _1}{\kern 1pt} MM{V_{p,d,t - 1}} + {\tilde \rho _0}{\kern 1pt} {d_{p,d,t}} + {\tilde \rho _1}{\kern 1pt} {d_{p,d,t}} \cdot MM{V_{p,d,t - 1}} + {\epsilon _{p,d,t}}.$$

Remarks

• The equivalence relies on the assumptions above: if ${b_{p,d,t}} \ne 1$ in general or if ${d_{p,d,t - 1}}$ does not coincide with ${d_{p,d,t}}$ , then equation (6) cannot be reduced to (5) without additional restrictions.

• Intuitively, equation (1) bundles together the baseline intercept/slope ( $\tilde \gamma $ ) and the incumbency effect ( $\tilde \rho $ ), which in the richer specification (equation (2)) are decomposed into the “structural” effects ( $\alpha, \beta $ ) and the “personal” effects activated by ${b_{p,d,t}}$ ( $\gamma, \delta $ ).

• If in the data ${b_{p,d,t}}$ varies (is not always equal to one) or if one wants to explicitly separate partisan (β) from personal (δ) incumbency, it is preferable to keep the full specification in equation (6) and report both sets of coefficients rather than relying on the reduced form in equation (5).

According to Fowler and Hall (Reference Fowler and Hall2014), δ ₀ can be written as:

(6) $${\delta _0} = - P(Reru{n_{Candidate}}) \times Incumbenc{y_{Candidate}.}$$

These developments yield a system of equations relating the estimated coefficients to the parameters of interest, which can be derived from standard OLS estimation.Footnote ²⁷

(7)

Solving this system provides the following expressions for the separate individual and partisan incumbency effects. A key contribution of this approach is showing that the coefficients from equations 5 and 6 cannot be directly interpreted as pure incumbent effects due to the duplication problem and the role of re-run probability. Importantly, partisan incumbency is the most straightforward to estimate, as it can be obtained directly from the regression coefficients without requiring external estimation of $P(Reru{n_{Candidate}})$ (we address this further in the next section). The final expressions for the parameters of interest are:

(8)

Robustness Checks

The results of the robustness checks are reported in the Appendix, with the discussion reserved for this section. Unless otherwise stated, estimate (2) from Table 3 is taken as the reference specification for all comparisons. The first set of checks, presented in the previous section, involved the inclusion of control variables and the relaxation of the definition of open elections to encompass a broader set. These modifications lead to minor changes in the coefficients’ magnitudes but do not alter their signs or statistical significance.

Second, we replicate the estimations while excluding key elections, as shown in Table A9 in the Appendix. Specifically, we exclude the years 1971, 1984, 1971 and 1984 jointly, and 2005. Dropping 1971 yields coefficients with unchanged signs but reduced significance. A similar pattern is observed when omitting 1984, although the significance of covariates increases. The joint exclusion of 1971 and 1984 results in coefficients with consistent signs but a sharp decline in statistical significance—likely due, at least in part, to the substantial reduction in sample size. The year 2005 marked the first national victory of the left-wing party Frente Amplio, potentially affecting departmental elections through a coat-tail effect (see, for example, Ames Reference Ames1994 for the Brazilian case). Excluding 2005 from the estimation leads to improved significance for the coefficient of interest, Diff-in-Disc, and for the indicator of open elections, relative to the full sample estimates. However, the constant loses statistical significance. This result may reflect the influence of national-level dynamics on departmental outcomes in 2005, when Frente Amplio simultaneously captured the national government and several departmental governments.

Third, we conduct a series of placebo tests. We randomly reassign the values of the variables Open, Margin of Victory, and Incumbency across the sample, preserving their means and standard deviations, and re-estimate the models. The results, presented in Table A10 in the Appendix, are null, providing additional support for the robustness of our findings.

Fourth, we examine the sensitivity of results to bandwidth choices.Footnote ²⁹ Table A11 in the Appendix presents results using narrower bandwidths. Reducing the bandwidth naturally reduces the sample size. Estimates remain statistically significant with a bandwidth of (−15, 15), based on 122 observations. However, when the bandwidth is reduced to (−10, 10), the sample falls to 91 observations, and the running variable loses significance.

Fifth, to test the hypothesis that results may be driven by Montevideo—the capital city, home to half the country’s population—we exclude its observations and re-estimate the model. As shown in Table A12 in the Appendix, the coefficients maintain both their signs and levels of significance.

Finally, we conduct a placebo test on the timing of the constitutional reform. We artificially shift the reform’s implementation year to 1990, 1997, and 2001, and test for equality of pre- and post-reform coefficients in each case. Results are reported in Table A12 in the Appendix. No significant changes are found in pre-post differences—except for the covariate Open. We also separately estimate individual and partisan incumbency effects for each placebo reform year, with results shown in Table A13 in the Appendix. These results suggest that the observed changes occur across all years considered, but a distinction emerges between the pre-post 1990 case and those of 1997 and 2001. Specifically, although individual and party coefficients change in 1990, their signs are preserved—albeit with reduced significance. In contrast, for the 1997 and 2001 cases, significance is lost in the post-period and the signs of the estimated incumbency effects reverse.

In sum, the results indicate that the constitutional reform had an effect on incumbency dynamics. This robustness check, which reveals changes in individual and party-level effects across different pre- post periods (1990, 1997, and 2001), invites us to reconceptualize the reform as a consolidation of political shifts already underway in the Uruguayan system. One such shift is the growing willingness, following the return to democracy, of political actors to pursue departmental executive positions as part of their career trajectories. This emerging “appetite for the position of mayor” (Cardarello Reference Cardarello2011; Chasquetti Reference Chasquetti2014) likely contributed to an increase in candidate “quality,” potentially explaining the changes observed across periods.

Extensions

To evaluate the effect of the constitutional reform on the incumbency advantage, we divide the sample into two periods. The first sub-sample includes the elections of 1971, 1984, 1989, and 1994, while the second comprises the elections of 2000, 2005, 2010, 2015, and 2020. We repeat all estimations for both sub-samples to assess whether the results differ. Specifically, we re-estimate the Difference- in-Discontinuities (Diff-in-Disc) models and present the results for our preferred specification (2) in Table A13 in the Appendix.

When examining the p-values, we observe that all coefficients remain unchanged except those associated with the Incumbent variable and the key coefficient of interest, Diff-in-Disc, which captures personal and partisan incumbency effects. This pattern suggests that both types of incumbency effects may have changed following the reform. The estimated parameters for individual and party incumbency are reported in Table 7 below.

Table 7. Extension: Diff-in-disc Estimation, |Pre- and Post-1997 Electoral Reform

Standard errors in parenthesis. Significance levels: ***p<0.01, **p<0.05, *p<0.1. The third column presents the t-statistic and p-value associated with test of difference between coefficients in columns 1 and 2. Source: own elaboration based on Boreluy.

Table 8. Extension: Individual and Partisan Separate Incumbency Effects (System Solution) Before and After Electoral Reform

Standard errors obtained by bootstrap (300 repetitions, seed 123). Source: own elaboration based on Boreluy. All estimates control for party and department fixed effects and consider only legally open elections.

The results show, first, that the estimated effect of incumbency using pre-reform data is statistically significant, in contrast to the post-reform estimates. Second, regardless of the statistical significance of the post-reform coefficients, their point estimates lie outside the confidence intervals of the pre-reform estimates. This indicates that the constitutional reform led to a decrease in the personal incumbency advantage and an increase in the partisan advantage.

Delving deeper into the 1997 reform, note that it had important implications for the dynamics of electoral competition in Uruguay, and it plausibly helps to explain why incumbency effects moderated after its implementation. The reform introduced three major changes: (i) separating national and departmental elections in time, (ii) introducing limits on the number of candidates per party at the departmental level, and (iii) requiring that these candidacies be validated by internal party conventions. While the empirical analysis in this article shows that both individual and partisan incumbency effects shifted after the reform, a closer look at its institutional consequences sheds light on the mechanisms at play.

Campaign financing. Before 1997, departmental elections were held simultaneously with national ones. This allowed local candidates to “ride along” with national campaigns, benefiting indirectly from broader fundraising structures, campaign advertising, and party financing at the national level. After the reform, departmental elections became temporally separate, which forced mayoral candidates to finance and manage their campaigns in a more autonomous fashion. On the one hand, this separation increased the financial and organizational costs of running for office, likely raising the “quality threshold” of candidates willing and able to compete. On the other hand, incumbents could no longer rely as heavily on national party machinery and coat-tail effects, which reduced partisan incumbency. In this sense, the reform rebalanced the playing field, making campaign resources more individualized and contingent on the candidate’s own ability to mobilize local support.

Media access. The reform also altered how candidates gained visibility. When departmental races coincided with national presidential campaigns, media coverage was overwhelmingly concentrated on national politics, limiting the space for mayoral contenders to differentiate themselves. The decoupling of electoral calendars after 1997 gave departmental elections their own media cycle, thereby increasing the exposure and scrutiny of individual mayoral candidates. Incumbents may have benefited from greater visibility during their term in office, but challengers also received enhanced opportunities to compete on a more level informational field. In this sense, separating the elections created conditions under which media attention became less of a zero-sum game dominated by national leaders, but at the same time made individual performance in office more salient to voters.

Competition structures. By capping the number of candidates per party at three and requiring their approval through internal conventions, the reform reshaped intra-party competition. Prior to 1997, the DSV system allowed parties to present a multiplicity of candidates, which diluted competition and facilitated the re-nomination of incumbents by default. The post-reform rules forced parties to pre-select their strongest candidates, limiting ballot fragmentation and increasing intra-party discipline. This reduced the ability of incumbents to exploit party divisions to their advantage, while simultaneously strengthening the incentives for parties to nominate candidates with broader appeal. From the perspective of incumbency effects, this meant that the personal advantages of incumbents were tempered by the higher “quality” of challengers who emerged under the new institutional environment.

In sum, the 1997 reform can be understood as having simultaneously increased the salience of individual performance (through media visibility), raised the costs of candidacy (through more autonomous financing requirements), and enhanced the competitiveness of challengers (through stricter nomination rules). These changes help explain the observed decline in individual incumbency effects and the moderation of partisan effects after the reform. Rather than a sharp rupture, the reform consolidated ongoing trends in the personalization and professionalization of departmental politics, while also introducing institutional safeguards that limited incumbents’ ability to translate their office-holding advantage into secure re-election.

Limitations

First, without detracting from the substantive contribution of the RDD and Diff-in-Disc techniques to the identification of causal effects, it is important to note that the estimates obtained are local in nature. They are valid only in the vicinity of the cutoff point that defines treatment—winning or losing a departmental election. This means that candidates or parties who won or lost by a wide margin are not directly considered in the estimation.

Second, individual incumbency was defined based on whether the incumbent was serving at the time of the election, excluding cases such as candidates who had held office in earlier terms but not in the immediately preceding one—that is, mayors seeking mediate rather than immediate re-election.Similarly, the classification of elections as open or closed was based on the status of the elected mayors, leaving out those who served in an interim or auditing role. A third limitation concerns the possibility that the individual incumbency effect estimated through the “unconditional RDD” may be overstated due to varying application rates. Considering a “conditional RDD” falls beyond the scope of this article and is acknowledged as a limitation.

Along these lines, an important methodological choice concerns how to handle candidate attrition, in other words the fact that not all incumbents seek re-election. A common approach in the literature is to restrict the sample to candidates who run again, thereby conditioning on re-entry. However, this restriction can introduce selection bias: the decision to run for re-election is itself endogenous and may be correlated with candidate quality, perceived competitiveness, or strategic party considerations. Conditioning on re-entry therefore risks distorting the estimated incumbency effect by excluding systematically different subsets of candidates.

For this reason, we adopt an unconditional RDD approach that retains all candidates, regardless of whether they reappear in the following election. This strategy avoids introducing additional selection mechanisms into the estimation, ensuring that the estimated effect reflects the causal impact of incumbency on re-election probabilities without conditioning on a post-treatment variable. While unconditional estimates may understate the incumbency effect relative to a re-candidacy sample—sincesome incumbents choose not to run—they provide a more transparent measure of incumbency as it actually operates in the electoral process.

A fourth limitation relates to the differential effort a mayor may exert when legal restrictions prevent re-election and there is no individual-level accountability. This could influence the performance of municipal governments and, consequently, affect the role of the political party in open elections. The estimates assume identical party responsibility in both open and closed elections.

Finally, and related to the previous point, another limitation of this study is the absence of any consideration of performance or citizens’ evaluations of it. Cases involving corruption, misuse of public funds, or policy failures can significantly influence the re-election prospects of both candidates and parties. Including variables related to economic management and administrative performance could provide a richer understanding of the nature of political responsibility—offering a promising avenue for future research.