Julieta Peveri
email: julieta.peveri@univ-amu.fr.

Marc Sangnier
email: marc.sangnier@univ-amu.fr.

Nicolas Berman

Alessandra Casarico

Renaud Coulomb

Habiba Djebbari

Vincenzo Galasso

Cecilia Garcia-Peñalosa

Gender differences in re-contesting decisions: New evidence from French municipal elections *

Keywords: Gender, Competition, Persistence, Candidates, Self-selection, Elections JEL Codes: J16, D72, J24

This paper studies differences across genders in the re-contesting decisions of politicians following electoral wins or defeats. Using close races in mixed-gender French local elections, we show that women are less likely to persist in competition when they lose compared to male runners-up, but are equally or more prone than male winners to re-contest when they win. Differences in observable characteristics or in the expected electoral returns of running again cannot fully account for these gender gaps in persistence. In contrast, the heterogeneity of the results across political ideology, age, experience and occupation suggests that behavioural explanations are at play. Additionally, we provide evidence that a woman's victory encourages former female challengers to re-contest but does not trigger the entry of new female candidates.

Introduction

Achieving gender balance among decision-makers has become a goal in many countries for at least two reasons. First, because it is a normative objective that should characterize modern societies. Second, because evidence indicates that women are more likely to take decisions that are more relevant to the needs and complaints of female citizens than male politicians; therefore, only equal representation of genders among officeholders can ensure a fair representation of a society's preferences. 1 However, we are far from this target, as women occupy only 25.5% of the world's parliamentary seats in 2021. This share increases to 29.3% for countries with a 2019 Human Development Index that qualifies them as very highly developed and only to 37.2% in the world's 10 most developed countries. Even in the 21 countries where the Human Development Index of women is higher than that of men, only 23.0% of the members of parliament are women. 2 These facts suggest that women's under-representation in politics is not only driven by development or social gender inequality.

Understanding what drives the low presence of women in politics is thus key to eliminate this gender gap.

Women's reluctance to run for office and voters or political parties' discrimination against female candidates have been active topics of research. 3 In contrast, gender differences vis-àvis persistence in political competition have received much less attention with the exception of the recent work by Wasserman (forthcoming). There are however many reasons to believe that women may not react in the same manner as men when winning or losing an election given that differences across genders in attitudes toward competition outcomes, self-confidence and negative feedback aversion are reported in laboratory experiments and in competitive education contexts. 4 In this paper, we study differences across genders in the re-contesting decisions of candidates who ran as heads of lists in the 2008 and 2014 French municipal elections in cities with more than 3, 500 inhabitants. Using a regression discontinuity design to examine mixedgender races, i.e., elections whose top two candidates are of different genders, we find that female candidates appear to be more affected by the outcome of the vote than male candidates. This difference in the win-loss gap across genders is mainly driven by female runners-up recontesting less often than male runners-up. In contrast, female winners prove to be as or more persistent in political competition than male winners. To ensure that this result is not driven by particular decisions of male candidates involved in mixed-gender races, we verify that their behaviour does not significantly differ from that of male candidates participating in men-only races. We show that this difference between genders cannot be explained by female and male candidates having systematically different characteristics in terms of past participation in elections, age, occupation, political orientation or affiliation to a political party. We explore the heterogeneity in candidates' decisions and find that the win-loss gender gap mostly appears among older and more experienced candidates, candidates occupied in the public sector, left-wing candidates and candidates formally affiliated to a political party. We also show that the cross-gender structure of probabilities of victory in past and future elections cannot fully explain the documented gender gap. These two sets of results are consistent with behavioural explanations being at play. When we assess the relative importance of the uncovered gender gap in politicians' persistence vis-à-vis other channels, we find that it can at best account for one-tenth of observed women's under-representation among office holders. This finding echoes the conclusion by Wasserman (forthcoming) and highlights the role of voter preferences and, more important, of the simple shortage of female candidates that remain the most important factors in explaining women's under-representation in politics.

We also analyse whether the electoral victory of female candidate differently affects the re-contesting decisions of candidates other than the top two and whether it favours the entry of new candidates of the same gender. Evidence indicates that lower-performing female candidates are more likely to re-contest whenever the election is won by a female candidate.

In contrast, we do not find any evidence that a victory by a woman attracts more new female candidates in the next election.

To the best of our knowledge, Wasserman (forthcoming) is the only other paper that explicitly studies cross-gender differences in re-contesting decisions following electoral outcomes. Wasserman (forthcoming) focuses on novice candidates running in Californian local elections and provides evidence that female candidates are less likely to re-contest than male candidates following an electoral defeat. She further presents evidence in favour of an important role of behavioural explanations. While our results are consistent with this finding and Wasserman (forthcoming)'s preferred interpretation, they differ in several aspects. First, Wasserman (forthcoming) shows that the cross-gender differential reaction to an electoral defeat only holds for novice politicians. In contrast, we find that gender differences in recontesting behaviour, both among winners and runners-up, are more pronounced among older or former candidates. Second, the evidence we report suggests that female candidates also re-contest more frequently than male candidates following an electoral victory. These facts suggests that results reported by Wasserman (forthcoming) do not hold universally.

While we are not able to conclude about the core reason(s) for these discrepancies, the studied contexts differ in several dimensions. First, while Californian local elections are organized using a plurality voting system, French municipal elections use a proportional closed-list majority voting system. Second, the candidates we observe are heads of lists and will become mayors in the event of electoral victory while Wasserman (forthcoming) studies candidates running for a variety of municipal, city, county, and school district councils. As we document below, mayors of French municipalities face important legal and executive responsibilities that substantially exceed those faced by other members of the municipal council. This goes along with mayors benefiting from higher trust from citizens than other politicians and municipal elections being the elections with the highest turnout in France. These latter features also make French municipal elections an appropriate context in which to study candidates' persistence in electoral competition. Finally, California and France generally differ in their institutional and cultural contexts.

More generally, this paper also speaks to the literature that documents differences in attitudes across genders in competitive contexts. Works by Niederle and Vesterlund (2007, 2011) and Kanthak and Woon (2015), among others, demonstrate that women are less comfortable than men in competitive environments and are more likely to shy away from such contexts. This feature is consistent with women representing a smaller share of candidates than men in elections but could also explain the cross-gender difference in persistence following an electoral loss that we document. Closely related is the evidence provided by Kolev et al. (2019), who explore gender differences in funding proposals and document that women are less likely than men to apply again following a rejection of their proposal. Nonetheless, our evidence of a higher propensity of women to stay in electoral races following a victory questions the generalization of women being less competitive than men and opens doors for further research on the asymmetry of persistence in competitive environments with respect to the outcome of the competition.

Additional results we present contribute to the literature on role models in politics. In particular, our finding of lower-performing female candidates being more likely than male candidates to re-contest if the election is won by a woman suggests that a high-achieving female candidate can act as a model for other female office-seekers. Since other male candidates do not modify their decisions in a symmetric direction, this evidence is also consistent with behavioural explanations of the main results, as candidates of different genders interpret the same signal in different ways. In contrast, our investigation of gender differences in the profile of candidates who will enter political competition suggests that electoral victories by women do not trigger the entry of new female candidates. This finding limits the aforementioned role model effect to the set of current candidates and is consistent with Broockman (2014) and Bhalotra et al. (2018), who study close US and Indian legislative elections and find no support for a larger entry of women in politics in the aftermath of a female candidate winning an election.

The remainder of the paper is organized as follows. Section 2 describes the institutional and political context of French municipal elections. Section 3 lays out the data and the estimation strategy that will help us to study cross-gender differences in candidates' recontesting decisions. The empirical results are presented, challenged and interpreted in Section 4. Last, Section 5 contains concluding remarks.

Institutional context

Elections take place every six years in French municipalities, the country's lowest level of administrative organization. Voters elect a municipal council, whose members designate the mayor.

A proportional two-round ordered-and closed-list voting system with a majority premium is used in municipalities of more than 3, 500 inhabitants. 5 If no list reaches an absolute majority of votes cast in the first round, a second round takes place between lists whose firstround score is above 10% of registered voters. Municipal council seats are then allocated to the lists as follows: half of the seats are first allocated to the list with the highest vote share; then, the remaining seats are allocated to lists in proportion to votes cast in the decisive round. This allocation ensures that the winning list secures the majority of seats. The total number of municipal councillors is determined by law and ranges from 7 to 69 depending on the size of the municipality. Members of the newly elected council elect the mayor during the first session of the council. While it is not a legal requirement, the mayor is virtually always the candidate who was ranked first on the winning list. The latter is actually the most prominent person on the list as best illustrated by the sample of campaign posters of candidates in the 2008 and 2014 elections, which are available in Online Appendix Figure A1.

Once in office, the mayor is an agent of both the state and the municipality. As an agent of the state, the mayor fulfils administrative duties that include the publication of general laws and executive orders, the application of national safety rules and some judiciary tasks. As an agent of the municipality, the mayor presides over the municipal council, signs contracts on behalf of the municipality, prepares and administrates the budget, rules on municipal properties, organizes the work of the municipal staff and is head of the local police. The mayor is also responsible for building permits and vehicle traffic organization in the municipality's territory. Finally, other important responsibilities of the municipal council to be assumed by the mayor include the security of the town, the professional insertion of the active population, and childhood and youth policy (including the logistics of primary education). Ultimately, the mayor assumes a large number of responsibilities in a variety of areas. While some tasks can be delegated to deputy mayors, the mayor is the only executive authority of the municipal council and is the only member to be legally responsible for the management of the city.

Data from the Baromètre de la confiance politique make it possible to track reported trust of citizens in different political personalities since late 2009. Figure 1(a) displays the share of interviewees who report having much or some trust in different political personalities. French mayors appear to consistently benefit from a higher trust from citizens than other politicians. This and the importance of mayors' responsibilities mentioned above translate into a higher turnout in municipal than in other local elections. As shown by Figure 1(b), which plots turnout in the different rounds of all elections held in France from 1995 to 2020, presidential elections are the only elections to outclass municipal elections in terms of turnout.

Formal involvement of political parties is typically limited in municipal elections. Together with official results, the Ministère de l'Intérieur releases ad hoc political orientation codes that describe local lists' broad political orientation or associate them with national parties or national party alliances. According to these codes, only 46.69% of the lists that ran in the 2008 and 2014 elections were associated with a political party. The remaining lists are predominantly labelled as "liste divers gauche [droite]" (miscellaneous left-[right-]wing list), or simply as "liste divers" (miscellaneous list) if no party affiliation or political orientation is attributed.

A 2000 law mandated lists to be balanced in terms of gender. It was first in force for the 2001 municipal elections and was further complemented by a 2007 law that mandates strict alternation of women and men on lists starting with the 2008 municipal elections.

Importantly, there is no restriction regarding the gender of the head of the list. This decision remains at the complete discretion of participating groups. Only 16.79% of all the lists running in the 2008 and 2014 municipal elections were led by female candidates. These elections resulted in 9.93% of mayor positions being occupied by women.

Data and methodology

This section describes the data used in this paper and describes the estimation strategy.

Election data

We collected the universe of electoral results of municipal elections held in 2008 and 2014 in 2, 853 French municipalities with more than 3, 500 inhabitants. 6 In what follows, we use the term candidate to refer to individuals who are the head of a list.

Of these 5, 706 local elections, we exclude 392 elections (6.87%) that attracted only one candidate. We further restrict the sample to municipalities where the winning candidate actually completed her term. Namely, we further exclude from the sample 807 municipalities (14.14%) in which by-elections will take place before the next national wave of municipal elections or in which the winning candidate is no longer in office by this time. 7 While comprehensive information about the reasons for such events are not readily available, potential causes include cancellation of the election by the national commission in charge of monitoring local elections, massive dismissal of the municipal council and death of the mayor. All these situations are likely to affect the decision of former candidates to run for office again by the time of the next election.

The above restrictions leave us with 4, 572 elections. We exploit candidates' gender information to categorize these elections as single-gender and mixed-gender races depending on the gender of the two candidates who received the highest vote share in the decisive round. 8 Only 80 elections (1.75%) have two women as top two candidates. We further exclude these women-only races from the analysis because they represent an insufficient number of observations for any conclusion to be drawn. This left us with 4, 492 elections, of which 3, 304 (73.55%) are men-only races-elections where the top two candidates are both male-and 1, 188 have top two candidates of different genders. These mixed-gender races account for 26.44% of elections.

We complement the data with 2020 municipal elections results and use fuzzy matching à la Raffo and Lhuillery (2009) on the first and last names of candidates to track candidates across consecutive elections within each municipality. This enables us to determine whether each candidate who runs in 2008 and 2014 will run again for office in 2014 and 2020, respectively.

In total, 14, 382 candidates participated in the selected 2008 and 2014 elections. The average raw re-contesting probability amounts to 39.72%. This figure peaks at 51.63% for the sub- 7 We assemble the list of by-elections using information available from the Ministère de l'Intérieur and from Wikipedia. We use the Répertoire national des élus to check the identity of the mayor by the time of the next election.

8 2, 790 elections (61.02%) were resolved in one round only.

category composed of the top two candidates in each election.

The first round of the 2020 municipal elections took place on March 15, 2020, i.e., just at the start of COVID-19 anti-contagion policies in France. The second round, first scheduled to take place on March 22, was postponed until June 28. This naturally raises the question of whether these elections can be considered comparable to the preceding elections.

For instance, turnout in the first round dropped dramatically to 44.6%, against 65.0% on average in the first rounds of the 2008 and 2014 municipal elections as shown in Figure 1(b).

While some or all of this change might be due to the start of the COVID-19 pandemic, we are not aware of any consistent evidence that the pandemic affected electoral outcomes.9

However, even if the COVID-19 pandemic had impacted the outcome of the 2020 vote, our use of the 2020 data is mainly limited to the identification of candidates. Several facts advocate in favour of the use of 2020 data not being a threat to our results. First, citizens' awareness of the local emergence of the pandemic was low before February 27, 2020, the deadline for candidacy declarations. This is best illustrated by the daily Google search index of the "coronavirus disease 2019" topic plotted in Online Appendix Figure A2(a). This series shows that while interest in the pandemic started before the candidacy declaration deadline, it was still very low compared to that measured by mid-March. This sharply contrasts with the timing of candidacy announcements that is illustrated by Online Appendix of the pandemic (the March 15 peak actually contains articles that discuss the postponing of the second round). Third, our main interest lies in the comparison of the re-contesting decision of female and male candidates, so that the early pandemic would have needed to affect decisions differently for male and female candidates to threaten the use of 2020 data.

While the literature does document differences in risk attitudes across genders and while the average of the re-contesting rate differs over time-for the top two candidates in each election, this share moved from 55.24% to 47.86% between 2008 and 2014-a formal test rejects the hypothesis that the re-contesting rate evolved differently between genders (p-value = 0.377). Finally, differences estimated between genders are of the same order of magnitude when separately using the 2008 and 2014 elections, as we will show.

Methodology

Our analysis of the difference in competition-related persistence across male and female candidates exploits close electoral races and uses a regression discontinuity design.

Political persistence of winners and runners-up

We first study how the re-contesting probability of the top two candidates in each election varies across genders and election outcomes by examining the re-contesting decisions of candidates who barely won or barely lost the election. We follow Cattaneo et al. (2020a, forthcoming, 2020b) by fitting order 1 polynomials using observations that lie within an optimal range of vote margins. 10 Formally, we select the top two candidates in mixed-gender races and estimate the following expression:

P (R i,t+1 ) = α L g + α W g × 1(Margin i,t > 0) +β g × Margin i,t + γ g × Margin i,t × 1(Margin i,t > 0) + ε i,t , if g(i) = g, for g = m, f, (1)
where

P (R i,t+1 ) is equal to 1 if candidate i running in t = 2008, 2014 runs again in t + 1 = 2014, 2020, Margin i,t is the victory or loss margin of candidate i in t, 1(Margin i,t > 0)
identifies winners, ε i,t is the error term, g(i) is the gender of candidate i, and m and f identify male and female candidates, respectively.11 We select observations to be used in the estimations by allowing for different optimal bandwidths for each gender and each vote outcome. The bounds of these intervals are used to construct triangular kernel weights that assign greater importance to observations near the cut-off.

The estimate of α L g provides us with the re-contesting probability of losers, while that of winners is given by α L g + α W g . The effect of an electoral victory on the re-contesting decision is captured by α W g . Differences in these quantities across genders can be calculated directly from differences in estimates obtained for male and female candidates. To further facilitate the interpretation of these estimated re-contesting probabilities, we also estimate expression

(1) over the sample composed of the top two candidates in men-only races. We account for the small sample size by calculating p-values of differences across genders, vote outcomes and groups calculated from permutations of gender, outcome and group.

Persistence of other candidates and attraction of new candidates

Comprehensive election results also allow us to observe the re-contesting decision of candidates in an election other than the top two. To formally study how the electoral victory of a woman affects other candidates' decision to run again for office, we select all but the top two candidates in mixed-gender races and estimate the following expression:

P (R i,t+1 ) = α L g + α W g × 1(Margin j(i),t > 0) +β g × Margin j(i),t + γ g × Margin j(i),t × 1(Margin j(i),t > 0) + ε i,t , if g(i) = g, for g = m, f, (2)
where the notation is the same as in expression (1) except that Margin j(i),t denotes the vote margin of a female candidate who is among the top two candidates in election j in which candidate i participates.

In expression (2), α L g captures the re-contesting probability of candidates of gender g if a male candidate barely wins the mixed-gender race and α L g + α W g denotes the re-contesting probability of candidates of gender g if a female candidate wins the election. As before, α W g measures the change in the re-contesting decision that is induced by the victory of a woman.

In contrast to the analysis of the top two candidates, no similar estimates can be constructed for male and female candidates in races where the top two candidates are both male. We will thus simply compare the estimates of interest to raw re-contesting probabilities of male and female candidates among the top two candidates in men-only races.

While the above-presented analyses study the re-contesting decision of running candidates, the comprehensive list of candidates also allows us to identify new candidates, i.e., candidates who ran in some election but did not run in the preceding election. This makes it possible to test whether the gender of future new candidates differs depending on the gender of the current winning candidate. To this end, we use mixed-gender races and estimate the following expression:

n j,t+1 = α L + α W × 1(Margin j,t > 0) +β × Margin j,t + γ × Margin j,t × 1(Margin j,t > 0) + ε j,t , (3)
where n j,t+1 denotes the number of new candidates of some type in an election held in municipality j at time t + 1 and Margin j,t denotes the vote margin of the female candidate who is among the top two candidates in the election held in municipality j at time t.

In expression (3), α L captures the limit value of n when a female candidate barely lost the election against a male candidate, α L + α W represents the mirror quantity when the genders of the winner and runner-up are switched, and α W is the difference between these two situations. As in the analysis of the re-contesting decision of other candidates, comparing these estimates to the average value of n in men-only races will facilitate interpretation.

Results

In this section, we first present estimates of differences across genders in win-induced changes in the re-contesting decisions of the top two candidates. We then investigate the robustness of results and discuss mechanisms at play. Finally, we study how the decisions of other candidates are affected by the gender of the winner and whether the latter affects the entry of new candidates in the next election. (runners-up). Estimating expression (1) will allow us to obtain more precise estimates thanks to polynomial approximations obtained from observations that lie within optimally selected ranges.

Political persistence of winners and runners-up

Main results

Estimates of re-contesting probabilities that flow from expression (1) are displayed in Table 1.

Unsurprisingly, winners of an election are more likely than runners-up to run again in the next election. The difference in the re-contesting rate across vote outcomes is positive and statistically significant within both genders. The win-loss gap amounts 42.8% among female candidates and 28.9% among male candidates. The difference in this gap across genders equals 13.9% (p-value = 0.026). This suggests that the electoral outcome has a stronger effect on the re-contesting decision of female candidates than on that of male candidates.

As shown by the re-contesting probabilities estimated separately for runners-up and winners, this difference consists of both a lower re-contesting rate for female candidates among runners-up and a higher re-contesting rate of female candidates among winners. However, these differences exhibit p-values that question their robustness.

The bottom part of Table 1 displays the estimated re-contesting probabilities of runnersup and winners in men-only races and compares them to those of female and male candidates in mixed-gender races. There are two reasons that the sub-sample of men-only races is an important comparison benchmark. First, the number of observations is larger than for mixed-gender races, thereby leading to a priori more precise estimates. Second, candidates in this sub-sample are, by construction, of the same gender as their opponent, which allows checking whether differences across genders and electoral success observed in mixed-gender races are driven by candidates' gender or by that of their opponent. 12,13 The penultimate line in the bottom panel of Table 1 shows that male candidates in mixed-gender races behave as male candidates in men-only races. This suggests that the effect of the outcome of electoral competition for the former is not driven by the fact that their opponents are female candidates. The last line of Table 1 confirms that female candidates are more affected than male candidates by the outcome of the vote. It also suggests that this difference is mostly driven by a 6.7% lower persistence of female runners-up than that of male runners-up (pvalue =0.049). The positive difference across genders among winners is of the same order of magnitude (4.1%) but is not statistically significant at conventional levels.

Robustness tests

Panels A and B of Online Appendix Table A1 display estimates obtained after modifications to how the optimal bandwidths are selected. The results are hardly affected by using only gender-specific bandwidths or a unique common optimal bandwidth in lieu of gender-and vote outcome-specific bandwidths. Estimates obtained when separately using the 2008 and 2014 elections are presented in panels C and D of Online Appendix Table A1. While the p-values differ, the point estimates are similar across the two sub-samples. A potential explanation for the uncovered cross-gender differences in the decisions to re-contest in municipal elections is that it is a by-product of cross-gender differences in broader political career choices, i.e., of cross-gender differences in the decision to run for other positions. Unfortunately, the French institutional design does not allow us to properly test this because higher-level elections exhibit several features that would make the identification of cross-gender differences in participation decisions unreliable. First, départemental, regional and parliamentary elections are events in which (national) political parties are systematically and strongly involved, what would make it difficult to draw conclusions about candidates' decisions. Second, gender quotas directly or indirectly apply in these elections. Online Appendix C nevertheless tentatively explores cross-gender differences in the decisions of municipal election candidates to run for other local elections.

While designed to explore the mechanisms at play, some of the tests presented below also serve as robustness tests.

Mechanisms

Three potential channels can account for the above-documented gender gap in re-contesting decisions. First, it can be driven by differences in observable characteristics, such as occupation, political ideology, previous experience, incumbency status, age, occupation or municipality size, which may trigger different re-contesting decisions across genders because they may correlate with unobserved selection mechanisms or different outside options or attitudes toward competition. Table 2 and Figures 3(a)-(f) display and plot differences in candidates' observable characteristics across genders and electoral outcomes. Compared to female candidates, male candidates are more likely to have previous electoral experience and are more likely to be on the right in terms of political orientation, and male winners are more likely to be incumbents.14 On the other hand, in close elections, they are similar in terms of age, occupation and likelihood of being the head of a list that is affiliated with a (national) party. Online Appendix Figure A4(a) further shows that male candidates tend to win in slightly larger municipalities. This difference is however driven by very large municipalities as best illustrated by Online Appendix Figure A4(b) that excludes municipalities that have more than 100, 000 inhabitants.

Second, a demand effect could be at play. Uncovered differences in political persistence are consistent with an expected higher probability of being re-elected for female incumbents and a lower probability for female runners-up than for their male counterparts, i.e., a higher incumbency (challenger) advantage (dis-advantage) for women. In addition to this demand by voters, the lower (higher) persistence of female runners-up (winners) could be driven by participating groups deciding to replace female candidates more (less) frequently when they lose (win) than they would for male candidates. Third, behavioural explanations of gender differences in competitiveness may play a large role (Niederle and Vesterlund 2007). These include gender differences in general attitudes towards competition, differences in beliefs about relative performance, and risk and feedback aversion.

Differences in candidates' characteristics

To account for cross-gender differences in observable characteristics that might correlate with the above-documented differences in re-contesting decisions by male and female candidates, we follow Calonico et al. (2019) and re-estimate expression (1) but add variables that identify categories displayed in Table 2 andFigure 3. We allow the effect of these variables to differ across genders and across election outcomes and centre each variable on its sample average to preserve the immediate interpretation of constant terms in model (1). Panels A-H of Online Appendix Table A2 display the estimates of interest obtained when separately accounting for past participation of candidates, incumbency status, age, occupation, political orientation, population and party involvement. Panel G presents estimates that simultaneously account for all dimensions. The estimated re-contesting probabilities and the associated cross-gender differences are similar to those displayed in Table 1 for runnersup. For winners, the positive difference between female and male candidates is stronger and statistically significant when controlling for observable covariates. This suggests that, while female and male candidates do differ on various dimensions, these dimensions do not drive the uncovered differences in re-contesting decisions.

We further explore heterogeneity effects in re-contesting probabilities by estimating (1) for different sub-populations defined by the dimensions previously noted. Table 3 displays the estimates of interest. Panel A splits the sample with respect to candidate participation in the previous election. Among new candidates, women are significantly less likely to re-contest than men regardless of the outcome of the vote. As this lower re-contesting probability is similar for runners-up and winners, it translates to a similar win-induced change in decision across genders. For former candidates, female runners-up are also less likely to re-contest than male runners-up. In contrast, persistence is much larger for female winners who have already participated. These results sharply differ with evidence reported by Wasserman (forthcoming) who uses Californian elections for local councils and documents that new female candidates are more affected by the outcome of political competition than new male candidates and that this difference vanishes with previous electoral experience. In contrast, our estimates indicate that while they are less likely to run again, new female candidates are affected by the electoral outcome like new male candidates and that the gender difference in persistence induced by electoral victories mostly applies to more experienced candidates.

Panel B of Table 3 shows differences in re-contesting probabilities when distinguishing between challengers and incumbents. Among runners-up, the gender gap in political persistence is stronger for challengers. This is consistent with the negative gap in persistence being driven by differences in self-confidence, which translates into greater discouragement for women if they lose, which is mitigated if they have won in the past. Note that the greater perseverance of female winners reported previously is no longer significant when dividing the sample along the incumbency dimension and when controlling for incumbency status alone (Panel B of Table A2). Thus, the higher proportion of male incumbents combined with the overall propensity of candidates to run for a third consecutive term (regardless of their gender) partially explains the average positive gender gap in persistence among women.

Panel C of Table 3 displays the estimates when splitting the sample into younger and older candidates using 56 years, the median age, as a cut-off. Among runners-up, the gender gap is negative for both groups. Among younger winners, there is no significant difference in persistence across genders, while among older candidates, female winners are more likely to re-contest than male winners. Interestingly, this difference, contrary to the previous ones, appears to be partly driven by the opponent's gender as suggested by the comparison with males running in men-only elections. Older male winners are less likely to re-run when they win facing a woman than when they win facing another man. 3 further divides the sample depending on candidates' broad political orientation. It shows that left-wing female candidates are less likely than male candidates to re-contest following a loss. In contrast, right-wing female candidates seem to be as persistent as male candidates when losing and slightly more persistent when winning.

Panel D of Table

Panel E of Table 3 tabulates estimates obtained for candidates in different occupations.

It shows that the excess re-contesting probability of female winners only appears for retired candidates and that there are hardly any differences in the re-contesting decisions of female and male candidates who hold occupations in the private sector. In contrast, female candidates employed in the public sector are significantly less likely to re-contest than males employed in the same sector following an electoral loss.

Panel F of Table 3 differentiates between candidates from small and large municipalities, corresponding to those below and above 10,000 inhabitants, respectively. The differences when dividing along this dimension are sharp. While in small municipalities, both female runners-up and winners are less likely to run than their male counterparts, in more populated localities, we recover the asymmetry in cross-gender persistence from the baseline results.

Nonetheless, the estimates are larger in magnitude and significant at the 95% confidence level. Overall, the outcome of an election has an effect 49% higher for female than for male candidates in large municipalities, which is more than three times higher than the baseline estimates. The level of political competition and/or the degree of responsibilities accentuate the cross-gender differences in re-contesting decisions. 15 The estimates for men in men-only elections presented in panels A-F of Table 3 suggest that the documented differences among winners may be triggered by male candidates running in mixed-gender elections behaving differently than male candidates running in men-only races. For instance, older and left-wing male winners of mixed-gender races appear to be less likely to re-contest than male winners of men-only races, while this difference is positive for candidates in small municipalities. In contrast, their female counterparts behave like male candidates in men-only races in these sub-samples. This suggests that the opponent's 15 The estimates are robust when controlling for incumbency status as shown in Online Appendix X.

gender might play a role in explaining some decisions of these particular male winners but not those of comparable female winners.

Ultimately, the sub-sample analyses suggest that the outcome-induced gender gap is concentrated among candidates that are more experienced, challengers, older, retired or occupied in the public sector, and running in large cities. However, the estimates show that differences in these dimensions across genders are not sufficient to explain the uncovered different attitudes across genders following the outcome of elections.

As stated above, another potential explanation for our results is that they are not driven by cross-gender differences in individual decisions but rather by different decisions by other agents depending on the candidate's gender and on the outcome of the elections when selecting the candidate to be head of the list in the next election. To explore this mechanism, panel G of Table 3 distinguishes between candidates depending on whether the list they head is affiliated with a political party. While women are as likely as men to head an affiliated list (see Table 2), a sharp difference in re-contesting probabilities appears along this dimension.

The evidence indicates that non-affiliated female candidates behave like non-affiliated male candidates and that there is no difference in outcome-induced change in behaviour across genders in this sub-sample. In contrast, the sub-sample composed of affiliated candidates features both a smaller re-contesting probability for female runners-up and a slightly larger probability for female winners. This results is compatible with local party members or national parties' staff members taking different decisions toward male and female candidates depending on the outcome of the election. However, it is also compatible with mixed-gender election candidates taking different decisions depending on their gender, the outcome of the vote, and the existence or nature of other involved groups.

Differences in expected outcome

Whether they arise from individual candidates or from the group they are affiliated with, cross-gender differences in re-contesting decisions might be driven by the expected outcome of running again. We undertake two analyses to assess whether such expectations can explain the structure of uncovered decisions.

Let us first assume that candidates form expectations about future elections from the average gender-specific outcome of the election in which they just participated. Figure 4(a) uses 2.5% vote share intervals to plot the distribution of mixed-gender races along the margin of victory of the female candidate. It shows that female candidates are more likely to win close races. As further illustrated by Figure 4(b), the share of winning women is above 50% in races that are resolved with a victory margin that is below 5% of votes cast.

While this contrasts with the average lower probability of female candidates to win against a male opponent, this finding indicates that just-elected female candidates benefit from a vote advantage. This should encourage both female runners-up and winners involved in close races to expect a win if they run again, thereby leading them to re-contest more frequently.

This prediction is at odds with the reported results and cannot explain them.

Another way to form expectations about the returns of re-contesting is to examine the incumbency advantage, i.e., the difference between the future electoral performance of recontesting winners and that of re-contesting runners-up. To check whether this quantity differs between genders, we limit the sample to re-contesting candidates and re-estimate expression (1) replacing the dependent variable with a dummy variable that is equal to one if the candidate wins the next election. This approach provides us with estimates of the (re-)election probabilities of runners-up and winners and allows us to compute the associated incumbency advantage for each gender. Figure 5 plots the probability of victory in the next election for candidates in mixed-gender races. It shows that winners of both genders experience a large electoral advantage over runners-up in the next election. This suggests that female and male candidates benefit from a past electoral victory compared to candidates of the same gender who lost. This is confirmed by formal estimates displayed in the upper part of Table 4 that show that the incumbency-advantage is identical when computed within each gender. However both female incumbents and female runners-up are less likely to be elected in the following election than their male counterparts. In fact, men who previously lost seem to be approximately as likely to be elected as women who previously won. Overall, the evidence suggests that female winners hardly outperform male runners-up in the next election and that female runners-up will likely not perform better if they run again. The bottom lines of Table 4 and Online Appendix Figure A5, that plots the probability of victory of candidates running in men-only races, suggest that the uncovered male-female structure of the incumbency (dis)advantage is particular to mixed-gender races, as male candidates in mixed-gender races also outperform male candidates in men-only races. This is further confirmed by the fact that female winners under-perform less relative to male winners of menonly races than relative to male winners of mixed-gender races. In summary, the returns of running again in the next election appear significantly lower for female candidates regardless of the outcome of the vote. 16,17 This finding is consistent with female candidates being less likely to re-contest regardless of the outcome of the vote but cannot explain the abovedocumented cross-gender difference in the win-induced change in the re-contesting decision because the latter consists of both a lower persistence of female runners-up and a higher or equal probability of female incumbents to re-contest. 16 Brollo and Troiano (2016) also report a lower re-election rate for female incumbents in Brazilian municipal elections than for male incumbents. They attribute it to gender differences in strategic behaviour when seeking re-election, as male incumbents attract more campaign contributions and are more likely to increase temporary public employment. This gap could also be explained by differences in performance if female incumbents prove less successful than male incumbents in managing the municipality during their term. Lippmann (2019) studies French municipal elections in the smallest municipalities and reports that female candidates have more difficulty replacing a female than a male incumbent. He discards supply-side mechanisms, such as a shortage of qualified women or differences in performance, and instead highlights behavioural effects such as a backlash or stereotype threat.

17 As discussed in Section 3, the first round of the 2020 municipal elections took place at the onset of the COVID-19 pandemic, and both rounds were characterized by unusually low turnout rates as shown by Figure 1(b). These features might have affected the choice of voters and the observed distribution of (re-)election outcomes of re-contesting 2014 candidates. To ensure that this particular context does not drive our estimates of the incumbency advantage, Online Appendix Table A3 displays the (re-)election probabilities estimated when separately using the 2008 and 2014 elections (and the 2014 and 2020 election outcomes, respectively). Importantly, the structure of the incumbency (dis)advantage across genders is similar in both election waves as shown by panels A and B. Only the reference gap (estimated from men-only elections) fully differs. The incumbency advantage cannot be regarded as different from zero for the 2008 candidates who ran in the 2014 elections. In contrast, it is very large for the 2014 candidates who ran in the 2020 elections. Explaining this important average change and assessing whether it is due to the COVID-19 pandemic or to other events that occurred between 2014 and 2020 is beyond the scope of this paper.

Behavioural explanations

Behavioural explanations of gender differences in attitudes toward competition are hardly testable outside the experimental environment. However, several arguments speak in favour of this class of mechanisms to explain the documented cross-gender differences in re-contesting decisions. First and as discussed above, composition effects and differences in expected returns cannot fully explain the uncovered differences. Second, the sub-sample analysis that splits the sample along candidates' political orientation shows that differences across genders are more important among left-wing than among right-wing women (Table 3, panel D). This dimension likely correlates with unobserved but large differences in values, norms, beliefs and attitudes. This therefore leaves room for an important role of behavioural explanations that would also be consistent with the fact that reported differences are larger when the candidate's list is formally affiliated with a political party.18

Persistence of other candidates and the attraction of new candidates

Figure 6 plots the local average re-contesting rate of candidates who are not among the top two candidates in each election depending on candidates' gender and the gender of the winning candidate of a mixed-gender race. Both male and female candidates seem to be less likely to run again in the next election if the race is won by a male than by a female candidate. Visual observation further suggests that female candidates are more likely than their male counterparts to run again if a female candidate wins the election. Estimates of expression ( 2) are displayed in Table 5 and help us to rigorously test these claims.

Formal tests reject the hypothesis that men behave differently when a man or a woman wins the election (p-value = 0.217). In contrast, female candidates experience a 24.0% increase in their re-contesting decision rate if a woman wins the race (p-value = 0.008). To further interpret the estimates, we compare the re-contesting probabilities of male and female candidates in mixed-gender races to the raw re-contesting rate of male and female candidates in men-only elections. As shown by the bottom panel of Table 5, formal tests suggest that the only group that consistently differs from the others is female candidates who are more likely to run again if a woman wins the election. This effect can arise from women updating their beliefs on voters' preference for politicians' gender and greater self-confidence after a woman has won the previous election. It is however not accompanied by a decline in the re-contesting decision of male candidates when the election is won by a woman. This would therefore suggest that male and female candidates differently interpret the same signal.

Table 6 displays estimates of expression (3). While the total number of new candidates seems to be slightly larger when a man wins a mixed-gender race than when a woman does, both quantities cannot be considered statistically different from the average number of new candidates observed in men-only races. Similarly, electoral victories by female candidates do not appear to induce a significant change in the number of male or female new candidates. This result is consistent with Broockman (2014) and Bhalotra et al. (2018) who study close US and Indian legislative elections and find no evidence of a larger entry of women in politics in the aftermath of a female candidate winning an election.

Conclusion

The evidence we present in this paper documents cross-gender differences in re-contesting decisions following electoral victories and defeats. We find that women are equally or more likely to re-contest than men if they win. In contrast, our results indicate that female candidates are significantly more likely than male candidates to exit political competition after an electoral defeat. Importantly, we show that differences in characteristics between women and men enrolled in close elections do not drive these differences and that voters discrimination against women cannot fully account for the documented gaps. This leaves room for behavioural explanations of these differences, as further suggested by their stronger expression among sub-categories of candidates that share specific characteristics. Our results are thus generally consistent with the literature that documents differences in attitudes across genders in competitive contexts (see Niederle and Vesterlund 2007, 2011 and Kanthak and Woon 2015, among others). Specifically, the observed higher discouragement of female runners-up supports previous findings by Kolev et al. (2019) and Wasserman (forthcoming), who emphasize that, following a negative competition outcome, women are less likely than men to make a new attempt.

We also analyse whether the electoral victory of a female candidate differently affects the re-contesting decision of candidates other than the top two candidates and favours the entry of new candidates of the same gender. Evidence indicates that lower-performing female candidates are more likely to re-contest whenever the election is won by a female candidate.

In contrast, we do not find any evidence that a victory by a woman attracts more new female candidates in the next election.

We undertake a final quantification exercise to assess the relative contribution of crossgender differences in persistence in explaining women's under-representation in politics. Online Appendix D presents the simplified model we use and calibrate by employing estimates presented in the paper. We find that differences in persistence across genders cannot be considered the main driver of women's under-representation among office holders. This channel can at best account for one-tenth of observed female under-representation. This finding is in line with Wasserman (forthcoming) and contrasts with the importance of voters discrimination representing the most important mechanism to explain the low share of women among office holders for a given intensity of female participation in politics. In addition, both mechanisms hardly compete with the simple shortage of female candidates that remains the main driver of women's under-representation in politics. We developed an ad hoc procedure to distinguish between new and former candidates among participants in the 2008 municipal elections. To ensure that the above-presented procedure introduced no bias in the reported estimates, Table B1 reproduces the sub-sample decomposition along past electoral participation of candidates but excluding all 2008 municipalities for which information about 2001 candidates is incomplete. The estimates differ little from those displayed in panel A of Table 3. elections. In parliamentary elections, candidates run in ordered pairs consisting of a main and a substitute candidate. We collected the composition of the 6, 602 (7, 877) pairs of candidates that participated in the 2012 (2017) parliamentary elections.

B Incomplete information about 2001 candidates and imputed past participation of 2008 candidates

We next matched these lists to that of candidates in the municipal elections to assess whether the latter decided to run in higher administrative level elections before the next municipal election took place. We matched 2008 candidates to candidates in the 2010 regional, 2011 départemental and 2012 parliamentary elections and 2014 candidates to candidates in the 2015 regional, 2015 départemental and 2017 parliamentary elections. We then estimated model (1) using as the dependent variable a dummy variable equal to one if a candidate in the 2008 or 2014 municipal elections ran in any of the next higher-level elections. Table C1 displays the estimates of interest and shows that candidates in municipal elections are less likely to run for other local elections than to re-contest the next municipal election (see Table 1). This fact is however likely to be largely mechanical because there are more positions to be taken in municipal elections than in other local elections.

Table C1 conveys several important messages. It first shows that female runners-up's decisions about participating in other elections do not significantly differ from those of male runners-up. Second, while female winners appear slightly less likely than male winners to participate in other elections, so do the latter when compared to male winners of men-only races. Third, win-induced changes in running probabilities are lower than those estimated for the probabilities to run again in municipal elections. Ultimately, the estimates do not provide evidence of female candidates having an attitude that strikingly differs from that of male candidates regarding decisions about participating in other elections, and the revealed differences in these attitudes cannot account for the documented cross-gender differences in re-contesting decisions.

D Comparison of the relative importance of channels in explaining the gender gap in office holding

Let us consider a population of female and male candidates who run for office in pairs.

Genders are denoted by g = f, m. Candidates can be either new or experienced depending on whether they are running for the first time. Let us model the victory probability of candidate i who is opposed to candidate j using a simple contest success function:

P (e i , e j ) = e i e i + e j , where (i, j)

∈ f N , f E , m N , m E 2 .
After elections have taken place in t, the quantity of winners of type g Y is given by:

W Y g (t) = s Y g (t) 2 + 2s Y g (t) s j (t)P e Y g , j , j∈{( f N ),( f E ),( m N ),( m E )}\( g Y ) (D1)
and the quantity of losers of the same type is:

L Y g (t) = 2s Y g (t)
s j (t) 1 -P e Y g , j .

j∈{( f N ),( f E ),( m N ),( m E )}\( g Y ) (D2)

These quantities enable us to express the share of women among elected candidates as:

S f (t) = W N f (t) + W E f (t) 1/2 . ( D3
)
Let us further model candidate persistence in political competition with p W g and p L g being the probabilities that a candidate of gender g will re-contest the next election if she won or lost, respectively.20 Using the above expressions, the quantity of t candidates of gender g = f, m who will re-contest in t + 1 and be considered experienced by this time is:

s E g (t + 1) = p W g W Y g (t) + p L g L Y g (t), (D4)
and, assuming that exiting candidates are randomly replaced by new candidates among whom the share of women is denoted by θ 0.5 that captures whether women are less, equally or more likely than men to enter political competition, the quantity of new female candidates running in the next elections is:

s N f (t + 1) = θ   1 - g=f,m (1 -p W g )W Y g (t) + (1 -p L g )L Y g (t)   , ( D5
)
while that of new male candidates is:

s N m (t + 1) = (1 -θ)   1 - g=f,m (1 -p W g )W Y g (t) + (1 -p L g )L Y g (t)   . (D6)
Denote by S t = S f (t), s N f (t), s E f (t), s N m (t), s E m (t) the state vector that describes the outcome of elections and the composition of the pool of candidates at time t. S t+1 is linked to S t+1 via equations (D1)-(D6). It can be verified that the S t series converges to S * , the stationary equilibrium value of the series.

While the model can a priori be solved analytically, the number of possible pairs of candidates makes the necessary expressions nearly intractable. We thus opt for a numerical solution approach. For each potential value of θ, we simulate the model over 1, 000 periods and store the average value of the share of women among office holders in the last 90% of periods. 21 by 1% if the gender gap in persistence is at play. This discrepancy sharply underlines the relative importance of both channels in explaining the gender gap in office holding.

Alternatively, the share of women among office holders for a given share of women among new candidates can also help to grasp the relative importance of the channels. As shown by Figure D1(b) for a gender-balanced set of new candidates (θ = 0.5), this quantity amounts to 39.5% when both voters discrimination and the gender gap in persistence are at play, against 40.9% and 49.0% when only the former and the latter are active. This suggests that differences in persistence explain only 10% of the gender gap in office holding (as measured with respect to the share of women among new candidates). 23 Finally, the overall pattern of Figures D1(a) and (b) makes clear that none of the abovediscussed mechanisms can account for the gender gap in office holding as much as a simple shortage of female candidates. This suggests that the latter remains the main driver of women's under-representation in politics.

Figure

  FigureA2(b). This series was constructed using Cision Europresse-a media monitoring platform-and counting the weekly number of French press articles that relate to candidacy announcements. It shows that candidacy announcements occurred many months before the official candidacy declaration deadline and before COVID-related interest actually started.Second, the pandemic spread was low at the time candidates decided to run for election.As shown by Online Appendix FigureA2(c), no hospitalizations for COVID-19 suspicion were recorded before February 27. Similarly, postponing the municipal elections was not

Figure 2

 2 Figure 2 uses moving windows of 2% vote margin to plot the re-contesting probability of the top two candidates in mixed-gender races by gender and vote outcome for candidates whose vote margin lies within the [-25%, 25%] interval. The quantities of interest are the values of the four series next to the 0% margin. Visual observations of the series suggest that female winners (runners-up) are slightly more (less) likely to re-contest than male winners

Figure 1 :

 1 Figure 1: Trust in political personalities and electoral turnout.

  (a) Trust in political personalities. (b) Turnout. Sub-figure (a) uses the Baromètre de la confiance politique and plots, for each wave of the survey, the share of interviewees who report to have much or some trust in different political personalities. The question is framed as follows: "Avez-vous très confiance, plutôt confiance, plutôt pas confiance ou pas confiance du tout dans les personnalités politiques suivantes: Le maire de votre commune (your municipality's mayor) ; votre conseiller général (your representative at the départemental level) ; vos conseillers régionaux (your representatives at the regional level) ; votre député (your member of parliament) ; le président de la République actuel (the current President)." Sub-figure (b) uses official reports from the Ministère de l'Intérieur and plots turnout at the different rounds of all elections held in France from 1995 to 2020, but at referenda and European elections. For each series, the line goes through the values of average turnout across the two rounds of each election.

Figure 2 :

 2 Figure 2: Re-contesting probability of runners-up and winners by gender in mixed-gender races.

Figure 3 :

 3 Figure 3: Differences in individuals' characteristics.

Figure 4 :

 4 Figure 4: Wins of female candidates in mixed-gender races.

  (a) Distribution of races. (b) Female candidate's probability of victory. The sample is made of 2008 and 2014 elections whose two best candidates are of different genders. Sub-figure (a) plots the distribution of gender-mixed races along the margin of victory of the female candidate using 2.5% vote share intervals. Sub-figure (b) plots the share of winning females within each interval.

Figure 5 :

 5 Figure 5: Probability of victory in the next election of runnersup and winners by gender in mixed-gender races.

Figure 6 :

 6 Figure 6: Re-contesting probability of other candidates by gender in mixed-gender races.

Figure A2 :

 A2 Figure A2: COVID-related online search, press coverage of candidacy announcements, COVID-related hospitalizations and press coverage that report about postponing the election around the 2020 candidacy declaration deadline.

Figure A3 :

 A3 Figure A3: Re-contesting probability of runners-up and winners in men-only races.

Figure A4 :

 A4 Figure A4: Differences in municipality size.

  Population, excluding municipalities of more than 100, 000 inhabitants.

Figure A5 :

 A5 Figure A5: Probability of victory in the next election of runnersup and winners in men-only races.

Figure

  Figure B1(a) illustrates the initial situation in a fictitious municipality. This municipality has 7 and 5 candidates in the 2008 and 2001 municipal elections, respectively. 19 The data allow us to identify all of the 2008 candidates but only a share s 2001 of the 2001 candidates as illustrated by the presence of (fictitious) first names or question marks next to candidates' symbols. Starred 2008 candidates are the top two candidates in this election. We first use the comprehensive list of 2008 candidates and link them to identifiable 2001 candidates using a fuzzy matching à la Raffo and Lhuillery (2009) on candidates' first and last names within each municipality. Matches allow us to identify some 2008 candidates who were former 2001 candidates, such as Gabriel and Emma in Figure B1(b), as well as 2001 candidates who will run in 2008 as illustrated by the case of Lucas in Figure B1(b). This step leaves us with a set N 2001 of n 2001 non-identifiable 2001 candidates and two types of 2008 candidates: n * 2008 ∈ {0, 1, 2} candidates of type N * 2008 who belong two

Figure B2 :

 B2 Figure B2: Distributions of past candidacy status of 2008 candidates across municipalities with incomplete and full information about 2001 candidates.

Table 1 :

 1 Re-contesting probability of runners-up and winners by gender. of differences reported in brackets. Re-contesting probabilities estimated from expression (1) with gender-and vote outcomespecific optimal bandwidths and triangular kernel weights. Observations are candidates who ran in the 2008 and 2014 municipal elections. A 2008 (2014) candidate is considered as re-contesting if she will run again for office in 2014 (2020). The sample is restricted to the best two candidates of each election. Mixed-gender races are elections whose two best candidates are of different genders. Men-only races are elections who two best candidates are both males. P-values of differences across genders, vote outcomes and groups calculated from 1, 000 permutations of gender, outcome and group, respectively.

	Runners-up	Winners	Win -loss gap

Table 2 :

 2 Within-gender distributions of past participation, incumbency status, age, political orientation, occupation, municipality size and party involvement.Observations are candidates who ran in the 2008 and 2014 municipal elections. The sample is restricted to the best two candidates of each election. Mixed-gender races are elections whose two best candidates are of different genders. Men-only races are elections who two best candidates are both males. New and former candidates are 2008 (2014) candidates who did not or did run in the 2001 (2008) elections. See Online Appendix B for the ad-hoc procedure used to assess participation of 2008 candidates in 2001 elections. Young (old) candidates are candidates who are younger (older) than 55 by the time if the election. Incumbents are listed in the Répertoire national des élus. Left-and right-wing candidates are identified from lists' political orientation as coded in official elections results. Occupations listed in the Répertoire national des élus have been used to asses whether candidate are retired or occupied in the public or private sectors by the time of the election. Small and large municipalities are municipalities with less and more than 10, 000 inhabitants, respectively. Candidates are considered as affiliated or non-affiliated depending on whether the list is linked to a national political party or parties alliance or not in official elections results.

		Mixed-gender races	Men-only races
		Females	Males	Males
	New candidates	797 (67.1%)	510 (42.9%)	3,460 (52.4%)
	Former candidates	384 (32.3%)	671 (56.5%)	3,106 (47.0%)
	Unknown	7 (0.6%)	7 (0.6%)	42 (0.6%)
	Challengers	889 (74.8%)	561 (47.2%)	3,979 (60.2% )
	Incumbents	299 (25.2%)	627 (52.8%)	2,629 (39.8%)
	Young candidates	592 (49.8%)	450 (37.9%)	2,802 (42.4%)
	Old candidates	566 (47.6%)	713 (60.0%)	3,608 (54.6%)
	Unknown	30 (2.5%)	25 (2.1%)	198 (3.0%)
	Private sector job	388 (32.7%)	420 (35.4%)	2,444 (37.0%)
	Public sector job	334 (28.1%)	250 (21.0%)	1,475 (22.3%)
	Retired candidates	359 (30.2%)	500 (42.1%)	2,576 (39.0%)
	Unknown	107 (9.0%)	18 (1.5%)	113 (1.7%)
	Left-wing candidates	587 (49.4%)	489 (41.2%)	2,862 (43.3%)
	Right-wing candidates	544 (45.8%)	632 (53.2%)	3,341 (50.6%)
	Others	57 (4.8%)	67 (5.6%)	405 (6.1%)
	Small municipalities	743 (62.5%)	743 (62.5%)	4,186 (63.3%)
	Large municipalities	445 (37.5%)	445 (37.5%)	2,422 (36.7%)
	Non-affiliated candidates	574 (48.3%)	571 (48.1%)	3,259 (49.3%)
	Affiliated candidates	614 (51.7%)	617 (51.9%)	3,349 (50.7%)

  Available data for the 2001 municipal elections are separated into two distinct data sets. On the one side, official elections results are made available at the list level, but the data do not contain the name of the list or the name of the candidate who leads it. Only the political orientation code created by the Ministère de l'intérieur is available from these data. On the other hand, a list of all heads of list is available. This data set also contains the name of the list and its political orientation code. The data set is however incomplete because not all municipalities are included in these data and because the name of the candidate is blank for 35.01% of the observations and only all 2001 candidates are identifiable in only 42.40% of the 2008 municipalities. Neither source can thus be used to directly identify 2008 candidates who ran in 2001.

  These types are denoted by N and E, respectively. Label shares of types of candidates in the population at time t as s N f (t), s E f (t), Y g the exogenous campaigning effort of a candidate of gender g = f, m and experience Y = N, E. Let us assume that experienced candidates benefit from an electoral advantage E and that female candidates suffer from a disadvantage F because of voters discrimination. The campaigning efforts of the different types or candidates are:

	s N m (t) and s E m (t).
	Denote by e

See Niederle and Vesterlund (2007),[START_REF] Niederle | Do women shy away from competition? Do men compete too much?[END_REF],[START_REF] Rask | The role of grade sensitivity in explaining the gender imbalance in undergraduate economics[END_REF],[START_REF] Kanthak | Women don't run? Election aversion and candidate entry[END_REF],[START_REF] Ellison | Dynamics of the Gender Gap in High Math Achievement[END_REF],[START_REF] Kolev | Is Blinded Review Enough? How Gendered Outcomes Arise Even Under Anonymous Evaluation[END_REF],[START_REF] Kaganovich | Gender Differences in Persistence in a Field of Study[END_REF] and[START_REF] Kugler | Choice of majors: are women really different from men?[END_REF], among others.

The electoral system varies according to the size of municipalities. Two-round plurality-at-large with panachage voting is used in smaller municipalities: voting takes place at the candidate rather than at the list level, and voters can vote for more than one candidate and/or vote for candidates from different lists. The threshold below which this voting system is used was lowered to 1, 000 inhabitants beginning with the 2014 municipal elections.

As of 2014, France comprised 36, 617 municipalities and had a total population of 64, 129, 660 inhabitants (Insee, 2016). The 2, 853 municipalities with more than 3, 500 inhabitants contain 28, 3555, 634 registered voters. This represents 59.57% of 47, 602, 881, the total number of registered voters in 2014.

[START_REF] Cassan | Contaminé? Estimating the impact of French municipal elections on COVID-19 spread in France[END_REF] provide suggestive evidence that turnout differences across départementsthe third-highest administrative level in France-were not associated with differences in the early spread of the pandemic, measured by official hospitalization records, by the time of the first round.

The main assumption for the validity of this regression discontinuity design is the continuity of potential outcomes. Although "inherently untestable"[START_REF] Cattaneo | Randomization Inference in the Regression Discontinuity Design: An Application to Party Advantages in the U.S. Senate[END_REF], its violation would require "a substantive scenario about particular sorting behavior" of candidates "that [would push] would-be barely-losers up above the threshold or [would move] potential barely-winners down below the threshold" (de la Cuesta and Imai 2016).

Estimating (1) for each gender is fully equivalent to estimating an unique more general expression that would include all interaction terms between genders and winning statuses or to estimating a separate expression for each of the four combinations of gender and winning status.

As explained in Section 3, the number of female-only races is unfortunately too low to allow for a similar comparison with candidates in elections in which the top two candidates are both women.

See Online Appendix FigureA3for a graphical representation of the re-contesting probabilities of runners-up and winners in men-only elections that mirrors Figure2.

The participation of 2014 candidates in 2008 elections is assessed exactly as future participation of 2008 candidates in 2014 elections. Data on the 2001 elections do not allow us to identify all participating candidates, and the participation of 2008 candidates in the 2001 elections is thus assessed using available information and an ad hoc imputation procedure. See Online Appendix B for more details.

This interpretation leaves unanswered the question of the main source of the behavioural bias. While political party staff can play a role, it is also possible that candidates take different decisions when surrounded by affiliated partisans or that members of a list behave differently when affiliated with a political party.

The sample is made of 2008 and 2014 elections whose two best candidates are of different genders. Each sub-figure plots the local average of municipalities' size along the margin of victory of the female candidate using 2.5% vote share intervals. Sub-figure (b) excludes 35 municipalities with more than 100, 000 inhabitants.

We use official results to retrieve the number of candidates running in

in municipalities that are missing from the list of candidates.

This simplified framework neglects the possibility of an incumbency (dis)advantage and, therefore, of a possible difference in this dimension between genders. However, if relevant in explaining the gender gap in office holding, such a mechanism would mostly translate into cross-gender differences in persistence as discussed in the main text, which are explicitly modelled here.

The number of replications ensures that numerical solutions converge to the solution that would be obtained after the model is solved analytically.

Introducing only the experience premium has no impact on the share of women among office holders because it has no gender-related effect in the absence of voters discrimination or a gender gap in persistence.

The share that can be attributed to differences in persistence between genders is 50-49.0 50-39.5 = 0.097. The share that can be attributed to voters discrimination against women is50-40.9 50-39.5 = 0.867. The share that can be attributed to the interaction of the two channels is 1 -0.097 -0.867 = 0.036. Performing the same calculation at other values of θ leads to similar results.

This work was supported by the French National Research Agency (grant ANR-17-EURE-0020), by the Excellence Initiative of Aix-Marseille University -A*MIDEX, by the Région Provence-Alpes-Côte d'Azur (APEX 2019 : POLF) and by the Fonds Wetenschappelijk Onderzoek -Vlaanderen (FWO) and the Fonds de la Recherche Scientifique -FNRS under EOS Project O020918F (EOS ID 30784531).

a Aix-Marseille University, CNRS (Aix-Marseille School of Economics).

Online Appendix

A Supplementary tables and figures

C Participation of winners and runners-up in higher-level elections

As stated in the main text, the French institutional setting does not make it possible to properly study cross-gender differences in the decisions of municipal election candidates to run in other local elections. Départemental, regional and parliamentary elections are indeed elections in which (national) political parties are much more involved than in municipal elections, and gender quotas directly or indirectly apply in these elections. These features would therefore make it difficult to draw conclusions about cross-gender differences in candidates' decisions to participate.

In départemental elections, which use an uni-nominal majority two-round voting system at the canton level to elect members of the départemental assembly, representatives are elected in unordered pairs consisting of one female and one male candidate since 2015, such that exactly 50% of candidates are female. The scope of regional elections, which use the same proportional two-round ordered-and closed-list voting system as municipal elections, mechanically reduces the number of heads of list, whose gender is unregulated, such that only the detailed lists would contain a sufficient number of observations. Lists must however be gender-balanced such that half of the candidates are female. Finally, funding penalties have been imposed since 2002 on political parties that do not nominate enough women in parliamentary elections, which use a uni-nominal majority two-round voting system at the legislative constituency level to elect members of the French parliament, such that the proportion of women in candidates has consistently increased, reaching approximately 40% in 2017 (Lippmann 2021).

Ultimately, départemental, regional and parliamentary elections are contexts that do not allow us to cleanly investigate cross-gender differences in individuals' decisions to run. To nevertheless explore these dimensions, we collected the lists of candidates running in local elections that followed the 2008 and 2014 municipal elections. We collected the names of the 10, 357 (18, 187) candidates running in the 2011 (2015) départemental elections and of the 262 (183) heads and 20, 671 (21, 880) members of lists in the 2010 (2015) regional Finally, introducing an electoral advantage in favour of experienced candidates makes the situation, as depicted by the sold grey line, closer to gender parity because, among winnerswho are more likely to re-contest than losers-women are marginally more likely to re-contest than men and are therefore more likely to benefit from this experience premium. 22 The curves in Figure D1(a) allow us to compute the share of women among newly entering candidates that would be necessary to achieve gender parity among office holders under the different scenarios. If voters discrimination against women is the only active mechanism, then women should represent 59% of new candidates. This necessary share is further increased