Can even still be uneven? The effect of quotas in Portuguese local governments

ABSTRACT Portuguese society has undergone considerable progress towards addressing gender issues. From the education system to the job market, many changes promoting gender equity have taken place. In the political sphere, the implementation of regulations on gender quotas marked a significant milestone. Since 2006, party lists have been required to meet a gender diversity quota of at least 33%. However, the implementation of such policies necessitate a more detailed analysis. This paper focusses on the impact of quota regulations on the composition of municipal councils. Based on an analysis of the data from the municipal elections from 1978 to 2017, our research supports two major findings. First, the introduction of quota regulations considerably increased the number of women in office, but also created a glass ceiling around the legal threshold. Second, an institutional history of gender diversity and a competitive political environment are both factors that boost the number of women elected.


Introduction
The last decade has seen major improvements in the level of female representation in elected positions.In late 2020, there was an average female representation of 25.5% in lower or single house seats worldwide, which marked an improvement from the 19% recorded in 2010 and 12% in 1997 1 .Although there have been improvements in female representation in elected offices in the past decade, the results fall short, considering the overall gender distribution in the population.The literature labels this form of underrepresentation of women in politics as political bias (Lawless 2004;Koenig et al. 2011;Rainbow, Lena Krook, and Opello 2012;Devroe 2019).
Across nations, the implementation of gender quota regulations has emerged as a viable solution to remedy the lack of women in politics in a timely manner (Rosen 2017;Jones 2004).These kinds of regulations create a rapid and considerable increase in the number of women in office by establishing a minimum threshold, either in partisan lists or in elected bodies.In this way, such quotas could be considered an extremely effective way to address the issue.Nevertheless, some scholars have pointed out major problems and potential failures with this system (Rainbow, Lena Krook, and Opello 2012;Fréchette, Maniquet, and Morelli 2008).Dahlerup and Freidenvall (2010) claim that one of the most undesirable outcomes of quota regulations is the production of a 'glass ceiling'.Once the defined level of gender diversity is reached, political parties have no incentive to put any additional effort into including more female candidates.This phenomenon is inherent to the very nature of the solution.Quotas do not address the actual internal biases of political actors.They are an outside force imposed on the behaviours and choices of political parties, and are not the result of a gradual repudiation of political bias.
In Portugal, a quota regulation was adopted in 2006.Previously, the data indicated a scarcity of women in politics, at approximately 4% in the first elections after the 1976 democratic revolution.The percentage increased to an average of 7% in the 1980s and 17% in the 1990s.Although some parties had already introduced quotas, a mandatory quota regulation was not implemented until 2006, imposing a minimum of 33% female representation.However, the introduction of quotas had differing impacts depending on the type of election: national parliament, european elections, or local governments.The first aim of this paper is to evaluate the outcomes of these regulations and to examine the creation of a glassceiling effect.
The second is to assess the effectiveness of the changes that resulted from the reform.Building on the work of Verge and Espírito-Santo (2016) and Simón and Verge (2016) this paper analyses how certain factors, such as institutions and political competition, increase the probability of electing more women to office beyond the legal threshold.
The effects of quota legislation have already been studied in Portugal, albeit mainly by focusing on national parliament elections or european elections (Baum and Espírito-Santo 2012;Verge 2013;Verge and Espírito-Santo 2016).In contrast, this paper uses data from the 308 municipal councils of local governments in Portugal.First, by examining the data from 1978-2017 using interrupted time series as the estimation strategy, we assessed the degree of the glass-ceiling effect.Then, using data from the post-quota elections, 2009-2013-2017, we used a multinomial logistic regression to compute the odds of having more women in municipal councils.This research led us to two main conclusions.First, we found evidence that parties with a long history of gender diversity maintain a higher percentage of women in office.Second, a more competitive environment also favours the presence of women above the minimum threshold.
This study aims to clarify the complex dynamics involved in the imposition of quotas.The literature on this subject is not in unanimous agreement, with different studies pointing to both positive and negative effects.Our research also contributes an analysis of a tier of Portuguese government than had not previously been studied.Finally, we add to the literature by exploring how institutions and competition play a role in overcoming the glass-ceiling effect.
The paper is organised as follows: after a discussion about the origins and sources of political bias, we introduce a literature review of gender quota implementation.Then, we present our theoretical hypothesis, followed by the context of analysis.Subsequently, we describe our estimation strategies to fit the main goals of the paper.Lastly, we discuss the results, outline the main findings, and present our conclusion.

Political bias
The problem of political bias is one factor that leads to gender inequality in elected positions.According to the data available at the Inter-Parliamentary Union 2 , women tend to be less represented than men in public offices.These asymmetries in the allocation of men's political power over women reflect the bias present in the structure of institutions, political parties, and society as a whole (Verge 2010).The literature identifies at least three different explanations for this phenomenon: party bias; voter bias; and entry barriers women face in the political sphere.
The party bias links the underrepresentation of women to certain practices and choices made by political parties.This assumption relies on the in-group effect (Niven 1998).That is, people tend to trust and recognise qualities in people who are very similar to themselves.When men dominate the core leadership of political parties, they tend to promote other male candidates, either by putting them in more desirable positions -that is, in higher positions on partisan lists -or in less competitive electoral districts (Fréchette, Maniquet, and Morelli 2008).Women, who do not already belong to the close inner circle of power, suffer, by opposition, from the out-group effect.Members of the in-group consider the out-group to have fewer desirable qualities and weaker political abilities.Hence, party gatekeepers make a poor assessment of the female candidates' political skills, which undermines the odds of making the cut to an elective position or leading the list in an electoral pool (Lovenduski and Norris 1993).
Empirical research has found evidence to support these arguments.Rainbow, Lena Krook, and Opello (2012) found evidence in the French elections from 1997 to 2007 that female candidates were allocated the most challenging seats, while men ran for the most desirable ones.Similarly, Gendźwiłł and Żółtak (2020) stated that when parties reach a decisive moment in terms of ranking their candidates, they will use informal criteria and the perception of the male party elite to exclude women from the distribution of the best positions.
Voter bias can be defined as the prejudice voters have regarding the candidates' gender and their capacity to deal with politics, its procedures and rituals.Fox and Lawless (2004) argued that gender socialisation theory explains the origin of this perception.Society sees women as having different roles to play than men.While men are entitled to have a substantial public and extra-familial career, women are expected to have a private, intra-familial role, carry out housework, and take on family responsibilities much more than their male counterparts.This asymmetric distribution of labour (whereby men can freely adhere to informal schedules of politics) allows men to build a social network that boosts their chances of running for office.
Empirical data portray a reality that places female candidates in a difficult position by reducing their chances of being elected.Additionally, Devroe (2019) and Kahn (1996) have found evidence that voters assume that men are better qualified than women.Giger et al. (2014) found that while women tended to vote without any predetermined gender preference, men usually chose male candidates as their representatives.
Finally, another source of political bias concerns the barriers and lack of incentives women face when entering the political arena.This has more to do with social and political culture, as well as with a sense of self-awareness.Fox and Lawless (2004) found that women perceive parties' political cultures to be excessively hostile.Hence, regardless of their professional accomplishments, women usually consider themselves less qualified than men when running for office.Furthermore, the costs of entering the political realm are gendered: entering the eligibility pool represents a high cost for women compared to the potential gain they have yet to earn (Wolak 2015).

Quota regulation
The introduction of gender quota regulations is one of the most common political solutions employed to overcome the problem of the gender gap in political representation.The use of quotas can circumvent obstacles women face, lead to more egalitarian representation, and rebalance the vertical distribution of power within parties and parliamentary structures (Verge 2010;De Paola, Scoppa, and Alberto De Benedetto 2014).Quotas can be seen as a method of affirmative action intended to compensate those who have faced gender discrimination in politics (Rosen 2017;Fréchette, Maniquet, and Morelli 2008).For Aldrich and Daniel (2019), the adoption of a quota regulation helps to ensure a suitable environment for women running for office, thereby reinforcing the legitimacy and trust in institutions.As mentioned by Baum and Espírito-Santo (2012), quota regulations can be implemented for a variety of reasons, such as pressure from activist groups, strategic decisions made by political elites, general societal values of equal representation, or international trends.Several countries have adopted quota regulations as a solution to unequal representation (Rosen 2017;Jones 2004): Argentina (1991), Belgium (1994), Brazil (1997), Mexico (1996), Peru (1997), France (2007), Spain (2007), Poland (2006), Slovenia (2005), and Portugal (2006).
Since quotas began to be implemented, research has focused on assessing the effects of such regulations.Rosen (2017) finds that the very nature of quotas -voluntary or mandatory -is tied to the magnitude of the increase of women in the national parliament.De Paola, Scoppa, and Alberto De Benedetto (2014) demonstrated that quota regulations had a positive impact on voter turnout, while Aldrich and Daniel (2019) found evidence that suggested quotas may reduce barriers to entry and promote the election of women with prior political experience.Górecki and Kukołowicz (2014) showed that the introduction of a quota initiative had a complex and nonlinear relationship with the electoral system; while some researchers reported positive impacts (Krook 2009;Zetterberg 2009;Beauregard 2017), others collected evidence indicating otherwise (Murray 2004;Kroeber et al. 2019).Therefore, gender quota regulations can differ in their nature, outcome, and effectiveness.

Nature
The nature of quota regulation varies in accordance with each country's political environment and electoral system (Beauregard 2014).According to Dahlerup and Freidenvall (2010), quotas vary in design and method of adoption.The solution for any given country can be found in voluntary quotas, also known as party quotas, where political parties make internal decisions to establish a threshold to be met.Alternatively, the solution can be reached through a legal process that binds all political parties to the same threshold.In this case, sanctions of non-compliance go from simples financial penalties to the exclusion of the list of candidates.
Quotas can also be applied to a pool of candidates (shortlist), candidates nominated by political parties (electoral quota system), and the elected representatives (reserved seats systems) that guarantee a certain level of women's representation and prevent a situation where women are allocated to non-eligible seats.Quotas tend to be quickly adopted after a relevant group (either women or political elites) deems the initiative.

Outcome
According to Dahlerup and Freidenvall (2010), the implementation of quotas has sparked an intense debate over its positive or negative outcomes.These outcomes can be divided into formal and material outcomes.
In formal terms, outcomes are related to observable effects of quota implementation.The clearest of these is the increase in the number of women elected.In practice, the adoption of quotas is a fast-track to boosting the number of women in politics and solving the problem of underrepresentation.With strict implementation, mandatory quotas can rapidly transform the representation of women in office within a single electoral cycle.However, it may carry the risk of breaking the incremental trajectory.That is, there is a chance that quota regulation might disrupt an existing trend of a steady rise of women in politics.Additionally, it might contribute to the formation of a glass-ceiling.Once the percentage of women meets the legal threshold, political parties may feel relieved from pursuing further action to engage women in politics.
Quota regulations can also be credited for enlarging the pool of female candidates.Imposing a minimum level of gender diversity can change the strategies of political parties, forcing them to search for female candidates.In a sense, the demand is creating its own supply, and some barriers put in place by political parties are, by necessity, being overcome.Opponents of quotas claim that there is a risk related to scarcity of supply.If a sufficient number of female candidates are not available, the demand that the quota regulation imposes will compromise the quality and merit of the candidate pool.Female candidates may end up being selected simply because they are needed.
In material terms, the outcomes are more related to the implications for the political debate and for a specific agenda that arises due to the implementation of quotas.In fact, quotas can also create the opportunity to bring up new topics of discussion and contribute to more gender-sensitive dialogue.They also have a potential positive effect on the quality of democracy and the legitimation of policies.Nevertheless, gender quotas can also open the door to other groups demanding positive discrimination initiatives, gradually leading to the 'Balkanisation' of politics.

Effectiveness
The effectiveness of gender quotas depend on the how well the regulations fit the institutions (systematic and normative) of the political system (Krook 2009;Verge 2013).
On one hand, some of the most important institutions are related to the political system, and are therefore common to all parties.One of them is the set of rules of the electoral system.The general understanding is that under a proportional system, gender quotas are more favourable to the election of women compared to majoritarian systems.The explanation is straightforward.If the goal of the quota is measured by the number of women elected, a list of candidates elects more women than does a system where only one winner is elected out of many.
The rules of the electoral party system also play a relevant role.Having a closed or open list leads to different outcomes.While an open list can provide opportunities to move female candidates to more winnable positions, a closed list may ensure compliance to a minimum threshold.A closed list also enhances the power of political parties to impose their choices and reduce the voter's margin of action, which, in this case, is limited to choosing a list and casting a vote.
On the other hand, some institutions are linked with parties and vary across them.The importance of path-dependency and the history of each party should notbe overlooked (Hall and Taylor 1996;Greener 2005).Parties that display an earlier commitment to gender diversity tend to develop internal procedures that lead to the selection of female candidates as a natural part of the party's evolution rather than as an external imposition.Hence, political parties that first started to promote quotas mechanisms have the tendency to develop these norms.These ideals and conventions are self-propagating, leading to more gender diversification than in parties that followed alternative routes.

Main hypotheses
So far, we have discussed political bias as the source of the problem that leads to the underrepresentation of women.Although gender quota regulation has emerged as a solution, there are many constraints to its effectiveness and limitations to the range of its outcomes.Our analysis aims to examine these constraints and limitations.
Our theoretical hypotheses will be divided in two groups: one concerning the outcomes of quotas; the other concerning their effectiveness.
Concerning the outcomes, such a fast track solution has the potential to generate a two stage movement: first, the number of women in office increases substantially; then, there is a chance that the proportion of women in office will display a tendency to 'freeze' around the level defined by the legal threshold (Dahlerup and Freidenvall 2010).This can be identified as the glass-ceiling effect, which has been described as an unseen barrier that keep minorities and women from advancing, regardless of their qualifications or achievements (U.S.Department of Labor 1995).Folke and Rickne (2016) clarify that the glass-ceiling can be noticed in respect to several forms of inequality.It can take the form of unequal access to higher offices that cannot be explained by job-relevant characteristics; gender/racial inequality in appointments to influential positions; poor cross-sectional estimations of inequalities in the probabilities of holding influential positions; or, finally, gender/racial inequalities over the course of a career.
In the case of quota regulation, the glass-ceiling effect is evident through the nature of compliance with the legal imposition, as parties often fail to elect a percentage of women beyond the quota requirement (Darhour and Dahlerup 2013).Benny and Sørensen (2019) found empirical evidence of the glass-ceiling effect in the lack of overlap between the implementation of quota regulation and the presence of women in the rest of the local government bodies.Jalalzai (2008) argues that although some initiatives enable women to reach higher positions, only institutional changes can shatter the glass-ceiling that prevents gender equality.Thus, our first theoretical hypothesis is: The implementation of quotas tend to create a glass-ceiling around thelegal threshold.
For the second set of hypotheses, we shift our focus to the effectiveness of quotas.Concerning this topic, the discussion does not centre so much on the overall effect of quotas on the number of women in office, but rather aims to gauge how institutions and competitiveness drive local governments to favour gender equality.
According to the work of Turnbull (2019), political parties tend to fit into one of three categories in terms of their response to quota regulations: (1) those that comply with the rules and rely on the minimum threshold as the maximum effort to integrate women in their lists; (2) those that push forward and add a surplus of gender representation beyond the legal threshold; and (3) those meet the official standard, but reserve unwinnable seats for women.It is critical to assess the factors and incentives that push political parties forward in terms of gender equality, regardless of the defined minimum threshold.
As already argued by Jalalzai (2008), enacting change in institutions is crucial to breaking the barriers for women in politics.The second theoretical argument addresses the links between the engagement of the political party with the effective implementation of quotas.Verge and Espírito-Santo (2016) stressed that the legal adoption of quotas falls short of actual implementation by political parties.Despite quotas taking immediate effect on paper, 'old' institutions often still create an environment hostile to actual change.Hence, a party that had previously adopted its own quotas already has an environment that fosters female participation.The institutionalisation of gender diversity enacts a set of procedures that favour compliance with legal quotas in the everyday life of a political party, from the composition of the governing board to process of list building, Thus, we argue that: H 2 : The institutionalisation of gender diversity through party quotas will encourage practices that push the percentage of women in office above the legal threshold.
In addition to our arguments on importance of institutions, we also postulate that political parties change their stance on gender quota regulation if they believe that they can benefit from it.That is, regardless of whether or not they have a history of adopting of gender quotas, political parties are open to considering anything that will maximise their votes.Hence, the third theoretical argument claims that certain environments result in the faster adoption of gender diversity strategies.Simón and Verge (2016) stated that competition, emulation, and learning processes are important elements in this process.Competition creates rapid and natural change in the perceived advantages of gender diversity.On the other hand, because emulation and learning entail changing political beliefs, attitudes, and normative judgements, they tend to incite change at a slower pace.In the political sphere, competition naturally leads to strategical changes in order to maximise the number of votes.If one party opts to integrate more women in their list, give women more winnable positions, or let women lead the electoral list, competitors will tend to follow the same path if those actions are perceived as advantageous.Through a process of diffusion, the competitive trend will spread gender diversity throughout running parties.Therefore, our last theoretical hypothesis is: H 3 : Competitive environments push parties to increase the number of women in political office.

Research context
In 2006, gender quota regulation was legally adopted in Portugal.Hitherto, the percentage of women in the municipal councils had been growing, but never came near the 20% mark.Before the legal initiative, a few parties endeavoured to adopt diversity-promoting policies on gender by implementing party quotas.In 1988, the Socialist Party (PS) adopted a party quota of 25%, which was never really enforced.It took more than a decade for the PS to finally comply with its own goal, which it finally did in 1999 (Verge 2013).
From 1989 until 2006, the PS and the Left-Block (BE) 3 proposed several bills to push quota regulation, but none gathered enough political support to be approved (Espirito-Santo 2015).Even when the PS won the legislative election, had a prime minister (António Guterres) with a record of supporting gender equality in politics, and revised the Constitution by adding explicit clauses that addressed the political equality between men and women, gender quota laws were rejected.The Communist Party opted to set an example by creating a gender balance without the need for any regulation.The Social Democrats and Democratic Christians endorsed a more incremental approach, advising against the adoption of quotas as the solution (Espirito-Santo 2015; Verge and Espírito-Santo 2016).
Only in 2006, again under a PS government (although this time with the majority) the parliament approved the gender quota regulation.The law 4 stipulated that the lists for the national parliament, european parliament, and local governments must be composed in advance to guarantee a minimum gender balance of 33%.Furthermore, parties were not allowed to consecutively place more than two candidates of the same gender in the final ordering of their lists.Non-compliance meant strict sanctions on political parties: parties that did not adhere to the quota were singled out by the courts and the national electoral commission and faced a financial penalty with a reduction in the public subsidies to which they were entitled 5 .
Portugal uses a proportional system with a partisan close list to the election of national and european parliaments, as well as local governments.The Figure 1 displays the evolution of the proportion of women elected in all elections.In all cases, we witness a positive trend in the number of women in office.Moreover, there is a noticeable gap before and after the implementation of quotas.The largest effect was recorded in the election to the european parliament, with an increment of 11.36% points, while the national parliament only had an increase of 6.06% points.The effect of quota regulation for the election of the municipal council settles with an increment of 9.46% points, but two major aspects should be highlighted to justify the aim of this research for the municipal councils: • Local governments display the lowest percentage of women elected compared to other political bodies, both before (16.47%) and after (28.9%) the quota regulation.• After the implementation of quotas, in the municipal election, the proportion of women elected shows a much more pronounced downward trend when compared with the other two.
All local government data are related to the municipal council 6 .In the Portuguese context, election to local governments, at the municipal level, implies the election of the executive (municipal council) and legislative (municipal assembly) branches.In either case, all parties have their votes converted into seats.This means that even at the executive level, there is a balance and coexistence between winner and losers 7 .
In conducting a more detailed analysis of the proportion of women elected to the municipal councils, local governments may be divided into three groups: (1) Local Governments that still do not have any women in the municipal council (2) Local Governments in which the number of elected women goes from zero to the threshold defined by the quota regulation (3) Local Governments that elected a percentage of women above the threshold established by the quota regulation Table 1.shows the variation over the years, in the number of women in the municipal council.The year 2005 was to the last election held before the implementation of quotas, and therefore can be used for the sake of comparation.Even after the implementation, in approximately 10% of the municipalities, female candidates were not entitled to a place in the municipal council.Notwithstanding, due to the use of a quota system in the party list, even under a proportional electoral system, any further effort towards gender diversity was eliminated.However, data also show that the number of local governments exhibiting this phenomenon is gradually reducing.On the other hand, the number of cases that record a proportion of women in the Municipal Council higher than the established threshold is increasing at a steady pace.Data related to the size of the local governments (Table A3) also show that Group 1 is composed of small units of approximately 5000 voters, while the other groups have, on average, more than 30,000 voters.

Data & methods
The first goal of the paper is to assess the outcome of the implementation of gender quotas.As argued by Dahlerup and Freidenvall (2010), there is a liability that quota regulation might produce a glass-ceiling effect.Although an initial significant positive impact on the number of women elected can be expected in the short-term, in the long-run, quotas might produce a stabilisation in the number of elected women around the imposed threshold.To test this argument, we gathered data on the number of women in office for the election of local governments from 1979 to 2017.We used interrupted time series (ITS) with single group analysis, as suggested by Linden (2015), and equation 1 as the estimation strategy.
Following Bernal, Cummins, and Gasparrini (2016), Anderton and Carter (2001), Anthony, Ary, and Wagenaar (2000), McDowall, McCleary, and Bartos (2019) and Huitema and Mckean (2000), the ITS design required a minimum of three variables: one accounting for the time elapsed from the start of the study (Time t ); a dummy variable accounting for the pre-intervention or accounting for the pre-intervention or the post intervention period (QuotasRegulation t ); and the outcome variable (ln WinO t ð Þ).The variables were used in a conventional multiple linear regression with the predictor of time and treatment and their interaction.The results of the regression equation provide the effect of the treatment on the level and slope.The contrafactual was modelled by extrapolating the pre-intervention trend.The effect of the intervention was then measured by the deviation from the counterfactual.
In equation 1, ln WinO t ð Þ is the natural log of the number of women in the executive of the local governments in year t (between 1978 and 2017).The coefficient β 1 provides the impact of the time trend by indicating the slope of the outcome variable until the implementation of quotas.The coefficient β 2 gives the change in the outcome, i.e., number of women elected, owing to the implementation of the quota regulation.The coefficient β 3 is the result of the interaction of the time and quota regulation.It provides information about the change of slope in the evolution of the dependent variable, thus giving an indication of the treatment effect over time.If positive, it indicates that quota regulation increased the pace of growth of female candidates elected to local government offices.If negative, it provides evidence that the introduction of quotas reduced the rate of inclusion of female candidates.
The second goal of this study is to gauge the effectiveness of gender quota regulation.In particular, we aim to assess the effect of party institutions and competitive environments on gender diversity.On one hand, the theoretical arguments establish a positive relationship between a party's history of adopting voluntary quotas and its willingness to elect female candidates.On the other hand, competitive environments also provide a suitable environment for increasing the chances of more women being elected.To test our arguments, we opted to use a multinomial logistic regression as an estimation strategy 8 .
We classified the local governments into three categories 9 : 1: no women elected; 2: proportion of women elected above 0% and below 33% (the legal threshold); and 3: proportion of women elected above 33%.Thus, our dependent variable is an unordered multi-category.Assuming a reference category (in this case, the second group), the multinomial logistic estimation provides the odds, in probabilistic terms, of the other categories (following equation 2 10 ).
In this case, the independent variables are grouped in two categories: one related to the institutionalisation of gender diversity in the political parties; and the other related to political competitiveness at the local level.
In the first case, we used the number of seats (Seats i ) won by the parties that advocated for the introduction of a quota regulation (PS and BE).As discussed in section 4, these parties have a long history of supporting the push for more women in politics, as well as for the introduction of quota regulations.Hence, we expected a positive relationship between the number of seats won by these parties and the number of women elected.Thereafter, we used a variable to assess which party wins the local government: PS or BE.This is a dummy variable (PartyWinner i ) that assumes the value of 1 when the winning party is either the PS or the BE, and 0 otherwise.As in the previous indicator, the argument is that these are the parties that historically adopted gender diversity policies; hence, we expected to see more women elected in these parties than under governments ruled by any other party.
In the second category, we used a variable (Competitiveness i ) to measure the minimum number of additional votes needed to win an additional seat.Since we were dealing with a proportional electoral system, we opted to base our approach off the work of (Blais and Lago 2009), and measured the level of competitiveness by: 100 x (votes needed to win one additional seat/number of ballots per seat).Additionally, we used another variable (Diversity i ) to measure the number of different political parties with seats in the municipal council.Both variables rely on the same argument, which is based on the assumption that a competitive environment promotes new strategies from political parties and positively affects the number of women elected.The logic is that more diversity comes from more political competition, favouring a higher number of women in office.
We used several control variables in the multinomial logistic models.First, we controlled for the effect of governments that already had a woman acting as mayor (WomenPresident i ).The dependent variable can be skewed in either direction in governments that have already had a woman elected to such an important role.This variable was measured as the number of women elected mayor in that local government.We also controlled for the size (ElectorsðlnÞ i ) of the local government.This was particularly important, as the dimension determines the number of seats in the municipal council.We used a dummy variable (Urban i ) that assumed value 1 for urban regions and 0 for rural.We also used a variable to assess the level of income (WealthðlnÞ i ) which aims to control for the different levels of wealth that can more easily support a gender equality agenda.The variable (Women % ð Þ) assess the percentage of women in each municipality.Finally, we also controlled for evolution over time (Year 2013 , Year 2017 ).

Results
The results presented in Table 2. show the interrupted time series models.The three models were computed using alternative estimation strategies.We can observe consistency in the results across the different models.Notes: All the models were estimated using an ordinary least squares regression-based model.Model #2 includes standard error produced by Newey-West to address autocorrelation; the model uses #1 lag in its autocorrelation structure.Model #3 has the parameters estimated by the generalised least-square method in which the errors are assumed to follow an autoregression (1) (For more information see Linden (2015)).Robust standard-errors are in parenthesis.Significance levels: 1%, ***; 5%, **; 10%, *.
The coefficient of the variable Time t shows the evolution of the number of women in the municipal council before the implementation of the quota regulation.That is, this variable represents the base level trend of the outcome at the beginning of the series.The results indicate that, in every case (specifications 1, 2 and 3), there is a positive rate of evolution of the number of women elected in every election before the implementation of quotas.According to the results of the first specification, the coefficient β 1 has a value of 0.248.After converting to the exponentiated coefficient, the results show an average trend of 28.15% in the evolution of the number of women in the municipal council since the first election.
The coefficients of the variable QuotasRegulation t show the effect of the implementation of a quota regulation.This variable represents the change in the level/intercept.The results demonstrate a positive effect in all models.Again, using the first specification of the model, β 2 has value 0.482.After converting to the exponentiated coefficient, the results show a 53.41% rise in the number of women in the municipal council upon implementation of a quota.
In the case of the variable QuotasRegulation t � Time t , the results display a negative coefficient.This interaction between time and the quota regulation shows the effect that the quota regulation has on the growth rate of the number of women -that is, it represents the differences in the slopes.Evidently, the effect is negative, meaning that, although the quota regulation has a positive effect on the number of female candidates elected, it also reduces the rate of growth recorded before the implementation of quotas.The value of the coefficients of β 3 varies between −0.194 and −0.184, which represents a decrease of around 20%.
The reduction was not large enough to completely eliminate the positive evolution that was registered before the quota regulation, but it did almost flatline it (see Figure 2).Thus, the results display evidence to support the claim that the quota regulation created a glass-ceiling effect.
Figure 2 depicts the estimation of the effect of the quota regulation on both the number of women elected and its growth rate.As discussed previously, the estimation before the quota regulation is represented by a line with a greater slope compared to the one after the quota regulation.It is also evident that there was a positive jump in the number of women after the implementation of a quota regulation.However, the downside of the quota is the reduction in the growth rate of the number of women to the municipal councils.Political parties quickly consider themselves confined to the minimum threshold established by the gender quota, and therefore they do not make any extra effort to exceed that threshold.
The results presented in Table 3. refer to the multinomial logistic regression models 11 .Models #1 and #2 are presented as robustness checks from the results of model #3, which integrates all independent and control variables.All results are expressed in odd-ratios, moving from the base category (stage 2) to the alternatives.
The results indicate that, on the one hand, the institutionalisation of gender diversity prevents the absence of women in the municipal council.On the other hand, more competition in municipal elections not only prevents the absence of women in office, but also pushes the number of women in the municipal council above the legal threshold defined by the quota regulation.
Results from the variable Seats i display evidence that more seats allocated to PS or BE decrease, by approximately 40%, the odds of municipalities integrating stage 1.This result is in line with the theoretical argument presented by Verge and Espírito-Santo (2016).The earlier-stated parties that acknowledge gender diversity and adopt party quotas successfully enact change in their institutions.Gradually, old routines and practices are no longer tolerated, and new procedures replace them.
Results from the variable Competitiveness i produce evidence that supports the argument that more competitive elections prevent parties from placing women in unwinnable positions.More competition leads local governments to move away from stage 1.However, no evidence was found that this factor promotes the election of women above the legal threshold.The results from variable Diversity i are in line with the theoretical arguments.They indicate that an increase in the number of parties entitled to seats in the municipal council will boost the odds by 29% of a local government electing a number of women to office above the legal threshold (stage 3).As expected, the political competition, gauged by the number of parties with seats in the municipal council, drives the parties to assume a different strategy in order to win votes and place more women in the topranking positions on their lists.
Control variables delivered results in line with our expectations.Larger local governments (ElectorsðlnÞ i ) with more seats available in the municipal council have lower odds of being in stage 1-less than 50%.The number of previous terms of female mayors (WomenPresident i ) in that local government increases the odds by 36% of the municipality being in stage 3.If the local government is situated in an urban area (Urban i ), it also reduces the odds of a municipality falling into the first category.Wealthier municipalities (WealthðlnÞ i ) also display results that support the claim that more affluent areas foster gender equality.The variables concerning the years show that, with time, there are incremental increases in the odds of a local government moving from stage 2 to stage 3.In Table 4., we present the results of the marginal effects.We computed the average marginal effects followed by discrete changes and standard deviations.We also present a graphic representation of the marginal effects (Figure 3).
We can see that an increase in the number of seats in parties that first supported quotas leads to a reduction in the odds of having a municipal council without any women.A high degree of competitiveness in local elections has the same effect.This is relevant only in the case of movements from stage 1 to other stages.On the other hand, the number of parties in the municipal council becomes relevant in the case of movements to stage 3.The more parties are entitled to seats in the municipal council, the higher the odds of having more women than the minimum threshold established by the quota regulation.Finally, in Figure 4, we computed the predicted probabilities of each stage depending on the evolution of the relevant independent variables.Again, results show that the highest probability of change between stages 1 and 2 occurs with higher levels of competitiveness and in municipalities won by the parties that institutionalised gender diversity.However, the highest probability of change between stages 2 to 3 occurs with the increase of the number of parties with seats in the municipal council.

Conclusion
Democracy is a system based on the principle of freedom, in which people are able to freely express their opinions, organise themselves, and elect their representatives.The fact that a large portion of the population (in this case, women) are kept away from public office poses challenges and endangers the quality of democracy.Therefore, gender quota regulations were created to prevent political bias and avoid imbalance in the distribution of elected positions.
The legal initiative of 2006 implemented, for the first time, obligatory gender diversity (33%) for the local, national, and european elections.Before the legal implementation, some parties (PS and BE), which had already adopted internal procedures to promote gender diversity, proposed several initiatives to approve a bill related to gender diversity.In every case, they failed to gather sufficient support.Our paper explores the composition of the municipal councils in Portugal, addresses the issue of the underrepresentation of women in politics, and examines the nature, outcomes, and effectiveness of gender quota regulations.With respect to define the nature the Portuguese solution of quota regulation, we can state it can be identified as a legal electoral quotas applied to a proportional system of closed party lists.
Regarding the outcomes, the first visible result of the quotas was a clear increase in the number of women in the municipal councils.Before quotas, women occupied a share of seats below 20%.Overnight, quotas increased the level of women's representation.The 2006 election recorded a jump of approximately 10 percentage points.However, after this sudden increase, the pace of growth almost flatlined.We used interrupted time series to compare the rate of increase in the number of women before and after quotas.Results (Table 2.) show evidence of a reduction in pace after the application of quotas.This indicates the presence of a glass-ceiling effect, as discussed in the literature (Dahlerup and Freidenvall 2010;Folke and Rickne 2016;Darhour and Dahlerup 2013;Benny and Sørensen 2019).In light of this finding, two major changes can be implemented: one is to increase the level of the legal threshold.If results show evidence of a glass-ceiling around the legal threshold, one way to circumvent it is to increase the minimum level of gender diversity in the lists.This strategy would not shatter the glass-ceiling, but it would push it higher.The second proposed change is the implementation of reserved quotas.That way, we can overcome the problem of the party lists, although following the rules of gender quotas, place women in unwinable positions.This solution guarantees the number of women in office established in the legal threshold.
Grounded on the work of Verge and Espírito-Santo (2016) and Simón and Verge (2016), we aim to understand the role of party institutions and competition in determining the effectiveness of gender quota regulations.The results (Table 3.) show that party institutions are influential factors in avoiding a municipal council without women.Whenever parties that adopted voluntary quotas have more seats in the municipal council, there is evidence of an increase in the probability of having at least one woman.Results also suggest that the diversity of parties with seats in the municipal council increases the probability of having a percentage of women above the legal threshold.In this way, electoral law should provide a more flexible administrative procedure for increasing number of new parties, but, above all, independent movements that wish to run for office.Lately, the Portuguese political context has witnessed a growing number of activists willing to engage and be politically active at local level.Having a smother process of application and validation of independent movements could open the door to more women in the municipal council.
This research focuses on the gender equality and quota regulation from the demand side of the problem of the underrepresentation of women in politics.Further investigation should focus on the supply side, or the pipeline problem, as Benny and Sørensen (2019) called it.Some aspects of the social and political culture may cause certain hostility towards female candidates.Hence, regardless of their professional accomplishments, women could perceive themselves as less qualified than men when running for office.All of these factors may also contribute to the scarcity of women in politics.

Notes
1. Data retrieved from Inter-Parliamentary Union.2. https://www.ipu.org.3.Both parties had already adopted and enforced party quotas.4. Gender parity Act 3/2006 of 21 August.5. Recently, in 2019, the gender quota regulation was updated.Party lists now need to ensure a minimum representation of 40% gender diversity.Furthermore, sanctions for non-compliance ceased to be financial; the lists were rejected outright.6.Additional data about the evolution of women in the municipal council can be found in A2. 7. Data about the size of the municipal council are available in A1. 8.The dependent variable can also be understood as ordered.Local Governments in the second stage have more women in their council than the those in the first stage, and, consequently, those in the third stage have more than those in the second.Hence, ordered logit regression could be used as an alternative estimation strategy.Appendix A4 displays the results of such an approach.Results are consistent with the ones concerning the multinomial logistic regression presented in section 5.1.Due the design of this estimation strategy, we computed the odds ratio for a one unit increase in the dependent variable, thus losing the information related to the odds ratio to each category (Stage 1 and Stage 3).9. Following the rationale used in the Table 1. of the section 4. 10.Where: j=categories, k= independent variables, i=cases.11.As robustness check, we computed a multinomial logistic regression models with the lags of the independent variables tabel A5.Results do not display significant changes.As expected, institutional path has been pressuring local governments, where PS and BE accumulate more seats, to have women in their municipal councils.The implementation of quotas made this pressure more evident and is now a factor pushing municipalities towards stage 3.The level of competitiveness pressure local governments to avoid the stage 1, and only have an effect after the implementation of quota regulation.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Figure 2 .
Figure 2. Results of the implementation of the quota regulation.

Table 1 .
Distribution of local governments by groups.

Table 2 .
Estimation results for interrupted time series.

Table 3 .
Estimation results from the multinomial logistic regression.
Figure 3. Graphic representation of the marginal effects.

Table A4 .
Estimation results from the ordinal logistic regression.The dependent variable is the ordinal category of the local government as defined in Table1..All results are expressed in odd ratios.Ro-bust standard-errors in parenthesis and clustered at municipalities.Significance levels: 1%, ***; 5%,**; 10%, *.

Table A5 .
Estimation results from the multinomial logistic regression -with lags.The dependent variable is the category of the local government as defined in Table1.Stage 2 is the base category.All results are expressed in odd ratios.Robust standard-errors in parenthesis and clustered at municipalities.Significance levels: 1%, ***; 5%, **; 10%, *.