23 Mar 2015
Many existing explanations of electoral volatility in Latin America have been tested at the country level, but they are largely untested at the individual party level. In this paper, I apply a hierarchical linear model (HLM) to test various explanations of electoral volatility on data of 128 parties in the lower house elections of 18 Latin American countries from 1978 to 2011. My most important finding pertains to the conditional effect of a party's incumbency status on electoral volatility. First, the results show that the effect of party age on reducing electoral volatility is stronger for incumbent parties. Second, an incumbent party has a lower level of electoral volatility than opposition parties during periods of stronger economic performance. Last, while an irregular alteration of political institutions is hypothesized to increase the level of volatility for all the parties in a country, the effect is more significant for the incumbent party.
Concerns with party system institutionalization and its consequences in developing countries have grown in the past decade. Extant literature underscores that political parties play an important role in linking diverse social forces with democratic institutions, channeling societal demands, managing sociopolitical conflicts, holding government officials accountable to the electorate, and legitimizing the regime (Dix 1992; Sartori 1968; Schattschneider 1942). In this sense, political parties with stable and consistent support across elections not only ensure their long-term survival, but also help institutionalize the party system. A stable and institutionalized party system fosters more effective programmatic representation (Mainwaring and Zoco 2007, 157) and facilitates the institutionalization of political uncertainty (Przeworski and Sprague 1986). In contrast, a democratic country with a poorly institutionalized party system where electoral volatility is very high tends to produce populist leaders and discourage the incumbent party from making long-term policy commitments (Mainwaring and Scully 1995). 
In comparison to Western Europe and the United States, the level of electoral volatility is exceptionally high in Latin America (Payne et al. 2002). In the 1990s, the overall electoral volatility in this region was about twice that in the developed world (Roberts and Wibbels 1999). Weak partisan identities of voters, rapid voting choice changes, and unpredictable election campaigns are prevalent political characteristics in this region (Baker, Ames, and Renno 2006), but what explains the variation in electoral volatility in Latin America? Previous work on electoral volatility has provided explanations about political institutions, national economic performance, social cleavages, ethnic heterogeneity, and historical factors (Hicken and Kuhonta 2011; Madrid 2005; Mainwaring and Zoco 2007; Roberts and Wibbels 1999; Tavits 2005). These explanations have been tested at the country level, but they are largely untested at the individual party level, even though that is the level at which the effects of certain relevant explanatory factors are expected to work.
Why do some parties have higher levels of electoral volatility than others? Do factors cause electoral volatility at the country level have the same impact on party level volatility? Does the incumbent party enjoy certain advantages that opposition parties do not have to secure electoral stability? This paper aims to address these questions by examining electoral evidence at the party level in Latin America. I generated a value of electoral volatility for each party between elections by performing Morgenstern and Potthoff's (2005) components-of-variance model on an original dataset of lower house electoral results at the district level for 128 parties in 18 Latin American countries from 1978 to 2011. I first demonstrate that the patterns of electoral volatility at the party-level differ from that at the country level. I then apply a hierarchical linear model (HLM) to test country-level, party-level, and cross-level hypotheses regarding why some parties are more electorally volatile than others.
The most important result of this study is that the incumbent parties and opposition parties have different behavioral patterns under certain conditions. Specifically, I find that a better national economic performance helps the incumbent party, rather than every party in the country, to reduce the level of electoral volatility. Moreover, I demonstrate that an irregular institutional change greatly increases the incumbent party's electoral volatility, rather than that of every party in the country. At the party level, I find that the effect of a party's incumbency status is contingent on certain party-specific characteristics. The results show that incumbent parties that were founded in earlier periods are generally less volatile than younger incumbent parties. These findings are robust after controlling for a variety of other explanatory factors that will affect electoral volatility, using a different sample of parties, or adopting a different model specification. In sum, relative to previous work, this study is distinctive in that it uncovers patterns of electoral volatility and provides a better understanding of the dynamics of party politics in new democracies.
I focus on party volatility in this paper, and I argue that examining electoral volatility at the party level facilitates a better understanding of the patterns of party development. In general, electoral volatility refers to the phenomenon in which voters switch voting choice in consecutive elections. Many previous have used the Pedersen Index  (Pedersen 1983) to operationalize the level of party system electoral volatility (Birch 2003; Kuenzi and Lambright 2001; Mainwaring 1999; Roberts and Wibbels 1999). However, as Mair (1997, 66) argues, aggregate volatility measurement such as the Pedersen Index explains little about the persistence or decay of political cleavages. Mainwaring et al. (2010) argue that the Pedersen Index fails to distinguish between the volatility caused by vote switches from one party to the other and the volatility caused by the entry and exit of parties from the political system.
Morgenstern and Potthoff's (2005, 30) critique is that the Pedersen Index fails to account for the relative electoral movement of individual parties within the system; in other words, the Pedersen Index tells nothing about which party is more volatile than the others. This problematic feature may produce mistaken if not biased inferences. For instance, although the Pedersen Index indicates that Argentina's mean party system institutionalization is lower than that of Brazil and Mexico from the 1980s to the 2000s (Mainwaring and Zoco 2007, 159), it does not indicate that Argentina's electoral volatility is largely a result of the crisis of the Unión Cívica Radical (UCR) instead of the incumbent Partido Justicialista (PJ) (Levitsky 1998, 461). In short, aggregate electoral volatility is likely to mask patterns of party-level electoral volatility.
The level of electoral volatility matters for a party because it is an important indicator of a party's long-term survival. Party volatility is also an indicator of party institutionalization (Dalton and Weldon 2007; Mainwaring and Scully 1995). According to Janda (1980, 26-7), an institutionalized party should have stable partisan support because it can secure stable representation by building strong and regular societal ties with the electorate. A more institutionalized party should have a lower level of electoral volatility and a higher probability to survive over time, and it also implies that this party has a stable, routinized organizational structure and/or supporters with strong partisanship (Levitsky 1998).
As Randall and Svåsand (2002) contend, a high level of party system institutionalization does not necessarily indicate that all the parties within the system have an equally high level of party institutionalization. In other words, it is not necessarily the case that a high level of country volatility implies that all the parties in this country are equally volatile between elections. Therefore, a more important research question needs to be addressed: Is a party's electoral volatility determined by country-level factors, features of the party, or both? In the next section, I will discuss and propose testable hypotheses for the empirical analyses.
Party volatility considers the degree to which a party's average vote is stable across two consecutive elections. Previous studies about country-level electoral volatility have considered national economic performance, political institutions, and social structural factors as three competing theoretical explanations of electoral volatility. However, some of the tested hypotheses, particularly those regarding economic voting and institutional theories, are actually derived from behavioral patterns of individual parties. Thus, these hypotheses should be tested at a more appropriate level, that is, the party level.
Unlike previous studies of electoral volatility that focus on country-level explanations, this paper focuses on explaining party-level volatility, and such a research design facilitates the testing of party-level, country-level, and cross-level hypotheses. In particular, I argue that the behavior of the incumbent party is different from opposition parties. Moreover, I contend that the effect of a party's incumbency status is contingent on certain factors. Next, I will discuss various competing theoretical arguments about party electoral volatility at different analytical levels.
Previous studies have discussed how time affects electoral volatility at the country level. Roberts and Wibbels (1999) argue that an older system is likely to have deeper and stronger historical roots in society than younger ones. Therefore, the level of electoral volatility will decrease with the age of a party system. Adopting a similar approach, Mainwaring and Zoco (2007) propose a democratization timing explanation for why some party systems are more stable than others. The authors demonstrate that the level of democratic governance voters have experienced will affect the level of electoral volatility. In other words, what matters for accounting for stabilization of party competition is the timing when democracy began in the country. Voters in democracies that were created in earlier periods had stronger attachments to parties, so that can help forge stable patterns of party competition (Mainwaring and Zoco 2007, 163). In contrast, political elites in new democracies have less incentive to make efforts in party building, since they tend to depend on mass media and modern campaigns to win the elections.
While Mainwaring and Zoco's thesis sheds light on the relationship between democratic learning and party system stabilization, it ignores the variation of party age within a country. Clearly, old and young parties can exist in both old and new democracies in Latin America.  However, Mainwaring and Zoco's argument might imply that party volatility will be higher in a newly-founded democracy, regardless of how old a party is in this country. To avoid this problematic inference, a more appropriate research strategy is to test Mainwaring and Zoco's argument at the party level. Specifically, if Mainwaring and Zoco's argument holds at the party level, we may expect that political parties that were founded in earlier periods will have lower levels of electoral volatility, because their supporters have much stronger partisan attachments than the supporters of younger parties. In contrast, younger parties will have higher levels of electoral volatility because the elites of these parties will have less incentive to delve into party building. Accordingly, the following hypothesis is generated:
H1: A party that was founded in earlier periods will have a lower level of electoral volatility than a party that was founded later.
The second testable hypothesis of this study is about a party's incumbency status. Some scholars argue that institutions such as states and parties might have their own strategic goals and "behave as political actors in their own right" (Cox and McCubbins 1993). While parties can be different in terms of various characteristics, whether or not a party is the president's party is a crucial for explaining differences in party behavior. Incumbency advantage generally implies that incumbents are more likely to win an election than the counterpart nonincumbents (Erikson 1971; Mayhew 1974). Cox and Katz (1997) and Levitt and Wolfram (1997) decomposed the concept of incumbent advantage into three elements: (1) direct officeholder effect, such as opportunities for providing constituency services (Fiorina 1977; King 1991) and using legislative resources such as personal staff for performing casework (Cover and Brumberg 1982); (2) the ability of incumbents to scare off high-quality challengers (Krasno and Green 1988); and (3) the generally higher quality of the incumbents due to their experiences and campaign skills (Fenno 1978).
The literature on incumbent advantage provides useful insights for this study. Since presidency is often considered as an extraordinarily important political institution in Latin America (Mainwaring and Shugart 1997), it is expected that the president's party has advantages that opposition parties do not have. In particular, the incumbent party is more likely to receive access to public funds and more capable in allocating targeted resources to secure its survival (Calvo and Murillo 2004). Although being an incumbent party does not necessarily indicate a higher probability of winning an election in the contemporary Latin American context, it is reasonable to expect that an incumbent party should have a more stable electoral performance than opposition parties.
However, an incumbent party in a new democracy might not have a stable electoral performance under certain circumstances. The experience in Latin America suggests that, when a country is governed by a new party, the patterns of electoral competition will become more unstable. In Peru, Alberto Fujimori's self-coup in 1992 and the adoption of a new constitution in 1993 helped to dramatically increase votes for the incumbent Cambio 90 in the 1995 election. However, Fujimori's 40-point plunge in public approval ratings in mid-1997 (Roberts and Wibbels 1999, 586), and the demise of Fujimori's party in the 2000 and 2001 elections, not only suggest a high level of unpopularity of Fujimori's neoliberal structural reforms, but also a high level of fluid electoral preference when a country is governed by a new party.
Although the effect of a party's incumbency status on party electoral volatility might not be clear, it is possible that this effect is conditional on other factors. In particular, if party age helps to reduce electoral volatility, it then makes sense that the effect should be stronger for the incumbent party. An incumbent party with an older age suggests that it not only has more access to use state resources to enhance its electoral competitiveness, but it also has stronger party organizations and members. Put differently, an older incumbent party might have a lower level of electoral volatility than a young incumbent party. Therefore, I generate the following hypothesis:
H2: The effect of party age on reducing electoral volatility is stronger for an incumbent party.
Besides the party-level hypotheses, I also test cross-level hypotheses to see whether the effect of a party's incumbency status is contingent on certain country-level factors. The first cross-level explanation concerns the interaction between incumbency and economy. Economic voting theory argues that some citizens will respond to the waxing and waning of the economy by shifting their votes to reward or punish incumbent parties and officeholders (Lewis-Beck 1988). In other words, electoral volatility is driven by voters' retrospective evaluations of economic performance of the incumbent government. More specifically, economic hardship can be expected to increase electoral volatility by undermining the loyalties and support for the incumbent party and by increasing the opposition parties' votes. By contrast, in a better economic climate, one would expect that people prefer to maintain the status quo by continuing to support the incumbent party so that electoral volatility decreases.
The proposition that economic conditions shape election outcomes in democratic countries is robust for studies using individual survey data (Lewis-Beck and Stegmaier 2000). In contrast, analyses of electoral volatility at the country level find inconsistent evidence about economic voting. Remmer (1991; 1993) and Madrid (2005) demonstrate that economic performance has a significant impact on the level of electoral volatility in Latin America. The evidence in advanced democracies also shows that economic performance strongly shapes electoral volatility (Bischoff forthcoming). However, recent analyses of new democracies in post-communist Europe (Epperly 2011) and Africa (Ferree 2010) show that economic voting is not a crucial factor in explaining party system volatility.
One possible explanation for these inconsistent findings pertains to the appropriateness of the level of analysis. Specifically, since economic voting theory suggests that national economic performance will affect the extent of vote switches between the incumbent party and opposition parties between elections, it is more appropriate and necessary to test this argument at the party level. If the economic voting argument holds, it is expected that the incumbent party will have a lower electoral volatility than opposition parties when the economic performance is better. Conversely, the incumbent party is expected to have a higher electoral volatility than the opposition parties when the economy is in crisis. Based on the logic of economic voting, I propose the following economic voting hypothesis on party volatility:
H3: The incumbent party will have a lower level of electoral volatility than opposition parties when the national economy is better.
The second cross-level explanation is about the interaction between incumbency and institutional change. As the literature of rational choice institutionalism indicates, institutions matter because political actors' behavior is driven mainly by a strategic calculus facing the limitation and opportunities that particular institutional or organizational settings offer (Hall and Taylor 1996). The stable persistence of political institutions that regulate electoral competition helps political parties to socialize their voters over time, and upholds the legitimacy of a democratic regime. Therefore, a fundamental alteration or an irregular discontinuity in important political institutions is expected to have a "shock" effect on the competitive equilibrium of elections.
Based on evidence from Latin American countries, Roberts and Wibbels (1999) and Madrid (2005) find that the electoral dynamics of a party system is greatly altered by the adoption of a new constitution, a significant enfranchisement, and/or irregular changes in the executive branch such as a presidential "self-coup" (autogolpe), or a forced resignation of the president. Although these dramatic and irregular alterations of existing institutions are found to increase electoral volatility at the country level, it makes sense that such shocks should also influence party-level electoral volatility.
In particular, it is expected that such irregular institutional changes will increase the volatility of the incumbent party to a greater extent. Recent political developments in Latin America suggest that this hypothesis is reasonable. For instance, in Ecuador the adoption of a new constitution in 2008 helped the incumbent Alianza PAIS increase its level of voter support in the 2009 election. In contrast, irregular removal of presidents also leads to higher electoral volatility for incumbent parties, but in a negative direction. The 2009 Honduran coup d'état with the removal of President Manuel Zelaya made his Partido Liberal de Honduras (PLH) suffer a significant loss in the election at the end of the year. Likewise, the resignation of President Alberto Fujimori in Peru in 2000 also led to an electoral fiasco for the governing Cambio 90-Nueva Mayoria. Based on the discussion above, I propose the following hypothesis:
H4: The incumbent party will have a higher level of electoral volatility than opposition parties after a shock of an irregular institutional discontinuity.
In the empirical analysis, I control for a number of factors that are likely to affect party volatility. At the party level, I control for the size of a party. Party size may influence the stability of electoral performance. The literature of legislators party switching suggests that larger parties in the legislature are more attractive to potential party switchers because they generally have more political influence (Desposato 2006; Heller and Mershon 2008). Therefore, it is possible that a larger party should have a lower level of electoral volatility because it is more attractive to voters who are unwilling to "waste" their votes on parties with little chance to win the elections. However, it is also possible that smaller parties, especially those with strong regional base, may have low electoral volatility. It is because such parties are able to sustain their survival by securing a small but strong portion of the electorate over time.
At the country level, I control for party system fragmentation and ethnic fractionalization. First, according to Pedersen (1983), electoral volatility increases with the number of parties in a system because a greater number of parties suggests that the ideological difference between the parties is small so that voters tend to switch their votes from one party to another between elections. In addition, party system fragmentation will destabilize democratic regimes because it "tends to inhibit the construction of inherent legislative majorities" (Roberts and Wibbels 1999, 578). Although the hypothesis of party system fragmentation has only been tested at the country level in previous literature (Bartolini and Mair 1990; Birch 2003; Roberts and Wibbels 1999; Tavits 2005), it is possible that a fragmented party system will increase electoral volatility at the party level.
Another factor that may explain electoral volatility is social cleavages. Madrid (2005, 3) observes that the theoretical expectation that stronger ethnic cleavages help stabilize party systems (Lipset and Rokkan 1967) presumes that parties will provide quality representation of distinct ethnic groups and establish strong linkages with them. In Latin America, this expectation does not hold since most party systems have been composed principally of catch-all parties that have drawn support from a variety of social groups. Because minority ethnic groups would not feel well-represented under this context, the level of electoral volatility tends to be higher since it is unlikely for them to form strong partisan identities (Birnir and Van Cott 2007; Madrid 2005). In short, it is expected that Latin American parties in a highly ethnically fragmented social context will have higher levels of electoral volatility.
Last, following previous studies of country-level electoral volatility (Roberts and Wibbels 1999; Tavits 2005; Madrid 2005), I control for a trend factor of party electoral volatility in the model. In a cross-sectional time-series design, Trend controls for the potential problem of spurious correlation when the values of the dependent variable and the independent variables vary independently but in a consistent direction over time.
The unit of analysis in this research is party-elections-country (e.g. Partido dos Trabalhadores 1994-1998 in Brazil). My conception of the dependent variable requires the collection of legislative electoral returns at the district level across time, differentiated by party or party coalition.  The data include 128 parties in the lower house elections of 18 Latin American countries from 1978 to 2011 (N=527).  Most district-level electoral data are compiled from official electoral results on the website of each country's electoral administrative body.  For the countries that were democratized later in the 1980s or in the 1990s, only the elections after the first democratic election were included.  Since Latin American countries have different timing of democratization and term length, the data structure of this analysis is unbalanced. A party is selected for the analyses if the party once obtained more than 5% of votes in any legislative election held between 1978 and 2011 in the country. This selection criterion ensures the inclusion of a diversity of parties.
To generate the value of party volatility, I adopted Morgenstern and Potthoff's (2005) components-of-variance model on district-level data between two consecutive legislative elections held within the same constituency border.  One major advantage of this components-of-variance model is that it simultaneously takes into account various features of a party's electoral performance when generating the value of party volatility. Specifically, Morgenstern and Potthoff's model enables the calculation of three components of a party's vote share in a particular election: volatility, district heterogeneity, and local vote. While Morgenstern and his colleagues have used the latter two components for the research about party nationalization (Morgenstern and Swindle 2005; Morgenstern, Swindle, and Castagnola 2009), I focus on the first component, i.e., party electoral volatility, in this paper. The volatility score assigned for each observation is a continuous variable with values that range from 0 to Ã¢Ë†Å¾, where higher numbers indicate a higher level of electoral volatility for the party.
My primary party-level independent variables are Incumbency, Party age, and Incumbency*Party age. Incumbency is a dichotomous variable, measuring whether a party was the president's party in two consecutive elections. Following Mainwaring and Zoco (2007), I measure Party age as the natural log of the number of years from the year when the party was officially founded to the year of 2011. The value of this variable does not vary over time, but is constant for all electoral periods for a given party. The interaction term, Incumbency*Party age, examines whether the effect of a party's age on volatility is contingent on a party's incumbency status.
To test the economic voting hypothesis, I use two economic indicators: GDP growtht1 and Inflationt1.  GDP growtht1 is lagged by one year to capture the short term economic impact on volatility. Inflation rate is operationalized as the logged value of the inflation rate for the year before the election year. The logged inflation rate is used to prevent cases of hyperinflation from skewing the results.  To test whether the effect of the national economy on party volatility is conditional on a party's incumbency status, I include two interaction terms: Incumbency*GDP growtht1 and Incumbency*Inflationt1.
In addition, to test whether a shock of institutional alteration will affect the incumbent party to a greater extent, I include two variables: Institutional discontinuity and Incumbency*Institutional discontinuity. I use the index constructed by Roberts and Wibbels (1999) to measure institutional discontinuity. The index ranges from 0 to 3, assigning one point to each of the following types of discontinuities: the adoption of a new constitution; an increase in voter turnout of more than 25 percent due to the enfranchisement of new voters; and an irregular change in executive authority, including a presidential "self-coup" (autogolpe), a forced resignation of the president, the ouster of the president due to impeachment, or a failed coup d'état attempt when the president was temporarily ousted from the office. 
Finally, I control for several party-level and country-level variables in the model. Party size is measured as the vote share of the party in the previous election.  Party system fragmentationt1 is measured as the index of the effective number of parties (ENP) (Laakso and Taagepera 1979), lagged by one election.  Ethnic Fragmentation is measured as Fearon's (2003) ethnic fractionalization index. Last, the variable Trend is measured as the number of years since the first election in which a party participated.
To test the hypotheses about party-level electoral volatility, I employ a hierarchical linear model (HLM) on my three-level data. The three-level model is specified as a level-1 submodel that describes how each party changes over time, a level-2 submodel that describes how these changes differ across parties, and a level-3 model that describes how parties and changes differ across countries. An attractive feature of a multilevel models is its ability to model cross-level interactions in the estimation. Another important advantage of the HLM approach is being able to account for both "fixed effects" and "random effects." In this study, the fixed-effects coefficients and parameters of the HLM estimate a regression line that describes the sample of parties as a whole, while the random-effect parameters reflect variation across parties and variation across countries. Application of the HLM in this study will specify three different levels of analysis: The level-1 submodel represents the relationship of time-varying characteristics on party volatility, the level-2 model will incorporate party-level effects that are fixed over time, and level-3 will introduce country-level effects that are fixed over time. I estimate the model using restricted maximum likelihood estimation (REML). In contrast to full MLE estimation, REML takes into account the degrees of freedom consumed by estimation of the fixed effects by eliminating fixed effects from the likelihood function. REML calculates a residual for each unit at each point in time. It then maximizes the likelihood of observing those residuals across the entire sample, making the estimation more conservative and less biased in small samples of level-2 units (Steenbergen and Jones 2002, 226). However, one downside of REML is that it disallows for comparison to other models based on the log-likelihood function unless the fixed components are identical.
The REML model was estimated using the Stata 11.1 xtmixed module. Since the default REML model in Stata assumes that random intercept and slopes are uncorrelated, which is not always reasonable, I specify a "covariance (unstructured)" option to allow for a distinct, nonzero covariance between random effects to run the REML models (Hamilton 2008, 424; Rabe-Hesketh and Skrondal 2008, 155). The formal equation of my full specified multilevel model can be specified as:
where in equation (1), Incum, Size, and Trend are time-varying party-level covariates, with the latter two as control variables. is the regression coefficient that represents mean party volatility, represents regression coefficients linking incumbency to , represents regression coefficients linking party size to , and is a random error term for party i in country j at time t. In equation (2), is the average party-level intercept in country j, is the regression coefficient that link Age, a time-invariant party-level covariate, to , and is the deviation, or residual, of the party's intercept from the predicted value. In equation (3), is the slope for incumbency, and are regression coefficients that link pth (1, 2, 3, 4) covariates to . In equation (4), is the grand mean of party volatility, represents regression coefficients linking the qth (1, 2, 3, 4, 5) time-varying covariate to , and is the random error term at the country level. The error terms for equation (1), (2), and (4) are assumed to be random and normally distributed. The exclusion of error term in equation (3) assumes that the effect of Incum is fixed for all parties.
To illustrate how aggregate electoral volatility measure masks patterns of party electoral volatility, I compare the difference of country-level volatility and party-level electoral volatility for Mexico and Uruguay in Table 1. The country-level volatility is operationalized as the Pedersen Index, while the party-level volatility is calculated by using Morgenstern and Potthoff's components-of-variance model.
[TABLE 1 ABOUT HERE]
Table 1 shows that there is a great variation in aggregate electoral volatility over time in Mexico and Uruguay. In addition, party electoral volatility for each of the parties also varies in both countries. More importantly, Table 1 demonstrates how the Pedersen Index masks electoral dynamics for individual parties in a country. For instance, the Pedersen Index of 8.5 for Mexico's 2000 and 2003 elections tells nothing about the fact that the Partido Acción Nacional (PAN) was more volatile than the Partido de la Revolución Democrática (PRD) and the Partido Revolucionario Institucional (PRI). Moreover, the Pedersen Indices in Mexico show that the elections have become more volatile over time since the 2000 election. However, inspection of the Pedersen Indices is unable to provide the information that the volatility of the PRI drove the overall electoral volatility in Mexico and that, in contrast, the incumbent PAN had relatively low volatility.
Table 1 also demonstrates interesting patterns of electoral volatility in Uruguay. If we only compare the Pedersen Index of Uruguay's 1994 and 1999 elections and that of the 1999 and 2004 elections, we may draw a conclusion that parties in Uruguay were becoming less volatile over time. However, Table 1 shows that each of the three major parties' electoral volatilities actually became higher from the 1994 election to the 2004 election. Additionally, we observe that the incumbent Partido Colorado (PC) had a low electoral volatility between the 1994 and 1999 elections, but it had a very high electoral volatility between the 1999 and 2004 elections as a result of a strong challenge from the Frente Amplio (FA). In short, one important implication from Table 1 is that merely relying on the Pedersen Index to analyze electoral volatility may impede a better understanding of the dynamics of electoral change at the party level.
Before estimating the full-specified HLM for the empirical analyses, I shall provide justifications on why estimating a random effects model (RE) is more appropriate than estimating a fixed effects model (FE) for this study.  The Hausman test shows that the chi-squared value with 13 degrees of freedom is 21.66 significant at the p<0.061 level, indicating that the difference between FE and RE is not significant so that the null hypothesis cannot be rejected.  This statistic suggests that FE and RE are two different ways to obtain the correct estimates, but RE is more efficient for fitting the data. In short, the Hausman test suggests that it is appropriate to estimate a RE estimator for this study.
[TABLE 2 ABOUT HERE]
Table 2 displays the results of two hierarchical linear models with full specification described in Equations 1 through 4. These models seek to capture the variance in electoral volatility within parties, among parties, and among countries. The estimated results of Model 1 largely support my hypotheses. First, the interaction variable of incumbency and economic voting, Incumbency*GDP Growtht1, has a statistically significant effect on party electoral volatility. The coefficient is negative and statistically significant, suggesting that a better national economic performance helps an incumbent party by reducing its electoral volatility. In contrast, GDP Growtht1 does not attain statistical significance, suggesting that a better economy does not affect an opposition party's electoral stability.
In addition, while irregular institutional discontinuities are hypothesized to significantly increase the level of electoral volatility for all parties in a country, the coefficient on Incumbency*Institutional discontinuity shows that this effect is stronger for incumbent parties. Within the group of incumbent parties, an institutional discontinuity will increase the electoral volatility score by an average of 6.18 for an incumbent party than an incumbent party that experienced no institutional discontinuity, which is about one third of Fujimorist party's mean volatility scores (19.5) from 1990 to 2011 in Peru.  The statistical insignificance of Institutional discontinuity suggests that an institutional discontinuity does not affect the electoral volatility of opposition parties. Therefore, the argument about institutional discontinuity and country electoral volatility (Madrid 2005; Roberts and Wibbels 1999) is modified in my analysis, which shows that the effect of such institutional alteration shock is contingent on a party's incumbency status.
The coefficient of Incumbency*Party age also attains statistical significance, indicating that the effect of party age on reducing electoral volatility is stronger for incumbent parties. Another way to interpret this result is that an older incumbent party will have a lower level of electoral volatility than a younger incumbent party. According to the results, an incumbent party has an average volatility score 1.92 units lower than another incumbent party if the former party was established ten years (i.e., log of 10 equals 1) earlier than the latter party, which is about half of the mean volatility scores of the PJ (3.8) in Argentina from 1983 to 2011. The result is robust even when using a different party age variable in which the operationalization is the log of the number of years from the year that the party participated in the first democratic election to the year 2011. The statistical insignificance of Party age suggests that the timing of the birth of an opposition party, whether earlier or later, does not influence this opposition party's electoral volatility. In short, the findings about the conditional effects of party age sharpen Mainwaring and Zoco's democratization timing theory of electoral volatility.
The effect of Incumbency is positive and statistically significant, but the interpretation of this result is not straightforward. Since Incumbency is interacted with many other variables in the model, the interpretation of its coefficient must take into account certain conditions. The estimated coefficient of Incumbency means that an incumbent party has a 7.7 volatility score higher than an opposition party's score when all of the following conditions are met: 1) the party is only one year old (i.e. the log of party age equals zero); 2) both GDP growtht1 and Inflationt1 in the party's country equals zero, and 3) the party's country had no institutional discontinuity between the elections.
Among the control variables, only Party size attains statistical significance. The result shows that larger parties have higher levels of electoral volatility than smaller parties. However, this effect is not substantively important. A party that obtained 10% more vote share than another party in the previous election will only have a 0.86 higher electoral volatility score. The country-level control variables bear little relation to party electoral volatility in my sample. Contrary to many previous studies of electoral volatility at the country level, Party system fragmentation does not have a significant effect on party electoral volatility. This finding is robust even when using a different measure of effective number of parties that is calculated by using the share of seats in the legislature. The variable of Ethnic fractionalization has no significant effect on party electoral volatility, suggesting that the ethnic cleavage argument that has been tested and supported at the country-level volatility (Madrid 2005) does not hold at the party level. Last, Trend does not have a significant effect on electoral volatility, indicating that time does not matter for explaining whether a party becomes more or less volatile over time.
Model 2 is a trimmed model in which the insignificant variables in Model 1 are excluded. The results of the primary explanatory variables are consistent, and thus they provide a robustness check for the findings in Model 1. One way to compare goodness-of-fit between Model 1 and Model 2 is to use deviance statistics (Singer and Willett 2003, 119-20). The deviance statistic provides a conservative test by comparing a log-likelihood current model (LLc) and log-likelihood saturated model (LLs). This statistic is equal to -2 multiplied by the log-likelihood ratio, and a value closer to 0 indicates a better fit. In this case, Model 1's deviance statistic is 2850.99, and Model 2's value is 2843.2. Therefore, we can conclude that Model 2 has the better fit.
Besides the deviance statistics, I also use the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) to compare the goodness-of-fit between these models (Long 1997, 109-12). Similar to the deviance statistic, these are based on log-likelihood tests, and a number closer to 0 is the better fit (Singer and Willett 2003, 120-22). Again, Model 2 has smaller AIC and BIC statistics than Model 1. Moreover, according to Raftery's (1995, 139) suggestion, an absolute value of the between-model differences in BIC larger than 10 is considered as very strong evidence that a model is preferred to the other. Since the absolute value of between-models difference in BIC for Model 2 and Model 1 is almost 50, it suggests that Model 2 is much better than Model 1.
Beyond the results presented earlier, I have conducted extensive sensitivity analyses to check the robustness of my results.  First, while the previous estimations allow intercepts and slopes to vary across parties and countries, I re-estimated the following alternative models: 1) a model that allows only the party-level intercept and slope to vary across parties; 2) a model that allows only the country-level intercept and slope to vary across countries; and 3) a model that disallows random intercepts and slopes at both levels, which means that intercepts and slopes are meant to describe the population as a whole. The re-estimated results of these models are substantively equivalent to those presented in Table 2, and thus they provide some evidence that my findings are robust.
Second, to avoid a potential problem that the results are driven by the cut-off point of my selection criteria on party data, I re-estimated the hierarchical model using a different sample of parties. The data are based on the parties that obtained 10% of vote shares in at least one election during the period under study, and thus the total number of observations is reduced from 527 to 440. Again, the re-estimated results remain identical to those presented in Table 2.
My third robustness check is to use a different model specification by including country-level fixed effects. It is possible that the relationship between party volatility and other independent variables might be a result of their joint relationship to some country-level variables that we were unable to be included in the analyses. If we assume that the unobserved country-level factors are stable over time, we may control for their potential biasing effect by estimating models with fixed effects for each country's mean party volatility intercepts. Such a model is equivalent to one produced through the inclusion of dummy variables for all but one country in the data set. An important difference between this model and the hierarchical model is that while the intercept of the hierarchical model is assumed to be a normally distributed random disturbance that is unrelated to all other variables in the model, the intercept in the fixed effect model comprises unknown, stable country-level factors that may covary freely with observed independent variables.
I estimated the country-level fixed-effect model using the Stata 11.1 xtregar module, which includes first-order auto-correlated disturbances. The results are similar to those presented in Table 2, indicating that my hypotheses are largely supported even after controlling for country-level fixed effects. 
High electoral volatility often characterizes electoral politics and plagues democratic stability in Latin America. While previous studies have provided explanations for country-level volatility, few studies have attempted to analyze what makes individual parties more volatile between elections. This study contributes to the literature by "bringing the parties back" to the research agenda of electoral volatility. Calculating party volatility by using a components-of-variance model, I first demonstrated that patterns of volatility at the country level differ from those at the party level. Then I estimated a hierarchical model to test party-level, country-level, and cross-level explanations of party volatility. The empirical findings are robust across different model specifications, showing that party volatility is affected by factors at different levels.
The empirical analysis illustrates that whether a party is an incumbent party or an opposition party matters for explaining the level of its electoral volatility, but the effect of incumbency is contingent on party age, national economic performance, and institutional discontinuity. The finding about the interaction effects of incumbency and party age strengthens the democratization timing argument proposed by Mainwaring and Zoco (2007). The empirical analysis implies that if two parties were founded in the earlier periods, both of them may have lower electoral volatility than other younger parties, but the one that is an incumbent party will have a more stable electoral performance that the other that is an opposition party.
In addition, the result that the incumbent party is more likely to have a stable electoral performance when the economy is better provides rigorous evidence to sharpen the economic voting explanation of electoral volatility (Epperly 2011; Remmer 1991, 1993; Tavits 2005). This finding has a strong policy implication that, in order to secure its electoral stability, the incumbent party needs to make the national economy stronger. Third, the stronger effect of a fundamental alteration of political institutions for increasing an incumbent party's electoral volatility suggests a more nuanced perspective for the research on the consequences of institutional change. The finding indicates that institutional discontinuity has more significant effects in reducing the electoral stability of the incumbent party than that of the opposition parties.
A surprising finding in this study is that the variables that have great explanatory power for analyzing country-level electoral volatility are not necessarily useful for explaining party-level volatility. For example, various previous studies have found that party system fragmentation and ethnic cleavage have significant effects on the electoral volatility of Latin American countries (Madrid 2005; Remmer 1991; Roberts and Wibbels 1999), but the effects of these variables are modest for explaining party volatility in Latin America. Overall, the insignificance of these results suggests an important caveat regarding ecological fallacy for the theory of electoral volatility.
To conclude, this study sheds light on the patterns of party development in Latin America. The multilevel analysis shows that, when taking party-specific features into account, more nuanced explanations of electoral volatility can be discovered. However, my exploration of the dynamics of party politics does not go far enough. One next step for future studies is to construct an appropriate research design to analyze country-level and party-level volatility simultaneously. This kind of research may provide more insights about the relative importance of different explanations concerning electoral volatility at different levels. Last, but not least, it will be promising for future studies to conduct comparative analyses on party volatility in different regional contexts.
Intercept (Initial status)
Party System Fragmentationt-1
Initial status ()
Initial status ()
Wald Chi2 (d.f.)
Prob > Chi2
*** p<0.001, ** p<0.01, * p<0.05
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