The Components of elections : district-times effects, district heterogeneity, and volatility

The Components of Elections: District-Time Effects, District Heterogeneity, and Volatility SCOTT MORGENSTERN Assistant Professor of Political Science Duke University RICHARD F. POTTHOFF Senior Research Scientist Department of Political Science Duke University WP núm. 213 Institut de Ciències Polítiques i Socials Barcelona, 2003 2 Scott Morgenstern; Richard F. Potthoff The Institute of Political and Social Sciences (ICPS) is a consortium created in 1998 by the Barcelona Provincial Council and the Universitat Autònoma de Barcelona, the institution to which the ICPS is officially linked for academic purposes. “Working Papers” is one of the collections published by the ICPS, specialising in the publication of work currently being undertaken by social researchers -in the author’s original languagewith the aim of facilitating their subsequent scientific debate. Inclusion of work within this collection does not prohibit its future publication by the author, who maintains full rights over the article. The work in question cannot be reproduced without the permission of the author. Publication: Institut de Ciències Polítiques i Socials (ICPS) Mallorca, 244, pral. 08008 Barcelona (España) http://www.icps.es © Scott Morgenstern [email protected] Richard F. Potthoff [email protected] Design: Toni Viaplana Printer: a.bís Travessera de les Corts, 251, entr. 4a. 08014 Barcelona ISSN: 1133-8962 LD: B-16.359-03 The Components of Elections 3 To what extent do legislative elections turn on national issues, rather than constituency service, candidate qualities, and the provision of pork? This question has been a central concern in both the comparative and the American politics literature, as it drives our understanding of the links between citizens and their representatives. It also has important normative implications. Writing for the American Political Science Association's Committee on Political Parties (1950), Schattschneider emphasized the benefits of a system in which the political parties take a leading role in debating and ultimately defining national issues. Schattschneider contrasted "responsible" party systems with that of the United States, where legislators are relatively independent of their political parties and are protected from national swings in the vote. As a result, national issues are of less consequence in legislative elections than are the candidate's abilities to bring resources to the district, solve minor constituent demands, and run a successful campaign. He argued the implications for national welfare were decidedly negative. The comparative literature has taken a similar stand, contrasting the quality of political representation and the prospects for development in porkridden systems such as Italy, Colombia, and Brazil with more nationally centered party systems (Mainwaring, 1999; Cain, Ferejohn and Fiorina, 1987; Geddes, 1991; Shugart and Carey, 1992; Haggard and Kaufman, 1995). This work has helped to establish the conventional wisdom about the difference between politics and elections in the United States and the United Kingdom, as well as provoking a growing body of literature about the problems of political accountability in the less industrialized regions of the world. It has also been very influential in defining the incentives of legislators in pursuing a "personal vote" (Carey and Shugart, 1995). The substantive and methodological issues raised by Schattschneider and his followers (see especially Stokes, 1965, 1967) are closely related to two other sets of literature. First, Rose and Urwin (1970), Bartolini and Mair (1990), Coppedge (1998), Mainwaring and Scully (1995), and Roberts and 4 Scott Morgenstern; Richard F. Potthoff Wibbels (1999) have argued about the causes and effects of electoral "volatility". An important purpose of Bartolini and Mair's work is to counter the work about the growing instability in European elections, an issue with direct consequences for accountability and representation in the short run and democratic consolidation in the long run. While other factors can cause electoral volatility, these authors explain that it has frequently been associated with a decline of longstanding cleavage structures, which "encapsulate" and constrain political conflicts. It is also related to questions about the national consensus, the homogeneity of political culture, and the institutionalization of democracy generally. Roberts and Wibbels focus on Latin America, arguing that "electoral volatility is a function of short-term economic perturbations, the institutional fragilities of both democratic regimes and party systems, and relatively fluid cleavage structures" (p. 575). The second body of related work has focused on the "nationalization" of elections, a term that applies to two different concepts. First, Stokes (1967), Katz (1973), and Claggett, Flanigan, and Zingale (CFZ; 1983) have used it to discuss the degree to which a party's electoral support responds uniformly to national events or issues. This concept is thus related to Schattschneider's concerns. More recently Caramani and Mainwaring/Jones have used this term to apply to parties that have relatively homogeneous electoral support across districts. Caramani argues that the degree to which support is homogenous is related to the "territoriality of political cleavages" (p. 67), and has important ramifications for the "standardization" of government processes, military socialization, social welfare, and economic policies (p. 68). In a manner not dissimilar from Schattschneider and Stokes, he argues further that as nationalization increases, "local candidates…lose their character of representing the local community. Rather they become the representatives of the national centre of the political organization" (p. 68). This, he continues, leads the voters to shift their attention from local to national issues. As a consequence of its effects on policy and the political process, Mainwaring and Jones add that nationalization has implications for the survival of democracy. The Components of Elections 5 In spite of clearly separable meanings of the terms "nationalization", "district effects", and "volatility", a debate has continued as to the appropriate definition, interpretation, and measurement of each concept. This paper, in response, offers definitions of the concepts with more precise theoretical and statistical meanings and develops a methodology to analyze the concepts simultaneously. In so doing we are able to separate the concepts -which we name district heterogeneity, the district-time effect, and electoral volatilityand explain the theoretical and empirical relationships among them. Our main conclusion is that there is no theoretical basis for conflating these terms, and empirically the relations are very weak. The statistical methodology that we draw upon is based on Stokes' original model. In two landmark studies Stokes (1965, 1967) analyzed U.S. and U.K. district level electoral results through a components of variance model. Our version of that model -which we apply to 20 countries in Europe and the Americasallows us to parse the data and study district heterogeneity, district-time effect, and electoral volatility as independent aspects of electoral competition. We argue that without such parsing there is a danger of biased results resulting from a conflation of issues. We draw on Stokes' model as it allows us to distinguish and explore the interrelationship among these three issues. We argue, however, that his and other similar models all have important flaws, the interpretation of the effects is imprecise, and they require some reorientation for application to comparative work. In this paper we focus the majority of our attention on developing the statistical model for studying the different components of elections. We do, however, also reach several theoretical and empirical conclusions. Our primary theoretical conclusion is that, despite their presumed ties in the literature, there are neither statistical nor theoretical links between the district-time effect and district heterogeneity, and neither is linked with volatility either. The three concepts are, instead, three separable characteristics of parties. But, because they all relate to electoral data, statistical studies that focus on just one or two of the concepts run the danger of generating biased results. At the empirical level, this paper focuses on the US-UK comparison, using 6 Scott Morgenstern; Richard F. Potthoff the results from 18 other countries to test the theoretical proposition about the relationships among the different components and put the results regarding the United States and Great Britain into a wider perspective. This allows us to argue that these two Anglo countries are more similar than different. We show, in particular, although the conjunction of traits is not unique, the parties in these two countries are among the very few that combine very heterogeneous support across their nations, relatively stability over time, and a significant role of local forces in their elections. At the same time, we find that in recent decades the parties in the United States and Great Britain have separated on the last of these traits (what Stokes called the "district effect"), as the effect has grown considerably in Britain's former colony. This is a noteworthy change given that Schattschneider and Stokes were very concerned about the relatively small differences in the 1950s. In order to put forth this argument, we first develop an example that allows us to clearly define the effects that we are measuring. We then discuss some of the problems with recent attempts to address these issues. Next, we develop our components of variance model which we apply first to the US-UK comparison and then to a broad set of cases across Europe and Latin America. We use the empirical section to categorize 63 parties according to the three traits and buttress our claim that the different aspects of representation are not highly correlated. The concluding section summarizes the findings and suggests directions for future research by noting a few of the comparative patterns and discussing issues related to defining a model for explaining these patterns. DEFINITIONS AND PREVIOUS ANALYSES The following example illustrates our definitions for district heterogeneity the district-time effect and electoral volatility. The example assumes two hypothetical countries, A and B each with three equally sized districts D1, D2 and D3. For both countries party P1 is assumed to have won 59 percent in D1, 53 percent in D2 and 47 percent in D3 for the first year, Y1. This The Components of Elections 7 represents relatively consistent support across districts, or a relatively low district heterogeneity. In second electoral year, Y2, the overall average support for party P1 dropped by 10 points in both countries, representing at least a moderate level of volatility. The distribution of that loss, however, varied in the two countries. Country A's party P1 lost exactly 10 percent in each district, while in country B the 10 point total loss between the two years is not distributed equally among the districts. The perfect consistency of the electorate's movements across districts and over time would therefore yield a district-time effect equal to zero in country A and considerably higher in country B. Volatility, in sum, is a measure of the degree to which a party's average vote is stable across different electoral time periods. It should be high in countries where successful new parties form or the electorate easily shifts among parties. We apply the term district heterogeneity to conjure an image of the degree to which a party wins consistent support across districts. It should be relatively high for the U.S. parties, since their support varies greatly between rural Kansas and metropolitan New York. Finally, the district-time effect addresses the localism issue that concerned Schattschneider and Stokes. Having once accounted for movement over time and across districts, what is left are the idiosyncratic qualities and characteristics of candidates and districts. Stokes interpreted this as a measure of the importance of the idiosyncracies to the election, apart from national events. As we discuss in more detail below, Katz and others have argued that these idiosyncracies may also yield systematic (but not uniform) responses of the districts to national events. Regardless of this interpretive distinction, the district-time effect captures the degree to which variance in electoral returns is accounted for by characteristics particular to districts (or candidates) at a particular time. 8 Scott Morgenstern; Richard F. Potthoff Though under different guises the concepts represented by district heterogeneity, the district time effect, and electoral volatility have been at the core of studies on electoral politics and representation, they have not been clearly tied together either substantively or methodologically. Instead, comparativists have generally addressed single dimensions of the problem. For example, Caramani's historical study of Europe and Mainwaring and Jones' interesting study of the "nationalization of parties and party systems" in Latin America only address the homogeneity of support across districts1. These are both important works that offer compelling findings and useful methodological innovations. The above example, however, well illustrates the problems with their unidimensional approach. In the first of these studies, Caramani uses the coefficient (or index) of variation2 to consider the spread of electoral returns to each party in each district. If the returns are relatively consistent, then the party is considered nationalized. He finds important variation across the countries of Europe, but his main finding is increased homogenization of districts over time. For both countries in Table 1, the standard deviation for party P1 in both years is 6, and thus for both countries he would calculate a coefficient of 6/53 in Y1 and 6/43 for Y2, numbers that would indicate relatively high levels of nationalization. His measure, however, would miss the perfectly parallel movement of the districts in country A and a lack of such parallelism in country B. It is important to note that Caramani calculated his statistics without regard to whether a party competed in all districts. This may be defensible since part of his interest was to show increasing levels of coverage for the parties and in most of Europe the proportional representation systems The Components of Elections 9 encourage parties to compete in most districts. But, the model will not return reasonable results for the United States, Great Britain, or other countries where major parties fail to compete in all districts as a result of the use single-member districts and incumbency advantages. In our analysis of the single-member district countries, therefore, we exclude districts where either of the two parties did not receive at least 2.5 percent of the vote in each election years3. Mainwaring and Jones have a similar goal in their tests for Latin America. Instead of the coefficient of variation, they argue that the Gini coefficient provides a better measure of inter-district homogeneity. Like the coefficient of variation, the Gini coefficient yields a scaled statistic that is useful in comparing results among countries or over time for a single country. They then use this method to show which parties in which countries have had more success in developing consistent support levels. While they do provide interesting comparisons, the works by Caramani and Mainwaring/Jones, in focusing solely on homogeneity of districts, have important limitations. First, the measures are flawed, in that they effectively conflate the issues of district heterogeneity and district-time, even though seemingly they purport to assess only district heterogeneity. Second, while it is useful to have a statistic that points to the different levels of Democratic support in Massachusetts and Utah, it is also interesting to know whether a scandal or its inverse in Washington produces consistent changes in the Democratic votes in the two states. It is also important to capture the degree to which the Democrats retain relatively consistent support across time. In the terms of country A in the above example, the Caramani and Mainwaring/ Jones approaches would capture the important static differences between districts D1, D2 and D3, but not the relatively volatile average support for the party across time nor the remarkable dynamic consistency in the movements across time for the P1 party. Along these same lines, offsetting district support levels would go undetected in these homogeneity studies. That is with either of the two approaches, if P1's vote totals for D1 and D2 were interchanged for any year as shown in the comparison of the countries A and B, the statistics 16 Scott Morgenstern; Richard F. Potthoff 2 A σ and 2 σ , but not one that pertains to variability among districts. This seems to us an inappropriate assumption. The decision to apply random or fixed effects is not always clear-cut. According to Jackson and Brashers (1994), random factors should be applied if the factors can be treated as if they were chosen at random from a population, if the sample could be replaced by another sample without changing the research question, or if the conclusions can be generalized to other levels of the variable (p. 5-6). In this case, while our districts are exhaustive for a particular year, they are simply the observed sample of all district years. Further, we could hypothetically redraw the district boundaries and rerun our analysis without changing our research questions. Still another conception of this issue is to consider the districts (or the times, for that matter) as being drawn randomly from a superpopulation (Deming and Stephan, 1941). The superpopulation of districts would be the hypothetical infinite set of districts from which the actual districts could have been drawn. Thus, it seems clear that district heterogeneity should be treated as emanating from a random effect. The consequence of treating random (in this case district heterogeneity) effects as fixed is that an important source of variation is simply left out of the analysis. All the variation is thus attributed to the time (national) and residual components. As a result, by making the inappropriate assumption that the effects for district heterogeneity are fixed, the utility of the results is dubious. Stokes apparently reasoned that any effect involving time should be treated as random, but that any effect involving only geography should be treated as fixed on the grounds that the population of a district (or state) is given. Our alternative formulation postulates random rather than fixed variation with respect to district heterogeneity. Our solution to this problem is to simply replace the β i with a Bi, where Bi is a random effect (covering all years) for district i, assumed to have The Components of Elections 17 mean 0 and variance 2 B σ . We therefore apply the model: Model AB: ikikik CBAy +++= µ In this model Ak and Cik have the same expectations and variances as in model A*, and also 2 A σ and 2 σ are estimated the same as before. We now require, however, expressions to estimate 2 B σ , MB, and 2 B S, respectively the mean square and the sum of squares reflecting district heterogeneity, are calculated as: 1 2 − = I S MB B and ∑ = −= I i iB yyKS 1 2 ... 2)( Under model AB, the statistic K MM RB B − = 2 ˆ σ is used to estimate (and has the expected value of) 2 B σ . Under Model A*, however, K MM RB − does not estimate 2 B σ because the model has no 2 B σ . Instead, this statistic has expectation )1( .)(2 − − ∑I i i ββ , where β . is the mean of the I β i's. Though Model AB is our preferred model, it is important to discuss another variant, proposed by Kawato (1987). Kawato uses a different form of a components of variance model to reexamine Stokes' findings about the increasing role of national forces in U.S. elections. His model, however, makes what we consider to be some untenable assumptions that result in the 18 Scott Morgenstern; Richard F. Potthoff exclusion of certain sources of variation. He assumes a nested model of districts within states and states within the nation14. To explain, we first modify Kawato's model as we did with the Stokes model to account for just two geographic levels (district and nation) instead of three (district, state, and nation). The two-level analogue of Kawato's model is Model A: . ikkik CAy ++= µ Because Model A is a nested model of districts within the nation, it has the same type of flaw as the corresponding three-level model. It is, however, a simpler model and therefore easier to present. Because of its nested nature, Model A has neither a random effect (Bi in Model AB) nor a fixed effect ( β i in Model A*) to take account of district heterogeneity. In fact, it rests on the dubious assumption that variability among districts is nonexistent, that is, that 2 B σ = 0 in the context of Model AB or that all β i's are the same in the context of Model A*. As a consequence, if variability among districts does exist, then the Model A estimates of both 2 σ and 2 A σ (whose formulas are given in Table 2) will be distorted, with the former estimate being inflated and the latter too low15. Model AB treats time and districts symmetrically, whereas Models A* and A do not. That is, Models A* and A retain a random effect for time but not for district heterogeneity. Why, one might wonder, would it not be equally logical to apply a model that has a random effect for district heterogeneity but not for time? This query leads to the last two models that we cover, Model B*: ikikik CBy +++= αµ and Model B: . ikiik CBy ++= µ Model B* is the same as Model AB except that Ak, a random effect for time k in Model AB, has been replaced by α k, a fixed effect for time k. Model B is like Models AB and B* except that it has neither a random nor a fixed effect for time. The Components of Elections 19 Of course, we mention Models B* and B not because we advocate them, but rather to give a fuller perspective. Although models like A* and A have appeared in the literature whereas models like B* and B apparently have not, there would seem to be little more reason to treat the effects for time but not district heterogeneity as random than to treat the effects for district heterogeneity but not time as random. We prefer both to conceive of districts as being drawn randomly from a superpopulation of districts and to conceive of times as being drawn randomly from a superpopulation of times. The Table 2 indicates the primary elements of the different models. The models are differentiated as to which effects are included and whether these effects are dealt with as fixed or random effects. There are methods to estimate variance components other than through the traditional formulas that we have used16. These traditional formulas are simple, are consistent with the work of Stokes (1965) and Kawato (1987), and in most cases would appear to give results that differ little if any from those of other, newer methods. Although some other methods do avoid negative 20 Scott Morgenstern; Richard F. Potthoff estimates of variance components, such negative estimates did not arise often in the data analyzed for the present paper. APPLYING THE MODEL Results for the Hypothetical Countries In order to show the validity of the different approaches, we first return to the simple three-district example we used earlier. Under our model the estimates for the time, district heterogeneity, and residual (district-time) effects for country A are, respectively: 2 ˆA σ = 50.0, 2 ˆB σ =36.0, and 2 ˆ σ = 0.0.17 Consistent with the data, 2 ˆA σ implies that there is an important degree of volatility in the party's support over time (the party having lost 10 percent of its support), 2 ˆB σ implies that the party's base support levels among the districts are somewhat variable (with a 12 percent difference in support separating the two most extreme districts), and 2 ˆ σ implies that the party's vote across the districts moves in perfect tandem (each district having lost exactly 10 points). The estimate for district heterogeneity is about average in comparison with most of the actual cases we detail below, while most actual parties sport lower values for their time components. Of course, no actual party scored a perfect zero for the district-time component, but the analysis did yield very low scores for some parties in both Latin America and Europe. The parties of the United States and Great Britain, in contrast, scored much higher. As we noted earlier, Kawato's model generates biased results. His model ignores 2 ˆB σ and for both countries A and B it would calculate 2 ˆA σ = 38 and 2 ˆ σ = 36. The associated bias yields very misleading results (as he underestimates 2 ˆA σ and overestimates 2 σ for both countries). Another problem with the Kawato model (as with the Caramani and Mainwaring/Jones models) is that it yields identical results for countries A and B. In contrast, our preferred The Components of Elections 21 model (AB) accurately reveals important differences between the hypothetical countries. For country B our model would yield 2 ˆA σ = 44.0, 2 ˆB σ =18.0, and 2 ˆ σ = 18.0. The measures proposed by Caramani and Mainwaring/Jones for district heterogeneity also yield misleading results. The problem with these measures is that they reflect the district heterogeneity component and the residual component combined. Note that for both countries A and B the sum of 2 ˆB σ and 2 ˆ σ is 36, the square root of which is the standard deviation of the party's vote percentages across districts in each year (equal to 6, as noted earlier) that Caramani would obtain through his analysis. For both countries A and B, Stokes' model would yield the same values as ours for 2 ˆA σ and 2 ˆ σ but would not produce a 2 ˆB σ at all. Results for Actual Cases To review, our model produces three components of variance. In nontechnical terms, the district heterogeneity component measures the degree to which the vote share for a party is consistent across the country. Bigger values of that component therefore mean that the party's vote shares are less consistent across districts. The time component is analogous to studies of volatility, in that it measures the degree to which a party's national vote share varies across time. Larger values of this component, therefore, imply that a party's national vote share is less consistent over time. The residual component, finally, measures the degree to which the returns to a party vary across elections within a particular district, having accounted for the other effects. Here larger values imply more inconsistency in how a national level shock is distributed across districts. To begin to understand and compare these three concepts crossnationally, we first focus on the United States-Britain comparison. As noted, for the United States, we followed conventional practice and only used districts where both of the main parties won at least 2.5 percent support in every 22 Scott Morgenstern; Richard F. Potthoff election over the time period18. In effect, however, a cutoff point of up to 20 points yields substantially the same set of districts. For that country, we show results for the 1950s, 1970s, and 1980s, accounting for redistricting. Since there are just two parties competing, the results are the same for each. For Britain, redistricting led us to assemble three periods for the analysis: the five elections from 1955-1970, the three elections between 19741979, and the two elections of 1983-1987. Following Stokes' practice, we conducted the analysis on districts where either the same two parties or all three parties competed in every year of the period. In the latter two periods we were able to run the analysis on the Conservatives, Labour, and the Liberals. For the first period, while the Liberals ran in enough districts for us to calculate separate results for Labour and the Conservatives, the party did not run in enough districts for us to estimate separate results for it. Further details are in Appendix I. In the multi-country below we present tables on both the raw estimates as well as the proportions of the variance explained by each component. Here, however, we focus on the raw values in order to draw attention to the amount of variance inherent in the system. The table below portrays the estimates for the three components of variance for the United States and the United Kingdom, showing important similarities for two components, but important differences for the district-time component, especially in the 1970s and 1980s. The statistics under the time component heading reflect the parties' changing support levels in the three sets of elections. For Britain, the Conservatives saw important changes in their support levels between 1955 and 1979 (for example, falling about seven percent from 1959 to 1966), but between the 1983 and 1987 elections their aggregate totals were virtually unchanged. The statistics also reveal that a switch between the Conservatives and the Liberals accounted for most changes in the 1970s, as Labour's support remained quite stable. For the United States, there was greater volatility in the 1950s than in the later decades, with tremendous stability in the parties' vote totals for the 1980s. This stability is reflected in the remarkably The Components of Elections 23 small change in the congressional division of seats resulting from those four elections. Next and more dramatically, the table shows that the district heterogeneity component dominates the other components for both countries, and is similar in both absolute and relative terms for the two countries. Moreover, in comparison to the other countries that we explore below, the British and American figures stand out as among the largest. In both countries this heterogeneity -which the statistics underestimate due to the exclusion of uncontested districtshas manifested itself in the large number of safe seats for one or the other of the main parties. To show the validity of these data, Table 4 displays statistics that correspond with Caramani's analysis of the spread of the party vote across districts. While he does not dwell on the issue, his analysis of 1918 to the present shows that the British electorate is the least homogeneous of any 24 Scott Morgenstern; Richard F. Potthoff European country (see his Table 3.3, p. 75)19. Eliminating any district in which the pattern of competition changed (e.g. the status of the Liberals changed with respect to whether or not they competed) or where either the Conservatives or Labour did not win at least 2.5 percent of the vote, the standard deviation of the Conservative vote has varied between 10 and 15 points, and has been even higher for the Labour Party. The coefficient of variation that Caramani studied has also been consistently higher since the election in 1983 than in the previous quarter century. For Labour the coefficient of variation is markedly higher than for either the British Conservatives or the U.S. Democrats. In sum, as our components of variance model suggests and this table confirms, parties in both countries experience wide differences in their support levels across districts, even when accounting for uncontested races and the occasional inclusion of third parties. While the estimates for district heterogeneity are relatively similar for the two countries, the estimates for district-time show important differences. The figures in the last column of Table 3, as well as the columns indicating the standard deviation of the swing in Table 4, resonate with standard descriptions of the two systems, in that they imply that the electoral tides are spread much more evenly across British districts than in the United States. Comparing the results for the district heterogeneity and the districttime effects highlights the problem with the term "nationalization". These statistics imply that while Stokes and Schattschneider were right about how national issues or events are translated more consistently across Britain than in the United States, in neither country are elections "nationalized" by the standards applied by Caramani20. Aside from the terminological issues, the two tables also suggest a modified view of the comparison between the United States and the United Kingdom. Stokes concluded that although the district-time effect (to use our term) for the United States had shrunk considerably throughout the first half of the 1900s, it was still much greater than in the United Kingdom. This helped substantiate Schattschneider's fears about U.S. elections having The Components of Elections 25 32 Scott Morgenstern; Richard F. Potthoff but heterogeneous support, plus an important district-time effect. This could be contrasted with much of Europe, where parties have more homogenous but less stable support, combined with minimal local/ephemeral effects. Table 6 also reinforces the similarity of these two countries in terms of what Stokes labeled the national effect. As discussed above, he uses 2 A σ expressed as a percentage of total variance as his indicator of this effect. Table 6 shows that in both United States and the United Kingdom are well below the mean on this dimension. These two typologies are not opposing ends of a unidimensional continuum, because the three effects do not co-vary. If we eliminate the parties that have less than 5 percent support, the Pearson correlation coefficient between the time and district heterogeneity components is -0.09 and between the time component and our residual component it is only 0.3125. The relationship between the residual and district heterogeneity components is also, 0.31. If we apply the tests to the ranks instead of the actual values (i.e. Spearman's rank correlation coefficient) the strength of the relationship between the district heterogeneity and residual components rises considerably (to 0.57), but the relationship is still far too weak to conjoin these components into a single dimensional continuum26. Moreover, if we restrict the analysis to parties that have at least 10 percent, the Spearman coefficient drops sharply (to 0.38). The similarities of the United States and the United Kingdom, as well as the weak relationships among the variables, is shown in the Table 7. Dividing each of the components at its median, the table shows that all eight possible combinations of the three components are filled and that while their position is not unique, the United States and all the parties in the United Kingdom do occupy the same cell. The Components of Elections 33 This weak empirical relationship stands in contrast to the presumed strong relationship implicit in studies of single aspects of volatility, district heterogeneity, and the district-time effects. There is very little basis for a strong theoretical relationship either. Consider, for example, the relationship between district heterogeneity and district-time. If district heterogeneity is minimal, then one would not be surprised to find that the district-time effect is also minimal, since the districts generally must move together to yield the district homogeneity27. The reverse, however, is not true. A party with heterogeneous support across districts may experience a small district-time effect (as in classical analyses of Britain) or a large district-time effect (as in the United States). It is therefore of little surprise that the statistical relationship between these two variables is very weak. This pattern is evident in the data. Of the 63 cases in our sample (ignoring the parties with less than an average of five percent support), five of 34 Scott Morgenstern; Richard F. Potthoff the six with the lowest levels of district heterogeneity are also among the ten cases with the lowest residual components. In contrast, of the six cases that are found at the other end of the heterogeneity scale, only three rank among the ten with the highest residual components. The theoretical relationship between either of these variables and time is even weaker. When district-heterogeneity is low, then perturbations in a party's support would be magnified across the country, thus augmenting volatility. But, it seems unlikely that a party that was entrenched enough to have gained relatively homogeneous support across a country would also suffer from significant volatility. Alternatively, we would expect rising new parties or those led by crashing populists to have uneven support across the country. The United States and the United Kingdom, however, show that even over a long period of time, heterogeneous support levels do not necessarily imply large levels of volatility. Our data empirically confirm these expectations about weak links between volatility and district-heterogeneity. Of the six most homogenous parties, two experienced high levels of volatility (the Netherlands' Democracy 66 and Denmark's Conservatives). At the same time, other parties (notably Italy's Socialists and MSI) were both very stable over time and could count on very homogeneous support across districts. Towards the other end of the scale we find the U.S. parties and the British Conservatives of 1983-1987, which combined stability over time with heterogeneous support across districts. There is little theoretical basis to expect a strong relation between volatility and the district-time effects either. While elections focused on local issues could help a party stave off large fluctuations in its national vote share (e.g. the United States), a high district-time effect would not necessarily preclude sharp aggregate changes (unequally distributed amongst districts). High volatility could also imply the coming and going of parties with strength in only subsets of a country's districts (such as the Liberals in Britain in the 1950s and 1960s). The relationship is also ambiguous at the other end of the scale. Where the district-time effect is very small, we should find some of The Components of Elections 35 the more volatile parties, since they could both take advantage of and be vulnerable to changes in salient issues. A populist or Green party, for example, could experience a meteoric rise or crash, since voters would be focused on the national leaders and their issues. But, as argued above, where there is low district heterogeneity there should also be a low district-time effect (though the reverse is not true). The low district heterogeneity, we further argued, was likely to be associated with established parties, which, in turn, impede volatility. To further illustrate this weak relationship, imagine two countries each with two districts. Assume further the ruling party has very different levels of support in the two districts in one country, but its counterpart has consistent levels support in the other country. If both ruling parties crashed to zero support, then the volatility would be high in both cases, but the district-time effect would be high in the first country and low in the other. Again, the data bear out this expectation. While five of the ten most stable cases of parties over time rank among the seven with the highest residual effect, Italy's Socialists and MSI have very low ranks for both of these components. At the other extreme is Venezuela's AD, for example, which was both the second most volatile party in the sample, as well as the case with the sixth highest district-time component. CONCLUSION Though traveling under different pseudonyms, the concepts of district heterogeneity, volatility, and the district-time effect have long been at the center of debates about democratic stability and representation. In this paper we have argued that analyses of these concepts have been hampered by imprecise definitions, measurement techniques that are not broadly applicable, and important flaws in the statistical models. In our effort to explore these issues we have rejected recently developed methodological tools, and have instead reverted to Stokes' original components of variance model. In so doing we discovered an important flaw in his methodology, and have thus offered here a modified version of his model. In 36 Scott Morgenstern; Richard F. Potthoff addition to correcting a flawed statistical assumption, our alternative allows straightforward analysis for countries that unlike the United States, use proportional representation electoral systems. The method is also valid for single-member district systems as found in Britain and its former colonies, because for these countries it focuses on districts instead of states or provinces as the proper level of analysis. Finally, while explaining the algebra behind the model involves multiple lines of equations filled with Greek letters, the model has the virtue of requiring only a few lines of code and a built-in SAS function. In applying the model we have focused on our finding that, although they have separated on one dimension (the district-time effect) in recent decades, the United States and the United Kingdom have some important similarities that bi-country analyses have overlooked. As this paper has focused more on methodological themes than on comparisons and explanation, we have not attempted to develop a model to explain the many suggestive patterns revealed in the empirical data. That data, for example, suggests that in spite of Caramani's finding that nationalization has progressed throughout Europe, most parties' support levels are still quite variable across districts. The data also shows that aside from a few exceptions, the time components in both Europe and the Americas are quite small. While the data set does not include some of the more volatile countries such as Ecuador, Bolivia and Peru, this is still a particularly noteworthy finding for Latin America where historically parties have experienced high levels of volatility. Another avenue for future research could explore the dramatic differences between Europe and the Americas in terms of the interelection changes at the district level (as captured by the residual component). With the exception of the Portuguese Alliance of the CDS and PSD, no party in Europe scored above 12.7 for this component. For Latin America only the Uruguayan parties, the Colombian Conservatives, and the Brazilian PT scored below 29.4. In moving towards an explanation of these and other patterns, future researchers will have to contend with variation among regions, as well as The Components of Elections 37 among and within countries. Some apparent variables, such as the use of single member district electoral systems, therefore, can only provide partial explanations. The use of single member districts may help separate the U.K. and U.S. cases from the pack, but that variable cannot explain the widening gap in those two cases or the differences among other cases. It is also clear that the size of the party or the number of districts in a system cannot account for the size of any particular component uncovered in this analysis, or even the amount of total variance. For example, joining the parties of the United States and its former colonist in portraying a high level of total variance are parties from Portugal, Venezuela, and Brazil, which have just 20, 23, and 27 districts respectively. At the other end of the scale, some of the parties in Chile, Italy, and Spain have relatively low amounts of total variance in spite of having to compete across a relatively large number of districts (60, 95, and 52, respectively). Use of our methodology, in sum, provides a useful window on three types of variability exposed in district level electoral data. While we leave the difficult task of explaining the revealed patterns to future efforts, we would suggest that any full explanation will require a combination of macro or institutional variables to capture the inter-country and inter-regional differences and a set of variables that can differentiate amongst parties within a single country. 38 Scott Morgenstern; Richard F. Potthoff Appendix The countries selected to test for this model were all those available in Caramani's dataset (available on CD) and those Latin American cases for which we could acquire data. The U.S. data is available from the InterUniversity Consortium for Political and Social Research (ICPSR). We ran the analysis for the most recent time period in which there were at least three consecutive elections in which the main parties did not change and there were no districting changes. As explained in the text, we also required that the parties compete in all districts in all years. As a result, in cases such as France or Germany, where two or more parties joined in at least occasional alliances, we were forced to run the model as if the parties were always in alliance. Similarly, for Chile we could only run the analysis on the two coalitions instead of the parties, since no party has competed in every district. As stated in the text, for the United States and Great Britain, we followed conventional practice and eliminated districts in which the two main parties did not each win between 2.5 and 97.5 percent (if the criterion were changed to between 20 and 80 percent very few additional districts would drop out). This is a less important restriction where there are multiple parties running under proportional representation rules, and thus, for example, we have calculated estimates for the Italian MSI, for example, in spite of their support falling to under 2.5 percent (but not to zero) in some districts. It is important to note the very serious errors that we found in Caramani's dataset. For Britain we found about 20 errors (for the period 1955-1987) in which a digit was dropped or added to the reported statistic, numbers were erroneously transcribed, or the Labour and Liberal votes were interchanged. The errors that we discovered all changed the affected party's vote by at least 15 percent, and usually by at least 20 percent. We also found two districts in Spain where there was a serious error in the statistic listed for the Alianza Popular in 1982. We have verified that there are no significant errors in other countries by looking at the inter-election changes at the district level. A list of the errors we found is available upon request. The Components of Elections 39 The following table details the specific coding arrangements we followed, the years of the included elections, and the number of included and excluded districts. 40 Scott Morgenstern; Richard F. Potthoff NOTES 1. Their statistics, however, effectively conflate district heterogeneity and the district-time effect. 2. Coefficient of variation = Standard deviation/mean. 3. This is Kawato's cutoff point. Excepting 0, the choice of cutoff points has almost no bearing on the analysis. As noted later, we also excluded one Italian district where not all major parties competed. The Components of Elections 41 4. A final problem with either approach is that for two-party systems, the results are dependent on which party the investigator chooses as a reference. For example, the index of variation would be different for the Democrats and Republicans in the United States, even though one is a reflection of the other. 5. There is an important distinction between the "national effect" and a nationalized election. For Stokes and Schattschneider the term nationalization appears to mean that the national events drive elections. As such, Stokes terms an election nationalized if the district effect (what we call the districttime effect) is small. What he terms "national effect," however, is closer to our measure of "district heterogeneity". The confusion is even greater if we bring in Caramani and Mainwaring/Jones, whose use of the term nationalization reflects the idea of district heterogeneity. 6. He then turns to a criticism of Katz's methodology. 7. See footnote 14 for details. 8. Bartolini and Mair, for example, largely debunk the notion that Europe experienced an increase of volatility in the 1970s. 9. Bartolini and Mair even note: "there has been remarkably little debate or disagreement concerning the actual mathematical formula from which the index of aggregate volatility is derived" (p. 20). 10. A related difference between our model and that of Stokes involves his use of nesting. In his model he nests congressional districts within states, in order to account for systematic movements of all districts within a state. CFZ, alternatively, nest the districts (actually counties in their case) within regions. Neither of these techniques can be applied comparatively, for, among other reasons, the fact that under most PR systems there is but a single district per state (or province). We see the justification for nesting a sub-sub-national level within a sub-national level as rather underdeveloped and imprecise. While Stokes' method assumes the possibility of state tides, CFZ argue in favor of a model that measures regional tides. An alternative approach could test for tides among districts based on rural-urban categories, their relative wealth, ethnic makeup, or some other characteristic(s) of districts. All the points just mentioned lead us to use a basic model without nesting -a model with the district as a single sub-national level, and with the district effects random rather than fixed as will be explained shortly. 11. An alternative to dropping the extra geographic level would be to assign a regional component to the European and Latin American countries that would 198/02 UCELAY-DA CAL, Enrique: The shadow of a doubt: fascist and communist alternatives in catalan separatism, 1919-1939 199/02 CAZORLA, José: El dilema norte-sur al inicio del siglo XXI 201/02 MURILLO, Gabriel; VALDIVIESO, Yanina: El escalonamiento de la crisis política colombiana 202/02 RIVAS LEONE, José Antonio: Transformaciones y crisis de los partidos políticos. La nueva configuración del sistema de partidos en Venezuela 203/02 MARTÍ i PUIG, Salvador: La izquierda revolucionaria en Centroamérica: el FSLN desde su fundación a la insurrección popular 204/02 NÚÑEZ VEGA, Jorge: La República ambigua. 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The evolution of the Communist Party of Spain (PCE) and the United Left (IU) 210/02 FONT, Joan: Local participation in Spain: beyond associative democracy 211/02 BARRACHINA LISÓN, Carles: El retorno de los militares a los cuarteles: militares y cambio político en España (1976-1981) 212/02 GARCÍA MONTERO, Mercedes; SÁNCHEZ LÓPEZ, Francisco: Las comisiones legislativas en América Latina: una clasificación institucional y empírica 213/03 MORGENSTERN, Scott; POTTHOFF Richard F.: The Components of Elections: District-Time Effects, District Heterogeneity, and Volatility 214/03 CURBET, Jaume: Una seguridad ilusoria 215/03 CASTRO, Carles: Escenaris electorals de futur a Catalunya 216/03 BOSCH, Agustí; RICO, Guillem: Leadership Effects in Regional Elections: the Catalan Case 217/03 TORRES VELA, Javier: Una propuesta de reforma del sistema electoral "Working Papers" is a collection of publications published and distributed by the Institut de Ciències Polítiques i Socials (ICPS). 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