Concept of Internal Political Efficacy

The concept of political efficacy was originally defined as the “feeling that individual political action does have, or can have, an impact upon the political process, i.e., that it is worthwhile to perform one's civic duties” (Campbell, Gurin, and Miller Reference Campbell, Gurin and Miller1954, 187). As noted by Lane (Reference Lane1961, 149), however, this definition includes two dimensions of efficacy: one related to self-image, which is closely related to the concept of subjective political competence analyzed by Almond and Verba (Reference Almond and Verba1963, 181–213), and one to the image of democratic government. The two dimensions are referred to as internal political efficacy, defined as “beliefs about one's own competence to understand, and to participate effectively in, politics,” and external political efficacy, which is “beliefs about the responsiveness of governmental authorities and institutions to citizen demands” (Niemi, Craig, and Mattei Reference Niemi, Craig and Mattei1991, 1407). Since the 1960s, internal political efficacy has been a central measure in the literature; Morrell (Reference Morrell2003, 591) has thus identified more than 75 studies of its measurement, causes, and consequences.

The feeling of political efficacy is positively correlated with participation (Clarke and Acock Reference Clarke and Acock1989; Pollock Reference Pollock1983, 404), but although empirically related, feelings of efficacy and actual participation are two distinct phenomena. First, just that people feel more competent to participate does not imply that they will participate more. Despite confidence in their own competence, they may believe that government is unresponsive (i.e., they may have low external political efficacy), or they may simply be too busy or uninterested in participating. It is also perfectly possible to feel efficacious and have plenty of time without having particular reasons to participate. We do not have data on whether individuals actually participate less in the large amalgamated jurisdictions of Denmark or whether governments in small jurisdictions are more responsive to citizen demands. Second, feelings of IPE and rates of participation have different implications for democracy. Almond and Verba (Reference Almond and Verba1963, 255–57) conclude that the feeling of efficacy, compared to actual participation, which may also have a destabilizing effect, has several desirable effects: It increases the legitimacy of a system; it leads to political stability, greater acceptance of participatory democratic systems, and higher valuation of the participation of fellow citizens; and it “may be taken as an index of the extent to which they consider their nation democratic.” Self-confident citizens are also more likely to be active (Almond and Verba Reference Almond and Verba1963, 257; Pollock Reference Pollock1983) and more satisfied (DeHoog, Lowery, and Lyons Reference DeHoog, Lowery and Lyons1990), and a well-functioning participatory democracy increases feelings of efficacy (Clarke and Acock Reference Clarke and Acock1989; Madsen Reference Madsen1987). When it comes to the quality of a democratic order, the question of whether citizens believe that they have adequate possibilities to participate in and influence political decision making, rather than whether they believe that they have sufficiently weighty reasons to actually participate, is crucial. According to Dahl (Reference Dahl1989, 109), the central question is whether citizens “have adequate and equal opportunities for placing questions on the agenda and for expressing reasons for endorsing one outcome rather than another.”

IPE has been measured in a number of ways. Five survey questions, labeled Qualified, Understand, Public office, Informed, and Complex, have been used in different combinations. We use these questions, translated into Danish (see Lolle Reference Lolle, Kjær and Mouritzen2003) and adapted to local politics (see Table 2 for wordings). Niemi, Craig, and Mattei (Reference Niemi, Craig and Mattei1991) recommend using Qualified, Understand, Public office, and Informed, but not Complex. Morrell (Reference Morrell2003, 592) identifies four frequently used ways of measuring IPE. He concludes that the four-item index developed by Niemi, Craig, and Mattei (Reference Niemi, Craig and Mattei1991) is among the most popular, and that it consistently performs as a reliable and valid measure (Morrell Reference Morrell2003, 600). We call this measure IPE-Niemi. The survey question “Complex,” which is not employed in IPE-Niemi, is used much more in the American National Election Studies (ANES), where it, unlike the other questions, has appeared since 1952 (ANES 1994, 504)—and, in contrast to Qualified, Public office, and Informed, still appears. Together with “Understand,” this question offers an alternative and, we believe, more robust measure because it does not involve indirect evaluations of the respondent's organizational and managerial capacity. We call this measure IPE-Complex and employ both measures in the empirical analysis that appears later in this article, commenting on differences where appropriate.

Empirical studies of the causes of individual citizens’ sense of IPE show the importance of several individual-level factors, including gender, age, education, and income (Almond and Verba Reference Almond and Verba1963; Hayes and Bean Reference Hayes and Bean1993, 269–70; Titus Reference Titus1981). As seen, although the results of existing studies are not unequivocal, the effect of size on internal political efficacy, if any, is negative. This also applies to other aspects of democracy. For example, Verba and Nie (Reference Verba and Nie1972, 237–47) conclude that participation tends to be higher in small local government units. Dahl and Tufte (Reference Dahl and Tufte1973, 63) report evidence from Swedish local government that supports the size–participation relationship. Following Dahl and Tufte, a large number of studies have investigated the effects of jurisdiction size and consolidation on democracy broadly construed; some with specific focus on size, and some as parts of studies of decentralization more broadly.Footnote ² In a study of the longitudinal relationship between aggregate turnout and waves of municipal consolidation, Morlan (Reference Morlan1984) finds that turnout is higher in national elections than in local elections. However, at the local level, turnout is inversely related to jurisdiction size (see also, among others, Larsen Reference Larsen2002 and Oliver Reference Oliver2000). Jurisdiction size is also negatively related to citizens’ likelihood of contacting officials and politicians (Verba and Nie Reference Verba and Nie1972, 231), as well as to attending meetings on local issues or in local organizations (Larsen Reference Larsen2002; Oliver Reference Oliver2000).

To sum up, many cross-sectional, and a few longitudinal, studies investigate the democratic consequences of differences in jurisdiction size, and there is some, but by no means unequivocal, evidence that larger size is associated with lower quality, however measured, of democracy and its underpinnings. However, these studies face two methodological challenges.

A Simple Idea, But a Difficult Test

The idea that jurisdiction size matters for IPE in a causal sense is simple, but due to two thorny methodological challenges, it is difficult to evaluate empirically. First, differences in observable, but unmeasured or poorly measured population characteristics can affect estimates, as shown in Finifter and Abramson (Reference Finifter and Abramson1975). The populations of small and large jurisdictions can be different on many dimensions, which causes problems of common support rarely addressed in this literature. Education is one important example, but also income levels, occupations, and employment patterns are different in small and large jurisdictions. This problem can be partly solved by statistical control for the confounding variables, but a fully satisfactory solution requires that all such variables are known, identified, and measurable.

Second, cross-sectional studies cannot address problems of selection that arise if people with unobservable preferences over local democracy self-select into jurisdictions of different size, partly with an eye on exactly this. The idea that people may sort themselves into different jurisdictions is classic (Tiebout Reference Tiebout1956), and solid evidence for sorting based on preferences for local public goods such as school quality and environmental quality is beginning to emerge (Banzhaf and Walsh Reference Banzhaf and Walsh2008). This constitutes a problem of endogeneity. When sorting effects exist, differences in political efficacy among citizens residing in jurisdictions of varying size may reflect reverse causality (i.e., that people with interest in local politics are drawn to smaller jurisdictions), rather than a causal effect of jurisdiction size on IPE.

The problem of endogeneity is difficult to handle statistically. One way to correct for endogeneity is to use an instrumental variable approach, but valid instruments can be difficult to find, and we have not seen any studies on size and democracy that attempt this. Another solution would be to study jurisdiction size and the quality of local democracy over time, but this is often infeasible because important jurisdictional boundaries rarely change. When change is observed in connection with large-scale reform, two additional complications arise. First, in large-scale reforms, several factors, such as local political institutions or systems of intergovernmental grants, often change simultaneously, making it difficult to isolate the effects of changing jurisdiction size. Second, such reforms are often encompassing, leaving no individuals or jurisdictions unaffected.

In addition, when jurisdictional change occurs, or is refrained from, it typically does so endogenously. In many settings, jurisdictional change, whether at the city (Lassen Reference Lassen2005), county (Alesina, Baqir, and Hoxby Reference Alesina, Baqir and Hoxby2004), or country level (Alesina and Spolaore Reference Alesina and Spolaore1997), is often decided by voting. Alesina, Baqir, and Hoxby (Reference Alesina, Baqir and Hoxby2004) find that jurisdictions in the United States forego consolidation by voting against it, if it means increasing population heterogeneity. Such majority consent is necessary for consolidation in most countries and introduces the issue of selection bias into estimates of the effect of jurisdiction size on local democracy indicators.Footnote ³

To identify a causal effect of the size of the populace on IPE, it is therefore necessary to identify a quasiexperiment that provides an exogenous source of variation in jurisdiction size. In the next section, we introduce the SR of Danish municipalities and argue that this is an excellent opportunity to test how jurisdiction size affects IPE.

Danish Local Government

The local level is a vital part of the Danish public sector, both culturally and politically. Culturally, a majority of Danes identify primarily with their local area, rather than with their region or country.Footnote ⁴ Politically, Danish local governments are responsible for about 40% of total Danish public expenditure and are relatively autonomous. They are, within certain restrictions, free to set the local income tax rate and have wide discretion in most policy areas. Most notably, they control welfare services such as the school system, child care, and elderly care. The municipalities are governed by a city council elected for 4-year terms in popular elections. Turnout is generally high, typically 70% to 80%. The mayor is elected indirectly by the city council. In addition to presiding over the council and being the formal head of the municipality, the mayor is the only full-time politician, head of the local administration, and chairman of the economic committee, which assumes a central role in the political process (Berg and Kjær Reference Berg and Kjær2005). The local party systems are typically dominated by local branches of the national parties, but there are some so-called local lists.

Just as in Almond and Verba's results, the sense of political efficacy in Denmark tends to be higher toward the local level than toward the national level and the European Union, although the differences between the local and the national levels are limited (Andersen Reference Andersen, Andersen, Torpe and Andersen2000, 128–30). In a thorough cross-sectional study of the effect of jurisdiction size on IPE in Danish municipalities, Lolle (Reference Lolle, Kjær and Mouritzen2003) concludes that jurisdiction size does not have a strong effect on political efficacy. The association between characteristics of citizens and their sense of political efficacy is much stronger. In particular, education is strongly correlated with IPE (Andersen Reference Andersen, Andersen, Torpe and Andersen2000, 141–42).

Structural Reform of 2007

The SR has three parts. First, the number of municipalities was reduced from 271 to 98, increasing average jurisdiction size from 20,100 to 55,600 citizens. Second, 14 counties were merged into five new administrative units, so-called regions. Third, municipalities were given additional responsibilities (most important, certain social services for the disabled, health-related prevention, and environmental regulation), whereas tax collection was transferred away from municipalities. The net transfer of tasks to the municipalities was limited and amounts to DKR 25 billion compared to the total municipal expenditure of (in 2007) DKR 333 billion.

The idea of reforming Danish local government was first mentioned in 2002. The SR was enacted in 2004, and took effect starting on January 1, 2007. The reform process was initiated by the central government, with the explicit aim to generate larger municipalities to reap economies of scale in local public goods production. The process began in 2002, when the government appointed the Commission on Administrative Structure with a chairman appointed by the Minister of the Interior, three independent expert members, four representatives from municipalities and counties, and four civil servants from Danish ministries. In January 2004, the committee published its four-volume report, which recommended a large-scale structural reform. Based on this, the center-right minority government introduced a bill, which immediately got a majority when the Danish People's Party declared that it had only one question: Where do we sign? In June 2004, it was clear that Danish local government would experience dramatic reform. It is the fact that the SR was imposed on municipalities by the central government, combined with the fact that not all municipalities were equally affected by the SR, that makes it an attractive setting for studying the causal effect of jurisdiction size on the quality of local democracy.

According to the agreement between the government and the Danish People's Party, municipalities would be merged into larger units with at least 30,000 citizens. In practice, all municipalities with less than 20,000 citizens (205 of the 271 municipalities) were asked to arrange for mergers before January 1, 2005. Only neighboring municipalities would be allowed to merge; however, apart from this general restriction, the central government did not choose the merging partners.Footnote ⁵ Already before this agreement, 11 of the new 98 municipalities had announced how they wanted to merge, and most of the remaining municipalities were very close to agreeing on whom to merge with (Blom-Hansen, Elklit, and Serritzlew Reference Blom-Hansen, Elklit, Serritzlew, Blom-Hansen, Elklit and Serritzlew2006, 17–18). A few municipalities, especially islands, would be allowed to continue with less than 20,000 citizens, but would have to cooperate with larger neighbors on service provision. The end result is seen in Figure 1: many small municipalities before the reform, whereas larger municipalities dominate after the reform.

FIGURE 1.

Danish Municipalities before and after 2007 Reform; Relative Shares by Population

A Quasiexperiment

The SR changed the municipal structure, notably the size of jurisdictions, in a way that would not have occurred otherwise. In this sense, the SR constitutes an exogenous shock to the size of more than 200 municipalities, and we use this exogeneity to break the correspondence between preferences and choice, which leads to selection problems in observational data. We classify this type of intervention as a quasiexperiment, following Campbell (Reference Campbell1969), but note, as Barabas and Jerit (Reference Barabas and Jerit2010, 227), that the literature does not agree on experimental terminology. For example, some see natural experiments as synonymous with quasiexperiments, defining as “[g]ood natural experiments . . . studies in which there is a transparent source of exogenous variation in the explanatory variables that determine the treatment assignment” (Meyer Reference Meyer1995, 151), whereas others, for example, Shadish, Cook, and Campbell (Reference Shadish, Cook and Campbell2002), distinguish between natural experiments, reserved for a “naturally occurring contrast between a treatment and a comparison condition” (17) and quasiexperiments, with the latter term now being reserved for “experiment[s] in which units are not assigned to conditions randomly” (12). Angrist and Krueger (Reference Angrist and Krueger2001) share, without mentioning quasiexperiments explicitly, Meyer's sentiment, writing that natural experiments are “situations where the forces of nature or government policy have conspired to produce an environment somewhat akin to a randomized experiment” (73). In sum, our opinion is that because the SR provides exogenous variation in the explanatory variable, but is neither a naturally occurring event nor a source of random shocks, it constitutes a quasiexperiment rather that a natural experiment.

This exogenous variation is a crucial component in our research design. However, for us to be able to interpret any postreform differences in IPE as being caused by larger jurisdiction size, we need to address three additional issues. First, differences unrelated to jurisdiction size between small and large municipalities could imply a problem of comparability. Second, citizens relocating as a result of the reform could be a source of endogeneity. Third, change itself could affect feelings of IPE. We discuss these issues in turn.

The problem of comparability will arise if, for example, larger jurisdictions are subject to different institutional constraints, tasks of larger units are different or more complex in nature, or harder to understand because these factors alone could affect feelings of IPE. However, due to regulation from the central government, Danish municipalities have the same set of tasks, are organized in similar ways, and follow identical rules for the democratic process. The differences between large and small municipalities have to do with the process citizens need to engage in if they aspire to influence political decisions. Although the formal democratic rights of citizens are identical, strategies that are effective in small jurisdictions are likely to fail in large jurisdictions. For example, parallel to the argument presented previously, organizing protests among citizens affiliated with a certain municipal institution would be fairly easy in a small municipality and could quickly involve quite a large proportion of the electorate. Simple messages on specific problems concerning this particular institution are likely to be heard. However, such strategies would often be inadequate in a large municipality. Protests from users of one particular institution do not carry much weight, and, to be effective, citizens need to organize much broader, principled protests. This requires the citizen to be capable of formulating an abstract political problem. In a large municipality, a promising strategy would be to mobilize support from interest groups. Although the formal democratic rights are identical, and the tasks of large and small municipalities are of the same inherent complexity, the political process may well be more complex and difficult for many citizens to understand in larger jurisdictions. Hence, if changes in jurisdiction size affect IPE, this is not the result of differences between the tasks of small and large municipalities.

The second issue is the possibility that individual citizens respond to the new municipal structure by relocating, which would be a source of endogeneity. Individuals with strong preferences for political participation at the local level who suddenly find themselves in a large municipality may move to a small municipality. In practice, we do not consider this a major problem because the postreform survey was conducted within a year after the reform, and we exclude recent movers from the analysis. In addition, although individuals were not allowed to choose whether and how their municipality should be merged, the municipalities and their citizens did have some influence on the merger. For example, municipalities of citizens with a strong preference for local democracy may have aimed for a merger with a small municipality. In our analysis, this would make citizens of such municipalities relatively happier with the amalgamation, which would bias the analysis against finding a detrimental effect of the reform on IPE. Finally, although the assignment of the treatment is not random, the municipalities were severely constrained by the size requirements and the condition that merging municipalities should be geographically connected. Bhatti and Hansen (Reference Bhatti and Hansen2011) show that, apart from the obvious geographic constraints, social connectedness, measured by shared commuters, is the most important predictor of mergers such that socially connected municipalities are more likely to merge. Hence, the nonrandomness of the treatment may imply that merged municipalities are more connected and coherent. If this causes bias, then the bias will again be against finding a negative effect of size.

Some insight into the process of amalgamation can be obtained from the fact that referenda were held in 63 of the original 271 municipalities (Jørgensen Reference Jørgensen and Mouritzen2006, 168). Most of the referenda were concerned with adjustments of boundaries, but some involved the choice of which municipality to merge with. In our sample of 32 municipalities, referenda took place in six cases, marked with asterisks in Table A.1 in the Appendix. In these cases, the group of citizens did have a direct influence on what would happen to their municipality, but individual citizens, of course, only had a minuscule chance of affecting the result. We observe no differences in results.

The final issue is that change in itself may alter feelings of IPE. The major components of the SR that did not involve changing jurisdictional boundaries are, as already discussed, accounted for by having a control group in the sample. However, for the amalgamated municipalities, we can decompose the jurisdictional change into two components: the fact that jurisdictional boundaries change at all and the fact that population size increases. If citizens react in a negative way to change per se, then any change in jurisdiction size, both positive and negative, should be associated with lower political efficacy. If population size is more important and has a systematic effect on political efficacy, then increasing and decreasing population size should have differing effects, and the effect should be larger, the larger the change in population. Although we distinguish amalgamated municipalities by the change in size when conducting the analysis, we do not observe jurisdictions decreasing in size as a consequence of the SR.

Evidence against the hypothesis that change in itself matters can be drawn from an experiment involving decentralization of the municipality of Copenhagen, the capital and by far the largest municipality in Denmark, into 15 administrative and political districts. Four city districts were exogenously selected as pilot districts, providing a natural experiment for the entire city to learn about the consequences of decentralization; Lassen (Reference Lassen2005) documents the exogenous selection process, although with focus on information. In surveys carried out after a citywide referendum on implementation of the city district model, survey respondents overwhelmingly favored smaller units with respect to political efficacy, both internal and external, even if the proposal eventually failed due to concerns about economic efficiency (Lassen Reference Lassen2005). The fact that the selection process was exogenous, allowing citizens to learn about the consequences of smaller jurisdictions in an unbiased way, as well as the finding that citizens overwhelmingly favored change rather than the status quo when considering IPE, in combination support the hypothesis that changes in population size rather than change per se cause lower IPE in large jurisdictions.

The Difference-in-Difference Estimator

Let the internal efficacy of an individual i be Y ¹_i in the treated case, that of municipal amalgamation, and Y ⁰_i be the outcome for the same person in case of no treatment. Our object of interest is the difference Δ_i=Y ¹_i−Y ⁰_i, which is the causal effect of municipal population size on the IPE experienced by individual i. In practice, however, an individual i cannot be treated and nontreated at the same time, which means that either Y ¹_i or Y ⁰_i will be missing. The difference Δ_i results from the pair of potential outcomes, a term coined by Rubin (Reference Rubin1974), which is to be distinguished from the realized outcome Y_i. Because a counterfactual for the realized outcome is not available at the individual level, the statistical approach is to estimate the missing variable from appropriate group means.

We study a repeated cross-section model of different individuals surveyed before and after the reform:

where I is the set of respondents. M_i∈{0, 1} is an indicator for reform (as opposed to continuing) municipalities. Later, we also consider a treatment indicator of the form M_i∈{0, SS, SL, LS, LL}, where we distinguish treated municipalities both by their prereform size and by their postreform relative size, as explained previously. T_i∈{0, 1} is a time period indicator equal to 0 before the reform and 1 after the reform. The interaction(s) M_iT_i take(s) on the value 1 for reform municipalities after implementation, and zero otherwise. Finally, u_i represents unobservable characteristics and is assumed to be independent of treatment status conditional on observables and across periods; we return critically to this assumption later.

It can be useful to consider the conditional means for the four groups: reform and nonreform municipalities before and after reform:

(1)

The before–after estimator for the treated (BAT), used when no control group is available, is given by (1.D) – (1.C):

(2)

The BAT estimator includes both the effect of treatment and the common trend or aggregate change. In our case, γ_P includes the effects on IPE from overall trends and aspects of the reform common to all municipalities. To estimate consistently the effect of size, we need to subtract this common trend, which is equal to the before–after estimator of the control group (BAC):

(3)

The BAC estimates the effect of reallocation of government tasks and any aggregate time trends, possibly due to changing survey participation, in IPE with respect to local government; the latter may have increased or decreased in reaction to the substantial nationwide public debate on municipal politics and the SR. Similarly, increased fiscal pressure will also be captured by this trend, as long as it is similar across all municipalities. Based on our setup in Eq. (1), we get the DiD estimator as BAT – BAC; that is,

(4)

The assumption that the trend in Eq. (2) is common for treatment and control groups alike is a key identifying assumption in the DiD approach (Blundell and MaCurdy Reference Blundell, MaCurdy, Ashenfelter and Card1999). We first proceed under the assumption that this assumption is satisfied; for example, as noted previously, the reallocation of government tasks across vertical levels of government was the same for all municipalities. However, if the impact of the reform is heterogeneous with respect to observable characteristics, and the distributions of such observable characteristics differ across control and treatment groups, then additional assumptions are needed to ensure that a comparison is based on suitably similar groups; we return to this later, where we consider matching. The second key identifying assumption, denoted no composition bias (Blundell and MaCurdy Reference Blundell, MaCurdy, Ashenfelter and Card1999, 1612), is that the populations considered are the same across time. At the population level, this means that no individuals change from treatment to control group and vice versa. This is sometimes problematic in studies of individual responses to changes in taxation or job training programs; however, in our case, this would be directly relevant only if people moved with the explicit aim of living in a treatment or control municipality, which seems highly unlikely. In addition, our empirical analysis excludes respondents who recently relocated from another municipality. The assumption is more problematic when we consider the actual sampling of individuals; we return to this later in the article.

When estimating individual-level responses to aggregate-level variables, here treatment status and other municipal-level variables, it is important to account for the possible covariance in errors. We do this by allowing for clustering at the municipal level.

Nonrandom Assignment: Different Surveys and Differences in Observables across Treatment Groups

In existing DiD studies on repeated cross-sectional data, the analysis is typically carried out on different waves of a particular representative survey, such as the General Social Survey. In our case, we compare IPE measures across surveys carried out in the same municipalities, using identically worded questions, but with different sampling strategies. The existence of differential sampling probabilities across surveys raises the problem that the surveys are not stratified in the same way, which means that controlling for confounding variables may not solve the problem of composition bias, the absence of which, as noted previously, is necessary for identification of causal effects in a DiD model. To solve this problem, we want to match respondents across surveys on a number of individual-level variables.

At the same time, treatment and control municipalities may differ with respect to observable characteristics, which can lead to a violation of the common trend assumption if effects of the reform are heterogeneous across observables. As noted previously, for example, an explicit aim of the SR was to create municipalities with a minimum of 30,000 inhabitants, which in itself affects the probability of treatment. To solve this issue, we want to match survey respondents across treatment status. In sum, there are two assignments that may be nonrandom: assignment to treatment or control group and assignment to prereform or postreform survey. To address this, we employ a variant of difference-in-difference with matching (DiDM), an estimator developed in the program evaluation literature by Heckman, Ichimura, and Todd (Reference Heckman, Ichimura and Todd1997) and Heckman et al. (Reference Heckman, Ichimura, Smith and Todd1998).

We proceed by propensity score matching (see, e.g., Dehejia and Wahba Reference Dehejia and Wahba2002). Although intuitively desirable, exact matching on a vector of characteristics is often infeasible. However, Rosenbaum and Rubin (Reference Rosenbaum and Rubin1983) show that if potential outcomes are independent of treatment conditional on X, which is a precondition for estimating a causal effect from the data anyway, then this is also the case conditional on the propensity score, defined as the probability of receiving treatment conditional on X. Because we have two assignments that are potentially nonrandom, we follow Blundell et al. (Reference Blundell, Dias, Meghir and Van Reenen2004) in defining two propensity scores. Conditional on X, P _M = Pr(M = 1|X) is the probability of being observed in a treated municipality and P _T = Pr(T = 1|X) is the probability of being surveyed in the postreform sample. Based on the propensity scores, we can now write the identifying common trend assumption as

This allows the time effects to differ by X and assures that the distribution of observed characteristics is the same across all four samples. In practice, we estimate the two propensity scores by running a probit regression of assignment status (treatment and time, respectively) on X. The resulting predicted values are the estimated propensity scores. Our point of departure is the group of individuals in the treated group, pretreatment (M = 1, T = 0). To match these individuals with respondents in each of the three comparison groups, we perform a variant of nearest-neighbor caliper matching with replacement by pairing each treated respondent with a respondent in each comparison group. The respondent in each comparison group is chosen to minimize the Euclidean distance from the treated individual's two estimated propensity scores, given restrictions on the maximum allowable distance (the caliper) as well as a common support restriction. Based on these matched samples, we carry out standard DiD analysis to form estimates of the average treatment effect on the treated (ATT) under the assumption of separable additivity of time and group effects.Footnote ⁷ Because matching is carried out with replacement, we correct the sample sizes of the comparison groups to reflect this procedure; the distribution across municipalities within each of the four groups is shown in Table A.1 in the Appendix for both the regression and the matching analyses.

As is standard in the literature, we report bootstrapped standard errors throughout for the estimated ATTs based on the DiDM procedure. One study shows that this may, in fact, result in biased estimates for the standard error, but the issue is not resolved (Abadie and Imbens Reference Abadie and Imbens2008). In performing the bootstrap, we resample at the cluster level of new municipalities, as previously described.

Balance, Unobserved Heterogeneity, and Exact Matching

Although the DiDM procedure allows for unobserved heterogeneity under the assumption of a common trend conditional on X and, as such, represents a considerable improvement of the use of standard cross-section estimators, two potential sources of bias remain. First, remaining unobserved heterogeneity can obviously influence results; and second, to the extent that propensity score matching does not achieve perfect balance across treatment regimes on variables that are strong predictors of the outcome, observed differences in outcomes may be erroneously attributed to treatment, in which case it may be efficient to match directly, or exactly, on these key variables (Barnard et al. Reference Barnard, Frangakis, Hill, Rubin, Gatsonis, Kass, Carlin, Carriquiry, Gelman, Verdinelli and West2002; Rosenbaum and Rubin Reference Rosenbaum and Rubin1983).

We explicitly include population size as a matching criterion in the calculation of propensity scores to reflect decision making, and, as a consequence, the matching procedure allows us to compare individuals in both small and large municipalities. However, if there are systematic differences in unobserved attitudes toward and interest in local politics among citizens in small and large municipalities, which we suspect ex ante, then including population size alongside individual-level variables in the calculation of propensity scores may not be a sufficient safeguard because population size may carry little weight in the calculation of the propensity scores. To address this, we carry out additional analyses where individuals in small (large) treatment municipalities are explicitly restricted to be matched with individuals in small (large) control municipalities. As emphasized by Heckman, Ichimura, and Todd (Reference Heckman, Ichimura and Todd1997) and Cook, Shadish, and Wong (Reference Cook, Shadish and Wong2008), DiDM functions best when matching individuals who reside within a given geographic unit and, if possible, who are administered identical surveys. This is what we do here.

Finally, to address concerns arising from the less than perfect balance of covariates in the main matching specification, we carry out propensity score matching under the restriction of exact matching on public sector employment; this being an example of an important explanatory variable for which it is difficult to achieve balance in the simple propensity score specification.Footnote ⁸ In practice, this requires the matching procedure to look for matches based on the two-dimensional propensity score only among individuals with the same type of employment.Footnote ⁹

Retrospective Evaluations

To supplement the evidence from the repeated cross sections, we also asked postreform survey respondents to assess, in retrospect, the consequences of the SR for measures of IPE. Although there are well-known issues with retrospective questions of this kind, they allow us to address unobserved heterogeneity in a different way: By asking one person to evaluate the differences before and after the reform, we essentially control for individual-level factors and get a direct estimate of the first-level differences. Hence, the retrospective evaluations serve as a robustness check. The limitations of retrospective questions are of a different nature than the potential methodological problems of comparing answers across samples.

We can now compare these differences across treatment and control municipalities as well as within the group of treatment municipalities. We analyze these data using both a regression-based, cross-sectional framework and matching across treatment and control groups. Throughout, we take into account the clustered nature of the data by allowing for within-municipality dependence in estimated standard errors.