Abstract

We study the effects of intergovernmental grants on school spending within the Finnish system of high school education funding. Using a kinked grant rule, the system allocates lump-sum intergovernmental grants to local high school education providers. Utilizing the quasi-experimental variation in grants given by the rule, we identify the effects of the grants on municipal high school education expenditures. Our results indicate that the grants stimulate spending, while local tax rates or revenues do not seem to be responsive to the grants, suggesting the presence of a typical flypaper effect. However, we also consider the possibility that the grant responses might be heterogeneous among municipalities. Based on our heterogeneity results, the grant response is positively associated with the share of the high school age population, and a higher share of elderly persons is related to a lower propensity to spend on education out of grant funding. This result is in line with the idea of intergenerational conflict in education spending preferences presented in education finance literature.

1.  Introduction

Intergovernmental transfers1 play an important role in education finance (see, e.g., Fisher and Papke 2000 for a review). In many countries there are state programs or policies that provide nonmatching grants to local governments or school districts to support the provision of education services. This is also the case in Finland, where part of education services at the primary and secondary levels is funded by the central government, along with local governments. In this paper, we study the effects of intergovernmental grants on school spending within the Finnish system of high school education funding. In particular, we investigate the effectiveness of the policy that aims to support municipalities with small schools. The main aim of this policy is to provide additional financial support for those municipalities for which the provision of high school education is more expensive because of relatively small age cohorts and which consequently have fewer opportunities to benefit from any economies of scale in education. It is important to examine the effectiveness of this policy, as municipalities can, in principle, offset these additional revenues by reducing their own funding for high schools. This question is also connected to the well-known flypaper effect studied in local public finance literature (see, e.g., Hines and Thaler 1995; Gamkhar and Shah 2007; Inman 2008; and Payne 2009, for reviews). In this context, the flypaper effect corresponds to a case where a government grant to a recipient municipality increases the level of local public spending more than an increase in local income of an equivalent size.

Although the Finnish school funding system is generally multifaceted, the funding of Finnish high schools in particular provides an interesting opportunity to study the functionality and the intended policy effects of the education grants. Because the system provides an empirically tractable identification strategy, we are able to circumvent the typical challenge of endogeneity of grants in spending equations. Importantly, several studies in education finance have adopted quasi-experimental identification strategies utilizing specific school finance reforms or funding formulas in order to identify the causal effects of grants on local education spending (Guryan 2001; Hoxby 2001; Card and Payne 2002; Gordon 2004; Baicker and Gordon 2006; Cascio, Gordon, and Reber 2013). The Finnish system also includes such a formula-based funding mechanism, which allows us to utilize quasi-experimental identification strategy to estimate the effect of grants on spending (see, e.g., European Commission/EACEA/Eurydice 2014). The system is based on a funding rule where funding for smaller high school education providers increases in a piecewise linear manner. Because this piecewise linear rule is kinked at certain thresholds based on the number of students, we can utilize the regression kink design (Card, Lee, et al. 2015) to identify the effects of grants.

In general, the evidence for the effects of intergovernmental grants in Finland is scarce and previous studies are mostly outdated, investigating funding systems that were in place in the 1990s using only descriptive methods (Oulasvirta 1997; Moisio 2002). More comparable to our efforts is the study by Lundqvist (2015), who improves the empirical methods compared with these earlier studies. She found a significant negative association between general intergovernmental grants and tax revenues of local governments. This relationship was, nevertheless, much smaller than between general grants and expenditures, suggesting the presence of a flypaper effect because grants increased spending more than they crowded out local tax revenues. Interestingly, her results also pointed out that school expenditure increases were more associated with labeled education grants than with unlabeled general grants, further suggesting that grants stimulate spending as intended. Our study, however, differs from Lundqvist (2015) as we examine a different time period and utilize an alternative identification strategy to estimate the effects. Furthermore, we concentrate solely on high school spending instead of overall local spending.

Besides studying the existence of flypaper effect in the context of high school funding, we introduce the possibility that spending responses to grants are heterogeneous among Finnish municipalities. In particular, we focus on age-related heterogeneity. Heterogeneous grant responses due to demographic variation in local jurisdictions have received less attention in the literature. This is despite having a plethora of research (owing much to Poterba 1996, 1998) studying variations in local preferences toward public education spending due to the age composition of localities.2 Generally, the empirical consensus in this literature has supported the so-called intergenerational conflict hypothesis, which posits that a larger share of elderly persons in the population significantly decreases support for education expenditures (Brunner and Baldson 2004; Fletcher and Kenny 2008; Cattaneo and Wolter 2009; Figlio and Fletcher 2012; Reback 2015; de Mello et al. 2016; Brunner and Johnson 2016). Nevertheless, to our knowledge there has been rather little overlap between the intergenerational conflict and intergovernmental transfer literatures. Only few studies have considered age-related education grant effect heterogeneity. For example, Mattos, Politi, and Yamaguchi (2018), Cascio, Gordon, and Reber (2013), and Ahlin and Mörk (2008) all examine education grant effect heterogeneity, but none of them considers age structure as a potential driver of this heterogeneity. In Baicker and Gordon (2006) and Dahlberg et al. (2008), age structure heterogeneity is only cursorily examined. Only Baicker and Gordon (2006) consider age-related heterogeneity in the education grant setting, finding no significant heterogeneity with respect to the age distribution of jurisdictions. Our research question is distinctively different than theirs, however, as they study the reactions of grantor jurisdictions to spending mandates. We, on the other hand, examine the reactions of grantee jurisdictions to exogenous funding policy changes induced by a grant formula.

Our main results indicate the presence of a flypaper effect, suggesting that the policy of supporting smaller municipalities generally works as intended, since municipalities mainly use the funding for its purported use. However, we also observe that the policy responses seem to vary among municipalities. In accordance with the intergenerational conflict hypothesis, this variation in responses at least partly arises from age-related heterogeneity. Our results highlight that in municipalities with a larger share of elderly population, high school spending responds less to education grants. Heterogeneity in responses speaks in favor of another aspect of the Finnish system that gives municipalities discretion in the use of funds.

This paper is organized as follows. In section 2 we summarize the institutional background, namely, the main aspects of the Finnish system of funding local public services and the high school funding system. In section 3 we describe the research design and identification strategy. The data and the validity of our research design are examined in section 4. The estimation results concerning the flypaper effect are presented in section 5. Section 6 focuses on the heterogeneous effects of grants. Section 7 concludes.3

2.  The Institutional Background

Funding of High School Education in Finland

In Finland, municipalities provide both basic compulsory education (grades 1–6, primary education; grades 7–9, middle school) and academically orientated upper secondary schooling, which we will for brevity refer to as high school education.4 The provision of high school education is not mandatory for each municipality and not all municipalities have high schools. Besides municipalities, some private institutions, municipality cooperatives, and university practice schools also provide high school education. All potential providers of high school education have to apply for permission from the Ministry of Education and Culture. We will focus on high school education provided only by the municipalities.5

To understand the overall context in which the Finnish high school funding system operates, it is important to briefly discuss how the funding of local public services is divided between the state and local governments. The local financing of services is mainly based on a flat rate municipal tax set by the municipalities themselves. In addition, municipalities obtain own-source revenues from property tax, community tax, and operational revenues.6 Besides own-source funding, municipalities receive a significant proportion of their funding directly from the state through state transfers. In 2016, the share of state transfers was on average about 20 percent of the revenues of municipalities, although the variation among municipalities is large as some municipalities get over 50 percent of their funding from the state transfers. Although in terms of overall municipal finances high school education forms a relatively small share, in some municipalities it is a significant driver of local livelihood.7

Given the importance of high school education, the funding system seeks to support municipalities by providing more financial resources. Smaller, often rural, municipal providers cannot exploit economies of scale as extensively because there is a limited student pool seeking admittance to their schools. Because all high school education providers must meet certain national curricula criteria and offer the basic student services (e.g., lunches and school health care) regardless of their size, smaller providers are unable to respond to a smaller student pool by cutting back the level and quality of teaching and other services. This is especially true in terms of teaching expenditures as specialized teachers for every subject are generally needed to provide the required curriculum.

To conclude this section, we note two important details about the high school grant. First, while the high school grant is nominally labeled, the grant is not tied to any specific purpose and municipalities are able to divert state high school transfers to other uses. Consequently, it makes sense to study the potential flypaper effect in this context. Second, the funding mechanism applies at the provider level, not at the level of individual schools. Larger municipalities as providers generally have multiple individual high schools. It is at the level of municipality where decisions about the use of grant is made, allowing the possibility of diverting funding to other services at the municipal level.

The Grant Formula and the Distribution of Grant

The funding given to high school providers is the product of the number of students and the provider-specific unit price of a single student, as defined in equation 1.
pit=Mit×N×pa100=(100+mit)×N×pa100.
(1)
In equation 1, pit is the unit price for provider i in year t. The component, pa, is the national average unit price based on the actual realized costs of some predetermined range of previous year(s) and it is set by the Finnish National Board of Education. Certain budgetary, legislative, and index corrections may also be applied when setting this average price.8N is a national multiplier that smooths out the mechanical changes in the average price pa due to the changes in provider-specific prices. Because both pa and N are constant across all providers, they have no effect for our analysis and we omit further details of them. The provider-specific multiplier Mit is defined in equations 2 and 3, where st-1 is the number of students observed in the fall of year t − 1 (the start of the academic year). The multiplier is visualized in figure 1 and we see that for providers below 200 students, it is higher than one, implying an increased unit price. No official documents reveal why the threshold of 200 has been chosen as the critical point. We assume that it has been set relatively arbitrarily as a result of political negotiations. It is worthwhile noting that high schools in Finland are most commonly in the size range of 100 to 299 students.9 This might have partly directed the choice of the threshold. There is also another threshold at 60 students, which entitles institutions to an even higher multiplier, with a cap at 40 students. Below 40, the multiplier is a constant of 2.06.
Mit=100+mit,
(2)
mit=0ifsi,t-12000.4×(200-si,t-1)if60si,t-1<2000.4×(200-si,t-1)+2.1×(60-si,t-1)if40si,t-1<60106ifsi,t-1<40.
(3)

To clarify the process of distributing the grant, in figure 2 we illustrate the grant process, using the year 2013 as an example. The number of students in year t − 1 sets the unit price multiplier for year t because the academic and accounting (fiscal) years do not match (stage A). The former runs from the fall of year t − 1 to the spring of year t, and the latter is defined as the calendar year. The number of students is subject to fiscal year adjustments (stages B to D2), but our identification strategy is based on the initial multiplier set at the beginning of the academic year. The grant is paid in monthly installments, but it can be viewed as a lump sum grant, since, except for the fiscal year adjustments, providers know the total grant amount for 2013 in the fall of 2012.

Figure 1.

Provider-Specific Unit Price Multiplier Divided by 100 (vertical axis) Against the Number of Students (horizontal axis)

Notes: We illustrate the formula only up to 250 students because after 200 students the formula flattens at the value of 1.

Figure 1.

Provider-Specific Unit Price Multiplier Divided by 100 (vertical axis) Against the Number of Students (horizontal axis)

Notes: We illustrate the formula only up to 250 students because after 200 students the formula flattens at the value of 1.

Figure 2.

Timeline of the Grant Process for the 2013 Grant

Notes: Q1—Q4 refer to quarters of the year and the letters refer to the different stages of the process. The approximate location of the letter indicates when during the process the stage is set to happen. Stage A: The initial unit price and the grant for the year 2013 are based on the number of students in the last fall, recorded on 20 September 2012. Stages B and C: The number of students is measured again on 20 January 2013 and 20 September 2013. Based on a weighted average of these two (weights 7/12 and 5/12), the grant is adjusted to correspond to the student number of the budgetary year (2013) at the end of 2013 (stage D). The adjusted number of students applies only to the amount of the grant paid, not to the determination of the multiplier, which is solely based on the number of students in the previous fall. The adjustment sum is paid around February 2014, but it is still included in the financial statements for 2013.

Figure 2.

Timeline of the Grant Process for the 2013 Grant

Notes: Q1—Q4 refer to quarters of the year and the letters refer to the different stages of the process. The approximate location of the letter indicates when during the process the stage is set to happen. Stage A: The initial unit price and the grant for the year 2013 are based on the number of students in the last fall, recorded on 20 September 2012. Stages B and C: The number of students is measured again on 20 January 2013 and 20 September 2013. Based on a weighted average of these two (weights 7/12 and 5/12), the grant is adjusted to correspond to the student number of the budgetary year (2013) at the end of 2013 (stage D). The adjusted number of students applies only to the amount of the grant paid, not to the determination of the multiplier, which is solely based on the number of students in the previous fall. The adjustment sum is paid around February 2014, but it is still included in the financial statements for 2013.

Empirical Flypaper Effect and Its Potential Mechanism

In this section we briefly discuss the interpretation of the flypaper effect in our setting and the potential mechanisms behind it. Because municipalities can either divert the grant to other uses or supplement it with other revenues, actual expenditures on high school education do not necessarily correspond to the grant obtained. For a flypaper effect to exist empirically, a (strong) positive relationship between grants and observed high school expenditures should be observed. Obviously, the flypaper effect can still manifest itself in spending categories other than high school education if a municipality diverts funds to those categories. This is an important question to study because, if the high school spending does not fully respond to grants, it must be either changes in local taxes or expenditures in other spending categories that encompass the response.

Next, we discuss a few potential mechanisms that we believe could accommodate the potential flypaper effect in municipal funding decisions. In municipalities, it is effectively the municipal council that decides how funds should be used. Consequently, it is likely that the mechanisms of the flypaper effect are within the council decision making. One possible mechanism is the so-called labeling of grants, as suggested by Lundqvist (2015) following the notions of mental accounting and labeling (see, e.g., Thaler 1985). Even if there is freedom in the use of funding, the nominal labeling of grants through the formula might direct spending decisions. That is, the grant formula may act as a de facto binding restraint on local decision makers not to divert funding elsewhere. For example, Brooks and Phillips (2008) have observed that in the presence of budgetary rules that limit local government discretion in providing services, grants are viewed as a relaxation of these rules. As a result, grants foster a tendency to increase local spending on public services. If we view the grant formula as a budgetary rule, then this line of reasoning might be one potential explanatory mechanism behind the potential flypaper effect. Age-related heterogeneity may be present in this context as citizens, represented by the council, might view the fungibility of funds differently. Citizens who are inclined to support educational services may see a grant being more tied to its nominal category whereas older citizens preferring health care services might find the funds more fungible to other uses.

A flypaper effect could also emerge through municipal council decisions since the preferences in the use of funding may be shaped by the composition of the council. A recent study by Hyytinen et al. (2018) finds that a higher number of health care sector public employees in Finnish municipal councils induces the councils to spend more on the health care sector. This might apply similarly in the case of educational sector employees. Unfortunately, we have no way of explicitly testing this hypothesis as we lack sufficient data on the employment background of councilors.

Lastly, maintaining good high school education may reflect the view that having a high school is essential for a municipality to prosper. This may be especially so in smaller municipalities with just one high school, where the school may be the only way to attract younger citizens and maintain the vitality and prosperity of the municipality. If so, a municipality may be willing to invest as much as possible in high school education. Given the sample restrictions we describe in section 4, this consideration may be relevant in our application.

3.  Identification and Empirical Estimation

The positive relationship between grants and spending might be simply due to differences in resource needs of the municipalities. Thus, the grant variable is likely to be endogenous as both spending and grants are jointly determined by these inherent resource needs. In this case, the estimated grant effect would likely be biased. But by comparing municipal high school providers that are relatively similar in size and that are differentiated only by a discrete change in the grant amount, we can possibly reveal the causal effects of grants on expenditures, net of other characteristics of the municipalities.

More formally, the kinked grant formula introduced in section 2 gives rise to an identification strategy utilizing regression kink design (RKD) formalized by Card, Lee, et al. (2015, 2017; see also Nielsen, Sørensen, and Taber 2010). Regression kink design is a close relative of the more popular regression discontinuity design, but instead of discontinuities in levels, RKD utilizes slope changes in identification by using the discrete change in the slope of the formula as an excluded instrument.10 Following Card, Lee, et al. (2015) and Nielsen, Sørensen, and Taber (2010), the RKD strategy is described in equation 4,
Y=τB+gS+ɛ,
(4)
where Y is the local expenditure per student and B is the amount of state grant per student. The g(.) is some smooth function of the number of students (previous fall) S, which is our forcing variable, and ɛis the standard randomly distributed zero mean error term. The parameter of interest is τ. Assuming that the formula thresholds are exogenous, the variation in grants near the threshold can be considered as good as random. Our design is a fuzzy design because of the fiscal year adjustments and some discretionary components in the unit price. This means that in equation 4 we have B=b(S,ɛ), as B is not a deterministic function of S. Discretionary components account for extra expenditure needs because of certain special tasks or conditions (e.g., placing emphasis on some areas, such as sports, math/science, or multi-language teaching).
The estimation of τ generally applies local linear regression on both sides of the threshold using a bandwidth (h) of observations around the threshold. We take an agnostic view and alternate the bandwidth over a wide range of values. To weight the observations around the threshold, we use the uniform kernel. This effectively translates the estimation into a standard instrumental variable estimator, as shown in equations 5 and 6,
Yit=β0+β1B^it+p=1p*γpSit-s0p+ɛit,
(5)
Bit=α0+p=1p*αpZ*Sit-s0p+p=1p*δpSit-s0p+ηit,
(6)
where [Sit-s0] is the number of students centered around the kink point (s0) and Z=I[Sits0]. Their interaction term (and the possible higher order terms of it) is the excluded instrument. Initially, we use several different local polynomial orders (p) for the control function g(.), but for reasons stated later, we will focus on the first-order specification. The key identifying assumption after controlling for this smooth relationship is that any kinked relationship between the expenditures and the number of students is due to the kinked grant formula. This requires that the densities of the running variable and all other relevant covariates behave smoothly around the kink point.11 In other words, if the design is valid, then the point estimate of interest should not change much when additional covariates are included as controls.

4.  Data and the Validity of the Design

Data

Our dataset includes an unbalanced panel of all high school education providers in the period 2001–14, but we focus only on municipal providers.12 We have data on total high school expenditures and grants (both per student), and the number of students, obtained from the National Board of Education funding data repository. The funding data are merged with data on municipal-level characteristics obtained from Statistics Finland. These data include information on the number of high schools, municipal tax rates and tax revenues, other state transfers, the average income level of residents, demographic data (years 2003–14 only13), expenses on social and health care (SOHC) costs, and political variables related to municipal elections. All the data are publicly available on the Web sites of each data source.14

We cannot attribute expenditures to single schools in a municipality with several high schools because the funding data are at the municipal level. Thus, the observed expenditures do not necessarily reflect the actual spending behavior of any individual school since there can be large intra-municipal expenditure differences among schools. That is why we focus on municipalities with one school. We also check whether our results are affected if we include municipals with multiple schools (see Häkkinen, Kirjavainen, and Uusitalo 2003). However, few multi-school municipalities are affected by the formula because they are generally much larger than 200 students. Furthermore, our analysis will focus on the threshold of 200. We present summary statistics of our data in table 1 for municipalities with one school and at least 60 students. These restrictions result in a total of 2,649 observations for the main variables of interest over all the years in the raw sample (additional summary statistics are available in OR-1).

Table 1.
Summary Statistics of Key Variables
VariableNMeanSDMedianMinMax
High school education costs, €/student 2,649 7,737.32 1,604.69 7,503.35 4,569.58 15,744.12 
Grant, €/student 2,649 6,880.71 1,353.81 6,663.72 4,932.48 12,495.74 
Cost vs. grant difference, €/student 2,649 856.64 901.77 796.26 −2,899.11 8,296.33 
Students (previous fall) 2,649 182.89 125.9 148 60 1,014 
SOHC net costs, €/residenta 2,649 3,277.23 494.72 3,211.28 2,208.3 5,679 
Tax income, €/resident 2,649 3,040.63 451.62 2,969.81 2,080.68 7,144.98 
Population 2,172 9,560.11 6,909.33 7,513.5 1,567 40,390 
0—14 years, share of total 2,172 0.17 0.04 0.17 0.09 0.35 
15—19 years, share of total 2,172 0.06 0.01 0.06 0.04 0.1 
20—24 years, share of total 2,172 0.05 0.01 0.04 0.02 0.09 
Over 65 years, share of total 2,172 0.21 0.05 0.21 0.06 0.35 
Municipal election voter turnoutb 542 62.93 4.89 62.6 42 79.7 
Municipal loan stock, €/resident 2,603 1,796.92 1,068.84 1,678.74 1.13 6,153.44 
Municipal tax rate 2,649 19.15 0.92 19 16 22.5 
Size of local councilb 540 31.58 7.91 27 17 75 
Taxable income, t − 1, €/resident 2,639 12,756.54 2,147.24 12,381.61 8,063.38 27,553.4 
Other state transfers, €/resident 2,649 2,173.6 785.49 2,203.62 222.9 5,416 
Municipal staff (per 1,000 residents) 2,645 61.36 14.51 61 133 
VariableNMeanSDMedianMinMax
High school education costs, €/student 2,649 7,737.32 1,604.69 7,503.35 4,569.58 15,744.12 
Grant, €/student 2,649 6,880.71 1,353.81 6,663.72 4,932.48 12,495.74 
Cost vs. grant difference, €/student 2,649 856.64 901.77 796.26 −2,899.11 8,296.33 
Students (previous fall) 2,649 182.89 125.9 148 60 1,014 
SOHC net costs, €/residenta 2,649 3,277.23 494.72 3,211.28 2,208.3 5,679 
Tax income, €/resident 2,649 3,040.63 451.62 2,969.81 2,080.68 7,144.98 
Population 2,172 9,560.11 6,909.33 7,513.5 1,567 40,390 
0—14 years, share of total 2,172 0.17 0.04 0.17 0.09 0.35 
15—19 years, share of total 2,172 0.06 0.01 0.06 0.04 0.1 
20—24 years, share of total 2,172 0.05 0.01 0.04 0.02 0.09 
Over 65 years, share of total 2,172 0.21 0.05 0.21 0.06 0.35 
Municipal election voter turnoutb 542 62.93 4.89 62.6 42 79.7 
Municipal loan stock, €/resident 2,603 1,796.92 1,068.84 1,678.74 1.13 6,153.44 
Municipal tax rate 2,649 19.15 0.92 19 16 22.5 
Size of local councilb 540 31.58 7.91 27 17 75 
Taxable income, t − 1, €/resident 2,639 12,756.54 2,147.24 12,381.61 8,063.38 27,553.4 
Other state transfers, €/resident 2,649 2,173.6 785.49 2,203.62 222.9 5,416 
Municipal staff (per 1,000 residents) 2,645 61.36 14.51 61 133 

Notes: Municipalities with one school and over 60 students included. Sample covers years 2001—14 except for demographic data, for which it is 2003—14. SOHC = Social and health care; SD = standard deviation; €= euros.

aSOHC net costs are the difference between gross operating costs and operating income.

bNote that municipal elections are held every four years. In our data they occur in 2004, 2008 and 2012. In the actual estimations we use versions of the variables such that all years within a single electoral cycle get the values observed in the year of the last elections.

All the monetary variables have been deflated to 2014 euros. The size of the municipal student pool varies from 60 students to over 1,000. On average, the observed expenditures per student are about €857 higher than the grants (difference variable), implying that municipalities supplement the grant with their own funding. For some municipalities, the difference is negative, indicating that these municipalities divert grant money elsewhere. In OR-2 we conduct a correlation analysis among some of our key variables to provide additional insights into how municipal characteristics move together. The correlations suggest the presence of economies of scale in high school education since costs per student correlate negatively with the number of students. In smaller municipalities with fewer high school students, costs per student are generally higher.

Validity of the Research Design

First, we check the distribution of the running variable, the number of students. In figure 3 we plot the distribution of the bin means of frequencies. We use a bin width of 2 and restrict the illustration to municipalities with fewer than 500 students. The distribution runs smoothly through the thresholds of 40 and 200 students, but in the former case there are relatively few observations for a meaningful analysis. At the threshold of 60 the distribution has a jump, casting doubts on whether the design is valid at this point.15 The formal statistical tests of smoothness are in OR-3, where we conduct both the McCrary test of smoothness and a test for the continuity of the first derivative of the running variable. These tests indicate that concentrating on the threshold of 200 is warranted.

Figure 3.

Distribution of the Bin Means of the Running Variable (the number of students)

Notes: Only municipalities with one school are included in the figure. Bin width is 2.

Figure 3.

Distribution of the Bin Means of the Running Variable (the number of students)

Notes: Only municipalities with one school are included in the figure. Bin width is 2.

Although the formal tests indicate a smooth density at the 200 threshold, one could argue that the running variable is still susceptible to manipulation because schools can alter their student intake through entry grade requirements. In our view, however, the incentives for such manipulation are low. Although municipalities get a higher unit price below the threshold, they also lose funding on students who do not enroll. Because schools close to the threshold require more or less similar resources to teach their students regardless on which side of the threshold they are, expenditures cannot be adjusted similarly to losses in grant funding. As a consequence, incentives for manipulation are low since the unit price increases at the threshold cannot compensate the lost funding due to non-enrolled students. Recall also that because prospective students can seek admittance to any school they wish, the allocation of students to schools can be considered random from this perspective as well. In addition, municipalities may face uncertainty in terms of the yearly student pool due to dropout, school switching, school closures, and flexible degree completion times.

Another source of potential manipulation is the possible discretionary components in funding due to some special tasks, as municipalities may wish to provide such services to attract more students. We consider a few points that alleviate the potential risk of manipulation for this reason. First, municipalities cannot decide themselves to start providing services that would make them eligible for extra compensation. Rather, they have to apply for permission in order to arrange such services. Only municipalities with enough initial resources and a local need for these services are in a position to obtain permission. Because the demand for such services is exogenously given, arranging these services is not a decision variable that municipalities can decide upon alone. Secondly, the incentives for this type of manipulation should be inconsequential within the formula-based system, where there are incentives to decrease the number of students. Lastly, this type of manipulation would likely have little impact within our effective sample because we concentrate on relatively small municipalities in our estimations (single school municipalities). Such municipalities rarely arrange such services, as most of the demand is in larger urban centers.

Overall, given the above considerations, we argue that the exact or precise manipulation of the number of students is difficult and unlikely. The distinction between precise and imprecise manipulation is important here. Card, Lee, et al. (2015) point out that whereas precise manipulation would violate the validity assumptions, RKD still allows imprecise manipulation in which some influence over the running variable is acceptable.

Next, in figure 4, we plot bin means (using 50 bins) of expenditures and grants against the number of students and examine graphically whether grants act similarly to actual expenditures.16 Note that the linear regression lines are estimated using the underlying data, not the binned points. Although the slope changes at the kinks are less pronounced in terms of expenditures, there are still visually detectable changes in the slopes of the linear fits of expenditures. The fit line on the left side of 40 should be close to flat, but because of outliers this is not the case. Figure 5 visually illustrates that the slope changes are possibly a relevant instrument by running two regressions: regression A, where grants are explained by the three indicator variables, indicating whether an observation is on the right side of the cutoff, and regression B, in which regression A is augmented with the slope change variables. The strategy is to examine the linear fits of the residuals of these regressions. In regression A, the slopes of these fit lines should have the same sign as in the actual grant formula, whereas the residuals in regression B should be relatively flat around zero.17 The residual plots with the corresponding fits are shown in panels a and b of figure 5. Apart from the interval from 0 to 40, the behavior of the residuals is as expected.

Figure 4.

Total Costs per Student and Grants per Student Against the Number of Students

Notes: The number of students is limited to 500 and only municipalities with one school are included. We have defined 50 bins to be used so the bin width is 5.

Figure 4.

Total Costs per Student and Grants per Student Against the Number of Students

Notes: The number of students is limited to 500 and only municipalities with one school are included. We have defined 50 bins to be used so the bin width is 5.

Figure 5.

Visual Examination of Instrument Relevance Following Dahlberg et al. (2008)

Note: Model descriptions in the main text.

Figure 5.

Visual Examination of Instrument Relevance Following Dahlberg et al. (2008)

Note: Model descriptions in the main text.

Last, we test the covariate balance and placebo thresholds. In table 2 we run regressions where each covariate is in turn explained by the smooth function of students and the slope change variable. We report the results with polynomial orders 1 to 3 and include year and regional (county) fixed effects.18 For these estimations we use the Calonico et al. (2017) optimal bandwidth selector because, a priori, we have no insight into which bandwidth to choose for this validity test. In OR-4 we report results using alternative bandwidths and the results remain largely the same. In table 2, only the share of the high school age population and general grants are marginally significant at the 5 percent significance level, and the significance depends highly on the order of the polynomial control. In table 3 we check the effects at three different placebo thresholds by running a linear regression where grants per student are explained both with formula-induced slope changes and placebo slope changes at points 150, 300, and 500 in the same equation. That is, we control for all the original kink points (40, 60, 200) when examining the effects of the placebo thresholds. None of the placebo thresholds is significant, while the slope changes at kinks 40, 60, and 200 are significant and have the expected signs even after inclusion of the placebo thresholds.

Table 2.
Covariate Balance Tests at Threshold Of 200 Students
1st Order2nd Order3rd Order
VariableRK effectp-valueRK effectp-valueRK effectp-value
0—14 years old, % of total 0.000 0.233 0.000 0.571 0.003 0.168 
15—19 years old, % of total 0.000 0.044 0.000 0.424 0.000 0.901 
Over 65 years old, % of total 0.000 0.230 −0.001 0.256 −0.003 0.165 
Population 25.286 0.306 58.867 0.422 155.760 0.235 
Average taxable income, €/resident 2.259 0.856 57.3 0.146 149.886 0.071 
Tax revenue, €/resident 1.975 0.422 8.746 0.248 24.330 0.117 
SOHC net costs, €/resident 1.824 0.491 −4.43 0.548 −15.918 0.347 
Municipal council size −0.011 0.762 0.011 0.924 −0.050 0.789 
Municipal election voter turnout −0.053 0.154 −0.17 0.073 −0.173 0.341 
Political orientation 0.001 0.819 0.002 0.884 −0.008 0.707 
Swedish teaching 0.001 0.585 −0.002 0.315 −0.001 0.844 
Loan stock, €/resident 3.313 0.645 23.53 0.299 9.276 0.835 
General state grants, €/resident 0.239 0.956 −17.215 0.161 −54.233 0.039 
Municipal staff 0.011 0.911 0.206 0.397 0.651 0.299 
1st Order2nd Order3rd Order
VariableRK effectp-valueRK effectp-valueRK effectp-value
0—14 years old, % of total 0.000 0.233 0.000 0.571 0.003 0.168 
15—19 years old, % of total 0.000 0.044 0.000 0.424 0.000 0.901 
Over 65 years old, % of total 0.000 0.230 −0.001 0.256 −0.003 0.165 
Population 25.286 0.306 58.867 0.422 155.760 0.235 
Average taxable income, €/resident 2.259 0.856 57.3 0.146 149.886 0.071 
Tax revenue, €/resident 1.975 0.422 8.746 0.248 24.330 0.117 
SOHC net costs, €/resident 1.824 0.491 −4.43 0.548 −15.918 0.347 
Municipal council size −0.011 0.762 0.011 0.924 −0.050 0.789 
Municipal election voter turnout −0.053 0.154 −0.17 0.073 −0.173 0.341 
Political orientation 0.001 0.819 0.002 0.884 −0.008 0.707 
Swedish teaching 0.001 0.585 −0.002 0.315 −0.001 0.844 
Loan stock, €/resident 3.313 0.645 23.53 0.299 9.276 0.835 
General state grants, €/resident 0.239 0.956 −17.215 0.161 −54.233 0.039 
Municipal staff 0.011 0.911 0.206 0.397 0.651 0.299 

Notes: Municipalities with one school included. Standard errors are clustered at the municipal level. Calonico et al. (2017) optimal bandwidth selector used here is 44.78. Robust p-value reported. RK = regression kink; € = euros; SOHC = social and health care.

Table 3.
Placebo Thresholds
No ControlsControls
Slope ChangeCoefficientSEp-valueSlope ChangeCoefficientSEp-value
K40 −235.63 33.48 0.00 K40 −195.49 17.10 0.00 
K60 215.57 34.31 0.00 K60 178.11 18.27 0.00 
K200 22.70 2.23 0.00 K200 21.93 2.39 0.00 
K150 −3.26 2.99 0.28 K150 −4.37 3.24 0.18 
K300 0.51 0.91 0.58 K300 −0.19 1.22 0.88 
K500 0.15 0.76 0.85 K500 −0.18 1.00 0.86 
No ControlsControls
Slope ChangeCoefficientSEp-valueSlope ChangeCoefficientSEp-value
K40 −235.63 33.48 0.00 K40 −195.49 17.10 0.00 
K60 215.57 34.31 0.00 K60 178.11 18.27 0.00 
K200 22.70 2.23 0.00 K200 21.93 2.39 0.00 
K150 −3.26 2.99 0.28 K150 −4.37 3.24 0.18 
K300 0.51 0.91 0.58 K300 −0.19 1.22 0.88 
K500 0.15 0.76 0.85 K500 −0.18 1.00 0.86 

Notes: Standard errors (SE) clustered at the municipal level. All models include year and regional fixed effects and only municipalities with one school are included. The set of controls includes the variables from table 2.

5.  Empirical Results

Flypaper Results

In this section we present our main flypaper results. We consider three different model specifications, labeled A, B, and C. Specification A is the baseline and has only one explanatory variable, grant, on the right-hand side, B adds the set of control variables, and C adds the regional (county) fixed effects to B. All the specifications naturally control for the smooth function of the running variable and they also include the year fixed effects. The standard errors are clustered at the municipal level. The monetary variables are in levels since the propensity to spend out of grant money corresponds to a grant coefficient estimated in level variables (see, e.g., Fisher 1982).19 The set of control variables includes a standard set of municipal-level socioeconomic and political variables commonly applied in the literature (see, e.g., Gennari and Messina 2014; Lundqvist 2015; Baskaran 2016; Ferede and Islam 2016). We use the share of the population of three different age groups (0–14 years, 15–19 years, and over 65 years), total population, SOHC costs, taxable income in the previous year, and tax revenues, to account for the fiscal capacity of the municipality. To control for the political situation, we use voter turnout in municipal elections, the size of the local council, and a dummy, as controls for whether the main left-wing party gained a higher share of votes in municipal elections than the main right-wing party. We also include a dummy variable if the municipality offers teaching in Swedish.

The results are shown in figure 6 (p = 1 for panels a–c, p = 2 for panels d–f). To avoid distortion in the figures, we omit coefficient estimates for which the absolute value of the 95 percent confidence interval limits are above 2 and for which there are too few observations per estimated parameter using the rule of thumb, “ten observations per parameter” (small bandwidths). We report only bandwidths below 140 since beyond that we would confound the effect of the 60 and 200 kinks with each other. The bandwidth value is the length on one side of the threshold, the total bandwidth length being twice this value.

Figure 6.

Regression Kink (RK) Estimates of the Flypaper Effect

Notes: All figures have high school expenditures as the dependent variable and grant as the independent variable of interest. Mean beta = average coefficient estimate over all reported values.

Figure 6.

Regression Kink (RK) Estimates of the Flypaper Effect

Notes: All figures have high school expenditures as the dependent variable and grant as the independent variable of interest. Mean beta = average coefficient estimate over all reported values.

The first-order polynomial provides significant and fairly robust results across the specifications, at least from the bandwidth of 75 onwards. The second-order polynomial results are insignificant, and the estimates are on average close to zero (for the results of the third-order polynomial specification, see OR-6 and figure OR-5). The inclusion of covariates (specifications B and C) generally results in smaller coefficient estimates on average, but with the first order polynomial specification the results stay relatively robust as the mean effect (mean beta) is around 0.5–0.6 in all the specifications. As expected, small bandwidth values produce volatile and imprecise results. With bandwidths from 75 to 100, we see relatively robust positive coefficients, whereas with larger bandwidths there is a slightly detectable increasing trend in the coefficient estimates toward unity. Because on average municipalities seem to spend more than the grant, it is not surprising that by including more municipalities in the estimation the effects seem to increase toward unity and possibly beyond. Among larger municipalities the grant corresponds more closely with expenditures, probably because the average unit price they receive represents more closely the earlier cost structure of high schools that the average price is based on. On the other hand, smaller providers may spend as much as possible to maintain a high school in their municipality, often possibly exceeding the grant in their spending. Both of these channels can contribute to the trend in the estimates with larger bandwidths. However, our interest is in the local estimate of the effect at the threshold, preferably using smaller bandwidths than the extremes where this trend is mostly observed.

First Stage Results and Additional Robustness Checks

The higher-order polynomial specifications might lead to the poor first stage of instrumental variables due to weak identification problems. For example, Card et al. (2017) seem to favor first-order specification (see also Ando 2017; Gelman and Imbens 2018). We test this in table 4, where we present the coefficient estimates of the first stage along with its significance and the Kleibergen-Paap test statistic for a weak identification test (see, e.g., Baum, Schaffer, and Stillman 2007).20 We use all three polynomial orders and specifications A and C.

Table 4.
First-Stage Results and Weak Identification Test
Specification ASpecification C
1st-Stage Coefficient1st-Stage Coefficient
Polynomial OrderPolynomial Order
Bandwidth123Bandwidth123
25 18.60*** 10.69 52.24* 25 21.23*** 10.13 50.29* 
50 23.20*** 14.02 3.722 50 22.00*** 12.82 1.171 
75 21.73*** 26.15** 4.695 75 21.27*** 23.02*** 4.868 
100 20.22*** 24.99*** 24.77* 100 19.98*** 22.95*** 22.95** 
125 19.63*** 23.07*** 27.23* 125 19.98*** 21.70*** 24.83** 
Kleibergen-Paap Test Statistic Kleibergen-Paap Test Statistic 
 Polynomial Order  Polynomial Order 
Bandwidth 1 2 3 Bandwidth 1 2 3 
25 15 0.40 2.28 25 37.29 0.32 2.56 
50 30.83 3.00 1.11 50 36.36 4.92 1.37 
75 86.96 4.38 3.99 75 76.31 7.32 4.72 
100 244.7 7.48 4.37 100 258.4 7.05 5.84 
125 296 16.68 14.44 125 477.6 15.91 16.39 
Specification ASpecification C
1st-Stage Coefficient1st-Stage Coefficient
Polynomial OrderPolynomial Order
Bandwidth123Bandwidth123
25 18.60*** 10.69 52.24* 25 21.23*** 10.13 50.29* 
50 23.20*** 14.02 3.722 50 22.00*** 12.82 1.171 
75 21.73*** 26.15** 4.695 75 21.27*** 23.02*** 4.868 
100 20.22*** 24.99*** 24.77* 100 19.98*** 22.95*** 22.95** 
125 19.63*** 23.07*** 27.23* 125 19.98*** 21.70*** 24.83** 
Kleibergen-Paap Test Statistic Kleibergen-Paap Test Statistic 
 Polynomial Order  Polynomial Order 
Bandwidth 1 2 3 Bandwidth 1 2 3 
25 15 0.40 2.28 25 37.29 0.32 2.56 
50 30.83 3.00 1.11 50 36.36 4.92 1.37 
75 86.96 4.38 3.99 75 76.31 7.32 4.72 
100 244.7 7.48 4.37 100 258.4 7.05 5.84 
125 296 16.68 14.44 125 477.6 15.91 16.39 

*p < 0.05; **p < 0.01; ***p < 0.001.

With larger bandwidths, all the polynomial orders provide a significant coefficient for the first-order instrument (the interaction Z*[Sit-s0] in equation 6). The addition of higher order instruments leads to a weak identification problem, as indicated by low Kleibergen-Paap statistics. Using the Staiger and Stock (1997) rule of thumb, only the first-order specification consistently produces test statistics higher than 10, suggesting a preference for this polynomial order.21 Furthermore, the results are robust between specifications A and C. In our subsequent analysis we focus on specification A with the first-order polynomial.

Table 5 presents several robustness tests using bandwidth values of 50, 75, and 100. The results in model 1 reproduce the estimates for model A1 at these bandwidths for comparison, while robustness checks in models 2 to 4 use the baseline specification but modify the estimation sample or the chosen fixed effects. Model 2 checks whether our replacement strategy for the missing values for 2001–02 demographic data has any consequence for our estimations, and we drop all the observations from the sample for which the original data had no values for these years for the demographic variables. Model 3 examines whether the results change if we include municipalities with multiple schools and as expected, we see little change in results. Model 4 uses a specification where the base specification is augmented with regional fixed effects. The results in model 5 reproduce specification C1 and model 6 adds three additional controls to this specification—namely, the number of municipal staff, and other state transfers and loan stock per resident—while model 7 omits the years 2001–02, similarly to the robustness test in model 2. Overall, the robustness checks indicate that the results are quite stable with bandwidths larger than 50.

Table 5.
Robustness Checks
(1)Baseline; 1st Order, Specification A
BandwidthCoefficientStandard Errorp-valueN
50 0.544 0.231 0.020 782 
75 0.625 0.178 0.001 1196 
100 0.631 0.132 0.000 1627 
(2) A1+Excluding Years 2001 and 2002 
Bandwidth Coefficient Standard Error p-value N 
50 0.625 0.247 0.013 615 
75 0.675 0.179 0.000 969 
100 0.687 0.135 0.000 1332 
(3) A1+ Municipalities with Many Schools Included 
Bandwidth Coefficient Standard Error p-value N 
50 0.493 0.292 0.094 841 
75 0.633 0.176 0.000 1289 
100 0.607 0.135 0.000 1739 
(4) A1+Regional Fixed Effects Added 
Bandwidth Coefficient Standard Error p-value N 
50 0.519 0.250 0.040 782 
75 0.689 0.172 0.000 1196 
100 0.689 0.128 0.000 1627 
(5) Specification C1 
Bandwidth Coefficient Standard Error p-value N 
50 0.280 0.225 0.215 765 
75 0.511 0.162 0.002 1161 
100 0.617 0.134 0.000 1585 
(6) Specification C1 with Added Controls 
Bandwidth Coefficient Standard Error p-value N 
50 0.278 0.216 0.199 759 
75 0.528 0.161 0.001 1150 
100 0.636 0.133 0.000 1559 
(7) Specification C1 Excluding Years 2001 and 2002 
Bandwidth Coefficient Standard Error p-value N 
50 0.275 0.273 0.316 603 
75 0.506 0.158 0.002 943 
100 0.603 0.134 0.000 1303 
(1)Baseline; 1st Order, Specification A
BandwidthCoefficientStandard Errorp-valueN
50 0.544 0.231 0.020 782 
75 0.625 0.178 0.001 1196 
100 0.631 0.132 0.000 1627 
(2) A1+Excluding Years 2001 and 2002 
Bandwidth Coefficient Standard Error p-value N 
50 0.625 0.247 0.013 615 
75 0.675 0.179 0.000 969 
100 0.687 0.135 0.000 1332 
(3) A1+ Municipalities with Many Schools Included 
Bandwidth Coefficient Standard Error p-value N 
50 0.493 0.292 0.094 841 
75 0.633 0.176 0.000 1289 
100 0.607 0.135 0.000 1739 
(4) A1+Regional Fixed Effects Added 
Bandwidth Coefficient Standard Error p-value N 
50 0.519 0.250 0.040 782 
75 0.689 0.172 0.000 1196 
100 0.689 0.128 0.000 1627 
(5) Specification C1 
Bandwidth Coefficient Standard Error p-value N 
50 0.280 0.225 0.215 765 
75 0.511 0.162 0.002 1161 
100 0.617 0.134 0.000 1585 
(6) Specification C1 with Added Controls 
Bandwidth Coefficient Standard Error p-value N 
50 0.278 0.216 0.199 759 
75 0.528 0.161 0.001 1150 
100 0.636 0.133 0.000 1559 
(7) Specification C1 Excluding Years 2001 and 2002 
Bandwidth Coefficient Standard Error p-value N 
50 0.275 0.273 0.316 603 
75 0.506 0.158 0.002 943 
100 0.603 0.134 0.000 1303 

Grant Effects on Other Outcomes

The results so far suggest that high school grants contribute positively to local high school spending. Whether this indicates a flypaper effect also depends on the size of the local income or tax effect. If local grants and local incomes affect spending similarly, they could be viewed as similar sources of income, and, in principle, grants could foster tax cuts. The challenge is that we lack a good research design to infer the causal effect of local income on high school expenditures. To gain some insight about the potential effects, we look at the coefficient estimate of the income variable when it is included as a control. The results reported in OR-6 suggest that taxable income has little effect on spending. Our results are in line with previous studies, which report that the effect of the income variable is generally an order of magnitude smaller than the effect of grants (Oulasvirta 1997; Moisio 2002; Gennari and Messina 2014; Dahlby and Ferede 2016; Ferede and Islam 2016).

Instead of the effect of the income variable on spending it is more straightforward and natural in this context to directly examine whether local tax rates or tax revenues respond to grants (see, e.g., Dahlberg et al. 2008; Lundqvist 2015; Baskaran 2016). In panel a of figure 7, we explain the municipal income tax rate with grants and find insignificant results, suggesting that tax rates do not respond to grants. Variation in spending may also occur because there are changes in the tax base. Although on average grants seem to have a positive effect on tax revenues, this effect is not significant and is much smaller than the grant effect on spending (panel b in figure 7). Finally, it is possible that municipalities simply divert grant money away from high school education. Panel c in figure 7 examines the effect of high school grants on social and health care spending. Based on the results, municipalities may slightly increase their SOHC spending instead of tax cuts as a result of high school grants, but this effect is small relative to its effect on high school spending and is often statistically insignificant. Note that in all the panels in figure 7 we report results from bandwidth 25 onwards, as the confidence intervals below this bandwidth are so wide they distort the figures, making them unreadable. All the coefficient estimates below the bandwidth of 25 are insignificant, however.

Figure 7.

Grant Effects on Tax Rates, Tax Revenues, and Social and Health Care (SOHC) Spending

Notes: Single school municipalities included in all three panels. RK = regression kink.

Figure 7.

Grant Effects on Tax Rates, Tax Revenues, and Social and Health Care (SOHC) Spending

Notes: Single school municipalities included in all three panels. RK = regression kink.

Discussion of the Results

Overall, our results in the three previous sections support the existence of a flypaper effect in the context of Finnish high school education funding. Our preferred linear model produced a quite large positive effect across a wide range of bandwidths, although the effect was insignificant with smaller bandwidths as the sample size was decreased. Our estimates also survived multiple robustness checks, suggesting that the observed effect was relatively robust to certain variations of model specification. The results in the last subsection imply that the effect of grants on local taxation is modest at best, giving further evidence of a flypaper effect. While inherently in the RKD approach it is challenging to separate the effect of the functional form from the true treatment effect, we also need to keep in mind that as long as the identification assumptions hold, RKD produces equally internally valid results as regression discontinuity design near the threshold.

Because we are able to establish a certain degree of a flypaper effect, our results would suggest that the purported aim of the funding formula in supporting smaller municipalities has been effective as municipalities mostly seem to direct the funding to its intended use. We cannot infer the exact mechanism for the observed effects from these results, however. Variation in the point estimates with different bandwidths, on the other hand, would suggest that there might be some heterogeneity in this effect. Next, we will examine the potential explanations of this possible heterogeneity.

6.  Heterogeneous Local Responses to High School Education Grants

In this section we examine the possible heterogeneous spending responses to high school grants. We do this by dividing the data into subsamples according to some municipal characteristics. We then replicate the earlier estimations (using specification A with the first-order polynomial) for these subsamples and look for any differences between the grant coefficients between these subsamples. Due to sample split, we cannot consider very short bandwidths, and based on our visual observation of earlier results, we use the bandwidth of 75.

Before presenting the results, we briefly discuss the municipal characteristics that we consider as the potential sources of heterogeneity. Our main interest is in the intergenerational conflict hypothesis. To test this source of heterogeneity we use the share of the population in the municipality aged 65 years and over, a variable also used in many other studies examining the intergenerational conflict issue. For a consistency check, we also use the share of the population in the municipality aged 15–19 years. We would expect estimations using these two variables to produce opposing results. In addition to demographics we also examine other possible sources of heterogeneity identified earlier in the literature.

First, following Vegh and Vuletin (2016), we divide the sample by different tax rates, because with higher tax rates, the higher resulting tax distortion may induce more to be spent from transfers than from income (see also Dahlby and Ferede 2016). Second, we examine subsamples with respect to income levels because the ability of a municipality to offset local funding with grants may depend on this (Lutz 2010). Third, we consider whether the political participation (voter turnout) of citizens affects how municipalities respond to grants. For example, Borge, Falch, and Tovmo (2008) and Geys, Heinemann, and Kalb (2010) have provided evidence that local government (cost) efficiency is positively related to higher voter turnout due to higher accountability. According to Geys, Heinemann, and Kalb (2010) this effect is larger the greater the degree of local fiscal autonomy.22 Fourth, we divide the sample with respect to SOHC costs. For example, de Mello et al. (2016) find that areas with a higher share of elderly residents prefer higher health care expenditures over education expenditures. Last, the size of the municipal council might affect preferences toward spending. For example, Egger and Koethenbuerger (2010) found that larger councils tend to spend more, consistent with the standard fiscal commons problem. Petterson-Lidbom (2012), on the other hand, found, using both Swedish and Finnish data, that the size of a local council negatively affects local spending. According to Petterson-Lidbom, larger councils are in a better position to supervise budget-maximizing bureaucrats who often might have considerable power in setting the actual spending agenda.

The data are divided into two subsamples based on the median value of a given variable among municipalities. Because tax rates and council size change discretely, a number of observations fall on the exact median. In these cases, we divide the sample so that values below the median form their own group and values at the median or above form the other group. The results for the subsample analysis are presented in table 6.

Table 6.
Heterogeneous Grant Responses
VariableMedianGrant Effect When Below MedianObservationsGrant Effect When Above MedianObservationsDifference Between the Coefficients; p-value of χ2-test
Share of 65-year-olds 0.201 0.665*** 643 0.377 553 0.403 
and over (0—1)  (0.184)  (0.303)   
Share of 15—19-year-olds (0—1) 0.063 0.404 444 0.697** 752 0.339 
  (0.261)  (0.206)   
Voter turnout (%) 62.00 0.193 541 0.890*** 655 0.041* 
  (0.267)  (0.217)   
Taxable income (€/resident) 12,805.92 0.459 648 0.869*** 548 0.212 
  (0.296)  (0.196)   
Social and health care 3,251.818 0.608** 754 0.497 442 0.755 
costs (€/resident)  (0.182)  (0.356)   
Municipal tax rate (%)a 19.00 0.465 478 0.775*** 718 0.316 
  (0.273)  (0.203)   
Municipal council sizea  0.989*** 468 0.493* 728 0.105 
  (0.189)  (0.243)   
VariableMedianGrant Effect When Below MedianObservationsGrant Effect When Above MedianObservationsDifference Between the Coefficients; p-value of χ2-test
Share of 65-year-olds 0.201 0.665*** 643 0.377 553 0.403 
and over (0—1)  (0.184)  (0.303)   
Share of 15—19-year-olds (0—1) 0.063 0.404 444 0.697** 752 0.339 
  (0.261)  (0.206)   
Voter turnout (%) 62.00 0.193 541 0.890*** 655 0.041* 
  (0.267)  (0.217)   
Taxable income (€/resident) 12,805.92 0.459 648 0.869*** 548 0.212 
  (0.296)  (0.196)   
Social and health care 3,251.818 0.608** 754 0.497 442 0.755 
costs (€/resident)  (0.182)  (0.356)   
Municipal tax rate (%)a 19.00 0.465 478 0.775*** 718 0.316 
  (0.273)  (0.203)   
Municipal council sizea  0.989*** 468 0.493* 728 0.105 
  (0.189)  (0.243)   

Notes: Median calculated among all municipalities, but estimation results include only municipalities with one school. Standard errors are clustered at the municipal level in parentheses. Bandwidth: 75, polynomial order: 1, specification: A in all estimations. €= euros.

aAbove median group also includes the median values.

*p < 0.05; **p < 0.01; ***p < 0.001.

For municipalities with an above-median share of elderly residents, the response to grants is statistically insignificant. On the other hand, municipalities with a below-median share of elderly residents have a relatively large and significant response. We interpret this as meaning that in municipalities with a high share of elderly residents, high school spending does not respond to additional grants as much as they probably divert the money to other uses. As expected, when we divide the sample according to the share of the population aged 15–19 years, the magnitude and the significance of the coefficients is reversed. Now, the municipalities with a higher share of high school age residents respond more to grants. The results hold for various bandwidths (see OR-7). These results provide support for the intergenerational conflict hypothesis in the sense that demographically older areas seem to direct less grant funding toward education.

The results concerning voter turnout imply that the higher the turnout the larger the grant response. One possible explanation is that councilors may feel greater accountability in their spending decisions under higher control by the electorate. The higher incidence of grants in high-income municipalities suggests that these municipalities do not need to shift state funding to other areas. The demand for education is also likely to be higher in these areas. With respect to the tax rate, a higher tax rate seems to be related to a larger grant effect. According to Dahlby and Ferede (2016), higher taxation is related to larger marginal costs of public funding, which again is related to a higher degree of a flypaper effect.

The sample split in terms of SOHC costs produces the expected results in that aging municipalities prefer SOHC spending over education spending. The effect of the size of the local council seems different from what Egger and Koethenbuerger (2010) found. Our results indicate that the grant response in municipalities with smaller councils is much higher. One explanation may be that the size of the council interacts with its composition. It is possible that in smaller councils, public (education) employees who are councilors exert more influence on how the grant should be spent than in larger councils (see Hyytinen et al. 2018). The explanation offered by Petterson-Lidbom (2012) also coincides with our results, as in municipalities with smaller councils, administrative (education) officials may have more influence on how the funds are spent. Note also that council size is directly determined by municipality size and the results might reflect that smaller municipalities spend more in per student terms, which again might explain the higher level of grant incidence.

There are some caveats to these heterogeneity results. First, the measured municipal characteristics may mask the actual mechanism causing heterogeneity. For example, voter turnout does not reveal who in fact votes, although the mechanism probably runs through the composition of the active electorate (see Fletcher and Kenny 2008). Demographic characteristics alone, on the other hand, do not necessarily capture the possibility that the elderly may actually prefer education spending for altruistic reasons or because of possible increases in property values. Moreover, as many of the municipal characteristics go hand in hand it might be difficult to pinpoint the origins of heterogeneity to any single variable. Second, small sample sizes lead to relatively large standard errors for the coefficient estimates. As we see, only in the case of voter turnout is the difference in the effects significant between the subsamples, although many of the effects are individually significant. Lastly, we have taken it for granted that the identification assumptions of our design are valid in each of the subsamples.

Despite the above caveats, the heterogeneity results suggest the current policy of not tying the grants to any specific purpose may be well founded. Although nominal labeling of grants seems to guide local spending to a certain extent (the flypaper result), following the standard arguments of fiscal federalism literature, it seems beneficial to allow leeway in municipal spending decisions when municipalities have varying preferences toward different spending categories. This interpretation of our findings is also supported by the interviews conducted with a number of municipal officials (see OR-8).

7.  Conclusions

This study examines the Finnish system of high school education funding, its effects on local municipal high school spending, and especially whether the policy aim of financially supporting small municipalities in the provision of high school education has worked as intended. Utilizing exogenous variation in state high school grants, we found that grants have a statistically significant positive effect on high school spending. On the other hand, because the effect of grants on municipal tax rates and tax revenues was invariably insignificant, our results support the presence of a flypaper effect. This implies that municipalities tend to use the funding to its purported use. The distinctive feature of our study is that we also examine heterogeneity in grant responses. Our results indicate that a larger share of elderly residents in a municipality is related to a lower propensity to spend on education out of high school grant funding. This result supports the hypothesis of intergenerational differences in preferences toward education spending. In policy terms this suggests that it is important to acknowledge that the responses to a supposedly targeted policy, such as the high school funding policy studied here, may still have multiple responses due to the differences between municipalities. These results should provide valuable insights for policy makers designing intergovernmental transfers.

In future analyses, some aspects of our study could be improved upon. First, because of data limitations our analysis was restricted to the municipal level and the mechanism underlying the allocation of grants at the school level remains unrevealed. Second, the examination of heterogeneous responses to grants would require a more careful account of the endogeneity. In particular, the demographic structure of a municipality is likely to be endogenous due to Tiebout-type sorting as older citizens may move to areas that provide fewer schooling services to begin with. Third, our results mainly concern a restricted subset of Finnish high schools as we only examined single school municipalities. Consequently, we are wary of generalizing our results to larger municipal providers of high school education.

Acknowledgments

Antti Saastamoinen thanks VATT Institute for Economic Research for the support for this research. The authors would like acknowledge the contribution of Mikko Silliman and Kalle Manninen in assisting with the interviews of municipal officials and the data compilation. The authors would also like to thank Jaakko Meriläinen for his contribution in the initial stages of this project. We thank Robert P. Inman, Sanna Lehtonen, and Tuukka Saarimaa for their valuable comments and insights, which improved the paper. We also thank for their comments all the participants of the 2016 Summer Seminar of Finnish Economists, the 4th Workshop on Efficiency in Education (Milan), the VATT Institute for Economic Research weekly seminar, the 2017 Meeting of the Finnish Economic Association, and the 73rd Annual Congress of IIPF.

Notes

1. 

We use the terms “transfer” and “grant” interchangeably in this paper.

2. 

Many other sources of heterogeneous grant responses have been suggested in the literature of intergovernmental transfers as a whole. These include sources such as: voter information (Strumpf 1998), interest groups (Singhal 2008), the democratic responsiveness of local government and income levels of municipalities (Lutz 2010), local ability to offset grants through taxation (Cascio, Gordon, and Reber 2013), budgetary constraints (Brooks and Phillips 2008), property ownership (Rockoff 2010), distortionary taxation (Vegh and Vuletin 2016), and local fiscal conditions (Ando 2015).

3. 

Throughout the text we will also refer to our online resource (OR) material for additional details. Although all this material is contained in a single file, we will denote the sections of this material as OR-1, OR-2, and so forth. These resources are available in a separate online appendix that can be accessed on Education Finance and Policy’s Web site at www.mitpressjournals.org/doi/suppl/10.1162/edfp_a_00284.

4. 

Another main form of secondary education is vocational training.

5. 

Practice schools offer teaching practice to university students studying to become teachers. Because their funding is part of the university budget, not part of municipal funding decisions, we exclude these schools from our analysis. Municipality cooperatives are also excluded because their decision making is beyond any single municipality. Although private institutions are within the same funding system as municipal high schools, we also exclude them from the analysis as they are fully funded by state transfers and have no equivalent source of own funding to the local taxes that municipals have (because private institutions cannot collect any tuition fees).

6. 

Community tax is effectively a corporate tax levied by the state from which municipalities receive their own share.

7. 

The overall magnitude of state transfers was €8.8 billion in 2016, whereas high school expenditures of municipalities were about €650 million.

8. 

For the year 2016, the average price was set at €6,122.06/student.

9. 

In 1999 and 2000, around 48 percent of high schools fell within this range. Although the share has declined over the years, school sizes of 100–299 is still the most common. Source: https://shop.kuntaliitto.fi/download.php?filename=uploads/p080303131559X.pdf.

10. 

RKD has been applied to study the effects of the replacement rate of a social (sickness) insurance system on sickness absence from work (Böckerman, Kanninen, and Suoniemi 2018), the effects of unemployment benefits (Card, Johnston, et al. 2015; Landais 2015; Kyyrä and Pesola 2016), student aid on college enrollment (Nielsen, Sørensen, and Taber 2010), and intergovernmental grants on local employment, spending, and tax rates (Dahlberg et al. 2008; Lundqvist, Dahlberg, and Mörk 2014; Ando 2015; Baskaran 2016).

11. 

To be accurate, RKD requires the density of the running variable to be continuously differentiable at the kink point, implying that the derivative of the density at the kink point is continuous.

12. 

Of the total of 323 providers observed at any point in time, there are 32 private providers and 286 municipal providers. The remaining 5 institutions are run by joint municipal providers. University practice high schools are not included in the funding data at all because they are not within the same funding system.

13. 

In order to increase the sample size, our estimations use versions of the demographic variables where missing values for the years 2001–02 have been replaced with values for 2003. The demographic composition of the municipality is unlikely to change much within in a timespan of a few years. The main results (using our preferred specification in section 5) are similar if we restrict our estimation sample to the years 2003–14.

14. 

See further details in the data description appendix of our online resources and the following Web sites: National Board of Education funding data repository (https://vos.oph.fi/rap/) and Statistics Finland (http://stat.fi/).

15. 

The jump in the proximity of the 60-student threshold might be partly explained by the fact that typical high school education lasts three years/grades, and in Finland, there is a tendency to gravitate class sizes toward 20 students.

16. 

Additional scatter plots of raw data are in OR-4.

17. 

This is a similar strategy to what Dahlberg et al. (2008) use when examining instrument relevance. Because we have multiple cutoff points, we have to account for all these “treatments” in our graphical test of instrument relevance.

18. 

We use regional rather than municipal fixed effects because the research design utilizes the cross-sectional variation among municipalities. In addition, we examine covariate balance with the covariate index approach suggested by Card et al. (2017). These results can be found in OR-5.

19. 

Some authors have suggested that flypaper effects should be estimated using a log-linear specification (Becker 1996; Worthington and Dollery 1999; Melo 2002). However, because most of the flypaper literature uses level specification, we follow the same tradition for better comparison.

20. 

We report a Kleibergen-Paap statistic instead of the usual Gragg-Donald statistic because the former is robust to within-cluster correlation.

21. 

In OR-9 we present Akaike information criterion values for different models, varying the polynomial order. These results also suggest that the first-order polynomial is a reasonable choice.

22. 

Martin (2003) has pointed out that in the United States, members of Congress may distribute federal funding toward areas with higher voter turnout as these areas are more likely to provide future support for them.

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Supplementary data