Public Choice
DOI 10.1007/s11127-012-0009-y
Common pool size and project size: an empirical test
on expenditures using Danish municipal mergers
Sune Welling Hansen
Received: 8 June 2011 / Accepted: 5 July 2012
© Springer Science+Business Media, LLC 2012
Abstract The paper examines the proposition from the law of 1 over n (Weingast et al.
1981) that project size tends to increase with common pool size. Comparable studies have
tended, firstly, to focus on assets and debt rather than on expenditures and, secondly, on
district population rather than on the number of districts as in the original formulation of
the law. Both issues are sought to be remedied in this paper. The proposition is examined on
Danish municipal expenditures from 1996 to 2006, using municipal mergers towards the end
of this period as a quasi-experiment. A difference-in-difference identification strategy and a
subsample strategy are used to identify the effect of the availability and size of a common
pool on municipal expenditures. The paper finds positive, statistically and economically
significant effects of the availability and size of a common pool in the final year of the
treatment period. The importance of the number of districts over district population suggests
a reappraisal of the law of 1 over n as originally formulated.
Keywords Local government mergers · Common pool size · Law of 1 over n ·
Quasi-experiments
1 The importance of polity size and the law of 1 over n
The issue of polity size has been debated since the time of Aristotle and remains alive today,
as do attempts to rescale local and regional government (Baldersheim and Rose 2010). Such
reforms can at times be used as cases of more general political issues, such as the persistence
of common pool problems in political systems. This paper examines recent municipal mergers in Denmark to test the proposition that project size tends to increase with common pool
size, derived from the law of 1 over n (Weingast et al. 1981). In this paper, projects refer to
spending on services provided by the Danish municipalities, such as child care, primary education, old age care, and local roads. The paper proceeds in the following manner: Below,
S. Welling Hansen ()
The Danish Analysis and Research Institute for Local Government, Købmagergade 22,
1150 Copenhagen K, Denmark
e-mail: [email protected]
Public Choice
the law is outlined and related to the case of municipal mergers. Danish local government is
described in Sect. 2, and outcome measures in Sect. 3. Sections 4, 5, 6 contain the empirical
specification, Sect. 7 the empirical analysis, and Sect. 8 concludes.
Political scientists have been aware of common pool problems in politics for decades
(see, e.g., Ostrom 1990), including the importance of the number of decision-makers (Olson
1965). Weingast et al. (1981) formulated a related version of the law of 1 over n, which
has been applied to a wide range of political phenomena under equally far-ranging institutional conditions, including local government. The general claim is that the number of
decision-makers affects public spending. This is a model of political decision-making under
institutionally stable conditions, where policy-makers decide on pork-barrel projects within
a geographical area containing multiple jurisdictions: An area is divided into n districts of
equal size. Each district is represented by a political representative on a joint board for the
entire geographical area. Each representative is assumed to care exclusively for benefits and
costs that accrue to his or her district (Weingast et al. 1981: 650), and each can propose
projects in his or her district that are financed collectively. Under these circumstances, a district receives all benefits from projects initiated in its area but pays only 1/n’th of the costs.
Three propositions are derived from the law: Inefficiency, total spending, and project size
tend to increase with common pool size, that is, the number of districts n (Weingast et al.
1981: 645, 653, 654). This paper examines the last-mentioned proposition.
The law of 1 over n is also applicable to situations of institutional change: Local politicians may face a common pool problem when their jurisdictions, or governmental entities
such as municipalities, are to be merged, because the merger process links the present policies of the merging entities to the future policies of the newly merged entity. Suppose that a
geographical area is divided into a number of politically independent districts, and that each
is able to set service and tax levels, issue debt and so forth independently. The elected politicians are accountable only to the electorate in their local jurisdiction. Suppose now that the
government implements a merger reform: Each group of merging entities constitutes a common pool area, and the fiscal policy of each member affects the entire group as the merged
entity inherits all finances and obligations. For example, if a merging entity opts to reduce
its assets or increase its debt to finance local projects, that choice automatically will affect
the assets or debt transferred to the new, merged entity.
However, the potential for collective action problems is not limited to these types of
spending, as the new merged entity also inherits responsibility and accountability for the
services provided in the merging entities, and once provided it can be exceedingly difficult to
remove or reduce them. This has inter alia been attributed to inconsistent fiscal preferences in
the electorate (Citrin 1979), which are exacerbated when the decision processes on spending
are atomized (Kristensen 1980, 1987). This is certainly the case in fiscally decentralized
countries such as Denmark, where many spending decisions are left to the municipalities.
A substantial share of the Danish electorate exhibits such inconsistencies with regard to
municipal expenditures and taxes (Mouritzen 1991: 179ff; Winter and Mouritzen 2001).1
The empirical evidence for the law of 1 over n is generally mixed (Primo and Snyder
2008). With regard to local government mergers, Hinnerich (2009) and Jordahl and Liang
1 The Danish municipal mergers deviate from the model by Weingast et al. (1981) in two respects: Firstly, the
decision-making process did not follow a norm of universalism, but the collective decision materializes as
the product of the merging municipalities’ decisions. Secondly, the model assumes that only a single political
representative is elected from each district while multimember districts are used in Danish local government.
However, this is arguably less important as it is already assumed that politicians care exclusively for their
local electorate’s interests.
Public Choice
(2010) examine the relationship between relative district size and project size in mergers of
Swedish municipalities. They use identification strategies akin to those used in this paper,
and examine assets and debt but not expenditures. This is remedied in a third study by
Blom-Hansen (2010), who, using a cross-sectional identification strategy, examines budget
overruns on current and capital accounts in connection with recent mergers in Denmark. The
latter two studies find that the availability of a common pool matters, but not its size, while
the first examines only common pool size and finds substantiating evidence. One possible
reason for this mixed evidence is in the application of the law of 1 over n. In Weingast et al.’s
model, district population is fixed while the number of districts is allowed to vary, but the
cited studies allow for the opposite (one study cites the modified model proposed by Primo
and Snyder 2008).
This leads to the expectation that project size will tend to increase with district size, defined as a relative measure of the ratio between the merging municipality’s population and
the population of the new, merged municipality. In the case of merging entities such as municipalities, however, both district size and common pool size are likely to vary at the same
time: Municipalities that merge are likely to differ in population size as will the number of
municipalities that merge with each other. In the recent Danish mergers, relative municipal
size varies from 1 to 23 (defined by Blom-Hansen 2010) and the number of municipalities
in a merger from two to seven. Two of the authors’ nonfindings with respect to relative
municipal size, and the substantiating evidence found by the third, may be caused by not
acknowledging that the number of merged municipalities actually varies.2 This is tested on
the same case as Blom-Hansen (2010): First, it is examined on whether the availability of a
common pool affects project size (as his results may be affected by the cross-sectional identification strategy), and second whether the number of municipalities in a merger affects
project size. These results are then compared to results for relative district size.
The question is how the number of municipalities in a merger reflects the logic of the law
of 1 over n. One can argue that applying the law of 1 over n using relative district size, as
in the aforementioned studies, is not consistent with the general claim of the law, that is, the
number of decision-makers in a common pool area affects public spending. Instead, this can
be directly measured by how many municipalities take part in each merger. The problem
with relative district size is that it is a measure of the local populations which comprise
the common pool area. However, decision-making power lies with the municipal councils
rather than with the populations (the latter calls for local referendums on fiscal policy, which
are not used in Denmark). The important question is: When local councilors in a merging
municipal council decide on the fiscal policy, do they enact a given policy on the basis of
the size of their local population relative to the size of the common pool area? The argument
behind relative district size is that two councils respectively representing, for example, 10 %
and 20 % of the population in the common pool area will adopt markedly different policies.
To illustrate with a simple example: A common pool area has 100,000 inhabitants of
which 10,000 reside in one municipality, 20,000 reside in another municipality, and the
remaining 70,000 in a number of additional municipalities. In this case, the relative district
size of the first municipality is equal to ten (using the definition of Blom-Hansen 2010:
69), which is twice as large as that of the second municipality. We here expect the level,
or change, in public spending in the former to be twice that in the latter. However, is it
2 One might argue that the latter will act as a proxy for the former. However, a merging municipality’s pop-
ulation can account for a small or a large share of the newly merged municipality’s population without the
number of municipalities in the merger being correspondingly lower or higher. Such deviations occur frequently in the case examined in this paper (r = 0.50; n = 217).
Public Choice
reasonable to expect that local councilors, when deciding on fiscal policy, will decide on the
basis of demographic considerations, and furthermore be so precise in their reasoning about
their ability to externalize costs? I argue that it is more reasonable to expect that councilors
will base their decision on how many municipalities take part in the merger. This reflects
how many districts with distinct geographical interests are pitted against each other, and
hence how politically fragmented the common pool area is. It is in this sense a measure of
the potential for externalizing costs. Even though the validity of this operational definition is
arguably more in line with the general claim of the law, both definitions discussed here will
be assessed empirically later. First, however, the case examined in the paper is described in
detail.
2 Local government in Denmark
The Danish public sector has one of the highest levels of fiscal decentralization among the
OECD countries (Thießen 2003). Danish local government consisted of 270–275 municipalities until 2007. In 2005, the municipalities agreed on mergers, which reduced the number to
98. These mergers were accompanied by a new division of tasks and burdens (for a description of the reform, see Mouritzen 2010). Talk of local government reform was first sparked
in the summer of 2002. In his opening address to the parliament on 1 October, the prime
minister announced the Commission on Administrative Structure, which would assess the
public sector’s existing structure. On 9 January 2004, the Commission publicized its findings, concluding that there were a number of weaknesses in the municipal structure. Five
months later, on 24 June, an agreement was reached on a comprehensive reform (Ministry
of the Interior and Health 2004). Municipalities with less than approximately 20,000 inhabitants were forced to merge, while municipalities with larger populations could choose
whether to merge or not. However, a loophole allowed municipalities with less than 20,000
inhabitants to avoid mergers if they entered into binding partnerships. The deadline for voluntary mergers was 1 January 2005. In numerical terms, nine out of ten municipalities (237
of the 270) merged into 65 new municipalities, leaving 33 municipalities unaffected.
Common pool problems can be solved or alleviated by regulating access to the common
pool (see, e.g., Ostrom 1990). One solution is to impose fiscal restrictions on the municipalities prior to the mergers, which the Danish government was quick to do. First off, examining the law of 1 over n under conditions that are less favorable to its validity constitutes
a strong test of its importance in municipal mergers. Consequently, if the law is supported
empirically under these conditions, we would firstly expect the law to remain valid under
more favorable conditions, such as less severe restrictions, and secondly that we obtain more
conservative estimates. The first restriction was effectuated already on 22 December 2003,
when the municipalities were instructed to report all construction appropriations over 1 million DKK to the Ministry of the Interior and Health (later subject to approval for fiscal years
2004 to 2006). For the 2005 fiscal year, consumption of liquid reserves was restricted by a
mandatory deposit of a large share of those assets. For fiscal years 2006 to 2007, municipal
taxation privileges were suspended. For the 2006 fiscal year, fiscal regulation of the merging
municipalities was, with few exceptions, decentralized to so-called integration committees
established for each group of merging municipalities. The committees consisted of the councilors for the new, merged municipalities elected at the 16 November 2005 local elections,
and were granted some powers of approval over the municipal councils in their merger group
with respect to both current and capital expenditures.
Public Choice
3 Outcome measures
First, severe restrictions on taxation, liquid reserves, debts, and capital expenditures make
these less interesting compared to current expenditures. Second, expenditures can pertain
to municipal appropriations, final accounts, or a combination of the two. Appropriations
are unreliable and of limited informational value because Danish municipalities often run
budget deficits. Furthermore, they are subject to considerable political attention and public
scrutiny from the government, parliament, and the media. In addition, municipalities decide
on appropriations for the coming fiscal year at least two and a half months prior to its beginning, which allows the government to identify, and ipso facto approve, any attempt at
opportunistic behavior before a fiscal year commences (Blom-Hansen 2007: 30). The final
accounts, which reflect actual municipal spending and receive less political attention and
public scrutiny, are made public ex post facto six months after the conclusion of the fiscal
year. Only then can opportunistic behavior be identified. It is therefore more plausible that
opportunistic behavior on the part of the municipalities involves the final accounts, and there
are two relevant outcome measures: The one-year change in final accounts, and a measure of
budgetary balance, budget overruns, defined as the difference between appropriations and
final accounts. Both are examined in this paper, thereby extending Blom-Hansen (2010),
who examines the latter.
The next question is when we should expect common pool size to affect municipal
spending. Firstly, the year 2003 is chosen as a cutoff point for separating the pre- and posttreatment period, although the mergers were not agreed on until 2 years later. However, the
appointment of the Commission on Administrative Structure in the fall of 2002 may have
led the municipalities to anticipate a merger already in 2003 and 2004. It is therefore sensible to view these 2 years as an intermediate period wherein the municipalities may or may
not have acted opportunistically. Here is a potential problem with Blom-Hansen’s analyses (2010: 58), as 2003 is used as “control year”. Secondly, the government potentially can
equalize increases in spending if they can be identified and this is possible for the final accounts in the first 3 years of the post-treatment period (2003–2005), but not in the last year
(2006). This potentially limits the influence of common pool size to the final year, where we
are left with a “push and a pull” effect as the strongest restrictions on current expenditures
are also in place here. Whether the former or the latter has a greater impact is a matter of
empirical investigation.
4 Difference-in-difference strategy for merged and nonmerged municipalities
The proposition is firstly examined on the full sample by comparing merging and nonmerging municipalities.3 In the former, common pool size varies between two and seven municipalities, but equals one in the latter. We can therefore examine whether or not the availability
of a common pool matters.
In quasi-experiments, causality is established by comparing an analytical unit’s observed
outcome with a counterfactual outcome, inferred from the observed outcome of a comparable unit. Controlling for the nonrandomness of the assignment allows us to assume that the
3 The number of municipalities varied between 270 and 275 from 2003 to 2006. Of these, 21 to 26 were
excluded based on three criteria: if a municipality has had both municipal and county tasks, has been part of a
merger not directly associated with the 2007 merger reform, or has been put under administration in the time
period or a number of years before.
Public Choice
Table 1 Tabulation of the demographic criterion and mergers
Demographic
No
criterion met?
Yes
Considered merging?
Actually merged?
No
Yes
No
Yes
3
182
3
182
(1.2 %)
(74.9 %)
(1.2 %)
(74.9 %)
28
30
23
35
(11.5 %)
(12.4 %)
(9.5 %)
(14.4 %)
Note: n = 243. Reported are cell percentages
units of analysis will conditionally be independent of treatment with respect to potential outcomes. After the assignment, a treatment is administered to the treatment group, whereas the
control group receives no treatment. In the present context, the treatment is administered at
the point in time when the municipalities anticipate or know that they are to be merged. The
pre- and post-treatment period, respectively, cover the years 1996–2002 and 2003–2006. The
assignment mechanism is the set of criteria stipulating under what circumstances a municipality should be merged. In the case of a merger reform, a bias in the assignment mechanism
arises naturally as a primary purpose of the reform is to increase the demographic size of the
local municipalities. The municipalities subjected to treatment will therefore tend to be the
demographically small. Besides size, small and large municipalities differ in other respects
which affect expenditures, and these are also controlled.
The nonrandomness of the assignment is one possible source of bias, and a second source
is self-selection after treatment is anticipated or becomes known, which concerns whether
the units had a choice between merging or not. This is examined by using ex post information
and comparing the demographic criterion (a population of 20,000) to, firstly to determine
whether the municipalities considered merging by participating in negotiations (based on
near-monthly maps published by Local Government Denmark), and secondly, whether they
actually merged. A lack of correspondence between these three indicates that a municipality
has exercised some form of choice. Of the 243 municipalities included in the analyses (cf.
footnote 3), 24 % (58) met the demographic criterion and 76 % (185) had to consider merging. The results are shown in Table 1: As for the merger negotiations (the left-hand side),
three municipalities did not meet the criterion and did not participate in negotiations (made
possible by the loophole condition). Thirty met the criterion and still engaged in negotiations. These results are nearly identical when we look at the actual mergers (the right-hand
side). All in all, there are indications of possible self-selection for municipalities on the
principal diagonal for each cross-tabulation, which together contain 22 % (54) of the municipalities. These observations are potentially cases of doubt, the inclusion of which may
bias estimates of the treatment effect, and they are referred to as subsample #1.
The panel structure of the data allows us to try to counter the effect of differences that
exist to begin with Cook and Cambell (1979: 98) by conditioning on initial characteristics.
This is usually not possible in cross-sectional analyses, which therefore are more sensitive
to selection bias. A difference-in-difference (DD) identification strategy is used in this paper
(Imbens and Wooldridge 2008: 64ff). Consider a specification with two binary indicators:
Yit = β0 + δ0 Mergedi + β1 Postt + δ1 (Mergedi · Postt ) +
k
βk Xkit + εit
(1)
The zero-one group indicator Mergedi reflects whether a unit i is merged or not, and its
effect δ0 accounts for unobservable and persisting between-group heterogeneity exogenous
Public Choice
to treatment. The period-specific zero-one indicator Postt reflects whether the municipalities have knowledge of the mergers, or anticipate them, in a given year t , and its effect
β1 accounts for unobservable heterogeneity over time exogenous to treatment.4 The effect
δ1 is the product of the two indicators, Mergedi · Posti , and equals the average treatment
effect
k on the treated, ATT, with the expectation that δ1 > 0. Finally, β0 is the intercept,
βk Xkit is a set of k covariates, and εit is the unexplained variation for each municipality
i in year t . A more flexible specification allows for between-year heterogeneity
in the treatment effect by firstly replacing Postt with a set of u binary year indicators, u βt Tt (using
the pretreatment period as reference category),
and secondly, replacing Mergedi · Postt with
a corresponding set of u interactions, u δt (Mergedi · Tt ), with the expectation that ∀δt > 0.
This specification allows for the estimation of year-specific ATT effects and is less sensitive
to the choice of cutoff point used to separate the pre- and post-treatment period.
5 Subsample strategy for merged municipalities
A second identification strategy is used for the subsample of the 217 merged municipalities
in the post-treatment period, referred to as subsample #2. This allows us to assess whether
the size of the common pool matters, by comparing expenditures across common pool areas
of different sizes. Common pool size is defined as the number of municipalities in each
group of merging municipalities h: NoMunich ∈ {2, . . . , 7}. Using a period-specific effect,
Yit = β0 + δ0 NoMunich +
u−1
β t Tt +
k
βk Xkit + εit
(2)
The coefficient estimate of primary interest is δ0 , which is the effect of increasing common
pool size by one municipality, with the expectation that δ0 > 0. To account for unobservable
between-year heterogeneity exogenous to treatment, a set of u − 1 binary year indicators
is included (using 2003 as reference category). Again, we can allow for between-year heterogeneity in the effect of common pool size,
by adding u − 1 binary interactions between
common pool size and the year indicators, u−1 δt (NoMunich · Tt ), with the expectation that
∀δ > 0. In the reference year (2003), the effect of common pool size is equal to the direct
effect, δ0 , and in the remaining years the linear combination of the direct and indirect effect
for year t , δ0 + δt .
A bias can arise from self-selection if the municipalities could choose with whom to
merge and thereby influence their common pool size. The choice of merger partner(s),
however, was quite restricted: the municipalities were given only six months to find their
partner(s). Geographical contiguity was required and it was stressed that the municipalities
“. . . should take correlation between cultural and business activities into account, and efforts
should be made to include both rural and urban areas” (Ministry of the Interior and Health
2004: 11). A recent study confirms that the societal connectedness of the merging municipalities was systematically related to their propensity to merge (Bhatti and Hansen 2011).
The choice of partner(s) must therefore be presumed to have been based on a host of social,
cultural, economic, and other ties (Mouritzen 2010: 12).5
4 The assumption of a common trend in the DD design makes it well suited for analyses of subnational
governments such as the Danish municipalities, which are all subject to the same overall legal and political
framework.
5 The specifications of Eqs. (1) and (2) can be extended to account for persistence over time. Firstly, the
period-specific specification in Eq. (1) is less sensitive to persistence over time as collapsing the data into a
Public Choice
Table 2 Means and standard deviations for variables
Name
Election year
Expenditure needs (1996/2003)
Period
Pre- and post-treatment
1996–2006 (n = 2673)
Post-treatment
2003–2006 (n = 868)
Mean
Mean
SD
SD
0.273
0.445
0.250
0.433
24.231
1.220
28.106
1.226
Expenditure needs
0.420
0.706
0.415
0.341
Number of municipalities in merger
4.124
1.330
4.124
1.330
Relative municipal size
5.795
3.903
5.795
3.903
Logged population (1996/2003)
2.508
0.761
2.420
0.646
Population
Share elderly (1996/2003)
Share elderly
Share young (1996/2003)
0.315
0.824
0.379
1.011
15.115
3.061
15.428
2.436
0.100
0.250
0.195
0.261
22.853
1.993
23.873
1.956
Share young
0.075
0.278
−0.019
0.317
Tax base (1996/2003)
2.037
3.053
1.722
1.966
Tax base
0.851
3.669
−0.718
3.729
Note: Descriptive statistics for uncentered variables. Statistics for stock variables are for 1996 and 2003
6 Controls
To account for differences in demographic size between the municipalities that are and are
not merged, a logged capital stock measure of population is included in the analyses on
the full sample. The DD strategy allows for conditioning on pre- and post-treatment characteristics, but the latter only insofar as it is reasonable to assume that they are exogenous
to treatment. A set of stock measures is included, reflecting the level of the measure at the
beginning of the time period (1996 or 2003), and a corresponding set of flow measures for
annual changes. Included are the share of young people (aged 0–17) and elderly people
(aged 65 and older), municipal tax base (e.g., used by Blom-Hansen 2002), and expenditure needs (e.g., used by Serritzlew 2005). Opportunistic political business cycles are also
controlled for in the DD strategy, as such cycles are well documented in Danish local government (Houlberg 1999; Mouritzen 1989, 1991; Serritzlew 2005). Descriptive statistics are
given in Table 2.
7 The Danish municipal mergers
Over the 11-year period from 1996 to 2006, the average level of appropriations and final
accounts on current expenditures has increased by approximately 24 %: Municipal appropriations from 24,017 DKK per capita (2000 prices) to 29,826 DKK, and final accounts from
24,211 DKK per capita (2000 prices) to 30,086 DKK. On average, the latter have increased
pre- and post-treatment period produces consistent standard errors when serial correlation is present (Bertrand
et al. 2004). Secondly, all models are estimated with standard errors clustered at the municipal level. Finally,
fixed effects specifications of all models, estimated using deviations from means, are also considered.
Public Choice
Fig. 1 Mean final accounts
by 534 DKK per capita per year over the time period. As seen in the top halves of Figs. 1
and 2, average current expenditures consistently are higher for the non-merged municipalities by more than 3,300 DKK per capita, or 11–12 %. The annual changes in final accounts
for the two groups are given in the lower half of Fig. 1: Clearly, there is considerable variation in the changes over the period, but the trend in change is similar for the two groups,
except for the last year, 2006.
Public Choice
Fig. 2 Mean appropriations and budget overruns
Turning to budget overruns, final accounts have on average exceeded appropriations by
364 DKK per capita, or approximately 1 13 %. The lower half of Fig. 2 gives average overruns
for the merged and nonmerged municipalities, and there is considerable variation over the
period. As previously noted, the trend in the average budget overrun is similar for the merged
and nonmerged municipalities, except at the beginning and at the end of the period (1996–
1998 and 2006).
Public Choice
All in all, the overall similarity in trends for the merged and nonmerged municipalities
over the pretreatment period, and the first years of the post-treatment period, substantiate
the parallel trends assumption. Therefore, there is also no indication that early anticipation
of the mergers has led to systematic opportunism on the part of the municipalities, neither
in 2003–2004 nor in earlier years.
7.1 Difference-in-difference strategy: results
It is assumed in the DD strategy that there is no mean group difference in outcome prior to
treatment when controlling for the nonrandomness of the assignment. This is tested by estimating a model for the pre-treatment period containing the binary group indicator Mergedi
and binary year indicators for all but the first year (only selected results are reported). Without controls, the mean group difference in change in final accounts equals −19 DKK (SE
of 34 DKK), which is revised to 10 DKK (SE of 34 DKK) when controls are included
(except for election year). The group mean budget overrun, however, differs significantly
when controls are not included, and the merged municipalities exceed their appropriations
by 131 DKK (SE of 66 DKK) more than the nonmerged ones; but the controls reduce the
difference to an insignificant 62 DKK (SE of 58 DKK). The controls are therefore able to
account for the group differences on both outcome measures in the pre-treatment period.
The parallel trends assumption can also be examined by including a set of interactions between the binary group indicator and the year indicators: For budget overruns, the value of
the joint F test for the interactions is 1.544 (p-value of 0.164), which decreases to 1.072
(p-value of 0.380) when controls are included. For change in final accounts, however, the F
test is significant with a value of 2.643 (p-value of 0.017) and including controls increases
the value to 3.497 (p-value of 0.002). Results for this outcome measure should therefore be
interpreted more cautiously.
The empirical results for the two specifications of Eq. (1) are given in models (1)–(4) in
Table 3 and models (9)–(12) in Table 4 for the two outcome measures: A strongly significant and positive period-specific treatment effect is found for change in final accounts of
196 DKK per capita. The controls reduce the estimate by a fourth to a significant 151 DKK,
while excluding cases of doubt (subsample #1) reduces the estimate to an insignificant
144 DKK (results omitted to conserve space). The estimates are sizable and amount to 27–
37 % of the average annual change over the whole time period (equal to 534 DKK per capita,
as noted earlier) and when compared to the estimates for the controls. However, no treatment
effect is found on budget overruns. A possible explanation is that the treatment effect may
vary over the post-treatment period, which is considered next.6
The results for the year-specific specification of Eq. (1) are given in models (3), (4), (11),
and (12). In the first 3 years of the post-treatment period, there is no significant treatment
effect for either outcome measure, except for budget overruns in 2003 when excluding cases
of doubt (not reported). The estimate is here barely significant and negative, as are the other
estimates for budget overruns in the first 2 years. The estimates’ lack of significance and
varying signs reveal the considerable variation over the years 2003–2006 and underlines the
need for calculating year-specific treatment effects. There is a strongly significant, positive,
and sizeable treatment effect on both outcome measures in the final year, 2006. Firstly, for
6 The explanatory power of the models with controls for changes in final accounts is a respectable 14–19 %.
For budget overruns, however, the explanatory power is lower at 4–6 %. The explanatory power of the subsample design (examined in the next section) is similar at 11–15 % and 3–7 %.
Public Choice
Table 3 Results on one-year change in final accounts on current expenditures
Model No.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Sample
F
F
F
F
S2
S2
S2
S2
Controls
No
Yes
No
Yes
No
Yes
No
Yes
Merged
−19
−16
−19
−21
(34)
(34)
(34)
(34)
Post
−344**
−256**
(66)
(66)
Merged · Post
196**
151*
(69)
(67)
−457**
−283*
(133)
(136)
−2
205
279**
235**
272*
205
(135)
(137)
(57)
(74)
(123)
(130)
−68
85
259**
192**
208
96
2003
2004
2005
(154)
(154)
(56)
(61)
(123)
(126)
−850**
−1,042**
43
1
−346**
−379**
(117)
(120)
(62)
(82)
(122)
(124)
163
129
(138)
(141)
−12
−69
57**
29*
4
−29
(16)
(14)
(34)
(34)
No. munic.
· 2004
3
13
(49)
(49)
No. munic.
· 2005
24
45
(47)
(47)
No. munic.
· 2006
183**
177**
(54)
(54)
2006
Merged · 2003
Merged · 2004
Merged · 2005
Merged · 2006
(141)
(138)
34
5
(159)
(159)
599**
570**
(127)
(124)
No. munic.
Ln population
(96/03)
−107**
−103**
(21)
(21)
Population
−11
2
42
(18)
(18)
(30)
(31)
Share elderly
(96/03)
2
3
31**
32**
(5)
(5)
(11)
(11)
Share elderly
6
28
145
172
(68)
(64)
(94)
(91)
−8
−8
22
23
(7)
(7)
(15)
(15)
Share young
(96/03)
42
Public Choice
Table 3 (Continued)
Model No.
(1)
Share young
Tax base (96/03)
Tax base
(2)
(3)
(4)
(5)
(6)
(7)
(8)
8
−2
−20
(51)
(50)
(88)
−16
(88)
1
1
−31**
−31**
(3)
(3)
(10)
(10)
17**
17**
21*
19*
(6)
(6)
(9)
(8)
Expenditure
needs (96/03)
41**
44**
31
31
(7)
(8)
(18)
(18)
Expenditure
needs
234**
171**
354**
342**
(19)
(19)
(67)
(67)
Election year
147**
377**
(30)
Intercept
(34)
670**
25
670**
−118
237**
−1467
349**
−1403
(32)
(320)
(32)
(320)
(51)
(759)
(84)
(758)
7
−16
Linear combinations:
No. munic., 2004
No. munic., 2005
No. munic., 2006
(30)
(29)
28
16
(29)
(28)
187**
149**
(43)
(40)
0.147
R2
0.020
0.141
0.044
0.190
0.056
0.124
0.082
Obs.
2673
2673
2673
2673
868
868
868
868
max(VIF)
9.918
10.010
9.814
10.370
1.500
3.043
5.829
6.060
Note: Reported are unstandardized coefficients and standard errors in parentheses. All models are estimated
using ordinary least squares with standard errors clustered at the pre-merger municipal level. Sample abbreviations: F = full sample (n = 243 · 11 = 2673) and S2 = subsample #2 (n = 217 · 4 = 868). Results for
subsample #1 are not reported to conserve space. The treatment effects of common pool size in 2004–2006
are calculated as linear combinations of the main effect plus the interaction effect in each year
* Significant at the 5 % level
** Significant at the 1 % level
change in final accounts the estimate is two and a half to four times the period-specific estimate. The controls lower the estimate marginally, while omitting cases of doubt leads to
a 30 % increase. The estimates are sizeable and correspond to 107–140 % of the average
annual change in final accounts over the whole time period and when compared to the estimates for the controls. Secondly, the size of the treatment effect for budget overruns has
quadrupled or more compared to the period-specific effect. Including controls reduces the
estimate slightly while omitting cases of doubt increases it by a fourth. The estimates equal
149–184 % of the average budget overrun over the whole period (equal to 364 DKK per
capita, as above) and compared to the estimates for the controls.
Public Choice
Table 4 Results on budget overruns on current expenditures
Model No.
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
Sample
F
F
F
F
S2
S2
S2
S2
Controls
No
Yes
No
Yes
No
Yes
No
Yes
Merged
131∗
79
131∗
80
(66)
(58)
(66)
(58)
−63
−50
123
179
(158)
(156)
179
214
40
45
66
66
(125)
(120)
(41)
(50)
(75)
(80)
38
−58
−1
−13
−28
−57
(111)
(111)
(52)
(54)
(114)
(113)
−590∗∗
−543∗∗
−113
−147∗
−508∗∗
−543∗∗
(128)
(131)
(62)
(69)
(123)
(122)
−32
−40
(163)
(161)
−49
−51
15
7
−31
−41
(21)
(22)
(30)
(32)
No. munic.
· 2004
−12
−11
(29)
(30)
No. munic.
· 2005
12
21
(43)
(42)
No. munic.
· 2006
186∗∗
185∗∗
(50)
(50)
Post
Merged · Post
(103)
(102)
134
128
(107)
(108)
2003
2004
2005
2006
Merged · 2003
Merged · 2004
Merged · 2005
Merged · 2006
(131)
(130)
51
37
(118)
(116)
568∗∗
543∗∗
(139)
(143)
No. munic.
Ln population
(96/03)
Population
−71
−70
(38)
(38)
57∗∗
67∗∗
96∗∗
95∗∗
(21)
(22)
(31)
(31)
Share elderly
(96/03)
−0
1
−22
−21
(11)
(11)
(22)
(22)
Share elderly
24
39
−14
13
(78)
(79)
(129)
(129)
−24
−24
−42
−41
(13)
(13)
(27)
(27)
Share young
(96/03)
Public Choice
Table 4 (Continued)
Model No.
(9)
Share young
(10)
(11)
(12)
(13)
(14)
(15)
(16)
139∗
102
−8
(54)
(55)
(89)
(90)
−10
−10
−53∗∗
−53∗∗
−4
Tax base
(96/03)
(7)
(7)
(15)
(15)
Tax base
−4
−4
2
0
(3)
(3)
(5)
(4)
Expenditure
needs (96/03)
31
30
37
38
(23)
(23)
(31)
(31)
Expenditure
needs
−4
−0
2
−15
(14)
(15)
(66)
(65)
110∗∗
148∗∗
Election year
(20)
(22)
226∗∗
254
226∗∗
230
414∗∗
824
513∗∗
881
(63)
(656)
(63)
(657)
(59)
(1337)
(77)
(1344)
No. munic.,
2004
−43
−52
(30)
(31)
No. munic.,
2005
−19
−21
(31)
(32)
No. munic.,
2006
155∗∗
144∗∗
(41)
(41)
0.068
Intercept
Linear combinations:
R2
0.012
0.045
0.026
0.060
0.008
0.043
0.035
Obs.
2673
2673
2673
2673
868
868
868
868
max(VIF)
9.918
10.000
9.814
10.110
1.500
3.043
5.829
6.060
Note: See notes for Table 3
7.2 Subsample strategy: results
Equation (2) is used to examine whether the size of the common pool matters on the subsample of merged municipalities in the post-treatment period (subsample #2). The empirical
results for the period-specific specification are reported in models (5)–(8) and (13)–(16).
Firstly, for change in final accounts there is a significant positive period-specific effect of
common pool size, but it is halved when controls are included or cases of doubt omitted (not
reported), and turns insignificant in the latter case. The period-specific estimates for budget
overruns also retain the expected sign but are clearly insignificant. A possible explanation
for these nonfindings is that the effect varies over the years in the post-treatment period,
and this is examined using the year-specific specification in models (7), (8), (15), and (16).
Again, there are no significant treatment effects on either outcome measure in the first 3
years. Moreover, the signs of the estimates are in many instances negative for both. However, there is a significant and positive treatment effect in the final year of 2006 for both;
see models (7), (8), (15), and (16). Firstly, for change in final accounts the effect of increasing common pool size by one municipality equals 177 DKK when controls are included.
Public Choice
As the groups consist of two to seven merging municipalities, this yields a maximum difference between the common pool groups of 885 DKK, which amounts to 166 % of average
annual change over the whole time period. Secondly, the effect for budget overruns equals
185 DKK per capita, which yields a maximum difference of 925 DKK, amounting to 254 %
of the average annual budget overrun over the whole period.7
7.3 Considerations on capital expenditures and district size
All models were estimated on capital expenditures (not reported) but no evidence supports
the conclusion that the availability or size of the common pool matters (although this is a
cautious non-finding due to high variance inflation factors). First, a plausible explanation is
that the restrictions imposed through the approval scheme have been too severe to allow for
opportunistic behavior. Second, the nonfinding for availability of a common pool contrasts
with that of Blom-Hansen (2010: 62), who finds that availability has a significant effect
on budget overruns on capital expenditures in 2006. However, these results are obtained
from a cross-sectional identification strategy which assumes that no initial differences exist,
and reestimating models (1) and (2) as cross-sectional models produce similar results (not
reported).
The second matter concerns the importance of the number of districts compared to district size. The year-specific specifications of Eq. (2) were first estimated with common pool
size defined as relative municipal size (cf. Blom-Hansen 2010: 69; only some results are
reported and variance inflation factors do not exceed 4.4): District size is significant only
for budget overruns on current expenditures in 2006 when controls are not included, with
an estimate of 35 DKK (SE of 15 DKK; p-value of 0.020), but is reduced to an insignificant 26 DKK by the controls (SE of 16 DKK; p-value of 0.100). Second, it is possible
that district size is conditional on the number of districts or vice versa; and such parameter
heterogeneity is examined by including higher-order interactions: Two-way interactions between relative municipal size and number of municipalities in the merger, and between each
of them and the year indicators; and their three-way interactions (only selected results are
reported; variance inflation factors do not exceed six). The effect of district size is insignificant in all cases except being barely significant for budget overruns on current expenditures
in 2004 when controls are included, with an estimate of −31 DKK (SE of 15 DKK; p-value
of 0.047). Conversely, the effect of the number of municipalities in a merger remains significant for change in final accounts and budget overruns in 2006 with effect sizes similar to
7 For both outcome measures, excluding cases of doubt leads to marginal increases in the treatment effects.
Furthermore, models (1)–(16) were reestimated using robust regression to investigate the influence of outliers.
The treatment effects retain their significance except for model (2), and the estimates tend to be reduced, but
decrease by no more than about a third. All models were also re-estimated with White heteroscedasticityconsistent standard errors, which make the treatment effect in models (2) and (6) turn insignificant. This
does not lead to a different conclusion for the availability or size of the common pool. In addition, fixed
effects specifications of all models were also estimated, which likewise produces very similar results. Models
(2), (4), (10), and (12) were also reestimated with a binary indicator of population size (below, equal to or
above 20,000 inhabitants, cf. the agreement on the reform) instead of logged population size. However, this
yields only small changes in the treatment effects. As a final note, the identification strategy calls for the
use of interactions which can create problems with multicollinearity. This can result in too large standard
errors that increase the chance of Type II error, and hence, overly conservative test statistics (Gujarati 2003:
Chap. 10). Multicollinearity is therefore more problematic in cases with nonfindings. The largest variance
inflation factors are around ten in the models estimated on the full sample, and at the most six in the models
for subsample #2. The highest values are found primarily for the interactions.
Public Choice
those obtained in previous models. All in all, there is little evidence to support the conclusion that district size has been a factor in the Danish municipal mergers, which is consistent
with Blom-Hansen’s (2010) nonfinding.
8 Conclusions
The paper has examined and found substantial evidence in favor of the proposition that
project size tends to increase with common pool size, derived from the law of 1 over n as
originally formulated. The effect is limited to the last year prior to the mergers, arguably
due to two factors: Firstly, the government had the opportunity to identify and equalize
opportunistic behavior in the first 3 years but not in the last. Secondly, prior to 2005, the
municipalities did not know with certainty whether they would be merged, and if so with
whom. The municipalities might have anticipated the mergers, but there is no evidence that
they acted on these anticipations.
The proposition has been examined using two identification strategies, estimated on the
full sample and a subsample, respectively. The empirical results indicate that both the availability and size of a common pool matters. However, the evidence for availability on one of
the two outcome measures, changes in the final accounts, should be interpreted cautiously
as there are indications of systematic differences in trends prior to treatment. Given that the
law has been examined under conditions that are less favorable to its validity, the estimates
obtained should be conservative and lend considerable support to the proposition relating
common pool size and project size. Furthermore, the effect of the number of districts holds
when district size is controlled for. The results indicate that the crucial factor is the number
of decision-makers, and suggests a reappraisal of the original formulation of the law.
The question is whether the causal claim is reasonable or not. The effect of the number of
municipalities in a merger may to some extent reflect transitory costs relating to reorganization and harmonization of service levels. It is difficult to distinguish opportunism empirically
from such transitory costs (Jordahl and Liang 2010 discuss a similar issue) and it cannot be
examined more closely here. But whether the observed pattern in public spending is caused
by transitory costs or opportunism, the findings imply that the long-term expected benefits of
public sector reforms need to be weighed against the short-term costs associated with them.
This is becoming an important issue as the frequency and scope of public sector reforms
have been increasing over time. Such reforms, however, can prove feasible only when their
benefits outweigh their costs.
Acknowledgements The study is based on the author’s dissertation initiated in 2006 and concluded in 2009
(Hansen 2011). The author thanks the Research Programme on the Structural Reform, the Local Government
Foundation for Education and Research, the Ministry of Social Welfare, and the Department of Political
Science and Public Management at the University of Southern Denmark, for funding my Ph.D. project as well
as Professors Poul Erik Mouritzen and Asbjørn Sonne Nørgaard, Associate Professor Robert Klemmensen,
and numerous other people, who shall remain unnamed for the sake of brevity, for constructive thoughts and
comments.
Appendix: variable definitions
All economic variables are deflated using prices and wages for the municipal sector with
base year in 2000.
Budget overruns Appropriations subtracted from final accounts on tax-financed current
expenditures in a given year. Sources for final accounts and Statistics Denmark’s StatBank,
tables BUD1, BUD32X, and BUD32.
Public Choice
Election year Coded one in election years and zero in nonelection years.
Expenditure needs Calculated by the Ministry of the Interior and Health (source is
http://www.noegletal.dk). Change from preceding year is expressed as actual change, not
in percent.
Merged Coded one for merged and zero for not merged municipalities (source is Executive
order 656/2005).
Number of municipalities in merger Coded as number of municipalities in each group of
merging municipalities (ibid.).
One-year change in final accounts Change in tax-financed current expenditures from preceding year (source is Statistics Denmark’s StatBank, tables REG11 and REG31).
Population Municipal population in 1000 s as of 1 January (source is Statistics Denmark’s
StatBank, table BEF1A). Change from preceding year is expressed in percent.
Share of young and elderly Share of inhabitants aged 0–17 or 65+ in percent of municipal
population, both as of 1 January (source is Statistics Denmark’s StatBank, table BEF1A).
Change is expressed as changes in percentage.
Tax base Budgeted total tax base (source is Ministry of the Interior and Health, http://www.
noegletal.dk). Change from preceding year is expressed as actual change, not in percent.
References
Baldersheim, H. & Rose, L. E. (Eds.), (2010). Territorial choice: the politics of boundaries and borders.
Hampshire: MacMillan.
Bertrand, M., Duflo, E., & Mullainathan, S. (2004). How much should we trust differences-in-differences
estimates? Quarterly Journal of Economics, 119, 249–275.
Bhatti, Y., & Hansen, K. M. (2011). Who ‘marries’ whom? The influence of societal connectedness, economic
and political homogeneity, and population size on jurisdictional consolidations. European Journal of
Political Research, 50, 212–238.
Blom-Hansen, J. (2002). Budget procedures and the size of the budget: evidence from danish local government. Scandinavian Political Studies, 25, 85–106.
Blom-Hansen, J. (2007). Pengeafbrænding før lukketid? Om kommunernes økonomiske dispositioner op
mod kommunesammenlægningerne i 2007. In V. L. Nielsen & N. Ploug (Eds.), Når politik bliver til
virkelighed. Festskrift til professor søren winter, Copenhagen: The Danish National Centre for Social
Research.
Blom-Hansen, J. (2010). Municipal amalgamations and common pool problems: the Danish local government
reform in 2007. Scandinavian Political Studies, 33, 51–73.
Citrin, J. (1979). Do people want something for nothing: public opinion on taxes and government spending.
National Tax Journal, 32, 113–129.
Cook, T. D., & Campbell, D. T. (1979). Quasi-experimentation. Design & analysis issues for field settings.
Boston: Houghton Mifflin.
Executive order No. 656 of 06/29/2005. Bekendtgørelse om revision af den kommunale og regionale inddeling
og om forpligtende kommunale samarbejder.
Gujarati, D. N. (2003). Basic econometrics (4th ed.). New York: McGraw Hill/Irwin.
Hansen, S. W. (2011). Towards genesis or the grave. Financial effects of local government mergers. Odense:
University of Southern Denmark Press.
Hinnerich, B. T. (2009). Do merging local governments free ride on their counterparts when facing boundary
reform? Journal of Public Economics, 93, 721–728.
Houlberg, K. (1999). Budgetoverskridelsernes anatomi. Nordisk Administrativt Tidsskrift, 80, 200–232.
Imbens, G. W., & Wooldridge, J. M. (2008). Recent developments in the econometrics of program evaluation.
Discussion Paper No. 3640. IZA DP No. 3640. Bonn: Institute for the Study of Labor.
Jordahl, H., & Liang, C.-Y. (2010). Merged municipalities, higher debt: on free-riding and the common pool
problem in politics. Public Choice, 143, 157–172.
Public Choice
Kristensen, O. P. (1980). The logic of political bureaucratic decision-making as a cause of governmental
growth: or why expansion of public programs is a “private good” and their restriction is a “public
good”. European Journal of Political Research, 8, 249–264.
Kristensen, O. P. (1987). Væksten i den offentlige sektor. Institutioner og politik. Copenhagen: Juristog
Økonomforbundets Forlag.
Ministry of the Interior and Health (2004). Agreement on a structural reform. Copenhagen: Ministry of the
Interior and Health.
Mouritzen, P. E. (1989). The local political business cycle. Scandinavian Political Studies, 12, 37–55.
Mouritzen, P. E. (1991). Den politiske cyklus. En undersøgelse af vælgere, politikere og bureaukrater i kommunalpolitik under stigende ressourceknaphed. Aarhus: Politica.
Mouritzen, P. E. (2010). The Danish revolution in local government. How and why? In H. Baldersheim & L.
E. Rose (Eds.), Territorial choice: the politics of boundaries and borders. Hampshire: MacMillan.
Olson, M. (1965). The logic of collective action. Public goods and the theory of groups. Cambridge: Harvard
University Press.
Ostrom, E. (1990). Governing the commons. The evolution of institutions for collective action. Cambridge:
Cambridge University Press.
Primo, D. M., & Snyder Jr., J. M. (2008). Distributive politics and the law of 1/n. The Journal of Politics, 70,
477–486.
Serritzlew, S. (2005). Breaking budgets: an empirical examination of Danish municipalities. Financial Accountability & Management, 21, 413–435.
Thießen, U. (2003). Fiscal decentralisation and economic growth in high-income OECD countries. Fiscal
Studies, 24, 237–274.
Weingast, B. R., Shepsle, K. A., & Johnsen, C. (1981). The political economy of benefits and costs: a neoclassical approach to distributive politics. The Journal of Political Economy, 89, 642–664.
Winter, S., & Mouritzen, P. E. (2001). Why people want something for nothing: the role of asymmetrical
illusions. European Journal of Political Research, 39, 109–143.