Scale economies in local public administration

ABSTRACT

A renewed interest in decentralisation has profoundly affected local public governance around the world. Faced with an increasing number of tasks, Dutch municipalities have recently sought physical centralisation, merging into larger jurisdictions in order to target new policy areas more effectively and cost efficiently. Is such a policy of physical centralisation wise? We study economies of scale in local public administration, and find – given transfer payments from central government and current cooperation between municipalities and after controlling for geographical, demographic and socioeconomic variables – substantial unused scale economies of 17% for the average municipality. Between 2005 and 2014 the optimum size of municipalities increases from around 49,000 to 66,260 inhabitants, pointing at an increased importance of fixed costs relative to variable costs in local public administration.

KEYWORDS:

• Fiscal federalism
• decentralisation
• local public administration
• municipalities
• scale economies

Introduction

A large body of research has shown that local jurisdictions in many instances do not meet the optimal scale for the delivery of specific goods and services, given the allocation of competencies and fiscal instruments across different levels of government. In order to still be able to reap unused economies of scale, municipalities have resorted to outsourcing and cooperation with other municipalities. These policies of outsourcing or cooperating give rise to additional administrative costs. Administrative costs themselves may also be subject to scale economies, as argued by Bel, Fageda, and Mur (2014).

The Netherlands forms an interesting case to study these economies of scale in local public administration for two reasons, as it has recently witnessed a paradoxical combination of policies aiming at increased decentralisation of social welfare tasks while exerting pressure for physical centralisation of local authorities to larger jurisdictions through amalgamation (Allers and De Kam 2010). Complexity at the local level has increased since central government delegated its Social Support and Provision Act (Wet Maatschappelijke Ondersteuning; in Dutch) to local government level, and recently nearly doubled central government transfers to municipalities, further delegating a wide array of new tasks including welfare and child welfare services to its lowest level of government. In order to target these new policy fields effectively, central government asserts that jurisdictions must merge to 100,000 residents or more.

This article focuses specifically on local public administration expenditure in the Netherlands, assessing at which number of inhabitants the optimum size for public administration is achieved. The second section gives an overview of the literature, while the third section presents our method, proposing a new set of functional forms in order to test for optimum size. The fourth section includes economies of scale estimates in local public administration. In the fifth section we show our method can simultaneously distinguish between scale economies and managerial or X-inefficiency, which we show to be independent from scale. We conclude with a reflection on our findings in the sixth section.

Theoretical framework

Fundamental to economic thought about decentralisation is the assumption of variance in demand for public goods. Heterogeneity in preferences can be utilised locally if the benefits of decentralisation have a positive correlation with variance in demand (Panizza 1999). As the literature assumes, highly centralised systems are unable to respond to variance in preferences at the local level (Koethenbuerger 2008); in highly centralised systems with uniform levels of public goods and national taxes, individuals can only exert pressure on the allocation of their gross income through voice (Hirschman 1970). In his seminal paper, Tiebout (1956) introduces the exit option for individuals, claiming that demand and supply for local public goods can also be influenced by ‘voting with one’s feet’. A fully mobile consumer-voter can relocate to a district that satisfies his demand for local public goods at the cost of a matching local tax rate. While in centralised systems there is no incentive to reveal one’s true preferences for public goods in order to free ride on others’ demand for these goods, Tiebout (1956) claimed that when one ‘votes with one’s feet’, moving to the region that better combines one’s preferred level of local public goods and accompanying taxes, there is no longer an incentive to hide one’s preferences. Using this information to coordinate local taxation and spending may then improve well-being throughout society.

But how much decentralisation should we demand, and to whom we should decentralise? Oates (1972) decentralisation theorem seeks to answer this question, stating that from an efficiency perspective fiscal responsibilities should always be decentralised as long as there are (i) no cost savings to be gained from centralisation and (ii) no interjurisdictional externalities.

Our article focuses on the first argument, seeking to estimate the optimum size for municipalities in terms of local public administration (LPA). Our choice is guided by the fact that (i) costs of LPA generally does not seem to impose externalities on neighbouring municipalities; (ii) LPA is a service comparable across municipalities in which the type of tasks performed does not largely depend on the size of municipalities, as may be the case with other areas of spending; and (iii) LPA pertains to a core task of municipalities. All local authorities face the costs of public administration, and larger municipalities can spread the costs across a larger number of inhabitants. This classic explanation of economies of scale, however, wears out as size increases further, as managerial problems, complexity, bureaucracy, declining motivation and commitment of staff etc., may again induce rising costs of inefficiency from a certain point onward. The key question is whether such large local public administrative inefficiencies outweigh the basic effect of the monotonically declining fixed costs.

Two main strands of empirical literature have touched upon cost efficiency and scale at the local level. A first strand uses cross-sectional or panel data to study the general relationship between local government expenditure and population size, while a more recent strand of literature has provided quasi-natural experimental evidence for economies of scale. Regressing local expenditure classes on a linear and quadratic population variable while controlling for a range of confounding variables, Drew, Kortt, and Dollery (2016) provide evidence of U-shaped cost curves in Queensland, Australia, with economies of scale up to 98,000 inhabitants. With Cobb–Douglas and translogarithmic cost functions, Geys, Heinemann, and Kalb (2007) estimate the cost elasticity with respect to inhabitants for five different population classes of municipalities in Baden-Württemberg, Germany. The authors find substantial economies of scale that, however, wear out after approximately 10,000 inhabitants. Solé-Ollé and Bosch (2005) use a piecewise linear function postulating a nonlinear relationship between population size and costs in Spain, concluding that two local optimums at 5,000 and 50,000 inhabitants exist.

Quasi-natural experimental evidence is given by several studies that have used amalgamations of municipalities. Reingewertz (2012) uses a difference-in-difference framework to study the effects of municipal amalgamations and shows that amalgamations of small municipalities (around 10,000 inhabitants) lead to lower per capita expenditure levels, while not affecting quality. Using a government reform as an exogenous shock to the scale of Danish municipalities, Blom‐Hansen, Houlberg, and Serritzlew (2014) perceive scale effects with lower administration costs per inhabitant up to 100,000 inhabitants. While amalgamations were not exogenously determined as in the Danish case, Allers and Geertsema (2014) for the Netherlands show that voluntary amalgamations do not affect aggregate spending, while providing evidence for reduction in spending on local public administration. Finally, Hanes (2015) finds amalgamations in Sweden decreased overall spending up to a critical size of around 12,800 inhabitants, pointing at scale economies.

Research design

Functional forms for local public administration

This section discusses the functional form of several familiar cost models and their underlying assumptions with respect to the shape of average costs per unit curve, which have a major impact on the existence and size of an optimum scale. Next, we develop empirical models for local public administration (LPA). This section also explains the measurement of economies of scale.

The measurement and analysis of differences in LPA cost levels is based on the assumption that LPA production technology can be described by a production function that links the various types of LPA output to input factor prices, such as wages, office space rent, and so on. Though costs form a crude proxy for the actual output of local governments, costs data for the Netherlands is readily accessible and hence forms the best proxy available. Unfortunately, we lack comparable data on the quality of local public administration across municipalities.

Under certain conditions, a dual cost function can be derived, using output levels and factor prices as arguments (Coelli, Prasada, and Battese 1998, 43–49). In the literature, the translog cost function (TCF) to describe costs dominates other model specifications. Christensen and Greene (1976) proposed the TCF as a second-order Taylor expansion, usually around the mean, of a generic function with all variables appearing as logarithms. This TCF is a flexible functional form that has proven to be an effective tool for the empirical assessment of efficiency. It is an extension of the Cobb–Douglas function, which is capable of fitting U-shaped average cost functions.¹ The TCF has also been applied for scale economies in local expenditure on waste, roads and parks by Drew, Kortt, and Dollery (2016) and Geys, Heinemann, and Kalb (2007). A simple TCF reads as follows:

(1)

with LPAC for local public administration costs and ‘inh’ or inhabitants for output volume, where we use the number of inhabitants. Note that in the squared term we take the logarithm of output in deviation from its mean (denoted by the bar above the variable), in line with the Taylor expansion.² In that case the model is extended with cross terms from both output measures. Since the Netherlands is a relatively small country, and government employees are covered by a collective bargaining agreement, we expect little or no variation in input prices across municipalities (Swank 1996), but changes over time may have effects. Therefore, we include an hourly wage index in real terms. Actually, LPAs do not report data on input prices, so that we are also unable to include municipality-specific prices in the cost functions.³ Unused scale economies exist where β₁ < 0, while concavity or a U-shaped average cost function requires β₂ > 0.

Shaffer (1998, 94) proves that for a sample of monotonically declining average costs, the TCF would estimate a concave function with an optimum scale, so that the existence of an optimum size and diseconomies of scale for larger firms is (incorrectly) imposed.⁴ Indeed, the left leg of the TCF can be fitted to the hyperbolically declining average costs, with the optimum scale in the right-hand tail of the sample, or beyond the largest observation. Consequently, Shaffer (1998) suggests two additional cost functions to estimate scale economies, which do not impose this U-shaped average-cost function.

The first alternative is the unrestricted Laurent function (ULF), which is similar to the TCF, but with two inverse terms added:

(2)

The ULF can describe monotonically declining average cost, does not impose an optimum scale and allows different degrees of curvation for smaller and larger municipalities. For the concave properties to hold, the coefficients β₃ and β₄ should both be positive, next to β₂. According to Shaffer (1998), the improvement of the ULF over the TLF may die down for skewed size as the squared nature of the cost–output relationship is built up by the relatively large share of observations in the smaller size region of the data sample. He consequently proposes a second alternative: the hyperbolically adjusted Cobb–Douglas (HACD) cost function; see also Adanu, Hoehn, and Iglesias (2009). Again, ignoring input prices, this model reads as follows:

(3)

Thanks to the additional reciprocal term, this model can portray the U-shaped average cost function (β₁ > β₂), monotonically declining average costs (β₁ > 1 and β₂ > 0) and the L-shaped average cost function (β₁ < 1). Finally, we suggest an asymmetric TCF (ATCF) and quadratic spline regression (QSR), where the coefficient of the squared term may differ for different segments. In the ATCF, these segments are the two legs of the U-shaped unit cost curve above and below the mean number of inhabitants, where the squared term is split into positive and negative deviations from the mean, each with its own coefficient. In the QSR we allow for more flexibility, where we split the squared term in three such segments with their own respective coefficients. We restrict our estimations to two knot points, as we find that increasing the number of knot points does not significantly improve the model. The quadratic terms are all taken in deviation of the first knot point , noting that alternative specifications are also possible. The knots are located at 17,598 and 32,165 inhabitants, respectively, based on a pilot goodness-of-fit (GOF) test (see Jann and Gutierrez 2008). The model reads as follows:

(4)

The last equality sign defines the terms , and , abbreviations used in Table 3.

Table 1. Average budgeted expenses per inhabitant for each cost category (2005–2014, in 2005 EUR).

	Number of inhabitants (×1000)
	<10	10–20	20–50	50–100	>100
1. Local public administration (LPA)	270	163	142	137	170
2. Public order and safety	94	68	66	87	102
3. Infrastructure	171	155	147	195	279
4. Economic affairs	13	15	18	31	62
5. Education	157	142	150	203	245
6. Culture and recreation	222	192	214	259	314
7. Social services	400	476	551	814	1094
8. Public health and environmental affairs	284	236	227	243	292
9. Spatial planning and housing	256	290	348	449	597
10. Total expenses	1868	1737	1863	2419	3154
% of spending on public administration	14.4	9.4	7.6	5.7	5.4
Average number of municipalities	48	128	188	43	26

The municipal classes with the lowest average costs per inhabitant are marked in bold.

Table 2. Key features per municipality (2005–2014).

		Mean	SD	Min	Max	Observations
Local public administration costs, per capita (in 2005 EUR)	Overall	163.33	79.93	29.46	1138.95	N = 4327
	Within		27.59
Inhabitants	Overall	38239	60701	932	810937	N = 4327
	Within		2286
Demographic pressure	Overall	68.9	7.1	44.3	109.9	N = 4327
	Within		2.6
Average home value (in current 10,000 EUR)	Overall	24.355	6.337	11.600	70.200	N = 4327
	Within		1.713
Surface land (in 10 sq. km)	Overall	0.78	0.69	0.018	4.6	N = 4327
	Within		0.05

SD is standard deviation. ‘Within’ refers to ‘within’ municipalities.

Table 3. SCF estimates of economies of scale in local public administration (2005–2014, in 2005 EUR).

	TCF	ATCF	ULF	SULF	HACD	QSR
Inhabitants (in log.)	0.823^***/000 (52.24)	0.766^***/000 (25.93)	2.990^000 (0.63)	−0.442^000 (-1.02)	0.906^***/000 (36.43)	0.747^***/000 (20.65)
Inhabitants^2 (ln, mean dev.)	0.095*** (8.30)		0.045 (0.17)	0.230*** (4.43)
1/inhabitants					1292.796*** (4.09)
1/(ln inhabitants)			525.694 (0.59)	−126.709** (-2.91)
1/(ln inhabitants)^2			−1526.791 (-0.74)
Inhabitants^2 (ln, mean dev., below mean)		0.053** (2.89)
Inhabitants^2 (ln, mean dev., above mean)		0.142*** (5.09)
						0.058* (2.36)
						0.123*** (5.63)
						0.129*** (5.89)
Average house value (in 10,000 EUR)	0.002 (1.10)	0.002 (1.10)	0.002 (1.15)	0.002 (1.12)	0.003 (1.25)	0.002 (0.99)
Surface land (in 10 sq. km)	−0.039* (-2.21)	−0.039* (-2.23)	−0.038* (-2.19)	−0.039* (-2.24)	−0.041* (-2.25)	−0.038* (-2.17)
Demographic pressure	−0.001 (-0.45)	0.000 (0.01)	0.000 (0.11)	0.000 (0.10)	−0.003 (-1.66)	0.000 (0.06)
G4 municipalities	0.194 (1.13)	−0.052 (-0.24)	0.001 (0.00)	−0.089 (-0.43)	0.787*** (3.66)	−0.067 (-0.32)
Wadden Islands	0.530*** (3.34)	0.680*** (5.10)	0.730*** (5.73)	0.723*** (5.67)	0.569* (2.39)	0.684*** (4.87)
Wage rate (in log., in 2005 EUR)	1.302*** (7.85)	1.325*** (8.09)	1.330*** (8.14)	1.331*** (8.16)	1.200*** (6.85)	1.337*** (8.20)
Year	0.009*** (3.86)	0.008*** (3.71)	0.008*** (3.69)	0.008*** (3.70)	0.010*** (4.20)	0.008*** (3.67)
Constant	2.379*** (4.06)	2.829*** (4.60)	−56.747 (-0.49)	27.547** (3.19)	1.992** (3.03)	2.991*** (4.55)
(X-inefficiency)	0.119	0.117	0.116	0.116	0.126	0.116
(model and data errors)	0.224	0.224	0.224	0.224	0.231	0.223
	0.529	0.522	0.516	0.520	0.545	0.520
F-statistic	4,739.3***	5,257.3***	5,155.1***	5,457.1***	3,507.1***	5,237.2***
Wald test ^a	225.5***	250.9***	261.5***	254.6***	110.8***	251.2***
Cost elasticity at mean ^b	0.823	0.766	0.802	0.796	0.872	0.830
Scale economies at the mean	0.177	0.232	0.197	0.203	0.128	0.170
ln (mean)	10.114	10.114	10.114	10.114	10.114	10.114
Optimum size (in inhabitants)^c	62,700	56,300	55,400	57,100	-	48,200
Lower 95% bound	49,100	47,500	45,200	47,600	-	38,800
Upper 95% bound	90,500	77,500	74,700	75,800	-	67,500
First-order homogeneity^d	3.322	3.928*	4.086*	4.131*	1.299	4.273*
Akaike’s IC	400.31	369.27	354.95	355.47	691.67	340.71
Number of observations	4,111	4,111	4,111	4,111	4,111	4,111

Standard errors clustered by municipality. *, ** and *** mean significantly different from zero at, respectively, the 95%, 99% and 99.9% confidence level, while ⁰⁰⁰ indicates that the Wald test on constant returns to scale (see footnote a) is rejected at the 99.9% confidence level.

^a The Wald test regards the constant returns to scale hypothesis: the coefficient of the linear term ln (number of inhabitants) is equal to 1, and the coefficient(s) of the nonlinear term(s) is (are) equal to 0; ^b With mean referring to the mean value of the output measure, the number of inhabitants, see the third section; ^c The optimum scale is calculated by setting the first derivative equal to one, see the third section for details; ^d Tests whether the coefficient on the wage rate significantly differs from one.

Another approach to overcome the limitations of the TCF includes the Fourier Flexible Form (as proposed by Gallant 1982). Dijkgraaf and Gradus (2015) use this functional form besides the TCF and two alternative specifications to estimate cost functions for municipal waste collection. We however do not apply the Fourier form, as its complexity impedes clear interpretation.

To investigate which functional form best suits the sample data, we will apply Akaike’s (1974) information criterion (AIC). Cost elasticity (CE) is defined as the proportional increase in costs as a result of a proportional increase in output. In mathematical terms this results in the following formula for elasticity: CE = ∂ ln LPAC/∂ ln inh. Using Equations (1–4), this results in for TCF, ATCF, ULF, HACD and QSR, respectively:

(5)

(6)

(7)

(8)

(9)

The second term of the CEs in the TCF and the ULF becomes zero if the CEs are evaluated around the mean of the sampled logarithms of inhabitants inh_i, that is: . The CE for the TCF (and the ATCF) is then equal to β₁, while for the ULF and the HACD, it depends on the sample observations.⁵ We have also assumed a simplified ULF (SULF), that is Equation (2) with β₄ = 0 where the two inverse terms are too highly intercorrelated.

The scale economies (SE) can easily be distilled from the above by subtracting CE from unity: SE = 1 – CE. If the calculated CE has a value larger than 1, this indicates diseconomies of scale; a value smaller than 1 indicates economies of scale and a value of exactly 1 indicates constant returns to scale. To calculate a possible optimum size of a LPA, a value for inh has to be found to set CE equal to one (or to set SE to zero).

Data

We use annual data on budgeted municipal spending on LPA, collected by Statistics Netherlands (CBS 2014).⁶ These data do not include capital spending. Table 1 shows the averaged costs per inhabitant for each of the nine expenditure items facing municipalities, divided into five municipal size classes, over the 2005–2014 period. Local public administration forms only between 14.4% and 5.4% of total local expenditure. During these years, the size of Dutch municipalities increased markedly, while the number of municipalities fell to 403 from 467. This decline was most profound for municipalities with fewer than 20,000 inhabitants (declining in number to 137 from 223). Table 1 shows how costs for most categories initially decrease as size (measured in number of inhabitants) increases, hinting at economies of scale. However, as size increases further, costs rise again, suggesting larger-sized municipalities face increasing complexity and inefficiency. This pattern is clearly visible for the LPA cost categories, public order and safety and public health and environmental affairs, indicating U-shaped cost curves.

Social services are by far the largest expenditure item in municipal budgets – a cost category which in the light of future decentralisation of tasks in the Netherlands is likely to keep increasing. For certain expenditure items municipalities act as mere intermediaries of national policies and have limited spending autonomy. More local autonomy is found in cost items such as spatial planning and housing, public transport, education – especially the housing thereof, waste management and the organisation of bureaucracy. For some of the items we must assume cascading cost functions: the number of municipal tasks increases with size. For instance, small municipalities may suffice with just one grade school while larger municipalities serve a more regional function, also offering high schools or vocational education. This regional function entails higher costs, but at the same time this municipality also provides a higher level of services, possibly also to surrounding municipalities.

A final note should be made on central government transfers from the municipal fund (Gemeentefonds) and on intermunicipal cooperation. A large share of local revenue in the Netherlands is made up of central government transfers, which among other factors in its distribution takes into account local expenditure needs and the capacity for local revenue collection. Consequently, our findings are to be interpreted given the current distribution of transfers. Second, Bel, Fageda, and Mur (2013) show for the Spanish case, cooperation in the production of local services may lead to small municipalities in fact reaching their optimum scale. This is uncertain in the Dutch case, as cooperation between municipalities differs between both countries, where findings show cooperation significantly reduces costs in Spain, while cooperation in the Netherlands has been associated with higher costs (Dijkgraaf and Gradus 2007). Bel et al. (2010) argue that differences between the two countries are partly due to the smaller average size of municipalities in Spain, leading to relatively more cooperation, but also depend on the institutional framework. While Spanish cooperation is compatible with privatisation, in the Dutch case inter-municipal cooperation is organised through legal constructions which are always run as public bodies, incompatible with privatisation. Our results measure scale economies including the impact of outsourcing and cooperation.

Figure 1 shows the LPAC per inhabitant for the year 2013 in ten size classes. We find that average costs decline as the municipality grows (particularly for the smallest size classes), as well as strong variation within each size class. The former hints at economies of scale, while the latter points at differences in either efficiency across municipalities irrespective of their size, or heterogeneity where different municipalities have different tasks or service levels. Figure 2 gives the spatial distribution of LPAC per head for 2013. We find that relatively high per head LPAC costs are concentrated in the West Frisian or Wadden islands (averaging EUR 714 per head compared to the national average of EUR 163 per head), yet apart from this we have not observed a clear relationship between geographical location and costs. The three large cities (Amsterdam, Rotterdam and The Hague) rank relatively high, as do the Flevoland province and the western part of the South Holland province.

Figure 1. Costs of local public administration per inhabitant for ten size classes (for 2013 in current prices).

Figure 2. Spatial distribution of the costs of local public administration per inhabitant (for 2013 in 2005 prices).

Economies of Scale estimates in local public administration

This section includes our results for a cross-sectional stochastic cost frontier (SCF) estimation (Coelli, Prasada, and Battese 1998; see Greene 2008 for a survey) for economies of scale in LPA activities using six functional forms. The SCF approach allows estimations using two error term components under the assumption of interindependency. The first error term is normally distributed and represents errors in data and model specification, while the second error term is a one-sided non-negative disturbance and approximates managerial or X-inefficiency. Throughout our estimations we have assumed to be exponentially distributed with (Meeusen and Van den Broeck 1977).⁷ This estimation technique allows us to simultaneously study the existence of economies of scale in LPA work, and to estimate efficiency differences across similarly sized municipalities. In measuring scale economies, it is better to take inefficiencies into account and use SCF than to ignore inefficiencies and use OLS. Our model for LPA costs reads as follows:

(9)

where X_ijt represents variables (j = 1, …, N) relating to the number of inhabitants in municipality in year , and depends on our six functional specifications (TCF, ATCF, HACD, ULF or SULF and QSR). As exclusion of control variables may distort the estimation of the relationship between scale and LPAC, Z_ikt contains a number of control variables (k = 1, …, M): demographic pressure, defined as the sum of young (under 16 years of age) and old inhabitants (over 65 years of age) as a share of the working population (between 16 and 65), wealth, measured as the average home value (in current EUR 10,000), land surface (in 10 square kilometres), a dummy for the ‘G4’ (the four largest municipalities: Amsterdam, the Hague, Rotterdam and Utrecht), a dummy for the Wadden Islands (Texel, Vlieland, Terschelling, Ameland and Schiermonnikoog), the hourly wage rate (in real terms) for staff in public administration and government services and a time trend (year). Table 2 shows summary statistics for our dependent and control variables, including the within component of the standard deviations. For most variables, the table shows little variance within municipalities over time. In order to correct for the ensuing expected high correlations within municipalities, we cluster the standard errors by municipality.

Table 3 presents the estimation results, estimated using Maximum Likelihood. According to the Wald test, all six models reject the constant returns to scale hypothesis. Based on the Akaike Information Criterion (AIC), the rather restricted HACD shows the worst performance, while the other models’ performance does not diverge much. For the QSR, we find the coefficients for the second and third segments only slightly differ, suggesting one knot point would nearly be sufficient to describe our data. The ATCF outperforms the TCF, but this model is still not sufficiently flexible, as it is outperformed by the ULF models. We find the lowest AIC values for the QSR, followed by the ULF and SULF. For the QSR, we find a cost elasticity of 0.830 at the geometric mean of 24,686 inhabitants.⁸ Hence, keeping our control variables constant, we find that a 1% increase in the number of inhabitants pushes up costs for public administration by 0.83%. This implies average unused scale economies of 17%. Note that the estimation results across the models with regard to scale economies as well as for the control variables are roughly equal, except for the poorly performing HACD.

Turning to the QSR model, a number of control variables significantly affect the costs of local public administration. On average, municipalities covering larger areas have lower costs, as a 10 square kilometre increase in surface depresses costs by 3.7%, holding other factors constant. Possibly, more agricultural municipalities have more austere preferences. The isolated Wadden islands, all other things being equal, on average spend 98% more on local public administration than other municipalities, while we find no discernible differences between the ‘G4’ municipalities and others, indicating that these large municipalities are a good fit to our model. A 1% increase in the real wage rate increases LPA costs by 1.3%, holding all other variables constant. We reject first-order homogeneity in prices for this variable at the 95% confidence level (not at the 99% confidence level), implying this coefficient significantly differs from one (homogeneity is not rejected in the TCF and HACD models). In addition, we observe that spending on local public administration (in constant prices) increases over time by 0.8% annually. refers to the (estimated) signal-to-noise ratio (), which lies around 50% for all models. Low values for may infer that it is difficult to differentiate between efficiency and noise from the model, which does not seem to be the case for our model specifications.

The coefficients of the squared and inverse terms of the QSR are quite large and all significant, implying substantial curvature in scale economies, see Figure 3. This graph reflects the predicted cost elasticity for our six estimations over the 2005–2014 period as a function of the number of inhabitants, including 95% confidence bands for the SULF. The confidence bands for the ULF are wider, as this model is less parsimonious, while the bands for the QSR, TCF and the HACD are much smaller. This graph shows the effect of the nonlinear terms of the output measure inhabitants. The TCF is a straight line, while the ULF and SULF results in a convex curve. By nature the HACD is concave. The background histogram gives the size distribution for inhabitants. All models except the HACD are close to each other for the most frequent municipal sizes. Small changes in the curvature result in more substantial changes in the optimum scale. The intersection with the horizontal line y = 1 (reflecting constant returns to scale) gives the optimum sizes of the local public administration over our sample. The optimum size according to QSR is 48,200 inhabitants, with a 95% confidence interval ranging between 38,800 and 67,500. With the exception of the HACD, the other models give higher optimal scales, ranging between 55,400 and 62,700.

Figure 3. Cost elasticity of local public administration according to six models (2005–2014, in 2005 EUR).

Fixed Effects is not an appropriate estimation strategy for our models, as it ignores the average size, thereby neglecting the richest source of information with respect to scale economies. When we nevertheless estimate with Fixed Effects, cost coefficients turn out to be lower (reflecting underestimation) and scale economies higher (pointing to overestimation).

In order to investigate whether the cost or production structure has changed over time, with possible consequences for scale economies and optimal scale, we disaggregate the data into annual samples and estimate the SULF model for each year separately; see Table 4. We prefer this relatively more parsimonious model over QSR as it aids comparability over time, rather than the QSR, where the number and location of knot points may differ across years. The cost elasticity at the mean is virtually stable over time, showing a slightly decreasing tendency, which points to somewhat higher scale economies in later years. The smaller annual sample lowers the significance level of the control variable coefficients, so that only the Island dummy remains statistically significant. Our analysis reveals that the optimum size has grown over the 2005–2014 period, as in 2005 the optimum size is 49,000 (with 95% confidence interval 39,910–68,420 inhabitants), while in 2014 the optimum size is 66,260 (with 95% confidence 52,690–102,310 inhabitants). Figure 4 shows this development of optimum scale over all our sample years for the ULF and SULF models (with SULF confidence bounds). Given the wide confidence bands, this increase is not statistically significant, however. The estimates in the graph for ULF show that both models have comparable estimates of the optimum size over time.

Table 4. Annual SCF estimation of economies of scale in local public administration for 2005, 2010 and 2014 using the SULF model.

	2005	2010	2014
Inhabitants (in log)	0.311^000 (0.67)	−0.144^000 (-0.27)	−1.088^*/000 (-1.99)
Inhabitants^2 (logs, mean dev.)	0.159** (2.88)	0.194** (3.07)	0.295*** (4.18)
1/(ln inhabitants)	−49.331 (-1.10)	−97.329 (-1.80)	−192.588*** (-3.45)
Demographic pressure	0.002 (1.04)	−0.001 (-0.56)	−0.000 (-0.09)
Average home value (in 10,000 EUR)	0.002 (0.57)	0.002 (1.10)	0.003 (1.04)
Surface land (in 10 sq. km)	−0.034 (-1.47)	−0.039* (-2.00)	−0.037 (-1.69)
G4 municipalities	−0.101 (-0.36)	0.084 (0.35)	−0.263 (-0.96)
Wadden Islands	0.487*** (5.06)	0.738*** (3.69)	0.869*** (9.01)
Constant	16.397 (1.80)	26.152* (2.43)	44.994*** (4.09)
(X-inefficiency)	0.145	0.117	0.128
(model and data errors)	0.205	0.228	0.233
	0.706	0.513	0.548
F-statistic	1,989.25***	1,697.50***	1,450.96***
Wald test	236.54***	142.53***	182.02***
Cost elasticity at mean	0.808	0.805	0.759
Scale economies at mean	0.192	0.195	0.241
ln (mean)	9.965	10.128	10.210
Optimum size (in inhabitants)	49,000	60,100	66,300
Lower bound	39,900	47,000	54,000
Upper bound	68,400	96,300	102,300
Akaike’s IC	45.34	70.23	94.39
Number of observations	427	425	396

Huber–White standard errors. For all other items, see the footnotes below Table 3.

Figure 4. Annual estimates of the optimum size for local public administration according to the ULF and SULF models (2005–2014).

Inefficiency

This section presents the managerial or X-inefficiency terms u_it from stochastic cost frontier as presented in Table 3 for the entire 2005–2014 sample. We found all models but the HACD give nearly identical efficiency estimates. Similarly, we show the X-inefficiency terms u_i for the series of single-year observations from the model in Table 4. We present the inefficiency estimates for the annual SULF models of the previous section. For both the cross-section and yearly regressions, inefficiency scores on average are 11.6%. Table 5 gives the descriptive statistics for these two groups of predicted inefficiency terms. We find that around half of the municipality observations have a predicted inefficiency score of 10% or above, while 16% have an inefficiency of 20% or above. Both methods of estimation show a strong correlation (ρ = 0.906).

Table 5. Summary statistics for X-inefficiency (estimates from pooled model and annual regressions).

		Mean	SD	Min	Max	Observations
X-inefficiency (pooled OLS model)	Overall	0.116	0.063	0.034	0.760	N = 4,111
	Within		0.040
X-inefficiency (aggregated yearly regressions)	Overall	0.116	0.076	0.031	0.858	N = 3,286
	Within		0.053

SD is standard deviation. Within refers to within municipalities.

Such levels of X-inefficiency are not uncommon in these kinds of analyses. Kalb, Geys, and Heinemann (2012) give an overview of studies on technical efficiency of local government, and themselves find average inefficiencies of between 11% and 20% for municipalities in Baden-Württemberg, Germany, depending on the specification. In different sectors, such as banking and insurance, average X-inefficiencies of 20% and 30% have been found (Bikker 2010), typically much higher than unused scale economies at 5% and 10%. For LPA in this case the reverse holds true: the levels of inefficiencies are around half that of scale economies. When interpreting these figures, we should take into account that our X-inefficiency estimates pick up possible managerial inefficiency, which may also stem from costs due to heterogeneity in terms of differences in service levels, e.g. costs related to administrating high schools and professional education in larger cities. Such differences in service levels occur in many spending areas and are consequently spread across a wide range of sizes. Figure 5 presents the distribution of X-inefficiencies across ten size classes. The pattern is quite similar along these size classes, yet shows that X-inefficiencies peak at the smallest class (between 900 and 9,800 inhabitants) and the sixth largest size class (between 24,000 and 27,500), largely due to one outlier municipality with special circumstances (with a mean X-inefficiency term of 0.50).

Figure 5. X-inefficiencies across ten classes of municipality size (2005–2014).

Finally, we can compare the inefficiency terms over time. Figure 6 presents rather constant inefficiency over time.

Figure 6. X-inefficiency term by year.

Figure 7 presents the geographical distribution of the efficiency term for 2013, based on pooled regression. We find evidence of regional clustering efficiency terms as the test of Moran’s I reveals significant spatial autocorrelation in the inefficiency term.⁹

Figure 7. Geographical distribution of the efficiency terms for 2013.

Conclusions

In order to answer whether and how activities should be allocated to lower levels of government, the decentralisation theorem claims in the absence of externalities and economies of scale that the provision of all public goods and services should be decentralised. The aim of this article is to discover the possible existence of economies of scale in local public administration (LPA) in the Netherlands, a good comparable across municipalities, which pertains to the core of municipal tasks.

We test for the existence of economies of scale using a number of nonlinear functional forms in a stochastic cost frontier estimation over the 2005–2014 period and find that traditional functions, such as the Translog Cost Function, are not sufficiently flexible to describe the production of LPA properly. A quadratic spline regression function appears to provide the optimum model. This model indicates that scale economies for LPA exist at 17% around the mean – higher for smaller and lower for larger municipalities. While this model gives an optimum size of 48,200 inhabitants, the optimum size for municipalities in other models hovers around 57,100 inhabitants. Disaggregated analyses on annual data using the SULF model show that the optimum size increased over our sample period to 66,300 inhabitants in 2014 from around 49,000 inhabitants in 2005. For LPA, this points at the increasing importance of fixed costs over variable costs over time.

Beyond the number of inhabitants as a measure of size or output, LPA costs are to a large extent determined by the surface area. While the model can accommodate the LPA costs of the four largest municipalities, the specificity of its geographies cause the Wadden island municipalities in the Netherlands to be generally more expensive. Furthermore, the real wage rate staff in public administration and government services is found to significantly increase costs as expected, in addition to a general increasing trend over time.

Applying stochastic cost frontier estimation allows us to differentiate between managerial or X-efficiency and noise. We find that roughly half of the municipality observations have a predicted inefficiency score of 10% of costs or above, while 16% have inefficiencies of 20% of costs or more. These inefficiencies appear spatially correlated, as we find evidence of geographic clustering. We should be cautious in interpreting these figures, as inefficiency indicates possible managerial inefficiency, but may also represent heterogeneity, i.e. costs related to differences in service levels across municipality sizes. Data limitations do not allow us to adequately control for quality differences across municipalities.

In the Netherlands where central government recently delegated a range of new tasks to local authorities, we expect increased complexity to lead to further rises in fixed costs for LPA relative to its variable cost components, moving the optimum scale regarding public administration costs further upwards. Whether the optimum scale for local public administration costs will rise to 100,000 residents, as put forth by central government, remains to be seen. The consideration of municipalities to amalgamate, however, should not be based on the above analysis alone, as many other local tasks may have different optimal sizes, and possible non-cost arguments should also be considered.

Acknowledgements

The authors are grateful for useful comments from two anonymous referees of this journal and from Mark Kattenberg and participants of the workshop on local government reform in the Netherlands and Spain (Universitat de Barcelona, 28 October 2014).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Jacob Bikker

Jaap Bikker is a professor of Banking and Financial Regulation at the School of Economics, Utrecht University, The Netherlands, and Senior Researcher at the Strategy Department, Supervisory Policy Division, De Nederlandsche Bank (DNB). His research focuses on financial institutions, competition, efficiency and optimal scale. He has published on efficiency and the optimal scale of financial institutions in publications including the Journal of Pension Economics and Finance, the Journal of Risk and Insurance, and Applied Economics.

Daan van der Linde

Daan van der Linde is a PhD candidate at the Department of Public Sector Economics at the School of Economics, Utrecht University, The Netherlands. His research focuses on public economics, specifically concerning questions of (local) governance and inequality.

Notes

1. For shortcomings of the TCF, see Shaffer (1998).

2. White (1980) and Shaffer (1998) explain that this specification also helps to avoid multicollinearity. Note that is the arithmetic average of the logarithms of output measure inh_i.

3. To simplify the presentation, we do not include one or more input prices in Equation (1).

4. Except possibly over limited ranges of scale with steeply declining marginal costs.

5. For the reciprocal terms in the ULF, we replace ln inh by the geometric mean of the output term. For the reciprocal term in the HACD model, arguments (to replace inh) exist in favour of both the geometric and arithmetic mean. This choice has no further consequences.

6. In the remainder of the article we use budgeted, not actual expenditure due to data availability. When data overlap, we find both accounts are highly correlated and find that estimates are robust to regressions on actual expenditure.

7. Our estimates are robust to Half-normal and Truncated normal distributions of the inefficiency term.

8. The logarithm of the geometric mean 24,686 is 10.114; see Table 3.

9. Results are insensitive to controlling for the degree of complexity of coordination for a municipality (proxied by the number of neighbouring municipalities). The spatial dependence in our estimation, however, is not strong enough to bias results, and hence does not require a spatial heteroscedasticity and autocorrelation consistent estimator.