Evaluating Administrative Efficiency Change in the Post-Merger Period

Abstract

This article analyzes the change in municipal administrative efficiency in the post-merger period using the data of 92 municipalities in Ibaraki prefecture for the period 1979–2004. For this purpose, the authors employ a nonparametric programming method to compute a data envelopment analysis (DEA)/Malmquist indices (MI). These indices are decomposed into two component measures, namely, catch-up (CU) and frontier shift (FS) indices. The authors found that the administrative efficiency in Ibaraki prefecture in the post-merger period was monotonically regressed; however, the efficiency scores of merging municipalities were found to be higher than those of nonmerging ones. Scale change did not necessarily contribute to an efficiency change in the post-merger period. In the short run, scale affected Tsukuba city, which was formed by consolidating smaller municipalities.

Keywords

municipal mergers data envelopment analysis Malmquist index Japanese municipal administration

Introduction

The factors affecting municipal administrations in Japan, such as a declining birthrate, an aging population, and financial difficulties faced by both national and local governments, have changed. In order to take advantage of ongoing decentralization and to maintain municipal administrative services, the national government revised the Special Law on Municipal Mergers in 1995 with the aim of promoting voluntary municipal mergers. As the law was to remain in effect only until March 2005, over 700 municipalities completed the required procedures for mergers. The total number of municipalities consequently decreased from 3,229 in 1999 to 1,788 in 2008.

Municipal mergers have been surrounded by controversy. Cross-comparisons of populations of varying sizes carried out in the past have reported economies of scale in populations of 100,000–200,000 (Yokomichi and Okino 1996; Saito 1999). The benefit of these economies of scale is lost on smaller scales, and administrative costs have increased due to higher overheads in the field of general macro economics (e.g., Hughes and Edwards 2000). This empirical evidence is consistent with the view that mergers improve the efficiency of administrative operations and financial management systems of small local governments. Therefore, evaluation of efficiency in terms of cost minimization is a criterion for mergers.

On the other hand, consolidations and amalgamations do not necessarily improve administrative efficiencies. Labor-intensive public services, such as municipal education or police and community-building functions need a relatively small local government (Ostrom, Bish, and Ostrom 1988; Hayes and Wood 1995; Schacter and Toonen 2010). The convenience enjoyed by residents is based on geographical conditions and population structure. Since collective choices for public services differ among municipalities, merging them to only pursue economies of scale causes deterioration in administrative efficiencies. Therefore, essential public services and facilities that a municipality needs is also a criterion for mergers (Yokomichi 2003).

This article examines the changes in municipal public services in the pre- and post-merger periods in 1979–2004. Our purpose is threefold.

First, we measure the administrative efficiency of municipalities and suggest criteria for mergers. Governance structures vary and relate to physical circumstances. Therefore, by means of a nonparametric approach, considering various specifications of municipalities, we define administrative efficiency in terms of the characteristics of municipalities, rather than defining it by means of an ordinary cost function (i.e., a parametric approach). In the current study, we employ a data envelopment analysis (DEA; e.g., Cooper, Seiford, and Tone 2000) by considering two dimensions of public services: scope and quality. DEA is a nonparametric method for measuring the relative efficiency—known as DEA efficiency—of decision-making units (DMUs) with multiple inputs and outputs. We replace the outputs with indicators that represent the scope and quality of public services, thus allowing for an evaluation of the DMUs' administrative efficiency.

Second, we examine the change in administrative efficiency following a municipal merger. In this study, we apply the DEA/Malmquist index (DEA/MI) approach (e.g., Färe et al. 1994; Thanassoulis 2001)—which is actually a DEA time-series analysis—to the DMUs' outputs. The MI is decomposed into two component measures: catch-up (CU) and frontier shift (FS). We use the FS measure to see chronological efficiency changes in Ibaraki prefecture in the pre- and post-merger periods. Moreover, we can observe the differences between merging and nonmerging municipalities.

Third, we analyze the scale effect of merged municipalities in the post-merger period. We further decompose the CU into two indices related to efficiency gains and scale gains in order to clarify the source of efficiency change, that is, to identify the factor that contributes to shifting municipalities closer to the frontier. We select two merging cities, Tsukuba and Hitachinaka, and calculate the cumulative indices using the pre-merger and post-merger periods as our reference points. In terms of scale efficiency change, we examine the extent to which an alteration in scale in the post-merger period contributes to an efficiency change in municipalities.

The results show the notable importance of evaluating administrative efficiencies in pre- and post-merger periods. We found that regardless of the mergers, the overall performance of Ibaraki prefecture regressed in the period 1979–2004, mainly in terms of FS. However, the efficiency scores of the merging municipalities were greater than those of the nonmerging ones. In terms of the efficiency scores with MI, CU and FS, the effect of municipal mergers differed between the two cases of merging cities in the post-merger period. In the short run, scale gains affected Tsukuba city, but did not necessarily contribute to efficiency change.

The article is organized as follows. The Data section introduces the data set employed in this study and discusses the approach for applying DEA to the evaluation of the municipalities. The Method section briefly explains the basis for the computation of DEA and DEA/MI. Our approach maintains the same sample size in the pre- and post-merger periods. The section on DEA Analysis of Efficient Municipal Administration explains the calculated efficiency scores of the municipalities with two examples; it also contains a prefecture analysis and a comparative analysis of merging and nonmerging municipalities. The Summary and Conclusions section summarizes the article and presents the conclusions.

Data

In this section, we briefly explain municipal mergers in Japan, our views on the municipalities' role in providing local public services, and the data employed in this study.

Merger and Dissolution of Municipalities in Japan

Municipal mergers take place in the following two ways: the formation of a newly established municipality or by incorporation. A newly established municipality is formed when more than two existing municipalities amalgamate with a new one, while incorporation involves at least one municipality being absorbed into another city. The difference between the two concerns the extent of municipal incorporation. While an absorbed municipality loses its name, members of the municipal assembly and municipal regulations, a newly established municipality is able to create these anew.

Municipalities are classified into five categories on the basis of their population: designated city, core city, special city, city, and town/village. A town/village is ranked on the same level as a city by the Local Autonomy Law of 1947. It is generally promoted to a city when the population passes 5,000. Larger cities can be delegated functions normally carried out by prefectural governments. They are categorized as a special city when the population reaches at least 200,000, a core city when the population passes 300,000, or a designated city when the population reaches over 500,000, as determined by the Local Autonomy Law, Article 252. The enlargement of a city assembly, which can be authorized in order to plan and execute public works related to public health, urban planning, social welfare, or education, depends on the population (Steiner 1965). The central government thus encourages mergers with the hope of (1) increased convenience for residents and (2) highly specialized and diversified services.

Consequently, besides increasing the diversification of public services, mergers increase the total number of municipal employees. There are approximately 40 public employees per 1,000 residents in Japan; this is a rather small number considering that Japan is an advanced country (Tachi 1998). The public employees thus have to perform several tasks in addition to their regular ones. With an increase in the number of municipal employees, mergers are expected to lead to greater specialization something that was difficult to achieve earlier.

While the benefits of mergers are emphasized, there exists an opposing view with regard to the quality of public services in the post-merger period. In this view, mergers lead to a deterioration in public services since they reduce the number of municipal employees per resident (Konishi 2003). The central government decides to maintain a certain level of local public services, regardless of population size, and thus a municipality with a smaller population needs more public employees per resident, for instance, 1,300–1,400 public workers for 200,000 residents as compared to 60–80 for 5,000 residents. As noted here, diversification and quality of public services are both essential for evaluating administrative efficiency in the post-merger period.

Input–Output Data

We used the data from 92 municipalities in Ibaraki prefecture for the period 1979–2004. Ibaraki prefecture is in the northern part of the Kanto region and is famous for its energy industry, particularly nuclear energy. Ibaraki is a suburb located in the Tokyo region and its population is gradually increasing along with the expansion of the Greater Tokyo region.

Figure 1 presents the municipal mergers in Ibaraki chronologically; the years in which the respective municipalities were founded are indicated in parentheses.

Figure 1.

History of mergers in Ibaraki prefecture.

Ibaraki experienced seventeen mergers during the sample period and thirteen of them were after the year 2000. Ten of them were incorporations and the rest were newly established municipalities. As a result of these municipal mergers, the number of municipalities decreased from 92 in 1979 to 62 by the end of 2004. Moreover, municipalities with populations of 5,000–20,000 grew from 4.4 percent to 27.4 percent, but those with populations under 5,000 decreased from 19.6 percent to 6.6 percent in the same period. The scope of services provided by the amalgamated municipalities increased in the post-merger period.¹ In the case of Mito city, which underwent incorporations twice, and Tsukuba city, which was newly established from five small villages/towns (both cities had populations of over 200,000), they were designated as special cities in the post-merger period.

The total number of public employees increased during the post-merger period. In Mito city, there was an increase from 1,727 to 1,969 and in Tsukbua city, from 221 on average to 1,777. On the other hand, the number of public employees per 1,000 residents actually fell during the post-merger period by 0.9 percent in Mito city and by 1.6 percent in Tsukuba city. Although residents of the cities enjoy a greater scope of services in the post-merger period, the number of public employees who provide these services is decreasing.

In this section, we evaluate a municipality as an efficient administration that produces more public services with fewer production resources. We propose the following three dimensions as inputs:

Capital

Total current municipal revenue (1,000 yen/year, deflated to the 1995 value)

Labor

Number of public employees (1,000/year)

Assets

Area (km²)

It is important to note that our approach measures multidimensional public services. Therefore, we use two outputs as indicators of public services, thus allowing for an evaluation of the municipalities' administrative efficiency:

Scope of services

Population size (1,000/year)

Quality of services

Number of employees (per 10,000 residents)

Potential sources of municipal efficiencies are provided by De Borger and Kerstens (1996, 2000), who examined local administrative services in the fields of education, social and recreational services, and overall administrative services. We collapsed these multiple services into two proxies. A proxy for the scope of services, which are public services provided by the Japanese local government, diversifies by the number of residents in principle. For instance, the official requirement for the establishment of a junior high school is per 9,700 residents and for a nursing care hospital for the elderly is per 20,000. A proxy for the quality of services indicates the familiarity between local government and the residents, that is, this indicator implies that the local administration can give careful instructions to residents.

The data are drawn from the Annual Report on Municipal Financial Results (Tokyo: Ministry of Internal Affairs and Communications) for the fiscal years (April 1–March 31) in question.

Method

Since DEA is employed as the analytical method in the current study, we present a brief discussion of its underlying characteristics.

DEA

DEA was first presented in a seminal article by Charnes, Cooper, and Rhodes (CCR 1978). For the past 30 years, this method has enjoyed a wide acceptance and application (Boisso, Grosskopf, and Hayes 2000; Emrouznejad, Parker, and Tavares 2008). Mathematically, the CCR model, in its weak efficiency, input-oriented, and envelopment form, generates an efficiency score for DMUs of interest $j_{0}, g_{j 0} (0 \leq g_{j 0} \leq 1) .$ It is formulated as the following linear program (LP):

\begin{aligned} M i n i m i z e g_{j 0} = θ_{C C R} \\ s u b j e c t t o Σ_{j = 1}^{n} λ_{j} y_{j} \geq y_{j 0}, \\ Σ_{j = 1}^{n} λ_{j} x_{j} - θ_{C C R} x_{j 0} \leq 0, \\ λ_{j} \geq 0, j = 1, \dots, n, \\ (θ u n c o n s t r a i n e d), \end{aligned}

where

\begin{aligned} n = n u m b e r o f D M U s, \\ y_{i} = [y_{1 j}, \dots, y_{r j}, \dots, y_{t j}] = o u t p u t v e c t o r f o r D M U j, \\ y_{r j} = o u t p u t r f r o m D M U j, \\ t = n u m b e r o f o u t p u t s, \\ x_{j} = [x_{1 j}, \dots, x_{i j}, \dots, x_{m j}] = i n p u t v e c t o r f o r D M U j, \\ x_{i j} = i n p u t i t o D M U j, \\ m = n u m b e r o f i n p u t s, \\ θ_{C C R}, λ_{j} (j = 1, \dots, n) = m o d e l^{'} s d e c i s i o n v a r i a b l e s . \end{aligned}

We can generate DEA scores

g_{j o} (= θ_{C C R})

for all DMUs by solving equation (1)

n

times, setting each DMU as the target DMU

j_{0}

in turn. Here, DMUs

j_{0}

with the optimum

g_{j 0}^{*} = 1

are judged DEA efficient, while those with

g_{j 0}^{*} < 1

are defined as DEA inefficient.

While the CCR model assumes constant returns to scale (RTS) with the input and output, the flexible Banker, Charnes, and Cooper (BCC 1984) mode allows variable (increasing, constant, or decreasing) RTS by adding the following restriction to equation (1):

\sum_{j = 1}^{n} λ_{j} = 1 .

We can generate DEA BCC scores

(θ_{B C C})

for DMU

j_{0}

by solving equation (1) with restriction (2), in which

θ_{C C R}

is replaced by

θ_{B C C}

θ_{B C C}

measures technical efficiency, and the following is defined as scale efficiency (SE):

{S E}_{j 0} = \frac{θ_{C C R}}{θ_{B C C}} .

We thus view

θ_{C C R}

as the combined indicator of technical efficiency and SE. In the input-oriented DEA here, SE = 1 implies that the output is of the most productive scale size (MPSS). Formula (3) thus measures the appropriateness of the production size for a given DMU to the MPSS.

Table 1 summarizes the yearly average of efficiency scores computed under CCR and BCC; the SE scores, with standard deviations indicated in parentheses; and the number of DMUs below (and above) the average $\pm 2 σ$ of the SE distribution. The table indicates that there is a heterogeneity associated with municipal size in the sample period 1979–2004. We observe a marginal decrease in SE from a value of 0.962 to 0.922 for twenty-five years, and find DMUs in excess below (and above) $2 σ$ of the distribution. The municipalities are now positioned farther from the MPSS.

Table 1.

Average DEA Scores and Scale Efficiency

Year	CCR	BCC	Scale	Above 2σ
1979	0.853 (0.092)	0.886 (0.085)	0.963 (0.050)	3
1980	0.859 (0.095)	0.899 (0.081)	0.956 (0.058)	3
1981	0.856 (0.096)	0.886 (0.087)	0.967 (0.043)	1
1982	0.868 (0.099)	0.896 (0.090)	0.969 (0.036)	3
1983	0.847 (0.100)	0.882 (0.090)	0.960 (0.044)	4
1984	0.865 (0.097)	0.887 (0.088)	0.975 (0.040)	3
1985	0.809 (0.104)	0.833 (0.103)	0.970 (0.040)	4
1986	0.870 (0.094)	0.886 (0.089)	0.982 (0.023)	5
1987	0.840 (0.099)	0.873 (0.088)	0.963 (0.044)	6
1988	0.857 (0.093)	0.890 (0.086)	0.963 (0.048)	5
1989	0.857 (0.089)	0.891 (0.084)	0.964 (0.053)	5
1990	0.850 (0.094)	0.881 (0.085)	0.965 (0.048)	7
1991	0.868 (0.085)	0.893 (0.080)	0.972 (0.044)	5
1992	0.876 (0.086)	0.898 (0.078)	0.975 (0.032)	8
1993	0.827 (0.103)	0.853 (0.095)	0.970 (0.043)	7
1994	0.829 (0.107)	0.866 (0.096)	0.957 (0.052)	6
1995	0.835 (0.101)	0.877 (0.091)	0.952 (0.047)	7
1996	0.827 (0.105)	0.874 (0.096)	0.947 (0.050)	5
1997	0.836 (0.103)	0.884 (0.094)	0.946 (0.050)	5
1998	0.861 (0.090)	0.892 (0.086)	0.965 (0.040)	8
1999	0.846 (0.094)	0.884 (0.090)	0.957 (0.045)	10
2000	0.848 (0.093)	0.888 (0.088)	0.955 (0.056)	5
2001	0.840 (0.091)	0.888 (0.090)	0.946 (0.058)	5
2002	0.840 (0.090)	0.893 (0.090)	0.940 (0.065)	7
2003	0.860 (0.088)	0.899 (0.085)	0.956 (0.052)	9
2004	0.826 (0.123)	0.896 (0.095)	0.922 (0.088)	6

It is important to note that in the current study, we employ the BCC model in considering the DMU scale, rather than the CCR model. We thus compute the MI relative to the BCC frontier (Ray and Desli 1997) in the following subsection.

DEA/MI Analysis

In this subsection, we examine the change in municipal administrative efficiency using a DEA/MI approach, which measures the Malmquist (productivity) index (Malmquist 1953) within a DEA framework. This allows for the measurement of the ratio of DEA efficiencies in two different time periods with dynamic/moving efficiency frontiers. The details of this approach are given below.

Figure 2 illustrates a single input and output DEA case where DMU $j_{0}$ was at point A in period $α$ and the connected line $x^{α} R S T y^{α}$ indicates the BCC DEA frontier. The input-oriented efficiency of DMU $j_{0}$ is then measured by PC/PA (<1, DEA inefficient). When point A is on the frontier, its score is 1 (DEA efficient). Suppose that in period $β (β > α),$ DMU $j_{0}$ has moved to point B and the frontier itself has shifted to $x^{β} U V W y^{β}$ . The efficiency change in DMU $j_{0}$ can be measured by the ratio of its DEA score in period $β$ to that in period $α$ ; however, since the frontier has shifted, we must compute the geometric mean of the ratios for the two frontiers in those same periods. The DEA (BCC input-oriented)/MI for DMU $j_{0}$ between periods $α$ and $β$ is given in equation (4):

{M I}_{j 0} [α, β] \equiv {(\frac{Q D / Q B}{P C / P A} \cdot \frac{Q F / Q B}{P E / P A})}^{1 / 2} .

Here, MI > 1 implies a gain in DEA efficiency by DMU

j_{0}

from period

α

β

, while MI = 1 and MI < 1 imply the status quo and loss, respectively.

Figure 2.

DEA efficiency changes with the frontier over time.

Transforming equation (4), the MI can be decomposed into two components as follows:

{M I}_{j 0} [α, β] = \frac{Q F / Q B}{P C / P A} \times {(\frac{P C}{P E} \cdot \frac{Q D}{Q F})}^{1 / 2},

= {C U}_{j 0} [α, β] \times {F S}_{j 0} [α, β]

= \frac{Q F / Q B}{P C / P A} \times {(\frac{P C / P A}{P E / P A} \cdot \frac{Q D / Q B}{Q F / Q B})}^{1 / 2} .

In the first term on the right-hand side (RHS) of formula (5), CU indicates the catch-up index; that is CU > 1 suggests that DMU

j_{0}

has moved closer to the period

β

frontier than to the period

α

frontier. CU = 1 and CU < 1 thus indicate that the same distance or more, respectively, has been covered. We define the second term on the RHS of equation (5) as the frontier shift index, where FS > 1 indicates a gain in the DEA frontier shift from period

α

β

as measured from DMU

j_{0}

. In other words, the frontier has moved onward, generating more output but with less input (again, see Figure 2). As in the previous cases, FS = 1 and FS < 1 imply no change and loss (backward shift), respectively.

Since PE/PA in Figure 2 is, for example, the BCC DEA score $θ_{B C C}$ of the period $α$ DMU $j_{0}$ measured by means of the period $β$ frontier, we denote it as $θ_{B C C} [D^{α}, F^{β}]$ . Then, from equation (7), we obtain the following:

{M I}_{j 0} [α, β] = \frac{θ_{B C C} [D^{β}, F^{β}]}{θ_{B C C} [D^{α}, F^{α}]} \times {(\frac{θ_{B C C} [D^{α}, F^{α}]}{θ_{B C C} [D^{α}, F^{β}]} \cdot \frac{θ_{B C C} [D^{β}, F^{α}]}{θ_{B C C} [D^{β}, F^{β}]})}^{1 / 2} .

By letting $x_{j}^{α}, y_{j}^{α} = x_{j}, y_{j}$ , respectively, in period $α$ , we can obtain $θ_{B C C} [D^{α}, F^{α}]$ as the optimum of the following LP, which is the classic DEA model:

\begin{aligned} M i n i m i z e θ_{B C C} \\ s u b j e c t t o Σ_{j = 1}^{n} λ_{j} x_{j}^{α} \geq y_{j 0}^{α}, \\ Σ_{j = 1}^{n} λ_{j} x_{j}^{α} - θ_{B C C} x_{j 0}^{α} \leq 0, \\ Σ_{j = 1}^{n} λ_{j} = 1, \\ λ_{j} \geq 0, j, \dots, n, \\ (θ u n c o n s t r a i n e d), \end{aligned}

θ_{B C C} [D^{β}, F^{β}]

can also be obtained by the LP in equation (9) by replacing

α

with

β

When $θ_{B C C} [D^{α}, F^{β}]$ is obtained as the optimum of

\begin{aligned} M i n i m i z e θ_{B C C} \\ s u b j e c t t o Σ_{j = 1}^{n} λ_{j} y_{j}^{β} \geq y_{j 0}^{α}, \\ Σ_{j = 1}^{n} λ_{j} x_{j}^{β} - θ_{B C C} x_{j 0}^{α} \leq 0, \\ Σ_{j = 1}^{n} λ_{j} = 1, \\ λ_{j} \geq 0, j, \dots, n, \\ (θ u n c o n s t r a i n e d), \end{aligned}

this forms the DEA exclusion model (Andersen and Petersen 1993). Finally, we can obtain

θ_{B C C} [D^{β}, F^{α}]

by once again using the DEA exclusion model of equation (10) with

α

and

β

switched.

The BCC input-oriented MI is computed from equation (8). However, there is a case in which we cannot necessarily compute the MI. In Figure 2, suppose that in period $β$ , DMU $j_{0}$ has moved from point A to point $B^{'}$ ; then the value of $θ_{B C C} [D^{β}, F^{α}]$ is infinity. Briec and Kerstens (2009) have recently proven the problem is inevitable, even for a more general indicator like the Luenberger productivity indicator. Several studies have touched on this “unbounded” problem. One solution is to replace the value with an output-oriented score (González and Gascón 2004), and another solution is to substitute the unbounded value with 1 and omit the observation in the computation of averages (Coelli, Rao, and Battese 1998).

We found that some observations (less than 1 percent of the total computation cases for the particular municipalities) had values of 1 in both the input- and output-oriented scores. We thus substituted the unbounded value with 1.

Applying Data of Municipal Mergers to DEA/MI

When applying the DEA panel data to the DEA/MI analysis in our research, we should note that the municipality in each year (DMU) is not completely identifiable in the sample period; consolidated or incorporated municipalities are included.

Figure 3 (1) is a case of consolidation. Tsukuba city was newly established in 1987 by consolidating five villages/towns (Oho, Sakura, Toyosato, Tsukuba, and Yatabe). Figure 3(1)a illustrates that we do not observe data for the five villages/towns after 1987 or for Tsukuba city prior to 1987. The normal computation of DEA/MI for the five municipalities after 1987 is impractical due to the incomplete panel data. Since we investigate the efficiency change before and after the consolidation, it would be much better to consider the consolidation as a series of DMUs than to analyze them separately. As shown in Figure 3(1)b, we thus apply the data for Tsukuba city to each of the five villages/towns after 1987 as if they continued to exist in the post-merger period.

Figure 3.

Data set of merging municipalities applied to DEA/MI.

Figure 3(2) illustrates a case of incorporation. Tsunezumi village was incorporated by Mito city in 1992. Therefore, we do not observe data for Tsunezumi after 1992. We complete the construction of the full panel data for the two municipalities by applying data for Mito to Tsunezumi after 1992 in a similar manner.

It is important to note that, for each case, the DMUs of each year in the portion that we colored accurately indicate the same DMU with the same data. In other words, we can track the DMUs even though they have been formally designated as different DMUs by consolidation or incorporation. We specify five data panels of DEA inputs and outputs, each of which represents the 92 municipalities for 26 years (1979–2004), although there is a decrease in the total number of municipalities actually observed in the post-merger period. In our empirical application below, we successfully applied these panels to the DEA/MI analysis. It is significant to take care with the actual total number of municipalities in each year when averaging the indices annually. (See also Tsuneyoshi, Hashimoto, and Haneda 2009 for a DEA/MI application to the merger and splitting of countries.)

DEA Analysis of Efficient Municipal Administration

This section shows the result of the DEA/MI analysis of municipalities. We introduce the average FS index, allowing for an administrative efficiency change in Ibaraki prefecture. In addition, we select two merging cities, Tsukuba and Hitachinaka, and examine the main source of their efficiency changes.

Cumulative MI

By applying our data to the LPs of equations (9) and (10) and using formulas (6) and (8), we compute ${C U}_{j 0} [α, β]$ , ${F S}_{j 0} [α, β]$ , and ${M I}_{j 0} [α, β]$ . Normally, these indices for year $β$ would be compared to those in the preceding year, that is, $α = β - 1$ . However, such annually successive indices do not seem suitable when we consider the full sample period. We thus propose an alternative index in the spirit of Hashimoto and Haneda (2008). We therefore employ the following parameters in the current analysis: ${C U}_{j 0} [1979, β]$ , ${F S}_{j 0} [1979, β]$ , and ${M I}_{j 0} [1979, β]$ , where $β = 1979, \dots, 2004.$ We then compare these values to those in the standard year 1979, the beginning of our sample period. Since these indices measure the successive changes from the standard year to year $β$ , we refer to them as cumulative indices. In this case, the cumulative index values when $β$ = 1979 are all 1. Berg, Førsund, and Jansen (1992) and Färe et al. (1994) used the sequential product of successive indices to demonstrate the cumulative change from a given year. However, as the latter authors state, the Malmquist index, as well as the FS index does not satisfy the circular test, that is, ${M I}_{j 0} [α, α + 1] \times {M I}_{j 0} [α + 1, α + 2] \neq {M I}_{j 0} [α, α + 2] .$ In order to avoid this problem and to be able to properly compute the cumulative change, we employ the cumulative indices without using the sequential product (Hashimoto, Sugita, and Haneda 2009).

Figure 4 shows three cumulative indices for Sanwa village and Edosaki town. We note that in the base year, 1979, each municipality was treated as a separate DMU, indicating that the municipalities were all on the efficient administrative frontier. For Sanwa village, the cumulative CU is 1; this indicates that Sanwa was on the frontier throughout the sample period. From formula (6), the MI and FS move together. Since the MI implies an administrative efficiency change by considering the FS, the administrative efficiency in 2004 decreased by 22 percent from the base year due to the FS backward. For Edosaki town, having been on the efficiency frontier in the base year 1979, the CU was frequently better than the efficiency frontier. The MI, moving backward from the base year, thus moves differently from the FS. Therefore, our cumulative indices quantitatively show the chronological changes in municipal administrative efficiency.

Figure 4.

Cumulative indices for two municipalities.

Efficiency Changes in Ibaraki Prefecture

Recall that CU measures the proximity of a municipality $j_{0}$ relative to the efficient frontier in each period, FS indicates the movement of the efficient frontier between two periods, and MI measures the change in efficiency of a municipality $j_{0}$ by considering the FS index as well as the CU index.

While ${C U}_{j 0}$ and ${M I}_{j 0}$ indicate the movement of municipality $j_{0}$ , ${F S}_{j 0}$ indicates the shift of the efficient frontier, which is composed of the most efficient (i.e., DEA efficient) municipalities in administration but not necessarily of municipality $j_{0}$ itself. In other words, ${F S}_{j 0}$ indicates Ibaraki prefecture’s administrative efficiency change as measured from the location (viewpoint) of municipality $j_{0}$ . Therefore, we propose an average FS index of all municipalities, that is, an efficient frontier shift measured from the viewpoint of the average municipality, as an appropriate indicator to view the efficiency change in the administration of Ibaraki prefecture.

Figure 5 shows the average $F S [1979, β]$ , where $β = 1979, \dots, 2004$ with a base year of 1979. It indicates the movement of Ibaraki prefecture’s administrative efficiency from the viewpoint of the average municipality. The average FS shifted backward between 1979 and 2004. Although a recovery was observed in 1984, the administrative efficiency in Ibaraki decreased almost monotonically from 1987, and it finally dropped to 23.1 percent in 2004. This indicated a big loss in municipal administrative efficiency in Ibaraki for 1979–2004.

Figure 5.

Administrative efficiency change in Ibaraki prefecture (1979–2004).

In order to examine the impact of municipal mergers, we classified our sample into merging and nonmerging municipalities and calculated the respective averages. It is important to note that the loss in Ibaraki prefecture’s administrative efficiency, regardless of merging is rather apparent. When we considered the average of merging municipalities, efficiency showed a marginal regression in the sample period; however, the scores of merging municipalities were slightly higher than those of nonmerging ones.

The CU for merging and nonmerging municipalities explains the difference. Figure 6 shows the cumulative $C U [1979, β]$ on average, where $β = 1979, \dots, 2004$ , with a base year of 1979. A graph of the merging municipalities indicates that their CU was maintained above 1 in the sample period; thus, they moved closer to the best practice frontier, which is composed of DEA-efficient DMUs in period $β$ . The CU for the nonmerging municipalities moved almost the same distance or more, relative to the efficient frontier, and the scores were much lower than those of the merging municipalities in the sample period. On the basis of a comparison of their average FS, we conclude, in this regard, that the administrative efficiency of the merging municipalities was better than that of the nonmerging ones for 1979–2004.

Figure 6.

Average CU for merging and nonmerging municipalities (1979–2004).

Analysis of Merging Municipalities

To examine the pattern of administrative efficiency change in both the pre- and post-merger periods, we include illustrations of newly established municipalities Tsukuba city and Hitachinaka city (see Figures 7 and 8 , respectively). Tsukuba city was founded in 1987 by consolidating five municipalities with populations under 30,000 (Oho, Sakura, Toyosato, Yatabe, and Tsukuba; Kukisaki was absorbed in 2002). Hitachinaka city was founded in 1994 by consolidating Nakaminato city (population 34,000) and Katsuta city (population 115,000). The populations of the two newly established municipalities in 2004 were 191,814 and 151,673, respectively.

Figure 7.

Cumulative indices for base year 1987 for Tsukuba city.

Figure 8.

Cumulative indices for base year 1994 for Hitachinaka city.

Figure 7 shows Tsukuba city’s cumulative indices relative to the foundation year of 1987. A graph after 1987 thus indicates its chronological changes in MI, CU, and FS relative to these values in the foundation year. Since five municipalities were consolidated to form Tsukuba city, five graphs before 1987 show the sequential changes of the three indices using the consolidation as the reference point. Recall that if the cumulative MI or any of its components is less than 1, it indicates deterioration in the efficiency of a given DMU from the base year. Moreover, these indices capture the performance relative to the best practice in the sample, where best practice represents a “prefecture frontier” in our sample.

Five graphs before 1987 of the cumulative MI reveal that not all the municipalities consolidated into Tsukuba city improved their administrative efficiency. In the case of Yatabe, it improved its efficiency as compared to the score of 1987, while the efficiency for Toyosato decreased, with some fluctuation. In this regard, Tsukuba city was characterized with having administratively efficient and inefficient municipalities.

A graph after 1987 shows that, on average, Tsukuba city’s administrative efficiency regressed slightly in the post-merger period: the cumulative MI was less than 1 but only slightly. Decomposed the MI into CU and FS using formula (6), three graphs after 1987 thus show that the efficiency change was due to FS rather than CU. The cumulative FS was below 1, thus the FS, which was composed of the most efficient municipalities in the year, moved monotonically backward in the post-merger period. However, the merger made Tsukuba city move closer to the yearly efficiency frontier: the CU was over 1 in the post-merger period. As a result, the MI was not entirely incorporated with the strong regress of the FS and remained almost 1 in the post-merger period. We thus conclude that the merger resulted in Tsukuba city retaining its efficiency with an increase in the CU, against the steep regress in the FS.

Figure 8 shows the cumulative indices for Hitachinaka city calculated relative to its foundation year of 1994. The values of 1 for cumulated CU imply that Hitachinaka city had been—except for Katsuta in 1979 and Nakaminato in 1992—on the prefecture frontier in the associated year. From formula (6), MI and FS for Hitachinaka move together. The two MI graphs before 1994 show that the efficiency values for both Nakaminato and Katsuta regressed but maintained above 1. Hitachinaka remained on the prefecture frontier in the post-merger period, and the values of MI after 1994 gradually improved. We thus note that Hitachinaka city was established after two administratively efficient cities were consolidated, and the merger resulted in an improvement in administrative efficiency.

Change in SE

In this subsection, we assess the impact of municipal mergers on SE by applying equation (3). We computed the DEA CCR/Malmquist index $({M I}^{C})$ and decomposed the CU index $({C U}^{C})$ into two components.²

In Figure 3, line $O C^{'} D^{'}$ and line $O E^{'} F^{'}$ show the CCR DEA frontier in period $α$ and period $β$ , respectively. The ${M I}^{C}$ for DMU $j_{0}$ between periods $α$ and $β$ is defined as follows:

{M I}_{j 0}^{C} [α, β] \equiv {(\frac{Q D^{'} / Q B}{P C^{'} / P A} \cdot \frac{Q F^{'} / Q B}{P E^{'} / P A})}^{1 / 2} .

Likewise from equation (8),

\begin{aligned} {M I}_{j 0}^{C} [α, β] = \frac{θ_{C C R} [D^{β}, F^{β}]}{θ_{C C R} [D^{α}, F^{α}]} \times {(\frac{θ_{C C R} [D^{α}, F^{α}]}{θ_{C C R} [D^{α}, F^{β}]} \cdot \frac{θ_{C C R} [D^{β}, F^{α}]}{θ_{C C R} [D^{β}, F^{β}]})}^{1 / 2} \\ = C U [α, β] \times F S_{j 0}^{C} [α, β] . \end{aligned}

Here, we enhance the decomposition of

{C U}^{C}

into two components that measure pure efficiency change (PEC) and scale efficiency change (SEC; Ganley and Cubbin 1992; Färe et al. 1994; Ray and Desli 1997; González and Gascón 2004). Using equation (4),

\begin{aligned} {S E C}_{j 0} [α, β] = \frac{θ_{C C R} [D^{β}, F^{β}]}{θ_{C C R} [D^{α}, F^{α}]} / \frac{θ_{B C C} [D^{β}, F^{β}]}{θ_{B C C} [D^{α}, F^{α}]} \\ = {C U}_{j 0}^{C} [α, β] / {P E C}_{j 0} [α, β] . \end{aligned}

Therefore,

{M I}_{j 0}^{C} [α, β] = {S E C}_{j 0} [α, β] \times {P E C}_{j 0} [α, β] \times {F S}_{j 0}^{C} [α, β] .

A numerator of the RHS of equation (13) is

{C U}^{C} [α, β]

, which is calculated relative to the CCR frontier, and the denominator is

C U [α, β]

, which is calculated relative to the BCC frontier, indicating

P E C [α, β]

; thus, SEC captures changes in the deviation between the BCC and CCR frontiers. We see a given DMU’s SEC between two periods

α

and

β

; for example, SEC > 1 suggests that the production size of an interest DMU

j_{0}

moves closer to the MPSS in the sample period. SEC = 1 and SEC < 1 thus indicate that the same distance or more, respectively, has been covered. In our study, we calculate the cumulative

S E C [α, β]

relative to the foundation year of Tsukuba city and Hitachinaka city and examine the transition of each city in the post-merger period. The results of equation (14) are shown in Tables 2 and 3 .

Table 2.

Decomposition with Scale Effects for Tsukuba City

Year	MI^c	FS^c	CU^c	PEC	SEC
1987–1988	1.018	0.935	1.089	1.128	0.965
1987–1989	0.980	0.881	1.113	1.199	0.928
1987–1990	0.939	0.870	1.079	1.121	0.962
1987–1991	0.975	0.808	1.206	1.092	1.104
1987–1992	0.938	0.791	1.185	1.112	1.066
1987–1993	0.920	0.910	1.011	0.994	1.017
1987–1994	0.912	0.930	0.980	1.036	0.946
1987–1995	0.880	0.872	1.009	1.034	0.975
1987–1996	0.895	0.882	1.015	1.041	0.975
1987–1997	0.905	0.876	1.033	1.049	0.985
1987–1998	0.933	0.809	1.154	1.126	1.025
1987–1999	0.915	0.825	1.109	1.089	1.018
1987–2000	0.952	0.860	1.107	1.181	0.937
1987–2001	0.977	0.851	1.149	1.200	0.958
1987–2002	0.982	0.820	1.197	1.221	0.981
1987–2003	0.904	0.756	1.196	1.196	1.000
1987–2004	0.935	0.773	1.210	1.233	0.981

Table 3.

Decomposition with Scale Effects for Hitachinaka City

Year	MI^c	FS^c	CU^c	PEC	SEC
1994–1995	0.957	0.989	0.968	1.000	0.968
1994–1996	0.978	0.978	1.000	1.000	1.000
1994–1997	1.004	1.004	1.000	1.000	1.000
1994–1998	1.006	1.006	1.000	1.000	1.000
1994–1999	0.986	1.002	0.983	1.000	0.983
1994–2000	1.011	1.052	0.962	1.000	0.962
1994–2001	0.999	1.043	0.958	1.000	0.958
1994–2002	1.023	1.052	0.973	1.000	0.973
1994–2003	1.032	1.040	0.992	1.000	0.992
1994–2004	1.021	1.052	0.970	1.000	0.970

Table 2 shows the cumulative indices PEC and SEC computed under CCR for Tsukuba city. From the results of the DEA in each year, Tsukuba city was not on the frontier in the period of its consolidation year, 1987. From the optimal value of $\sum λ_{j}^{*}$ in formula (1), Tsukuba city had a larger output than the MPSS in 1987 and has continued with the output larger than the MPSS in the post-merger period. The SEC scores in Table 2 indicate that Tsukuba city’s output size relative to the MPSS of the consolidation year, 1987, became small or big, and finally reached almost the same relative size in 2004. We calculated the allocation ratio of the scale gains (SEC) to efficiency gains (PEC). It reached its peak of 1.023 in 1993, the fourth year after the merger, and monotonically decreased to 0.795 by 2004. This implies that scale was the more dominant effect on the administrative efficiency for Tsukuba city in the short run; however, the allocation of scale gains gradually shifted to that of efficiency gains.

Table 3 shows the sources of Hitachinaka city’s efficiency change in the post-merger period. Hitachinaka was on the efficiency frontier in its incorporation year, 1994, and has been on the efficiency frontier annually through the post-merger period. Hitachinaka was found to have larger sized output than the MPSS by the value of $\sum λ_{j}^{*}$ in 1994. The values of SEC imply that Hitachinaka remained almost the same distance to the MPSS in the post-merger period. Since ${C U}^{C}$ is composed of SEC and PEC, the allocation between SEC and PEC did not change in the post-merger period.

From the viewpoint of SEC and PEC in the post-merger period, these findings imply that altering a municipal scale had a more dominant effect on the allocation between scale and technology in terms of municipal efficiency in Tsukuba city, which was formed by consolidating small-population municipalities, as compared to that for Hitachinaka city. Furthermore, scale change was not necessarily a major source for efficiency.

Summary and Conclusion

Our article extended the research on municipal mergers and suggested a criterion for mergers. We used DEA/MI analysis by considering multiple dimensions of public services—the scope and quality of municipal outputs—and applied them to 92 municipalities in Ibaraki prefecture for the period 1979–2004. We evaluated a DEA-efficient DMU as an efficient administrative municipality and observed the successive changes in the efficiency for 92 municipalities from 1979 using the cumulative MI.

The MI indices were decomposed into two component measures: CU and FS indices. Since the FS indicates the shift of the efficient frontier, which is composed of the most efficient municipalities in each year, we introduced the average FS of all municipalities, that is, the efficient frontier shift measured from the viewpoint of the average municipality in Ibaraki prefecture. The average FS showed that administrative efficiency in Ibaraki prefecture marginally regressed in the sample period. Mergers did not improve efficiency on average; therefore, we concluded that municipal mergers in Ibaraki prefecture did not contribute to an improvement in the administrative efficiency. However, the score of an average FS for merging municipalities was slightly higher than that for nonmerging municipalities; this is because merging municipalities moved much closer to the efficient frontier than nonmerging ones in the sample period.

We examined the successive changes on administrative efficiency in the pre- and post-merger periods using two examples. Tsukuba city, which was formed by consolidating five small municipalities, kept efficiency scores almost at 1 and was not involved in the rapidly regress of the FS. Hitachinaka city, which was formed by consolidating two efficient cities, remained on the efficiency frontiers in the post-merger period. We further decomposed the CU into scale gains and efficiency gains, to estimate the scores of the DMU’s efficiency change in the post-merger period. From the overall results, restricted to our sample, we concluded that enlargement of municipal scale did not move DMU’s production size to the MPSS. The allocation to scale gains was more dominant in the short run for Tsukuba city; however, the scale effect did not necessarily contribute to an efficiency change in the post-merger period.

The results surely indicate that administrative efficiencies were higher in merging municipalities than in nonmerging ones in the period 1979–2004. For every merging municipality, for example, Tsukuba or Hitachinaka, mergers contributed to the retention of efficiency. To some extent, a comparative analysis of merging and nonmerging municipalities corroborates the results of general cost-minimization studies. The results also imply that merging municipalities in Ibaraki prefecture coordinated their collective choices for public services. That is, the mergers were voluntary, and we suspect that their physical circumstances and governance structures improved after reflecting on their decisions.

From a methodological viewpoint, our research involved a unique analysis of municipal mergers. First, we applied the data of a newly established municipality to all the municipalities that were consolidated to form the former. We were able to hold DMUs in the sample time frame and were able to analyze municipal mergers with DEA/MI analysis. Second, we employed the average FS, which is useful for a prefecture analysis. The FS graphically represents the shift in administrative efficiency at a prefecture level. Third, we calculated the cumulative indices using the pre-merger and post-merger periods as our reference points. These indices obviously display the administrative efficiency change of the given merging DMUs and allow for a comparative analysis of municipalities in the pre- and post-merger periods. We especially believe that the cumulative indices in an analysis of municipal mergers allows for new directions in the development and application of DEA/ MI-based models. In this regard, our empirical approach of applying the data of municipal mergers to DEA/MI extends the applicability of the DEA time-series analysis and is a giant step toward its evolution.

Worthing and Dollery (2000) were convinced of the relevance of the administrative efficiencies to gauge the provision of local services for taxpayers. We were also convinced that the results of this study are useful to both residents and policy makers when deciding on municipal mergers. A resident can use cumulative indices relative to the foundation year of a municipality and appreciate that administrative efficiency has significantly improved in the pre-merger period. Furthermore, a resident can realize that altering municipal scale is effective for moving the municipality close to the efficiency frontier by observing the cumulative SEC in the post-merger period. At the same time, a policy maker can measure change in administrative efficiency using multiple dimensions of public services. In addition, a policy maker can infer the change at the prefecture level from the average FS and evaluate the decision on a merger through a comparison of the FS of merging and nonmerging municipalities. Although the evaluation of municipal mergers is performed a posteriori, it is, nonetheless, helpful for formulating and revising policy decisions.

It is important to note that our results depend on the nature of the input–output data that we employed. This is a common limitation of empirical studies using DEA “data-oriented” methods. One must therefore select the DEA inputs and outputs carefully and reasonably. On the other hand, the methodology presented here is applicable to all subjects of DEA besides municipal mergers. One could thus extend a proposed approach to the use of DEA time series and related models.

Footnotes

Acknowledgment

The authors are sincerely thankful to Prof. Sergio J. Rey (editor) and two anonymous reviewers for their constructive comments and valuable suggestions that proved most useful in improving the contents of the previous drafts of this article.

The authors declared no conflicts of interest with respect to the authorship and/or publication of this article.

The authors received no financial support for the research and/or authorship of this article.

Notes

References

Andersen

Petersen

N. C.

1993. A procedure for ranking efficient units in data envelopment analysis. Management Science, 39, 1261–64.

Banker

R. D.

Charnes

Cooper

W. W.

1984. Some models for estimating technical and scale efficiencies in data envelopment analysis. Management Science, 30, 1078–92.

Berg

S. A.

Førsund

F. R.

Jansen

E. S.

1992. Malmquist indices of productivity growth during the deregulation of Norwegian banking 1980-89. Scandinavian Journal of Economics, 94, 211–28.

Boisso

Grosskopf

Hayes

2000. Productivity and efficiency in the US: Effects of business cycles and public capital. Regional Science & Urban Economics, 30, 663–81.

Briec

Kerstens

2009. Infeasibilities and directional distance functions: With application to the determinativeness of Luenberger productivity indicator. Journal of Optimization Theory and Applications, 141, 55–73.

Charnes

Cooper

W. W.

Rhodes

1978. Measuring the efficiency of decision making units. European Journal of Operational Research, 2, 429–44.

Coelli

Rao

D. S. P.

Battese

G. E.

1998. An introduction to efficiency and productivity analysis. Boston: Kluwer Academic Publisher.

Cooper

W. W.

Seiford

L. M.

Tone

2000. Data envelopment analysis: A comprehensive text with models, applications, references and DEA-solver software. Boston: Kluwer Academic Publisher.

De Borger

Kerstens

1996. Cost efficiency of Belgian local governments: A comparative analysis of FDH, DEA, and econometric approaches. Regional Science & Urban Economics, 26, 145–70.

10.

De Borger

Kerstens

2000. What is known about municipal efficiency? The Belgian case and beyond. In Blank

J. L. T.

(Ed.), Public Provision and Performance: Contributions from Efficiency and Productivity Measurement. Amsterdam: Elsevier.

11.

Emrouznejad

Parker

B. R.

Tavares

2008. Evaluation of research in efficiency and productivity: A survey and analysis of the first 30 years of scholarly literature in DEA. Socio-Economic Planning Sciences, 42, 151–57.

12.

Färe

Grosskopf

Norris

Zhang

1994. Productivity growth, technical progress, and efficiency change in industrialized countries. American Economic Review, 84, 66–83.

13.

Ganley

J. A.

Cubbin

J. S.

1992. Public sector efficiency measurement: Applications of data envelopment analysis. Amsterdam: North-Holland.

14.

González

Gascón

2004. Sources of productivity growth in the Spanish pharmaceutical industry (1994–2000). Research Policy, 33, 735–45.

15.

Hashimoto

Haneda

2008. Measuring the change in R&D efficiency of the Japanese pharmaceutical industry. Research Policy, 37, 1829–36.

16.

Hashimoto

Sugita

Haneda

2009. Evaluating shifts in Japan’s quality-of-life. Socio-Economic Planning Sciences, 43, 263–73.

17.

Hayes

Wood

1995. Utility maximizing bureaucrats: The bureaucrat’s point of view. Public Choice, 82, 69–83.

18.

Hughes

P. A. N.

Edwards

M. E.

2000. Leviathan vs. Lilliputian: A data envelopment analysis of government efficiency. Journal of Regional Science, 40, 649–69.

19.

Jacobs

A. J.

2004. Federations of municipalities: A practical alternative to local government consolidations in Japan? Paper presented at the annual meeting of the American Sociological Association, Atlanta Hilton Hotel, Atlanta, GA, August 16, 2003.

20.

Konishi

2003. Shichouson Gappei no Ketsudan [Decision Making in Municipal Mergers]. Japan: Gyousei Publisher.

21.

Malmquist

1953. Index numbers and indifference surfaces. Trabajos de Estadistica, 4, 209–42.

22.

Ostrom

Bish

Ostrom

1988. Local government in the United States. San Francisco: ICS Press.

23.

Ray

Desli

1997. Productivity growth, technical progress, and efficiency change in industrialized countries: Comment. American Economic Review, 87, 1033–39.

24.

Saito

1999. Gyousei Kibo to Keizai Kouritusei [Scale and efficiency on administration]. Toshi Mondai, 90, 27–37.

25.

Schacter

H. L.

Toonen

2010. Resilience in public administration: The work of Elinor and Vincent Ostrom from a public administration perspective. Public Administration Review, 70, 193–202.

26.

Steiner

1965. Local government in Japan. Stanford: Stanford University Press.

27.

Tachi

1998. Zaisei no Genjou to Tenbou [Data and chart on national finance] Japan: Okura Zaimu Kyokai.

28.

Thanassoulis

2001. Introduction to the theory and application of data envelopment analysis: A foundation text with integrated software. Boston: Kluwer Academic Publisher.

29.

Tsuneyoshi

Hashimoto

Haneda

2009. Quantitative evaluation of nation stability. Department of Social Systems and Management Discussion Paper Series 1245, University of Tsukuba.

30.

Worthington

A. C.

Dollery

B. E.

2000. An empirical survey of frontier efficiency measurement techniques in local government. Local Government Studies, 26, 23–52.

31.

Yokomichi

2003. Shichouson Gappei no Hitsuyousei to Kadai [A requirement and a problem on municipal mergers]. Toshi Mondai, 94, 3–12.

32.

Yokomichi

Okino

1996. Zaisei Kouritusei kara mita Shichouson Gappei [Evaluation on municipal administrative efficiency]. Jichi Kenkyu, 72, 69–87.