Local Governments' efficiency: is there anything new after Troika's intervention in Portugal?

Maria Basílio CIGES and Management Department, Polytechnic Institute of Beja (IPBeja), Escola Superior de Tecnologia e Gestão, R. Pedro Soares, Campus do Instituto Politécnico de Beja, 7800-295

Beja. Phone: +351 284 311 541 maria.basilio@ipbeja.pt

Clara Pires CIGES and Management Department, Polytechnic Institute of Beja (IPBeja), Escola Superior de Tecnologia e Gestão, R. Pedro Soares, Campus do Instituto Politécnico de Beja, 7800-295

Beja. Phone: +351 284 311 541 clara.pires@ipbeja.pt

Carlos Borralho CIGES and Management Department, Polytechnic Institute of Beja (IPBeja), Escola Superior de Tecnologia e Gestão, R. Pedro Soares, Campus do Instituto Politécnico de Beja, 7800-295

Beja. Phone: +351 284 311 541 cborralho@ipbeja.pt

José Pires dos Reis CIGES and Management Department, Polytechnic Institute of Beja (IPBeja), Escola Superior de Tecnologia e Gestão, R. Pedro Soares, Campus do Instituto Politécnico de Beja, 7800-295

Beja. Phone: +351 284 311 541 pires.reis@ipbeja.pt

Área Temática: I - Setor Público e Não Lucrativo

2

Local Governments’ efficiency: is there anything new after Troika’s

intervention in Portugal?

ABSTRACT

The austerity policies being implemented in many European countries and in Portugal,

particularly as a consequence of the bailout agreement signed between the Portuguese

Government and the Troika, bring measures to increase performance and reduce costs. The

analysis of Local Governments’ efficiency and the assessment of its determinants is highly

relevant for policy purposes. The aim of this research is to evaluate the efficiency of the 278

mainland municipalities in Portugal with a two-stage procedure, combining DEA methods in

a first phase with fractional response models in the second stage. The analysis is performed

for 2010 and 2015, before and after the Troika’s intervention in Portugal. Results show a

similar pattern for both years, in the two stages. Performing a Chow test, no structural change

occurred from 2010 to 2015, suggesting that the reforms implemented in municipalities did

not succeed.

Keywords: Municipalities, Data Envelopment Analysis, Efficiency, Fractional

Response models.

JEL classification: C14, C35, H72, D60

3

1. Introduction

The topic of efficiency and performance measurement has been long investigated in public

administration. Under the New Public Management paradigm which emerged in the 1980’s,

the challenge has been to create governments that “works better but costs less”1. But how to

reconcile the trade-off between more and better services to citizens with fewer resources?

How to effectively measure governments’ outcomes? These are still questions hard to answer.

In recent years this topic has taken a renewed importance. For countries like Portugal,

due to its economic and financial situation that emerged from the sovereign and international

crisis. In fact, from May 2011 to May 2014, the country was under an economic and financial

assistance program negotiated between the Portuguese authorities and the European

Commission (EC), the European Central Bank (ECB) and the International Monetary Fund

(IMF) - the Troika. The bailout agreement required fiscal consolidation and several structural

reforms. Among them, the reorganisation of local government administration in order to

reduce the number of parishes,2 to improve efficiency and quality, and to reduce costs.

The goal of this research is twofold. First, we assess the relative efficiency of each

Portuguese municipality for the years 2010 and 2015, before and after Troika’s intervention

in Portugal using Data Envelopment Analysis (DEA) methods - standard DEA and Inverted

DEA. Second, we adopt fractional response models, to reveal potential determinants of these

efficiency levels. It should be emphasized that as far as we know, no other study concerning

Portuguese municipalities has used these methodologies.

1 This phrase turned into a slogan after the publication of a report in 1993, by Al Gore (then vice-president under

the Bill Clinton presidency in the United States) untitled “Creating a Government that Works Better and Costs

Less”.

2 The merger of civil parishes was one of the solutions suggested by the Troika to increase efficiency of local

governments, in line with the argument of scale economies (Tavares et al., 2012). The number of parishes in

Portugal was reduced from 4260 (in 2010) to 3092 (in 2015).

4

The main contribution of this research is to increase the discussion about efficiency

and its drivers in Local Government entities and to provide empirical evidence about the

impacts of the recent financial crisis on Portuguese municipalities.

The plan of this paper is structured as follows. Section 2 provides a short description

of the characteristics of Portuguese municipalities. Section 3 reviews some of the recent

literature using DEA and second-stage procedures to evaluate local governments’ efficiency.

Section 4 explains the research methodology and the econometric approach, detailing the

data. Section 5 presents and discusses the results. Finally, Section 6 draws the main

conclusions and avenues for future research are highlighted.

2. Characteristics of Portuguese Municipalities

According to the Portuguese Constitution, there are three types of local governments: parishes

(freguesias), municipalities, and administrative regions. From these three types,

municipalities assume more importance, taking into account their political decision power and

financial expression (Jorge et al., 2008). Parishes are small jurisdictions with few own

competencies and administrative regions are not yet implemented in Portugal mainland. There

are currently 308 municipalities, 278 are located in Portugal mainland and the remaining 30

are overseas municipalities belonging to the autonomous regions of Azores and Madeira.

Local governments in Portugal have their own budgets and property, and are all

subject to the same legal and institutional framework. Recent years have witnessed a

progressive trend of decentralization of competencies from the Central Government to local

authorities. However, the weight of local governments in general government finances is

small compared to other European countries. As mentioned in Carvalho et al. (2016), local

expenditures of Portuguese municipalities in 2015, accounted for only 15% of total public

5

expenditure and local revenue for 17% of total public revenue, which is the lowest when

compared to the European average (29% and 32%, respectively).

Municipal public expenditures are divided into capital and current expenditures. The

former include investment, their main component, capital transfers to parishes, financial

assets and liabilities, and other capital expenditures. As for current expenditures, their sub-

components are expenditures on goods and services, financial expenditures, human resources,

current transfers to parishes, and other current expenditures. The main sources of municipal

revenue are transfers from the central government, local taxes (being the property tax the

largest own-revenue source of municipalities) and other revenues (fees and fines, property

income, and financial liabilities, among others).

As mentioned in Costa, Veiga and Portela (2015), Portugal is an interesting case study

because municipalities are all subject to the same rules and legislation and have the same

policy instruments and resources at their disposal.3

Following the Local Administration Reform implemented in 2012, a number of legal

reforms were introduced changing significantly the financial, control and reporting

framework of Portuguese municipalities. Some of these changes resulted directly from the

bailout agreement.

The most significant legal diplomas are the current Local Finance Law (Law 73/2013)

and Local Authorities Law (Law 75/2013). Portuguese municipalities’ main competences are

established in art. 23 of this last diploma and includes: urban and rural infrastructure, energy,

transport and communications, education, patrimony, culture and science, sports and leisure,

healthcare, social services, housing, civil protection and police, environment and basic

sanitation, consumer protection, social and economic development, territory organisation and

external cooperation.

3 They may be considered a set of homogenous entities, a prerequisite to use a DEA approach.

6

3. Literature Review

Performance and efficiency are difficult to measure, particularly for non-profit organizations.

In what concerns local governments outcomes, it is even a more difficult task, given the

nature of the services provided that are market-aside and difficult to valuate.

One way to access efficiency is to use Cost Accounting information. Several attempts

were made to develop a Cost Accounting subsystem to be applied to public entities; however

the great majority of the municipalities have not implemented it yet. More recently, with the

new accounting system (SNC-AP, the Accounting Standardization System for Public

Administrations), it is expected to ascertain the cost of services provided by municipalities to

the populations, and thus to allow an effective control of their efficiency and effectiveness

(Carvalho et al., 2016). The implementation of Management Accounting systems in Public

Administrations is of great importance in the current context in which the various entities are

faced with the need to properly manage the resources at their disposal and to manage public

institutions efficiently and economically. These systems will provide managers with a set of

tools essential to decision making, including planning and execution of control functions.

The literature about local governments’ efficiency is extensive. According to Narbón-

Perpiña and De Witte (2017a), adopting a systematic literature review and with a focus on

local government efficiency from a global point of view4, from 1990 to 2016, 84 empirical

studies were identified. The large majority of these studies have adopted only one approach,

mainly a nonparametric, being Data Envelopment Analysis (DEA) the most used, followed by

Free Disposal Hull (FDH). A wide variety of input and output variables were used depending

on the competences of local governments in each country and naturally, on the availability of

4 By contrast, some studies have concentrated the analysis on a particular local service. For instance water

provision (Picazo et al. 2009, Byrnes at al. 2010) or refuse collection (Bosch et al. 2000).

7

data. The collection of data and particularly, the measurement of local services are complex

and difficult tasks.

The operational environment strongly affects the performance of local governments.

Municipalities face different environmental conditions, namely different social, demographic,

economic, political, financial, geographical and institutional conditions (Narbón-Perpiña &

De Witte, 2017b). In order to take into account the effects of these external factors, a two-

stage procedure is common in nonparametric efficiency studies. In the first phase, DEA

efficiency scores are obtained. In the second phase, a regression model is estimated for DEA

scores in order to examine the effect on the efficiency of potential relevant factors that are

beyond control (the so-called environmental, contextual or non-discretionary variables).

From the 84 empirical studies mentioned above, 63 included environmental variables

in the analysis, and 40 of them adopted a two-stage analysis. In most cases, the second-stage

regression relies on Tobit models (17 papers) or bootstrapped truncated regressions (11

papers), or even Ordinary Least Squares OLS (12 papers), as mentioned in Narbón-Perpiña

and De Witte (2017b). To the best of our knowledge, fractional response models were not

tested in this context. This option will be discussed in the next section.

Specifically about Portugal, five studies have evaluated the efficiency of local

governments. Afonso and Fernandes (2006) studied 51 municipalities in the region of Lisbon

and Vale do Tejo, for the year 2001. This analysis was extended to the entire Portuguese

mainland in Afonso and Fernandes (2008). In this last paper, the authors used DEA with one

input variable (per capita municipal expenditures) and one output variable (the Local

Government Output Indicator - LGOI - a composite index to proxy for the global performance

of the municipality) for 2001. The results by regions showed that Alentejo (0.654) and

Algarve (0.608) have the highest values, on average. The Centro region was, on average, the

least efficient (0.237). On a municipal level the results were quite uneven. In a second stage,

8

through a Tobit analysis, the most relevant environmental factors, which contribute positively

to increase efficiency, were the level of education (secondary or tertiary); municipal per capita

purchasing power; and geographical distance to the capital of district.

Jorge et al. (2008) used data from 2004 municipal accounts and estimated DEA scores

to 274 municipalities in Portugal mainland (three were excluded due to unavailability of data).

With an input-oriented approach and grouping the municipalities by size, the results showed

that larger municipalities tend to be more efficient.

Cruz and Marques (2014) used the super-efficiency DEA model of Andersen and

Petersen (1993) in a first stage using data for the year of 2009 and for all the Portuguese

municipalities (308). To explore the determinants of economic efficiency, in a second-stage,

different models were compared, namely, Tobit, OLS and double-bootstrap. The results seem

to indicate that concentration of population; illiteracy rate; net debt and purchasing power of

the population have a negative effect on the municipalities’ performance.

With a different approach, Cordero et al. (2016) applied time-dependent conditional

frontier estimators to assess the performance of the 278 municipalities for the period of 2009-

2014. One of the strongest limitations of two-stage approaches is that the results may be

biased and inconsistent due to the existence of serial correlation among the estimated

efficiencies obtained with nonparametric methods (Simar & Wilson, 2007, 2011). To deal

with this shortcoming, the authors adopted conditional measures of efficiency, to directly

account for the effect of external variables on the estimation of the efficiency measures of

local government performance. The results suggested that the average efficiency level has

remained stable over the period of 2009-2014, with a slight improvement in the last year.

Larger municipalities performed better, but the gap between these and small municipalities

narrowed notably after the local reforms implemented in 2013. The Lisbon region exhibits the

most efficient municipalities. Concerning the environmental variables, population density and

9

socioeconomic factors do not have a significant impact on efficiency, while a coastal location,

the number of civil parishes and the level of net debt affect municipalities’ efficiency.

4. Methodology

Several methods have been developed to estimate efficiency, and can be classified into two

main groups: parametric (namely, Stochastic Frontier Approach – SFA, Distribution Free

Approach – DFA) and nonparametric (Data Envelopment Analysis – DEA, Free Disposal

Hull - FDH). The main difference between parametric and nonparametric methods relies on

the assumptions about the random errors and on the underlying distribution. While the

parametric approaches have the advantage of decomposing deviations between “noise” and

pure inefficiency, the nonparametric approaches classify the whole deviation as inefficiency,

but otherwise they have the advantage of not imposing a particular parametric functional

form, avoiding misspecification errors. Nonparametric methods have received the authors’

preference because they have less-restrictive assumptions, greater flexibility and can easily

handle multiple outputs and inputs (Ruggiero, 2007).

DEA is based on the idea of technical efficiency, measured by the ratio of output to

input. It allows the identification of the efficient and inefficient units in a comparison of each

unit with its peers (within the group). This programming technique was first developed by

Charnes, Cooper and Rhodes (1978) – CCR model - and since then it has been used to assess

efficiency in areas such as health, prisons, courts, schools and universities and, more recently,

transit and banking.5

DEA compares the relative performance of each decision-making unit (DMU) with the

“best” performance. It is a tool to access the relative performance of homogeneous units. The

advantages of DEA include its ability to accommodate a multiplicity of inputs and outputs;

5 For more details about the DEA methodology, see for instance, Ray (2004).

10

there is no need to specify a particular functional form for the production frontier, and no

prior establishment of rules for the weights is necessary. In addition it works particularly well

with small samples. By contrast, several limitations may be pointed out, namely: the

assumption that there is no random error (any deviation from the estimated frontier is

considered inefficiency); the results’ sensitiveness to the selection of inputs and outputs; and

the number of efficient DMUs on the frontier tends to increase with the number of input and

output variables. As a rule of thumb, the number of DMUs is usually required to triplicate the

number of variables.

The efficiency scores obtained with constant returns to scale (CRS) indicate the

overall technical efficiency (OTE).6 Banker, Charnes and Cooper (1984) develop the use of

variable returns to scale (VRS) – BCC model - which allow the decomposition of OTE into a

product of two components:

𝑂𝑇𝐸 = 𝑃𝑇𝐸 𝑥 𝑆𝐸

where, PTE is pure technical efficiency obtained under VRS and relates to the ability of

managers to use municipalities’ resources. These scores are higher than or equal to those

obtained under CRS. SE is scale efficiency and refers to exploiting scale economies and

measures whether a municipality produces at an optimal size of scale. SE is obtained by

dividing OTE by PTE.

The mathematical characteristics of the BCC model allow the DMUs that have the

lowest value in one of the inputs (or the highest value in one of the outputs) to be considered

efficient, even if the other variables do not have the best relations (Ali, 1993). These DMUs

are called false efficient, efficient from the start or by default.

6 The efficiency scores may be obtained with constant returns to scale (CRS) or variable returns to scale

(VRS). With CRS, the assumption is that DMUs are capable of linearly scaling the inputs and outputs, without

affecting efficiency. In other words, there is no significant relationship between the scale of operations and

efficiency. With VRS, an increase in inputs does not result in a proportional change in the outputs.

11

In order to better understand the results obtained by standard DEA models, some

complementary models emerged, such as the super-efficiency model (Andersen & Peterson,

1993) or the Inverted DEA model (Yamada, Matui & Sugiyama, 1994). Although these are

not very recent in the literature, there are few empirical studies that used these approaches.7

Most of the time, the limitations of the DEA standard model are ignored.

In this empirical application, we will use Inverted DEA (IDEA), based on the

inversion between inputs and outputs, to identify false efficient DMUs in the BCC model.

While standard DEA models are considered optimistic - DMUs are considered efficient

through the subset of variables that are more favourable to them - IDEA models represent a

pessimistic assessment of each DMU, since the inverted frontier is composed of the worst

DMUs with poor practices, and it represents an “inefficient frontier”. Thus, the higher the

level of inverted efficiency, the lower the efficiency of the DMU.

To provide a more realistic assessment of the “true” efficiency score, we follow Meza

et al. (2007) and compute a compound PTE* score, following:

𝐶𝑜𝑚𝑝𝑜𝑢𝑛𝑑 𝑃𝑇𝐸∗ = 𝑃𝑇𝐸𝐷𝐸𝐴 + (1 − 𝑃𝑇𝐸𝐼𝐷𝐸𝐴

∗ )

2

Because IDEA reflects a measure of inefficiency, its complement is used to get the

average of efficiency levels. Lastly, the normalized compound efficiency score is computed,

dividing each DMU’ value by the higher value.

In the second stage, we perform individual regressions for each year and using the

whole sample (through a pooled cross-section regression) against several potential exogenous

7 Notably exceptions using Inverted DEA models include Meza et al., (2007), Entani et al., (2002), Pimenta et al.

(2004) and Mello et al., (2005), although not in Local Governments’ context. Authors using DEA super-

efficiency models include Cruz and Marques (2014) and Liu et al. (2011).

12

variables. The efficiency scores are proportions, therefore classified as a fractional response

variable, ranging from 0–1. We use the generalized linear models (GLM) approach, first

proposed by Papke and Wooldridge (1996), with robust standard errors and quasi-maximum

likelihood estimation. Several functional forms for the conditional mean of y that enforce the

conceptual requirement that 𝐸(𝑦|𝑥) is in the unit interval, may be used. We have,

𝐸(𝑦|𝑥) = 𝐺(𝑧) (1)

where G(. ) is a known nonlinear function satisfying 0 < G(. ) < 1. The logistic and standard

normal specifications for G(. ) are symmetric about the point 0.5 and consequently approach 0

and 1 at the same rate. Given our data and testing for both models, logit and probit, a

fractional logit model was used.8

Here, it is important to stress that traditional linear models or Tobit approaches to

second-stage DEA analysis do not constitute a reasonable data-generating process for DEA

scores. Following Ramalho, Ramalho and Henriques (2010), the standard linear model using

OLS is not appropriate since the predicted values of 𝑦 may lie outside the unit interval and the

implied constant marginal effects of the covariates on 𝑦 are not compatible with both the

bounded nature of DEA scores and the existence of a mass point at unity in their distribution.

A different approach is to use a two-limit Tobit model, but this is also problematic. In DEA

applications, there is an accumulation of observations at unity, and this is a natural

consequence of the DEA methodology rather than the result of a censoring mechanism. In

addition, efficiency scores of zero are typically not observed.

Two particular problems arise from using DEA scores in the second-stage regression

analysis: first, the input/output variables used in the first stage may be correlated with the

explanatory variables used in the second stage; and second, DEA scores are dependent on

8 For a detailed analysis of fractional response models (FRMs), see Ramalho, Ramalho and Murteira (2011).

13

each other, which is against the within-sample independence requirement. Therefore, the

standard approaches to statistical inference are invalid and the estimated effects of the

environmental variables on DMUs efficiency may be inconsistent. Simar and Wilson (2007)

proposed two alternative bootstrap methods to construct confidence intervals, and although

these algorithms solved some of the theoretical limitations of traditional regression models,

they still impose a restrictive condition of separability between the input-output space and the

space of external variables that should be tested in advance. This separability restriction

implies to assume that the exogenous variables included in the second stage cannot affect the

support of the input and output variables included in the first stage, which is often an

unrealistic assumption (Cordero et al., 2016).

In this research, we follow a different approach, adopting FRMs following Ramalho et

al. (2010).9 Under the assumption that DEA scores are observed measures of the relative

performance of units in the sample, FRMs are the most natural way of modelling bounded,

proportional response variables such as DEA scores. Advantages of using FRMs include the

fact that they may be estimated by quasi-maximum likelihood, unlike Tobit models, FRMs do

not require assumptions about the conditional distribution of DEA scores or

heteroskedasticity patterns.

4.1. Data and variables

The empirical analysis is based on the 278 mainland municipalities. We adopt a similar

approach as Afonso and Santos (2008) and Cordero et al. (2016) and the 30 overseas

municipalities were excluded. Differences in the territorial organization, the fact that

inhabitants of the islands may have different needs from those living in continental Europe,

9 Other approaches were also tested. See for instance, the nonparametric kernel regression (Balaguer-Coll, Prior

& Tortosa-Ausina, 2007), or the conditional nonparametric approach (Asatryan & De Witte, 2015; Cordero

et al., 2016).

14

and the status of ultra-peripheral regions that allow them to receive additional European

Union’s funds, are among the reasons for that exclusion (Costa et al., 2015).

Following the criteria of Carvalho et al. (2016), we group municipalities by population

size: small ≤ 20 000 inhabitants; medium > 20 000 and ≤ 100 000 inhabitants; large >

100 000 inhabitants. Results by size and by regions (NUTS II) are presented in Table 1.

Table 1: Distribution of municipalities by size and NUTS II

NUTS II Small Medium Large Total

regions N % N % N %

Norte 46 53.5% 30 34.9% 10 11.6% 86

Centro 63 63.0% 35 35.0% 2 2.0% 100

Lisboa 1 5.6% 6 33.3% 11 61.1% 18

Alentejo 45 77.6% 13 22.4% 0

58

Algarve 7 43.8% 9 56.3% 0

16

Portugal mainland 162 58.3% 93 33.5% 23 8.3% 278

The majority of municipalities are small (58.3% of the total), particularly in the

Alentejo, Centro and Norte regions. By contrast, the Lisboa region has 11 municipalities with

more than 100 000 inhabitants.

The choice of the inputs and outputs is critical for the DEA model. Our model uses

one input variable - current expenditures - and four output variables:

Resident population (number);

Area of the municipality (measured in Km2);

Kindergarten and primary education students (number of enrolled students);

Senior citizens, older than 65 years (number).

According to Narbón-Perpiña and De Witte (2017a), current expenditures are the most

widely used input indicator to measure the costs incurred by municipalities to provide local

services. Capital expenditures are not included since they are highly volatile, being affected

15

by large infrastructure investments made by municipalities. As already mentioned, the

selection of outputs must proxy the specific municipalities responsibilities, defined by law.

We use resident population and the area of the municipality as measures of the total demand

of public services.10 Education and social services (the care for elderly) are measured by the

number of enrolled students in kindergarten and primary education and by the number of

senior citizens older than 65 years old, respectively.

For the years of 2010 and 2015, standard DEA models were estimated using CRS and

VRS and the IDEA model was estimated adopting VRS (the BCC model), with an input

minimization orientation. With an input-oriented DEA model, the goal is to study how much

input quantities can be proportionally reduced in order to keep the same quantities of outputs

produced. This is a rational option for local governments that are facing pressures to reduce

costs and simultaneously to maintain a certain level of services.

The input data used to perform the DEA analysis was obtained from the

municipalities’ annual reports from Portal Autárquico (available online at

http://www.portalautarquico.pt/). Concerning output variables, data was collected from the

Portuguese National Statistics Institute.

Differences in the operational environment of each municipality may affect

performance outcomes. Any study about local governments’ efficiency that do not control for

this heterogeneity, will have only a limited value (Cruz & Marques, 2014).

Therefore, in the second stage, exogenous factors were tested as independent variables

to explain the compound efficiency scores. These factors that are beyond municipalities’

control were grouped in several dimensions in order to characterize the operational

environment of each municipality. We consider the following variables:

10 These two indicators are among the most used, 46 papers used total population and 10 papers the municipal

area. For more details, see Narbón-Perpiña and De Witte (2017a).

16

Table 2: Exogenous variables definition

Dimension Variable Definition

Social and demographic

determinants

Population density (-) The number of inhabitants of each municipality divided by its

extension (measured in squared kilometres)

Education level (+) The number of students enrolled in primary, secondary and

tertiary education divided by the resident population

Economic determinants Unemployment (-) The percentage of unemployment related to the working

population of each municipality

Political determinants Democratic

participation (+)

It represents the political participation of the citizens in local

elections. It is measured by the number of votes divided by the

total number of citizens entitled to vote

Financial determinants Debt (-) Measured by the weight of financial liabilities on total

municipalities' assets

Geographical determinants Coastal (+) A dummy variable to account if the municipality is on the littoral,

has a coastal area (1) or not (0)

Territory organization Parishes (-) Number of civil parishes

Data on each municipality was obtained for the years of 2010 and 2015. Concerning

the variables, the dummy on the coastal location and the variable of Democratic participation

were computed by the authors, as well as the variable Debt, using information available on

http://www.portalautarquico.pt/. It should be noted that Democratic participation is related

the local elections of 2009 and 2013 and is used as a proxy for the years 2010 and 2015,

respectively. The remaining variables were obtained through online INE and PORDATA

databases.

We expect that if the population concentration is larger, it will increase the costs of

providing public services (due to higher complexity, congestion) and it will lower the average

efficiency. However, the effect of this variable on efficiency is not straightforward, see, for

instance, Afonso and Santos (2008) or Lo Storto (2016).

By contrast, more educated citizens will demand better public services, which will

have a positive effect on the efficiency level of each municipality. The same effect is expected

concerning the democratic participation variable. Geys, Heinemann and Kalb (2010) reported

that higher voter involvement is indeed associated with increased government efficiency.

17

Regarding unemployment and debt, it is expected that municipalities’ facing high

levels of unemployment and debt to be less efficient. Several authors reported that higher

income citizens paying greater taxes will require more and better local services and facilities

(Afonso & Fernandes, 2008; Asatryan & De Witte, 2015). Municipalities’ debt has been a

major concern in recent years and we expected higher levels of indebtedness to affect

negatively efficiency, as a higher share of resources will be employed in payments: interests

and amortizations (Cruz & Marques, 2014; Geys, 2006; Geys & Moesen, 2009). A positive

relation with efficiency is expected for coastal location. Municipalities near the coast are able

to achieve higher levels of development and as a consequence, to increase tax revenues

(Cordero et al., 2016). Lastly, the number of civil parishes is included to ascertain if their

reduction has the expected effect of increasing efficiency, supporting the argument of scale

economies. The expected effect, of these variables on the efficiency score, is presented in

brackets in the table above and Appendix A presents the descriptive statistics.

It should be noted that there is a wide variety of efficiency’ determinants that may be

considered and results are strongly dependent on the variables and models chosen by the

authors. Many determinants present ambiguous and mixed effects and results should be

interpreted with caution since they are country-specific (for a detail analysis of these results,

see Narbón-Perpiña & De Witte, 2017b).

5. Empirical Results

5.1. First-stage DEA results

All the results were obtained using DEAP software. It should be emphasized, that the results

by municipality are quite uneven (results on each municipality are presented in Appendix B).

Next table reports the results by NUTS II regions, for both years under analysis.

18

Table 3: Average DEA scores for municipalities grouped by regions for the years 2010 and 2015

NUTS II N

2010 2015

regions OTE PTE SE PTE* OTE PTE SE PTE*

Norte 86 0.622 0.733 0.838 0.678 0.609 0.721 0.839 0.666

Centro 100 0.617 0.758 0.815 0.707

0.623 0.768 0.810 0.712

Lisboa 18 0.650 0.736 0.896 0.645

0.701 0.768 0.924 0.685

Alentejo 58 0.621 0.761 0.818 0.666

0.642 0.796 0.813 0.699

Algarve 16 0.418 0.490 0.860 0.424

0.432 0.506 0.859 0.435

Portugal mainland 278 0.610 0.734 0.831 0.669 0.616 0.744 0.830 0.677

Considering the scale of the Portuguese mainland municipalities, on average, results

for both years show that around 17% of inefficiency is explained by scale inadequacy.

However, better results are presented by the Lisboa region, particularly in 2015 (SE = 0.924).

At this purpose, we should recall that 11 of the 18 municipalities of the Lisboa region are

large municipalities, what suggests the existence of economies of scale.

Next, we will focus our analysis on the PTE* score because, as explained before, it is

expected to present a more realistic efficiency measure. The analysis of the results by regions

shows a similar pattern for both years. PTE* is the lowest for the Algarve region and the

highest for the Centro region in both years under analysis. Additionally, all regions exhibit a

slight, but positive trend from 2010 to 2015, with the exception of the Norte, where the

average PTE* score declined 1.77%.

For the full sample of the 278 Portuguese municipalities the average PTE* score is

0.669 in 2010, and 0.677 in 2015, which means that the average municipality in the sample

could have theoretically achieved roughly the same outputs, with about 33.1% and 32.3% ,

fewer resources, respectively.

Grouping the results by municipality’s size, we have the following results (Table 4).

19

Table 4: Average DEA scores by municipalities’ size for the years 2010 and 2015

Comparing 2010 and 2015, a slightly improvement has occurred, in all the three

groups of municipalities, being more notorious in large municipalities. Focusing our attention

on the PTE*, large municipalities grew 4.43% on the average efficiency score. Comparing our

results with previous findings, it is important to note that Jorge et al. (2008) and Cordero et al.

(2016) also report that, on average, large municipalities were more efficient.

Using simple comparisons, the results for both years appear to be not significantly

different. To give support to that claim, we compute a two-group mean comparison test, a

paired t-test achieving -1.37 and as such, not rejecting the null hypothesis, i.e., there is no

statistically significant difference between the average PTE* score for the years of 2010 and

2015.

5.2. Second-stage regression results

In the second stage of the analysis, the efficiency’ determinants were investigated in

2010 and 2015, adopting the fractional logit model. The estimations were conducted using

STATA 14. To avoid collinearity problems, a statistical test was performed using the VIF

(variance inflation factor) measure available in STATA, with no problems identified (mean

VIF in 2010 of 1.25 and, in 2015 of 1.35).11 These results were confirmed by the correlation

matrix (not presented here, for convenience purposes).

11 VIF is an indicator of how much of the inflation of the standard error could be caused by collinearity. As a

rule of thumb, values above 10 should be a cause for concern and must be corrected.

Municipalities N

2010 2015

Size OTE PTE SE PTE* OTE PTE SE PTE*

Small 162 0.561 0.741 0.754 0.644 0.554 0.741 0.751 0.648

Medium 93 0.657 0.695 0.945 0.699

0.683 0.724 0.944 0.711

Large 23 0.761 0.843 0.907 0.722

0.788 0.853 0.927 0.754

Portugal mainland 278 0.610 0.734 0.831 0.669 0.616 0.744 0.830 0.677

20

Next, we applied a specification error test (linktest in STATA) which demonstrated

the meaningfulness of the covariates chosen and a correct assumption for the specified link

function. Table 5 presents the regression results from the fractional logit model for the years

of 2010 and 2015, with robust standard errors and quasi-maximum likelihood estimation. The

third column presents a pooled cross-section regression including all observations and a

dummy for the year (1 if the year is 2015 and 0 for the base year of 2010) and column 4, an

expanded model with interactions between this dummy variable and all the explanatory

variables, to perform a Chow test, in order to check for a structural change across time,

comparing both years.

Table 5. Regression results – Fractional logit regressions

Dependent variable: PTE*

2010 (1) 2015 (2) Pooled Regression

(3)

Expanded Regression

(4) βa AMEb

βa AMEb Unemployment -0.005 -0.0076

-0.033*** -0.0583

-0.019 -0.005

Parishes (nº) 0.016*** 0.0474

0.012*** 0.0262

0.015*** 0.016***

Democratic particip. -2.201*** -0.3029

-1.539*** -0.1966

-1.874*** -2.201***

Debt -1.028*** -0.0483

-0.842*** -0.0274

-0.942*** -1.028***

Pop. density -0.000*** -0.0088

-0.000** -0.0054

-0.000*** -0.000***

Education level 1.681*** 0.0649

1.701*** 0.0550

1.689*** 1.680**

Coastal Dummy -0.449*** -0.0243

-0.361*** -0.0188

-0.403*** -0.449***

Year Dummy

0.008 -0.2

Unemployment_year

-0.029

Parishes_year

-0.004

Democratic part_year

0.662

Debt_year

0.186

Pop. Density_year

0

Education level_year

0.022

Coastal Dummy_year

0.089

Constant 1.977***

1.777***

1.860*** 1.977***

Number of observations 278

278

556 556

Pseudo R2 0.0209

0.0115

0.0159 0.0162

Correlation (y yhat)^2 0.2433

0.1419

0.1916 0.1957

Linktest (p-value hatsq) 0.317 0.692 0.28 0.295 Legend: * statistically significant at 10% level, ** at 5% level, *** at 1% level.

y – observed values; yhat –fitted values (prediction); hatsq - prediction squared. a - Regression coefficients; b – AME – Average Marginal Effects Robust t statistics in parentheses

21

In the individual specifications (1) and (2), almost all the variables appear statistically

relevant in explaining the efficiency of the municipalities, with the exception of the

unemployment rate in 2010. Additionally, the results are very similar comparing both years.

The opposite effect on efficiency levels was obtained for the variables democratic

participation, coastal dummy and the number of parishes. However unexpected, these

findings were in line with previous studies. Cruz and Marques (2014) also find that the

number of civil parishes seem to affect local governments’ efficiency positively. Reinforcing

this idea, Cordero et al. (2016) reported that the reorganization of civil parishes implemented

in 2013 has enhanced more substantially the efficiency of more divided municipalities, i.e.,

those with a higher number of civil parishes.

Concerning the proximity to the sea (coastal dummy), Carosi, D’Inverno and Ravagli

(2014) argued that municipalities with a littoral zone, can be subject to seasonality, which

could have a negative correlation with efficiency.

Contrary to what expected, the coefficient on democratic participation exhibits a

negative sign. This means that the higher the democratic participation of the citizens of each

municipality, the lower its efficiency. Apparently, this result suggests that the higher political

involvement is a citizens’ response to force improvements in inefficient municipalities. The

same negative effect was reported in Cruz and Marques (2014).

Discussing the expected results, we have a strong and positive effect of the variable

Education level on efficiency. A more educated population contributes to the improvement of

performance of each municipality, supporting the findings of Afonso and Fernandes (2008)

that already demonstrated the importance of the education level on efficiency.

A higher concentration of the population affects negatively the municipality’s

efficiency, in line with the results of Geys (2006). Although, it is not a strong economic result

22

if we analyse the average marginal effect. Debt and unemployment rate also report a negative

sign.

Performing a Chow test, comparing models 3 and 4, in order to explore the existence

of a structural change comparing the years of 2010 and 2015, it is possible to see that none of

the interactions terms were statistically significant and the Likelihood Ratio test performed

returned a p-value of 0.999, meaning that we cannot reject the null hypothesis, i.e., all the

coefficients on the dummy and related interactions terms are zero.12 That suggests that no

meaningful changes occurred from one year to the other. On this regard, Cordero et al. (2016)

already noted that over the period 2009-2014, no relevant changes were detected, leading to

the conclusion that the reforms to improve municipalities’ efficiency were not successful.

6. Conclusions

The current austerity forces public institutions to show value for money. Resources

should be spend as effective and efficient as possible. The main purpose of this research is to

evaluate efficiency of municipalities in Portugal mainland and to explore the importance of

potential factors in improving their performance. The analysis is conducted in two different

years 2010 and 2015, to detect if significant changes occurred after the reforms implemented

in local governments administration.

Answering our first question - Is there anything new after Troika’s intervention in

Portugal, concerning Local Governments’ Efficiency? – We find evidence that no significant

difference exists before and after the Troika intervention in Portugal.

12 The same conclusion and identical p-value is achieved if we compare the full model (3), with the two sub-sets

of the data (model 1 and 2).

23

This is verified in the DEA analysis, with similar results in both years. The average

PTE* score changed slightly from 0.669 to 0.677 and PTE* is the lowest for the Algarve

region and the highest for the Centro region. In addition, large municipalities tend to perform

better. In the second stage, through fractional logit models, the results obtained are very close

comparing the years of 2010 with 2015. Education level and the number of parishes affect

positively efficiency. The opposite effect is verified with debt, unemployment, proximity to

the sea and democratic participation of the citizens. The Chow test performed confirmed that

no structural change occurred from 2010 to 2015, providing further evidence to the claim that

no meaningful changes were detected concerning local governments’ efficiency after the

Troika’s intervention in Portugal.

Some policy recommendations may be drawn from this research. From the DEA

analysis, there is evidence that some efficiency improvements may be possible in several

municipalities. In the second stage, debt and the number of parishes effectively influence

municipalities’ efficiency levels. But only debt has the expected effect. The reduction of the

number of parishes (a measure adopted to fulfil the requirements of the bailout agreement) do

not appear a successful measure.

From a methodological point of view, this paper uses more realistic DEA scores,

adopting a compound measure of efficiency (the average between standard DEA and Inverted

DEA scores). In the second stage, fractional response models are used. To the best of our

knowledge, this is the first empirical study adopting these methodologies in order to measure

and explain the efficiency of local governments.

As already mentioned, results are strongly dependent from the variables and methods

used in the analysis and conclusions (with the correspondent policy implications) should be

country specific. However, it should be noted that our results are, to a certain extent, in line

with previous studies about the efficiency of local governments in Portugal. Topics for further

24

research include to test additional exogenous variables for the second stage and to account for

possible effects of reversed causality (for instance, with debt and efficiency levels) and

endogeneity. Unobserved factors that affect a municipality’s score of efficiency in one year

will also affect its score in a different year requiring more advanced methods (panel data

methods) to handle this feature.

25

References

Afonso, A. & Fernandes, S. (2006) Measuring local government spending efficiency:

evidence for the Lisbon region. Regional Studies. 40(1), 39-53.

Afonso, A. & Fernandes, S. (2008) Assessing and explaining the relative efficiency of local

government. Journal of Socio - Economics. 37(5), 1946–1979.

Ali, A. I. (1993) Streamlined computation for data envelopment analysis. European journal of

operational research. 64, 61-67.

Andersen, P. & Petersen, N. C. (1993) A procedure for ranking efficient units in data

envelopment analysis. Management Science. 39, 1261–1264.

Asatryan, Z. & De Witte, K. (2015) Direct democracy and local government efficiency.

European Journal of Political Economy. 39, 58–66.

Balaguer-Coll, M. T., Prior, D. & Tortosa-Ausina, E. (2007) On the determinants of local

government performance: a two-stage nonparametric approach. European Economic Review.

51(2), 425–451.

Banker, R., Charnes, A. & Cooper, W. (1984) Some models for estimating technical and scale

inefficiencies. Journal of Management Science. 30 (9), 1078-1092.

Bosch, N., Pedraja, F., & Suarez-Pandiello, J., (2000) Measuring the efficiency of Spanish

municipal refuse collection services. Local Government Studies. 26(3), 71–90.

Byrnes, J., Crase, L., Dollery, B. & Villano, R. (2010) The relative economic efficiency of

urban water utilities in regional New South Wales and Victoria. Resource and Energy

Economics. 32(3), 439-455.

Carosi, L., D’Inverno, G. & Ravagli, L. (2014) Global public spending efficiency in Tuscan

municipalities. Technical Report No. 175, Dipartimento di Economia e Management (DEM),

University of Pisa, Italy.

26

Carvalho, J., Fernandes, M. J., Camões, P. & Jorge, S. (2016) Anuário financeiro dos

municípios portugueses 2015. (Financial Yearbook of Portuguese Municipalities 2015),

Ordem dos Contabilistas Certificados. Lisbon.

Charnes, A., Cooper, W. & Rhodes, E. (1978) Measuring the efficiency of decision making

units. European Journal of Operational Research. 2(6), 429-444.

Cordero, J. M., Pedraja-Chaparro, F., Pisaflores, E. C. & Polo, C. (2016) Efficiency

assessment of Portuguese municipalities using a conditional nonparametric approach.

Technical report no. 70674, Munich University Library, Germany.

Costa, H. Veiga, L. G. & Portela, M. (2015) Interactions in Local Governments' Spending

Decisions: Evidence from Portugal. Regional Studies. 49(9), 1441-1456.

Cruz, N. F. & Marques, R. C. (2014) Revisiting the determinants of local government

performance. Omega. 44, 91–103.

Entani, T., Maeda, Y. & Tanaka, H. (2002) Dual models of interval DEA and its extensions to

interval data. European Journal of Operational Research, 136, 32-45.

Geys, B. (2006) Looking across borders: a test of spatial policy interdependence using local

government efficiency ratings. Journal of Urban Economics. 60(3), 443–462.

Geys, B. & Moesen, W. (2009) Exploring sources of local government technical inefficiency:

evidence from Flemish municipalities. Public Finance and Management. 9(1), 1–29.

Geys, B., Heinemann, F. & Kalb, A. (2010) Voter involvement, fiscal autonomy and public

sector efficiency: evidence from German municipalities. European Journal of Political

Economy. 26(2), 265–278.

Jorge, S. M., Camões, P. J., Carvalho, J. & Fernandes M. J. (2008) Portuguese Local

Government relative efficiency: A DEA approach. Workshop on Performance, Measurement

and Output Based Budgeting in the Public Sector, Hamburg. Available from:

http://hdl.handle.net/1822/8229. [Accessed 20 April 2017].

27

Liu, S.-C., Peng, P.S.-Y.,C.-J., & Wu, P.-C. (2011) Local government efficiency evaluation:

consideration of undesirable outputs and super-efficiency. African Journal of Business

Management. 5(12), 4746–4754.

Lo Storto, C. (2016) The trade-off between cost efficiency and public service quality: a non-

parametric frontier analysis of Italian major municipalities. Cities. 51, 52–63.

Mello, J. S., Gomes, E.G., Meza, L. A., Biondi Neto, L. & Sant’Anna, A.P. (2005) Fronteiras

DEA difusas. Investigação Operacional. 25 (1), 85-103.

Meza, L. A., Mello, J. S., Gomes, E. G., & Fernandes, A. S. (2007) Selecção de variáveis em

DEA aplicada a uma análise do mercado de energia eléctrica. Investigação Operacional, 27

(1), 21-36.

Narbón-Perpiñá, I. and De Witte, K. (2017a) Local governments' efficiency: A systematic

literature review — part I. International Transactions in Operational Research.

doi:10.1111/itor.12364

Narbón-Perpiñá, I. and De Witte, K. (2017b) Local governments' efficiency: a systematic

literature review — part II. International Transactions in Operational Research.

doi:10.1111/itor.12389

Papke, L. E. & Wooldridge, J. (1996) Econometric methods for fractional response variables

with an application to 401(k) plan participation rates. Journal of Applied Econometrics. 11(6),

619–632.

Picazo, T., González, G. F. & Sáez, F. J. (2009) Accounting for operating environments in

measuring water utilities’ managerial efficiency. The Service Industries Journal. 29 (6), 761-

773.

Pimenta, H., Macedo, M. & Mello, J. S. (2004) Decisão de realização de investimentos em

tecnologia da informação com análise envoltória de dados. Produção Online. 4 (2).

28

Ramalho, E., Ramalho, J. & Henriques, P. (2010) Fractional regression models for second

stage DEA efficiency analyses. Journal of Productivity Analysis. 34 (3), 239-255.

Ramalho, E., Ramalho, J. & Murteira, J. (2011) Alternative estimating and testing empirical

strategies for fractional regression models. Journal of Economic Surveys. 25 (1), 19–68.

Ray, S. (2004) Data Envelopment Analysis, Theory and Techniques for Economics and

Operations Research. Cambridge: Cambridge University Press.

Ruggiero, J. (2007) A comparison of DEA and the stochastic frontier model using panel data.

International Transactions in Operational Research. 14(3), 259–266.

Simar, L. & Wilson, P. W. (2007) Estimation and inference in two-stage, semi-parametric

models of production processes. Journal of Econometrics. 136(1), 31–64.

Simar, L., & Wilson, P. W. (2011) Two-stage DEA: caveat emptor. Journal of Productivity

Analysis. 36(2), 205-218.

Tavares, A. F., Rodrigues, M., Magalhães, C. & Carr, J. (2012) The Economic and Political

Impacts of Top-Down Territorial Reforms: The Case of Portuguese Parishes. Conferência

International Science Association de 08/07/2012, Madrid, Espanha.

Yamada, Y., Matui, T. & Sugiyama, M. (1994) New analysis of efficiency based on DEA.

Journal of the Operations Research Society of Japan. 37(2), 158-167.

29

Appendix A: Descriptive statistics of the variables used in the regression

Appendix B: Detailed DEA results for all the Municipalities

Municipality 2010 2015

OTE PTE SE Compound

PTE* OTE PTE SE

Compound PTE*

Abrantes 0.785 0.791 0.993 0.826

0.837 0.856 0.978 0.856

Águeda 0.66 0.661 0.999 0.739

0.776 0.799 0.971 0.837

Aguiar da Beira 0.484 0.803 0.603 0.691

0.47 0.78 0.603 0.704

Alandroal 0.44 0.505 0.872 0.289

0.634 0.753 0.843 0.679

Albergaria-a-Velha 0.662 0.743 0.891 0.780

0.69 0.777 0.888 0.802

Albufeira 0.224 0.247 0.905 0.139

0.256 0.269 0.953 0.154

Alcácer do Sal 0.897 1 0.897 0.775

0.829 1 0.829 0.706

Alcanena 0.527 0.664 0.794 0.674

0.559 0.698 0.8 0.683

Alcobaça 0.785 0.807 0.973 0.851

0.839 0.853 0.983 0.887

Alcochete 0.43 0.549 0.783 0.564

0.535 0.614 0.871 0.587

Alcoutim 0.774 0.908 0.853 0.512

0.683 0.851 0.802 0.488

Alenquer 0.641 0.654 0.979 0.721

0.664 0.701 0.947 0.765

Alfândega da Fé 0.302 0.409 0.737 0.230

0.448 0.617 0.726 0.559

Alijó 0.612 0.768 0.796 0.784

0.531 0.661 0.804 0.713

Aljezur 0.425 0.576 0.738 0.512

0.405 0.557 0.728 0.486

Aljustrel 0.575 0.687 0.838 0.679

0.587 0.711 0.825 0.730

Almada 0.843 1 0.843 0.842

0.869 0.927 0.938 0.817

Almeida 0.574 0.664 0.865 0.549

0.699 0.804 0.869 0.731

Almeirim 0.604 0.664 0.91 0.723

0.72 0.797 0.904 0.823

Almodôvar 0.757 0.811 0.934 0.690

0.722 0.781 0.924 0.662

Alpiarça 0.479 0.756 0.634 0.660

0.548 0.88 0.622 0.763

Alter do Chão 0.651 0.848 0.767 0.673

0.572 0.808 0.709 0.637

Alvaiázere 0.7 0.991 0.706 0.824

0.717 1 0.717 0.868

Alvito 0.622 0.961 0.647 0.670

0.577 0.978 0.59 0.645

Amadora 0.695 0.832 0.836 0.602

0.862 0.982 0.878 0.701

Variable Obs Mean Std. Dev. Min Max Mean Std. Dev. Min Max

PTE* 278 0.6690 0.1589 0.139 1 0.6775 0.1511 0.154 1

coastal Dummy 278 0.2302 0.4217 0 1 0.2302 0.4217 0 1

Unemployment 278 7.6284 2.2507 2.2 15.9 8.0385 2.3910 4 16.1

Parishes (nº) 278 14.5684 12.7764 1 89 10.3669 8.7444 1 61

Democratic particip. 278 0.6362 0.0758 0.4406 0.81118 0.5907 0.0913 0.3777 0.8139

Debt 278 0.2126 0.1273 0.0052 0.7025 0.1471 0.1164 0.0099 0.7314

Pop. density 278 311.6906 866.8126 5.2 7366.4 303.6540 830.7053 4.4 7413.7

Education level 278 0.1822 0.0614 0.0620 0.5250 0.1522 0.0556 0.0572 0.5290

2010 2015

30

Amarante 0.727 0.744 0.977 0.806

0.736 0.764 0.964 0.816

Amares 0.643 0.78 0.824 0.776

0.566 0.704 0.804 0.678

Anadia 1 1 1 0.982

0.869 0.923 0.942 0.903

Ansião 0.817 1 0.817 0.942

0.687 0.872 0.788 0.846

Arcos de Valdevez 0.745 0.766 0.973 0.761

0.664 0.711 0.934 0.656

Arganil 0.552 0.693 0.796 0.728

0.59 0.739 0.799 0.794

Armamar 0.354 0.619 0.573 0.535

0.344 0.617 0.558 0.507

Arouca 0.624 0.717 0.87 0.770

0.68 0.771 0.882 0.826

Arraiolos 0.865 0.946 0.914 0.823

0.862 0.954 0.904 0.884

Arronches 0.735 1 0.735 0.731

0.686 1 0.686 0.704

Arruda dos Vinhos 0.49 0.651 0.752 0.654

0.593 0.728 0.815 0.692

Aveiro 0.61 0.618 0.987 0.666

0.742 0.75 0.989 0.779

Avis 0.698 0.799 0.874 0.563

0.699 0.831 0.841 0.669

Azambuja 0.513 0.588 0.872 0.663

0.633 0.712 0.889 0.774

Baião 0.592 0.69 0.857 0.734

0.558 0.662 0.843 0.683

Barcelos 0.841 0.844 0.997 0.881

0.924 0.943 0.98 0.954

Barrancos 0.385 0.839 0.459 0.473

0.436 1 0.436 0.573

Barreiro 0.766 0.837 0.915 0.697

0.871 0.876 0.994 0.747

Batalha 0.668 0.84 0.796 0.832

0.576 0.706 0.817 0.707

Beja 0.858 0.881 0.973 0.897

0.851 0.865 0.984 0.855

Belmonte 0.604 0.981 0.615 0.807

0.448 0.778 0.576 0.696

Benavente 0.67 0.737 0.909 0.777

0.832 0.882 0.943 0.895

Bombarral 0.55 0.708 0.776 0.683

0.492 0.627 0.785 0.586

Borba 0.447 0.686 0.651 0.608

0.439 0.685 0.641 0.641

Boticas 0.538 0.73 0.737 0.636

0.537 0.728 0.738 0.678

Braga 1 1 1 0.882

0.822 0.882 0.932 0.778

Bragança 0.573 0.579 0.989 0.573

0.673 0.681 0.988 0.680

Cabeceiras de Basto 0.663 0.828 0.8 0.838

0.539 0.644 0.836 0.693

Cadaval 0.611 0.731 0.836 0.744

0.583 0.726 0.803 0.725

Caldas da Rainha 0.845 0.869 0.972 0.886

0.947 0.975 0.972 0.961

Caminha 0.416 0.49 0.849 0.481

0.442 0.534 0.828 0.503

Campo Maior 0.462 0.677 0.681 0.650

0.588 0.771 0.762 0.734

Cantanhede 0.794 0.803 0.989 0.839

0.949 0.978 0.971 0.977

Carrazeda de Ansiães 0.511 0.733 0.697 0.639

0.603 0.836 0.721 0.790

Carregal do Sal 0.602 0.859 0.701 0.796

0.669 0.952 0.702 0.861

Cartaxo 0.509 0.548 0.929 0.599

0.473 0.528 0.895 0.536

Cascais 0.485 0.541 0.896 0.338

0.497 0.526 0.945 0.369

Castanheira de Pêra 0.448 1 0.448 0.563

0.385 1 0.385 0.573

Castelo Branco 1 1 1 1

1 1 1 0.982

Castelo de Paiva 0.737 0.941 0.783 0.882

0.653 0.794 0.823 0.759

Castelo de Vide 0.52 0.781 0.666 0.602

0.526 0.848 0.62 0.659

Castro Daire 0.594 0.718 0.828 0.776

0.562 0.667 0.842 0.726

Castro Marim 0.318 0.45 0.706 0.367

0.35 0.482 0.726 0.386

Castro Verde 0.59 0.668 0.883 0.574

0.625 0.722 0.866 0.647

Celorico da Beira 0.301 0.45 0.669 0.407

0.437 0.627 0.697 0.657

Celorico de Basto 0.521 0.597 0.872 0.635

0.549 0.655 0.839 0.681

31

Chamusca 0.946 1 0.946 0.926

0.964 1 0.964 0.967

Chaves 0.788 0.799 0.986 0.854

0.598 0.609 0.982 0.581

Cinfães 0.73 0.848 0.861 0.868

0.546 0.636 0.858 0.689

Coimbra 0.601 0.717 0.839 0.664

0.769 0.856 0.898 0.814

Condeixa-a-Nova 0.659 0.798 0.826 0.757

0.576 0.708 0.814 0.683

Constância 0.354 0.801 0.442 0.509

0.4 0.859 0.466 0.559

Coruche 0.814 0.83 0.981 0.805

0.935 0.943 0.991 0.888

Covilhã 0.828 0.851 0.973 0.873

1 1 1 0.990

Crato 0.632 0.797 0.793 0.572

0.599 0.796 0.752 0.597

Cuba 0.414 0.778 0.533 0.641

0.49 0.892 0.549 0.736

Elvas 0.583 0.647 0.902 0.703

0.575 0.617 0.931 0.626

Entroncamento 0.591 0.708 0.835 0.399

0.588 0.692 0.85 0.397

Espinho 0.48 0.505 0.95 0.310

0.514 0.552 0.931 0.324

Esposende 0.723 0.809 0.894 0.791

0.67 0.738 0.908 0.726

Estarreja 0.592 0.641 0.924 0.681

0.792 0.88 0.901 0.857

Estremoz 0.589 0.693 0.851 0.734

0.619 0.71 0.871 0.742

Évora 0.553 0.555 0.997 0.598

0.649 0.652 0.995 0.675

Fafe 0.636 0.658 0.966 0.728

0.657 0.691 0.952 0.739

Faro 0.728 0.734 0.992 0.780

0.676 0.694 0.975 0.738

Felgueiras 0.644 0.668 0.964 0.652

0.655 0.68 0.964 0.666

Ferreira do Alentejo 0.587 0.645 0.911 0.563

0.685 0.762 0.899 0.713

Ferreira do Zêzere 0.542 0.762 0.711 0.727

0.483 0.696 0.695 0.697

Figueira da Foz 0.736 0.763 0.966 0.788

0.774 0.787 0.984 0.797

Figueira Castelo Rodrigo 0.648 0.755 0.859 0.676

0.528 0.618 0.855 0.515

Figueiró dos Vinhos 0.455 0.728 0.626 0.630

0.47 0.733 0.642 0.681

Fornos de Algodres 0.214 0.385 0.556 0.217

0.487 0.941 0.518 0.748

Freixo de Espada à Cinta 0.407 0.629 0.648 0.463

0.412 0.671 0.614 0.527

Fronteira 0.573 0.906 0.633 0.726

0.504 0.852 0.591 0.676

Fundão 0.795 0.824 0.966 0.851

0.691 0.729 0.948 0.719

Gavião 0.646 0.91 0.71 0.650

0.606 0.868 0.698 0.637

Góis 0.502 0.745 0.673 0.618

0.415 0.632 0.657 0.538

Golegã 0.348 0.697 0.5 0.530

0.382 0.725 0.527 0.575

Gondomar 0.902 0.914 0.987 0.806

0.854 0.869 0.982 0.793

Gouveia 0.842 0.967 0.871 0.919

0.759 0.884 0.859 0.879

Grândola 0.458 0.48 0.954 0.388

0.493 0.519 0.949 0.406

Guarda 0.609 0.635 0.959 0.717

0.526 0.547 0.96 0.578

Guimarães 0.786 0.795 0.989 0.763

0.762 0.781 0.975 0.775

Idanha-a-Nova 1 1 1 0.701

0.813 0.93 0.874 0.533

Ílhavo 0.662 0.692 0.957 0.669

0.802 0.866 0.926 0.801

Lagoa 0.309 0.358 0.866 0.328

0.302 0.341 0.884 0.268

Lagos 0.304 0.327 0.93 0.319

0.258 0.28 0.922 0.160

Lamego 0.727 0.782 0.93 0.814

0.481 0.538 0.895 0.554

Leiria 0.838 0.881 0.951 0.895

1 1 1 1

Lisboa 0.427 1 0.427 0.563

0.438 1 0.438 0.573

Loulé 0.298 0.301 0.99 0.170

0.341 0.342 0.999 0.222

Loures 0.616 0.684 0.9 0.599

0.693 0.741 0.935 0.684

32

Lourinhã 0.489 0.542 0.901 0.595

0.494 0.555 0.889 0.593

Lousã 0.533 0.66 0.808 0.692

0.477 0.579 0.824 0.611

Lousada 0.675 0.732 0.921 0.655

0.737 0.767 0.96 0.686

Mação 0.552 0.694 0.795 0.594

0.558 0.684 0.816 0.613

Macedo de Cavaleiros 0.638 0.691 0.923 0.718

0.564 0.605 0.932 0.475

Mafra 0.527 0.535 0.986 0.621

0.645 0.647 0.997 0.716

Maia 0.819 0.82 0.999 0.685

0.847 0.879 0.964 0.782

Mangualde 0.572 0.638 0.896 0.696

0.597 0.687 0.869 0.720

Manteigas 0.36 0.825 0.436 0.506

0.201 0.484 0.415 0.277

Marco de Canaveses 0.845 0.903 0.936 0.898

0.848 0.875 0.969 0.879

Marinha Grande 0.659 0.678 0.971 0.738

0.746 0.792 0.943 0.814

Marvão 0.435 0.825 0.527 0.531

0.493 0.995 0.495 0.595

Matosinhos 0.669 0.687 0.972 0.538

0.675 0.702 0.962 0.602

Mealhada 0.623 0.697 0.893 0.697

0.643 0.742 0.867 0.703

Mêda 0.512 0.729 0.702 0.607

0.517 0.725 0.713 0.650

Melgaço 0.543 0.678 0.801 0.573

0.501 0.627 0.799 0.560

Mértola 1 1 1 0.722

1 1 1 0.677

Mesão Frio 0.248 0.553 0.448 0.312

0.341 0.957 0.356 0.548

Mira 0.471 0.603 0.782 0.554

0.489 0.645 0.758 0.578

Miranda do Corvo 0.61 0.804 0.758 0.767

0.581 0.744 0.781 0.702

Miranda do Douro 0.655 0.768 0.852 0.688

0.607 0.711 0.855 0.687

Mirandela 0.529 0.593 0.893 0.661

0.555 0.608 0.913 0.613

Mogadouro 0.803 0.856 0.938 0.769

0.727 0.753 0.966 0.651

Moimenta da Beira 0.573 0.826 0.694 0.807

0.499 0.702 0.71 0.733

Moita 0.725 0.73 0.993 0.643

0.724 0.738 0.981 0.660

Monção 0.702 0.742 0.947 0.717

0.711 0.808 0.88 0.774

Monchique 0.685 0.855 0.801 0.732

0.577 0.728 0.792 0.684

Mondim de Basto 0.28 0.468 0.599 0.402

0.428 0.694 0.616 0.653

Monforte 0.75 0.932 0.805 0.697

0.771 1 0.771 0.744

Montalegre 0.66 0.697 0.947 0.623

0.664 0.684 0.97 0.438

Montemor-o-Novo 0.775 0.78 0.993 0.695

0.81 0.814 0.996 0.700

Montemor-o-Velho 0.686 0.714 0.961 0.735

0.694 0.76 0.912 0.760

Montijo 0.569 0.581 0.978 0.665

0.724 0.744 0.974 0.810

Mora 0.763 0.923 0.827 0.784

0.713 0.891 0.8 0.765

Mortágua 0.591 0.825 0.717 0.776

0.647 0.864 0.749 0.855

Moura 0.835 0.86 0.971 0.802

0.852 0.879 0.969 0.807

Mourão 0.444 0.658 0.675 0.371

0.475 0.749 0.634 0.429

Murça 0.461 0.78 0.591 0.677

0.464 0.764 0.608 0.706

Murtosa 0.709 1 0.709 0.853

0.749 1 0.749 0.900

Nazaré 0.414 0.519 0.797 0.499

0.389 0.483 0.805 0.418

Nelas 0.462 0.563 0.821 0.590

0.584 0.716 0.816 0.704

Nisa 0.625 0.705 0.886 0.635

0.715 0.798 0.896 0.745

Óbidos 0.273 0.367 0.743 0.323

0.35 0.45 0.778 0.442

Odemira 0.754 1 0.754 0.766

0.755 1 0.755 0.773

Odivelas 0.786 0.811 0.97 0.638

0.803 0.841 0.955 0.672

Oeiras 0.588 0.695 0.846 0.531

0.684 0.759 0.902 0.617

33

Oleiros 0.804 0.954 0.843 0.713

0.657 0.782 0.839 0.551

Olhão 0.535 0.546 0.981 0.590

0.709 0.747 0.949 0.760

Oliveira de Azeméis 0.753 0.754 0.999 0.760

0.826 0.841 0.982 0.815

Oliveira de Frades 0.549 0.789 0.697 0.765

0.583 0.821 0.71 0.794

Oliveira do Bairro 0.619 0.676 0.915 0.678

0.669 0.757 0.884 0.733

Oliveira do Hospital 0.674 0.741 0.909 0.787

0.589 0.662 0.89 0.706

Ourém 0.666 0.677 0.984 0.751

0.701 0.724 0.968 0.782

Ourique 0.723 0.804 0.9 0.634

0.711 0.82 0.867 0.680

Ovar 0.654 0.672 0.973 0.712

0.717 0.75 0.955 0.763

Paços de Ferreira 0.84 0.896 0.938 0.765

0.885 0.91 0.973 0.775

Palmela 0.53 0.542 0.978 0.629

0.553 0.558 0.991 0.628

Pampilhosa da Serra 0.574 0.715 0.803 0.430

0.449 0.572 0.785 0.328

Paredes 0.834 0.849 0.983 0.805

0.742 0.744 0.997 0.730

Paredes de Coura 0.495 0.68 0.728 0.640

0.458 0.639 0.717 0.607

Pedrógão Grande 0.429 0.806 0.532 0.557

0.416 0.885 0.47 0.633

Penacova 0.736 0.894 0.823 0.857

0.642 0.78 0.823 0.769

Penafiel 0.902 0.942 0.958 0.924

0.92 0.928 0.991 0.916

Penalva do Castelo 0.655 0.95 0.689 0.810

0.611 0.887 0.689 0.796

Penamacor 0.874 0.992 0.881 0.761

0.614 0.693 0.885 0.422

Penedono 0.422 0.966 0.436 0.621

0.355 0.884 0.401 0.564

Penela 0.489 0.798 0.612 0.664

0.481 0.814 0.591 0.708

Peniche 0.58 0.62 0.936 0.629

0.647 0.714 0.907 0.681

Peso da Régua 0.541 0.654 0.827 0.673

0.536 0.655 0.818 0.631

Pinhel 0.579 0.68 0.851 0.684

0.645 0.75 0.86 0.736

Pombal 0.898 0.939 0.956 0.948

0.849 0.856 0.992 0.881

Ponte da Barca 0.406 0.537 0.757 0.541

0.434 0.576 0.755 0.583

Ponte de Lima 0.645 0.648 0.994 0.728

0.607 0.635 0.957 0.703

Ponte de Sor 0.741 0.776 0.956 0.793

0.676 0.703 0.962 0.687

Portalegre 0.588 0.636 0.925 0.722

0.684 0.744 0.919 0.816

Portel 0.681 0.765 0.89 0.655

0.638 0.741 0.862 0.666

Portimão 0.415 0.416 0.999 0.469

0.402 0.413 0.972 0.438

Porto 0.632 0.975 0.648 0.704

0.665 0.797 0.834 0.592

Porto de Mós 0.604 0.676 0.893 0.741

0.633 0.704 0.9 0.764

Póvoa de Lanhoso 0.645 0.769 0.839 0.794

0.61 0.716 0.852 0.740

Póvoa de Varzim 0.524 0.546 0.959 0.466

0.602 0.615 0.979 0.562

Proença-a-Nova 0.606 0.764 0.793 0.696

0.586 0.721 0.814 0.735

Redondo 0.484 0.626 0.774 0.591

0.486 0.642 0.757 0.628

Reguengos de Monsaraz 0.524 0.63 0.831 0.641

0.484 0.579 0.837 0.575

Resende 0.447 0.607 0.736 0.614

0.395 0.536 0.738 0.525

Ribeira de Pena 0.302 0.496 0.608 0.446

0.31 0.486 0.637 0.460

Rio Maior 0.442 0.515 0.858 0.589

0.528 0.596 0.887 0.674

Sabrosa 0.409 0.709 0.577 0.619

0.427 0.733 0.583 0.676

Sabugal 0.811 0.855 0.948 0.746

0.679 0.703 0.967 0.418

Salvaterra de Magos 0.762 0.852 0.895 0.876

0.779 0.867 0.899 0.884

Santa Comba Dão 0.576 0.747 0.771 0.721

0.552 0.74 0.746 0.677

Santa Maria da Feira 1 1 1 0.939

1 1 1 0.952

34

Santa Marta de Penaguião

0.457 0.723 0.633 0.544

0.42 0.721 0.582 0.494

Santarém 0.708 0.749 0.945 0.790

0.716 0.721 0.993 0.767

Santiago do Cacém 0.57 0.581 0.982 0.582

0.6 0.613 0.979 0.600

Santo Tirso 0.702 0.702 1 0.715

0.788 0.799 0.987 0.771

São Brás de Alportel 0.381 0.536 0.71 0.553

0.423 0.565 0.749 0.578

São João da Madeira 0.661 0.802 0.825 0.452

0.733 0.83 0.883 0.476

São João da Pesqueira 0.446 0.663 0.672 0.646

0.459 0.668 0.688 0.677

São Pedro do Sul 0.548 0.638 0.859 0.709

0.546 0.631 0.865 0.658

Sardoal 0.297 0.683 0.435 0.429

0.29 0.72 0.403 0.485

Sátão 0.67 0.91 0.736 0.872

0.667 0.877 0.76 0.862

Seia 0.57 0.611 0.933 0.649

0.534 0.581 0.919 0.546

Seixal 0.858 0.865 0.992 0.748

0.78 0.791 0.986 0.720

Sernancelhe 0.517 0.831 0.622 0.718

0.446 0.706 0.631 0.655

Serpa 0.816 0.829 0.984 0.780

0.757 0.771 0.982 0.684

Sertã 0.54 0.638 0.847 0.683

0.618 0.72 0.859 0.759

Sesimbra 0.433 0.447 0.968 0.499

0.451 0.468 0.964 0.519

Setúbal 0.711 0.763 0.932 0.758

0.629 0.637 0.989 0.654

Sever do Vouga 0.743 0.986 0.753 0.903

0.695 0.919 0.756 0.839

Silves 0.399 0.409 0.976 0.422

0.49 0.511 0.96 0.523

Sines 0.24 0.318 0.756 0.222

0.365 0.44 0.83 0.440

Sintra 0.886 1 0.886 0.828

0.941 1 0.941 0.909

Sobral de Monte Agraço 0.453 0.683 0.663 0.603

0.423 0.624 0.678 0.538

Soure 0.805 0.865 0.93 0.852

0.726 0.819 0.887 0.820

Sousel 0.594 0.858 0.692 0.750

0.532 0.78 0.682 0.720

Tábua 0.535 0.718 0.745 0.739

0.585 0.775 0.755 0.785

Tabuaço 0.232 0.428 0.541 0.303

0.42 0.761 0.551 0.665

Tarouca 0.3 0.494 0.607 0.430

0.358 0.596 0.601 0.521

Tavira 0.399 0.433 0.921 0.436

0.5 0.542 0.924 0.561

Terras de Bouro 0.429 0.629 0.682 0.611

0.395 0.573 0.689 0.589

Tomar 0.723 0.738 0.979 0.768

0.759 0.776 0.978 0.783

Tondela 0.688 0.69 0.997 0.705

0.754 0.795 0.949 0.771

Torre de Moncorvo 0.665 0.762 0.873 0.676

0.741 0.842 0.881 0.821

Torres Novas 0.585 0.595 0.983 0.652

0.755 0.787 0.959 0.815

Torres Vedras 0.744 0.771 0.964 0.819

0.687 0.697 0.986 0.758

Trancoso 0.628 0.819 0.767 0.812

0.641 0.8 0.8 0.838

Trofa 0.69 0.733 0.941 0.678

0.663 0.727 0.912 0.670

Vagos 0.668 0.738 0.906 0.765

0.671 0.765 0.877 0.775

Vale de Cambra 0.632 0.687 0.919 0.709

0.698 0.788 0.886 0.764

Valença 0.407 0.511 0.796 0.495

0.405 0.512 0.791 0.473

Valongo 0.977 0.994 0.983 0.854

1 1 1 0.896

Valpaços 0.739 0.84 0.88 0.842

0.724 0.808 0.896 0.736

Vendas Novas 0.518 0.689 0.752 0.725

0.62 0.786 0.788 0.797

Viana do Alentejo 0.693 0.871 0.796 0.780

0.654 0.851 0.768 0.757

Viana do Castelo 0.833 0.876 0.951 0.879

0.809 0.813 0.996 0.835

Vidigueira 0.675 0.934 0.723 0.842

0.567 0.791 0.717 0.738

35

Vieira do Minho 0.623 0.824 0.756 0.825

0.428 0.559 0.766 0.599

Vila de Rei 0.518 0.892 0.581 0.664

0.503 0.893 0.564 0.645

Vila do Bispo 0.236 0.428 0.552 0.276

0.238 0.422 0.563 0.284

Vila do Conde 0.56 0.571 0.981 0.578

0.636 0.643 0.988 0.660

Vila Flor 0.429 0.628 0.682 0.592

0.471 0.673 0.7 0.686

Vila Franca de Xira 0.829 0.83 0.999 0.843

0.926 0.97 0.955 0.944

Vila Nova da Barquinha 0.431 0.695 0.621 0.524

0.43 0.705 0.61 0.494

Vila Nova de Cerveira 0.319 0.486 0.656 0.428

0.361 0.522 0.692 0.477

Vila Nova de Famalicão 0.73 0.731 0.998 0.708

0.722 0.736 0.98 0.733

Vila Nova de Foz Côa 0.568 0.711 0.8 0.677

0.507 0.63 0.805 0.606

Vila Nova de Gaia 0.965 1 0.965 0.857

0.962 1 0.962 0.903

Vila Nova de Paiva 0.414 0.762 0.543 0.648

0.457 0.826 0.553 0.709

Vila Nova de Poiares 0.435 0.772 0.563 0.630

0.405 0.732 0.553 0.587

Vila Pouca de Aguiar 0.493 0.606 0.813 0.650

0.46 0.547 0.841 0.455

Vila Real 0.854 0.863 0.989 0.901

0.729 0.757 0.963 0.817

Vila Real de Santo António

0.262 0.31 0.846 0.175

0.304 0.357 0.853 0.221

Vila Velha de Ródão 0.626 0.839 0.745 0.473

0.55 0.763 0.722 0.437

Vila Verde 0.757 0.78 0.97 0.828

0.65 0.683 0.952 0.737

Vila Viçosa 0.429 0.714 0.602 0.677

0.502 0.771 0.65 0.751

Vimioso 0.797 0.946 0.843 0.693

0.625 0.757 0.825 0.560

Vinhais 0.849 0.92 0.922 0.768

0.763 0.812 0.94 0.618

Viseu 0.873 0.917 0.952 0.927

0.852 0.855 0.996 0.889

Vizela 0.72 0.848 0.848 0.610

0.602 0.725 0.831 0.468

Vouzela 0.55 0.722 0.763 0.715

0.632 0.829 0.762 0.805

Average 0.610 0.734 0.831 0.669 0.616 0.744 0.830 0.677

Maximum 1 1 1 1

1 1 1 1

Minimum 0.214 0.247 0.427 0.139 0.201 0.269 0.356 0.154

Note: OTE, PTE and SE obtained with standard DEA;

* Normalized Compound Efficiency Score: computed by the average of PTE and PTE*(obtained with Inverted DEA).