Munich Personal RePEc Archive

Environmental Efficiency and Regional
Convergence Clusters in Japan: A
Nonparametric Density Approach
Mendez-Guerra, Carlos
Nagoya University

18 February 2019

Online at https://mpra.ub.uni-muenchen.de/92245/
MPRA Paper No. 92245, posted 23 Feb 2019 14:24 UTC

Environmental Efficiency and Regional
Convergence Clusters in Japan: A
Nonparametric Density Approach
Carlos Mendez-Guerra*
Nagoya University
Graduate School of International Development(Preliminary Version 1.0)

Abstract
This paper studies environmental efficiency convergence across the prefecturesof Japan over the 1992-2008 period. Using a novel nonparametric density estimation clustering framework, two alternative indicators of environmental efficiency are contrasted: a conventional indicator, based on the ratio of gross regional product to CO2 emissions, and a more comprehensive indicator, based on
the data envelopment analysis (DEA) model. Results show, on the one hand, alack of intra-distributional mobility and potentially a unique convergence cluster when using the more conventional indicator. On the other hand, large backward mobility and at least two convergence clusters are identified when using
the DEA-based indicator of environmental efficiency. The paper concludes arguing the importance of accounting for production inputs, as they appear to be
driving the formation of regional convergence clusters in Japan.

Keywords:
environmental efficiency, convergence, nonparametric density, Japan* I am grateful to all participants of the Economic Development Policy and Management
seminar at Nagoya University for the insightful comments and suggestions.
Contact Email: carlos@gsid.nagoya-u.ac.jp
Homepage: https://carlos-mendez.rbind.io

2

1 Introduction
In accordance with the Paris agreement, by the year 2030, Japan is committed to reduce its CO2 emissions by 26 percent relative to its emissions
in 2013. To achieve this objective, Japan aims not only to increase the national—average—level of environmental efficiency, but also aims to reduce its
cross-regional dispersion (Ministry of Environment, 2013). Although considerable progress has been made on the former, reducing regional gaps in environmental efficiency remains challenging. In this context, this paper studies theevolution of environmental efficiency dispersion across 46 prefectures of Japanover the 1992-2008 period.
In particular, by using both classical measures of regional convergence
and a novel framework of distributional convergence, two alternative measuresof environmental efficiency are contrasted. The first measure is a conventional
environmental efficiency indicator (CEEI for short) that focuses only on thedesirable and undesirable outputs of the production process. It is constructed
as the ratio of gross regional product to CO2 emissions. The second measure(DEEI for short) is based on the data envelopment analysis (DEA) model. It
includes not only desirable and undesirable outputs, but also information about
production inputs such as the weight of buildings and roads, the monetary
value of private capital stock, and the number of employees.
In a recent work, Eguchi (2017) compares regional performance in these
two indicators. His work provides an informative and detailed ranking ofJapanese prefectures for each environmental efficiency indicator in the year
1992 and 2008.1 Although, from this ranking, it is possible to identify
the—average—regional progress in CEEI and the—average—regional regressin DEEI, a formal analysis of regional dispersion and convergence is stillneeded for a more complete understanding of the regional environmental efficiency dynamics of Japan.
The empirical literature on economic convergence that started in the late1980s has suggested a variety of statistical frameworks for evaluating the dynamics of inequality. The survey article of Magrini (2004) attempts to sum1

Based on this table, the author points out some ranking differences between the indicators
in each year.

3
marize some of these frameworks in the context of the regional territories of acountry. On the one hand, there are the classical convergence frameworks thatare based on single summary measures. Among them, the most commonlyused are the beta and sigma convergence statistics.2 On the other hand, there
are the distributional convergence frameworks that are based on modeling theshape and internal dynamics of the entire regional distribution.3
By applying these two convergence frameworks, and other related analyses, this paper extends the findings of Eguchi (2017) in six fronts. First, it documents a U-shaped relationship between CEEI and DEEI. Second, it points outthat low-efficiency regions are not catching-up with the high-efficiency regions(i.e., lack of beta convergence). Third, across multiple indicators of dispersion,
environmental differences across prefectures have actually increased (i.e., lackof sigma convergence). Forth, the nonparametric distribution of CEEI showsa constant spread with a unique mode, while the distribution of DEEI shows
an increasing spread from its lower tail and a drastic transformation of its
multiple modes. Fifth, the intra-distribution dynamics of CEEI mostly suggest
regional stagnation, while the dynamics of the DEEI mostly suggest backward
mobility within the distribution.
The last finding is based on the novel clustering approach via nonparametric (unconditional) density estimation of Azzalini et. al (2007) and Menardi
and Azzalini (2014). In the case of DEEI, this framework suggests the existence of tree groups of regions: a “Tokio-led” convergence cluster, a “medianled” convergence cluster, and a group of transitioning regions. Moreover, theconditional density estimation approach of Hyndman et. al (1996) helps us
extend this finding and points out that not all transitioning regions may necessarily end up in any of the two superior clusters. Conditional on their initial
position, it is possible that some transitioning regions could end up converging to two additional bottom clusters, one of which is considerably below themedian.
The rest of this paper is organized as follows. Section 2 describes the empirical framework, both in terms of the classical convergence approach and the
distributional convergence approach. Section 3 describes the data and presents
2
3

See Sala-i-Martin (1996) for an overview of this classical approach to convergence analysis.
See Magrini (2009) for an overview of this distributional approach to convergence analysis.

4
the results of the classical convergence approach. Section 4 presents the main
results of the distributional convergence approach. Finally, Section 5 offerssome concluding remarks.

2 Methods
2.1

Classical Convergence Approach

The seminal work of Baumol (1986) launched a large number of studies that
aim to test the convergence hypothesis across countries and regions within acountry. Among the early studies, the work of Barro and Sala-i-Martin (1992),
in the cross-country context, and Barro and Sala-i-Martin(1992), in the context of the prefectures of Japan and the states of the US, use the so-called beta
convergence approach. In their framework, economic growth is a function of
the initial level of income. If, in a regression setting, a statistically significant
negative coefficient is found, then poor economies tend to grow faster than richeconomies, and consequently a process of convergence takes place. More specifically, Barro and Sala-i-Martin (1991) suggest the following growth equation:
yt
1
log
t
y0

!

=γ−



1 − e−βtt

log y0 + ut ,(1)

where the left side is the average growth rate of the variable y, γ is a constant,
t is a time index, β is the speed of convergence, y0 is the initial level of thevariable under study, and ut is a random (white noise) disturbance.4 In the
cross-country context, the parameter γ should be replaced by a set of variables
that act as proxies for the unobservable technological and institutional differences that exist across countries. Within countries, however, these differences
are relatively minor, and thus γ is commonly assumed constant across regions.
In addition to the rate of convergence (β), a second parameter of interest,
known as the “half-life” measure of convergence, can also be computed as:
half -lif e =
4

log2
.
β

(2)

Note that for the purposes of the present paper, the variable y represents the level ofenvironmental efficiency.

5This second parameter is particularly informative because it measures thetime that a representative economy (or region) needs to halve the gap between
its initial level and its convergence equilibrium.
A more general notion of convergence has to do with the reduction of thecross-sectional dispersion of a variable over time. In the convergence literature,
this is the so-called sigma convergence approach, and it is commonly measured
by the standard deviation of the natural logarithm of the variable y or by its
coefficient of variation (CV). Specifically, a decrease in the sigma convergencestatistic indicates that the cross-sectional units of the sample (e.g., the regionsof Japan) are becoming increasingly more similar in terms of the level of thevariable y.
Regarding the relationship between beta and sigma convergence, Quah
(1993) and Sala-i-Martin (1996), show that beta convergence is a necessary—but not sufficient—condition to achieve sigma convergence. To derive
this relationship, let us first restate Equation 1 in a two-period setting:
yt
log
yt−1

!





= γ − 1 − e−β log yt−1 + ut .

(3)

Next, apply the variance operator (σt2 ) to the variable log yt in Equation 3 andassume the white noise properties of ut . After some algebraic operations, we
can find that σt2 evolves over time according to the following equation:22
σt2 = e−2β σt−1
+ σut
.

(4)

Equation 4 is just a first-order differential equation problem. If weassume that the variance of the random disturbance is constant over time2(σut
= σu2 ), then the solution to this problem is
σt2 =

σu2
σu2
2
+ σ0 −
1 − e−2β1 − e−2β!


e−2βt .

(5)
2Furthermore, in a the steady-state equilibrium σt2 = σt−1
= σ 2 , the crosssectional dispersion of y only depends on the beta convergence parameter (β)

6and the dispersion of the random disturbance (σu2 ). That is,
σ2 =

σu2
.
1 − e−2β(6)From Equation 6, it is clear that beta convergence (an increase in β) is nota sufficient condition for sigma convergence (a decline in σ 2 ). The effect ofbeta could be attenuated or even reversed by an increase in the dispersion of
random disturbances (σu2 ), which are commonly interpreted as random shocks
to the economies of this dynamical system.

2.2

Distributional Convergence Approach

One of the common criticisms to the classical measures of convergence (i.e.,beta and sigma) is that they fail to provide information about nonlinear dynamics, heterogenous patterns of convergence, and the formation of local convergence clusters. In essence, beta and sigma convergence are just summary
measures of a representative region (i.e., the average region) and, as such, they
abstract from important patterns of cross-sectional heterogeneity. Motivatedby this limitation, Quah (1993; 1996; 1997) introduced the distributional convergence approach, which goes beyond the performance of the representative
region and evaluates the dynamics of the entire cross-sectional distribution.5
Figure 1 presents an intuitive graphical summary of the distributional
convergence approach. First, in this example, the dynamics of the external
shape of the distribution point out not only the lack of overall convergence,but also the formation of two local convergence clusters. Second, the intradistributional dynamics emphasize the three sources of the clustering process.
Some regions, such as (a) and (d), could show large and persistent differences
over time. Others, such as (c), could move forward and catch-up with the upper
cluster. Lastly, the remaining regions, such as (b), could move backward andjoin the bottom cluster.
More formally, let us first economize notation and define the relative5

See Epstein et al. (2003), Magrini (2004, 2009), Bianco (2016) or Mendez-Guerra (2017;2018) for more recent and comprehensive presentations of this framework that include not
only an evaluation of the intra-distributional dynamics, but also the computation of the longrun (ergodic) equilibrium of the distribution.

7
Figure 1. External-shape dynamics and intra-distributional dynamics

(a)

(a)

(b)

(c)

(c)

(b)

(d)

(d)

t

t+s

Time

Note: y/ȳ indicates that the value of the variable y is expressed in relative terms. ȳ indicates the convergence benchmark, which is usually the cross-sectional mean, median, or any other referential observation.
Source: Adapted from Quah (1993).

t+s. Next,level6 of the variable y at time t as x ≡ yȳtt , and at time t + s as z ≡ ȳyt+s
let us define ft (x) as the entire cross-sectional distribution at time t and ft+s (z)is the distribution at time t + s. In the distributional convergence literature,
the evolution from time t to time t + s is commonly modeled as a first-order
autoregressive process of a time-homogeneous Markov chain. That is,

ft+s (z)| {z }

F uture Distribution=

ˆ

ft+s|Zt =x (z)
|

{z

}

ft (x)dx,(7)| {z }

T ransitional Operator Initial Distribution

where the transformation of the initial distribution, ft (x), into the future distribution, ft+s (z), is mapped out by the transitional dynamics summarized by theprobability operator, ft+s|Zt =x (z), which is commonly referred in the literature
6

For this analysis, the environmental efficiency level of each region is expressed relative tothat of Tokio.

8
as the stochastic kernel.
To estimate the transitional operator, most studies use nonparametricmethods (Wand and Jones, 1995; Henderson and Parmeter, 2015). In particular, it is common to define this operator as a conditional distribution:ft+s|Zt =x (z) =ft,t+s (z, x),
ft (x)(8)

where ft,t+s (z, x) is an unconditional joint distribution and ft (x) is the marginal
distribution of x. Next, let us define this unconditional joint distribution as:
ft,t+s (z, x) =nz − zi1 X
x − xiKz
Kx,nhz hx i=1
hz
hx









(9)

where Kz and Kx denote Gaussian kernel functions, and hz and hx denote thesmoothing parameters (flexible bandwidths) for z and x respectively.7 Lastly,similar to the joint distribution, the marginal distributions, ft (x), is estimatedusing a single Gaussian kernel function with a flexible bandwidth.
At this point, it is important to emphasize that intra-distributional dynamics8 are driven by two components: the unconditional joint distribution,
ft,t+s (z, x), and the initial marginal distribution, ft (x). To study the effects ofthe former, I implement the approach of Azzalini et. al (2007) and Menardi and
Azzalini (2014). To study the effects of the latter, I implement the approach of
Hyndman et. al (1996).
The work of Azzalini et. al (2007) and Menardi and Azzalini (2014) isuseful not only to estimate the unconditional joint distribution distribution,
ft,t+s (z, x), but also to identify and distinguish between convergence clusters
and transitioning regions. In a series of papers, these authors have develop
an innovative clustering algorithm that is based on the local modes of an estimated nonparametric distribution. More specifically, they exploit recent advances in computational geometry to identify spatially connected regions.
The work of Hyndman et al. (1996) is useful to evaluate the complete pro(z,x). Compared to the original conditional
cess of transitional dynamics, ft,t+s
ft (x)
7

Optimal smoothing parameters are derived from the the minimization of the asymptotic
mean integrated square error (AMISE).
8
Note that the terms intra-distributional dynamics, transitional operator, stochastic kerneland conditional distribution ultimately refer to the same concept. That is, the movement of theregional units within the cross-regional distribution.

9density estimator of Quah (1993,1997), the estimator of Hyndman et al. (1996)
has better asymptotic mean bias properties (Arbia et. al,2006). These authors
also propose two novel graphical methods for visualizing the estimated conditional densities. The first one is somewhat similar to Figure 1. It is stacked
conditional density (SCD) plot that displays a sequence of densities side by sidein a perspective fashion. This new graphical device is conceptually similar to a
Markovian transition matrix. That is, for a given level of a variable at time t,
the SCD traces its evolution and illustrates its final configuration at the timet + s. The second graphical method is called high density region (HDR) plot.
Along a series of vertical strips, the HRD plot illustrates the projection on thexz plane of the conditional density of z on x. Darker-shaded stripes indicate
higher density areas, and the mode for each conditional density is shown asbullet point.

3 Data and Some Stylized Facts
3.1

Data and Sample

This paper studies dispersion and convergence patterns of environmental efficiency across 46 prefectures of Japan9 in the year 1992 and 2008. The dataset
for this analysis is from Eguchi (2017), who computes both a conventional environmental efficiency indicator (CEEI for short), based on the ratio of grossregional product to CO2 emissions, and a more comprehensive indicator of environmental efficiency (DEEI for short), based on the data envelopment analysis (DEA) model. As noted by this author, the main advantage of the DEA
model is that it can include not only desirable and undesirable outputs (i.e.,
gross regional product and CO2 emissions), but also production inputs such asbuildings, roads, private capital stock, and the number of employees.10
Figure 2 shows a comparative ranking between the conventional environ9

Due to lack of systematic data, the prefecture of Okinawa is excluded from the analysis.
To estimate the relative efficiency index in the DEA framework, Eguchi (2017) uses both
physical and monetary capital inputs. To measure the former, estimates of the weight of buildings and roads are taken from Tanikawa et al. (2015). To measure the latter, estimates aretaken from the R-JIP database of the Research Institute of Economy, Trade and Industry ofJapan. Data on the number of employees and the gross regional product are also from thisoriginal source.
10

Relative CEEI in 1992 (Tokio=1)

Relative DEEI in 1992 (Tokio=1)
1.00

0.75

0.50

0.25

0.00

1.00

0.75

0.50

0.25

0.00

Regions(b) DEEI ranking in 1992

Regions(d) DEEI ranking in 200810

it
Yam TAokanakyoa
S sh
KyhoigaiOsa tok
Tok ToNt araa
ush tori
ima
K
Kagochiawakui
Yam FuagG
ucifhuF k Sag iNuuoaga kaasak
KaSnhimagaanei
IshHi yow
goa
kaw
Aic a
hi
OT
a
koay
m
yama
Ch
ibaa
O
i
i
y
HM
ta
irosazakim i
Wak Ehayhaimae
ma
ama M
KY
ie
Ku
agmoamgoatashToc imtoa
Sait higiama
ShGizunmaNaugaonkaI
w
Fuk Ibar atoe
ush aki
HoAkomimoa
Mkaidroi
Niiiy
gaag
tai

Figure 2. Comparison between the conventional environmental
efficiency indicator (CEEI) an the DEA-based environmental
efficiency indicator (DEEI)

1.00

0.75

0.50

Toky
K o
OsyotoYam Naakraa
anashGNaugnamai
T no
Saoitcahigim
Is Shiga
Nahgikaawaa
ma saki
FuYkauata
Kum shgim
am aKago Saogto
shima
KanaAkitaagawa
M GifuKagiyaagi
Shiz
u wa
F oka
TouttkouiNii
g trai
HokkAicah
Shimaidoi
IwaanteToMkuiysahzakei
Hyim
a
T og
Fuokyuamoa
Aomokao
Kochri
i
IbaMieWak Chraibkai
ayam
HiroEhimaekasyhaima
YaOm
a
agum
Ocithai

Relative DEEI in 2008 (Tokio=1)

it
Yam TAokanakyoa
shi
ShM
igie
T NaraTok oSttorai
ush aga
FuikmaKo ui
ShizKyochiokto
Fuk Touushchigai
iAm
chai
IsThoiyaim
kawa
Shim
Yam
a
Hir agu nae
osh chiYamagima
Nag Oaitta
KagKagaasakaio w
Nashgimaa
IbaranoO ak
KMniyaszakai
Waak
a ak
aygaawai
KumEh ma
ime
Gaum
nomto
OkH
ayyaogoa
Gm
ifua
MIiw
yaagteCh
N i i
S iigabtaa
Fuakitamu aA
Hokomooka
kaidrio0.25

Regions(a) CEEI ranking in 1992

Tok
K yo
Yam Osyaoto
Naangaskhai
I ShangoaSshhizikaiw
uoka
TocSagaa
Yamhig
Kag aNgataio ar
FuNkagsahsimaau aGsuhnimkai
Sait maKum
amaomaAk tota
KaFgukiu
awai
Tok G
ifu
Kanushim
Toaygawaaa a
MiyAimc i
NiaigzahkMiyatai
agi
M
ie
I
w
a
ottoteShTimr
Fuk an i
Ibaurokae
Aomakio
K ri
HokHyoocghi
k o
E aid
Wak Chhimoe
ib
Hir ayamosh aaima
Yam O
Okaagucita
yamhi
a

0.00

1.00

0.75

0.50

0.25

0.00

Regions(c) CEEI ranking in 2008

Note: To facilitate the comparison, both indicators have been rescaled relative to the efficiency level of Tokio. The
word “conventional” refers to the ratio the ratio of gross regional production to CO2 emissions. DEA stands for Data
Envelopment Analysis and it is a nonparametric analysis of relative efficiency. In this article, the DEA indicatoris based on measures of gross regional production, CO2 emissions, and production inputs (buildings, roads, private
capital stock, and the number employees).
Source: Eguchi (2017, p.12), Table 3.

Relative CEEI in 2008 (Tokio=1)

11
Figure 3. A U-shaped relationship between CEEI and DEEI?

area
Relative DEEI (Tokio=1)

1.0

●

●

●

●
●●● ● ● ●
●●

●

● ●

●
●

●
●

● ●

●

●
●

●

● ●
●●

●

●

●
●

●
● ●

●

●

●●
●●

●

●

●

Chubu

●

Chugoku●

Hokkaido

●

Kanto

●

Kinki

●

Kyushu●Shikoku●Tohoku

●
●

● ●
●

●
●

●

●

●

●
●

●

●●

●
● ●

●
● ● ●●

●●

●

●
● ●
●

0.8
●

●●
●
●
●

● ●●

●
●

●●
●

0.6
●

0.25

0.50

0.75

1.00

Relative CEEI (Tokio=1)

Note: CEEI stands for “conventional” environmental efficiency indicator and DEEI stands for DEA-based environmental efficiency indicator. The word “conventional” refers to the ratio the ratio of gross regional production to CO2emissions. DEA stands for Data Envelopment Analysis and it is a nonparametric analysis of relative efficiency. In thisarticle, the DEA indicator is based on measures of gross regional production, CO2 emissions, and production inputs(buildings, roads, private capital stock, and the number employees).
Source: Author’s calculations using data from Eguchi (2017).

mental efficiency indicator (CEEI) an the DEA-based environmental efficiency
indicator (DEEI). The first notable difference is that most CEE values tend tobe below 0.50, while most DEE values tend to be above 0.50. To some extend,
this difference is expected given the construction of both indicators. For instance, the CEEI is an unbounded absolute indicator, which means that theratio of gross regional product to CO2 emissions can continuously grow overtime and it is not necessarily bounded within a certain range of values. The
DEEI, however, is a bounded relative indicator, which means that it necessarily takes a value within a certain range. In the context of the DEA framework,
this efficiency value is between 0 and 1.11
When studying the empirical relationship between both indicators, Figure
11

In the original results of Eguchi (2017), the direction of efficiency improvements is from 1
to 0. In other words, maximum efficiency is attained when the DEEI equals 0. In the present
study, however, the direction of efficiency improvements is reversed, meaning that maximum
efficiency is attained when DEEI equals 1. As a result of this adjustment, the comparison
between CEEI and DEEI becomes more immediate and intuitive.

12
3 suggests that the relationship is not only highly non-linear, but also shows
signs of a U-shaped pattern. In particular, this U-shaped relationship holds
very well when CEEI is between 0 and 0.50, which is the range in which most
prefectures are located (See Figure 2). When trying to interpret this pattern,
the initial negative relationship between CEEI and DEEI could suggest that
initial improvements in environmental efficiency (higher CEEI) are associatedwith relatively inefficient use of production inputs (lower DEEI). On the other
hand, as regions keep developing and improving their environmental performance (higher CEEI), they may also learn how to use their production inputs
more efficiently, which improves even further their environmental performance(higher DEEI).

3.2

Lack of Beta and Sigma Convergence

Are the regions with the lowest environmental efficiency scores catching up
with the most efficient regions? The results of Table 1a suggest that this is
not the case for both indicators of environmental efficiency. Although the betacoefficient is negative, which is a sign of convergence, its p-value is indicatesthat this coefficient is not statistically significant. Moreover, even if we wereto ignore the statistical significance of the coefficient, the speed of convergenceis extremely slow. For instance, in the case of the CEEI, its half-life time value
suggests that it would take on average 281 years for the current disparities tobe halved.
Although—on average—there has been progress in both indicators of environmental efficiency (Eguchi, 2017), the standard sigma convergence analysis suggests that, after more than 15 years, there has been no significant
progress in terms of the reduction of environmental efficiency disparities. Table 1 shows that through the lens of two commonly used indicators of dispersion, the standard deviation and the coefficient of variation, the environmental
efficiency differences across prefectures have actually increased in most cases.
The only exception is the coefficient of variation of the CEEI, which indicates aminor reduction from 0.39 in the year 1992 to 0.36 in the year 2008.
In the convergence econometrics literature, a ratio of initial dispersion

>
1
is typically suggestive of reover final dispersion larger than one σσ1992
2008

13

Table 1Lack of beta and sigma convergence across Japanese prefectures(a) Lack of beta convergence

Dependent Variable
Growth of CEEI Growth of DEEI
(1992-2008)(1992-2008)
Beta coefficient- 0.039- 0.214
Speed of convergence
0.002
0.015
Half-life time (in years)281
46
R-squared
0.02
0.04
P-value of beta
0.41
0.16
(b) Lack of sigma convergence

Dispersion in1992
Dispersion in 2008

Dispersion Ratio σσ1992
2008
F-Statistic
P-value

CEEI
DEEI
Standard Coefficient Standard Coefficient
Deviation of Variation Deviation of Variation
0.39
0.39
0.12
0.12
0.40
0.36
0.15
0.14
0.99
1.08
0.79
0.80
0.98
0.92
0.62
0.69
0.95
0.77
0.11
0.21

Note: For the beta convergence analysis, all regressions include a constant term, which is not presented in the table.
For the sigma convergence analysis, following the convention of the literature, the standard deviation of the natural
logarithm of each indicator is computed. Also following this literature, the coefficient of variation is computed, but
this time without its natural logarithm. CEEI stands for “conventional” environmental efficiency indicator and DEEI
stands for DEA-based environmental efficiency indicator. The word “conventional” refers to the ratio the ratio ofgross regional production to CO2 emissions. DEA stands for Data Envelopment Analysis and it is a nonparametricanalysis of relative efficiency. In this article, the DEA indicator is based on measures of gross regional production,
CO2 emissions, and production inputs (buildings, roads, private capital stock, and the number employees).
Source: Author’s calculations using data from Eguchi (2017).

14
gional convergence. In this context, the results of Table 1b suggest the opposite:
the hypothesis of sigma convergence is actually rejected in all cases. Even in
the previously mentioned exceptional case, the F-statistic and p-value suggestthat the reduction in the dispersion is not statistically significant.

4 Distributional Convergence Results
4.1

External-Shape Dynamics

Figure 4 shows the regional composition and dynamics of the nonparametrickernel distribution of CEEI. In the year 1992, we can observe a highly asymmetric environmental efficiency distribution that is characterized by one major density peak at around 41 percent of the environmental efficiency level of
Tokio. Also, there is a minor density bump in the range between 50 to 70
percent, which is composed by tree prefectures: Nara, Osaka, and Kyoto. In
contrast, in the year 2008, we can observe a relatively more symmetric distribution with only one major peak at around 46 percent of Tokio. Moreover,there is no any minor bump, which indicates that over time Osaka and Nara inparticular have been gravitating towards the unique basin of attraction of the
distribution.
Figure 5 shows the regional composition and dynamics of the nonparametric kernel distribution of DEEI. In the year 1992, we can clearly observea trimodal distribution. The major peak is located at around 87 percent of
the environmental efficiency level of Tokio. In the year 2008, the distribution
drastically changed its shape. Starting from the central mode, a considerablylarge number of regions appear to be moving backwards and, thus, the separation between the lower and central mode has tended to disappear over time.
Likewise, the separation between the upper and central mode has tended todisappear, albeit to a lesser extend.
Figure 6 summarizes the distributional changes over time and contrasts
both indicators of environmental efficiency. In the case of the CEEI, although
the spread of the distribution seems be relatively constant over time (as pointed
out in the sigma convergence analysis), the mode of the distribution slightly
shifts to the right and becomes more symmetric. The spread of the DEEI, how-

15

Figure 4. The nonparametric distribution of CEEI: Composition andshape dynamics
4

Density

3

2

1

0

Miyagi
Gifu KanagawaKagoshima
Fukui Kagawa
Saga
Akita
Shizuoka
Tottori
Niigata
Yamagata
Kumamoto
Iwate
Shimane Ishikawa Nagasaki
1.00
Fukushima
Hyogo
Tokushima Hokkaido Shiga
Saitama
0.75
Aomori ToyamaAichi
MiyazakiTochigi
Kochi
Mie Fukuoka
0.50
NaganoIbaraki
Chiba
Ehime
Gunma
Wakayama
0.25
Okayama
Hiroshima Yamanashi
Osaka
Yamaguchi
Nara
Kyoto
Tokyo
Oita
0.1

0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Relative Conventional Environmental Efficiency Indicator in 1992 (Tokio=1)(a) Cross-sectional kernel distribution in the year 1992
4

Density

3

2

1

0

Kanagawa
KagawaAichi Tokushima
Gifu
MiyazakiToyamaAkita
Kumamoto
Fukui Saitama
Miyagi Niigata
Gunma
Shimane Iwate Mie
Fukushima Kagoshima
Kochi Fukuoka Nagasaki Shizuoka
Yamagata
Nara
Hyogo
Tottori
Hokkaido
Saga
Ishikawa
Wakayama Aomori Tochigi
NaganoShiga Yamanashi
Hiroshima Chiba Ibaraki
Ehime
Oita
Osaka
Okayama
Yamaguchi
Kyoto

1.0
0.8
0.6
0.4
0.2

Tokyo

0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Relative Conventional Enviromental Efficiency Indicator in 2008 (Tokio=1)(b) Cross-sectional kernel distribution in the year 2008
Note: CEEI stands for “conventional” environmental efficiency indicator and DEEI stands for DEA-based environmental efficiency indicator. The word “conventional” refers to the ratio the ratio of gross regional production to CO2emissions. DEA stands for Data Envelopment Analysis and it is a nonparametric analysis of relative efficiency.
Source: Author’s calculations using data from Eguchi (2017).

16

Figure 5. The nonparametric distribution of DEEI: Composition andshape dynamics
1.0

Miyazaki Oita Chiba Okayama
ToyamaIshikawa
Kanagawa
Hiroshima Ehime Wakayama Aichi Shimane
Kochi
Mie Yamagata Hyogo Kagawa
Kyoto
Tokushima
0.8 Kumamoto
Kagoshima Nagasaki
Saga
Tochigi
Fukuoka
Fukui
0.7
Nara
Yamaguchi Tottori
Ibaraki Saitama
Gunma Gifu Shiga Yamanashi
Fukushima
Iwate
AomoriShizuoka Osaka Tokyo Akita
Hokkaido Nagano
Miyagi
Niigata4

0.9

Density

3

2

1

0
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
DEA−Based Conventional Environmental Efficiency Indicator in 1992 (Tokio=1)(a) Cross-sectional kernel distribution in the year 1992
1.0

4

Nagasaki Hiroshima
Yamaguchi
Kagoshima Yamagata
Shimane Ishikawa
0.8
Nagano Kagawa Oita Tokushima
0.7
Ehime Ibaraki
Saga
Osaka Toyama
Miyazaki
0.6
Gunma
Fukui Mie
Kanagawa
Fukushima
Okayama
Kochi
Aichi
Kyoto
Chiba
Kumamoto Tochigi
Yamanashi
Niigata
Gifu Wakayama Shizuoka
Tottori
SaitamaMiyagi Hyogo
Shiga Nara
Fukuoka Iwate
Tokyo Akita
Aomori
0.9

Density

3

2

1

0

Hokkaido
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
DEA−Based Conventional Environmental Efficiency Indicator in 2008 (Tokio=1)(b) Cross-sectional kernel distribution in the year 2008
Note: CEEI stands for “conventional” environmental efficiency indicator and DEEI stands for DEA-based environmental efficiency indicator. The word “conventional” refers to the ratio the ratio of gross regional production to CO2emissions. DEA stands for Data Envelopment Analysis and it is a nonparametric analysis of relative efficiency.
Source: Author’s calculations using data from Eguchi (2017).

17
Figure 6. Comparison of the external-shape dynamics of CEEI and
DEEI: Nonparametric densities

2008

2008

1992

1992

0.25

0.50

0.75

1.00

Relative CEEI (Tokio=1)
(a)

0.6

0.7

0.8

0.9

1.0

Relative DEEI (Tokio=1)(b)

Note: CEEI stands for “conventional” environmental efficiency indicator and DEEI stands for DEA-based environmental efficiency indicator. The word “conventional” refers to the ratio the ratio of gross regional production to CO2emissions. DEA stands for Data Envelopment Analysis and it is a nonparametric analysis of relative efficiency.
Source: Author’s calculations using data from Eguchi (2017).

ever, increases overtime, particularly towards its left tail. Note that the standard sigma convergence analysis of Table 1b pointed out that the dispersion of
the DEEI was increasing over time, and in sharp contrast with the CEEI, theresults of the F-test for the DEEI were very close to be statistically significant
at the conventional level of 10 percent.

4.2

Intra-Distributional Dynamics

Figure 7 provides a comparison of the intra-distribution dynamics of each environmental efficiency indicator through the lens of estimated quantile trends.
In the case of CEEI, the analysis of the previous sections suggested a constantdispersion with a minor modal shift towards the upper tail. Panel (a) of Figure
6 not only confirms these findings, but also indicates that this modal shift is related with the dynamics of the 0.75 quantile. Also, relative to other quantiles,
the slope of the 0.75 quantile is considerably steeper. Thus, only the regions
from this quantile are showing some signs of convergence. In sharp contrast
with this pattern, most of the quantiles of DEEI show negative slopes, whichindicates intra-distributional divergence, which is particularly more evident in
the two bottom quantiles.

18

quantile

0.6

0.05

0.5

0.25
0.4

0.5

0.3

0.75

0.2

0.95
1995

2000

2005

(a)

Relative DEEI (Tokio=1)

Relative CEEI (Tokio=1)

Figure 7. Comparison of the intra-distribution dynamics of CEEI and
DEEI: Quantile trends
1.0

quantile
0.05

0.9

0.25
0.8

0.5
0.75

0.7

0.95
1995

2000

2005

(b)

Note: Since the data is only available for two years (1992 and 2008), a simple linear interpolation is applied toestimate the values of each intermediate year. CEEI stands for conventional environmental efficiency indicator and
DEEI stands for DEA-based environmental efficiency indicator.
Source: Author’s calculations using data from Eguchi (2017).

Figure 8 provides an alternative comparison of the intra-distribution dynamics of each indicator using mobility scatterplots. The advantage of thisapproach is that we can study the mobility of each region instead quantile
groups. In the case of CEEI, the most noticeable feature is that all regions
are lining up very close to a 45-degree line (Figure 8, Panel (a)). This patternindicates relative stagnation in the worst case or very limited upward mobility(i.e., catching up with Tokio) in best case scenario. The dashed lines indicate
the value of median observation in each year; they help us identify patternsof mobility in relation to the progress of the median region. Since almost all
regions are located either in the lower-left or upper-right quadrant, one canconclude that the regions that were below (above) the median in the year 1992,
remained below (above) it in the year 2008.
Panel (b) of Figure 8 shows a much more heterogeneous performance inthe case of the DEA-based environmental efficiency indicator (DEEI). Regions
are far away from the stagnation (45-degree) line. In fact, most of them arebelow it—including the median region. This downward mobility pattern reinforces previous findings regarding a tendency towards regional divergence thatis more evident in the case of DEEI.

19

Figure 8. Comparison of the intra-distribution dynamics of CEEI and
DEEI: Mobility Scatterplots
Tokyo
●
●

Relative CEEI in 2008 (Tokio=1)

1.00

Kyoto

0.75

Shizuoka

Saga

Shiga

● Osaka●
Yamagata Nagano
Yamanashi●●
Kagawa Fukushima ● ●● Ishikawa Tochigi Nara
●
● ●
●
●
●● ● Gunma
Aichi Fukui ●Tokushima
Nagasaki●●●●●● Kumamoto●
Toyama ●● ● ●● ● Gifu
Saitama●● ●MiyazakiAkita● ● Tottori
Mie Fukuoka● ● Aomori
Kanagawa
Miyagi●●●
Ibaraki ●●Kochi●
ShimaneNiigata●
Ehime
Wakayama
●
Iwate
Hyogo
●
Oita Hiroshima
Hokkaido
Chiba
Yamaguchi Okayama

Kagoshima

0.50

0.25

0.00

0.00

0.25

0.50

0.75

1.00

Relative CEEI in 1992 (Tokio=1)(a)Relative DEEI in 2008 (Tokio=1)

1.0

0.9

0.8

0.7

Mie

Yamanashi
Tokyo
ShigaAkita ●● Saga●●●Fukui Tottori Tokushima
Kochi
●
Nara
Aichi
Shizuoka
Tochigi
●
●
●
Kyoto
●
Toyama Ishikawa●●●●
Fukushima
Yamaguchi●●
Hiroshima ● ●●●●ShimaneKagawaYamagata Oita
Nagano●●●● ●NagasakiKagoshima
Miyazaki●●Ibaraki●Osaka
Wakayama ●●●●Kanagawa
●
Gunma
Ehime
●
●
●
Kumamoto
Hyogo
Okayama●●Miyagi
0.7

Iwate

Saitama
●

0.8

●

●

Gifu

Chiba
0.9

1.0

Relative DEEI in 1992 (Tokio=1)(b)
Note: CEEI stands for “conventional” environmental efficiency indicator and DEEI stands for DEA-based environmental efficiency indicator. The word “conventional” refers to the ratio the ratio of gross regional production to CO2emissions. DEA stands for Data Envelopment Analysis and it is a nonparametric analysis of relative efficiency.
Source: Author’s calculations using data from Eguchi (2017).

20

●

1.00

0.75

0.50

0.25
●●

●

●● ●
●
●●
●
●
● ●●
●
●●
●●●
● ●●
●
●
●
●
● ● ●●
● ●
●●● ●
●
●

●
●

0.25
0.50
0.75
Relative CEEI in 1992 (Tokio=1)

Relative DEEI in 2008 (Tokio=1)

Relative CEEI in 2008 (Tokio=1)

Figure 9. Comparison of the intra-distribution dynamics of CEEI and
DEEI: Bivariate nonparametric distribution
●

1.0
●

●●
●
●

●

0.6

1.00

(a)

●

●

●● ● ●
●
●

●

● ●

0.8
0.7

●

●

0.9

●●

●

●
● ●●

●
● ●

●
●
●
●
●
●

●

●
●

●
●

0.7
0.8
0.9
Relative DEEI in 1992 (Tokio=1)

1.0

(b)

Note: CEEI stands for “conventional” environmental efficiency indicator and DEEI stands for DEA-based environmental efficiency indicator. The word “conventional” refers to the ratio the ratio of gross regional production to CO2emissions. DEA stands for Data Envelopment Analysis and it is a nonparametric analysis of relative efficiency.
Source: Author’s calculations using data from Eguchi (2017).

4.3

Regional Convergence Clusters

Figure 9 builds on the findings of the previous mobility scatterplots. Throughthe lens of a nonparametric bivariate distribution, it shows the areas of highdensity of each environmental efficiency indicator. In the case of CEEI, there is
only one area of high density that is just above the median of each period. The
DEEI, however, shows two distinct areas of high density along the stagnation(45-degree) line. The first one is located just under the median and the second
one is located around the value of Tokio.
Figure 10 further evaluates the existence of two separate density areas forthe DEA-based environmental efficiency indicator (DEEI). In the convergence
literature, the existence of multiple areas of high density along the stagnation(45-degree) line is commonly interpreted as suggestive evidence of convergenceclubs or clusters. Using the density-based clustering algorithm of Azzalini et.
al (2007) and Menardi and Azzalini (2014), it is possible to identify two coreclusters of convergence. Panel (a) of Figure 10 shows both the regions thatbelong to each cluster of convergence (market with the number 1 or 2) and theregions that are still in a transitional stage (market with the number 0).
In terms of the size and composition of each group, the superior cluster,

21

2

0
2
22

0

2

2
0

0

0

0

0

1.0
0.8
0.2

0

0.0

0

2

0

0

2

2

0
0

0

22 2 2

22

0.4

0.9

0

1
1
1
0

0
2

0.8
0.7

0

0

0.6

DEEI2008

0 0

0

0.6

1.0

Figure 10. Density-based cluster analysis for the DEA-based
environmental efficiency indicator (DEEI)

1

0

0.7

0.8

0.9

1.0

DEEI1992
groups tree

(a)

(b)

cluster median dbs = 0.13

1mode function

2

dbs plot0

cluster median dbs = 0.01

0.0

0.2

0.4

0.6

0.8

1.0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

fraction of data points

(c)

(d)

Note: DEEI stands for DEA-based environmental efficiency indicator. DEA stands for Data Envelopment Analysis
and it is a nonparametric analysis of relative efficiency.
Source: Author’s calculations using data from Eguchi (2017).

which one may call it the “Tokio-led” cluster, is composed by 8 regions. On theother hand, the lower cluster, which one may call it the “median-led” cluster, iscomposed by 15 regions. Finally, the group of transitioning regions is composedby 23 prefectures.
The rest of the panels of Figure 10 provide additional clustering diagnostics that help us evaluate the possible destination of the transitioning regions.
As suggested by the mode function (Panel c) and the Density Based Silhouetteplot (Panel d), most of the transitioning regions would end up in the “medianlead” cluster. This cluster would increase its size from 15 regions to 34 regions.
On the other hand, the “Tokio-led” cluster would only receive 4 additional mem-22bers, ending up with 12 regions.
Finally, Figure 11 shows the conditional distribution version of the previously estimated intra-distribution dynamics. Through the lens of the conditional distribution estimator of Hyndman et. al(1996), we can observe theevolution of the environmental efficiency distribution, given its initial level inthe year 1992. Also, in this modeling framework, both the “Tokio-led” and the“median-led” clusters are clearly identifiable. However, two additional “bottom” clusters are also identified (See Panel b).
It is important to clarify and reconcile the difference in the number of clusters between the two methodologies. The framework of Azzalini et. al (2007)
and Menardi and Azzalini (2014) identifies modal clusters in two stages. In thefirst stage, the estimation of an un-conditional bivariate distribution suggest
the existence of two modes (Figure 10b and 10c), which are then used to map
two core clusters (Figure 10a and 10d). Transitioning regions that were notoriginally part of the core clusters are then allocated only to those two clusters
in a second stage.12 The framework of Hyndman et. al (1997), on the other
hand, estimates conditional-bivariate distribution that suggest the existenceof multiple modes depending on the initial level of the variable (Panel a).
Although these two frameworks differ in the allocation mechanism of thetransitioning regions, they share a common element: the unconditional bivariate kernel distribution. This distribution is the main criteria for finding theclusters of Menardi and Azzalini (2014). It is also a necessary input to estimate the conditional distribution of Hyndman (1996). Thus, to reconcile theresults, the Azzalini approach could be suggesting a lower bound (where theinitial conditions of the regions are not binding), whereas the Hyndman approach could be suggesting an upper bound (where the initial conditions of theregions are binding). More intuitively, not all transitioning regions may necessarily end up in any of the two superior convergence clusters. Specially someless developed regions may end up in a new equilibrium that is below the median. The approach of Hyndman emphasizes this possibility by pointing out
the existence of two separate areas of high density around the lower tail of theconditional distribution.
12

The statistical criteria for this allocation exploits recent advances in computational geometry, in particular the identification of a Delaunay triangulation and Voronoi tessellation.

23

ok
io

=1

)

Figure 11. Nonparametric conditional distribution for the DEA-based
environmental efficiency indicator (DEEI)

19

92

(T

1

iv

eD

EE

Ii

n

0.9

Re

lat

0.8

1

0.7
0.8
Relative

DEEI in

0.6

2008 (Tokio =1)

0.4

0.9

●

●
●

0.7

●

●

●

●

●

●
●

●

●

●

●

●

0.5

Relative DEEI in 2008

1.1

(a)

0.6

0.7

0.8

0.9

1.0

Relative DEEI in 1992(b)
Note: DEEI stands for DEA-based environmental efficiency indicator. DEA stands for Data Envelopment Analysis
and it is a nonparametric analysis of relative efficiency. Panel (a) shows a stacked conditional density (SCD) plot thatis conceptually similar to a Markovian transition matrix. For a given level of environmental efficiency in 1992, theSCD traces its evolution and illustrates its final configuration in the year 2008. Panel (b) shows high density region(HDR) plot. The darker-shaded stripes indicate higher density areas, and the mode for each conditional density isshown as bullet point.
Source: Author’s calculations using data from Eguchi (2017).

24

5 Concluding Remarks
Both increasing the national (average) level of environmental efficiency and reducing its cross-regional dispersion are important means to reduce CO2 emissions. Although Japan has made considerable progress on the former, it has
made much less progress on the latter. In this context, this paper studies
environmental efficiency dispersion across 46 prefectures in Japan over the
1992-2008 period. In particular, through the lens of both classical and distributional convergence frameworks, this paper quantifies progress in regional
convergence by using the two alternative measures of environmental efficiency
suggested by Eguchi (2017). The first measure is a conventional environmental efficiency indicator (CEEI for short) that focuses only on the (desirable andundesirable) outputs of the production process. It is constructed as the ratio ofgross regional product to CO2 emissions. The second measure (DEEI for short)
is based on the data envelopment analysis model, and it includes not only desirable and undesirable outputs, but also inputs such as buildings, roads, private
capital stock, and the number of employees.
The first empirical regularity documented in the paper is that the relation between CEEI and DEEI is highly non-linear. Interestingly, there appears
to be a U-shaped relationship between these two indicators of environmental
efficiency. This pattern could suggest that although initial improvements in environmental efficiency (higher CEEI) are associated with relatively inefficientuse of production inputs (lower DEEI), regions could also learn how to use theirproduction inputs more efficiently (higher DEEI) as they produce more output(higher CEEI).
The classical analysis of beta and sigma convergence suggests that—on
average—environmental efficiency differences across regions have not decreased during the 1992-2008 period. Low-efficiency regions are not catchingup with the high-efficiency regions in an statistically significant way (i.e., lackof beta convergence). Moreover, across multiple indicators of dispersion, environmental differences across prefectures have actually increased (i.e., lack ofsigma convergence).
The next section of the results goes beyond these two classical measuresof convergence. Through the lens of a series of nonparametric distributional

25
methods, it evaluates the evolution of the entire environmental efficiency distribution. This analysis points out three central aspects of distributional convergence: (1) the dynamics and composition of the external shape of the distribution; (2) the intra-distributional dynamics; and (3) the formation of local
clusters of convergence within the distribution.
As expected, there are considerable distributional differences between thetwo indicators of environmental efficiency. On the one hand, the cross-regional
distribution of CEEI shows a constant spread with a unique mode slightly shifting to the right. On the other hand, the distribution of DEE shows an increasing spread from its lower tail and a drastic transformation of its shape from a
trimodal distribution into a left-skewed more unimodal distribution.
There are also sharp differences in terms of intra-distributional dynamics.
In the case of the CEEI, all regions are lining up very close to the stagnationline of a mobility scatterplot. In contrast, in the case of the DEEI, most regions
are far away from the stagnation line. Also, consistent with the the lack ofsigma convergence finding, backward mobility appears to be the dominant force
within this distribution.
Given the lack of overall convergence and the particularly large degree of
backward mobility within the DEEI distribution, the last subsection of the paper evaluates the existence of local convergence clusters for the DEA-based indicator of environmental efficiency. The unconditional distribution frameworkof Azzalini et. al (2007) and Menardi and Azzalini (2014) suggests the existenceof tree groups of regions: a “Tokio-led” convergence cluster (composed by 8 prefectures), a “median-led” convergence cluster (composed by 15 prefectures), anda group of transitioning regions (composed by 23 prefectures). Moreover, further results from the conditional distribution framework of Hyndman et. al(1996) suggest that it is possible that some of those transitioning regions may
end up converging to two additional bottom clusters. Thus, the cross-regional
dynamics of the DEA-based environmental efficiency indicator (DEEI) may becharacterized by at least two convergence clusters.
To sum up, all the previous results highlight the lack of overall regional
convergence in both indicators of environmental efficiency. However, importantdifferences exist between these indicators. Perhaps the most important is thatthe DEA-based environmental efficiency indicator (DEEI) help us identify local

26
convergence clusters. This identification is potentially driven by two sources.
The DEA framework itself, which is used to aggregate the inputs and related
them to outputs. And the inclusion of production inputs in the calculationof the environmental efficiency index. If local convergence clusters are mostly
driven by the latter, then there is clear policy implication: environmental policy
efforts—focalized at the cluster level—should aim at improving the efficiency
with which production inputs are used.
Finally, further research on environmental efficiency convergence inJapan seems promising in at least two immediate fronts. First, one could exploit some of the recent advances in the spatial analysis of convergence andevaluate to what extend the spatial neighbors of a particular region help accelerate or retard its rate of convergence.13 Second, one could also exploit somerecent advances in dynamic panel data analysis. In particular, the convergencetest and clustering framework of Phillips and Sul (2007; 2009) could be usefulto evaluate how the cluster composition behaves over longer time horizons.

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