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Abstract and Figures

Reducing regional income disparities is a central challenge for promoting sustainable development in Indonesia. In particular, the prospect for these disparities to be reduced in the post-decentralization period has become a major concern for policymakers. Motivated by this background, this paper aims to re-examine the regional convergence hypothesis at the district level in Indonesia over the 2000-2017 period. By using non-linear dynamic factor model, this study analyzes novel data set to investigate the formation of multiple convergence clubs. The results indicate that Indonesian districts form five convergence clubs, implying that the growth of income per capita in Indonesian 514 districts can be clustered into five common trends. From the lens of spatial distribution, two common occasions can be observed. First, districts belonging to the same province tend be in the same club and second, the highest club is dominated by districts with specific characteristic (i.e., big cities or natural resources rich regions). From a policy standpoint, this findings of multiple convergence clubs at significantly different levels of income allows regional policy makers to identify districts facing similar challenges. It may have meaningful implications for regional development policies, including the call of inter-provincial development policy.
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Regional Income Disparities and
Convergence Clubs in Indonesia:
New District-Level Evidence
Harry Aginta
Nagoya University
Anang Gunawan
Nagoya University
Carlos Mendez
Nagoya University
November 20, 2020
This paper aims to re-examine the regional convergence hypothesis
on income in Indonesia over the 2000-2017 period. By applying a
non-linear dynamic factor model, this paper tests the club
convergence hypothesis using a novel dataset of income at the district
level. The results show significant five convergence clubs in
Indonesian districts’ income dynamics, implying the persistence of
income disparity problems across districts even after implementing
the decentralization policy. The subsequent analysis reveals two
appealing features regarding the convergence clubs. First, districts
belonging to the same province tend to be in the same club, and
second, districts with specific characteristics (i.e., big cities or natural
resources-rich regions) dominate the highest income club. Overall, our
findings suggest some insightful policy implications, including the
importance of differentiated development policies across convergence
clubs and inter-provincial development strategies.
Keywords: Regional inequality, Convergence, Indonesia
JEL Codes: O40, O47, R10, R11
Corresponding author:
1. Introduction
There is a growing recognition that reducing income inequality fosters
sustainable development. Specifically, lower levels of income inequality not
only prevent social conflict, but they are also a prerequisite for achieving
social justice. On the other aspects, some studies also find that income
inequality negatively affects economic growth (Barro,2008;Ostry et al.,
2014;van der Weide and Milanovic,2018). Moreover, widening income
inequality gives significant implications for economic growth as well as
macroeconomic stability (Dabla-Norris et al.,2015).
As one of the most heterogeneous countries in the world, Indonesia
consists of hundreds of ethnic groups with many different cultures and
religious beliefs spreading throughout the worlds largest archipelago. In
economic terms, the country has been experiencing high regional
inequality that persist since its independence. The inequality is shown by
the most developed region, particularly in Java and Sumatra islands with
capital intensive processing industries and the isolated regions that are
barely connected to few regions (Hill,1991). Therefore, one of the main
challenges in Indonesias development context is how to reduce regional
inequality and foster regional convergence (Mishra,2009).
The concern about regional inequality became greater when the
decentralization policy was implemented in 2000 (Nasution,2016;Mahi,
2016). The worry seems to be reasonable since the decentralization process
in Indonesia was implemented without much preparation, in the sense that
it was not accompanied by adequate institutional capacity or skilled
officials at the local level (Brodjonegoro,2004;Nasution,2016). Some
studies even argue that decentralization contributes to the negative growth
of investment (Brodjonegoro,2004;Tijaja and Faisal,2014) owing to
increased policy inconsistency and business uncertainty at the regional
level. Motivated by the limited research and an inconclusive answer about
the effect of decentralization on the regional income disparity dynamics,
this paper studies the evolution of regional income disparities and
prospects for convergence across 514 districts of Indonesia over the
2000-2017 period.
This study focuses on the period after the year 2000 because it
corresponds to the beginning of Indonesias decentralization era. In this
era, the state budget is allocated to regions, both to provincial and
municipal governments. However, the expected outcome from the
decentralizing policy in reducing regional inequality has yet to be seen
clearly, partly due to the diverse growth barriers and economic
preconditions in each region. Hence, identifying groups of regions facing
similar challenges is of particular relevance concerning the formulation of
policies aiming to reduce regional disparities.
In brief, the results of this paper show that Indonesian districts form five
convergence clubs, implying that the growth of income per capita in 514
districts can be clustered into five common trends. This study also finds a
”catching-up effect” within each club where the initially poor districts tend
to grow faster than the initially rich districts. Further analysis reveals two
appealing features about the convergence clubs. First, districts belonging to
the same province tend to be in the same convergence club. Second, the
highest income club is dominated by districts with specific characteristics
such as big capital cities or resources-rich regions. Furthermore, the
implementation of classical convergence tests provides supplementary
evidence about convergence speed within each club.
This paper contributes to the regional convergence literature in three
following ways. First, it is based on a convergence framework that
emphasizes the role of regional heterogeneity and the potential existence of
multiple convergence clubs. The results of club convergence analysis are
complemented by two classical tests of convergence, which are
implemented for each identified club. Second, the analysis is based on a
newly constructed dataset of per-capita income that covers 514 Indonesian
districts over the 2000-2017 period. This granular perspective opens the
possibility of identifying new patterns, which may remain hidden when
using province-level data. Finally, we extend our analysis by applying a
classical convergence test for all convergence clubs to inform the
convergence patterns.
The remainder of this paper is organized as follows. Section 2 discusses
the related literature about regional disparities and convergence in
Indonesia. Section 3 explains our research methodology, while section 4
presents the data and some stylized facts. The results of the formation of
convergence clubs are presented in Section 5. Section 6 discusses the
results in the context of classical convergence indicators, the spatial
distribution of the clubs, and policy issues. Finally, Section 7 closes the
paper with concluding remarks.
2. Related literature
2.1 Regional income disparities in Indonesia
A large body of research has been conducted to analyze economic disparity
among regions in Indonesia. Most of the studies argue that the large
socio-economic disparities among regions in Indonesia are due to larger
unequal economic activities, public infrastructure availability as well as
resource endowment (Esmara,1975;Akita,1988;Garcia and
Soelistianingsih,1998;Hill et al.,2008). One of the pioneers of regional
income disparities analysis in Indonesia at the provincial level was
conducted by Esmara (1975). He studies the inequality of Indonesian
economic development during 1970’s by analyzing per capita Gross
Domestic Product (GDP) without mining sector. The study finds that
non-mining per capita income differed by a factor of 12 between the
highest and the lowest income region.
Using Williamson Index, Akita and Lukman (1995) argue that regional
inequality at the provincial level, measured by GDP per capita, had
decreased during 1975-1992. However, using non-mining GDP per capita,
the regional inequality in the same period remained relatively stagnant.
Using a more extended period, Akita et al. (2011) examine the
inter-provincial regional income disparities over the 1983-2004 period. The
study indicates a large regional gap among the main islands in Indonesia.
In addition, they also find large disparities across districts within provinces
in the islands.
Moving to the different levels of observation, Tadjoeddin et al. (2001)
analyze the regional inequality at the district level by examining the Theil
and Gini coefficients of GDP per capita from 1993 to 1998. The study shows
that regional disparities in Indonesia are stable at the district level during
the period of analysis. Similarly, the study of Hill et al. (2008) finds that
regional disparities remained relatively unchanged during 1993-1998.
However, when oil and gas GDP per capita is excluded from the analysis,
the regional inequality kept increasing slightly until 1998.
In the context of the post-Asian Financial Crisis (AFC) 1997/98 era,
Aritenang (2014) argues that the implementation of the decentralization
policy has been considered to increase regional disparities. According to
the decentralization law, districts with abundant natural resources earn a
higher share of revenue than their provincial government and their peers in
the same province. Therefore, a natural resources-rich district receives a
higher revenue share and tends to grow faster. In the end, this might
increase disparities among districts.
2.2 Regional income convergence
A central prediction of the standard neoclassical growth model is that
under common preferences and technologies, economies would tend to
converge to a common long-run equilibrium (Barro and Sala-I-Martin,
1992;Mankiw et al.,1992;Islam,2003;Barro and Sala-I-Martin,2004).1
There is a large literature that aims to test this prediction both across and
within countries. Compared to national economies, the administrative
regions within a country are more likely to share common preferences,
technologies, and institutions. Thus, empirically testing for income
convergence across regions within a country has become a central topic in
the regional growth literature.
The seminal contributions of Barro (1991) and Barro and Sala-I-Martin
(1992) document regional income convergence across the states in the
United States, the prefectures of Japan, and the subnational regions of
Europe. Interestingly, in all these cases, regions appear to be converging at
a similar speed: 2% per year. These convergence dynamics imply that
regional differences within each country would be halved in about 35 years
(Abreu et al.,2005). These results have triggered a large empirical literature
that aims to test the regional convergence hypothesis (Sala-I-Martin,1996a;
Magrini,2004,2009). From a methodological perspective, most papers
evaluate convergence using two complementary analyses. On the one
hand, an analysis of sigma (σ) convergence evaluates whether the income
dispersion decreases over time. On the other, an analysis of beta (β)
1Although the original conception of the Solow growth model aims to explain the
evolution of a single economy over time, its convergence prediction has been empirically
tested across multiple countries, regions, industries, and firms. As a result, the convergence
hypothesis has been studied from multiple perspectives. The recent work of Johnson and
Papageorgiou (2020) provides a survey of the cross-country convergence literature. Magrini
(2004) provides a survey of the regional convergence literature. The work of Rodrik (2013) is
one of the most influential papers in the industrial convergence literature, and the work of
Bahar (2018) evaluates convergence across firms.
convergence evaluates whether initially poor economies grow faster than
initially rich regions. These two analyses are also related in the sense that
beta convergence is necessary but not sufficient for sigma convergence
More recently, the convergence literature has been shifting its focus
from the classical emphasis on average behavior and common long-run
equilibrium to a new emphasis on heterogeneous behavior and multiple
equilibria (Apergis et al.,2010;Bartkowska and Riedl,2005;Zhang et al.,
2019). This approach emphasizes the notion that, even within countries,
there could be persistent differences in endowments, preferences, and
technologies. As such, regional economies may not smoothly converge to a
unique long-run equilibrium, but instead, multiple convergence clubs may
characterize the regional economic system.
2.3 Regional income convergence in Indonesia
Many scholars have conducted studies on inequality at the regional level in
Indonesia using various convergence frameworks (see Table 1). Garcia and
Soelistianingsih (1998) employ beta convergence method to investigate the
existence of convergence in income per capita across provinces during
1975-1993. The study shows that regional income disparities tend to
converge, and it may take between thirty to forty years to reduce income
differences by half. However, Hill et al. (2008) argue that the results of
convergence by Garcia and Soelistianingsih (1998) are sensitive to the
period analyzed and the unstable performance of the oil and gas sector.
Also, the study of Hill et al. (2008) shows that during the financial crisis and
its aftermath, that is from 1997 to 2002, there was no significant
convergence at the regional level. Similarly, using conventional estimation
of sigma and beta convergence, Tirtosuharto (2013) does not find regional
convergence during the Asian financial crisis, the recovery period, and the
beginning of the decentralization era.
At the district level, the study by Akita (2002) shows a similar conclusion
that regional income inequality increased during 1993-1997. This result
does not contradict other studies at the provincial level since it shows that
inequality increased among certain districts within some provinces. In
addition, Akita et al. (2011) show that when the Asian financial crisis hit in
1997, regional inequality has declined since some big cities were hit harder
than less developed districts. However, during the recovery period, regional
inequality increased again until 2004 and remained uncertain afterwards.
Analysis at the district level has also been conducted by Aritenang (2014)
using exploratory analysis, Spatial Autoregressive (SAR) Lag Model, and
Spatial Error Model (SEM) to capture the spatial effects. By considering the
role of the neighborhood, the study finds that the convergence rate is
higher throughout the decentralization era. A similar approach was
conducted by Vidyattama (2013). However, the result of the study indicates
inconclusive finding on convergence. The Williamson index measurement
shows slight increases, although insignificant, while the beta convergence
estimates reveal convergence at both the district and the provincial levels
during 1999-2008. In addition, the study needs a longer period of
observation since the overall trend of convergence is still very weak.
Another recent study was conducted by Kurniawan et al. (2019) by
applying club convergence analysis on provincial dataset from 1969 to
2012. In their study, some missing data at the provincial level are
interpolated in order to build a balanced panel dataset. The results show
two convergence clubs in terms of all investigated variables.2Using a
similar method, Mendez and Kataoka (2020) examine the disparities in
2The study examines the dynamics of four socio-economic indicators: per capita gross
regional product, the Gini coefficient, the school enrolment rate, and the fertility rate.
Table 1: Studies on per capita income convergence in Indonesia
Author(s) Observation Methods Findings
Garcia and
(26 provinces)
Absolute and
conditional beta
Results: Absolute convergence;
conditional convergence
increases convergence speed.
Akita (2002)
(27 provinces
303 districts)
weighted coefficient of
variation (CVw)
and Theil index
Results: Convergence at province
and no convergence at district level.
The mining sector matters and
income inequality at the district
level increases in1993-1997.
Hill et al.
(26 provinces)
and conditional
beta convergence
Results: Convergence before the
Asian Financial Crisis (AFC) 1997
and no convergence after the AFC.
The speed of convergence declines
along with the decreasing in the
mining sector.
Akita et al.
(26 provinces)
Results: Convergence before
the AFC 1997 and no convergence
after the AFC. The convergence
before the AFC is due to poorer
performance of the resource-rich
(26 provinces)
Sigma convergence
and unconditional
beta convergence
Results: No sigma convergence,
beta convergence in 1997-2000 and
no beta convergence in 2001-2012.
(26 provinces
294 districts)
Unconditional beta
convergence, Spatial
Autoregressive Lag,
and Spatial Error Model
Results: Insignificant convergence in
income per capita and significant
convergence in HDI at both province
and district levels.
(292 districts)
Spatial autocorrelation,
Spatial Error Model, and
Spatial Autoregressive
Lag Model
Results: Strong evidence of spatial
autocorrelation, the convergence rate
is higher during decentralization.
Kurniawan et al.
(33 provinces)
1969-2012 Club convergence Results: Two convergence clubs in
four socio-economic indicators.
Mendez and
(26 provinces)
1999-2010 Club convergence
Results: Two convergence clubs in
labor productivity, four clubs in
physical capital, two clubs in human
capital, and unique convergence club
in efficiency.
Source: Authors’ documentation from many sources.
labor productivity, capital accumulation, and efficiency across 26 provinces
from 1990 to 2010. The study finds that labor productivity, physical capital,
and human capital are characterized by two, four, and two convergence
clubs, respectively. Meanwhile, a unique convergence club is found to be
related to the efficiency variable. The study suggests the importance of
capital accumulation and efficiency improvements in promoting
productivity growth as well as reducing the disparities among regions in
3. Methodology
3.1 Classical beta and sigma convergence
The most common method of convergence analysis is mainly based on
classical models such as namely sigma convergence and beta convergence
(Bernard and Durlauf,1995;Hobijn and Franses,2000;Phillips and Sul,
2007). Sigma convergence refers to the decreasing in growth dispersion (in
most cases, the growth of income per capita) across countries or regions
over time. Differently, beta convergence is seen in negative correlation
between the initial level of income capita and its growth. Implicitly, this
means that low-income countries tend to grow relatively faster than
high-income countries and thus are able to catch up (Barro,1991;Barro
and Sala-I-Martin,1992).
The concept of beta convergence can be differentiated into absolute and
conditional convergence (Islam,1995,2003;Mankiw et al.,1992;
Sala-I-Martin,1996b). On one side, absolute beta convergence assumes
that countries will approach a particular common steady-state growth path
over time, given the variability in the initial condition of each country. On
the other side, the notion of conditional beta convergence implies
convergence occurs towards different paths of steady-state growth given
the assumption that countries have distinctive characteristics, such as
accumulation in human and physical capital, institution, economic and
political system, and other factors affecting economic growth. Many
researchers find that the dispersion of income per capita across economies
follows the patterns of clusters rather than the direction of a common
growth path (Quah,1996;Phillips and Sul,2009;Basile,2009). This is not
only true for largely diversified cases such as cross country analysis, but this
trend has also been observed in more integrated economies like those in
Western Europe (Corrado et al.,2005).
Some studies also started to find convergence patterns across countries,
regions, industries, etc., when analyzing socio-economic variables (Barro,
1991;Barro and Sala-I-Martin,1992). According to Barro and Sala-I-Martin
(1992), this convergence pattern can be generalized as follows:
(1/T )·log yiT
=α[1 eβT ]
T·log(yi0) + wi,0T(1)
where yis the analyzed variable, irepresents a region, 0and Tare the initial
and final times, βis known as the speed of convergence, αincludes
unobserved parameters including the steady-state and wi,0Tis the error
term. Referring to equation (1), if there are robust signs of beta
convergence, then a different parameter known as the ”half-life” can be
defined as follows:
half ·lif e =log2
This parameter indicates the time required for the average region to reduce
the gap between its initial and the final equilibrium state by half.
3.2 Relative convergence test
Phillips and Sul (2007) develop log tconvergence test, an innovative
method to investigate the existence of multiple convergence clubs based on
a clustering algorithm. This method is favorable because of its superiority
in the sense that it allows the time series not to be co-integrated, thus
allowing individual observation to be transitionally divergent (Bartkowska
and Riedl,2005). The method also concludes that the absence of
co-integration in respective time series does not necessarily deny the
existence of convergence (Phillips and Sul,2007). Due to its advantages,
numerous researchers have utilized this approach with applications in
convergence analysis on various economic indicators such as per capita
income, financial development, and energy.
The relative convergence test suggested by Phillips and Sul (2007,2009)
is based on the decomposition of the panel-data variable of interest in the
following way:
yit =git +ait (3)
where git is a systematic component and ait is a transitory component.
To separate common from idiosyncratic components, equation 3can be
transformed with a time-varying factor as follows:
yit =git +ait
where δit contains error term and unit-specific component and thus
represents an idiosyncratic element that varies over time, and µtis a
common component.
To be more specific, the transition path of an observed economy
towards its own equilibrium growth path is explained by δit, while µtdepicts
a hypothesized equilibrium growth path that is common to all economies.
Equation 4is therefore a dynamic factor model containing a factor loading
coefficient δit that represents the idiosyncratic distance between a common
trending behavior, µt, and the dependent variable, yit. Furthermore, to
characterize the dynamics of the idiosyncratic component, δit,Phillips and
Sul (2007) propose the following semi-parametric specification:
δit =δi+σiξit
log (t)tα(5)
where δirepresents the heterogeneity of each economy but constant over
time, ξit is a weakly time-dependent process with mean 0 and variance 1
across economies. Under the condition given in equation 5, convergence
occurs when all economies move to the same transition path as such,
δit =δand α0(6)
In order to estimate the transition coefficient δit,Phillips and Sul (2007)
construct a relative transition parameter, hit, as
hit =yit
i=1 yit
i=1 δit
where the common component, µtin equation 4is eliminated by dividing
the independent variable, yit, with the panel average. Thus, hit represents
the transition path of economy iagainst the level of cross-sectional average,
implying the calculation of individual economic behaviors relative to other
economies. Then, hit converges to unity, that is hit 1, when t→ ∞.
Later, the notion of convergence can be transformed into the following
equation that describes the cross-sectional variance of hit,
(hit 1)20(8)
where the cross-sectional variance converges to zero, Ht0.
The null hypothesis in equation 6is verified in counter to the alternative
hypothesis HA:δi6=δfor all ior α0. Finally, Phillips and Sul (2007)
empirically evaluate this null hypothesis by using the following log t
regression model:
log H1
Ht2 log{log(t)}=a+blog(t) + εt
for t= [rT ],[rT ]+1, . . . , T with r > 0
where rT is the initial observation in the regression, which implies that the
first fraction of the data (that is, r) is discarded.
Based on Monte Carlo experiments, Phillips and Sul (2007) suggest
applying r= 0.3when the sample is small or moderate T50. A fairly
conventional inferential procedure is also suggested for equation 9. To be
more specific, a one-sided ttest with heteroskedasticity-autocorrelation
consistent (HAC) standard errors is used. In this setting, the null hypothesis
of convergence is rejected when the t-statistics (tˆ
b) is smaller than -1.65.
3.3 Clustering algorithm
Even though the null hypothesis of overall convergence in the full sample is
rejected, it does not necessarily mean that the convergence in the
subsample of the panel is not present. Therefore, following Phillips and Sul
(2007), we exploit the feature of the model in equation 7to reveal the
presence of multiple convergence clubs in subsample. For that purpose, we
use an innovative data-driven algorithm developed by Phillips and Sul
(2009), which can be summarized in the following four steps:
1. Ordering: Sample units (districts) are arranged in a decreasing order
according to their observation in the last period. In this paper, the
ordering is conducted using the average of the last 1
2. Constructing the core group: A core group of sample units (districts) is
identified based on the first kunit of the panel data set (2 kN).
If the tˆ
bof the kunit is larger than -1.65, the core group formation is
established. If the tˆ
bin the first kunit is smaller than -1.65, the first
unit is dropped, and then the log ttest for the next units is conducted.
The step is continued until the tˆ
bof the pair units is larger than -1.65.
If there are no pairs of units showing tˆ
blarger than -1.65 in the entire
sample, it can be concluded that there are no convergence clubs in the
3. Deciding club membership: Sample units (districts) not belonging to
the core group are re-evaluated once at a time with log tregression.
A new group is formed when the tˆ
bis larger than -1.65. Otherwise, if
the additional units give a result that tˆ
bis smaller than -1.65, then the
convergence club only consists of the core group.
4. Iteration and stopping rule: The log tregression is applied for the
remaining sample units (districts). If the process shows the rejection
of the null hypothesis of convergence, steps 1 to 3 are performed
again. The remaining sample units (districts) are labeled as divergent
if no core group is found, and the algorithm stops.
The representation of the relative transition curve for different
economies in the club convergence framework can be illustrated in Figure
1. The figure clearly shows that the transition curves for different regions
form a funnel. The four regions, which are region A, B, C, and D, differ in
their initial conditions as well as in their transition paths. However, region A
and region B’s relative transition curve converge into the same value, which
is Club 1. In comparison, region C and region D are characterized by
1 t
Club 1h1
Club 2
Region D
Region C
Region A
Region B Cross-sectional average
Figure 1: An illustration of transition paths and convergence clubs
medium and low initial conditions, consecutively reflecting a typical
developing region with a slow growth rate and a poor region that grows
rapidly. With time, the transition path of both regions converge into Club 2.
4. Data and stylized facts
4.1 Data construction
This study uses annual GDP per capita at the district level from 2000 to
2017. However, not all of the data are available for every year in each
district. In addition, there are some missing observations caused by the
splitting up of new districts during the decentralization period. Since the
club convergence test of Phillips and Sul (2007) requires balanced panel
data, we constructed a balanced panel dataset of 514 districts by solving the
missing observations through interpolation/imputation.3Similar with the
study of Kurniawan et al. (2019), the imputation process in our study was
conducted using a linear regression method with the year and reference
districts as candidates of regressors. Hence, since we only predicted the
missing values from its trend, it would not significantly alter the
convergence results.4Table 2shows the descriptive statistics of the dataset.
Table 2: Descriptive statistics
Mean Standard deviation Max/Min
2000 2017 2000/2017 2000 2017 2000/2017 2000 2017
GDP per capita (in thousand IDR) 25,032 36,041 0.69 62,172 42,823 1.45 465.40 105.05
Log of GDP per capita 9.57 10.20 0.94 0.81 0.67 1.20 1.81 1.56
Trend log of GDP per capita 9.57 10.20 0.94 0.81 0.68 1.20 1.81 1.56
Relative trend of log GDP per capita 1.00 1.00 1.00 0.08 0.07 1.28 1.81 1.55
As mentioned in the methodology, we transformed the GDP per capita
data into a log form. Like common macroeconomic data, the GDP per
capita has two prominent features, which are long-run growth trends in
aggregate and a cyclical component that represents fluctuations in the
shorter periods, known as the business cycles. When analyzing business
cycles in observed data by regression or filtering, it is necessary to isolate
the cyclical component from the trend (Phillips and Shi,2019). Therefore,
following Uhlig and Ravn (2002), we filtered the GDP per capita series using
Hodrick-Prescott (HP) filter technique with smoothing parameter (λ)
equals to 6.25.
3We combined actual data of the new districts and the reference districts and compared
them to ensure that measurement error caused by the interpolation is minimum. Details of
this interpolation process are provided in Appendix A.
4For the robustness check of our interpolation results, we implemented sigma and
beta convergence tests using the number of districts in the year 2000 (342 districts). As
reported in Appendix E, we found no significant difference in sigma and beta convergence
coefficients between the full sample of 514 districts and the smaller number of districts.
4.2 Stylized facts on regional disparities in Indonesia
This subsection illustrates how income disparities across districts in
Indonesia have evolved over time. Figure 2measures regional disparities as
the standard deviation of the log of GDP per capita. This measurement
approach is commonly used in the regional growth literature and is
generally referred to as the study of sigma convergence (Barro and
Sala-I-Martin,1992;Magrini,2004;Sala-I-Martin,1996b). A process of
sigma convergence occurs when regional disparities decrease over time.
Figure 2highlights this process by pointing out that the standard deviation
of the log of GDP per capita has been systematically decreasing over the
2000-2017 period.
SD of Log GDP per capita
2000 2005 2010 2015 2020
Figure 2: Evolution of regional disparities: Sigma convergence approach
Notes: GDP refers to the district-level gross domestic product, and it is measured based
on constant prices of 2010. The source of the data is the Central Bureau of Statistics of
Indonesia and interpolation results.
We also show the process where the initially poor regions are catching
up and growing faster than initially rich regions. This catching-up process is
largely documented in the economic growth literature and is referred to as
the study of beta convergence (Barro and Sala-I-Martin,1992;Magrini,2004;
Sala-I-Martin,1996b). Figure 3highlights this process by pointing out that
regions with a low GDP per capita in 2000 have grown faster than initially
rich regions over the 2000-2017 period. Interestingly, the richest regions in
1990 experienced large negative growth rates in subsequent years. Thus, the
(beta) convergence process is arising not only because of the faster growth of
the poorest regions but also because of a systematic reduction in the income
of the richest regions.
Growth Rate 2000-2017
810 12 14
Log GDP per capita in 2000
Figure 3: Evolution of regional disparities: Beta convergence approach
Notes: GDP refers to the district-level gross domestic product, and it is measured based
on constant prices of 2010. The source of the data is the Central Bureau of Statistics of
Indonesia and interpolation results.
By construction, the summary statistics of sigma and beta convergence
only describe the behavior of an average or representative economy
(Magrini,2004). They fail to describe more complex convergence dynamics
that could occur beyond the mean of the income distribution. They also fail
to accommodate the notions of multiple equilibria and convergence clubs,
which could arise when the regions’ performance is highly heterogeneous.
In Indonesia’s context, a high degree of regional heterogeneity has been
previously documented using province-level data. Moreover, it has been
argued that only focusing on average patterns is likely to be incomplete at
best or misleading at worst (Mendez and Kataoka,2020). In an attempt to
start documenting the degree of regional heterogeneity using district-level
data of recent years, Figures 4and 5show the evolution of regional
disparities beyond the scope of the average or median district.
Figure 4shows how the quantiles of the distribution have evolved over
time. Panel (a) indicates that when we evaluate the regional dynamics of
GDP per capita, within any logarithm transformation, regional disparities
have been increasing over time. Increasing disparities are evident not only
when we measure the gap between the quantile 95 and quantile 5, but also
when we measure the gap between the quantile 75 and 25. In the statistics
literature, this latter gap is referred to as the interquartile range (IQR) and is
commonly used as a dispersion statistic that is robust to extreme values.5
Panels (b) and (c) indicate that the logarithm version of GDP per capita
shows less diverging dynamics. Despite of this transformation, the IQR,
which encompasses half of the entire distribution, shows very little signs of
regional convergence. Panel (d) normalizes the trend of log GDP by the
cross-sectional mean of each year. This transformation helps to remove the
common increasing trends observed in panels (b) and (c). Based on this
transformation, regional disparities have been evolving differently within
the income distribution. Most of the reduction in the disparities arises from
the tails of this distribution, particularly the upper tail. In contrast,
disparities around the center of the distribution show little change. The size
of the IQR has been almost constant over the entire 2000-2017 period.
Figure 5provides a more detailed perspective on the dynamics reported
5In the convergence literature, the IQR is also used to study sigma convergence (Mendez-
2000 2005 2010 2015
GDP per capita
(a) GDP per capita
2000 2005 2010 2015
Log of GDP per capita
(b) Log GDP per capita
2000 2005 2010 2015
Trend Log of GDP per capita
(c) Trend log GDP per capita
2000 2005 2010 2015
Relative Trend Log of GDP per capita
(d) Relative trend log GDP per capita
Figure 4: Evolution of regional disparities: Distributional quantile approach
Notes: GDP refers to the district-level gross domestic product, and it is measured based
on constant prices of 2010. The source of the data is the Central Bureau of Statistics of
Indonesia and interpolation results.
Relative Trend Log GDP per capita
2000 2005 2010 2015 2020
Figure 5: Evolution of regional disparities: Relative convergence approach
Notes: GDP refers to the district-level gross domestic product, and it is measured based
on constant prices of 2010. The source of the data is the Central Bureau of Statistics of
Indonesia and interpolation results.
in Figure 4d. Instead of just displaying five hypothetical regions, Figure 5
shows the actual dynamics of all regions.6Its main finding is consistent
with that of Figure 4; that is, the process of regional convergence is not
homogeneous across the distribution of districts. Regions at the top of the
distribution are converging faster than those at the bottom. Regions around
the middle of the distribution show little progress in the reduction of
regional disparities.
5. Results
5.1 Relative convergence test
After applying the log ttest to the income per capita data across 514
Indonesian districts over the 2000-2017 period, we were able to reject the
null hypothesis of overall convergence at the 5% significant level, where ˆ
significantly <0 and tˆ
bis 22.28 (see Table 3). This implies that
convergence for all districts is not present, indicating that the income
growth process of 514 Indonesian districts from 2000 to 2017 does not show
a single equilibrium steady-state. This finding is consistent with the
empirical evidence documented in the study of Hill et al. (2008), where no
significant convergence was observed after the 1997/98 Asian financial
crisis period, as opposed to significant convergence before the crisis.7Our
finding also supports the study of Tirtosuharto (2013), who concludes the
lack of regional convergence for the period from 2003 to 2012 following
economic recovery from the Asian financial crisis and the beginning of the
6As regions can change their ranking in the income distribution, the quantiles of Figure
4do not necessarily track the performance of a unique region over time.
7The study of Hill et al. (2008) shows the variability in the pace of beta convergence
across subperiod during 1975-2002; 2% during the oil boom (1975-81), 2.8% in the era of
major policy reforms (1981-86), 1.7% for the period 1986-92 as the export-oriented reforms
took place, 1% during the 1990s, and no convergence in the crisis and post-crisis period.
decentralization era.
Table 3: Global convergence test
Coefficient Standard Error t-statistic
log(t) -0.52 0.02 -22.28
Note: The null hypothesis of convergence is rejected when
the t-statistic is less than -1.65.
This lack of overall convergence also entails policy implications related
to the implementation of the decentralization policy in Indonesia after the
crisis. As pointed out by Azis (2008) and Nasution (2016), by and large, the
performance of regional growth after the decentralization has been
unsatisfying. One of the major causes of this unexpected outcome is the
variability in the capacity of regional institutions and local leaders to
leverage local resources, in addition to counterproductive policies issued by
local governments (e.g., imposing hidden fees, allocating funds to
unnecessary projects), and inflexible and over-regulated national policies.
Therefore, to avoid potential detrimental effect of decentralization on
regional disparities, in particular developing countries like Indonesia, the
regional government is required to improve the quality of institutional
factors such as accountability, people’s empowerment as well as
redistribution capacity (Azis,2008;Rodriguez-Pose and Ezcurra,2010).
5.2 Clustering algorithm and convergence clubs
Although overall convergence across Indonesian districts does not prevail,
the log ttest brings the possibility to observe the existence of several
convergence clusters, as explained in Section 3.3. Therefore, we applied the
test procedure to investigate convergence clubs. As shown in Table 4, we
found five significant initial clubs.8The first convergence club consists of 6
districts; the second club consists of 126 districts; the third club consists of
178 districts; the fourth club contains 181 districts, and the fifth club
consists of 23 districts. The rows correspond to the fitted coefficients and
t-statistic in each club.
The order of the convergence clubs is sorted from the districts with the
highest to the lowest GDP per capita, that is, Club 1 refers to the highest
GDP per capita group and Club 5 displays the lowest GDP per capita group.
The result of this club convergence test implies that the development of
income per capita in 514 Indonesian districts can be grouped into five
common trends during 2000-2017.
Table 4: Local convergence test
Club1 Club2 Club3 Club4 Club5
Coefficient 0.42 -0.08 0.37 -0.04 0.49
t-statistic 4.97 -1.52 5.26 -1.60 6.55
N. of regions 6 126 178 181 23
Note: The null hypothesis of convergence is rejected when the t-
statistic is less than -1.65.
Then, following Phillips and Sul (2009), we checked the possibility of
whether any of those identified clubs can be merged to form larger
convergence clubs.9As shown in Table 5, the club merging test result
suggests that the convergence hypothesis is rejected (ˆ
bis significantly <0
and tˆ
bis smaller than -1.65). Hence, the initial five clubs are confirmed as
8See Appendix B for complete members of each club.
9The clubs merging steps are outlined in Appendix C.
the final convergence clubs.
Table 5: Clubs merging test
Club1+2 Club2+3 Club3+4 Club4+5
Coefficient -0.14 -0.27 -0.30 -0.20
t-statistic -3.08 -6.99 -15.44 -9.52
Note: The null hypothesis of convergence is rejected when the t-
statistic is less than -1.65.
Furthermore, measuring the gap between clubs is also useful to
understand the income disparities among convergence clubs. For this
purpose, we show the mean per capita income of each club in the second
column of Table 6. The statistics suggest that the gap of income per capita
between clubs is arguably large, particularly between Club 1 and Club 2,
where the average income per capita of districts in Club 1 is IDR 231
million, about four times larger than that in Club 2. This implies that Club 2
has very little progress in catching up with Club 1. Table 6also reflects
severe income inequality problems among districts in Indonesia, where the
average income per capita in the last club is only about 3% of the that in the
first club.
Table 6: Characteristics of the clubs 2000-2017
Mean Std. Deviation Min Max
Club 1 231,289 196,580 7,058 932,664
Club 2 56,961 58,557 7,718 658,303
Club 3 20,090 12,178 3,402 304,400
Club 4 13,469 7.952 4,005 194,717
Club 5 7,549 5.959 2,004 59,292
Note: The income per capita data is in a thousand IDR.
Figure 6shows the transition paths of members in each club by
comparing income per capita of each district (in log form) relative to clubs’
average. All five clubs exhibit different convergence behaviors and
transition paths within the club, depending on each district’s initial
conditions and development process. We also capture one asymmetric
transition pattern within the club. On the one hand, some districts with a
higher level of income at the initial period experience a sufficiently large
income reduction at the final period and move downwards to the clubs
average level. Most of these districts are those relying on natural resources
(e.g., mining and natural gas processing) such as Mimika (Club 1), Bontang
(Club 2), Lhokseumawe (Club 3), Aceh Utara (Club 4), and Aceh Timur
(Club 5). The last three districts also suffer from prolonged security issues
that led to the Martial Law enactment in 2003, followed by the Tsunami
disaster in 2004. On the other hand, none of the districts with a lower
income level at the initial period record significant improvement. This
asymmetrical pattern implies that the convergence process within clubs
(particularly Club 4 and 5) is influenced by the depleting income in
wealthier districts.
Similar to Figure 4d, in Figure 7we plot the transition paths of clubs over
time. However, instead of using the absolute income per capita (in log
form) on Y axes, in Figure 7we compare the transition of clubs relative to
the cross-sectional average of all clubs. The parallel pattern of the clubs’
transition path indicates that the clubs do not converge over time. Even
though Club 3 appears to slightly close its gap to Club 2, the transition path
of the other clubs reflects prolonged and stable dispersion between clubs,
where Club 4 and 5 are systematically below the average, while Club 1 and 2
are consistently above the average.
Relative Trend
Log GDP per capita
2000 2005 2010 2015 2020
Club 1
Relative Trend
Log GDP per capita
2000 2005 2010 2015 2020
Club 2
Relative Trend
Log GDP per capita
2000 2005 2010 2015 2020
Club 3
Relative Trend
Log GDP per capita
2000 2005 2010 2015 2020
Club 4
Relative Trend
Log GDP per capita
2000 2005 2010 2015 2020
Club 5
Figure 6: Convergence clubs and transition paths
Notes: GDP refers to the district-level gross domestic product, and it is measured based
on constant prices of 2010. The source of the data is the Central Bureau of Statistics of
Indonesia and interpolation results.
Relative Trend Log GDP per capita
2000 2005 2010 2015 2020
Club = 1
Club = 2
Club = 3
Club = 4
Club = 5
Figure 7: Convergence clubs trends
Notes: GDP refers to the district-level gross domestic product, and it is measured based
on constant prices of 2010. The source of the data is the Central Bureau of Statistics of
Indonesia and interpolation results.
5.3 Sensitivity to the trend estimation
We also implemented the log ttest by using the smoothing parameter (λ) of
Hodrick-Prescott (HP) filter equals to 400, which is used in the study of
Phillips and Sul (2007). Similar to the results discussed in the previous
section, the existence of global convergence is rejected at the 5% significant
level (ˆ
bis significantly <0 and tˆ
bis 23.02). Then we proceeded with the
club convergence test by following the same procedures discussed in
Section 3.3. We found twelve convergence clubs initially. Next, we applied
the merging test procedure to investigate whether any of those initial
subgroups can be merged to form convergence clubs with a larger number
of members.
As a result, we also found five final significant convergence clubs. The
Table 7: Characteristics of the clubs, 2000-2017 (Trend parameter 400)
Mean Std. Deviation Min Max
Club 1 198,036 166,863 7,058 932,664
Club 2 50.595 39,595 3,531 417,149
Club 3 20,534 12,502 2,102 304,400
Club 4 11,825 3,505 4,292 59,292
Club 5 5,809 1,746 2,004 10,376
Note: The income per capita data is in a thousand IDR.
first and second initial clubs merge into first convergence club with 14
members while the third initial club becomes the second club with 106
members. Next, the third new club is formed by the fourth, fifth, and sixth
initial clubs with 240 members and becomes the largest final club (47% of
the total number of districts). Next, the fourth final club is constructed by
clubs 7, 8, 9, 10, and 11 of the initial clubs with 132 members. Finally, the
twelfth (the last) initial club stays unmerged with 22 members (details of
results are presented in Appendix D). Consistent with the previous analysis,
the statistics shown in Table 7also imply a huge income gap among clubs.
Referring to the average of per capita income in all clubs, one may quickly
capture that the biggest income gap lies between Club 1 and Club 2, while
the income gap between districts in lower clubs (Club 4 and Club 5) is
much smaller.
6. Discussion
6.1 Convergence within clubs
This section evaluates the convergence patterns within each club using the
classical frameworks of sigma and beta convergence. Figure 8shows the
evolution of the standard deviation of the log of GDP per capita for each
club. All sub-figures share the same axes in order to facilitate comparability
between clubs. Consistent with Figure 6, there is a stronger process of
convergence within clubs than between clubs. In particular, the districts of
Club 1 (see Appendix B for a detailed list) show the largest reduction in
regional disparities. Although the other clubs start from lower levels of
disparities, they show relatively less progress over time.
Figure 9shows the negative relationship between the initial level of
income and its subsequent growth rate. Within each club, initially poor
regions are growing faster than initially rich ones. Thus, a process of beta
convergence is also taking place within each club. Compared to the global
convergence process suggested by Figure 3, the slope of each convergence
club is steeper. This difference suggests that the (local) speed of
convergence within each club is faster than that of the global process.
Table 8provides further details about beta convergence within each
club. Again, relative to the global fit (Figure 3), the fit of the local models is
higher. The R-squared ranges from 0.64 in Club 5 to 0.86 in Club 1. The
districts belong to Club 3 converge at the highest speed (5.3% per year).
Thus, it is expected that disparities within Club 3 would be reduced by half
in just under 13 years. This fast local convergence contrasts with the global
model, which predicts that disparities would be halved in 42 years.
SD Log GDP pc
2000 2005 2010 2015 2020
Club 1
SD Log GDP pc
2000 2005 2010 2015 2020
Club 2
SD Log GDP pc
2000 2005 2010 2015 2020
Club 3
SD Log GDP pc
2000 2005 2010 2015 2020
Club 4
SD Log GDP pc
2000 2005 2010 2015 2020
Club 5
Figure 8: Evolution of disparities within clubs: Sigma convergence approach
Notes: GDP refers to the district-level gross domestic product, and it is measured based
on constant prices of 2010. The source of the data is the Central Bureau of Statistics of
Indonesia and interpolation results.
Growth 2000-2017
810 12 14
Log GDP pc in 2000
Club 1
Growth 2000-2017
810 12 14
Log GDP pc in 2000
Club 2
Growth 2000-2017
810 12 14
Log GDP pc in 2000
Club 3
Growth 2000-2017
810 12 14
Log GDP pc in 2000
Club 4
Growth 2000-2017
810 12 14
Log GDP pc in 2000
Club 5
Figure 9: Evolution of disparities within clubs: Beta convergence approach
Notes: GDP refers to the district-level gross domestic product, and it is measured based
on constant prices of 2010. The source of the data is the Central Bureau of Statistics of
Indonesia and interpolation results.
Table 8: Evolution of disparities within clubs: Beta convergence approach
Beta Convergence Half-life R-square
coefficient speed in years
Club 1 -0,54∗∗∗ 0,046 15,09 0,86
Club 2 -0,43∗∗∗ 0,032 21,14 0,74
Club 3 -0,59∗∗∗ 0,053 12,98 0,83
Club 4 -0,51∗∗∗ 0,042 16,36 0,69
Club 5 -0,52∗∗∗ 0,043 15,05 0,64
6.2 Geographical distribution of the convergence clubs
Now, we provide a geographical view of club membership as seen in Figure
10. A few regularities are visible from the map. First, the province effect is
notably obvious; districts belonging to the same province tend to be in the
same club (Barro,1991;Quah,1996). This pattern applies almost to all
clubs. For example, districts in provinces of East Kalimantan and Riau tend
to be grouped in Club 2. Similarly, Aceh, West Sumatra, West Kalimantan,
and Central Kalimantan also show comparable pattern where most of the
districts in these provinces are clustered in Club 3, and mostly the districts
in Maluku and Nusa Tenggara provinces dominate Club 4 and Club 5. More
surprisingly, districts belonging to the same club also tend to be
geographically close. To put it another way, the clubs seem to be spatially
concentrated. This could indicate some spatial agglomeration effects
(Martin and Ottaviano,2001) driven by factors like spatial externalities or
spillovers (Quah,1996).
Second, the distribution of clubs is also related to the spatial
distribution, implying the prolonged existence of classical regional
Figure 10: Spatial distribution of the convergence clubs
development problem in Indonesia; that is, the eastern regions of the
archipelago are still lagged in development. It can be seen from the
membership of the fifth club where out of 23 members, 21 districts are
located in the eastern provinces of Indonesia, i.e., South Sulawesi, Nusa
Tenggara, and Papua.
6.3 Policy implications
The difference in the progress of inter-regional development is natural. It is
related to the variation in potential that each region has, both natural
resources and geographical location. In addition, variation in the regional
ability to manage their resources and potential are also factors that
differentiate the success rate of development in each region. Despite the
Indonesian economy’s ability to maintain robust economic growth after the
Asian financial crisis in 1997/98, the persistent income gap between regions
still becomes one of major problems that could potentially be a source of a
worse complication in the future. Not only could trigger social dispute
stemmed from the perception of injustice among fellow communities,
regional income inequality could also pose downside risks to the national
economic growth.
To reduce regional income inequality, the Indonesian government needs
to have a clear and accurate picture of regional imbalances among regions.
In this context, the results of this study suggest that the growth path of
income per capita among 514 Indonesian districts during the period of
2000-2017 does not converge to the same steady-state level. Similar to
Kurniawan et al. (2019), this finding implies the absence of global
convergence of income per capita among Indonesian regions. Instead, the
growth process of Indonesian districts constitutes five local convergence
Interestingly, there is distinct characteristic across clubs, in particular
between the highest income club (Club 1) and the lowest one (Club 5). At
one end, Club 1 is dominated by regions with typical characteristics, i.e., big
cities or natural resources-rich regions like Central Jakarta (the central
district of the nations capital city), Kediri (the largest national tobacco
producer), Morowali (the location of recently developing nickel-based
industrial park), Membramo Raya, Mimika and Teluk Bintuni (the natural
resources-rich districts in the coastal area of Papua island, respectively).
While at the other end, Club 5 predominantly consists of districts that have
long been struggling with poverty issues. In addition, the income gap
among these five clubs is also considerably large, suggesting that the
potential regional development policies might be different across clubs. For
example, the development policies for districts in Club 1 might be directed
to seeking new sources of growth to avoid income stagnation. Meanwhile,
the majority of districts in Club 2, 3, and 4 could focus their program on
developing the middle-sized cities and more programs on improving
connectivity. Differently, policies on basic infrastructures and public
services provision should be implemented in districts of Club 5.
Furthermore, the spatial distribution of clubs can provide non-trivial
information for inter-provincial policymaking to reduce income inequality.
For example, Figure 10 shows that some districts in Club 5 share the border
with districts in Club 1, implying the potential to further strengthen positive
spillover from the rich districts to their poor neighboring districts. In Papua
province, for instance, Pegunungan Arfak (Club 5) is the direct neighbor of
Teluk Bintuni (Club 1); Deiyai, Puncak, and Nduga (Club 5) share the border
with Mimika (Club 1); Puncak Jaya and Tolikara (Club 5) are the neighbors
of Membramo Raya (Club 1). Among others, inter-provincial policies such
as strengthening connectivity and promoting trade between these regions
are highly favorable. The same fashion can also be applied in some poor
districts of Club 5 such as Aceh Timur in Aceh province, Blora in Central
Java province, and Jeneponto in South Sulawesi province.
Lastly, given the persistence of the west-east development gap observed
in this study, the central government policies to support the development
of physical infrastructures and basic public services provision in the eastern
parts of the archipelago are strongly suggested to reduce regional income
7. Concluding remarks
A development process is sustainable when it favors social inclusion and
the reduction of regional disparities. In this context, our study documents
the evolution of disparities in income per capita among Indonesian
districts after the implementation of decentralization policy. We use a novel
district-level dataset that covers 514 Indonesian districts over the 2000-2017
period. From a methodological perspective, the convergence club test
proposed by Phillips and Sul (2007) is applied to evaluate whether all
districts converge to a common steady-state growth path.
The main findings are as follows. First, there is no overall convergence in
income per capita among Indonesian districts after decentralizing. Instead,
we find five convergence clubs that describe the evolution of income
disparities across Indonesian districts. Consistent with previous literature,
our results imply that income disparity across Indonesian districts remains
a major problem even after implementing decentralization policies in the
early 2000’s. Second, we observe large and persistent differences between
clubs, where the catching-up effects seem to exist only within clubs, but not
between them. This pattern calls for differentiated development policies
based on the composition of the clubs. Third, although districts belonging
to the same province tend to converge to the same club, there is evidence
that some provinces are composed of largely different districts, which
belong to different clubs. Finally, the spatial distribution of convergence
clubs clearly shows persistence in the east-west regional divide. In this
context, the central government should coordinate regional policies to
support the development in the eastern parts of Indonesia.
Based on the data construction and research methods of this paper,
there are at least three avenues for further research. First, the comparability
of regional data is crucial in the context of Indonesia, where the number of
districts has largely increased over time. In this paper, we use a simple
time-series interpolation method to construct a balanced panel dataset. As
there is no unique and optimal interpolation method, further studies could
apply other methods to re-evaluate the convergence clubs’ composition.
Second, alternative convergence analyses can be used to evaluate the
composition and dynamics of the convergence clubs. In particular,
distributional convergence methods could complement the club
convergence approach used in this paper. Finally, recent studies about
regional convergence emphasize the role of spatial spillovers in
accelerating the convergence speed. Hence, formally integrating spatial
spillovers into a club convergence framework is a promising direction for
further research.
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Appendix A: Interpolating new districts data
During the decentralization, the number of districts in Indonesia increased
significantly from 342 districts in 2000 to 514 districts in 2017. Due to this
administrative proliferation, the sequential time series of GDP per capita at
the constant price at the district level are difficult to obtain. Therefore, in
this paper, we construct the balanced panel dataset for 514 districts level
deflated by the constant price of 2010 from the Central Bureau of Statistics
and INDODAPOER-World Bank. Specifically, we interpolated all missing
values in both the regional GDP at constant price and the number of
population. Also, we adjusted the historical data in some reference districts
to avoid the structural break, i.e., the time series of reference districts before
and after split-up.
Similar to Kurniawan et al. (2019), this paper uses a linear regression
method with the reference district and (or) year as regressor(s) for the
interpolation. We assumed that the new district is having co-movement
with its reference district. The new districts’ trend refers to their actual
available data and follows its reference district (or year) when they are
interpolated. For example, in Figure 11 we illustrate the comparison of GDP
per capita of one of the proliferated districts, the Sungai Penuh City that
became a new district in 2009 after separated from its origin district, the
Regency of Kerinci.
In brief, our imputation/interpolation steps can be summarized as
1. Constructing the reference district: The historical data of original
district before split-up and the sum of the composite of new district(s)
data after the proliferation are used as reference district.
2. Imputation and data adjustment: The time-series data of the original
district are adjusted by subtracting the reference district’s time series
data with the new district’s imputed data before the proliferation year.
3. Constructing population data: The missing data of each district’s total
population are imputed using linear calculation of the populations
share to the total province population.
4. Calculating regional GDP per capita: The per capita GDP at constant
price for districts level is obtained by dividing GDP by each district’s
total population.
Figure 11: Comparison of imputed data and its reference
Appendix B: Club membership
Club 1 [6]: Jakarta Pusat, Kediri, Mamberamo Raya, Mimika, Morowali, Teluk
Club 2 [126]: Badung, Balangan, Balikpapan, Banda Aceh, Bandung,
Banggai, Bangka Barat, Banyuwangi, Barito Utara, Batam, Batang Hari, Batu
Bara, Bau-Bau, Bekasi, Bengkalis, Berau, Bima, Bintan, Bitung, Bojonegoro,
Bontang, Boven Digoel, Bukittinggi, Bulungan, Buton Utara, Cilacap,
Cilegon, Cirebon, Dumai, Fakfak, Gianyar, Gresik, Indragiri Hilir, Indragiri
Hulu, Jakarta Barat, Jakarta Selatan, Jakarta Timur, Jakarta Utara, Jayapura,
Jayapura, Kampar, Karawang, Karimun, Keerom, Kendari, Kepulauan
Anambas, Kepulauan Meranti, Kepulauan Seribu, Kolaka, Kolaka Utara,
Konawe Utara, Kota Baru, Kota Batu, Kuantan Singingi, Kudus, Kutai Barat,
Kutai Kartanegara, Kutai Timur, Labuhan Batu, Labuhan Batu Selatan,
Labuhan Batu Utara, Lamandau, Madiun, Magelang, Mahakam Ulu,
Makassar, Malang, Malinau, Mamuju Utara, Manado, Manokwari, Maros,
Medan, Mesuji, Minahasa Utara, Mojokerto, Mojokerto, Morowali Utara,
Muara Enim, Murung Raya, Musi Banyuasin, Nabire, Natuna, Nunukan,
Padang, Padang Panjang, Palembang, Palu, Pangkajene Kepulauan,
Parepare, Pariaman, Pasir, Pasuruan, Pekanbaru, Pelalawan, Pematang
Siantar, Pinrang, Purwakarta, Rokan Hilir, Salatiga, Samarinda, Sarmi,
Sawahlunto, Semarang, Siak, Sibolga, Sidoarjo, Sorong, Sorong, Sumbawa
Barat, Sungai Penuh, Surabaya, Surakarta, Tabalong, Tana Tidung,
Tangerang, Tanjung Jabung Barat, Tanjung Jabung Timur, Tanjung Pinang,
Tapanuli Selatan, Tarakan, Tegal, Wajo, Wakatobi, Waropen, Yogyakarta.
Club 3 [178]: Aceh Tengah, Agam, Asahan, Bandar Lampung, Banggai
Kepulauan, Banggai Laut, Banjarmasin, Bantaeng, Banyumas, Barito
Selatan, Barito Timur, Barru, Belitung, Belitung Timur, Bengkulu, Bengkulu
Tengah, Binjai, Blitar, Blitar, Bogor, Bolaang Mongondow Selatan, Bolaang
Mongondow Timur, Bolaang Mongondow Utara, Bombana, Bone, Buleleng,
Bulukumba, Bungo, Buol, Buton, Buton Selatan, Cimahi, Dairi, Deli
Serdang, Denpasar, Dharmasraya, Donggala, Enrekang, Gorontalo,
Gorontalo, Gorontalo Utara, Gunung Mas, Gunung Sitoli, Indramayu, Intan
Jaya, Jambi, Jayawijaya, Jember, Jembrana, Jombang, Kaimana, Kapuas,
Karanganyar, Karangasem, Karo, Katingan, Kendal, Kep.Siau Tagulandang
Biaro, Kepulauan Mentawai, Kepulauan Sangihe, Kepulauan Selayar,
Kerinci, Ketapang, Klungkung, Konawe, Konawe Kepulauan, Konawe
Selatan, Kotawaringin Barat, Kotawaringin Timur, Kubu Raya, Kupang,
Lahat, Lamongan, Lampung Selatan, Lampung Tengah, Lampung Timur,
Lampung Utara, Langkat, Lhokseumawe, Limapuluh Kota, Lingga,
Lumajang, Luwu, Luwu Timur, Luwu Utara, Magetan, Malang, Mamberamo
Tengah, Mamuju, Mandailing Natal, Mappi, Mataram, Merangin, Merauke,
Metro, Minahasa, Minahasa Selatan, Minahasa Tenggara, Muaro Jambi,
Muna, Muna Barat, Musi Rawas, Musi Rawas Utara, Nagan Raya, Pacitan,
Padang Lawas Utara, Padang Pariaman, Palangkaraya, Palopo, Pangkal
Pinang, Parigi Moutong, Pasaman Barat, Pasuruan, Pati, Payakumbuh,
Pegunungan Bintang, Penajam Paser Utara, Pesawaran, Pohuwato, Polewali
Mandar, Pontianak, Poso, Prabumulih, Pringsewu, Probolinggo, Pulang
Pisau, Raja Ampat, Rejang Lebong, Rokan Hulu, Sabang, Sambas, Samosir,
Sarolangun, Semarang, Serang, Serang, Serdang Bedagai, Sidenreng
Rappang, Sigi, Sijunjung, Simalungun, Singkawang, Sinjai, Sleman, Solok,
Solok, Soppeng, Sorong Selatan, Sragen, Sukabumi, Sukamara, Sukoharjo,
Sumbawa, Supiori, Tabanan, Takalar, Tana Toraja, Tanah Bumbu, Tanah
Datar, Tanah Laut, Tangerang Selatan, Tanjung Balai, Tapin, Tasikmalaya,
Tebing Tinggi, Tebo, Teluk Wondama, Ternate, Toba Samosir, Tojo
Una-Una, Toli-Toli, Tomohon, Toraja Utara, Tuban, Tulang Bawang, Tulang
Bawang Barat, Tulungagung, Yalimo.
Club 4 [181]: Aceh Barat, Aceh Barat Daya, Aceh Besar, Aceh Jaya, Aceh
Selatan, Aceh Singkil, Aceh Tamiang, Aceh Tenggara, Aceh Utara, Alor,
Ambon, Asmat, Bandung, Bandung Barat, Bangka, Bangka Selatan, Bangka
Tengah, Bangkalan, Bangli, Banjar, Banjar, Banjar Baru, Banjarnegara,
Bantul, Banyuasin, Barito Kuala, Batang, Bekasi, Belu, Bener Meriah,
Bengkayang, Bengkulu Selatan, Bengkulu Utara, Biak Numfor, Bireuen,
Boalemo, Bogor, Bolaang Mongondow, Bondowoso, Bone Bolango,
Boyolali, Brebes, Buru Selatan, Buton Tengah, Ciamis, Cianjur, Cirebon,
Demak, Depok, Dogiyai, Dompu, Empat Lawang, Ende, Flores Timur,
Garut, Gayo Lues, Gowa, Grobogan, Gunung Kidul, Halmahera Barat,
Halmahera Selatan, Halmahera Tengah, Halmahera Timur, Halmahera
Utara, Hulu Sungai Selatan, Hulu Sungai Tengah, Hulu Sungai Utara,
Humbang Hasundutan, Jepara, Kapuas Hulu, Kaur, Kayong Utara,
Kebumen, Kediri, Kepahiang, Kepulauan Aru, Kepulauan Sula, Kepulauan
Talaud, Kepulauan Tidore, Kepulauan Yapen, Klaten, Kolaka Timur,
Kotamobagu, Kulon Progo, Kuningan, Lampung Barat, Landak, Langsa,
Lebak, Lebong, Lombok Barat, Lombok Tengah, Lombok Timur, Lombok
Utara, Lubuklinggau, Madiun, Magelang, Majalengka, Majene, Malaka,
Maluku Barat Daya, Maluku Tengah, Maluku Tenggara, Maluku Tenggara
Barat, Mamasa, Mamuju Tengah, Manokwari Selatan, Maybrat, Melawi,
Mempawah, Mukomuko, Ngada, Nganjuk, Ngawi, Nias, Nias Barat, Nias
Selatan, Nias Utara, Ogan Ilir, Ogan Komering Ilir, Ogan Komering Ulu,
Ogan Komering Ulu Selatan, Ogan Komering Ulu Timur, Padang Lawas,
Padang Sidempuan, Pagar Alam, Pakpak Bharat, Pamekasan, Pandeglang,
Pangandaran, Paniai, Pasaman, Pekalongan, Pekalongan, Pemalang,
Penukal Abab Lematang Ilir, Pesisir Barat, Pesisir Selatan, Pidie, Pidie Jaya,
Ponorogo, Probolinggo, Pulau Morotai, Pulau Taliabu, Purbalingga,
Purworejo, Rembang, Sampang, Sanggau, Sekadau, Seluma, Seram Bagian
Barat, Seram Bagian Timur, Seruyan, Sikka, Simeulue, Sintang, Situbondo,
Solok Selatan, Subang, Subulussalam, Sukabumi, Sumba Barat, Sumba
Timur, Sumedang, Sumenep, Tambrauw, Tangerang, Tanggamus, Tapanuli
Tengah, Tapanuli Utara, Tasikmalaya, Tegal, Temanggung, Timor Tengah
Selatan, Timor Tengah Utara, Trenggalek, Tual, Way Kanan, Wonogiri,
Club 5 [23]: Aceh Timur, Bima, Blora, Buru, Deiyai, Jeneponto, Kupang,
Lanny Jaya, Lembata, Manggarai, Manggarai Barat, Manggarai Timur,
Nagekeo, Nduga, Pegunungan Arfak, Puncak, Puncak Jaya, Rote Ndao, Sabu
Raijua, Sumba Barat Daya, Sumba Tengah, Tolikara, Yahukimo.
Appendix C: Test for clubs merging
Phillips and Sul (2009) propose a merging test to evaluate whether the clubs
identified according to the clustering algorithm described in Section 3.3
can be merged. Thus, we used a club merging algorithm by Phillips and Sul
(2009) to test for merging between the adjacent clubs. The procedure works
as follows:
1. The log ttest is applied on the first two initial groups identified in the
clustering mechanism described in Section 3.3. If the t-statistic is
larger than -1.65, these two groups together form a new convergence
2. The log ttest is repeated by adding the next club, and the process
continues until the condition of t-statistic is larger than -1.65 is
3. If the convergence hypothesis is rejected, that is when t-statistic is
larger than -1.65 does not hold, we assume that all previous groups
converge, except the last added one. Hence, we restart the merging
algorithm from the club for which the hypothesis of convergence does
not hold.
Appendix D: Convergence test using a trend
parameter of 400
Table 9: Global convergence test (trend parameter of 400)
Coefficient Standard Error t-statistic
log(t) -0.53 0.02 -23.02
Note: The null hypothesis of convergence is rejected when the t-statistic is less than -1.65.
Table 10: Local convergence test (trend parameter of 400)
Club1 Club2 Club3 Club4 Club5 Club6
Coefficient 0.61 0.27 0.02 0.25 0.03 0.67
t-statistic 6.25 3.25 0.42 3.89 1.25 51.39
N. of regions 4 10 106 186 50 4
Club7 Club8 Club9 Club10 Club11 Club12
Coefficient 2.43 1.81 1.33 0.81 2.54 0.00
t-statistic 9.48 8.73 11.84 11.88 8.24 -.07
N. of regions 24 70 10 24 4 22
Note: The null hypothesis of convergence is rejected when the t-statistic is less than -1.65.
Table 11: Merge test (trend parameter of 400)
Club1+2 Club2+3 Club3+4 Club4+5 Club5+6 Club6+7
Coeff 0.30 -0.07 -0.24 0.02 0.08 2.25
T-stat 3.79 -1.49 -6.39 0.58 3.85 9.86
Club7+8 Club8+9 Club9+10 Club10+11 Club11+12
Coeff 1.08 1.32 0.19 0.27 -0.16
T-stat 8.41 8.56 6.20 6.49 -6.05
Note: The null hypothesis of convergence is rejected when the t-statistic is less than -1.65.
Table 12: After-merge clubs (trend parameter of 400)
Club1 Club2 Club3 Club4 Club5
Coeff 0.30 0.02 0.01 0.03 0.00
T-stat 3.79 0.42 0.41 0.71 -0.07
Size 14 106 240 132 22
Note: The null hypothesis of convergence is rejected when the t-statistic is less than -1.65.
GDP per capita
2000 2005 2010 2015 2020
Club 1
GDP per capita
2000 2005 2010 2015 2020
Club 2
GDP per capita
2000 2005 2010 2015 2020
Club 3
GDP per capita
2000 2005 2010 2015 2020
Club 4
GDP per capita
2000 2005 2010 2015 2020
Club 5
Figure 12: Convergence clubs and transition paths (trend parameter of 400)
GDP per capita
2000 2005 2010 2015 2020
Club = 1
Club = 2
Club = 3
Club = 4
Club = 5
Figure 13: Convergence clubs trends (trend parameter of 400)
Appendix E: Classical convergence analysis for a
sample of 342 districts
SD of Log GDP per capita
2000 2005 2010 2015 2020
Figure 14: Sigma convergence across 342 districts
Growth Rate 2000-2017
810 12 14
Log GDP per capita in 2000
Figure 15: Beta convergence across 342 districts
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