Examining the Convergence of Human Development using Sigma

Convergence Approach to Panel Data Analysis

IRWAN SAFWADI, RAJA MASBAR, ABD. JAMAL, T. ZULHAM

Department of Economics, Faculty of Economics and Business,

Universitas Syiah Kuala,

Kopelma Darussalam, Syiah Kuala, 23111 Kota Banda Aceh, Aceh,

INDONESIA

Abstract: - A special autonomy policy was implemented in Aceh in 2006, which differed in managing fiscal

transfers from the central government. To this end, we examined the convergence of human development in

districts/cities for thirteen years (period 2008-2020) as a form of development evaluation from the

implementation of special autonomy. Using a sigma convergence approach to panel data sets sourced from the

Central Bureau of Statistics (BPS), this study found a slow year-on-year movement of decreasing human

development disparities. On the contrary, it can be discovered that solid evidence of absolute convergence in

the 2011-2020 period, despite the differences between the 2008-2020 period, was applied. In line with these

discoveries, it will take over a decade to achieve a steady state of living standards, equalization, and quality of

human development between districts/cities. It could be the basis for policymakers to maintain a sustainable

sense of special autonomy.

Key-Words: - Human Development Index, Convergence, Panel Data Analysis

Received: April 29, 2022. Revised: August 14, 2022. Accepted: September 3, 2022. Available online: September 21, 2022.

1 Introduction

The convergence hypothesis that originated from the

views of Solow [1] and Swan [2] with the

Neoclassical growth model by Evan & Karras [3]

and Mazumdar [4] has become an exciting research

theme for researchers in parts of the world. Most

researchers focused on per capita income and labor

productivity to test the convergence hypothesis

(e.g., Baumol [5]; Baumol and Wolff [6]; De Long

[7]; Dowrick and Nguyen [8]; Bernard and Durlauf

[9]; Quah [10] and Zulham, Sirojuzilam & Saputra

[11]. Furthermore, Barro [12] and Barro & Sala-i-

Martin [13] expanded convergence analysis by

adding explanatory variables, such as migration, life

expectancy, investment, government consumption

ratios, inflation rates, etc.

However, in recent decades researchers have

devoted their attention to examining and

investigating the convergence of the Human

Development Index (HDI) after the United Nations

Development Program (UNDP) published its 1990

Annual Human Development Report (HDR). HDI is

considered a better and more comprehensive

measure than income per capita for the level of

welfare [4], [14], [15]. The same view is also

expressed by Mayer-Foulkes [16]. They conclude

that the socio-economic dimension is essential in

measuring welfare, not only based on the size of per

capita income.

If explored in-depth, empirical studies of

convergence in the context of living standards and

socioeconomics or using one of the components of

HDI indicators have been traced by leading

researchers. Hobijn & Frances [17] reviewed the

convergence of using a standard of living measure

by including one indicator of HDI (life expectancy

at birth), besides daily calorie supply, daily protein

supply, and infant mortality rates indicators. His

findings revealed that convergence in real GDP per

capita did not imply convergence for other social

indicators and the continuing inequality between

privileged and unprivileged people in real GDP per

capita and living standards. Mazumdar [4]

investigated the convergence based on the

classification of HDI development (high, medium,

and low) and income per capita in 91 countries for

thirty-five years (period 1960-1995). The findings

reveal no strong evidence for HDI convergence and

per capita income. It is noteworthy that Mazumdar's

empirical study only analyses the HDI convergence

and per capita income without including any HDI

dimensions.

Sab and Smith [18] focused on education that

found strong evidence of absolute and conditional

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DOI: 10.37394/23207.2023.20.14

Irwan Safwadi, Raja Masbar,

Abd. Jamal, T. Zulham

E-ISSN: 2224-2899

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convergence following the idea of beta

convergence. Mayer-Foulkes [19], meanwhile,

focused more on life expectancy indicators to

observe club convergence and concluded evidence

of club convergence, while absolute convergence

looks weak. Another study conducted by Neumayer

[20] found evidence of convergence in living

standards, including life expectancy and adult

literacy rates, among other well-being indicators.

Sutcliffe [21] investigated the relationship between

globalization and world inequality, including testing

HDI trends in 99 countries that revealed a

coefficient of ever-decreasing HDI variation or

evidence of convergence.

In further developments, some researchers are

increasingly eager to examine the convergence of

HDI between countries in parts of the world in

detail and comprehensively, along with variations in

econometric models and data. Noorbakhsh [22]

investigated the convergence of HDI and its

characteristics in 93 countries in Africa, Asia, the

Pacific, Latin America, and Europe period 1975 to

2002 with the OLS regression model. Konya also

applied the OLS regression approach, and Guisan

[23] and Konya [24] observed the HDI convergence

in European Union countries from 1975 to 2004.

Furthermore, Mayer-Foulkes [16] analyzed HDI

convergence and its inter-component interactions in

111 countries from 1970 to 2005 by expanding

explanatory variables, such as FDI, urbanization,

trade, and others, with static panel data regression

models. Other researchers, Jordá and Sarabia [25],

used OLS and PLM regression approaches to

analyze the interaction of the composite welfare

index covering the dimensions of health and

education in analyzing convergence processes in

132 countries from 1980 to 2012. Goswami, Roy &

Giri [26] recently implemented the Bootstrap

Quantile Regression and Pooled OLS approach

examining HDI convergence in 189 countries from

1990 to 2018.

In the regional context of each country, the issue

of HDI convergence is increasingly being looked at

by researchers. Interestingly, the overall results of

empirical studies tend to be inconsistent. For

example, in India, empirical studies of HDI and its

convergence characteristics were conducted by

Dholakia [27], Noorbakhsh [28], Ghosh [29], Roy

[30], Gaur [31], and Banerjee and Kuri [32]. In

Argentina, one of them was being researched by

Capello, Figueras, Freille & Moncarz [33], who

examined the role of regional public policy in

reducing the interprovincial development disparities

in Argentina. His findings revealed that transfers

from the central government to the provinces did not

positively affect HDI convergence indicators,

despite solid evidence of conditional convergence of

each welfare indicator. Meanwhile, recently

conducted by Yang, Pan & Yao [34] in China

resulted in conditional convergence findings related

to HDI, influenced by government spending in

education and health.

In Indonesia's case, convergence-related research

has long been initiated, but it is still focused on per

capita income gaps and economic growth. Esmara

[35] as early pioneer, followed by Uppal and

Boediono [36], Akita [37], Hill and Weidemann

[38], Hill [39], Akita and Lukman [40], Garcia and

Soelistianingsih [41], Wibisono [42], Resosudarmo

& Vidyattama [43], Hill, Resosudarmo, &

Vidyattama [44], Heriqbaldi [45], Aritenang [46],

Kataoka [47] and Kurniawan et al. [48]. However,

very few studies examined the HDI convergence

across Indonesia's regions. Recent studies have

focused more on inequality and convergence of per

capita income and economic growth before and after

the implementation of special autonomy. Zulham et

al. [49] outlined the impact of special autonomy on

the convergence of economic growth in Aceh before

and after the implementation of special autonomy.

Another empirical study conducted by Jamal et al.

[50] analyzed the success of district expansion to

reduce economic growth inequality between

districts in Aceh Province and the factors that

influence it. Another recent study on Aceh's special

autonomy was traced by Abrar et al. [51] but did not

comprehensively review HDI convergence. The

latest study was conducted by Miranti and Mendez-

Guerra [52], using a spatial approach to analyze

district-level HDI in Indonesia using a new HDI

method during the 2010-2018 period.

Despite the various empirical studies of HDI

convergence that we have put forward, the purpose

of this study is not to validate or disprove theoretical

models [53]. Instead, our primary goal is to examine

the HDI convergence between cities as a form of

development evaluation in scientific approaches to

the sustainability of community welfare in Aceh and

contribute to the HDI convergence literature. It is

important to note that Aceh, as one of the regions in

Indonesia that received Special Autonomy treatment

in 2006, after a prolonged political conflict ended

with peace in mid-2005 [54]. A devastating

earthquake and tsunami also hit this area at the end

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Irwan Safwadi, Raja Masbar,

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of 2004 [55]. Therefore, we will do this to increase

knowledge related to the HDI convergence between

regions in Aceh Province.

This article has three purposes. The first

objective is to elucidate human growth development

between districts/cities. The second goal is to

scrutinize the convergence of human development

sigma during the realization of special autonomy

(estimation period). The third and final intention is

to examine and investigate the absolute convergence

of human growth between districts/cities from 2008

to 2020.

2 Literature Review

2.1 Human Development Index

Measurement

Since the early 1990s, there has been a noticeable

shift in the development paradigm from economic

growth priorities to improving human well-being

(e.g., Sen [14] and Dasgupta & Weale [15]). In

1990, the United Nations Development Program

[56] published the first Human Development

Report. The report introduces HDI, which measures

human development in various countries. HDI is a

composite index constructed from four leading

indicators that reflect three dimensions: longevity,

knowledge, and access to resources [22]. At first,

the longevity dimension is measured by life

expectancy at birth, knowledge is quantified by

adult literacy and gross participation rates, and

access to resources is assessed by the logarithm of

real income per capita adjusted for purchasing

power parity. In 2010, UNDP changed its HDI

calculation methodology. Some indicators are

replaced to be more relevant. The Combined Gross

Enrolment Ratio indicator is revised with the

Expected Years of Schooling indicator. The Gross

Domestic Product (GDP) per capita indicator is

transformed with the Gross National Product (PNB)

per capita. In addition, the way of counting has also

altered. The average arithmetic method was changed

to a geometric average for calculating composite

indices.

In HDI calculations, minimum and maximum

values are set sequentially to convert the indicator

into an index between 0 and 1. The maximum value

is the highest observed value in a time series.

Minimum values are regulated at 20 years for life

expectancy, 0 years for educational variables, and

$100 for gross national income per capita. Each sub-

index is calculated as follows:

 



(1)

Where DI is Dimension Index, AV is Actual

Values, MinV is Minimum Values, and MaxV is

Maximum Values. Starting now, HDI is the

geometric average of a three-dimensional index

formulated as follows:

󰇛1/3. 1/3.1/3)

(2)

HDI is Human Development Index, LEXP is

Life Expectation, EDU represents education, and

INC is Income.

The Government of Indonesia is very committed

to using HDI as one of the measures in development

performance, including for provinces and

regencies/cities. Failure to pursue high economic

growth has made the Indonesian government

prioritize human development as leading in

accelerating development. The Indonesian

government establishes HDI as an essential

indicator in formulating the distribution of balance

funds transferred from the central government to the

regions. Likewise, special autonomy transfer funds

distribution with the Aceh Government also uses

HDI instruments. Human development performance

primarily determines the allocation and distribution

of special autonomy funds for each district/city.

In line with changes in HDI calculation

methodology, the Government of Indonesia, through

the Central Bureau of Statistics (BPS), began to

apply the new HDI calculation method in 2014. The

HDI indicators used in Indonesia are the same as

UNDP, except for Gross National Product (PNB)

per capita. The indicator is projected with per capita

expenditure. New HDI methods are calculated from

2010 to the provincial and district/city levels to

maintain the continuity of calculation. The

following year has used new methods in calculating

and presenting HDI between provinces and

regencies/cities in Indonesia.

2.2 Human Development Index:

Convergence: International Experience

The alternatives to per capita income, output, and

productivity in examining the convergence

hypothesis become interesting issues for researchers

worldwide. UNDP published the first Annual

Human Development Report (HDR) in 1990. Since

then, researchers have begun to turn their attention

to using HDI and the combination with the standard

of living in observing the convergence process.

Hobijn & Franses [17] reviewed convergence using

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a standard of living measure by including one

indicator of HDI (life expectancy at birth), besides

the daily calorie supply, daily protein supply, and

infant mortality rates indicators. His findings

revealed that convergence in real GDP per capita

does not imply convergence for other social

indicators and the continuing inequality between

privileged and unprivileged people in real GDP per

capita and living standards. Neumayer [20] also

focuses on convergence in living standards and,

among others, uses HDI indicators, such as life

expectancy and literacy. Unlike Hobijn & Franses

[17], Neumayer [20] found evidence of convergence

in living standards, especially life expectancy, infant

survival, educational enrollment, literacy, and the

availability of telephone and television.

Literature and other empirical studies that review

HDI convergence varies widely in variable

characteristics. Some focus on observing trends and

HDI convergences, including each HDI component

indicator, or on absolute convergence, and others

test by adding conditional convergence. The

findings are also diverse and tend to be inconsistent

with each other. Mazumdar [4] analyzed HDI

convergence in 91 countries from 1960 to 1995

based on HDI classification (High human

development countries, Middle human development

countries, and Low human development countries)

and tested them with per capita income. His findings

indicated divergence in HDI. Sutcliffe [21]

reviewed the relationship between globalization and

world inequality, including testing HDI trends in 99

countries that revealed a declining coefficient of

HDI variation or evidence of convergence.

Another comprehensive study was conducted by

Noorbakhsh [22]. She reviewed the rationale for

expanding and developing the Solow model to

explore the relevance of HDI convergence. Data

from 93 medium HDI and low HDI countries and

five-year HDI intervals from 1975 to 2002 revealed

weak absolute convergence. The shreds of evidence

were also reinforced by the verification results of

various conditional β convergence models. She uses

variables including foreign direct investment, trade,

foreign aid, gross domestic investment, the average

annual growth rate of public sector expenditure on

education and health, all given as a percentage of

GDP, and the number of telephone lines per

population.

Other empirical literature analyzes the HDI

convergence and determinant factors, such as

Mayer-Foulkes [16] and Jordá and Sarabia [25].

Mayer-Foulkes [16] conducted a cross-country

analysis of HDI components, income, life

expectancy, literacy, and gross enrollment ratios for

111 countries from 1970 to 2005. Meanwhile, Jordá

and Sarabia [25] analyzed living standards

(including HDI) in different countries from 1980 to

2012 using the concepts of absolute convergence,

sigma, and beta convergence. Using semiparametric

specifications, the results revealed absolute

convergence, sigma, and beta convergence in well-

being as measured by HDI, although the

convergence process only liners in the health index.

On the other hand, some researchers are only

interested in analyzing HDI convergence trends. For

example, Konya and Guisan [23] and Konya [24]

analyzed countries that joined the European Union

during the period 1975-2004 using HDI trends and

the concepts of convergence β (absolute) and σ-

convergence. The findings are fascinating, which

show that relatively underdeveloped countries have

succeeded in increasing their HDI faster than

developed countries, although the convergence

process is slow. Meanwhile, other researchers only

analyzed one of the HDI indicators or specific

sectors related to HDI, such as Sab & Smith [18],

Mayer-Foulkes [16], and Panopoulou & Pantelidis

[57]. Sab & Smith [18] empirically found a

substantial and conditional convergence in

education, while Mayer-Foulkes [19] focused on the

life expectancy indicator, one of the HDI indicators

from 1962-to 1997 in 159 countries. The

conclusions found evidence of weak absolute

convergence between countries despite club

convergence. Panopoulou & Pantelidis [57]

observed it from 1972-to 2006 and showed evidence

of the convergence of health spending per capita

among the 17 OECD countries that did not lead to

health outcomes.

The literature related to fiscal transfer's effect on

HDI convergence was examined more in-depth by

Capello et al. [33] in Argentina for well-being

indicators from 1970 to 2001. He also examined the

role of local public policy in reducing

interprovincial development disparities.

Interestingly, the finding of redistributive transfer

from the central government to the province did not

positively affect the convergence of HDI indicators,

despite solid evidence of conditional convergence of

each welfare indicator. Meanwhile, Agarwal [58]

highlighted Social Sector Expenditure and HDI in

India from 1999 to 2008 and found that the portion

of social sector expenditure in development

expenditure was a significant determinant of HDI.

However, real income per capita is comparatively

more essential than the share of social sector

expenditure in development expenditure.

Yang et al. [34] made the most recent

contribution in China, which examined HDI in 31

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Irwan Safwadi, Raja Masbar,

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Volume 20, 2023

provinces from 1997 to 2006. The results of his

study resulted in the findings of conditional

convergence. Some variables, such as government

spending on education, health, construction

infrastructure, and fixed-asset investment, positively

affect the convergence of social development. He

also used a weighted population analysis for HDI,

but the results showed weak convergence among

provinces.

2.3 Regional HDI Convergence in Indonesia

In Indonesia's regional context, empirical studies

and research related to HDI convergence began to

become the attention of researchers. Nevertheless,

our search results related to regional HDI

convergence literature in Indonesia are still limited

compared to regional inequality convergence

literature using per capita income, output, and

productivity. Some relevant literature is expected to

increase insight concerning observing the HDI

convergence process. Vidyattama [59], using HDI

variables and spatial approaches, observed whether

the performance of neighboring regions (covering

provinces and regencies) affected the speed of

regional convergence in Indonesia from 1999 to

2008. His research revealed ongoing convergence in

Indonesia in line with changes in HDI numbers,

although the pace is decreasing. On the other hand,

the influence of neighboring regions has little

influence on the speed of convergence.

Other literature can be observed from

Wakarmamua & Indrayono (2019), which examines

the relationship between government spending and

intergovernmental human development in Papua

Province. Using structural equation modeling shows

that capital expenditure as part of direct expenditure

has positively impacted HDI. However, such

empirical studies did not review convergence. The

relevant study conducted by Syukriyah (2016)

investigated the HDI convergence in 33 provinces in

Indonesia for the 2013-2015 estimation period. He

used the Generalized Least Square method (GLS)

model. She discovered the sigma convergence of

HDI and the absolute beta convergence of HDI

between provinces in Indonesia during the

estimation period.

The latest study was conducted by Ginanjar et al.

[60] and Miranti and Mendez-Guerra [52]. Ginanjar

et al. [60] found that human development inequality

between provinces in Indonesia decreased from

2010 to 2019. Meanwhile, the study conducted by

Miranti and Mendez-Guerra [52], using a spatial

approach, analyzed district-level HDI in Indonesia

from 2010 to 2018. His findings showed that the

performance of neighboring regions (districts) had a

significant effect on the HDI convergence. In

contrast, the gap between regions had decreased in

HDI, and the education component tended to

accelerate convergence compared to the components

of life expectancy and expenditure.

3 Materials and Methods

This paper used district/city-level regions for panel

data sets during the 2008-2020 period.

Administratively, Aceh Province, which is one of

the provinces in Indonesia, has 23 districts/cities

that, until now, have not changed since the

expansion of the territory in 2001. The panel data

includes HDI sourced from the publication of the

Central Bureau of Statistics (BPS) Indonesia. Table

1 shows descriptive statistics of HDI variables. 2008

was the beginning of the Special Autonomy

establishment for the Government of Aceh by the

Indonesian government as an implication of Law

No.11 in 2006 concerning the Aceh Government.

Therefore, 2008 is the fundamental reason for us to

begin research and analyze its development until

2020 or around thirteen years of special autonomy

implementation. In line with the initial year, we

used HDI data (2008-2009) based on old calculation

methodology (arithmetic) and HDI data (2010-

2020) using geometric formulations published by

BPS.

3.1 Convergence Model: Sigma and Beta

Convergence

The convergence models used in this study are

sigma (σ)-convergence) and beta (β)-convergence.

The σ-convergence analysis is a time-lapse analysis

to observe the occurrence of HDI convergence,

carried out by calculating the coefficient of variation

(CV), as done by Lei and Yao [61] and Jamal et al.

[50] as follows:

󰇛



󰇜







(3)

In this case, CV = Coefficient of Variation of the

HDI variable. HDIi = HDI variable of districts/cities

used in the study; 



= average of each HDI

variable (HDI average); and N = the number of

districts/cities in Aceh. If the HDI CV value

decreases, it indicates that there is σ-convergence

between districts/cities.

We tested the β-convergence hypothesis in the

form of absolute convergence by following the

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regression equations of the data panels used by

Noorbakhsh [22], and Yang et al. [34] are as

follows:

 

󰇩 

󰇪

󰇛



(4)

Yi,t in equation 4 is then used as a bound

variable to equation 5 as follows:

  

(5)



or

 

The specification model for the fundamental β

convergence approach is written in equation four as

follows:

󰇛󰇜󰇛󰇜

󰇛󰇜



(6)

The convergence process occurs when the

coefficient of β1 is less than 1, with the convergence

velocity expressed as . In this regard, λ is the

convergence velocity (e.g., Paas & Schilitte, [62])

which is formulated as follows:

󰇛󰇜



(7)

Meanwhile, half-time is the time needed by a

district/city in Aceh to halve the HDI gap to a stable

state (Barro & Sala-i-Martin, [63]; Paas & Schilitte,

[62]), using the half-convergence model (Paas &

Schilitte, [62]), as follows:

󰇛󰇜



(8)

4 Results and Discussion

4.1 Descriptive Statistics and Human

Development Index

This section summarizes HDI statistics and outlines

HDI development by region during the estimation

period. Table 1 summarizes HDI statistics for 23

districts/cities in Aceh from 2008 to 2020, including

averages, standard deviations, and minimum and

maximum amounts of total observations. In general,

the average HDI increased dramatically at the

beginning of the period (2008-2009) and declined in

2010. In the following year to the end of the

estimated period, the average HDI continued to

increase significantly, showing improvements in

HDI components in regencies/cities in Aceh. In

addition to knowing the variations in HDI each year

during the estimation period, the study displayed

minimum and maximum HDI data.

It is noteworthy that the minimum and maximum

HDI in the period 2008-2009 used the old HDI

calculation method (arithmetic) to look different for

the next period with the new (geometric) method. In

the old method, the level of HDI disparity was

deficient between high HDI and low HDI, which

ranged around 9 points. However, it is recognized

that the old arithmetic average method had

disadvantages [56], [64]. For the new method, the

level of disparity is higher than in the old method,

and the value ranges from 20-to 21 points. However,

the difference in points continues to decline,

implying improvements toward a better quality of

human development at the district/city level in

Aceh.

Table 1. Descriptive Statistics of Cross--District:

2008-2020 (N = 299)

Year

Mean

St.Dev

Min

Max

2008

70,813

2,495

67,170

76,740

2009

71,281

2,476

67,590

77,000

2010

65,840

4,862

58,970

80,360

2011

66,376

4,842

59,340

80,870

2012

66,934

4,856

59,760

81,300

2013

67,386

4,885

60,110

81,840

2014

67,771

4,910

60,390

82,220

2015

68,586

4,917

61,320

83,250

2016

69,199

4,859

62,180

83,730

2017

69,766

4,766

62,880

83,950

2018

70,181

4,588

63,480

84,370

2019

71,051

4,668

64,460

85,070

2020

71,236

4,608

64,930

85,410

Figure 2 reveals the HDI development of

Regencies/cities in Aceh during the implementation

of special autonomy (period 2008-2020). In general,

all districts/cities showed an increase in HDI,

particularly the period 2010-2020 (the new HDI

method). Areas with high-status HDI can sustain

their achievements (although some have fluctuated

ranking). In contrast, areas with low-status HDI

(moderate status) are increasingly encouraged to

improve human capabilities in each forming

component. Looking at HDI per district/city, three

areas with administrative city status are ranked at

the top, such as Banda Aceh, Lhokseumawe, and

Langsa, during the estimation period. These three

cities have adequate public facilities for health

services, education, and economic infrastructure.

Banda Aceh is the central government of Aceh

Province, and it is very reasonable to be ranked at

the top of HDI with various public service facilities.

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Lhoksumewe was once dubbed the petrodollar

city because of the development of the oil and gas

industry (90s era), fertilizer industry, and other

supporting industries. Special Economic Zones

(SEZ) are the central government's priority in

encouraging industry and investment acceleration,

one of them being developed in Lhokeumawe City.

On the other hand, Subulussalam, one of the

administrative cities, was in the lowest rank in

human development during the estimation period.

This city is an expansion of the region from Aceh

Singkil, which had a definitive status in 2003. The

Subulussalam City Government continues to

encourage the acceleration of human development

by implementing education, health development,

and agricultural resource-based economic

development focusing on oil palm commodities.

Fig. 1: HDI Development by Regencies/Cities in

Aceh

Concurrently, HDI growth showed varying over

the estimated period. Figure 4 shows HDI growth

according to the division of areas in Aceh (west-

south, north-east, central, and around the central

government). During the implementation of special

autonomy, the exceptionally high growth of HDI

occurred in 2010 and was in the region around the

central government. A similar fact is also seen in the

north-eastern region, although its growth is still far

from the central government area. A lower growth

rate occurred in the west-south region in the same

year. However, the high growth of HDI is more

influenced by changes in HDI calculation

methodology (from arithmetic methods to geometric

methods). This fact shows almost no drastic

difference in the HDI growth rate in each region

from 2011 to 2020 (new HDI method). During this

period, HDI growth rates in each region ranged

from 1 to 3 percent. At the end of the estimation

period, the new method shows that the HDI growth

rate in the area around the central government is

ranked second or not much different from the west-

south region, after the central region. Two districts

in the Central region (Gayo Lues and Southeast

Aceh), categorized as moderate HDI, contributed

significantly to accelerating human development in

the central region.

Fig. 2: HDI Growth by Regions

The coronavirus pandemic that hit Indonesia in

early 2020, including Aceh, did not wholly worsen

the achievement of accelerating human development

in each region and showed a positive growth rate in

human development performance.

4.2 - Convergence Estimation

β-Convergence is a necessary condition but not a

sufficient condition for σ-Convergence. In practice,

β-Convergence will be verified while σ-

Convergence is verified [42]. We examine and

analyze this convergence with static analysis using

the coefficient of variation (CV). In this regard, we

made two comparisons by including and excluding

Banda Aceh City. It should be noted that Banda

Aceh is the capital of Aceh Province and has

adequate public facilities compared to other

districts/cities in Aceh. Thus, the HDI of such cities

tends to be higher, and it becomes interesting to

examine the convergence process.

By including Banda Aceh city during the

implementation of special autonomy for Aceh, or

the period 2008-2020, the fall-off in human

development inequality is relatively small, as shown

in Figure 3. Likewise, there was no drastic

difference in the decline in human development

inequality during the estimation period without

including Banda Aceh. However, overall, there is a

difference in CV value between the presence and

absence of Banda Aceh in the period 2010-2020,

explaining the high CV value with Banda Aceh.

High CV scores during the period can reflect high

inequality in HDI, which is a noticeable difference

in the achievement of human development progress

between Banda Aceh City and other districts/cities

in Aceh.

A very drastic difference during HDI inequality

increase was seen in CV from 0.034 in 2009 to

0.072 in 2010. We ensure that all caused by

differences in HDI calculations by the Central

Bureau of Statistics (BPS) than previously using

arithmetic methods to geometric methods. In the

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2010 - 2020 period, there was a tendency to spread

HDI inequality in Aceh to slowly decline, from

0.072 to 0.063 and from 0.056 to 0.049 (out-off

Banda Aceh). This uncovering evinces that the HDI

convergence process comes about between cities in

Aceh, although the process tends to be flat and

relatively slow. The findings are not much different

from Vidyattama [59] and Ginanjar et al. [60] for

regional contexts in Indonesia. Vidyattama [59]

observed regional convergence in Indonesia, which

found a decrease in HDI inequality during 2005-

2008, which continued to slow down until the last

observation period. Ginanjar et al. [60] found that

the spread of human development inequality

between provinces in Indonesia decreased from

2010 to 2019, but this was not significant because

the rate of decline was relatively low. Decreases in

human development disparities also occurred in the

provinces in India between 1981-2001 [32] and the

period 1990 to 2015 [65].

Fig. 3: Sigma Convergence of HDI Variation

Coefficient Model

Considering the geographical area of the

district/city in Aceh, covering the north-east

(coastal), west-south (coastal), central

(mountainous), and around the center of

government, we also checked the CV during the

implementation of special autonomy (see Figure 4).

A decline in the high CV trend turned out in the

central region, illustrating the decrease in the HDI

disparity distance between regencies in the region.

As we revealed initially, the cv trend that increased

in the initial three years (2008-2010) was influenced

by differences in HDI measurement methodology,

including those occurring in the other three regions.

Simultaneously, the other three regions showed a

slight CV decline trend, meaning there are still

disparities in human development between

districts/cities in one area. During the observation

period, we found that CV in the region around the

central government was higher than in the three

regions, which signified a higher disparity in human

development. This fact reveals the striking

difference in HDI between Banda Aceh City as the

center of government, with the hinterland area of

Aceh Besar Regency and Sabang City.

Fig. 4: Sigma Convergence of HDI Variation

Coefficient

4.3 -Convergence Estimation

In the literature, the beta convergence hypothesis

explaining areas that were initially poor pursued and

grew faster than those originally rich [13]. This

process is seen in Figure 5, which shows that areas

with low HDI in 2011 have grown faster than those

initially high HDI from 2011 to 2020. Banda Aceh

City, the capital of Aceh Province, with a high HDI

status and ranked first HDI, showed a low average

of HDI growth. It indicates evidence of beta

convergence of the HDI process during the

implementation of special autonomy in Aceh. This

convergence process is affected by the faster growth

of moderate HDI areas and by continuing a

slowdown of HDI in high to very high

districts/cities status. This discovery follows

empirical evidence documented in the study by

Ginanjar et al. [60] for the regional context of

Indonesia, where areas with low HDI show above-

average HDI growth and, conversely, areas with

high HDI are showing below-average growth.

Fig. 5: Absolute Convergence of HDI

On average, at the beginning of 2011, several

districts/cities had above average HDI, including

Banda Aceh, Sabang, Langsa, Lhokseumawe, Aceh

Jaya, Bireuen, Aceh Besar, Pidie, Bener Meriah, and

Pidie Jaya. Interestingly, some districts/cities with

below-average HDI scores tend to show above-

average HDI growth, such as Subulussalam, Singkil,

Simeulue, Southeast Aceh, Southwest Aceh, and

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East Aceh, North Aceh, Gayo Lues, and Nagan

Raya. The three highest cities with HDI scores

(Banda Aceh, Langsa, and Lhokseumawe) showed

below-average HDI growth from 2011 to 2020. That

could be a positive sign in the future that the left-

behind HDI areas continue to encourage the

acceleration of human development. However, it

will take a relatively long time to be in line with

Banda Aceh city. For instance, in 2020,

Subulussalam, the lowest-ranked HDI (value of

64.93), requires at least 20.48 points to increase its

value to be equivalent to Banda Aceh City (value of

85.41). This point tends to decrease, indicating a

decrease in human development disparity compared

to 2011, at 21.53 points. In that year, the attainment

HDI of Banda Aceh amounted to 80.87, and the

HDI of Subulusalam amounted to 59.34. Likewise,

Singkil (16.47 points), Gayo lues (18.19 points),

South Aceh (18.29 points), Southwest Aceh (18.66

points), and Simeulue (19.38 points). In this regard,

the regency/city government must realize health

quality and education services utilized by the

community, encourage local economic potential

utilization, and accelerate investment for the

community income sustainability.

Between 2011 and 2020, there was a shift in HDI

ranking at the district/city level in Aceh. The

allocation of HDI categories (BPS, 2020) to

distinguish achievements between regions is

categorized to incorporate very high (HDI ≥ 80),

high (70 ≤ HDI <80), medium (60 ≤ HDI < 70), and

low categories (HDI < 60). Since 2013, there has

been no single district/city in the low category,

although, in previous years, the category has always

been achieved by Subulussalam City. Only Banda

Aceh City achieved the high HDI category from

2010 until the final estimation condition. This

achievement makes Banda Aceh one of the regions

with the highest HDI in Indonesia (BPS, 2020). In

addition, there are ten districts/cities for the high

category, which was previously nine regions in

2018, including Lhokseumawe, Langsa, Sabang,

Pidie Jaya, Bener Meriah, Bireuen, West Aceh,

Central Aceh, Aceh Besar, and Pidie.

The 12 districts/cities in the medium category,

previously 13 regions in 2018, including

Subulussalam, Simeulue, South Aceh, Aceh Singkil,

Southeast Aceh, East Aceh, North Aceh, Southwest

Aceh, Gayo Lues, Nagan Raya, Aceh Jaya, and

Aceh Tamiang. Changes in HDI ranking depend on

the development of HDI supporting elements in

each district/city; of course, there are different levels

of development changes. The expansion of several

districts/cities before implementing Special

Autonomy is considered one factor in the

development progress difference between the new

district and its parent district. In general, the

construction of facilities is usually first established

in urban areas so that the establishment will become

less attention in remote districts. Some districts

managed to maintain their rankings continuously,

such as West Aceh. It was caused by several parent

districts still maintaining some of their facilities, for

example, office buildings, schools, health facilities,

and economic support facilities. On the contrary, the

three districts/cities resulting from regional

expansion (Subulussalam, Simeulue, and Southwest

Aceh) still occupy the lowest position in achieving

human development. However, various

development programs listed in the medium-term

development plan (Rencana Pembangunan Jangka

Mengengah) continue to be rolled out by the

district/city government.

Table 2. Results of Absolute Convergence of HDI

Variable

Year

2008-2010

2011-2020

2008-2020

HDI 2008

-0.0825

(0.1373)

0.0571***

(0.019)

HDI 2011

-0.0312***

(0.009)

Implied 

9,68%

Half-life

7,15

F-statistics

( p -value)

0.36

(0.5542)

10.71***

(0.003)

8.51***

(0.008

R Squared

0.016

0.3339

0,2885

Note: Dependent Variables: Growth Rate HDI;

Parentheses are standard errors, ii) p -values are

reported in case of F-statistics, and ***, **, and *

denote significance levels at 1%, 5%, and 10%,

respectively.

Table 2 depicts the estimated absolute

convergence model results of districts/cities in Aceh

in different estimation periods. The arithmetic HDI

calculation method (period 2008-2010) confirms the

result in a negative direction. We found

unconditional convergence in this period but not

supported by statistical figures, such as t-statistics

and F-statistics, significant at 1 percent, 5 percent,

and 10 percent levels. The combined HDI

calculation methods for 2008-2020 reflect thirteen

years of implementing Special Autonomy in Aceh.

It emphasizes the process leading to the

convergence of human development between

districts/cities, even though it has not yet reached

the steady-state conditions hypothesized in the

classical theory of Solow Growth. That likely occurs

fluctuations in the rise and fall of HDI growth in the

2008-2010 period, which is very drastic from using

both HDI calculation methods. The results of

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empirical studies of these two methods are in line

with Wibisono's experience [42], who found the

insignificant absolute convergence hypothesis for

per capita income in the Indonesian regional context

in the 1995-2000 period, which is likely caused by

the 1997 economic crisis occurred in that period.

Using the geometric HDI calculation method, the

second-period model (2011-2020) shows the

coefficient of initial HDI growth towards a negative

direction that corresponds to the initial and

significant predictions. The HDI coefficient value is

smaller than 1 (<1), meaning that HDI between

districts/cities tends to converge (more evenly). The

'catch-up' phenomenon in the HDI development

period implies that areas with lower HDI continue to

do better to achieve higher income levels and a

better quality of life during the study period. This

finding is in line with sigma convergence analysis

and regression results providing strong evidence

against the existence of absolute convergence.

We found a negative and statistically significant

coefficient (p-value < 0.001) for the model period,

or significantly based on t-statistics and F-statistics

at a rate of 1 percent, revealing substantial evidence

of beta convergence over the estimation period.

Thus, the results indicate that economies with lower

initial HDI levels are pursuing higher HDI levels;

thereby, a more uniform distribution of HDI

achievements occurs in various economies from

2011 to 2020. The low R-squared value is 33.39%

can be understood due to regression based on cross-

section data [42]. The findings align with

Vidyattama [59] and Miranti and Mendez-Guerra

[52]. Vidyattama [59] found the HDI convergence

(other than per capita income) in Sumatra and Java

in Indonesia. In contrast, Miranti et al. found a

decrease in the HDI gap between districts/cities in

Indonesia. The homogeneity characteristics still play

a role in the absolute β convergence for human

development in Aceh; the difference between cities

is only at the initial development level of HDI. It is

not easy to find convergence if the characteristics

are very heterogeneous [66].

In the global context, our discoveries are in line

with Konya and Guisan [23], Jorda & Sarabia [67],

and Asongu [68]. Konya and Guisan [23] found β-

convergence of HDI during the period 1975-2004

among 101 countries, although the lagging countries

took a long time, almost nine decades, to cover half

of the retardation. Jorda & Sarabia [25] observed

132 countries in Western Europe, North America

and Oceania, Arab States, East Asia, the Pacific,

Europe and Central Asia, Latin America and the

Caribbean, South Asia, Latin America, and Sub-

Saharan Africa. Asongu [68] discovered the

absolute convergence of HDI for countries in North

Africa from 1981 to 2009 and concluded that

convergence in human development is faster than

per capita income. Meanwhile, Ghosh [29] disclosed

a definite convergence trend in HDI indicators, with

estimated convergence rates varying from 1.25

percent to 4.23 percent per year. Chaurasia [65]

found absolute convergence in human development

across Indian states, although human development is

still relatively low by global standards.

A λ value of 9.68 indicates that the speed of each

district/city in Aceh during the period 2011-2020 to

achieve steady-state conditions is 9.68% per year.

These results confirm that the regional HDI

convergence in Aceh over the past 11 years was

relatively fast when special autonomy was

implemented. It takes about 7.15 years to close half

of the initial gap in human development in the

district/city. In no more than a decade, it is expected

that human development inequality in inter-

district/cities in Aceh will continue to shrink.

Overall, the HDI of Aceh Province also increased,

which led to the HDI convergence in Aceh, where

the districts/cities having low HDI can catch up with

human development in developed districts/cities.

5 Conclusion

Aceh is one of the provinces in Indonesia that has

the authority of Special Autonomy, apart from the

Provinces of West Papua and East Papua. This

special authority makes the Aceh Government more

flexible in intervening in development policies in all

sectors, including human development. It became

the basis for us to fully evaluate and examine the

welfare of inter-district communities during the

implementation of Special Autonomy. This paper

uses HDI as the primary measure to investigate the

convergence hypothesis in all districts/cities in Aceh

from 2008 to 2020 or thirteen years of special

autonomy implementation. We use the concepts of

sigma convergence and beta (absolute) convergence

to examine human development convergence.

Furthermore, sigma convergence means that HDI

spread and disparity tend to decrease over time and

beta convergence (absolute) implies a negative

relationship between the initial level of HDI and its

growth rate.

Using the Coefficient of Variation (CV) in

investigating sigma convergence, we found results

that corroborate evidence of sigma convergence of

human development between cities from 2011 to

2020. HDI disparity declines despite its relatively

slow movement from year to year. Despite the

drastic increase in CV value at the beginning of the

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estimation period (2008-2010), it was substantially

more influenced by the methodology of arithmetic

HDI calculations to geometric methods. The high

decline in HDI inequality occurred in the central

region, implying that areas with moderate status

continue to accelerate human development towards

a steady state. In the other three regions (North-East,

West-South, and around the center of government),

the decreased human development disparity

movement is relatively slow, affecting the overall

movement towards sigma convergence.

Regarding beta convergence, the results obtained

from classical linear analysis show at least strong

evidence of absolute convergence in human

development over the estimation period (2011-

2020). This finding reveals the areas whose HDI is

constantly moving to pursue areas that have

advanced human development. Overall, in the 2011-

2020 period, convergence occurred at 9.68% per

year. It takes about 7.15 years to close the initial gap

in human development in districts/cities in Aceh. In

this direction, the role of the central government in

the form of special autonomy fund transfers is

needed in supporting the acceleration of the human

development convergence process in Aceh.

Following regulations, the implementation of

Special Autonomy in Aceh will end in 2027.

Therefore, it is worth considering by the central

government to extend the implementation of Special

Autonomy, including increasing the allocation and

distribution of transfers of this special autonomy

fund for areas that are still low in HDI. The

intervention is an essential factor in accelerating the

convergence process focused on the field of human

development in areas with lower HDI levels, such as

Subulusasalam, Simeulue, Aceh Singkil, and others.

These conditions will help increase the growth rate

for the convergence process of human development

to be faster.

Finally, we suggest further research in the future

to gain more knowledge and findings focused on

HDI convergence, following its interactions

between HDI components. In addition, to append

data variation and econometric modeling, it will be

interesting to focus on conditional convergence

approaches by expanding explanatory variables in

investigating HDI convergence. The relatively short

(approximately 13-year) data availability and

limited to one province should be a scenario for

other researchers. It aims to present long-term data

series and compare them between provinces in one

country and between countries to help understand

the continuous progress and trends HDI.

Furthermore, methodology and modeling are

expanded by examining spatial effects between

regions and dynamic effects and considering

economic fluctuations due to the economic crisis

and coronavirus pandemic.

This study focuses on using public budgets as a

vital part of the transfer of Special Autonomy funds

to priority sectors (including development programs

and activities) may be further scrutinized. It will

also be helpful to study the extent of the

effectiveness of the use of the sector's budget is

encouraging equalization of welfare and the

continuous reduction of disparities in the region. In

regions categorized as medium HDI, it is also

necessary to implement optimal public budgets amid

budget constraints concerning encouraging the

acceleration of human development during the

implementation of Special Autonomy. It would be

more interesting to compare provinces and countries

that both carry out broad autonomy to be a learning

for equalizing the quality of human development in

the future.

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Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

-Irwan Safwadi writing – original draft,

investigation, methodology, data analysis and

editing.

-Raja Masbar writing – editing, methodology, data

analysis and supervision.

-Abd. Jamal writing – editing, methodology, data

analysis and supervision.

-T. Zulham writing – editing, methodology, data

analysis and supervision.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

This research there is no received any special

funding.

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DOI: 10.37394/23207.2023.20.14

Irwan Safwadi, Raja Masbar,

Abd. Jamal, T. Zulham

E-ISSN: 2224-2899

143

Volume 20, 2023

Conflict of Interest

The authors have no conflicts of interest to declare

that are relevant to the content of this article.

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