Volume 40, Issue 4
Does the law of one price hold in 82 Indonesian cities? Evidence from clubconvergence approach
Harry Aginta
Graduate School of International Development (GSID) Nagoya University, JAPAN

Abstract
This study re-examines regional price convergence across 82 cities in Indonesia. We implement club convergence
analysis developed by Phillips and Sul (2007, 2009) on monthly aggregate consumer price data and its components
from January 2014 to December 2019. We do not find evidence of overall convergence in aggregate consumer pricedata. Instead, we identify four club convergence. Using disaggregated data, four new outcomes arise; first, none of theconsumer price components show overall convergence but multiple club convergence do exist, second, there isvariability in the number and composition of clubs among consumer price components, third, the price of foodstuffs
and education-related commodities in most cities converge to the higher level, and fourth, the formation of clubconvergence in aggregate price is attributed largely by housing, processed foods, transport, and health components.
Policy insights include improving market efficiency and controlling the inflation rate in targeted consumer pricecomponents and locations.

The author is grateful for the insightful comments and suggestions offered by the anonymous referees. The author also sincerely appreciates themembers of QuaRCS lab (https://quarcs-lab.org) for their support throughout the development of this paper.
Citation: Harry Aginta, (2020) ''Does the law of one price hold in 82 Indonesian cities? Evidence from club convergence approach'',Economics Bulletin, Volume 40, Issue 4, pages 2844-2858
Contact: Harry Aginta - aginta.harry@c.mbox.nagoya-u.ac.jp.
Submitted: July 06, 2020. Published: October 18, 2020.

1. Introduction
The recent development in economic literature has shown a growing interest inconvergence analysis. Started with economic growth issues, further progress of
convergence literature has broadened the focus to other economic subjects, including
monetary economics (De Grauwe, 1996; Evans and Karras, 1996; Rogers, 2007). In its
simplest form, convergence behavior is seen when cross-sectional units' variation
diminishes over time (Hotelling, 1933). For example, one may see convergence as a
gradually decreasing variance in income per capita across various countries. However,some scholars have shown evidence of another form of convergence, where the declining
variation is observed not in the entire units but within some sub-groups (Azariadis andDrazen, 1990; Galor, 1996). Usually sharing similar characteristics, the units within those
sub-groups assemble a relatively similar evolution path over time. In convergence
literature, this is called the club convergence hypothesis.
Why do we need to study price convergence? To answer this question, one shouldrefer to the root of price convergence analysis; the law of one price (LOOP). LOOP isdefined as the condition where the price of identical goods in separate places is uniform in
a common currency unit (Rogoff, 1996). Within a country where trade restrictions areminimal, LOOP implies a similar price level across regions in the long-run (controlling
logistics and transportation costs). In a very efficient market, any deviation from the LOOP
will be adjusted by the market mechanism. Nevertheless, due to some market rigidities
and complexities – including rigidities in the factor market and different exposure tointernational trade that raise uncertainty from exchange rate volatility – regional price does
not adjust, at least in the short-run.1
Using the concept of LOOP, the analysis of price convergence within a country
produces meaningful policy implications. For example, in the scope of monetary policies,
regional price convergence analysis can be useful in forecasting monetary policy impacts
on regional inflation (Cecchetti, Mark, and Sonora, 2000). In the context of broader
economic policies, the analysis is often used to understand some structural features suchas the degree of market integration among regions, the regional structure of input factors,
and productivity differentials (Tirtosuharto and Adiwilaga, 2014). Understanding thesestructural features are essential for regional economic development strategies.
These multiple benefits have attracted many studies to focus their analysis on priceconvergence within a country. Most of them attempt to validate the presence of
convergence by using classical models such as sigma and beta convergence (see Bernard
and Durlauf, 1995; Hobijn and Franses, 2000; Phillips and Sul, 2007). However, despite
widely used in convergence literature, the classical models have a drawback in the sensethat they mainly consider a single common steady state. This limitation restricts the models
to fully capture the possible real case of convergence given the heterogeneity in theobservation (Jangam, Akram, and Sahoo, 2020). In the context of income convergence,for instance, many researchers conclude that the dispersion of income per capita acrosseconomies systematically shows clustering patterns rather than follows the direction ofcommons growth path (Basile, 2009; Phillips and Sul, 2009; Quah, 1996).
Unlike the classical models, a novel approach to convergence analysis developed byPhillips and Sul (2007) allows a wide range of transitional dynamics and individual
1

Among others, the potential solutions to address the problems of market rigidities and complexities include
improving factor market efficiency and integration, eliminating implicit local protectionism, and minimizing
short-run exchange rate volatility (Tirtosuharto and Adiwilaga, 2014; Isard, 1977; Zax and He, 2016).

heterogeneity to capture convergence beyond single steady state outcomes. A substantive
number of price convergence studies have applied this new approach and documented new
empirical results; price converges in multiple club convergence.
The method is notably superior to capture price convergence in largely diversified
countries like Indonesia, where substantial price differential across regions is persistent.
The most recent study analyzing regional price convergence in Indonesia is conducted by
Jangam and Akram (2019). Applying the convergence approach of Phillips and Sul (2007)
on monthly aggregate Consumer Price Index (CPI) data in 82 cities, they do not findevidence of overall price convergence. Instead, they show evidence that regional priceassembles four club convergence. However, a more in-depth examination is needed tocomplement this general conclusion. By construction, CPI represents the aggregate priceof various commodities consumed in a society. Thus, the convergence patterns seen inaggregate CPI are the reflection of CPI components’ dynamics. To understand the sourcesof observed convergence patterns in aggregate CPI, further convergence analysis using
disaggregated data is required.
Moreover, Indonesian regions are highly interdependent, given the uneven supply
capacity (Jangam and Akram, 2019). More often than not, in such a situation, disruptions
in supply distribution risk country's inflation rate and volatility (Tirtosuharto andAdiwilaga, 2014). The risk can be mitigated by improving the quality of supply
distribution of a selected important group of commodities in selected regions. This can bedone if the underlying relationship of price dynamics among regions is fully understood.
Identifying club convergence in the disaggregated price level would help policymakers toacquire a correct picture of regional price interconnection.
Against such a background, our study fills this research gap by examining regional
price convergence across 82 Indonesian cities with disaggregated CPI data. To the best of
our knowledge, this is the first paper that analyzes price convergence across Indonesiancities with disaggregated CPI data. The multiple outcomes discussed in this paper
demonstrate the benefits of club convergence analysis using disaggregated CPI data over
the aggregated one.
The rest of this paper is organized as follows; Section 2 describes the econometricmethodology, Section 3 presents data description and discussion on the results, and finally,
Section 4 concludes the paper.

2. Econometric methodology
2.1. The framework of convergence
Following Jangam and Akram (2019), in this paper we apply the club convergence test byPhillips and Sul (2007). To begin with, we decomposed a panel-data variable of interest,��� , as follow:
��� = (

�� + ����) �� = ϒ�� ��(1)

where �� and �� represent a systematic and transitory component, respectively. ϒ�� is
an idiosyncratic element and contains the error term, while �� is a common component.
Thus, �� refers to a common equilibrium to all economies, while ϒ�� explains an
individual’s transition path towards its equilibrium.
Under equation (1), the convergence is defined as the common movements of all
individual economies towards the same transition path:lim ϒ�� = ϒ

(2)

�→∞

Then, Phillips and Sul (2007) define relative transition parameter, ℎ�� , to estimate thetransition coeﬃcient of ϒ�� , where a common component, �� , in equation (1) iseliminated by rescaling ��� with panel average:
ℎ�� =

�

���

�
���
��=

=

�

ϒ��

(3)

�
ϒ��
��=

Thus, ℎ�� corresponds to the relative transition path of economy i with respect to the levelof cross-sectional average. In this setup, convergence occurs when ℎ�� converges to unity,that is hit → 1 for all i and t → ∞. The null hypothesis of convergence deﬁned in equation(3) can be translated into an equation that describes the cross-sectional variance of ℎ�� ,�� = ∑�
ℎ�� −
� i=

→

(4)

where the cross-sectional variance converges to zero, �� → 0. Finally, Phillips and Sul(2007) evaluate this null hypothesis by using the following log t regression model:
log

for

�1
��

− log { log} = ̂ + �̂ log= [ �], [ �] + , . . . , � with

+ ��

>

(5)

where � is the ﬁrst fraction of the data used in the regression, that is, fraction of thedata is discarded. For sample size T ≤ 50, Phillips and Sul (2007) suggest = 0.3. Under
equation (5), a one-sided t test is used to prove convergence, where the null hypothesis ofconvergence is rejected when �̂ < −1.65.
2.2. Identifying club convergence

One advantage of the model of equation (5) is its ability to define multiple clubconvergence in the sub-sample when overall convergence in the entire sample is absent.
Thus, we use this appealing feature to identify multiple club convergence by implementing
an innovative data-driven algorithm. The summary of steps in the club convergenceidentification process is provided in Section 1 of the Appendix.

3. Data and results
3.1. Data
This paper uses the monthly CPI of 82 Indonesian cities from January 2014 to December
2019, published by the Indonesian Central Bureau of Statistics (2012=100). The
Indonesian regional CPI data consist of one aggregate price index that can be
disaggregated into seven components; 1) foodstuffs, 2) processed foods, 3) housing andutilities, 4) clothing, 5) health, 6) education, leisure and sports, and 7) transportation,communication, and financial services. The summary statistics of aggregate CPI in all 82
Indonesian cities presented in Table 1 of the Appendix suggest the heterogeneity of pricedynamics across cities. For the disaggregated data, summary statistics of CPI components
in Table 2 of the Appendix report that foodstuffs and clothing components have the highest
and the lowest mean. Meanwhile, processed foods and housing components show thehighest and the lowest standard deviation, respectively. Given this prevalent variability
across cities and across CPI components, we implement convergence analysis in two steps;
firstly, we identify club convergence using an aggregate price index, and secondly, we reapply the first step using seven components of CPI (we follow Akram, Sahoo, and Rath,
2020; Jangam, Akram, and Sahoo, 2020; Mendez and Kataoka, 2020). By doing so, we
can pinpoint the sources of club convergence in aggregate price.
3.2. Results and discussion: The identification of multiple club convergence
As discussed in the previous section, we applied a log t test to aggregate price index in thefirst step.2 The result suggests rejecting the null hypothesis of overall price convergenceat the 5% signiﬁcant level ( �̂ is signiﬁcant < 0 with t-statistic −106.97). Then, we
proceeded to the steps of club convergence identification discussed in section 2.2. Table 1
presents the results.
As shown in Panel A of Table 1, we found six signiﬁcant initial club convergenceand one diverging city. Then, we continued to test whether some of these clubs can bemerged. The merging test result show that club 2, club 3 and club 4 can be merged into
one club, reducing the number of club convergence from six to four, as shown in Panel B
of Table 1. Hence, our final finding of club convergence test using aggregate CPI data
confirms these four subgroups as the ﬁnal club convergence, while one city (Tual) is
diverging. In summary, this result implies that four common trends characterize pricemovements in 82 Indonesian cities. Our finding is very similar to the result of Jangam and
Akram (2019).

2

We applied the test in STATA by using the club convergence package by Du (2017).

Table 1. Club convergence in aggregate CPI
Club
Full sample
Club 1Club 2Club 3Club 4Club 5Club 6
No convergence

Number and name of cities
Panel A: Club convergence test result
All 82 cities[9 cities][17 cities][6 cities][11 cities][30 cities][8 cities][1 city]�̂ coefft-stats

-1.02
0.47
0.48
0.41
0.03
0.06
0.08

-106.97
10.60
15.75
5.72
3.14
-1.35
1.46

-0.08
0.27
0.31
-0.59
-0.66
-1.34

-2.72
5.23
5.22
-90.11-119.49-97.32

0.47

10.61

0.14

2.81

-0.08

-1.35

0.12

1.46

Panel B: Club merging result
Club 1 + 2
Club 2 + 3
Club 3 + 4
Club 4 + 5
Club 5 + 6
No convergence
Club 1Club 2(Merging fromClub 2 + Club 3+ Club 4)

Club 3Club 4
No convergence

Panel C: Final clubs[9 cities]: Bengkulu, Cilegon, Palu, Pangkal Pinang,Pontianak, Serang, Sibolga, Tanjung Pandan, Tarakan[34 cities]: Balikpapan, Bandar Lampung, Bandung,
Banjarmasin, Batam, Bekasi, Bima, Bogor, Bulukumba,
Bungo, Cilacap, Jakarta, Dumai, Jayapura, Kudus,
Makassar, Manokwari, Medan, Merauke, Metro,
Meulaboh, Padang, Pakanbaru, Palopo, Pematang
Siantar, Samarinda, Sampit, Singaraja, Singkawang,
Surabaya, Tangerang, Tembilahan, Ternate, Watampone[30 cities]: Bau-bau, Bukit Tinggi, Cirebon, Denpasar,
Depok, Gorontalo, Jambi, Jember, Kendari, Kupang,
Lhokseumawe, Lubuk Linggau, Madiun, Malang,
Mamuju, Manado, Mataram, Padang Sidempuan,
Palangkaraya, Palembang, Purwokerto, Semarang,
Sorong, Sukabumi, Sumenep, Tanjung, Tanjung Pinang,
Tasikmalaya, Tegal, Yogyakarta[8 cities]: Ambon, Banda Aceh, Banyuwangi, Kediri,
Maumere, Pare-pare, Probolinggo, Surakarta[1 city]: Tual

Note: Results show the evidence of club convergence. t-stats > -1.65 denotes that the null hypothesis of convergence
is not rejected. Source: Authors’ calculation.

Each club's relative transition path is shown in Figure 1, where the average CPI ineach club (in log form) is evaluated against the cross-sectional average of samples. It isclear that all four clubs exhibit different convergence behaviors and transition paths
starting from their initial conditions in 2014 until 2019. Since the transition path of clubs
is diverging over time, one may conclude that the dynamics of all variables that affectprice movements in each club are heterogeneous. In other words, the distinctive transition
path reflects regional heterogeneity in price dynamics across Indonesia.

Figure 1. Transition path of clubs
Source: Authors’ calculation.

Finally, we conducted a beta convergence test to confirm the robustness of the clubconvergence formation. To save space, we show the result of beta convergence test in
Table A3 of the Appendix. The beta coefficient for all clubs is negative and statisticallysignificant, suggesting the evidence of convergence in all clubs. In other words, the findingof club convergence formation is consistent with the result of the classical convergenceframework.
Next, we continued to investigate convergence patterns in CPI components that drive
the formation of four club convergence observed in aggregate CPI. Therefore, we reapplied the club convergence test to seven components of CPI repeatedly. It is important
to note that similar to testing the club convergence on aggregate CPI, the algorithm
generates the initial number of club convergence. Then, we proceeded with the clubmerging process to obtain final club convergence in each CPI component. Table 2 presents
the results of final clubs generated from these procedures that are comparable to Panel Cof Table 1. We also display the mean of CPI in each club to show the clubs’ order fromthe highest CPI (club 1) to the lowest CPI (club 4). Given this order, we classify club 1,
club 2, club 3 and club 4 as “high CPI”, “middle-high CPI”, “middle-low-CPI”, and “lowCPI”, respectively.

Table 2. Club convergence in aggregate CPI and components
Clubs merging results
t-stats
�̂ coeff
Aggregate CPI
Full sample-1.02 -106.97
Club 10.47
10.61
Club 20.14
2.81Club 3-0.08-1.35Club 40.12
1.46
Foodstuffs
Full sample-1.15 -138.35
Club 1-0.48-1.27Club 20.01
0.23Club 30.84
14.10
Club 40.49
9.72
Housing
Full sample-1.01 -619.70
Club 10.01
0.08Club 20.03
0.55
Club 3-0.06-0.82
Processed foods
Full sample-0.91-40.50Club 10.61
5.88
Club 20.12
1.73
Club 30.06
1.08Club 4
-0.02
-0.94
Club

CPIa

132.08127.89124.26122.17140.15132.73123.98118.42130.90124.42
119.47143.44135.61
126.97121.34Clubs merging results
t-stats
�̂ coeff
Clothing
Full sample-0.92-31.22Club 1-0.09-1.57
Club 20.29
5.99Club 3-0.05-1.04
Club 4-0.08-1.10
HealthFull sample-0.98 -432.94
Club 10.04
2.81Club 20.31
3.90Club 30.54
7.03
Club 40.09
1.60
Education
Full sample-1.08 -130.72
Club 10.10
0.65Club 2-0.04-0.60
Club 30.31
2.28
Transport
Full sample-1.21-66.91Club 10.36
2.77Club 20.06
1.41Club 3-0.03-0.64Club 4
0.35
6.53
Clubs

CPIa

127.69118.97116.78109.18132.89122.71118.59114.70129.52118.53112.76135.61
128.16121.95116.66

Note: t-stats > -1.65 denotes that the null hypothesis of convergence is not rejected.

a indicates the mean of CPI in each club from January 2014 to December 2019. Source: Authors’ calculation.

From the analysis using disaggregated CPI data, we found four appealing findings.
First, similar to the results on aggregate CPI data, we were also able to reject the null
hypothesis of overall convergence in all CPI components at the 5% signiﬁcant level (�̂ issigniﬁcant < 0 with t-statistic < -1.65). This evidence supports the validity of our finding
previously and reflects the presence of significant price divergence across Indonesian
regions that prevails not only in aggregate price but also in sub-group of commodities.3
From theory, we understand that the causes of price differentials across regions could besourced from both countrywide and regional factors. While countrywide factors mainly
related to the asymmetrical regional effects of common monetary regime and exchange
rate movements, region-specific factors are more likely related to non-monetary terms
such as the structure of labor market that shape the prices of input factor, different regional
economic structure and business cycle position (for further discussion, see Beck, Hubrich,and Marcellino, 2014).
Second, we found variability in the number and composition of clubs across CPI
components. By carefully looking at Table 2, one might notice the variability in thenumber of clubs across components where housing and education components havedifferent number of clubs compared to the aggregate price and other components. A
similar finding is also observed by Christou, Cunado, and Gupta (2018), where they obtaina smaller number of club convergence in housing price (7 clubs) compared to aggregate
price (11 clubs) across 50 U.S. states for the period 1960-2007. This variability is more
observable in terms of clubs' composition, represented by the number of cities in each club,3

We also plot the relative transition path of all clubs in each CPI component in Figure A1 of the Appendix.
Like that in aggregate CPI, the transition path of clubs in CPI components is diverging over time.

as shown in Figure 2. None of the CPI components show identical clubs' composition, butsome have a similar pattern. For example, in aggregate CPI, processed foods, health,transport, and housing components, most of the cities are in club 2 and club 3 (middlehigh and middle-low CPI). Differently, clubs’ composition in the clothing component isdominated by club 3 and club 4 (middle-low and low CPI). In contrast, most cities infoodstuffs and education components are in club 1 and club 2 (high and middle-high CPI).

Figure 2. Club’s composition in CPI components

Source: Authors’ calculation.

Third, related to the second finding, clubs’ composition in foodstuffs and education
components implies an alarming message. As shown in Table 3, cities in club 1 have thehighest inflation rate in all CPI components, followed by club 2, club 3 and, club 4 (lowest
inflation rate). This means that number of cities with the highest inflation rate is muchlarger in foodstuffs and education components. On the other hand, although the average
inflation rate of club 1 in the processed foods component is the highest among others, thenumber of cities in club 1 is minimal. The tendency of the foodstuffs component
converging to higher price level reflects the underlying problems of food price inflation inIndonesia. A number of discussions around policies on controlling food inflation inIndonesia advocate that supply shocks (e.g., crop failure, frequent disturbance in shipment),lack of agriculture-related infrastructure, productivity stagnation in agriculture due toclimate change, and seasonal religious events are the major factors that increase food priceinflation. Meanwhile, the similar club’s composition pattern in the education component
is largely influenced by seasonal factors. More precisely, education-related expenses (e.g.,school tuition fees, expenses for books and other school equipment) tend to increasearound July and August, where the new academic year begins. As a whole, this third
finding re-emphasizes the role of non-monetary factors in affecting the Indonesian
inflation rate (Affandi, 2011; Alamsyah et al. 2001; Tirtosuharto and Adiwilaga, 2014).
To further understand the geographical pattern of clubs in all components, we show
the details of the clubs’ composition based on regions in Table A4 of the Appendix.
Regarding the foodstuffs component, the highest percentage of cities in club 1 is observedin the Sumatra region, which is 43% (10 out of 23 cities), followed by the Java region,
which is 36% (10 out of 28 cities). This geographical representation of club convergencein disaggregated price will help policymakers to prioritize regional inflation management
policies. For example, if the goal is to control foodstuffs commodities' inflation rate, thepolicy could focus more on cities in Sumatra and Java regions. A similar analysis implies
that policy should aim for cities in the Kalimantan region for the education component.
Table 3. Average inflation rate in each clubClub
Inflationa
Aggregate CPI
Club 14.76%
Club 24.05%
Club 33.66%
Club 4
3.14%
Clothing
Club 15.38%
Club 24.28%
Club 33.42%
Club 42.28%

Club
Inflationa
Foodstuffs
Club 15.37%
Club 2
4.26%
Club 33.00%
Club 4
0.96%
HealthClub 15.73%
Club 24.37%
Club 33.43%
Club 42.65%

Club
Inflationa
Processed foods
Club 17.14%
Club 2
5.46%
Club 34.47%
Club 4
3.25%
Transport
Club 15.73%
Club 23.51%
Club 32.24%
Club 4
1.68%

Club
Inflationa
Housing
Club 14.92%
Club 23.80%
Club 3
3.05%
Education
Club 1
5.11%
Club 23.45%
Club 3
2.39%

Note: a Mean of inflation in each club from January 2015 to December 2019. Source: Authors’ calculation.

We further analyzed the relative contribution of CPI components towards the clubconvergence in aggregate CPI by comparing the number of common cities in aggregate
CPI and each component. From the results presented in Table 4, we show that there are 17
cities in the foodstuffs component which follow the same transition path of cities belong
to the aggregate CPI club convergence, 35 cities in processed foods, 41 cities in housing,
23 cities in clothing, 33 cities in health, 17 cities in education and 36 cities in transportcomponent. We justified our evaluation by computing each component's relative
contribution by dividing the total common cities in each component with the average
number of common cities across all components. As the final finding from thedisaggregated CPI data analysis, we reveal that housing, processed foods, transport, andhealth components make relatively larger (above average) contribution to the clubconvergence formation in the aggregate CPI, while foodstuffs, clothing, and education
components constitute smaller contribution (below average). The result of this evaluationsuggests the policymakers focus more on reducing regional price variability in housing,processed foods, transport, and health components to achieve a higher degree of
convergence in regional price.
Table 4. Relative contribution to aggregate CPI club convergence
Club
Club 1Club 2Club 3Club 4
Total
Contr.

Aggr.
CPI
9
34
30
8
82

Foodstuffs
vsAggr. CPI
9
4
2
2
17
0.59

Processed
foods vs
Aggr. CPI
1
19
13
2
35
1.21

HousingvsAggr. CPI
2
23
16
41
1.42

Clothing
vsAggr. CPI
0
5
17
1
23
0.80

HealthvsAggr. CPI
2
14
14
3
33
1.14

Education
vsAggr. CPI
9
6
2
17
0.59

Transport
vsAggr. CPI
1
17
17
1
36
1.25

Note: vs stands for versus. Aggr. CPI and Contr. refers aggregate CPI and to relative contribution. - denotes the absence of club 4 forthe housing and education component. The relative contribution is computed as total cities in each CPI component that follow the sametransition path in aggregate CPI club convergence divided by the average of total cities across CPI components that follow the sametransition path in aggregate CPI club convergence. The relative contribution shows that processed foods, housing, health, and transportcomponents contribute relatively higher (above average) to the aggregate CPI club convergence. Non-convergence cities for aggregate
CPI, health, education, and transport components are Tual, Tanjung Pandan and Ternate, Jakarta and Sorong, Tual, and Bengkulu,
respectively. In general, the format of the table follows Akram, Sahoo, and Rath (2020). Source: Authors’ calculation.

4. Conclusions
The purpose of this study is to examine price convergence across 82 cities in Indonesia byusing aggregate CPI and its components. We implement recent convergence frameworks
and clustering techniques developed by Phillips and Sul (2007, 2009) in two steps; first,
we identify club convergence using aggregate CPI, and second, we identify clubconvergence using seven components of CPI. The data used in this study is monthly CPI
from January 2014 to December 2019.
Using aggregate CPI data, we do not find evidence of overall price convergence.
Instead, we identify four club convergence. This result is consistent with the finding inprevious study by Jangam and Akram (2019). Next, further examination using CPI
components produces appealing outcomes. First, overall price convergence does not exist
in any of CPI components, supporting the result from aggregate CPI. Second, there isvariability in the number and composition of clubs across CPI components. Third, theprice of foodstuffs and education-related commodities in most cities converges to a higher
level, reflecting the role of non-monetary factors in affecting Indonesia's inflation
dynamics. Fourth, housing, processed foods, transport, and health components constitutea relatively larger contribution to the club convergence formation in the aggregate CPI.
Overall, our study demonstrates that club convergence identification using
disaggregated consumer price data would reveal some important details which are notobserved in aggregate price. In the context of Indonesian cities, the details are rich with
policy implications. First, the rejection of price convergence suggests price rigidities that
attribute to persistent regional price variability. In order to reduce the degree of variability
in aggregate price, policies should target improving market efficiency in housing,processed foods, transport, and health-related sectors. Second, when the goal is to control
the inflation rate, region-based price management policies can be implemented to control
the price of foodstuffs and education commodities or services, particularly in cities of
Sumatra, Java and Kalimantan regions. As for future research, our findings open theopportunities to investigate the conditioning factors of club convergence formation inIndonesian regional price, particularly by integrating the role of spatial spillovers asemphasized by recent convergence studies.
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Appendix
1. Four steps in identifying club convergence:i. CPI of 82 cities are arranged in decreasing order according to their value in the lastperiod, that is December 2019.
ii. A core group of sample cities is identiﬁed based on the maximum tk obtained from aseries of sequential estimations of equation (5) for the k largest group (2 ≤ kN).
iii. Cities not belonging to the core group are re-evaluated one at a time with log t
regression. A new group is formed when t-statistic > -1.65.
iv. Steps 1 to 3 are performed again for remining cities. If no core group is found, remining
cities are labeled as divergent, and the algorithm stops.
Table A1. Summary statistics of aggregate CPI in 82 Indonesian cities
No.
City
1 Ambon2 Balikpapan
3 Banda Aceh
4 Bandar Lampung
5 Bandung
6 Banjarmasin
7 Banyuwangi
8 Batam
9 Bau-bau
10 Bekasi
11 Bengkulu
12 Bima
13 Bogor
14 Bukit Tinggi
15 Bulukumba
16 Bungo
17 Cilacap
18 Cilegon
19 Cirebon
20 Denpasar
21 Depok
22 Dumai
23 Gorontalo
24 Jakarta
25 Jambi
26 Jayapura
27 Jember
28 Kediri
29 Kendari
30 Kudus
31 Kupang
32 Lhokseumawe
33 Lubuk Linggau
34 Madiun
35 Makassar
36 Malang
37 Mamuju
38 Manado
39 Manokwari
40 Mataram
41 Maumere

Mean Std Dev
123.876.95
129.649.14
120.086.9
126.578.81
125.148.31
125.61
9.23
122.72
6.04
126.16
9.43
128.147.9
123.827.85
133.25
10.52
128.9
8.3
126.768.85
123.717.32
132.03
8.55
124.598.06
128.598.28
130.85
10.49
122.47
6.56
123.157.49
125.06
7.64
127.3
8.52
122.03
7.61
126.558.21
125.437.67
127.879.23
122.966.76
122.995.76
121.937.63
131.81
8.55
126.787.5
121.81
7.77
123.238.4
123.797.69
126.41
9.66
126.34
7.96
124.42
7.86
125.4
8.33
121.15
9.09
124.417.44
119.815.9

Min.
108.58111.85107.26109.89109.87108.22111.04109.24109.84110.15112.57113.35111.73109.55116.06109.75112.9
111.46110.11109.14111.53110.67107.91110.75111.26111.64110.65111.91
107.34116.25111.39107.19106.76109.71108.65111.03108.75109.05106.28110.53108.76

Max.
134.47142.36130.34139.92
138.22140.15131.95140.33139.31137.79147.98141.86140.86135.18144.75137.75140.75
146.63132.58134.62
137.36139.49133.53139.62
137.3
142.49133.28131.63135.35145.17136.64132.73134.66135140.02
137.6
134.52140.99138.31135.15128.73No.
City
42 Medan
43 Merauke
44 Metro
45 Meulaboh
46 Padang
47 Padang Sidempuan
48 Pakanbaru
49 Palangkaraya
50 Palembang
51 Palopo
52 Palu
53 Pangkal Pinang
54 Pare-pare
55 Pematang Siantar
56 Pontianak
57 Probolinggo
58 Purwokerto
59 Samarinda
60 Sampit
61 Semarang
62 Serang
63 Sibolga
64 Singaraja
65 Singkawang
66 Sorong
67 Sukabumi
68 Sumenep
69 Surabaya
70 Surakarta
71 Tangerang
72 Tanjung
73 Tanjung Pandan
74 Tanjung Pinang
75 Tarakan
76 Tasikmalaya
77 Tegal
78 Tembilahan
79 Ternate
80 Tual81 Watampone
82 Yogyakarta

Mean Std Dev
129.699.84
130.148.5
133.146.64
126.047.55
130.79
8.94
124.5
7.94
127.058.99
123.477.31
123.52
8.03
124.4
8.52
128.31
9.71
130.1510.96
122.016.97
129.848.88
134.38
10.77
123.4
5.81
123.75
7.23
128.7
8.38
127.16
9.58
124.81
7.5
133.35
11.13
129.41
10.65
133.389.23
126.729.18
125.758.32
125.71
7.61
122.986.96
125.948.34
122.466.79
133.139.31
125.718.19
133.46
9.54
125.647.1
135.56
10.22
124.32
7.7
122.658.03
130.787.99
129.49
8.41
141
14.32
122.98
7.97
123.8
7.32

Note: The format of the table follows Jangam and Akram (2019). Source: Authors’ calculation.

Min.
111.57111.84120.34112.05113.48110.39110.92109.63108.41108.84110.78110.52108.21113.32111.78112.23110.49113.78109.94110.39111.98110.37114.67109.14108.43111.29109.42110.47109.5
114.82109.57114.68111.87113.64109.2
107.62115.63111.57112.53108.28110.77Max.
146.7
141.02143.58139.73144.55136.97141.09135.43134.81
136.62144.4
146.22132.6
143.12149.42132.35134.88140.25141.87136.59149.63148.33146.5
139.61137.06137.19133.45138.23133.1
147.82136.8
147.92136.54150.66134.58134.71144.3
141.42160.83135.06135.46

Table A2. Summary statistics of aggregate CPI and components
CPI component

Mean

Std. Dev.

Minimum

Maximum

Aggregate

126.449.04

106.28150.66

Foodstuffs

133.8412.91

101.02189.76

Processed foods

130.7013.32

103.06172.10

Housing

123.429.24

102.84157.31

Clothing

116.61

10.59

97.05

171.16

Health

121.0210.75

100.93166.64

Education

120.40

11.23

97.78

162.72

Transport

125.9310.07

103.04

191.42

Note: The Indonesian regional CPI data consist of one aggregate price index that can be disaggregated into sevencomponents; 1) foodstuffs, 2) processed foods, 3) housing and utilities, 4) clothing, 5) health, 6) education, leisure andsports, and 7) transportation, communication and financial services. Source: Authors’ calculation.

Table A3. Result of beta convergence test for each clubClub

Beta coefficientStandard error

R-squareClub 1Club 2Club 3Club 4-0.54***-0.42***-0.41***-0.49**

0.09
0.07
0.09
0.16

0.84
0.53
0.42
0.61

Note: ***, ** denote statistical significance at 1% and 5% levels respectively.
Source: Authors’ calculation.

Table A4. Number of cities in each club of CPI components by regions
CPI component
Aggregate CPI

Foodstuffs

Processed foods

Housing

Clothing

Health

Education

Transport

Club
Club 1Club 2Club 3Club 4
No convergence
Total
Club 1Club 2Club 3Club 4
No convergence
Total
Club 1Club 2Club 3Club 4
No convergence
Total
Club 1Club 2Club 3
No convergence
Total
Club 1Club 2Club 3Club 4
No convergence
Total
Club 1Club 2Club 3Club 4
No convergence
Total
Club 1Club 2Club 3
No convergence
Total
Club 1Club 2Club 3Club 4
No convergence
Total

Source: Authors’ calculation.

RegionNumberof cities

SumatraJava-Bali

Kalimantan

Eastern

9
34
30
8
1
82
27
41
8
3
3
82
4
35
32
11
82
8
47
27
82
11
12
38
21
82
9
31
24
16
2
82
22
47
11
2
82
4
37
36
3
2
82

4
11
7
4
23
10
10
2
1
23
10
9
4
23
2
17
4
23
3
4
11
5
23
12
4
6
1
23
8
12
3
23
1
9
12
1
23

2
9
13
4
28
10
13
2
2
1
28
1
13
8
6
28
2
17
9
28
3
2
14
9
28
4
8
11
5
28
5
20
2
28
13
14
1
28

2
5
2
9
2
6
1
9
4
5
9
2
5
2
9
1
2
5
1
9
3
5
1
9
4
4
1
9
2
3
4
9

1
9
8
3
1
22
5
12
3
1
1
22
3
8
10
1
22
2
8
12
22
4
4
8
6
22
2
6
8
5
1
22
5
11
5
1
22
1
12
6
2
1
22

Figure A1. Transition path of clubs for all CPI components

Foodstuffs

Processed foods

Housing

Clothing

Health

Education

Transport
Source: Authors’ calculation.