Bulletin of Monetary Economics and Banking, Vol. 22, No. 3 (2019), pp. 239 - 262

p-ISSN: 1410 8046, e-ISSN: 2460 9196

DO PRICES CONVERGE AMONG INDONESIAN CITIES?

AN EMPIRICAL ANALYSIS

Bhushan Praveen Jangam* and Vaseem Akram**

*Indian Institute of Technology, Hyderabad, India. Email: jbpraveen1@gmail.com

**Indian Institute of Technology, Hyderabad, India. Email: akramvaseem001@gmail.com

ABSTRACT

We investigate consumer price convergence for 82 Indonesian cities using monthly data from 2014 to 2019. To do so, we employ recent techniques of club convergence and weak sigma convergence. The results reveal, first, consumer price divergence, implying price rigidities across the cities. Second, we find four clubs, suggesting that Indonesian cities converge along four unique transition paths. Third, we find weak evidence of consumer price convergence, suggesting that prices among Indonesian cities adjust, but not freely. Policy should therefore consider unique convergence paths for each club to promote stronger consumer price convergence.

Keywords: Club convergence; Weak sigma convergence; Price convergence; Indonesian cities.

JEL Classifications: C23; E31.

Article history:
Received	: June 24, 2019
Revised	: October 2, 2019
Accepted	: October 11,	2019
Available online : October 15,		2019

https://doi.org/10.21098/bemp. v22i3.1152

Do Prices Converge Among Indonesian Cities? An Empirical Analysis	241

of distribution and transport systems to guarantee adequate and fair supply distribution. In 2012, national shipping fleets in Indonesia grew by 7%, which mostly helped domestic freight. Additionally, there has been an increase in the number of sea freight license holders in recent years.2 Despite improvement in the distribution and growth of transport services across the Indonesian cities, considerable price disparities remain a challenging issue. As Tirtosuharto and Adiwilaga (2013) mention, inflation in Indonesia is more volatile compared to its border countries, due to frequent disruptions in food supplies and distribution. Moreover, evidence of substantial consumer price disparities across Indonesian regions has been noted, with differences in transportation costs, levels of development, the logistical costs of goods, non-traded products, firm monopolies, labor market segmentation, informational asymmetries, and productivity (e.g., Tirtosuharto and Adiwilaga, 2013; Varela, et al., 2013).3 Moreover, Tirtosuharto and Adiwilaga (2013) state that inflation differs (or changes in price differ) from region to region, with a huge disparity across eastern Indonesian, Java, Jakarta, and Sumatra. The findings for Sumatra and Eastern Indonesian regions are more uneven compared to the other regions. According to the Indonesia investment database,4 the changes in prices in Indonesia are greater than in other emerging market nations. The Consumer Price Index (CPI) of emerging market nations rose by 5% from 2005 to 2014, whereas in Indonesia it increased by around 8.5%. However, since 2015, there has been little improvement in Indonesia’s inflation rate, and there is still vast disparity in consumer prices across Indonesian cities, despite the decentralization process, and it remains a contentious issue (Wimanda, 2009; Varela et al., 2013). Examination of LOOP or the convergence of the CPI is therefore vital for Indonesian cities for greater market integration and fair supply distribution. The main concept of LOOP is that, if the prices in one city increase considerably compared to other cities, market forces will equalize them across cities (Obstfeld and Rogoff, 2000). However, because of the rigidities pointed out above, the prices do not adjust.

Although considerable research has been performed on price convergence or LOOP across countries at an aggregate level, there are no studies in the context of Indonesian cities except for that of Wimanda (2009), who examines the issue of price convergence at the product level. More specifically, Wimanda studies price variability and convergence using the price index data of 35 products in 45 cities from 2002 to 2008. Our paper differs from Wimanda’s in three ways. First, it examines consumer price variability and the prospect of consumer price convergence for 82 Indonesia cities by considering the CPI of each city, unlike Wimanda’s study, which considers only product price convergence. Investigation of CPI convergence at the city level is vital, because of the vast disparities and variability observed (see Figures 1 and 2 and Table 1). Cities such as Batam, Kudos, Cilacap, Tanjung Pandan, Metro, Bengkulu, Tembilahan, Tual, Tarakan,

2Source: Ministry of Transportation of the Republic of Indonesia.

3For a good discussion of regional price disparities in Indonesia, see Tirtosuharto and Adiwilaga

(2013).

4For more details, see https://www.indonesia-investments.com/finance/macroeconomic-indicators/ inflation-in-indonesia/item254.

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and Padang have higher consumer prices compared to the others. Table 1 shows that the standard error is higher for Sibolga, Medan, Bengkulu, Pangkal Pinang, Tual, Tarakan, Pontianak, and Serang. This implies that these cities have greater variation in their CPIs. The same implication about disparities in consumer price is noted by Tirtosuharto and Adiwilaga (2013).

Figure 1. Bar Plots of Mean of Consumer Price Index Across Cities

This figure plots the mean of the consumer price index for each Indonesian city for which we have data. There is a sample of 82 cities in our analysis.

Sumenep
Jember
Tegal
Surakarta
Purwokerto
Tasikmalaya
Bekasi
Bandung
Bogor
Tanjung Pinang
Pangkal Pinang
Metro
Bengkulu
Palembang
Bungo
Pekanbaru
Bukit Tinggi
Padang Sidempuan
Pematang Siantar
Lhokseumawe
Meulaboh
110.000	115.000	120.000	125.000	130.000	135.000

Do Prices Converge Among Indonesian Cities? An Empirical Analysis	243

Figure 2. Bar Plots of Mean of Consumer Price Index Across Cities (continued)

See notes to Figure 1.

Jayapura

Merauke

Sorong

Manokwari

Ternate

Tual

Ambon

Mamuju

Gorontalo

Bau-bau

Kendari

Palopo

Pare-pare

Makassar

Watampone

Bulukumba

Palu

Manado

Tarakan

Samarinda

Balikpapan

Banjarmasin

Tanjung

Palangkaraya

Sampit

Singkawang

Pontianak

Kupang

Maumere

Bima

Mataram

Denpasar

Singaraja

Cilegon

Tangerang

Serang

Surabaya

Madiun

Probolinggo

Malang

Kediri

105.000

110.000

115.000

120.000

125.000

130.000

135.000

140.000

145.000

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Table 1.

Summary Statistics Results

This table reports the summary statistics of prices across Indonesian cities for the period 2014 to 2019. From mean, standard deviation (Std. Dev), minimum (min.) and maximum (max.) values, allow us to observe the dispersion or heterogeneity across the Indonesian cities.

	Cities	Mean	Std.	Min	Max	Cities	Mean	Std.	Min	Max
			Dev					Dev.
	Ambon	123.3	6.71	108.58	134.45	Medan	128.91	9.56	111.57	146.7
	Balikpapan	128.97	8.96	111.85	142.36	Merauke	129.66	8.5	111.84	141.02
	Banda Aceh	119.52	6.69	107.26	130.34	Metro	132.41	6.71	112.58	143.08
	Bandar Lampung	125.81	8.47	109.89	139.55	Meulaboh	125.26	7.02	112.05	138.22
	Bandung	124.4	7.95	109.87	137.97	Padang	130.1	8.73	113.48	144.55
	Banjarmasin	124.8	8.85	108.22	138.87	Padang Sidempuan	123.82	7.65	110.39	136.97
	Banyuwangi	122.2	5.81	111.04	131.46	Palangkaraya	122.84	7.02	109.63	133.87
	Batam	125.43	9.2	109.24	140.33	Palembang	122.88	7.81	108.41	134.44
	Bau-bau	127.62	7.82	109.84	139.31	Palopo	123.69	8.22	108.84	136.56
	Bekasi	123.03	7.35	110.15	136.95	Palu	127.43	9.25	110.78	144.15
	Bengkulu	132.43	10.26	112.57	147.98	Pangkal Pinang	129.26	10.63	110.52	146.22
	Bima	128.22	8.05	113.35	141.05	Pare-pare	121.46	6.77	108.21	132.6
	Bogor	125.96	8.45	111.73	140.54	Pekanbaru	126.25	8.61	110.92	141.09
	Bukit Tinggi	123.12	7.11	109.55	135.18	Pematang Siantar	129.18	8.71	113.32	143.12
	Bulukumba	131.3	8.22	116.06	144.46	Pontianak	133.52	10.46	111.78	148.97
	Bungo	123.88	7.73	109.75	137.75	Probolinggo	122.91	5.59	112.23	131.59
	Cilacap	127.91	8.01	112.9	140.58	Purwokerto	123.12	6.95	110.49	134.79
	Cilegon	130.16	9.89	111.98	145.91	Samarinda	128.05	8.17	113.78	140.25
	Cirebon	121.9	6.32	110.11	131.94	Sampit	126.35	9.24	109.94	141.16
	Denpasar	122.52	7.23	109.14	134.06	Semarang	124.14	7.19	110.39	136.02
	Depok	124.35	7.27	111.53	137.36	Serang	132.73	10.34	112.98	149.23
	Dumai	126.66	8.35	110.67	139.49	Sibolga	128.54	10.32	110.37	148.33
	Gorontalo	121.38	7.32	107.91	133.36	Singaraja	132.68	9.02	114.67	146.5
	Jakarta	125.8	7.84	110.75	138.7	Singkawang	126.04	8.99	109.14	139.61
	Jambi	124.81	7.43	111.26	137.3	Sorong	125.13	8.14	108.43	136.75
	Jayapura	127.15	8.97	111.64	142.49	Sukabumi	125.06	7.34	111.29	136.72
	Jember	122.39	6.53	110.65	132.5	Sumenep	122.4	6.74	109.42	132.17
	Kediri	122.53	5.59	111.91	130.77	Surabaya	125.26	8.08	110.47	137.16
	Kendari	121.29	7.36	107.34	135.35	Surakarta	121.87	6.53	109.5	132.39
	Kudus	131.05	8.18	116.25	144.56	Tangerang	131.81	9.63	111.46	146.86
	Kupang	126.26	7.39	111.39	136.34	Tanjung	125.12	8.03	109.57	136.2
	Lhokseumawe	121.21	7.58	107.19	132.5	Tanjung Pandan	132.63	9.17	114.68	147.46
	Lubuk Linggau	122.57	8.19	106.76	134.66	Tanjung Pinang	125.05	6.87	111.87	136.23
	Madiun	123.15	7.44	109.71	134.52	Tarakan	134.83	10.04	113.64	150.66
	Makassar	125.62	9.35	108.65	139.94	Tasikmalaya	123.73	7.54	109.2	134.58
	Malang	125.7	7.74	111.03	137	Tegal	121.97	7.74	107.62	134.25
	Mamuju	123.88	7.75	108.75	133.78	Tembilahan	130.07	7.66	115.63	144.3
	Manado	124.68	7.98	109.05	140.02	Ternate	128.83	8.19	111.57	141.42
	Manokwari	120.21	8.45	106.28	136.46	Tual	139.9	13.98	112.53	160.83
	Mataram	123.8	7.21	110.53	135.11	Watampone	122.28	7.64	108.28	134.96
	Maumere	119.35	5.74	108.76	127.33	Yogyakarta.	123.15	7.01	110.77	134.27

Do Prices Converge Among Indonesian Cities? An Empirical Analysis	245

Second, Wimanda (2009) considers only 45 cities and determines whether the product prices of poor cities converge toward those of prosperous cities, using the absolute and sigma notion of convergence, which seem to have been ruled out by the data in recent years, as discussed above. According to the neoclassical convergence approach (absolute or sigma), a steady state can be achieved if the consumer prices of all the cities increase at the same rate, which is not the case in the 83 Indonesian cities. Thus, we differ from Wimanda by relaxing this assumption, such that the cities do not need to have the same price level but, instead, the relative prices need to be the same along a transition path toward steady state. Third, our paper complements Wimanda’s by investigating the speed of convergence (or the transition path).

To achieve the goals of this paper, we apply the panel club convergence of Phillips and Sul (2007, 2009, hereafter PS) and the weak sigma convergence test of Kong et al. (2019). We consider the PS approach for the following reasons: (i) It addresses the issue of panel heterogeneity, (ii) it employs a nonlinear time-varying factor, (iii) it is ideal for the detection of asymptotic co-movement in the presence of a unit root, and (iv) it splits the full sample into clubs based on a clustering algorithm. Further, the weak sigma convergence test is useful when the panel data do not involve stochastic or divergent deterministic trends. The results derived from these tests show no evidence of overall consumer price convergence among Indonesian cities, unlike Wimanda’s (2009) study; rather, we find four clubs, suggesting four different transition paths. Further, we find evidence of weak consumer price convergence, suggesting that consumer prices among Indonesian cities adjust, but not freely. These findings suggest that a single policy might not work properly in Indonesian cities, contrary to Wimanda’s (2009) product price proposition. Thus, policy should be designed based on clubs to achieve stronger consumer price convergence.

The remainder of the paper is organized as follows. Section II describes the methodology and data. Sections III and IV present the empirical results and conclusions, respectively.

II.METHODOLOGY AND DATA

A. Sources of Price Variability

The price variability framework is based on the concept of purchasing power parity (PPP). Engel (1993) claims that deviations from LOOP across cities are the primary reason for the failure of PPP. This framework helps understand the importance of national borders in the integration of markets. Engel and Rogers

(2001) generalize Engel’s (1993) price variability approach to understand the importance of PPP violation across cities. They focus on two sources of variability:

(i) variability in individual prices across cities and (ii) variability of all product prices across cities. Engel and Rogers argue that LOOP will hold if the variability of each individual price across cities is less than the variability of prices of all products in each individual city. In other words, a relative LOOP will be validated if the ratio between the variability in the prices of all products in the same city and the variability in the prices of the same product across cities is greater than one.

Do Prices Converge Among Indonesian Cities? An Empirical Analysis	247

B. Coefficient of Variation (CV)

Numerous studies (e.g., Dalgaard and Vastrup, 2001; Miketa and Mulder, 2005; Liddle, 2009, 2010; Ram, 2017; Rath, 2019; Rath and Akram, 2019) have examined convergence through the CV. For preliminary purposes, this study analyzes variability considering the CV. Examining the CV provides a broad idea of whether price variability has been declining over the years across cross sections. The CV can be written as

(6)

where σ and μ denote the standard deviation and mean, respectively, of the consumer price across countries. We say there is convergence if the ratio of the standard deviation and mean decline over the years, and vice versa.

C. Absolute Convergence

In the next stage, we check for consumer price convergence by applying various panel techniques, such as pooled regression, a fixed dynamic panel model, and the system generalized method of moments (GMM) model of Arellano and Bover (1995) and Blundell and Bond (1998). We choose the system GMM over the differenced GMM model because the latter suffers from sample bias. The system GMM model corrects sample bias by including the momentum condition.

There are two advantages to using a dynamic panel data model. First, it includes a complete set of city-specific effects as exogenous variables, and the fixed effects specification avoids the omitted variable bias, which arises due to cross- city heterogeneity. Second, it takes into account the possible endogeneity of the independent variables (Castellacci and Archibugi, 2008; Narayan et al., 2011). In this paper, we conduct a cross-city analysis of CPIs. The model can be explained with the following equation:

(7)

for Indonesian city i=1,2,…,82 and time t=1,2,…,68, where Pit stands for the CPI, β is the coefficient of the CPI to be estimated, μi is a city-specific effect, λt is a time-specific constant, and εi,t is an error term. A negative and statistically significant coefficient of β suggests absolute consumer price convergence, and a positive and significant coefficient suggests consumer price divergence. Equation

(7) can be rewritten as

(8)

where η=1+β and pi,t=lnPi,t. We remove individual country- and time-specific follows:effects μi and λt, respectively, which can be done by differencing equation (8), as

248	Bulletin of Monetary Economics and Banking, Volume 22, Number 3, 2019

(9)

We do not estimate this equation using the Ordinary Least Squares (OLS) method, because the lagged dependent variables are correlated with the composite error through period t-1. Therefore, following Arellano and Bond (1991), we use all past values of the explanatory variables as instruments in the regression.

D. PS Technique

In the next stage, we apply the PS technique to determine club convergence. This technique is widely used in the literature, due to its uniqueness and superiority over conventional convergence tests. The PS test allows for a non–time-varying factor model. It forms clubs endogenously in a panel, using clustering algorithms, to estimate the relative convergence by averaging the cross section, unlike absolute convergence. The other feature of the PS test is that it does not depend upon a stationary/non-stationarity series, and it identifies multiple steady states. The test corrects the biases that arise from unit root properties and considers both individual-specific and common components.

In our case, the CPI is denoted by Pit for city i=1,2,…,82 and time t=1,2…,68. One factor model proposed by PS is

(10)

where δi denotes the idiosyncratic term that indicates the gap between systematic factors (Pit) and common factors (μt); μt is the accrued behavior of Pit, which affects city behavior; and uit is the white noise term. Thus, equation (10) verifies the progression for individual Pit values in relation to common factors, utilizing two idiosyncratic elements, namely, δi and uit. Next, we divide the Pit series into transitory components (Bit) and systematic components (Git):

(11)

where μt stands for a common steady-state trend function comprised of stochastic and deterministic components, and δit denotes an idiosyncratic term that includes city-specific and time effects. In other words, the coefficients of δit indicate the common factor share of μt for each individual in a panel. PS further state that convergence is not a static process, but a dynamic one. Furthermore, δit provides information about the transition paths that can be tested by the relative temporal evolution of δit.

The PS methodology does not make any assumptions about the parameters of μt, but factors it out by emphasizing δit which is not directly observable from equation (11), because there are fewer unknown parameters than observations. Hence, PS consider a semiparametric form to construct a formal test for convergence, which

250	Bulletin of Monetary Economics and Banking, Volume 22, Number 3, 2019

(15)

where Knty is the cross-sectional sample variation, with n = 1,…, N and t = 1,…, T, and ût is the fitted error. Next, we use a t-test to check whether the fitted coefficient is less than zero and statistically significant. A general time decay specification for all t is given by

(16)

where αn, bn, and vn,t embody the individual data generating processes of yit and the cross-sectional averages contained in Knty If the convergence parameter (λ) is greater than zero, cross-sectional dispersion (Knty) will decrease over time under the stability conditions of n→∞, which will result in weak sigma convergence. If the convergence parameter is less than zero, cross-sectional dispersion increases over time, indicating that some components of yit have heterogeneously divergent trend characteristics. Further, when the convergence parameter is equal to zero, there is no tendency to diverge or converge, and Knty fluctuates around the level of α. The standard robust t statistic with a time trend is given by

	(17)
The presence of weak sigma convergence diverges	to -∞. The long-run

variance ( ) is estimated by the residuals from (15), such as the Bartlett–Newey– West (BNW) estimate:

(18)

where vlL is the Bartlett lag kernel weight with lag parameter L=[Tk] for k>0. The one-sided critical values from a standard normal distribution are considered in testing for evidence of convergence.

There are two broad differences between the approaches of PS and Kong et al. (2019). First, the PS approach implements a log(t) regression, which considers variation in the cross section among relative transition paths, and a logarithmic trend regression to validate evidence of convergence. Kong et al. (2019), on the other hand, removes any common components in the cross section and implements linear trend regression to find trend decay. In this process, even though the regression is misspecified, the slope coefficient captures the trend decay.

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Further, to validate these results, we employ various panel data models, such as pooled regression panel, fixed dynamic panel, and system GMM panel data models. The results provided in Table 2 show that the coefficients of the lag of consumer prices are positive and significant for all models, which suggests that the variation between countries is increasing, validating the evidence of divergence in Indonesian cities. This finding motivates us to examine whether club convergence exists, where each club has a unique transition path.

Table 2.

Beta Convergence Results

The results of panel data models such as pooled ordinary least square (POLS), fixed-dynamic, and system-GMM are presented in this table. The variable lnPt-1 denotes the logarithm of price with one lag. Finally, *** indicates the 1% level of significance. p-values are given in the parenthesis.

Variable	POLS	Fixed-Dynamic	System-GMM
lnPt-1	0.99***(0.00)	0.98***(0.00)	0.98***(0.00)
Constant	0.06***(0.00)	0.08***(0.00)	0.09***(0.00)
Sargan test	…	…	81.96 (1.00)

B. Club Convergence

We apply the PS test to determine the formation of clubs. The results are presented in Table 3. Since the critical value is greater than the value of log(t), -242.98, for the full sample, we reject the null of convergence. This result suggests that the cities considered do not have a unique transition path. Therefore, PS use a clustering algorithm to form clubs for the cities that have a similar steady state. We find statistically significant four club convergence. Club 1 comprises 10 cities with a log(t) value of 10.58, which is evidence of convergence. Club 2 comprises 37 countries, club 3 comprises 27 cities, and club 4 comprises six cities, with log(t) values of 1.14, 7.82, and 5.59, respectively. Since the critical value is lower than the log(t) values computed for all the clubs, we do not reject the null of club convergence. Additionally, our results show two cities, Maumere and Tual, that do not converge with any of the above clubs. We thus infer that these two cities have a different transition path compared to the others.

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as determined by the PS technique. The figure shows that each club has a distinct transition path for consumer price convergence.

Table 4.

Club’s Speed of Convergence Results

This table reports the speed of convergence for each club.

Clubs	Speed of Convergence
Club 1	0.21
Club 2	0.05
Club 3	0.12
Club 4	0.95

Figure 4. Transition Paths of Clubs

In this figure, we plot the transition path of clubs identified by the PS technique. From this figure, we note that each club has a distinct transition path. The transition paths show the evidence of club convergence in price across the Indonesian cities.

1.08

1.06

1.04

1.02

1.00

0.98

0.96

Club 1

Club 2

Club 3

0.94

Club 4

Group

I

II

III

IV

I

II

III

IV

I

II

III

IV

I

II

III

IV

I

II

III

IV

I

II

III

2014

2015

2016

2017

2018

2019

In sum, the results obtained with the PS approach reject evidence of convergence when all cities are taken together. This is because consumer prices in Indonesian cities do not converge to a single steady state; instead, we find four converging clubs. These findings infer that prices in Indonesian cities are vastly heterogeneous, and a unique policy regarding market integration might not, therefore, work well in these cities. Our club convergence results suggest that a club-specific strategy could work better.

The results from the club convergence analysis can be compared to those of Holmes et al. (2019), who note evidence of club convergence for property prices in England and Wales. Our findings contrast with those of Wimanda (2009), who finds overall convergence at the product level in Indonesian cities, suggesting

Do Prices Converge Among Indonesian Cities? An Empirical Analysis	255

a unique policy for market integration. Further, our study differs from that of Bastianin et al. (2019), since they do not find any formation of clubs, but overall convergence of natural gas prices in the European Union. Similar results are found by Tsai I-Chun (2018) for housing prices in euro and non-euro countries.

C. Testing for Weak Sigma Convergence

In this section, we implement the weak sigma convergence test recently advanced by Kong et al. (2019) to determine if weak consumer price convergence exists when the cross sections are asymptotically stationary or weakly dependent series. Traditional approaches such as the CV or absolute convergence fail to account for this kind of data behavior and reject the presence of convergence. Further, this test is useful when the stochastic processes are unknown but exhibit diminishing/ increasing trends in variation.

Next, we test for weak sigma convergence. This test includes the common factor

(k) and lag truncation parameter settings	to construct the long-run variance
estimates. If the value of the slope coefficient		is negative and statistically

significant for the lag truncation parameter settings and common factors, then the null of no weak sigma convergence is rejected at the 5% level of statistical significance. Moreover, the weak sigma convergence test differentiates periods of stable, diverging, and converging phases, unlike standard testing approaches, which cannot. Identifying the different phases, controlling for heterogeneity, and incorporating weak dependent panels, we find weak consumer price convergence among Indonesian cities. The results presented in Table 5 show flimsy evidence of sigma convergence. Further, to determine the robustness and stability of the results, we implement an additional seven common factors (k = 2, …, 8) and seven

lag truncation settings ( = 2, …, 8). The choice of common factors and lag

truncation can differ from analysis to analysis. They are usually chosen such that the same results are obtained as for the first common factors and lag truncation. Again, the results in Table 5 suggest that the value of the slope coefficient is negative and statistically significant for all seven lag truncation parameter settings and seven common factors (k). Irrespective of the presence of common factors and lag truncation settings, our results still show weak evidence of consumer

price convergence among the 82 Indonesian cities. The evidence of weak sigma convergence suggests that the prices across Indonesian cities adjust, but not freely. The probable reason for the weak sigma convergence involves the price rigidities across the Indonesian cities. Therefore, these cities do not converge to a single steady state; instead, they converge to multiple steady states, as our PS findings show. Possible factors for price rigidities could be differences in transportation costs, levels of development, the logistical costs of goods, non-traded products, firm monopolies, labor market segmentation, informational asymmetries, and productivity (e.g., Tirtosuharto and Adiwilaga, 2013; Varela, et al., 2013).

256Bulletin of Monetary Economics and Banking, Volume 22, Number 3, 2019

Table 5.

Weak Sigma Convergence Results

This table presents the results of weak sigma convergence. k denotes the common factor.									is the coefficient and
indicates the t-statistics at lags 1 to 8.
	k
	1	-0.000018	-0.0022	-0.0019	-0.0017	-0.0016	-0.0015	-0.0015	-0.0015	-0.0015
2		-0.000018	-0.0022	-0.0019	-0.0017	-0.0016	-0.0015	-0.0015	-0.0015	-0.0015
3		-0.000018	-0.0022	-0.0019	-0.0017	-0.0016	-0.0015	-0.0015	-0.0015	-0.0015
4		-0.000018	-0.0022	-0.0019	-0.0017	-0.0016	-0.0015	-0.0015	-0.0015	-0.0015
5		-0.000018	-0.0022	-0.0019	-0.0017	-0.0016	-0.0015	-0.0015	-0.0015	-0.0015
6		-0.000018	-0.0022	-0.0019	-0.0017	-0.0016	-0.0015	-0.0015	-0.0015	-0.0015
7		-0.000018	-0.0022	-0.0019	-0.0017	-0.0016	-0.0015	-0.0015	-0.0015	-0.0015
	8	-0.000018	-0.0022	-0.0019	-0.0017	-0.0016	-0.0015	-0.0015	-0.0015	-0.0015

D. Robustness Checking

To determine the robustness of the clubs formed by the PS approach, we test whether convergence exists among them with a GMM approach. To validate the GMM model, we carry out two tests, specifically, the Sargan test, which checks for overidentification, and the Arellano–Bond test, to determine the presence of autocorrelation. The null hypothesis of the Sargan test is for the instruments as a group to be exogenous. The null hypothesis for the Arellano–Bond test for autocorrelation is ‘no autocorrelation’. Acceptance of the null for both tests validates the GMM estimates.

The GMM results are presented in Table 6. The coefficient of consumer price is negative and statistically significant for all four clubs formed by the PS approach. In other words, evidence of convergence is suggested. This infers that consumer prices converge when the cities share common fundamental characteristics. Results are validated by accepting the null of Sargan and autocorrelation tests. The GMM results are consistent with the PS findings.

Table 6.

Generalized Method of Moments Results for Each Club

This table presents the results of generalized methods of moments (GMM) for each club. The variable lnPt-1 denotes the logarithms of price with one lag. ***, **, and * indicate statistical significance at 1%, 5%, and 10% levels respectively. Finally, p-values are given in the parenthesis.

Variables	Club 1	Club 2	Club 3	Club 4
lnPt-1	-0.36***	-0.40***	-0.30***	-0.44**
	(0.01)	(0.00)	(0.00)	(0.02)
Constant	0.00	0.00**	-0.00*	0.00
	(0.41)	(0.39)	(0.07)	(0.15)
Sargan test	8.24	33.01	25.95	3.93
	(1.00)	(1.00)	(1.00)	(1.00)
AR	-0.93	0.91	1.44	-1.25
	(0.35)	(0.36)	(0.15)	(0.21)
No. Cities	10	37	27	6
Obs.	650	2405	1755	390
Wald test	7.24***	732.28***	221.22***	5.28***
	(0.01)	(0.00)	(0.00)	(0.00)

Do Prices Converge Among Indonesian Cities? An Empirical Analysis	257

IV. CONCLUSIONS

Although there are numerous studies examining price convergence, those associated with consumer price convergence across cities are scant. This study provides evidence of consumer price convergence among 82 Indonesia cities using the monthly CPI data over the period from 2014 to 2019. To examine consumer price convergence among these Indonesian cities, we first plot the CV between them. Further, to explore the results, we employ various panel data models, such as pooled regression panel, fixed dynamic panel, and system GMM panel data models. Second, we use the PS panel club convergence technique to examine different transition paths exist and club formation. Third, to examine convergence in panels of asymptotically stationary or weakly dependent series and determine whether there is weak overall convergence among Indonesian cities, we employ a novel technique recently proposed by Kong et al. (2019).

The findings are summarized as follows. First, the CV shows increasing price variability and dispersion among Indonesian cities over the years. The panel data models also yield the same results. Second, the results obtained through the PS approach reject the evidence of overall convergence, suggesting that consumer prices in Indonesian cities do not converge to a single steady state. Further, when cross sections are grouped into clubs based on long-run characteristics, we note four statistically significant converging clubs and a diverging group, indicating four different consumer price convergence paths in Indonesian cities. The speed of convergence among clubs 1 through 4 are found be 0.21%, 0.05% 0.12%, and 0.95%, respectively, suggesting that the cities in club 4 converge at a faster pace than in the other clubs. Third, the results obtained from Kong et al. (2019) test reveal weak consumer price convergence among Indonesian cities. This finding suggests that, although there are heterogeneities in consumer prices across Indonesian cities, the prices adjust, but not freely, indicating that the markets are becoming integrated.

From a policy perspective, our findings suggest that consumer prices among Indonesian cities adjust, but not freely, due to price rigidities that can be reduced by targeting transportation costs, uncertainty, and information costs. Since there is weak consumer price convergence, the forecasted consumer prices might not be robust. Additionally, policy should consider unique convergence paths for each club to obtain stronger consumer price convergence. Overall, this study provides different strategies to model convergence patterns.

Acknowledgments: The authors thank the editor Prof. Paresh Kumar Narayan and two anonymous referees for providing valuable suggestions, which improved this paper substantially. The usual disclaimer applies.

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Appendix

Table A1.

List of the Indonesian Cities

List of the cities of Indonesia are presented in this table. We total have 82 cities.

List of the Indonesian Cities

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

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