Club convergence of Japanese local price levels
Hidehiro Ikeno
Surugadai University,

1. Introduction
This article investigates the convergence of local price levels within Japan using a
non-parametric method. Phillips and Sul (2007 and 2009) developed a simple non-parametric test
for convergence among time series while allowing the possibility of convergence in subgroups, often
termed ‘club convergence’ The present work uses that method.
Many studies have been made of convergence of domestic price levels within a single country,
including studies of the Japanese economy. While most of these studies employ unit root tests, themethodology can handle only a restricted idea of convergence. A unit root test assumes that a timeseries follows a certain class of stochastic process. The method developed by Phillips and Sul (2007and 2009) can handle less restricted forms of convergence and allows heterogeneous transitions toconvergence.

It can also be used to identify groups of time series that converge to different

equilibria. This makes it possible to investigate the factors that set convergent values.
This empirical work on the Japanese local price levels has two aims. The first is to investigate
the convergence of local price levels while allowing for multiple convergences. Convergence within
subgroups should be investigated, as well as the convergence of all areas of Japan. The second is
to investigate the factors associated with high and low price levels. Income is often regarded asaffecting price levels through nontradable goods in the field of international economics. It is called
the Balassa-Samuelson effect. Its presence is examined among Japanese local economies.
Results from the Phillips-Sul procedure indicate that all local general price levels in Japan failto converge to a single price level. They do, however, form two groups, and members of each groupconverge. Local per-capita incomes also fail to converge to a single income level. They form
several groups, most of which indicate convergence. In regard to price levels and income, Japanese
economies are divided into groups. The results also show a positive correlation between generalprice levels and income levels. Many disaggregate price indexes indicate club convergence, andsome indicate unanimous convergence. It is also shown that price indexes of the nontradable
services are positively correlated with income levels.

The results are consistent with theBalassa-Samuelson effect.
2. Methodology
The procedure developed by Phillips and Sul (2007 and 2009) is as follows.
Convergence is tested by a ‘log t test’.

The null hypothesis implies that all times series

converge; the alternative hypothesis implies failure of convergence. Phillips and Sul show that thenull hypothesis of convergence can be tested using the following equation,⁄where=∑−2=+ℎ −1 ⁄, ℎ =+⁄ ∑hypothesis is rejected if the t-statistic of=⁄,⋯, ,, and= !" # for some " .

The nullis less than -1.65. If convergence is rejected for theoverall time series, the procedure is applied to subgroups.

1Phillips and Sul also provide analgorithm of clustering for examining the convergence of subgroups, i.e., club convergence.
3. DataThis paper uses three series of price indexes, all of which are compiled by the Statistical Bureauof Japan. The first set is the series of the regional difference index of consumer prices. They arecompiled for inter-regional comparison of price levels within Japan. They indicate relative local
price levels on the national common base for each year. The data comprises general consumer
prices. The second set is the series of local CPIs. The local CPIs are compiled for intertemporalcomparison of price levels for each area. They are not suitable for inter-regional comparison ofabsolute price levels. They contain the general price series and disaggregate price indexes in all
prefecture capitals and other cities. The third set is the National Survey of Prices, which wasconducted until recently but not any more. Indexes were compiled from the Survey in order tostudy price differences among regions and outlets.
This paper uses two variables per prefecture to represent income; per-capita prefectural income,and per-capita compensation of employees in the prefecture.

Income variables of cities are

generally unavailable in suitable form for a long period, partly because the boundaries of many
cities change substantially over time.
4. Convergence of general price levels and incomes
4-1 Price levels

The regional difference index of consumer prices is transformed by two steps, asfollows. First, the index is divided by the average over the 47 prefecture capitals and is thentransformed into a logarithmic form.

The HP filter is then applied to $"%&' , , following thesuggestion in Phillips and Sul (2007 and 2009).
The log-t test is executed on the whole set of the regional difference index with the data from1974 – 2013. The result is:⁄−2=−0.05 − 0.62
−2.56 −94.41

This result strongly rejects convergence of price levels in all cities.
unanimous convergence.

Convergence of subgroups is explored.

It implies a failure ofThe Phillips-Sul procedure

differentiates two convergent subgroups. These are shown in Table 1.
4-2 IncomesFirst, a log-t test is executed on the whole set of income indexes with the data over1975 – 2010.

The results from per-capital prefectural income and per-capita compensation ofemployees indicates a strong rejection of convergence of the whole set. Incomes fail to indicate
unanimous convergence. Convergence of subgroups is then explored. The Phillips-Sul procedurefrom the per-capita prefectural income leads to four convergent subgroups.

Results from theper-capita compensation of employees eventually leads to four convergent subgroups. Both incomeindexes indicate that Japan is divided into several groups.
4-3 Price levels and incomesThis section investigates the relation between regional price levels

and regional per-capita incomes.

A probit model is used. Since the price levels form twoconvergent subgroups, the following equation is estimated by maximizing the likelihood;2

= / 0 + 12
where

= 1 if city % belongs to Group1, the highest convergent group, of the regional difference

indexes, and= 0 otherwise. 2 represents the income level of city %. Table 2 shows results

using the per-capita prefecture income and the per-capita compensation of employees. The results
indicate that the high convergent price level is associated with the high per-capita income level,although there is a difference in the level of support between the two income indexes..
5. Convergence of the disaggregate price indexes
5-1 Compilation of disaggregate price indexes

New series are compiled based on the local CPIs

and on the National Survey of Prices. Inter-regional price indexes of the National Survey of Prices
are combined with intertemporal changes in the local CPIs. They are classified into three groups.
Group A includes price indexes in which weights of goods are dominant; ‘foods’, ‘fuel, light andwater charges’, ‘furniture and household utensils’, and ‘clothes and footwear’. Group B includes
price indexes in which weights of services are dominant; ‘housing’ and ‘education’. And Group C‘medical care’, ‘transportation and communication’,contains neither weights are dominant;‘culture and recreation’, and ‘miscellaneous’.
5-2 Disaggregate price indexes

Table 3 shows the results of these log-t tests. They indicate thatconvergence of the whole sample is rejected with all price indexes except ‘furniture and household
utensils’ and ‘medical care’. Convergence of subgroups is then examined for all price indexes.
Results indicate club-convergence of all disaggregate indexes except ‘furniture and household
utensils’ and ‘medical care’ with several convergent subgroups.
5-3 Price levels and income

Table 4 shows results from a probit or an ordered probit model withthe per-capita prefectural incomes, and Table 5 with per-capita compensation of employees. In
Group A, the income indexes are significantly negative for ‘fuel, light, and water charges’. They
are not significantly positive with any disaggregate price index, except the case of ‘clothes andfootwear’ with the per-capita compensation of employees. In Group B, both or either of the two
income indexes are significantly positive with both disaggregate price indexes. In Group C, theincome variables are not significant except for ‘transportation and communication’ with theper-capita compensation of employees.

These results generally support the claim that thedisaggregate price indexes of services are positively correlated with incomes.
6. Conclusion
The present results show that Japanese local economies do not unanimously converge as regards
the price level and also the per-capita price level. Japanese local economies are not unanimouslyconverging. Japanese local economies are in fact divided into subgroups, in which price levels andper-capita incomes converge. A high convergent price level is associated with the high per-capita
income level.

Many disaggregate price indexes fail to indicate unanimous convergence.

Thisstatement holds even for some indexes in which goods are dominant. Further, high convergent
price levels of service-dominated indexes are associated with a high per-capita income level. The
results are consistent with the Balassa-Samuelson effect. The difference in per-capita incomes is acause of disparity of Japanese local price levels.

3References
Phillips, P. C. B., & Sul, D. (2007) Transition modeling and econometric convergence tests,Econometrica 75, 1771-1855.
Phillips, P. C. B., & Sul, D. (2009) Economic transition and growth. Journal of Applied Econometrics
24, 1153-1185
Table 1. Club convergence of regional difference index of consumer prices
3Groupcities
t-values
Group 1
Yokohama, Tokyo, Saitama, Kanazawa, Nagasaki,
0.01
0.05
Wakayama, Kobe, Kyoto, Fukushima, Yamagata,Hiroshima, Matsue, Utsunomiya, Osaka, Okayama,Tokushima, Yamaguchi, Naha,
0.21
1.14Group 2Tsu, Kumamoto, Otsu, Kofu, Shizuoka, Sapporo, Kochi,Nagoya, Matsuyama, Aomori, Kagoshima, Morioka, Chiba,Niigata, Fukui, Mito, Toyama, Tottori, Oita, Takamatsu,Nagano, Gifu, Saga, Sendai, Maebashi, Nara, Fukuoka,Akita, Miyazaki
Notes: Data used in the regression start in 1974 and end in 2013. Cities are in descending order on
the basis of the observation of the index in 2013.
Table 2. Probit model with per-capita income= 4" 0 + 1 ∙ 2income variable01$6' 7 8prefectural income-0.134
1.616
0.028
(0.207)(1.412)compensation of
0.038
3.960 **
0.097
employees(0.254)(1.942)
Notes: ** and * denote significance at the 5% and 10% significance levels, respectively. Standard
errors are in parentheses. For the $6' 7 8 , see Estrella (1998).

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Table 3. The t-log test on the whole sample with the HP-filtered data in log⁄−2= + ∙3
price indext-value
Group AFoods-0.23 *-3.22
Fuel, light and water charges-0.75 *-9.87
Furniture and household utensils
0.01
0.03
Clothes and footwear-0.53 *
-5.90
Group B
Housing
Education-0.15 *
-0.47 *

-3.02
-3.09

Group C
Medical care
0.53
Transportation and communication-0.44 *
Culture and recreation-0.89 *
Miscellaneous-0.64 *
Notes: Data used in the regression start in 1975 and end in 2013.
‘*’ denotes rejection of the null hypothesis at the 5% significance level.
Table 4. Probit models with per-capita prefectural income= 4" 0 + 1 ∙ 2
Price index
0Group AFoods-0.091(0.240)Fuel, light and water charges-1.867 ***(0.510)
Clothes and footwear-0.482(0.354)
Group B
Housing
Education

2.364 ***
(0.658)0.676 **
(0.317)2.80-12.70-8.82-15.87

1$6' 7 8

2.008(1.434)-5.050 **(2.352)2.904 *(1.631)

0.043

6.060 **
(3.025)4.458 **
(2.049)

0.123

0.236
0.085

0.175

Group C
Transportation and communication-0.0432.322
0.065(0.827)(1.576)
Culture and recreation-0.853 *
2.807
0.071
(0.481)(2.135)
Miscellaneous-0.322
0.834
0.009
(0.395)(1.823)
Notes: ‘*’, ‘**’, and ‘***’ denote significance at the 10, 5, and 1 percent levels, respectively. 2 isthe average income index (per-capita prefectural income) over 1975-2010 in log. Standard errors
are in parentheses. For the $6' 7 8 , see Estrella (1998).

5Table 5. Probit models with per-capita compensation of employees= 4" 0 + 1 ∙ 2Price index
01Group A
Foods-0.1242.040(0.241)(1.795)
Fuel, light and water charges-1.187**-7.254 ***(0.494)(2.605)Clothes and footwear-0.5721.921(0.454)(2.382)
Group B
Housing
Education

1.802***(0.482)
1.844 ***
(0.348)

3.798(3.113)7.399 ***
(2.571)$6' 7 8
0.028
0.285
0.025

0.038
0.254

Group C
Transportation and communication-0.6953.409 *
0.087
(0.828)(2.067)
Culture and recreation
0.020
5.537
0.143
(0.559)(3.479)Miscellaneous-0.5493.288
0.080(0.342)(2.251)
Notes: ‘*’, ‘**’, and ‘***’ denote significance at the 10, 5, and 1 percent levels, respectively. 2 isthe average income index (per-capita compensation of employees) over 1975-2010 in log. Standarderrors are in parentheses. For the $6' 7 8 , see Estrella (1998).

6