Do different economic developments exhibit the same price index convergence?

Lee, Bi-Juan ; Huang, Bwo-Nung ; Lee, Jun-De 等

Abstract

In this paper, we employ the recently econometric technique proposed by Carrion-i-Silvestre et al. (2005) to investigate the stationary properties of consumer price index and wholesale price index for developed and developing countries from 1987:05 to 2007:11. When multiple structural breaks and cross-sectional correlations are allowed, the price series appear to be stationary in developed countries. In contrast, the price series are non-stationary in developing countries. Therefore, the government in developing countries needs to pay much attention to the price series and a target of price stabilization should be desirable as a sustainability strategy.

JEL classification: C33; E31

Keywords: Consumer price index; Wholesale price index; Multiple structural breaks; Panel stationary test

I. INTRODUCTION

The purpose of this paper is to investigate the stationary properties of price indices. This is a worthwhile question because there is a close link between price indices and the real economy. Price indices might be exposed to one or more structural breaks that is caused by either a huge magnitude of a shock, an oil crisis, a financial crisis, changes in law or some political changes. Our motivation is whether shocks to the time paths of price indices are permanent or temporary. If price indices are mean reverting, then the series should return to their trend path over time and it should be possible to forecast future movements in price indices based on past behavior. On the contrary, if price indices are non-stationary process, then any shock to price indices is likely to be permanent.

Past literature on this issue has shown that there are different methodologies on testing the stationarity in price series (see Table 1). There are two key features to characterize previous researches. First, most literature apply the traditional method in testing for the null hypothesis of a unit root of price indices. This is a well known weakness that the traditional unit root tests have low power if the true data generating process of a series exists structural breaks (Perron, 1989). Second, the findings are mixed, which means there is no conclusive evidence to the stationarity property for price indices. For example, Lee and Strazicich (2003) and Evren (2006) have concluded that the price indices are non-stationary. On the contrary, Cecchetti et al. (2002), Sosvilla-Rivero and Gil-Parejaz (2004), and Sonora (2005) have argued that the price indices are stationary.

Few studies in the literature focus on different economically-developed

countries for the price indices. In addition, the price indices are more stable rather in developed than developing markets. Therefore, we try to examine whether different economic developments exhibit the same price indices convergence. Besides, understanding the property of price indices is essential to the ability of policy makers to control inflation. The goal of this paper is to investigate the time series properties of consumer price indices (CPI hereafter) and wholesale price indices (WPI hereafter) for developed and developing countries.

Theoretically, investigating the behavior of consumer prices can realize the likely nature of inflation in demand side and so are the wholesale (production) prices in supply side. Moreover, our study tries to take on Perron's (1989) critique by controlling for structural instability in the data generating process of the price indices. For that purpose, we employ the panel stationarity test of Carrion-i-Silvestre et al. (2005; CBL hereafter) which assumes a highly flexible trend function by incorporating an unknown number of changes in level and slope based on the panel data version of the KPSS univariate test proposed by Hadri (2000) to examine the behavior of price indices.

There are several important factors when performing tests that allow for structural breaks. First, structural breaks might be associated with some atypical events, i.e., domestic or international market regulations, an oil crisis, a financial crisis, and some political changes. Second, considering structural breaks allows us to obtain more detailed information on the behavior of price indices. Thus, we apply the CBL (2005) panel data stationarity test, which simultaneously are a panel and individual data stationarity tests with multiple structural breaks. Third, the method of CBL (2005) is capable to consider multiple structural breaks positioned at different unknown dates in addition to a different number of breaks for each country. This test is thus more general than the panel unit root test by Im et al. (2005) that only incorporates a maximum of two changes in level but not in the slope coefficient.

This article contributes the debate about price indices in several respects. Firstly, important structural reforms are likely to first affect less rich countries, especially the developing world. It is looked more deeply at the response of such an impulse in the developing countries than the developed economies. For that reason, we divide our sample groups into two different economic development levels in order to realize the stationarity of CPI and WPI in each panel data set. Secondly, this paper is significant different from previous studies because we not only focus on the CPI but also on the WPI. Finally, we use the newly developed panel unit root test to investigate the stationarity of price indices with the presence of multiple structural breaks. It is also capable to consider multiple structural breaks at different unknown dates in addition to a different number of breaks for each country.

The remainder of this paper proceeds as follows. Section 2 introduces the econometric methodology that we employ. Section 3 describes the preliminary examination of the data and the main empirical test results. Section 4 presents the conclusions and some policy implications.

II. METHODOLOGY

We briefly describe the panel data stationary test of CBL (2005) model, which by design, has the capability to test the null hypothesis of panel unit root while allowing for multiple structural breaks. It is written as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where [P.sub.i,t] is consumer or wholesale price index in country i at time t; t = 1, ..., T time periods; i = 1, ..., N represents members of the panel; and [[epsilon].sub.i,t], is the error term. The dummy variables [DU.sub.i,k,t] and [DT.sup.*.sub.i,k,t] are defined as [DU.sub.i,k,t] = 1 for t > [T.sup.i.sub.b,k] and 0 otherwise, and [DT.sup.*.sub.i,k,t] = t [T.sup.i.sub.b,k] for t > [T.sup.i.sub.b,k] and 0 otherwise; and [T.sup.i.sub.b,k] denotes the kth date of the break for the ith individual, k = 1, ..., [m.sub.i], [m.sub.i] [greater than or equal to] 1.

The specification in Equation (1) is general enough to allow for unit-specific intercepts and time trends in addition to unit-specific mean and slope shifts. The test of the null hypothesis of a stationary panel follows Hadri (2000) who has designed a test statistic which is simply the average of the univariate stationary test of KPSS (1992). CBL computes the panel stationary test as the average of univariate KPSS tests:

LM([lambda]) = [N.sub.-1] [N.summation over (i=1)]([[??].sup.-2.sub.i][T.sup.2] [T.summation over (t=1)][S.sup.2.sub.i,t]) (2)

where [S.sub.i,t] = [[summation].sup.t.sub.j=1][[??].sub.i,j] denotes the partial sum process that is obtained using the estimated OLS residuals of Equation (1). [[??].sub.2.sup.i] is a consistent estimate of the long-run variance of [[epsilon].sub.i,t].

Once the dates for all possible [m.sub.i] [less than or equal to] [m.sup.max] for each i are estimated, where [m.sup.max] is the maximum number of breaks, we select the appropriate number of structural breaks using the modified Schwarz information criterion (LWZ) of Liu et al. (1997) which is designed for the case of trending variables. Once the vector [[??].sub.i]) is determined, we compute the normalized test statistic as follows:

Z([lambda]) = [square root of N](LM([lambda]) - [bar.[xi]]) / [bar.[zeta]] [right arrow] N(0,1) (3)

where [bar.[xi]] and [bar.[zeta]] are computed as averages of individual means and variances of [LM.sub.i]([[lambda].sub.i]). The computation of the Z([lambda]) statistic requires the individual series to be cross-sectionally independent along with asymptotic normality. Since these assumptions may be overly made, we will compute the bootstrap distribution of the panel stationary test with multiple breaks following Maddala and Wu (1999) in order to allow for any kind of cross-sectional dependence, thereby correcting for finite-sample bias.

Since the test is dependent on [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] which indicates the location of the breaks relative to the whole period T, we estimate the vector [[lambda].sub.i] for each unit using the procedure of Bai and Perron (1988) which is based upon the global minimization of the sum of squared residuals (SSR). The procedure is chosen as the estimation of the breaks location the argument that minimizes the sequence of unit-specific SSR([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) obtained from Equation (1) such that:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

III. DATA AND EMPIRICAL RESULTS

This study employs monthly data on the CPI for 38 countries and WPI for 20 countries. The empirical period depends on the availability of data, which ranges from 1987:05 to 2007:11. We focus on the behavior of aggregate price indices because they contain a broader basket of goods and services. This aspect would make the results applicable to the problems faced by monetary policy makers, whose attention is generally rather focused on measures of aggregate price than emphasis on the behavior of the price of individual commodities. All data were obtained from the OECD Main Economic Indicators and the International Financial Statistics published by International Monetary Fund.

As a preliminary examination, we draw the consumer and wholesale price indices for the developed and developing countries under analysis. We split our country groupings as developed and developing economies which are based on lists defined by the Food and Agriculture Organization of the United Nations. Figs. 1-4 clearly show the cross-country differences in consumer and wholesale price indices over the sample period. The plots suggest that the data might have one or more structural breaks. For that reason, the classical panel unit root tests that ignoring structural breaks may result in misinterpretations.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

In order to provide a robust analysis we first apply the Panel unit root tests without structural breaks, such as LLC (2002), IPS (2003), Breitung (2000), Fisher ADF, Fisher PP and Hadri (2000), to investigate the price indices in the developed and developing countries and report these results in Tables 2-5. To summarize our results, regardless of the econometric method, they strongly indicate that all price indices in our sample contain a unit root. Nevertheless, following Perron (1989)'s insights, studies employing panel unit root and stationarity tests which do not consider the structural changes in the trend function of the variables may be biased towards accepting a unit root, and thus leading to misinterpreting stationarity with structural change as a unit root.

To overcome the above problems, we then move to investigate the issue of price behaviors employing recently developed panel methods. More specifically, we present the results based on the panel stationarity tests of Hadri (2000) and its generalization by CBL (2005) for the case of multiple shifts in level and slope. Following the suggestion in Bai and Perron (2001), the number of structural breaks associated with each country is estimated using the modified Schwarz information criterion (LWZ). CBL (2005) suggests that the specified maximum number of structural breaks should be five in the empirical process. In order to control for finite-sample bias, we compute finite-sample critical values for the individual KPSS tests with multiple breaks by Monte Carlo simulations using 20,000 replications. Additionally, all bootstrap critical values allow for cross-section dependence.

Tables 6-9 show the results of the stationarity test with structural breaks for CPI and WPI in our sample of developed and developing countries. In these four Tables, we first report the results of the individual KPSS test for each country in Panel A. For completely, in Panel B we then report the results from the panel stationarity test for the case of homogeneity and heterogeneity in the long-run variance as well as the bootstrap critical values allowing for cross-sectional correlation.

As shown in Table 6, among the CPI series in developed countries considered, we fail to reject the null of stationarity at the 1% level for each country. That is to say, these series are stationary with structural breaks rather than a purely unit root. Moreover, Table 8 reports the results of WPI in developed countries from individual and panel KPSS tests after combining multiple structural breaks, upon which we are also unable to reject the null of stationarity at the 1% level significance. Taken together, among the developed countries considered, the price indices are not stationary when utilizing the traditional panel unit root tests which fail to allow for structural breaks, however, they follow a stationary process after taking the structural breaks and crosssectional correlations into account. Our findings support the convergence process and suggest that the majority of shocks to price indices are temporary in the case of developed countries.

Table 7 reports the results for CPI in developing countries. Obviously, among the developing countries except for Brazil, we fail to reject the null of stationarity at the 1% level for each country in the individual KPSS tests. However, the conclusion is overturned, the null of the jointly panel stationarity test are rejected, when we compare the test statistics with the critical values allowed for cross-section dependence from the bootstrap distribution. Additionally, similar results are also shown in Table 9 for WPI in developing countries. Interestingly, in Panel B of Table 7 and 9 for developing countries, the null of stationarity from which the panel KPSS tests assuming homogeneity and heterogeneity in the estimation of variance are strongly rejected at the 1% level. These conclusions, which are contrary to those from developed economies, may result from the immature regulations and market mechanism in the developing countries.

Overall, the price indices are mean reverting in the developed economies; in contrast, evidences in the developing countries differ remarkably from those after allowing for multiple shifts in level and slope as well as for cross-sectional dependence through bootstrap methods. In addition, observe that many countries have structural breaks occurring in the late 1990 and the early 2004. For the consumer price indices, we find that of the 38 countries examined, 23 are detected by breaks in 1990 and 17 are detected in 2004. For the wholesale price indices, we discover that of the 20 countries investigated, break points located in 1990 are found in eight countries and structural breaks occurring in 2004 are detected in ten out of the twenty countries. More specifically, the break dates in the late 1990 may emanate from the third energy crisis occurred as a result of the first Gulf War, while the breaks in 2004 are reasonably as a direct consequence of the Iraq War that followed the 2003 Invasion of Iraq, the oil production capacity was cut from more than three to two million barrels per day. The Iraq War coincided with an increase in global demand for petroleum and a reduction in the oil production as well as an overall upward price trend of oil. Moreover, producers for whom oil is a part of their costs could then pass this on to consumers in the form of increased prices.

In summary, important structural changes affect much more deeply for the price indices in developing countries than those in developed world. That is, the government need to pay much attention to the price series in developing countries, and a target of price stabilization should be desirable as a sustainability strategy.

IV. CONCLUSIONS AND POLICY IMPLICATIONS

This study explores the issue of whether the stationarity of prices both in developed and developing economies can be characterized more precisely by the recently panel unit root tests allowed for multiple structural breaks. This is an important issue for researchers and policy makers because the price is very closely correlated with the real economy. Several critical implications obtained from our empirical results are as follows. First, the overwhelming evidence in favor of the stationarity hypothesis for price indices in the majority of the developed countries is found. That is to say, it should be possible to forecast future movements in price based on past behavior. This result implies that following a major structural change in the world market, price in the well-developed economies will return to its original equilibrium eventually when we control for breaks. In other words, if most shocks to price indices are temporary, then the stabilization macroeconomic policy has long-lasting effects on the price indices in the developed countries according to our results. When the price indices temporarily deviates from the mean value, then at this time the administrative policy of a government should be not to adopt an excessive intervening target.

Second, a non-stationary price series for the developing countries suggests that price regulation policies should be implemented in order to stabilize the price level in demand side (for example, the price of food and agricultures, etc) and the price level in production side (for example, the price of oil, coal, gasoline, natural gas, and mental, etc). As part of the policy implemented by a government, the authorities surely need to pay much attention to the price series. To aim at the CPI and WPI in the subgroup of developing countries, a target of price stabilization should be feasible and desirable as part of a sustainability strategy.

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BI-JUAN LEE, BWO-NUNG HUANG

National Chung Cheng University, Taiwan

JUN-DE LEE *

Fortune Institute of Technology, Taiwan

CHUN-YUAN YE

Overseas Chinese Institute of Technology, Taiwan

* JUN-DE LEE, Department of Business Administration, Fortune Institute of Technology, Kaohsiung 831, Taiwan, E-mail:jundelee@yahoo.com.tw

Table 1
Comparison with Previous Studies from Various Unit Root Tests for
Price Index

Author(s)             Sample              Test

Cecchetti et al.      19 cities in US     LL (1993), IPS
(2002)                (CPI)               (1997)

Evren (2006)          Turkey (CPI)        HEGY (1990),
                                          CH (1995)

Lee and Strazicich    US (CPI)            Two-break Panel
(2003)                                    LM unit root test

Sonora (2005)         34 cities in        LL (1993),
                      Mexico (relative    IPS (1997)
                      price; CPI)

Sosvilla-Rivero       12 countries in     LL (1992)
and Gil-Parejaz       EU (CPI)
(2004)

Author(s)             Period       Results

Cecchetti et al.      1918-1995    Stationary
(2002)

Evren (2006)          1994M1-      Non-stationary
                      2003M12

Lee and Strazicich    1860-1979    Non-stationary
(2003)

Sonora (2005)         1982M1-
                      2000M12      Stationary

Sosvilla-Rivero       1975M1-      1) Stationary for
and Gil-Parejaz       1995M12      traded goods
(2004)                             2) Nonstationary for
                                   non-tradable goods
                                   and goods subject to
                                   tax or regulation

Table 2
Panel Unit Root Tests without Structural Breaks for CPI in Developed
Countries

Method              Statistic    Probability

LLC (2002)         -4.592 ***         (0.000)
Breitung (2000)     1.792             (0.964)
IPS (2003)          1.299             (0.903)
Fisher ADF         40.562             (0.699)
Fisher PP          45.562             (0.491)
Hadri (hom)        32.585 ***         (0.000)
Hadri (het)        27.239 ***         (0.000)

Note: The Fisher-type tests using ADF and PP tests proposed by Maddala
and Wu (1999) and Choi (2001). Hadri(hom) and Hadri(het) denote the
Hadri-KPSS test assuming homogeneity and heterogeneity, respectively,
in the estimation of long-run variance. The LLC, Breitung, IPS,
Fisher-ADF, and Fisher-PP examine the null of non-stationarity while
Hadri tests the stationary null hypothesis. The model contains both a
drift and a deterministic trend. *** indicates statistical
significance at the 1% level. Probabilities for Fisher-type tests were
computed by using an asymptotic [chi square] distribution. All other
tests assume asymptotic normality.

Table 3

Panel Unit Root Tests without Structural Breaks for CPI in Developing
Countries

Method              Statistic    Probability

LLC (2002)         -1.455 *           (0.073)
Breitung (2000)     0.783             (0.783)
IPS (2003)          3.672             (0.999)
Fisher ADF         11.626             (0.999)
Fisher PP           9.272             (0.999)
Hadri (hom)        37.087 ***         (0.000)
Hadri(het)         24.536 ***         (0.000)

Note: See Table 2.

Table 4

Panel Unit Root Tests without Structural Breaks for WPI in Developed
Countries

Method              Statistic    Probability

LLC (2002)          4.328             (1.000)
Breitung (2000)     0.827             (0.796)
IPS (2003)          6.644             (1.000)
Fisher ADF          3.854             (1.000)
Fisher PP           2.788             (1.000)
Hadri (hom)        24.314 ***         (0.000)
Hadri (het)        20.880 ***         (0.000)

Note: See Table 2.

Table 5

Panel Unit Root Tests without Structural Breaks for WPI in Developing
Countries

Method              Statistic    Probability

LLC (2002)         -0.676             (0.249)
Breitung (2000)     0.45              (0.674)
IPS (2003)          2.806             (0.998)
Fisher ADF          5.608             (0.992)
Fisher PP           4.884             (0.996)
Hadri (hom)        27.267 ***         (0.000)
Hadri (het)        17.856 ***         (0.000)

Note: See Table 2.

Table 6
Panel Stationarity Tests and Individual Tests with Structural Breaks
for CPI in Developed Countries

Panel A: Country-specific tests

Country           KPSS        m    [T.sub.b,1]    [T.sub.b,2]

Austria           0.024       4        M5-1990        M6-1993
Belgium           0.024       4        M7-1990        M9-1994
Canada            0.040 *     3       M12-1990        M1-1994
Denmark           0.020       4        M5-1990        M6-1993
Finland           0.024 *     5        M5-1990        M6-1993
France            0.026       4        M5-1992        M2-1996
Germany           0.026 *     4        M8-1990        M9-1993
Greece            0.070 **    2        M5-1990        M5-1996
Hungary           0.019       5        M5-1990        M8-1994
Iceland           0.023 **    5        M5-1990       M12-1993
Ireland           0.035       3       M10-1992        M2-2000
Italy             0.026 *     4        M9-1990        M1-1996
Japan             0.030 **    4        M8-1990        M9-1993
Luxembourg        0.050       3       M10-1994       M11-1998
Netherlands       0.020       4        M5-1990       M11-1994
Norway            0.021       3        M1-1991       M10-1997
Portugal          0.028       4        M3-1992        M4-1995
South Africa      0.028       3       M10-1990        M7-1999
Spain             0.046       3        M1-1996        M4-1999
Sweden            0.027 *     4       M12-1990        M5-1995
Switzerland       0.029       3        M7-1990        M8-1993
United Kingdom    0.032       3        M3-1991        M4-1997
United States     0.025 *     4        M7-1990        M2-1996

Country           [T.sub.b,3]    [T.sub.b,4]    [T.sub.b,5]

Austria               M7-1996        M1-2000
Belgium               M9-1998        M5-2002
Canada                M7-1998
Denmark               M2-1999        M6-2003
Finland               M8-1998        M9-2001       M10-2004
France                M6-1999        M2-2004
Germany               M8-1998        M4-2003
Greece
Hungary               M6-1998        M7-2001       M10-2004
Iceland               M4-1998        M5-2001       M10-2004
Ireland              M10-2004
Italy                 M5-1999        M8-2004
Japan                 M3-1997       M10-2001
Luxembourg            M5-2003
Netherlands           M9-1999       M10-2002
Norway                M4-2003
Portugal              M8-1999        M6-2003
South Africa         M10-2003
Spain                 M6-2003
Sweden                M2-2001       M10-2004
Switzerland           M6-1997
United Kingdom        M7-2004
United States         M2-2000        M2-2004

Country           Finite sample critical values (%)

                      90       95     97.5       99

Austria            0.028    0.033    0.037    0.042
Belgium            0.024    0.027    0.030    0.034
Canada             0.038    0.044    0.050    0.059
Denmark            0.024    0.027    0.030    0.034
Finland            0.021    0.024    0.026    0.030
France             0.032    0.039    0.046    0.057
Germany            0.024    0.027    0.031    0.035
Greece             0.049    0.057    0.067    0.078
Hungary            0.020    0.022    0.025    0.029
Iceland            0.020    0.022    0.025    0.029
Ireland            0.041    0.050    0.058    0.070
Italy              0.025    0.028    0.032    0.037
Japan              0.025    0.029    0.032    0.036
Luxembourg         0.056    0.071    0.087    0.110
Netherlands        0.024    0.027    0.030    0.033
Norway             0.031    0.036    0.040    0.046
Portugal           0.031    0.038    0.044    0.054
South Africa       0.035    0.040    0.046    0.053
Spain              0.072    0.093    0.113    0.142
Sweden             0.026    0.030    0.034    0.039
Switzerland        0.040    0.048    0.055    0.066
United Kingdom     0.033    0.038    0.043    0.048
United States      0.024    0.027    0.030    0.035

Panel B: Panel KPSS test with multiple breaks

KPSS test       Test statistics   Bootstrap critical values (%)

                                  1        2.5      5        10

Homogeneity     11.050            13.909   14.557   15.090   15.703
Heterogeneity   10.603 ***        2.677    2.955    3.186    3.466

KPSS test       Bootstrap critical values (%)

                90       95       97.5     99

Homogeneity     20.360   21.047   21.714   22.411
Heterogeneity   5.773    6.143    6.469    6.886

Note: *** indicates significance at the 1% level. The number of break
points is estimated using the LWZ information criteria allowing for a
maximum of five structural breaks (m). The long-run variance is
estimated using the Bartlett kernel with automatic spectral window
bandwidth selection as in Sul, et al. (2005). Additionally, all
bootstrap critical values allow for cross-section dependence.

Table 7
Panel stationarity tests and individual tests with structural breaks
for CPI in developing countries

Panel A: Country-specific tests

Country         KPSS         m    [T.sub.b,1]    [T.sub.b,2]

Brazil          0.052 ***    4        M3-1991        M4-1994
El Salvador     0.023        4        M8-1992        M6-1996
Hong Kong       0.021 *      5        M5-1990        M9-1994
India           0.032 **     4        M6-1990        M5-1994
Indonesia       0.050        2        M2-1998        M7-2004
Korea           0.021        4       M12-1990       M12-1997
Malaysia        0.032 *      3       M11-1990        M1-1998
Mexico          0.033        3       M12-1991        M2-1995
Panama          0.020        3        M5-1990        M2-2000
Paraguay        0.031        3       M12 1993        M7 2001
Philippines     0.022        4       M11-1990        M9-1994
Saudi Arabia    0.025 *      5        M1-1991       M12-1994
Singapore       0.030 **     4        M8-1990        M4-1994
Thailand        0.023        3       M12-1994        M1-1998
Turkey          0.025        4        M3-1994        M4-1997

Country         [T.sub.b,3]    [T.sub.b,4]    [T.sub.b,5]

Brazil              M5-1997        M1-2002
El Salvador        M11-2000       M12-2003
Hong Kong           M1-1998        M2-2001        M3 2004
India               M5-1998       M10-2004
Indonesia
Korea               M1-2001        M2-2004
Malaysia            M9-2003
Mexico              M3-2000
Panama             M10-2004
Paraguay            M8 2004
Philippines        M12-1999        M6-2004
Saudi Arabia        M1-1998        M8-2001       M10-2004
Singapore           M3-1998       M11-2001
Thailand            M9-2003
Turkey              M5-2000        M6-2003

Country         Finite sample critical values (%)

                    90       95     97.5       99

Brazil           0.027    0.031    0.036    0.041
El Salvador      0.034    0.042    0.050    0.062
Hong Kong        0.020    0.022    0.025    0.029
India            0.025    0.029    0.032    0.036
Indonesia        0.108    0.139    0.171    0.219
Korea            0.028    0.032    0.036    0.042
Malaysia         0.032    0.036    0.041    0.046
Mexico           0.037    0.043    0.048    0.056
Panama           0.038    0.044    0.050    0.059
Paraguay         0.052    0.064    0.077    0.092
Philippines      0.025    0.028    0.032    0.036
Saudi Arabia     0.022    0.026    0.030    0.035
Singapore        0.025    0.028    0.032    0.036
Thailand         0.059    0.075    0.092    0.113
Turkey           0.049    0.062    0.075    0.094

Panel B: Panel KPSS test with multiple breaks

KPSS test        Test statistics      Bootstrap critical values (%)

                                         1      2.5        5       10

Homogeneity      12.497 ***         -0.138    0.187    0.442    0.775
Heterogeneity    7.907 ***           1.359    1.595    1.783    2.024

KPSS test          Bootstrap critical values (%)

                     90       95     97.5       99

Homogeneity       3.812    4.411    5.002    5.724
Heterogeneity     4.020    4.343    4.633    5.044

Notes: See Table 6.

Table 8
Panel Stationarity Tests and Individual Tests with Structural Breaks
for WPI in Developed Countries

Panel A: Country-specific tests

Country           KPSS        m    [T.sub.b,1]    [T.sub.b,2]

Austria           0.035       3        M8-1990        M1-2000
Canada            0.031 *     4        M7-1991       M12-1994
Denmark           0.023 **    5        M5-1990        M4-1994
Germany           0.019       5        M1-1991        M4-1994
Hungary           0.020       5       M11-1990        M6-1994
Japan             0.025       3       M11-1990        M3-1997
Netherlands       0.027       3       M11-1993        M2-2000
Poland            0.022 *     5        M5-1990        M6-1993
South Africa      0.029       3        M8-1998        M9-2001
Switzerland       0.021       4        M5-1990       M10-1995
United Kingdom    0.022       3        M7-1990        M2-1996
United States     0.028       3        M2-1991       M12-1997

Country           [T.sub.b,3]    [T.sub.b,4]    [T.sub.b,5]

Austria              M12-2003
Canada               M11-1999        M4-2003
Denmark               M7-1998        M8-2001        M9-2004
Germany               M7-1998        M8-2001        M9-2004
Hungary               M7-1997        M8-2000        M9-2003
Japan                 M8-2003
Netherlands           M1-2004
Poland                M7-1996       M12-2000        M2-2004
South Africa         M10-2004
Switzerland           M1-2000        M1-2004
United Kingdom        M5-2003
United States         M9-2001

Country           Finite sample critical values (%)

                  90       95       97.5    99

Austria           0.036    0.043    0.049   0.056
Canada            0.028    0.033    0.037   0.044
Denmark           0.020    0.022    0.025   0.029
Germany           0.022    0.026    0.030   0.035
Hungary           0.021    0.025    0.028   0.033
Japan             0.031    0.036    0.040   0.045
Netherlands       0.049    0.061    0.073   0.090
Poland            0.020    0.023    0.025   0.029
South Africa      0.112    0.147    0.182   0.231
Switzerland       0.023    0.026    0.029   0.033
United Kingdom    0.031    0.035    0.039   0.044
United States     0.032    0.037    0.041   0.047

Panel B: Panel KPSS test with multiple breaks

KPSS test        Test statistics     Bootstrap critical values (%)

                                        1      2.5        5       10

Homogeneity           5.791        14.164   14.535   14.857   15.245
Heterogeneity         5.237         8.477    8.809    9.101    9.445

KPSS test           Bootstrap critical values (%)

                      90       95     97.5       99

Homogeneity       18.271   18.774   19.209   19.803
Heterogeneity     12.483   13.034   13.564   14.224

Notes: See Table 6.

Table 9
Panel Stationarity Tests and Individual Tests with Structural
Breaks for WPI in Developing Countries

Panel A: Country-specific tests

Country      KPSS    m    [T.sub.b,1]    [T.sub.b,2]    [T.sub.b,3]

Brazil       0.037    3       M4-1994        M6-1998       M10-2002
India        0.021    4       M5-1990       M12-1994       M11-1998
Indonesia    0.053    3      M12-1997        M2-2001        M3-2004
Malaysia     0.043    2      M10-1997        M9-2002
Mexico       0.035    3       M3-1995       M11-1998        M1-2004
Singapore    0.025    3       M2-1991        M8-1999        M4-2004
Thailand     0.021    4       M8-1992        M9-1997       M10-2000
Turkey       0.047    3      M10-1996        M5-2000        M6-2003

Country     [T.sub.b,4]    [T.sub.b,5]

Brazil
India          M12-2001
Indonesia
Malaysia
Mexico
Singapore
Thailand        M4-2004
Turkey

Country     Finite sample critical values (%)

                90       95     97.5       99

Brazil       0.051    0.065    0.078    0.098
India        0.024    0.028    0.031    0.035
Indonesia    0.101    0.134    0.168    0.211
Malaysia     0.099    0.131    0.162    0.202
Mexico       0.062    0.079    0.097    0.122
Singapore    0.035    0.041    0.046    0.053
Thailand     0.034    0.042    0.050    0.060
Turkey       0.083    0.108    0.136    0.171

Panel B: Panel KPSS test with multiple breaks

KPSS test        Test statistics    Bootstrap critical values (%)

                                          1       2.5         5

Homogeneity      7.077 ***           -0.561    -0.297    -0.056
Heterogeneity    5.607 **             1.498     1.767     2.016

KPSS test                 Bootstrap critical values (%)

                     10       90       95     97.5       99

Homogeneity       0.241    3.676    4.486    5.301    6.507
Heterogeneity     2.329    5.002    5.505    5.966    6.596

Notes: See Table 6.