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Tests of Purchasing Power Parity via cointegration analysis of heterogeneous panels with consumer price indices
Journal of Macroeconomics 27 (2005) 345–362 www.elsevier.com/locate/jmacro
Tests of Purchasing Power Parity via cointegration analysis of heterogeneous panels with consumer price indices Michael A. Jenkins a, Sean M. Snaith a b
b,*
Department of Economics, St. Lawrence University, Canton, NY 13617, United States Business Forecasting Center, Eberhardt School of Business, University of The Pacific, 3601 Pacific Avenue, Stockton, CA 95211, United States Received 10 January 2003; accepted 7 November 2003 Available online 29 April 2005
Abstract There has been significant interest in the empirical performance of the Purchasing Power Parity (PPP) hypothesis. Initial studies were, in general, unfavorable for PPP. These results led researchers into two directions. One branch of the literature employed price data for a limited range or goods (e.g., fruits or clothing). A second branch has reevaluated the performance of PPP with more powerful methods. In this paper we combine these two branches of the literature. We use consumer price sub-indices data and recently developed panel cointegration techniques to test weak PPP. Our results are suggestive that the failure of PPP can be attributed to inclusion of non-traded goods in the overall index. Ó 2005 Elsevier Inc. All rights reserved. JEL classification: F31 Keywords: Purchasing Power Parity; Panel cointegration
* Corresponding author. Address: Business Forecasting Center, 3601 Pacific Avenue, Stockton, CA 95211, United States. E-mail addresses: [email protected] (M.A. Jenkins), ssnaith@pacific.edu (S.M. Snaith).
0164-0704/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jmacro.2003.11.020
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1. Introduction It has been well documented that the power of traditional unit root and cointegration tests is dependent on the span of data series being tested, see for example Shiller and Perron (1985) or Pierse and Snell (1995). This is problematic when limited data are available or when the data stretch across distinct regimes. Panel unit root and cointegration tests evolved specifically to address this problem of the low power of standard unit roots tests to distinguish between unit roots and near unit roots. This paper uses panel cointegration techniques developed by Pedroni (2002) to conduct disaggregated tests of the weak version of Purchasing Power Parity (PPP). Weak PPP implies that while price ratios and exchange rates move together over long periods, they may not move in direct proportion and therefore would be cointegrated but not necessarily with a cointegrating coefficient of 1.0. PedroniÕs tests allow for heterogeneous slope coefficients and for differences in the short run dynamics of the individual members of the panels. Imposing a homogeneous cointegrating vector across the individual members of the panel when this is not the true relationship will result in a component of the error term from the cointegrating relationship being integrated of order one. This will be true even if cointegration represents the true relationship and the residual should therefore be stationary. Employing PedroniÕs tests on both aggregate and disaggregate price indices, we find support in our sample for the non-traded goods explanation of the failure of weak PPP in the post-Bretton Woods era. While PPP fails to hold (we fail to reject the null hypothesis of no cointegration) for the relative consumer price index as a whole, we find evidence that cointegration does exist between the price indices of traded goods and exchange rates but not for those goods that are non-traded. Thus, we combine two approaches that have heretofore been treated separately in the literature to address the failure of PPP in the post-Bretton Woods era: application of more powerful and appropriate statistical tests and an analysis of consumer price sub-indices data.
2. Summary of relevant literature Taylor (2002) notes that studies on PPP ‘‘have appeared in abundance’’ recently. This contrasts with Froot and RogoffÕs (1995) comment that as recently as the 1980s PPP was a ‘‘fairly dull research topic.’’ While there is a good deal of debate on a number of issues regarding PPP, it is widely accepted that large deviations from PPP exist over the short to medium term. With sample periods usually confined to the post-Bretton Woods era, results suggest either a unit root in the real exchange rate or a lack of cointegration between the nominal exchange rate and prices.1 Thus, PPP is considered to be at best a long-run phenomenon. Indeed, evidence on PPP in
1 See Rogoff (1996) and Froot and Rogoff (1995) for surveys of the literature on the empirical performance of PPP.
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the long run (e.g., with time series that span a century or more) has been more favorable; see, for example, Lothian and Taylor (1996) and Abuaf and Jorion (1990).2 The failure of PPP, at least during the post-Bretton Woods period, has led to several channels of research, one of which exploits competing theoretical arguments for the failure of PPP by price data. A second channel addresses the low power of the statistical tests frequently employed by re-evaluating the data with more powerful statistical tests. Each of these two channels will be briefly discussed. Given the frequently observed failure of PPP, a number of theoretical reasons have been discussed as possible sources. Among them are non-traded goods and sticky prices. The non-traded goods explanation is discussed by Balassa (1964) and Samuelson (1964). In these models market arbitrage does not exist to ensure a common currency price for a non-traded good or service (e.g., a haircut or a Big Mac). Frequently this theory is employed to explain why common currency prices are higher in more developed countries. The higher prices in developed countries are the result of productivity shocks that increase wages, and thus prices, in the non-traded goods sector. Weak relative PPP may be consistent with a Balasa–Samuelson type model. Again, this form of PPP would be satisfied when the nominal exchange rate and aggregate price ratios are cointegrated, though not necessarily with a cointegrating vector of one. This general idea of the importance of non-traded goods and relative productivity differences on the behavior of the real exchange rate has been expanded by Hsieh (1982), Bergstrand (1991) and Obstfeld (1993). In their models, changes in the relative price of non-traded versus traded goods cause movements in the real exchange rate. Obstfeld explicitly shows that the real exchange rate can exhibit stochastic behavior that is consistent with many of the empirical findings of non-stationarity of the real exchange rate. Others (Obstfeld and Rogoff, 1984) argue that sticky goods prices are the source of deviations from PPP. Under this explanation the common currency prices of traded goods are not necessarily equal. Moreover, in these models sluggish price adjustment can lead to a finding of a unit root in the real exchange rate. Pricing-to-market models such as those of Krugman (1987) and Dornbusch (1987) also suggest the common currency prices of traded goods may not be equal. These models assume an oligopolistic market structure and price discrimination to generate the inequality of common currency prices of traded goods. Ghosh and Wolf (1994) attempt to distinguish amongst these competing explanations with data from the prices of the Economist magazine. They argue sticky prices are at least part of the explanation for the failure. Among the first to address empirically the potential relevance of non-traded goods in the failure of PPP was Engel (1993). Engel considered more than 2000 pair-wise comparisons of the relative prices of different goods within either the US or Canada versus relative prices of a common good in both countries. He found much greater short-term variation in relative prices of the same traded goods across
2
Though recently Engel (2000) questioned these results. His argument involves the inability of the econometric tests to detect a small but non-stationary component of a real exchange rate due to movements in relative prices (traded versus non-traded) within a country.
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the border than with prices of two different goods within the same country. Engel contended that those results were consistent with the sticky price model. This was followed by Rogers and Jenkins (1995) who also looked at relative prices within and across the US and Canada. They argued that relative price differentials for a common good across the border were both more volatile and more persistent than the price differentials for different goods within a country. As with Engel, they favored a sticky price explanation. These studies were followed by Engel and Rogers (1996) and Jenkins (1997) who took the consumer price sub-indices a step further by examining price data from cities within the US and Canada. This allowed for an examination of the role of distance in the performance of PPP. Both studies find distance to be important; evidence favorable to PPP is more likely to be found between two cities close to one another as opposed to two cites separated by thousands of miles. Thus, the friction of transportation costs may be relevant in the performance of PPP. Both found a significant border effect. One aspect of crossing the border is exchange rate fluctuations. This is again evidence favorable to the sticky price explanation. Parsley and Wei (2001) examined individual price data from the US and Japan and came to similar conclusions. Another branch of the literature on PPP involves more powerful statistical methods. Given the low power of time series tests to distinguish unit roots from near unit roots, attempts have been made to increase the power of these tests. As mentioned above, some studies have employed data sets that span a century or more. Another technique is to pool data across countries. Several studies have applied panel unit root tests to real exchange rates. Frankel and Rose (1996) pooled data for dozens of countries over the period 1948–1992. They argue against a unit root in real exchange rates; i.e., they find evidence of mean reversion in real exchange rates. In particular, they contend that, on average, movements in real exchange rates (deviations from PPP) have half-lives of four years. OÕConnell (1998) also pools data over dozens of countries for a sample period of the post-Bretton Woods era. He also contends that real exchange rates are stationary. He also argues that this result holds on a continental basis, pooling over countries in Europe or Asia only. Traditional tests on panel unit roots in real exchange rates implicitly may impose a cointegrating vector, which is constrained to be both equal to one and homogenous across panel members. Again, testing weak relative PPP does not require restriction on the value of the cointegrating vector, just that exchange rates and relative price levels be cointegrated. Pedroni (2002) has devised a panel cointegration technique that allows for heterogeneous cointegrating vectors. Thus, with this technique, the cointegrating vector need not equal 1, and furthermore it need not be equal across country pairs. Pedroni (1995) and Canzoneri et al. (1999) employ this test and argue that nominal exchange rates and relative aggregate prices are cointegrated for a sample of industrialized countries. Thus, weak PPP holds. Two recent papers by Crucini et al. (2000) and Imbs et al. (2002) are closely related to the current study. Imbs et al. (2002) analyze data from the same source employed in this study. The authors find that the persistence of deviations from PPP can be largely attributed to the failure to account for the heterogeneity in the
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dynamics of relative sectoral prices and the resultant bias of econometric techniques that aggregate this heterogeneous sectoral data. Crucini et al. (2000) examine price data for over 1800 retail goods and services for 13 European countries from a 1985 Eurostat survey. The authors find support for the role of tradeabiltiy of both final goods and the inputs required to produce the goods in explaining price dispersion. The current study, which uses a panel data approach on price indices, may be viewed as an extension of these authorsÕ analysis.
3. The Pedroni statistics Pedroni (2002) develops a set of five statistics based on the following standard panel regression: y it ¼ ai þ di þ bi X it þ eit
ð1Þ
where yit and Xit are panels of observations over the members of the panel from i = 1, . . . , N and time periods t = 1, . . . , T and where Xit and bi are column and row vectors of m-dimension for each member of the panel. The variables yit and Xit are assumed to be integrated of order one (I(1)). The parameters ai and di allow for fixed effects and deterministic trends specific to each member. The null and alternative hypotheses examined are as follows: H0: All of the individuals of the panel are not cointegrated versus H1: A significant portion of the individuals are cointegrated. Under the null hypothesis, eit I(1) and under the alternative hypothesis eit I(0). The first set of three panel statistics is based on pooling the data along the within dimension of the panel. This involves summing the numerator and denominator terms of each statistic separately for the analogous times series statistics. The definitions of the panel variance ratio, panel rho and panel t statistics for a null of no co-integration in heterogeneous panels are given as follows: !1 N X T X 2 ^eit1 Panel variance ratio statistic: Z ^vNT L211 i¼1
Panel rho statistic:
Z q^NT 1
N X T X i¼1
Panel t statistic:
Z tNT
~2NT r
i¼1
!1 ^e2it1
t¼1
N X T X t¼1
t¼1
i¼1
!12 ^e2it1
N X T X ð^eit1 D^eit1 ki Þ
ð2Þ
t¼1
N X T X ð^eit1 D^eit1 ki Þ. i¼1
t¼1
The second set of statistics is based on pooling the data along the between dimension of the panel. The method used to construct these statistics involves calculating the ratio that corresponds to the conventional time series statistic and then computing the standardized sum of the ratio over the cross-section of the panel. These two group mean statistics are given below.
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Group rho statistic:
e q^ Z NT 1
N T X X i¼1
Group t statistic:
e tNT Z
N T X X i¼1
t¼1
!1 ^e2it1
t¼1
ð^eit1 D^eit1 ki Þ
t¼1
!12 r2 e2it1 i ^
T X
ð3Þ T X
ð^eit1 D^eit1 ki Þ:
t¼1
In the statistics given in Eqs. (2) and (3), ^eit is the residual from Eq. (1), P ~NT N 1 Ni¼1 r2i ; ki ¼ 12 ðr2i s2i Þ where r2i is the long run variance and s2i is the r individual contemporaneousPvariance of the residuals from the following equation ^eit ¼ qi^eit1 þ lit ; L211 ¼ N 1 Ni¼1 L211i . L11i is obtained by lower triangular decomposition of the asymptotic covariance matrix Xi and is given by L11i ¼ ðX11i 1 2 X021i X1 22i X21i Þ . These statistics are formed to take into account heterogeneity of the cointegrating vector for the members of the panel. Pedroni (2002) notes that asymptotic distribution properties of residual based tests of panel cointegration are dramatically affected by the averaging over in the cross-section dimension in these statistics. The estimated regressor effect in the estimation of panels will depend on whether or not the coefficients of the hypothesized cointegration relationship are constrained to be homo- geneous across the individual members of the panel. In the case where this relationship is allowed to vary, this may lead to a non-convergent test statistic as sample size increases. If no adjustments are made in this case it may lead to the rejection of the null hypothesis of no cointegration, regardless of the true relationship. On the other hand, if homogeneity of the cointegrating vectors is falsely imposed this will result in a portion of the residual that is integrated even when cointegration is the true relationship. Pedroni conducts Monte Carlo experiments on these five statistics and the results imply a rule of thumb in their application. The group rho statistic is best used when working with small panels, while the panel variance ratio statistic has the highest power relative to the other statistics for large panels. The other statistics fall into a range whose bounds are defined by the group rho and panel variance ratio statistics. For additional details on the derivation and asymptotics of these statistics, as well as the results of the Monte Carlo experiments see Pedroni (2002).
4. Data and analysis In our case the cointegrating regression we are interested in is expressed in Eq. (4). sit ¼ ai þ bi pkit þ eit :
ð4Þ
Here sit is the log of the nominal exchange rate at time t for country pair i, and pkit is the log relative price index differential for each country pair, for price index k. A total of 26 panels are formed using each of the price indices and sub-indices. These panels are then subsequently used to test the weak form of purchasing power parity.
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Unlike the strong form of long run purchasing power parity which requires that the exchange rate and relative prices be cointegrated with bi = 1, the weak version of long run PPP only requires that cointegration exist, a less stringent test of the theory. Specifically with the panel tests, the null hypothesis can be interpreted as ‘‘weak PPP does not hold for all members of the panel’’ while the alternative can be interpreted as, ‘‘weak PPP holds for a significant portion of the individuals in the panel’’. Using consumer price index and sub-index data, we hope to shed light on the role of nontraded goods in explaining the failure to find empirical evidence for PPP in the postBretton Woods era. Our initial analysis is conducted using monthly data from the Eurostat’s New Coronos data set. With this data set, we sought to maximize the number of observations along three dimensions: time period, number of countries and number of sub-indices. With this goal, our sample includes eleven countries for the period covering 1981:01 through 1995:06 for 26 price series (the aggregate CPI and 25 sub-indices). The sample was selected to ensure as complete a panel data set as possible and to end before the harmonization of price data that took place in the European Union in 1996.3 As pre-harmonized data, the goods categories are not always measuring the same items. For example, some countries include restaurant meals in the food category while others do not. Thus, the various categories of goods we consider are measuring prices of similar, but not necessarily identical, goods. Our study, though an improvement over analyzing aggregate CPI data, is still limited by the problem of aggregation bias remaining in the sub-indices.4 The countries in our sample group include Belgium, Denmark, Germany, Greece, Spain, France, Italy, Luxemburg, Netherlands, United Kingdom and the United States.5 The data were used to construct panels consisting of 54 cross-sectional members.6 Exchange rate data are monthly averages from the Federal Reserve Bank of St. LouisÕs FRED. Prior to evaluating these panel relationships, we first consider the time series properties of the data. Specifically we check for the presence of panel unit roots in sit and pkit ; using Levin-Lin and Im, Pesaren and Shin tests. The results are reported in Table 1. These results suggest that the panel exchange rates and panel consumer price indices used for subsequent cointegration analysis are consistent with the null of non-stationarity. Crucini and Shintani (2002), using micro-data on 270 comparable goods, reject the null hypothesis of a unit root in the real exchange rate for between 96% and 100% of the goods used in their study. This result in part contradicts some of our findings, but may be attributable to differences in data (their micro-data versus our price index data) as well as difference in the sample periods analyzed.
3
In 1993 the European Commission initiated the creation of a harmonized index of consumer prices (HIPC). It did so in coordination with the member state statistical agencies. The new harmonized series began January 1996. 4 See Crucini et al. (2000) and Parsley and Wei (2001) for studies which do employ absolute price for comparable individual goods and services. 5 Unfortunately, some European countries, notably Austria, Portugal, Ireland, Sweden and Finland either did not have data for some of the sub-indices or the data began at a later date. For this reason these countries were excluded. 6 The country pair of Belgium and Luxembourg is omitted due to their common currency.
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Table 1 Panel unit root tests Type of goods
L-L rho
L-L t–rho
L-L ADF
IPS ADF
Number of rejections *
**
#
Erate 1000 1110 1111 1112 1114 1116 1140 1150 1160 1200 1210 1220 1300 1310 1330 1410 1420 1600 1610 1630 1700 1710 1720 1730 1800 1830
0.16 2.16 3.18 0.43 0.57 0.15 1.66 1.51 0.82 0.98 0.90 1.63 0.43 1.23 0.22 0.84 1.48 0.72 1.95 4.42* 1.72 0.84 0.11 0.10 1.63# 0.12 1.34
1.12 0.57 0.86 1.05 1.26 1.91** 0.80 2.65 1.20 1.87 0.01 0.97 2.09** 0.12 0.19 0.45 0.90 1.32 0.76 1.56# 1.28 0.95 1.31 0.60 1.54# 0.83 0.30
1.46# 1.76 1.10 1.69 1.96 0.58 1.87 1.62# 1.14 0.36 0.98 0.19 0.12 0.94 0.18 0.16 1.68 0.71 0.34 1.42 1.15 1.04 1.40 0.07 1.07 0.93 1.92
2.24** 0.93 1.28 0.47 1.97 0.96 1.19 0.15 0.63 0.60 2.31 1.75** 0.08 1.25 0.73 0.31 1.88 2.09** 1.30# 0.34 0.83 0.97 0.83 1.88 1.08 1.22 1.39
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0
2 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 2 0 0 0 0 2 0 0
The column entitled Ônumber of rejectionsÕ list the total number of the four statistics that reject the null of a panel unit root at each level of significance, where *, ** and # represent the 1%, 5% and 10% levels of significance.
The results of the panel cointegration tests are reported in Table 2. The first three columns of statistics in each table display the panel statistics with a parametric panel augmented Dickey–Fuller statistic in the fourth column included for comparison purposes. The next two are the group statistics again followed by the parametric ADF version of this type of statistic. The normally distributed statistics listed in these tables have been standardized using the variances given in Pedroni (2002); thus, they are distributed as standard normal under the null hypothesis of no cointegration. For large negative values of these statistics the null hypothesis will be rejected, with the exception of the panel variance ratio statistic, which rejects the null hypothesis for large positive values of the statistic. The last column summarizes the results of the hypothesis tests in each row. These values indicate the number of rejections of the null hypothesis at the 1%, 5% and 10% levels of significance.
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Table 2 Panel cointegration tests Type of goods
1000 1110 1111 1112 1114 1116 1140 1150 1160 1200 1210 1220 1300 1310 1330 1410 1420 1600 1610 1630 1700 1710 1720 1730 1800 1830
Panel v-stat
5.00* 6.09* 3.90* 3.88* 2.19** 0.42 0.01 2.69* 2.04** 2.63* 2.07** 1.89** 1.79** 1.67** 2.46* 3.28* 2.34* 2.18** 2.12** 0.81 5.19* 2.31** 2.31** 3.69* 3.11* 1.88**
Panel rho-stat
0.93 3.33* 4.20* 2.54* 2.03** 19.69* 6.34* 2.56* 1.67** 7.58* 6.95* 6.33* 0.77 1.60# 5.46* 1.77** 3.67* 1.18 4.03* 5.80* 1.88** 4.21* 1.35# 3.11* 2.12** 0.94
Panel PP-stat
0.51 2.50* 3.67* 1.59# 2.06** 12.07* 5.46* 2.40* 1.90** 6.56* 6.15* 5.58* 1.27 1.44# 5.24* 2.05** 3.87* 1.46# 2.60* 5.24* 1.35# 3.58* 0.93 2.72* 1.62# 1.27
Panel ADF-stat
0.46 1.63# 2.15** 0.36 1.41# 0.25 0.19 0.99 1.69** 0.87 1.17 1.29# 0.90 0.31 1.57** 0.56 2.30** 0.75 0.01 2.51* 1.42# 1.08 0.29 1.75** 0.86 0.31
Group rho-stat
0.67 1.40# 1.96** 0.23 0.19 14.63* 2.01** 0.66 0.32 7.02* 6.11* 6.44* 0.05 0.56 5.59* 4.31* 6.95* 0.27 3.58* 3.74* 0.87 4.15* 0.38 3.35* 2.73* 0.88
Group PP-stat
0.45 1.35# 2.38* 0.01 1.17 10.20* 2.65* 0.83 1.16 6.04* 5.51* 4.65* 0.76 1.01 5.54* 4.88* 5.30* 0.47 2.28** 3.92* 0.84 3.46* 0.66 2.87* 1.89* 0.67
Group ADF-stat
0.26 1.40# 1.93** 0.11 1.71** 0.67 1.14 0.64 2.20** 1.49# 1.68** 0.96 0.47 0.08 1.42# 0.06 7.58* 0.41 0.27 2.02** 1.47# 0.84 0.46 2.80* 1.84* 0.20
Number of rejections *
**
#
1 3 4 2 0 4 3 3 0 5 4 4 0 0 5 3 6 0 2 5 1 4 0 6 4 0
1 3 7 2 4 4 3 3 5 5 6 5 1 1 6 5 7 1 5 6 2 5 1 7 5 1
1 7 7 3 5 4 4 3 5 6 6 6 1 3 7 5 7 2 5 6 5 5 2 7 6 1
Statistics reported in this table are generated from the following cointegrating regression: sit ¼ ai þ bi pkit þ eit and test the following hypothesis: H0: All of the individuals of the panel are not cointegrated (Weak PPP does not hold.). H1: A significant portion of the individuals are cointegrated (Weak PPP holds for a significant portion of the panel.). The column entitled Ônumber of rejectionsÕ list the total number of the seven statistics that reject the null at each level of significance, where *, ** and # represent the 1%, 5% and 10% levels of significance. The Eurostat goods categories are: 1000 All goods, 1100 Food, 1111 Bread and cereals, 1112 Meat, 1114 Dairy products, 1116 Fruits, 1140 Tobacco, 1150 Alcoholic and non-alcoholic drinks, 1160 Drink and tobacco, 1200 Clothing and footwear, 1210 Clothing, 1220 Footwear, 1300 Shelter, 1310 Rents, 1330 Fuels and energy, 1410 Furniture, 1420 Domestic appliances, 1600 Transport and communications, 1610 Vehicles, 1630 Public transport, 1700 Recreation, 1710 Sound and photographic equipment, 1720 Leisure, 1730 Books, 1800 Other goods and services, 1830 Hotels.
The first notable outcome is that the results for the aggregate CPI show a failure to reject the null hypothesis of cointegration that weak PPP does not hold for the
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panels constructed with this index. The sole exception to this result is with the panel variance statistic, which, as discussed earlier may lack the power to reject the null in our panel. This suggests that PPP as traditionally defined (i.e., with the aggregate CPIs) does not hold. Next, we consider the sub-indices. For example, the results for series 1111, breads and cereals, highly traded commodities, indicate a strong rejection of the null of no cointegration. This result supports the notion that weak PPP does in fact hold for this type of good. The other indices for food, drink and tobacco as well show support for the weak version of PPP. The panels constructed with the price indices for meat, dairy products, fruits, alcoholic and non-alcoholic drinks and tobacco all indicate rejection of the null hypothesis of no cointegration. There are several more results of a similar nature. Clothing and footwear (series 1200) and each of the component sub-indices (1210 and 1220) all show consistent rejection of the null hypothesis. Panels formed for fuels and energy, domestic appliances, vehicles and sound and photographic equipment generate values for several of the statistics that lead to rejection of the null hypothesis in favor of weak PPP. The categories that generate results that are supportive of weak PPP holding across our panel of countries are all by and large goods that are generally traded internationally. There are several panels that generate results that fail to support weak PPP; we now turn our attention to these goods and services. The two most obviously non-traded goods in our analysis are series 1310 and 1830 indices measuring rents and the prices of hotels. Since these commodities are clearly not subject to the trade arbitrage that is the underpinning of PPP, the results of the cointegration tests derived from the panels built using these indices are not surprising. For almost all statistics and levels of significance we fail to reject the null hypothesis of no cointegration for these commodities. For the more inclusive shelter index, series 1300, the results are similar. The results from the panel formed using the transport and communications index, series 1600, also show very little support for weak PPP. Several of the categories warrant further explanation, especially given that most of the country pairs in our sample are between two EU states. Evidence on food items may be difficult to interpret given the substantial government intervention in agricultural markets in Europe (under the common agricultural policy – CAP). For example, during the 1980s the European Commission made use of the so-called ‘‘green’’ exchange rates to provide monetary compensatory amounts (MCAs) to farmers. As noted by Fennell (1987), this practice, which included a great deal of fluctuations in the size of MCAs, often generated sizable gaps in the common currency prices of agricultural items in Europe. Also, our sample includes the introduction of the MacSharry reforms, which substantially altered agricultural support methods and payments to farmers. Yet in spite of the interventions, our results are generally supportive of PPP for food items. Another category, which merits special attention, is automotive goods, which are included in the ‘‘vehicles’’ category in our study. The European Commission over our sample period granted the automotive industry an exemption from its competition
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policy.7 This allowed automobile makers to segment the European market along member state borders by way of dealer restrictions on servicing contracts. For example, the European CommissionÕs survey of automobile prices in November 2001 reported frequent price differences across member states on identical cars of twenty percent or more (see European Commission, 2002). Thus, our results only suggest that common currency prices in the automotive sector move together, not that they are equal. While we do find evidence favorable to PPP with many categories of tradeable goods, this is not necessarily the case for non-traded goods. A category that stands out is shelter. In general, we do not reject the null of no cointegration for this category. Moreover, this category is significant in that for many countries it accounts for up to twenty percent of the aggregate CPI, large enough perhaps that the failure of prices in this category to move together may drive our finding that aggregate prices fail to move together as well. Our initial analysis focused on monthly data for the country set previously described. We now turn to evaluating the robustness of these results. In particular, we modify our sample group of countries to consider the possibility, as suggested by Parsley and Wei (1996) and others, that explanations for the failure of PPP may be a function of the country set analyzed. In order to investigate this possibility, we consider cross-sections using a single country as the numeraire (Belgium), and an EUonly subset of our original countries. Additionally we considered other periodicities of data, analyzing both quarterly and annual data in addition to the monthly data. To summarize our findings, the qualitative results of the original panel are reaffirmed throughout analysis of these alternative panels. Pedroni (2001) notes that with such data employed in this study there may be violation of the condition of independence of individual members of the panel. We employ a common technique to deal with this type of dependency, subtracting out individual time means. Thus, for the results presented in Table 3 the estimated panel becomes _ s it
_k
¼ ai þ bi p it þ eit
where
_
s it ¼ sit T 1
T X
sit
t¼1
and
_k p it
¼ pkit T 1
T X
pkit .
ð5Þ
t¼1
The results from both demeaned and unadjusted panels, however, paint a similar picture. Next we address the bilateral country construction of the panels. Initially we considered all bilateral combinations (exempting Belgium/Luxembourg). OÕConnell (1998) suggests that under certain conditions in panel tests all information is contained using only one country as a numeraire. That is, one need only compare each country with one other country, say Belgium, not with every other country. We initially used all bilateral comparisons because Papell and Theodoridis (2001) have 7
This exemption continues to the present, though recently there has been much discussion of ending it.
356
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Table 3 Panel cointegration tests (demeaned series) Type of goods
1000 1110 1111 1112 1114 1116 1140 1150 1160 1200 1210 1220 1300 1310 1330 1410 1420 1600 1610 1630 1700 1710 1720 1730 1800 1830
Panel v-stat
4.90* 5.60* 5.03* 4.17* 2.52* 0.65 0.59 2.96* 2.32** 2.53* 2.16** 1.89** 2.65* 0.24 3.73* 1.59# 1.69* 2.81* 0.50 0.78 6.11* 0.86 1.12 4.29* 3.50* 0.37
Panel rho-stat
0.74 2.52* 4.49* 2.71* 1.79** 17.92* 5.55* 2.35* 1.27# 6.82* 6.31* 6.33* 1.28 0.12 6.29* 2.90* 2.65* 1.39# 2.22** 4.42* 2.67* 1.76** 1.80* 2.93* 2.63* 0.03
Panel PP-stat
0.26 1.79** 3.70* 1.85** 1.71** 11.22* 4.52* 2.21** 1.51# 5.83* 5.36* 5.58* 1.50# 0.46 5.49* 2.87* 2.81* 1.54# 1.55# 4.23* 2.05** 1.78** 1.75** 2.49* 2.34* 0.13
Panel ADF-stat
0.94 1.14 2.51* 1.19 1.39# 0.62 0.61 1.03 1.82** 1.30# 1.38# 1.29# 1.60# 0.43 2.27** 1.15 0.64 0.51 0.67 2.18** 2.25** 0.51 0.42 2.13** 2.07* 0.34
Group rho-stat
0.99 0.25 1.80** 0.54 0.19 12.75* 2.88** 1.03 0.02 7.43* 6.65* 6.44* 0.25 0.54 5.52* 5.19* 7.13* 0.16 2.01** 1.62# 1.36# 3.72* 1.76** 2.73* 3.98* 1.49#
Group PP-stat
0.77 0.53 2.25** 0.47 0.59 8.98* 3.34* 1.28 0.85 6.00* 5.34* 4.65* 0.53 1.22 5.27* 5.78** 5.50* 0.74 2.00** 2.92* 1.51# 3.27* 2.57* 2.60* 3.08* 0.95
Group ADF-stat
0.15 0.18 1.42# 0.27 1.21 0.29 1.31# 1.16 2.10** 2.31** 2.27** 0.96 0.81 0.15 1.88** 1.63# 0.31 0.39 0.60 0.98 2.09** 0.02 0.41 2.48* 3.21* 0.72
Number of rejections *
**
#
1 2 4 2 1 4 3 2 0 5 4 4 1 0 5 3 5 0 0 3 2 2 2 6 7 0
1 3 6 3 3 4 4 3 3 6 6 5 3 0 7 4 5 1 3 4 5 4 4 7 7 0
1 3 7 3 4 4 5 3 5 7 7 6 3 0 7 6 5 3 4 5 7 4 4 7 7 1
Statistics reported in this table are generated from the following cointegrating regression: _ s it
_k
¼ ai þ bi p it þ eit
and test the following hypothesis: H0: All of the individuals of the panel are not cointegrated (Weak PPP does not hold.). H1: A significant portion of the individuals are cointegrated (Weak PPP holds for a significant portion of the panel.). The column entitled Ônumber of rejectionsÕ list the total number of the seven statistics that reject the null at each level of significance, where *, ** and # represent the 1%, 5% and 10% levels of significance. The Eurostat goods categories are: 1000 All goods, 1100 Food, 1111 Bread and cereals, 1112 Meat, 1114 Dairy products, 1116 Fruits, 1140 Tobacco, 1150 Alcoholic and non-alcoholic drinks, 1160 Drink and tobacco, 1200 Clothing and footwear, 1210 Clothing, 1220 Footwear, 1300 Shelter, 1310 Rents, 1330 Fuels and energy, 1410 Furniture, 1420 Domestic appliances, 1600 Transport and communications, 1610 Vehicles, 1630 Public transport, 1700 Recreation, 1710 Sound and photographic equipment, 1720 Leisure, 1730 Books, 1800 Other goods and services, 1830 Hotels.
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Table 4 Panel cointegration tests (Belgium as numeraire country) Type of goods
1000 1110 1111 1112 1114 1116 1140 1150 1160 1200 1210 1220 1300 1310 1330 1410 1420 1600 1610 1630 1700 1710 1720 1730 1800 1830
Panel v-stat
2.70* 3.26* 1.93# 1.16 2.14** 1.72# 0.71 2.02** 1.28 1.00 2.05** 2.32** 0.89 0.67 2.97* 2.06** 2.05** 2.69* 1.82# 1.95 1.31 0.95 1.36 0.96 1.97** 1.46
Panel rho-stat
1.28 3.38* 5.86* 3.42* 2.73* 6.95* 1.01 9.38* 1.22 0.55 3.33* 1.00 0.56 1.21 2.79* 2.26** 1.18 1.23 2.79* 3.44* 0.72 3.62* 0.85 0.65 2.14** 0.94
Panel PP-stat
1.14 2.80* 4.36* 2.72* 2.33** 4.71* 2.21** 5.42* 1.33 0.54 5.62* 1.63 1.13 0.96 2.32** 2.40** 1.99** 0.16 2.82* 2.90* 0.70 3.03* 1.67# 1.64 1.71# 1.03
Panel ADF-stat
1.30 2.40** 2.21** 1.23 1.89# 1.88# 1.61 2.33** 0.53 2.95* 1.31 2.29** 0.69 0.75 0.38 1.67# 2.55** 0.57 1.79# 1.70# 1.31 1.55 2.24** 2.35** 1.91# 0.66
Group rho-stat
0.54 2.65* 4.50* 2.06** 1.73# 5.71* 0.07 4.57* 0.52 2.10** 6.83* 0.28 1.99# 0.32 2.66* 1.68# 0.41 0.30 2.02** 2.56** 0.06 4.24* 0.40 0.30 1.43 0.05
Group PP-stat
0.91 2.61* 3.88* 2.37** 2.06** 4.85* 1.49 2.62* 1.18 1.83# 4.30* 0.71 1.82# 0.13 2.40** 2.58* 1.71 0.58 2.15** 2.69** 0.60 3.78* 0.90 0.99 1.70# 1.04
Group ADF-stat
1.28 2.62* 2.82* 1.22 2.47** 2.21** 0.81 2.31** 1.57 1.99# 1.52 1.89# 0.82 0.90 1.24 1.95# 2.70* 0.11 2.13** 1.75# 1.84# 1.93# 1.68# 2.57** 2.89* 1.23
Number of rejections *
**
#
1 6 5 2 1 4 0 4 0 1 4 0 0 0 3 1 1 1 2 2 0 4 0 0 1 0
1 7 6 4 5 5 1 7 0 2 5 2 0 0 5 5 4 1 5 4 0 4 1 2 3 0
1 7 7 4 7 7 1 7 0 4 5 3 2 0 5 7 4 1 7 6 1 5 3 2 6 0
Statistics reported in this table are generated from the following cointegrating regression: sit ¼ ai þ bi pkit þ eit and test the following hypothesis: H0: All of the individuals of the panel are not cointegrated (Weak PPP does not hold.). H1: A significant portion of the individuals are cointegrated (Weak PPP holds for a significant portion of the panel.). The column entitled Ônumber of rejectionsÕ list the total number of the seven statistics that reject the null at each level of significance, where *, ** and # represent the 1%, 5% and 10% levels of significance. The Eurostat goods categories are: 1000 All goods, 1100 Food, 1111 Bread and cereals, 1112 Meat, 1114 Dairy products, 1116 Fruits, 1140 Tobacco, 1150 Alcoholic and non-alcoholic drinks, 1160 Drink and tobacco, 1200 Clothing and footwear, 1210 Clothing, 1220 Footwear, 1300 Shelter, 1310 Rents, 1330 Fuels and energy, 1410 Furniture, 1420 Domestic appliances, 1600 Transport and communications, 1610 Vehicles, 1630 Public transport, 1700 Recreation, 1710 Sound and photographic equipment, 1720 Leisure, 1730 Books, 1800 Other goods and services, 1830 Hotels.
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Table 5 Panel cointegration tests (European countries only) Type of goods
1000 1110 1111 1112 1114 1116 1140 1150 1160 1200 1210 1220 1300 1310 1330 1410 1420 1600 1610 1630 1700 1710 1720 1730 1800 1830
Panel v-stat
4.20 4.91* 3.67* 3.17* 1.82# 1.90# 6.87* 2.52** 1.45 2.76* 2.14** 2.24** 1.36 1.89# 2.25** 6.68* 5.18* 2.48** 1.66# 0.55 4.27* 3.77* 1.30 3.12* 2.32** 3.20*
Panel rho-stat
0.59 2.45** 3.59* 2.45** 2.42** 10.54* 6.13* 0.91 1.01 8.71* 7.96* 7.48* 0.29 0.87 4.41* 6.30* 5.34* 0.84 2.45** 5.65* 1.28 8.43* 0.80 2.58* 1.41 0.83
Panel PP-stat
0.07 1.70# 2.87* 1.66# 2.45** 7.00* 4.58* 1.68# 1.01 6.95* 6.49* 6.02* 0.38 0.51 4.12* 5.17* 4.09* 0.73 1.24 4.66* 0.75 6.17* 0.13 2.04** 0.76 0.46
Panel ADF-stat
0.53 1.35 0.72 0.64 2.18** 0.83 0.81 3.12* 1.18 1.00 1.18 0.73 0.28 0.16 2.69* 2.26** 0.78 0.63 0.43 1.49 1.28 1.02 0.62 2.07** 0.23 0.54
Group rho-stat
0.74 0.94 2.04** 0.33 1.04 9.08* 6.28* 0.52 0.15 8.49* 7.49* 7.71* 0.52 1.34 4.49* 7.73* 7.69* 0.27 1.30 4.33* 0.51 8.79* 1.02 3.38* 2.84* 0.70
Group PP-stat
0.82 0.76 1.71# 0.22 1.84# 6.00* 5.06* 2.27** 0.44 6.73* 6.17* 5.24* 0.88 0.31 4.28* 6.05* 4.91* 0.06 0.41 3.50* 0.29 6.53* 0.97 2.50** 1.31 0.47
Group ADF-stat
0.04 1.02 0.69 0.25 2.64* 0.98 0.21 2.06** 1.72# 1.78# 1.80# 0.61 0.24 0.32 2.45** 2.96* 2.03** 0.01 0.10 0.72 1.34 1.20 0.22 3.26* 1.22 0.22
Number of rejections *
**
#
1 1 3 1 1 4 5 1 0 5 4 4 0 0 5 6 5 0 0 4 1 5 0 4 1 1
1 2 4 2 4 4 5 4 0 5 5 5 0 0 7 7 6 1 1 4 1 5 0 7 2 1
1 3 5 3 6 5 5 5 1 6 6 5 0 1 7 7 6 1 2 4 1 5 0 7 2 1
Statistics reported in this table are generated from the following cointegrating regression: sit ¼ ai þ bi pkit þ eit and test the following hypothesis: H0: All of the individuals of the panel are not cointegrated (Weak PPP does not hold.). H1: A significant portion of the individuals are cointegrated (Weak PPP holds for a significant portion of the panel.). The column entitled Ônumber of rejectionsÕ list the total number of the seven statistics that reject the null at each level of significance, where *, ** and # represent the 1%, 5% and 10% levels of significance. The Eurostat goods categories are: 1000 All goods, 1100 Food, 1111 Bread and cereals, 1112 Meat, 1114 Dairy products, 1116 Fruits, 1140 Tobacco, 1150 Alcoholic and non-alcoholic drinks, 1160 Drink and tobacco, 1200 Clothing and footwear, 1210 Clothing, 1220 Footwear, 1300 Shelter, 1310 Rents, 1330 Fuels and energy, 1410 Furniture, 1420 Domestic appliances, 1600 Transport and communications, 1610 Vehicles, 1630 Public transport, 1700 Recreation, 1710 Sound and photographic equipment, 1720 Leisure, 1730 Books, 1800 Other goods and services, 1830 Hotels.
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Table 6 Panel cointegration tests (annual observations) Type of goods
1000 1110 1111 1112 1114 1116 1140 1150 1160 1200 1210 1220 1300 1310 1330 1410 1420 1600 1610 1630 1700 1710 1720 1730 1800 1830
Panel v-stat
2.44** 2.17** 2.04** 3.63* 4.01* 4.76* 1.81# 2.77* 4.72* 3.22* 3.55* 4.18* 0.66 1.07 3.98* 0.56 1.16 1.06 1.82# 4.41* 3.72* 1.89# 0.98 3.42* 6.20* 0.32
Panel rho-stat
1.17 1.26 1.81# 0.99 1.25 0.52 0.39 1.24 0.79 0.16 0.69 0.08 0.59 1.44 0.82 0.20 0.48 0.01 0.97 1.13 0.39 0.88 1.51 0.75 0.09 1.29
Panel PP-stat
2.53** 3.45* 2.74* 3.86* 2.20** 4.16* 4.52* 3.14* 3.84* 4.37* 4.01* 4.99* 0.90 2.87* 4.39* 4.97* 6.40* 1.37 3.20* 3.36* 4.31* 3.15* 2.84* 4.31* 4.04* 0.23
Panel ADF-stat
0.39 1.28 1.90# 3.96* 2.12** 2.87* 3.09* 1.95# 2.37** 3.36* 3.53* 4.83* 0.34 1.23 3.49* 3.61* 4.49* 0.11 1.28 2.47** 2.32** 1.13 0.18 3.33* 3.14* 0.08
Group rho-stat
1.32 1.05 4.21* 3.56* 3.99* 3.54* 3.38* 3.96* 3.58* 3.23* 3.73* 3.03* 2.65* 4.04* 4.05* 2.91* 2.38** 2.09** 3.39* 4.22** 2.91* 3.19* 4.18* 3.67* 2.95* 3.49*
Group PP-stat
2.16** 3.71* 1.77# 2.42** 0.54 2.05** 3.78* 1.68# 2.58* 2.74* 2.24** 3.72* 1.77 2.02** 2.04** 3.94* 5.32* 0.78 2.59* 1.22 3.49* 3.00* 1.75# 2.65* 3.11* 0.08
Group ADF-stat
0.56 2.58* 1.43 4.43* 2.55** 2.25** 3.93* 0.78 2.22* 2.89* 1.84# 4.51* 0.12 0.59 0.87 4.46* 6.40* 0.28 1.29 1.23 3.44* 1.15 0.55 2.41** 3.52* 1.00
Number of rejections *
**
#
0 3 2 4 2 4 5 3 5 6 4 6 1 2 4 5 4 0 3 2 5 3 2 5 6 1
3 4 3 6 5 6 5 3 6 6 5 6 1 3 5 5 5 1 3 4 6 3 2 6 6 1
3 4 6 6 5 6 6 5 6 6 6 6 2 3 5 5 5 1 4 4 6 4 3 6 6 1
Statistics reported in this table are generated from the following cointegrating regression: sit ¼ ai þ bi pkit þ eit and test the following hypothesis: H0: All of the individuals of the panel are not cointegrated (Weak PPP does not hold.). H1: A significant portion of the individuals are cointegrated (Weak PPP holds for a significant portion of the panel.). The column entitled Ônumber of rejectionsÕ list the total number of the seven statistics that reject the null at each level of significance, where *, ** and # represent the 1%, 5% and 10% levels of significance. The Eurostat goods categories are: 1000 All goods, 1100 Food, 1111 Bread and cereals, 1112 Meat, 1114 Dairy products, 1116 Fruits, 1140 Tobacco, 1150 Alcoholic and non-alcoholic drinks, 1160 Drink and tobacco, 1200 Clothing and footwear, 1210 Clothing, 1220 Footwear, 1300 Shelter, 1310 Rents, 1330 Fuels and energy, 1410 Furniture, 1420 Domestic appliances, 1600 Transport and communications, 1610 Vehicles, 1630 Public transport, 1700 Recreation, 1710 Sound and photographic equipment, 1720 Leisure, 1730 Books, 1800 Other goods and services, 1830 Hotels.
360
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shown that empirically, for OECD countries, OÕConnellÕs conditions are not met and that panel tests on PPP are sensitive to the choice of the base country. However, for the purpose of comparison we perform the panel tests with the panels constructed with each country versus Belgium. The results are in Table 4. These results are quite similar to our initial set of results. Our next test is to address the inclusion of the US in our sample. Initially the US was included because we wanted, given our data set, to maximize the cross-section included in our panels. However, it should be noted that countries other than the US are all EU countries. They share geographic proximity and have relatively few official impediments to trade. In Table 5 we report the results from panel tests with an EU nations sample only. Again, these results are qualitatively similar to the initial results. Our final modification is to examine the results of our analysis using data of lower frequency. Multiple studies have examined the convergence toward PPP and the results indicate persistence in the deviations from PPP. Much of the literature indicates a half-life in the real exchange rate on the order of three to five years. More recent analysis by Imbs et al. (2002) and Crucini and Shintani (2002) find much shorter half-lives of around one year. All of these studies reaffirm the fact that the trade that drives PPP takes time and thus our results from monthly data may differ if data of different periodicities are employed. Thus, we re-evaluate our panel tests with annual and quarterly data in addition to monthly data. The annual results are reported in Table 6; quarterly results are not reported here for space considerations, but are available upon request. The trend in our results as we move from monthly to quarterly to annual data is that we are, in general, more likely to reject the null hypothesis of no cointegration across all panels. However, we still find that the evidence is not favorable to PPP using the aggregate CPIs but is more favorable toward PPP with traded goods sub-indices than with non-traded goods sub-indices. Thus, the non-traded goods explanation for the failure of weak PPP is upheld using these data sets and techniques.
5. Conclusions Using panel cointegration techniques we tested the validity of the weak version of Purchasing Power Parity using 26 panels formed from consumer price indices and sub-indices. Our results indicate that the failure to find cointegration evidence for weak PPP in the post-Bretton Woods era using aggregate CPI data is not necessarily a function of the low power of traditional time series tests for cointegration or unit roots. Instead, we find that the failure of PPP with the overall price index can be directly attributed to inclusion of non-traded goods in these aggregate indices. For those goods that can be characterized as highly traded between the members of our panel, we find evidence in support of weak PPP. However, for those goods and services that are not traded, we find very little evidence in support of weak PPP. Weak PPP does not imply a specific value of the cointegrating vector, just that relative prices and exchange rates be cointegrated. Future work will focus on the
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specific values of the estimated cointegrating vectors for the country pairs and panels analyzed in this study to see if there is support for the strong version of PPP within any of these panels. We also find differences in our results that appear to be systematically related to the periodicity of the data. The general trend in our results is that as we move from monthly to annual data, we are more likely to reject the null hypothesis of no cointegration in our panels. The trade that drives PPP takes time to occur and thus we are not surprised to find more evidence in support of PPP in the quarterly and annual data. However, systematic differences remain between the results for panels of price data for traded goods versus panels of price data for non-traded goods.
References Abuaf, N., Jorion, P., 1990. Purchasing power parity in the long run. Journal of Finance 45, 157–174. Balassa, B., 1964. The purchasing power parity doctrine. Journal of Political Economy 72, 584–589. Bergstrand, J.H., 1991. Structural determinants of real exchange rates and national price levels: Some empirical evidence. American Economic Review 81, 325–334. Canzoneri, M.B., Cumby, R.E., Diba, B., 1999. Relative labor productivity and the real exchange rate in the long run: Evidence for a panel of OECD countries. Journal of International Economics 47, 245– 266. Crucini, M.J., Shintani, M., 2002. Persistence in law-of-one-price deviations: Evidence from micro-data. Vanderbilt Working Paper 02-W22. Crucini, M.J., Telmer, C.I., Zachariadis, M., 2000. Dispersion in real exchange rates. Vanderbilt Working Paper No. 00-W13. Dornbusch, R., 1987. Purchasing power parity. In: Eatwell, J., Milgate, M., Newman, P. (Eds.), The New Palgrave Dictionary of Economics, vol. 3. Stockton Press, New York, pp. 1075–1085. Engel, C., 1993. Real exchange rates and relative prices: An empirical investigation. Journal of Monetary Economics 32, 35–50. Engel, C., 2000. Long-run PPP may not hold after all. Journal of International Economics 51, 243–273. Engel, C., Rogers, J.H., 1996. How wide is the border? American Economic Review 86, 1112–1125. European Commission, 2002. Car price differentials in the EU remain high, especially in the mass market segment. In Commission Press Room [Online], available: http://europa.eu.int/comm/competition/ car_sector/ (15 September 2002). Fennell, R., 1987. The Common Agricultural Policy of the European Community: Its Institutional and Administrative Organization. BSP Professional Books, Oxford, UK. Frankel, J., Rose, A., 1996. A panel project on purchasing power parity: Mean reversion within and between countries. Journal of International Economics 40, 209–224. Froot, K.A., Rogoff, K., 1995. Perspectives on PPP and long-run real exchange rates. In: Grossman, G., Rogoff, K. (Eds.), Handbook of International Economics, vol. 3. North-Holland, Amsterdam, pp. 1647–1688. Ghosh, A.R., Wolf, H.C., 1994. Pricing in international markets: Lessons from the economist, NBER Working Paper No. 4806. Hsieh, D., 1982. The determination of the real exchange rate: A productivity approach. Journal of International Economics 12, 355–362. Imbs, J., Mumtaz, H., Ravn, M.O., Rey, H., 2002. PPP strikes back: Aggregation and the real exchange rate. NBER Working Paper No. 9372. Jenkins, M.A., 1997. Cities, borders, distances, non-traded goods and purchasing power parity. Oxford Bulletin of Economics and Statistics 59, 203–213. Krugman, P., 1987. Pricing to market when the exchange rate changes. In: Arndt, S., Richardson, J.D. (Eds.), Real-financial Linkages among Open Economies. MIT Press, Cambridge, MA, pp. 49–70.
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Lothian, J.R., Taylor, M.P., 1996. Real exchange rate behavior: The recent float from the perspective of the past two centuries. Journal of Political Economy 104, 488–509. Obstfeld, M., 1993. Model trending real exchange rates. University of California Center for International and Development Economics Research Working Paper: C93-011. Obstfeld, M., Rogoff, K., 1984. Exchange rate dynamics with sluggish prices under alternative priceadjustment rules. International Economic Review 25, 159–174. OÕConnell, P.G.J., 1998. The overvaluation of purchasing power parity. Journal of International Economics 44, 1–19. Papell, D.H., Theodoridis, H., 2001. The choice of numeraire currency in panel tests of purchasing power parity. Journal of Money, Credit and Banking 33, 790–803. Parsley, D.C., Wei, S., 2001. Explaining the border effect: The role of exchange rate variability, shipping costs, and geography. Journal of International Economics 55, 87–105. Pedroni, P., 1995. Panel cointegration; asymptotic and finite sample properties of pooled time series tests, with an application to the PPP hypothesis. Indiana Working Papers in Economics No. 95-013. Pedroni, P., 2001. Purchasing power parity in cointegrated panels. Review of Economics Statistics 83, 727– 731. Pedroni, P., 2002. Panel cointegration; asymptotic and finite sample properties of pooled time series tests, with an application to the PPP hypothesis, Williams College Working Paper. Pierse, R.G., Snell, A.J., 1995. Temporal aggregation and the power of tests for a unit root. Journal of Econometrics 65, 333–345. Rogers, J., Jenkins, M., 1995. Haircuts or hysteresis, sources of movements in real exchange rates. Journal of International Economics 38, 339–360. Rogoff, K., 1996. The purchasing power parity puzzle. Journal of Economic Literature 34, 647–668. Samuelson, P.A., 1964. Theoretical notes on trade problems. Review of Economics and Statistics 46, 145– 154. Shiller, R.J., Perron, P., 1985. Testing the random walk hypothesis: Power vs. frequency of observation. NBER Working Paper No. 45. Taylor, A.M., 2002. A century of purchasing power parity. Review of Economics and Statistics 84, 139–150.
Tests of Purchasing Power Parity via cointegration analysis of heterogeneous panels with consumer price indices Michael A. Jenkins a, Sean M. Snaith a b
b,*
Department of Economics, St. Lawrence University, Canton, NY 13617, United States Business Forecasting Center, Eberhardt School of Business, University of The Pacific, 3601 Pacific Avenue, Stockton, CA 95211, United States Received 10 January 2003; accepted 7 November 2003 Available online 29 April 2005
Abstract There has been significant interest in the empirical performance of the Purchasing Power Parity (PPP) hypothesis. Initial studies were, in general, unfavorable for PPP. These results led researchers into two directions. One branch of the literature employed price data for a limited range or goods (e.g., fruits or clothing). A second branch has reevaluated the performance of PPP with more powerful methods. In this paper we combine these two branches of the literature. We use consumer price sub-indices data and recently developed panel cointegration techniques to test weak PPP. Our results are suggestive that the failure of PPP can be attributed to inclusion of non-traded goods in the overall index. Ó 2005 Elsevier Inc. All rights reserved. JEL classification: F31 Keywords: Purchasing Power Parity; Panel cointegration
* Corresponding author. Address: Business Forecasting Center, 3601 Pacific Avenue, Stockton, CA 95211, United States. E-mail addresses: [email protected] (M.A. Jenkins), ssnaith@pacific.edu (S.M. Snaith).
0164-0704/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jmacro.2003.11.020
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1. Introduction It has been well documented that the power of traditional unit root and cointegration tests is dependent on the span of data series being tested, see for example Shiller and Perron (1985) or Pierse and Snell (1995). This is problematic when limited data are available or when the data stretch across distinct regimes. Panel unit root and cointegration tests evolved specifically to address this problem of the low power of standard unit roots tests to distinguish between unit roots and near unit roots. This paper uses panel cointegration techniques developed by Pedroni (2002) to conduct disaggregated tests of the weak version of Purchasing Power Parity (PPP). Weak PPP implies that while price ratios and exchange rates move together over long periods, they may not move in direct proportion and therefore would be cointegrated but not necessarily with a cointegrating coefficient of 1.0. PedroniÕs tests allow for heterogeneous slope coefficients and for differences in the short run dynamics of the individual members of the panels. Imposing a homogeneous cointegrating vector across the individual members of the panel when this is not the true relationship will result in a component of the error term from the cointegrating relationship being integrated of order one. This will be true even if cointegration represents the true relationship and the residual should therefore be stationary. Employing PedroniÕs tests on both aggregate and disaggregate price indices, we find support in our sample for the non-traded goods explanation of the failure of weak PPP in the post-Bretton Woods era. While PPP fails to hold (we fail to reject the null hypothesis of no cointegration) for the relative consumer price index as a whole, we find evidence that cointegration does exist between the price indices of traded goods and exchange rates but not for those goods that are non-traded. Thus, we combine two approaches that have heretofore been treated separately in the literature to address the failure of PPP in the post-Bretton Woods era: application of more powerful and appropriate statistical tests and an analysis of consumer price sub-indices data.
2. Summary of relevant literature Taylor (2002) notes that studies on PPP ‘‘have appeared in abundance’’ recently. This contrasts with Froot and RogoffÕs (1995) comment that as recently as the 1980s PPP was a ‘‘fairly dull research topic.’’ While there is a good deal of debate on a number of issues regarding PPP, it is widely accepted that large deviations from PPP exist over the short to medium term. With sample periods usually confined to the post-Bretton Woods era, results suggest either a unit root in the real exchange rate or a lack of cointegration between the nominal exchange rate and prices.1 Thus, PPP is considered to be at best a long-run phenomenon. Indeed, evidence on PPP in
1 See Rogoff (1996) and Froot and Rogoff (1995) for surveys of the literature on the empirical performance of PPP.
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the long run (e.g., with time series that span a century or more) has been more favorable; see, for example, Lothian and Taylor (1996) and Abuaf and Jorion (1990).2 The failure of PPP, at least during the post-Bretton Woods period, has led to several channels of research, one of which exploits competing theoretical arguments for the failure of PPP by price data. A second channel addresses the low power of the statistical tests frequently employed by re-evaluating the data with more powerful statistical tests. Each of these two channels will be briefly discussed. Given the frequently observed failure of PPP, a number of theoretical reasons have been discussed as possible sources. Among them are non-traded goods and sticky prices. The non-traded goods explanation is discussed by Balassa (1964) and Samuelson (1964). In these models market arbitrage does not exist to ensure a common currency price for a non-traded good or service (e.g., a haircut or a Big Mac). Frequently this theory is employed to explain why common currency prices are higher in more developed countries. The higher prices in developed countries are the result of productivity shocks that increase wages, and thus prices, in the non-traded goods sector. Weak relative PPP may be consistent with a Balasa–Samuelson type model. Again, this form of PPP would be satisfied when the nominal exchange rate and aggregate price ratios are cointegrated, though not necessarily with a cointegrating vector of one. This general idea of the importance of non-traded goods and relative productivity differences on the behavior of the real exchange rate has been expanded by Hsieh (1982), Bergstrand (1991) and Obstfeld (1993). In their models, changes in the relative price of non-traded versus traded goods cause movements in the real exchange rate. Obstfeld explicitly shows that the real exchange rate can exhibit stochastic behavior that is consistent with many of the empirical findings of non-stationarity of the real exchange rate. Others (Obstfeld and Rogoff, 1984) argue that sticky goods prices are the source of deviations from PPP. Under this explanation the common currency prices of traded goods are not necessarily equal. Moreover, in these models sluggish price adjustment can lead to a finding of a unit root in the real exchange rate. Pricing-to-market models such as those of Krugman (1987) and Dornbusch (1987) also suggest the common currency prices of traded goods may not be equal. These models assume an oligopolistic market structure and price discrimination to generate the inequality of common currency prices of traded goods. Ghosh and Wolf (1994) attempt to distinguish amongst these competing explanations with data from the prices of the Economist magazine. They argue sticky prices are at least part of the explanation for the failure. Among the first to address empirically the potential relevance of non-traded goods in the failure of PPP was Engel (1993). Engel considered more than 2000 pair-wise comparisons of the relative prices of different goods within either the US or Canada versus relative prices of a common good in both countries. He found much greater short-term variation in relative prices of the same traded goods across
2
Though recently Engel (2000) questioned these results. His argument involves the inability of the econometric tests to detect a small but non-stationary component of a real exchange rate due to movements in relative prices (traded versus non-traded) within a country.
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the border than with prices of two different goods within the same country. Engel contended that those results were consistent with the sticky price model. This was followed by Rogers and Jenkins (1995) who also looked at relative prices within and across the US and Canada. They argued that relative price differentials for a common good across the border were both more volatile and more persistent than the price differentials for different goods within a country. As with Engel, they favored a sticky price explanation. These studies were followed by Engel and Rogers (1996) and Jenkins (1997) who took the consumer price sub-indices a step further by examining price data from cities within the US and Canada. This allowed for an examination of the role of distance in the performance of PPP. Both studies find distance to be important; evidence favorable to PPP is more likely to be found between two cities close to one another as opposed to two cites separated by thousands of miles. Thus, the friction of transportation costs may be relevant in the performance of PPP. Both found a significant border effect. One aspect of crossing the border is exchange rate fluctuations. This is again evidence favorable to the sticky price explanation. Parsley and Wei (2001) examined individual price data from the US and Japan and came to similar conclusions. Another branch of the literature on PPP involves more powerful statistical methods. Given the low power of time series tests to distinguish unit roots from near unit roots, attempts have been made to increase the power of these tests. As mentioned above, some studies have employed data sets that span a century or more. Another technique is to pool data across countries. Several studies have applied panel unit root tests to real exchange rates. Frankel and Rose (1996) pooled data for dozens of countries over the period 1948–1992. They argue against a unit root in real exchange rates; i.e., they find evidence of mean reversion in real exchange rates. In particular, they contend that, on average, movements in real exchange rates (deviations from PPP) have half-lives of four years. OÕConnell (1998) also pools data over dozens of countries for a sample period of the post-Bretton Woods era. He also contends that real exchange rates are stationary. He also argues that this result holds on a continental basis, pooling over countries in Europe or Asia only. Traditional tests on panel unit roots in real exchange rates implicitly may impose a cointegrating vector, which is constrained to be both equal to one and homogenous across panel members. Again, testing weak relative PPP does not require restriction on the value of the cointegrating vector, just that exchange rates and relative price levels be cointegrated. Pedroni (2002) has devised a panel cointegration technique that allows for heterogeneous cointegrating vectors. Thus, with this technique, the cointegrating vector need not equal 1, and furthermore it need not be equal across country pairs. Pedroni (1995) and Canzoneri et al. (1999) employ this test and argue that nominal exchange rates and relative aggregate prices are cointegrated for a sample of industrialized countries. Thus, weak PPP holds. Two recent papers by Crucini et al. (2000) and Imbs et al. (2002) are closely related to the current study. Imbs et al. (2002) analyze data from the same source employed in this study. The authors find that the persistence of deviations from PPP can be largely attributed to the failure to account for the heterogeneity in the
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dynamics of relative sectoral prices and the resultant bias of econometric techniques that aggregate this heterogeneous sectoral data. Crucini et al. (2000) examine price data for over 1800 retail goods and services for 13 European countries from a 1985 Eurostat survey. The authors find support for the role of tradeabiltiy of both final goods and the inputs required to produce the goods in explaining price dispersion. The current study, which uses a panel data approach on price indices, may be viewed as an extension of these authorsÕ analysis.
3. The Pedroni statistics Pedroni (2002) develops a set of five statistics based on the following standard panel regression: y it ¼ ai þ di þ bi X it þ eit
ð1Þ
where yit and Xit are panels of observations over the members of the panel from i = 1, . . . , N and time periods t = 1, . . . , T and where Xit and bi are column and row vectors of m-dimension for each member of the panel. The variables yit and Xit are assumed to be integrated of order one (I(1)). The parameters ai and di allow for fixed effects and deterministic trends specific to each member. The null and alternative hypotheses examined are as follows: H0: All of the individuals of the panel are not cointegrated versus H1: A significant portion of the individuals are cointegrated. Under the null hypothesis, eit I(1) and under the alternative hypothesis eit I(0). The first set of three panel statistics is based on pooling the data along the within dimension of the panel. This involves summing the numerator and denominator terms of each statistic separately for the analogous times series statistics. The definitions of the panel variance ratio, panel rho and panel t statistics for a null of no co-integration in heterogeneous panels are given as follows: !1 N X T X 2 ^eit1 Panel variance ratio statistic: Z ^vNT L211 i¼1
Panel rho statistic:
Z q^NT 1
N X T X i¼1
Panel t statistic:
Z tNT
~2NT r
i¼1
!1 ^e2it1
t¼1
N X T X t¼1
t¼1
i¼1
!12 ^e2it1
N X T X ð^eit1 D^eit1 ki Þ
ð2Þ
t¼1
N X T X ð^eit1 D^eit1 ki Þ. i¼1
t¼1
The second set of statistics is based on pooling the data along the between dimension of the panel. The method used to construct these statistics involves calculating the ratio that corresponds to the conventional time series statistic and then computing the standardized sum of the ratio over the cross-section of the panel. These two group mean statistics are given below.
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Group rho statistic:
e q^ Z NT 1
N T X X i¼1
Group t statistic:
e tNT Z
N T X X i¼1
t¼1
!1 ^e2it1
t¼1
ð^eit1 D^eit1 ki Þ
t¼1
!12 r2 e2it1 i ^
T X
ð3Þ T X
ð^eit1 D^eit1 ki Þ:
t¼1
In the statistics given in Eqs. (2) and (3), ^eit is the residual from Eq. (1), P ~NT N 1 Ni¼1 r2i ; ki ¼ 12 ðr2i s2i Þ where r2i is the long run variance and s2i is the r individual contemporaneousPvariance of the residuals from the following equation ^eit ¼ qi^eit1 þ lit ; L211 ¼ N 1 Ni¼1 L211i . L11i is obtained by lower triangular decomposition of the asymptotic covariance matrix Xi and is given by L11i ¼ ðX11i 1 2 X021i X1 22i X21i Þ . These statistics are formed to take into account heterogeneity of the cointegrating vector for the members of the panel. Pedroni (2002) notes that asymptotic distribution properties of residual based tests of panel cointegration are dramatically affected by the averaging over in the cross-section dimension in these statistics. The estimated regressor effect in the estimation of panels will depend on whether or not the coefficients of the hypothesized cointegration relationship are constrained to be homo- geneous across the individual members of the panel. In the case where this relationship is allowed to vary, this may lead to a non-convergent test statistic as sample size increases. If no adjustments are made in this case it may lead to the rejection of the null hypothesis of no cointegration, regardless of the true relationship. On the other hand, if homogeneity of the cointegrating vectors is falsely imposed this will result in a portion of the residual that is integrated even when cointegration is the true relationship. Pedroni conducts Monte Carlo experiments on these five statistics and the results imply a rule of thumb in their application. The group rho statistic is best used when working with small panels, while the panel variance ratio statistic has the highest power relative to the other statistics for large panels. The other statistics fall into a range whose bounds are defined by the group rho and panel variance ratio statistics. For additional details on the derivation and asymptotics of these statistics, as well as the results of the Monte Carlo experiments see Pedroni (2002).
4. Data and analysis In our case the cointegrating regression we are interested in is expressed in Eq. (4). sit ¼ ai þ bi pkit þ eit :
ð4Þ
Here sit is the log of the nominal exchange rate at time t for country pair i, and pkit is the log relative price index differential for each country pair, for price index k. A total of 26 panels are formed using each of the price indices and sub-indices. These panels are then subsequently used to test the weak form of purchasing power parity.
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Unlike the strong form of long run purchasing power parity which requires that the exchange rate and relative prices be cointegrated with bi = 1, the weak version of long run PPP only requires that cointegration exist, a less stringent test of the theory. Specifically with the panel tests, the null hypothesis can be interpreted as ‘‘weak PPP does not hold for all members of the panel’’ while the alternative can be interpreted as, ‘‘weak PPP holds for a significant portion of the individuals in the panel’’. Using consumer price index and sub-index data, we hope to shed light on the role of nontraded goods in explaining the failure to find empirical evidence for PPP in the postBretton Woods era. Our initial analysis is conducted using monthly data from the Eurostat’s New Coronos data set. With this data set, we sought to maximize the number of observations along three dimensions: time period, number of countries and number of sub-indices. With this goal, our sample includes eleven countries for the period covering 1981:01 through 1995:06 for 26 price series (the aggregate CPI and 25 sub-indices). The sample was selected to ensure as complete a panel data set as possible and to end before the harmonization of price data that took place in the European Union in 1996.3 As pre-harmonized data, the goods categories are not always measuring the same items. For example, some countries include restaurant meals in the food category while others do not. Thus, the various categories of goods we consider are measuring prices of similar, but not necessarily identical, goods. Our study, though an improvement over analyzing aggregate CPI data, is still limited by the problem of aggregation bias remaining in the sub-indices.4 The countries in our sample group include Belgium, Denmark, Germany, Greece, Spain, France, Italy, Luxemburg, Netherlands, United Kingdom and the United States.5 The data were used to construct panels consisting of 54 cross-sectional members.6 Exchange rate data are monthly averages from the Federal Reserve Bank of St. LouisÕs FRED. Prior to evaluating these panel relationships, we first consider the time series properties of the data. Specifically we check for the presence of panel unit roots in sit and pkit ; using Levin-Lin and Im, Pesaren and Shin tests. The results are reported in Table 1. These results suggest that the panel exchange rates and panel consumer price indices used for subsequent cointegration analysis are consistent with the null of non-stationarity. Crucini and Shintani (2002), using micro-data on 270 comparable goods, reject the null hypothesis of a unit root in the real exchange rate for between 96% and 100% of the goods used in their study. This result in part contradicts some of our findings, but may be attributable to differences in data (their micro-data versus our price index data) as well as difference in the sample periods analyzed.
3
In 1993 the European Commission initiated the creation of a harmonized index of consumer prices (HIPC). It did so in coordination with the member state statistical agencies. The new harmonized series began January 1996. 4 See Crucini et al. (2000) and Parsley and Wei (2001) for studies which do employ absolute price for comparable individual goods and services. 5 Unfortunately, some European countries, notably Austria, Portugal, Ireland, Sweden and Finland either did not have data for some of the sub-indices or the data began at a later date. For this reason these countries were excluded. 6 The country pair of Belgium and Luxembourg is omitted due to their common currency.
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Table 1 Panel unit root tests Type of goods
L-L rho
L-L t–rho
L-L ADF
IPS ADF
Number of rejections *
**
#
Erate 1000 1110 1111 1112 1114 1116 1140 1150 1160 1200 1210 1220 1300 1310 1330 1410 1420 1600 1610 1630 1700 1710 1720 1730 1800 1830
0.16 2.16 3.18 0.43 0.57 0.15 1.66 1.51 0.82 0.98 0.90 1.63 0.43 1.23 0.22 0.84 1.48 0.72 1.95 4.42* 1.72 0.84 0.11 0.10 1.63# 0.12 1.34
1.12 0.57 0.86 1.05 1.26 1.91** 0.80 2.65 1.20 1.87 0.01 0.97 2.09** 0.12 0.19 0.45 0.90 1.32 0.76 1.56# 1.28 0.95 1.31 0.60 1.54# 0.83 0.30
1.46# 1.76 1.10 1.69 1.96 0.58 1.87 1.62# 1.14 0.36 0.98 0.19 0.12 0.94 0.18 0.16 1.68 0.71 0.34 1.42 1.15 1.04 1.40 0.07 1.07 0.93 1.92
2.24** 0.93 1.28 0.47 1.97 0.96 1.19 0.15 0.63 0.60 2.31 1.75** 0.08 1.25 0.73 0.31 1.88 2.09** 1.30# 0.34 0.83 0.97 0.83 1.88 1.08 1.22 1.39
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0
2 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 2 0 0 0 0 2 0 0
The column entitled Ônumber of rejectionsÕ list the total number of the four statistics that reject the null of a panel unit root at each level of significance, where *, ** and # represent the 1%, 5% and 10% levels of significance.
The results of the panel cointegration tests are reported in Table 2. The first three columns of statistics in each table display the panel statistics with a parametric panel augmented Dickey–Fuller statistic in the fourth column included for comparison purposes. The next two are the group statistics again followed by the parametric ADF version of this type of statistic. The normally distributed statistics listed in these tables have been standardized using the variances given in Pedroni (2002); thus, they are distributed as standard normal under the null hypothesis of no cointegration. For large negative values of these statistics the null hypothesis will be rejected, with the exception of the panel variance ratio statistic, which rejects the null hypothesis for large positive values of the statistic. The last column summarizes the results of the hypothesis tests in each row. These values indicate the number of rejections of the null hypothesis at the 1%, 5% and 10% levels of significance.
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Table 2 Panel cointegration tests Type of goods
1000 1110 1111 1112 1114 1116 1140 1150 1160 1200 1210 1220 1300 1310 1330 1410 1420 1600 1610 1630 1700 1710 1720 1730 1800 1830
Panel v-stat
5.00* 6.09* 3.90* 3.88* 2.19** 0.42 0.01 2.69* 2.04** 2.63* 2.07** 1.89** 1.79** 1.67** 2.46* 3.28* 2.34* 2.18** 2.12** 0.81 5.19* 2.31** 2.31** 3.69* 3.11* 1.88**
Panel rho-stat
0.93 3.33* 4.20* 2.54* 2.03** 19.69* 6.34* 2.56* 1.67** 7.58* 6.95* 6.33* 0.77 1.60# 5.46* 1.77** 3.67* 1.18 4.03* 5.80* 1.88** 4.21* 1.35# 3.11* 2.12** 0.94
Panel PP-stat
0.51 2.50* 3.67* 1.59# 2.06** 12.07* 5.46* 2.40* 1.90** 6.56* 6.15* 5.58* 1.27 1.44# 5.24* 2.05** 3.87* 1.46# 2.60* 5.24* 1.35# 3.58* 0.93 2.72* 1.62# 1.27
Panel ADF-stat
0.46 1.63# 2.15** 0.36 1.41# 0.25 0.19 0.99 1.69** 0.87 1.17 1.29# 0.90 0.31 1.57** 0.56 2.30** 0.75 0.01 2.51* 1.42# 1.08 0.29 1.75** 0.86 0.31
Group rho-stat
0.67 1.40# 1.96** 0.23 0.19 14.63* 2.01** 0.66 0.32 7.02* 6.11* 6.44* 0.05 0.56 5.59* 4.31* 6.95* 0.27 3.58* 3.74* 0.87 4.15* 0.38 3.35* 2.73* 0.88
Group PP-stat
0.45 1.35# 2.38* 0.01 1.17 10.20* 2.65* 0.83 1.16 6.04* 5.51* 4.65* 0.76 1.01 5.54* 4.88* 5.30* 0.47 2.28** 3.92* 0.84 3.46* 0.66 2.87* 1.89* 0.67
Group ADF-stat
0.26 1.40# 1.93** 0.11 1.71** 0.67 1.14 0.64 2.20** 1.49# 1.68** 0.96 0.47 0.08 1.42# 0.06 7.58* 0.41 0.27 2.02** 1.47# 0.84 0.46 2.80* 1.84* 0.20
Number of rejections *
**
#
1 3 4 2 0 4 3 3 0 5 4 4 0 0 5 3 6 0 2 5 1 4 0 6 4 0
1 3 7 2 4 4 3 3 5 5 6 5 1 1 6 5 7 1 5 6 2 5 1 7 5 1
1 7 7 3 5 4 4 3 5 6 6 6 1 3 7 5 7 2 5 6 5 5 2 7 6 1
Statistics reported in this table are generated from the following cointegrating regression: sit ¼ ai þ bi pkit þ eit and test the following hypothesis: H0: All of the individuals of the panel are not cointegrated (Weak PPP does not hold.). H1: A significant portion of the individuals are cointegrated (Weak PPP holds for a significant portion of the panel.). The column entitled Ônumber of rejectionsÕ list the total number of the seven statistics that reject the null at each level of significance, where *, ** and # represent the 1%, 5% and 10% levels of significance. The Eurostat goods categories are: 1000 All goods, 1100 Food, 1111 Bread and cereals, 1112 Meat, 1114 Dairy products, 1116 Fruits, 1140 Tobacco, 1150 Alcoholic and non-alcoholic drinks, 1160 Drink and tobacco, 1200 Clothing and footwear, 1210 Clothing, 1220 Footwear, 1300 Shelter, 1310 Rents, 1330 Fuels and energy, 1410 Furniture, 1420 Domestic appliances, 1600 Transport and communications, 1610 Vehicles, 1630 Public transport, 1700 Recreation, 1710 Sound and photographic equipment, 1720 Leisure, 1730 Books, 1800 Other goods and services, 1830 Hotels.
The first notable outcome is that the results for the aggregate CPI show a failure to reject the null hypothesis of cointegration that weak PPP does not hold for the
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panels constructed with this index. The sole exception to this result is with the panel variance statistic, which, as discussed earlier may lack the power to reject the null in our panel. This suggests that PPP as traditionally defined (i.e., with the aggregate CPIs) does not hold. Next, we consider the sub-indices. For example, the results for series 1111, breads and cereals, highly traded commodities, indicate a strong rejection of the null of no cointegration. This result supports the notion that weak PPP does in fact hold for this type of good. The other indices for food, drink and tobacco as well show support for the weak version of PPP. The panels constructed with the price indices for meat, dairy products, fruits, alcoholic and non-alcoholic drinks and tobacco all indicate rejection of the null hypothesis of no cointegration. There are several more results of a similar nature. Clothing and footwear (series 1200) and each of the component sub-indices (1210 and 1220) all show consistent rejection of the null hypothesis. Panels formed for fuels and energy, domestic appliances, vehicles and sound and photographic equipment generate values for several of the statistics that lead to rejection of the null hypothesis in favor of weak PPP. The categories that generate results that are supportive of weak PPP holding across our panel of countries are all by and large goods that are generally traded internationally. There are several panels that generate results that fail to support weak PPP; we now turn our attention to these goods and services. The two most obviously non-traded goods in our analysis are series 1310 and 1830 indices measuring rents and the prices of hotels. Since these commodities are clearly not subject to the trade arbitrage that is the underpinning of PPP, the results of the cointegration tests derived from the panels built using these indices are not surprising. For almost all statistics and levels of significance we fail to reject the null hypothesis of no cointegration for these commodities. For the more inclusive shelter index, series 1300, the results are similar. The results from the panel formed using the transport and communications index, series 1600, also show very little support for weak PPP. Several of the categories warrant further explanation, especially given that most of the country pairs in our sample are between two EU states. Evidence on food items may be difficult to interpret given the substantial government intervention in agricultural markets in Europe (under the common agricultural policy – CAP). For example, during the 1980s the European Commission made use of the so-called ‘‘green’’ exchange rates to provide monetary compensatory amounts (MCAs) to farmers. As noted by Fennell (1987), this practice, which included a great deal of fluctuations in the size of MCAs, often generated sizable gaps in the common currency prices of agricultural items in Europe. Also, our sample includes the introduction of the MacSharry reforms, which substantially altered agricultural support methods and payments to farmers. Yet in spite of the interventions, our results are generally supportive of PPP for food items. Another category, which merits special attention, is automotive goods, which are included in the ‘‘vehicles’’ category in our study. The European Commission over our sample period granted the automotive industry an exemption from its competition
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policy.7 This allowed automobile makers to segment the European market along member state borders by way of dealer restrictions on servicing contracts. For example, the European CommissionÕs survey of automobile prices in November 2001 reported frequent price differences across member states on identical cars of twenty percent or more (see European Commission, 2002). Thus, our results only suggest that common currency prices in the automotive sector move together, not that they are equal. While we do find evidence favorable to PPP with many categories of tradeable goods, this is not necessarily the case for non-traded goods. A category that stands out is shelter. In general, we do not reject the null of no cointegration for this category. Moreover, this category is significant in that for many countries it accounts for up to twenty percent of the aggregate CPI, large enough perhaps that the failure of prices in this category to move together may drive our finding that aggregate prices fail to move together as well. Our initial analysis focused on monthly data for the country set previously described. We now turn to evaluating the robustness of these results. In particular, we modify our sample group of countries to consider the possibility, as suggested by Parsley and Wei (1996) and others, that explanations for the failure of PPP may be a function of the country set analyzed. In order to investigate this possibility, we consider cross-sections using a single country as the numeraire (Belgium), and an EUonly subset of our original countries. Additionally we considered other periodicities of data, analyzing both quarterly and annual data in addition to the monthly data. To summarize our findings, the qualitative results of the original panel are reaffirmed throughout analysis of these alternative panels. Pedroni (2001) notes that with such data employed in this study there may be violation of the condition of independence of individual members of the panel. We employ a common technique to deal with this type of dependency, subtracting out individual time means. Thus, for the results presented in Table 3 the estimated panel becomes _ s it
_k
¼ ai þ bi p it þ eit
where
_
s it ¼ sit T 1
T X
sit
t¼1
and
_k p it
¼ pkit T 1
T X
pkit .
ð5Þ
t¼1
The results from both demeaned and unadjusted panels, however, paint a similar picture. Next we address the bilateral country construction of the panels. Initially we considered all bilateral combinations (exempting Belgium/Luxembourg). OÕConnell (1998) suggests that under certain conditions in panel tests all information is contained using only one country as a numeraire. That is, one need only compare each country with one other country, say Belgium, not with every other country. We initially used all bilateral comparisons because Papell and Theodoridis (2001) have 7
This exemption continues to the present, though recently there has been much discussion of ending it.
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Table 3 Panel cointegration tests (demeaned series) Type of goods
1000 1110 1111 1112 1114 1116 1140 1150 1160 1200 1210 1220 1300 1310 1330 1410 1420 1600 1610 1630 1700 1710 1720 1730 1800 1830
Panel v-stat
4.90* 5.60* 5.03* 4.17* 2.52* 0.65 0.59 2.96* 2.32** 2.53* 2.16** 1.89** 2.65* 0.24 3.73* 1.59# 1.69* 2.81* 0.50 0.78 6.11* 0.86 1.12 4.29* 3.50* 0.37
Panel rho-stat
0.74 2.52* 4.49* 2.71* 1.79** 17.92* 5.55* 2.35* 1.27# 6.82* 6.31* 6.33* 1.28 0.12 6.29* 2.90* 2.65* 1.39# 2.22** 4.42* 2.67* 1.76** 1.80* 2.93* 2.63* 0.03
Panel PP-stat
0.26 1.79** 3.70* 1.85** 1.71** 11.22* 4.52* 2.21** 1.51# 5.83* 5.36* 5.58* 1.50# 0.46 5.49* 2.87* 2.81* 1.54# 1.55# 4.23* 2.05** 1.78** 1.75** 2.49* 2.34* 0.13
Panel ADF-stat
0.94 1.14 2.51* 1.19 1.39# 0.62 0.61 1.03 1.82** 1.30# 1.38# 1.29# 1.60# 0.43 2.27** 1.15 0.64 0.51 0.67 2.18** 2.25** 0.51 0.42 2.13** 2.07* 0.34
Group rho-stat
0.99 0.25 1.80** 0.54 0.19 12.75* 2.88** 1.03 0.02 7.43* 6.65* 6.44* 0.25 0.54 5.52* 5.19* 7.13* 0.16 2.01** 1.62# 1.36# 3.72* 1.76** 2.73* 3.98* 1.49#
Group PP-stat
0.77 0.53 2.25** 0.47 0.59 8.98* 3.34* 1.28 0.85 6.00* 5.34* 4.65* 0.53 1.22 5.27* 5.78** 5.50* 0.74 2.00** 2.92* 1.51# 3.27* 2.57* 2.60* 3.08* 0.95
Group ADF-stat
0.15 0.18 1.42# 0.27 1.21 0.29 1.31# 1.16 2.10** 2.31** 2.27** 0.96 0.81 0.15 1.88** 1.63# 0.31 0.39 0.60 0.98 2.09** 0.02 0.41 2.48* 3.21* 0.72
Number of rejections *
**
#
1 2 4 2 1 4 3 2 0 5 4 4 1 0 5 3 5 0 0 3 2 2 2 6 7 0
1 3 6 3 3 4 4 3 3 6 6 5 3 0 7 4 5 1 3 4 5 4 4 7 7 0
1 3 7 3 4 4 5 3 5 7 7 6 3 0 7 6 5 3 4 5 7 4 4 7 7 1
Statistics reported in this table are generated from the following cointegrating regression: _ s it
_k
¼ ai þ bi p it þ eit
and test the following hypothesis: H0: All of the individuals of the panel are not cointegrated (Weak PPP does not hold.). H1: A significant portion of the individuals are cointegrated (Weak PPP holds for a significant portion of the panel.). The column entitled Ônumber of rejectionsÕ list the total number of the seven statistics that reject the null at each level of significance, where *, ** and # represent the 1%, 5% and 10% levels of significance. The Eurostat goods categories are: 1000 All goods, 1100 Food, 1111 Bread and cereals, 1112 Meat, 1114 Dairy products, 1116 Fruits, 1140 Tobacco, 1150 Alcoholic and non-alcoholic drinks, 1160 Drink and tobacco, 1200 Clothing and footwear, 1210 Clothing, 1220 Footwear, 1300 Shelter, 1310 Rents, 1330 Fuels and energy, 1410 Furniture, 1420 Domestic appliances, 1600 Transport and communications, 1610 Vehicles, 1630 Public transport, 1700 Recreation, 1710 Sound and photographic equipment, 1720 Leisure, 1730 Books, 1800 Other goods and services, 1830 Hotels.
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Table 4 Panel cointegration tests (Belgium as numeraire country) Type of goods
1000 1110 1111 1112 1114 1116 1140 1150 1160 1200 1210 1220 1300 1310 1330 1410 1420 1600 1610 1630 1700 1710 1720 1730 1800 1830
Panel v-stat
2.70* 3.26* 1.93# 1.16 2.14** 1.72# 0.71 2.02** 1.28 1.00 2.05** 2.32** 0.89 0.67 2.97* 2.06** 2.05** 2.69* 1.82# 1.95 1.31 0.95 1.36 0.96 1.97** 1.46
Panel rho-stat
1.28 3.38* 5.86* 3.42* 2.73* 6.95* 1.01 9.38* 1.22 0.55 3.33* 1.00 0.56 1.21 2.79* 2.26** 1.18 1.23 2.79* 3.44* 0.72 3.62* 0.85 0.65 2.14** 0.94
Panel PP-stat
1.14 2.80* 4.36* 2.72* 2.33** 4.71* 2.21** 5.42* 1.33 0.54 5.62* 1.63 1.13 0.96 2.32** 2.40** 1.99** 0.16 2.82* 2.90* 0.70 3.03* 1.67# 1.64 1.71# 1.03
Panel ADF-stat
1.30 2.40** 2.21** 1.23 1.89# 1.88# 1.61 2.33** 0.53 2.95* 1.31 2.29** 0.69 0.75 0.38 1.67# 2.55** 0.57 1.79# 1.70# 1.31 1.55 2.24** 2.35** 1.91# 0.66
Group rho-stat
0.54 2.65* 4.50* 2.06** 1.73# 5.71* 0.07 4.57* 0.52 2.10** 6.83* 0.28 1.99# 0.32 2.66* 1.68# 0.41 0.30 2.02** 2.56** 0.06 4.24* 0.40 0.30 1.43 0.05
Group PP-stat
0.91 2.61* 3.88* 2.37** 2.06** 4.85* 1.49 2.62* 1.18 1.83# 4.30* 0.71 1.82# 0.13 2.40** 2.58* 1.71 0.58 2.15** 2.69** 0.60 3.78* 0.90 0.99 1.70# 1.04
Group ADF-stat
1.28 2.62* 2.82* 1.22 2.47** 2.21** 0.81 2.31** 1.57 1.99# 1.52 1.89# 0.82 0.90 1.24 1.95# 2.70* 0.11 2.13** 1.75# 1.84# 1.93# 1.68# 2.57** 2.89* 1.23
Number of rejections *
**
#
1 6 5 2 1 4 0 4 0 1 4 0 0 0 3 1 1 1 2 2 0 4 0 0 1 0
1 7 6 4 5 5 1 7 0 2 5 2 0 0 5 5 4 1 5 4 0 4 1 2 3 0
1 7 7 4 7 7 1 7 0 4 5 3 2 0 5 7 4 1 7 6 1 5 3 2 6 0
Statistics reported in this table are generated from the following cointegrating regression: sit ¼ ai þ bi pkit þ eit and test the following hypothesis: H0: All of the individuals of the panel are not cointegrated (Weak PPP does not hold.). H1: A significant portion of the individuals are cointegrated (Weak PPP holds for a significant portion of the panel.). The column entitled Ônumber of rejectionsÕ list the total number of the seven statistics that reject the null at each level of significance, where *, ** and # represent the 1%, 5% and 10% levels of significance. The Eurostat goods categories are: 1000 All goods, 1100 Food, 1111 Bread and cereals, 1112 Meat, 1114 Dairy products, 1116 Fruits, 1140 Tobacco, 1150 Alcoholic and non-alcoholic drinks, 1160 Drink and tobacco, 1200 Clothing and footwear, 1210 Clothing, 1220 Footwear, 1300 Shelter, 1310 Rents, 1330 Fuels and energy, 1410 Furniture, 1420 Domestic appliances, 1600 Transport and communications, 1610 Vehicles, 1630 Public transport, 1700 Recreation, 1710 Sound and photographic equipment, 1720 Leisure, 1730 Books, 1800 Other goods and services, 1830 Hotels.
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Table 5 Panel cointegration tests (European countries only) Type of goods
1000 1110 1111 1112 1114 1116 1140 1150 1160 1200 1210 1220 1300 1310 1330 1410 1420 1600 1610 1630 1700 1710 1720 1730 1800 1830
Panel v-stat
4.20 4.91* 3.67* 3.17* 1.82# 1.90# 6.87* 2.52** 1.45 2.76* 2.14** 2.24** 1.36 1.89# 2.25** 6.68* 5.18* 2.48** 1.66# 0.55 4.27* 3.77* 1.30 3.12* 2.32** 3.20*
Panel rho-stat
0.59 2.45** 3.59* 2.45** 2.42** 10.54* 6.13* 0.91 1.01 8.71* 7.96* 7.48* 0.29 0.87 4.41* 6.30* 5.34* 0.84 2.45** 5.65* 1.28 8.43* 0.80 2.58* 1.41 0.83
Panel PP-stat
0.07 1.70# 2.87* 1.66# 2.45** 7.00* 4.58* 1.68# 1.01 6.95* 6.49* 6.02* 0.38 0.51 4.12* 5.17* 4.09* 0.73 1.24 4.66* 0.75 6.17* 0.13 2.04** 0.76 0.46
Panel ADF-stat
0.53 1.35 0.72 0.64 2.18** 0.83 0.81 3.12* 1.18 1.00 1.18 0.73 0.28 0.16 2.69* 2.26** 0.78 0.63 0.43 1.49 1.28 1.02 0.62 2.07** 0.23 0.54
Group rho-stat
0.74 0.94 2.04** 0.33 1.04 9.08* 6.28* 0.52 0.15 8.49* 7.49* 7.71* 0.52 1.34 4.49* 7.73* 7.69* 0.27 1.30 4.33* 0.51 8.79* 1.02 3.38* 2.84* 0.70
Group PP-stat
0.82 0.76 1.71# 0.22 1.84# 6.00* 5.06* 2.27** 0.44 6.73* 6.17* 5.24* 0.88 0.31 4.28* 6.05* 4.91* 0.06 0.41 3.50* 0.29 6.53* 0.97 2.50** 1.31 0.47
Group ADF-stat
0.04 1.02 0.69 0.25 2.64* 0.98 0.21 2.06** 1.72# 1.78# 1.80# 0.61 0.24 0.32 2.45** 2.96* 2.03** 0.01 0.10 0.72 1.34 1.20 0.22 3.26* 1.22 0.22
Number of rejections *
**
#
1 1 3 1 1 4 5 1 0 5 4 4 0 0 5 6 5 0 0 4 1 5 0 4 1 1
1 2 4 2 4 4 5 4 0 5 5 5 0 0 7 7 6 1 1 4 1 5 0 7 2 1
1 3 5 3 6 5 5 5 1 6 6 5 0 1 7 7 6 1 2 4 1 5 0 7 2 1
Statistics reported in this table are generated from the following cointegrating regression: sit ¼ ai þ bi pkit þ eit and test the following hypothesis: H0: All of the individuals of the panel are not cointegrated (Weak PPP does not hold.). H1: A significant portion of the individuals are cointegrated (Weak PPP holds for a significant portion of the panel.). The column entitled Ônumber of rejectionsÕ list the total number of the seven statistics that reject the null at each level of significance, where *, ** and # represent the 1%, 5% and 10% levels of significance. The Eurostat goods categories are: 1000 All goods, 1100 Food, 1111 Bread and cereals, 1112 Meat, 1114 Dairy products, 1116 Fruits, 1140 Tobacco, 1150 Alcoholic and non-alcoholic drinks, 1160 Drink and tobacco, 1200 Clothing and footwear, 1210 Clothing, 1220 Footwear, 1300 Shelter, 1310 Rents, 1330 Fuels and energy, 1410 Furniture, 1420 Domestic appliances, 1600 Transport and communications, 1610 Vehicles, 1630 Public transport, 1700 Recreation, 1710 Sound and photographic equipment, 1720 Leisure, 1730 Books, 1800 Other goods and services, 1830 Hotels.
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Table 6 Panel cointegration tests (annual observations) Type of goods
1000 1110 1111 1112 1114 1116 1140 1150 1160 1200 1210 1220 1300 1310 1330 1410 1420 1600 1610 1630 1700 1710 1720 1730 1800 1830
Panel v-stat
2.44** 2.17** 2.04** 3.63* 4.01* 4.76* 1.81# 2.77* 4.72* 3.22* 3.55* 4.18* 0.66 1.07 3.98* 0.56 1.16 1.06 1.82# 4.41* 3.72* 1.89# 0.98 3.42* 6.20* 0.32
Panel rho-stat
1.17 1.26 1.81# 0.99 1.25 0.52 0.39 1.24 0.79 0.16 0.69 0.08 0.59 1.44 0.82 0.20 0.48 0.01 0.97 1.13 0.39 0.88 1.51 0.75 0.09 1.29
Panel PP-stat
2.53** 3.45* 2.74* 3.86* 2.20** 4.16* 4.52* 3.14* 3.84* 4.37* 4.01* 4.99* 0.90 2.87* 4.39* 4.97* 6.40* 1.37 3.20* 3.36* 4.31* 3.15* 2.84* 4.31* 4.04* 0.23
Panel ADF-stat
0.39 1.28 1.90# 3.96* 2.12** 2.87* 3.09* 1.95# 2.37** 3.36* 3.53* 4.83* 0.34 1.23 3.49* 3.61* 4.49* 0.11 1.28 2.47** 2.32** 1.13 0.18 3.33* 3.14* 0.08
Group rho-stat
1.32 1.05 4.21* 3.56* 3.99* 3.54* 3.38* 3.96* 3.58* 3.23* 3.73* 3.03* 2.65* 4.04* 4.05* 2.91* 2.38** 2.09** 3.39* 4.22** 2.91* 3.19* 4.18* 3.67* 2.95* 3.49*
Group PP-stat
2.16** 3.71* 1.77# 2.42** 0.54 2.05** 3.78* 1.68# 2.58* 2.74* 2.24** 3.72* 1.77 2.02** 2.04** 3.94* 5.32* 0.78 2.59* 1.22 3.49* 3.00* 1.75# 2.65* 3.11* 0.08
Group ADF-stat
0.56 2.58* 1.43 4.43* 2.55** 2.25** 3.93* 0.78 2.22* 2.89* 1.84# 4.51* 0.12 0.59 0.87 4.46* 6.40* 0.28 1.29 1.23 3.44* 1.15 0.55 2.41** 3.52* 1.00
Number of rejections *
**
#
0 3 2 4 2 4 5 3 5 6 4 6 1 2 4 5 4 0 3 2 5 3 2 5 6 1
3 4 3 6 5 6 5 3 6 6 5 6 1 3 5 5 5 1 3 4 6 3 2 6 6 1
3 4 6 6 5 6 6 5 6 6 6 6 2 3 5 5 5 1 4 4 6 4 3 6 6 1
Statistics reported in this table are generated from the following cointegrating regression: sit ¼ ai þ bi pkit þ eit and test the following hypothesis: H0: All of the individuals of the panel are not cointegrated (Weak PPP does not hold.). H1: A significant portion of the individuals are cointegrated (Weak PPP holds for a significant portion of the panel.). The column entitled Ônumber of rejectionsÕ list the total number of the seven statistics that reject the null at each level of significance, where *, ** and # represent the 1%, 5% and 10% levels of significance. The Eurostat goods categories are: 1000 All goods, 1100 Food, 1111 Bread and cereals, 1112 Meat, 1114 Dairy products, 1116 Fruits, 1140 Tobacco, 1150 Alcoholic and non-alcoholic drinks, 1160 Drink and tobacco, 1200 Clothing and footwear, 1210 Clothing, 1220 Footwear, 1300 Shelter, 1310 Rents, 1330 Fuels and energy, 1410 Furniture, 1420 Domestic appliances, 1600 Transport and communications, 1610 Vehicles, 1630 Public transport, 1700 Recreation, 1710 Sound and photographic equipment, 1720 Leisure, 1730 Books, 1800 Other goods and services, 1830 Hotels.
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shown that empirically, for OECD countries, OÕConnellÕs conditions are not met and that panel tests on PPP are sensitive to the choice of the base country. However, for the purpose of comparison we perform the panel tests with the panels constructed with each country versus Belgium. The results are in Table 4. These results are quite similar to our initial set of results. Our next test is to address the inclusion of the US in our sample. Initially the US was included because we wanted, given our data set, to maximize the cross-section included in our panels. However, it should be noted that countries other than the US are all EU countries. They share geographic proximity and have relatively few official impediments to trade. In Table 5 we report the results from panel tests with an EU nations sample only. Again, these results are qualitatively similar to the initial results. Our final modification is to examine the results of our analysis using data of lower frequency. Multiple studies have examined the convergence toward PPP and the results indicate persistence in the deviations from PPP. Much of the literature indicates a half-life in the real exchange rate on the order of three to five years. More recent analysis by Imbs et al. (2002) and Crucini and Shintani (2002) find much shorter half-lives of around one year. All of these studies reaffirm the fact that the trade that drives PPP takes time and thus our results from monthly data may differ if data of different periodicities are employed. Thus, we re-evaluate our panel tests with annual and quarterly data in addition to monthly data. The annual results are reported in Table 6; quarterly results are not reported here for space considerations, but are available upon request. The trend in our results as we move from monthly to quarterly to annual data is that we are, in general, more likely to reject the null hypothesis of no cointegration across all panels. However, we still find that the evidence is not favorable to PPP using the aggregate CPIs but is more favorable toward PPP with traded goods sub-indices than with non-traded goods sub-indices. Thus, the non-traded goods explanation for the failure of weak PPP is upheld using these data sets and techniques.
5. Conclusions Using panel cointegration techniques we tested the validity of the weak version of Purchasing Power Parity using 26 panels formed from consumer price indices and sub-indices. Our results indicate that the failure to find cointegration evidence for weak PPP in the post-Bretton Woods era using aggregate CPI data is not necessarily a function of the low power of traditional time series tests for cointegration or unit roots. Instead, we find that the failure of PPP with the overall price index can be directly attributed to inclusion of non-traded goods in these aggregate indices. For those goods that can be characterized as highly traded between the members of our panel, we find evidence in support of weak PPP. However, for those goods and services that are not traded, we find very little evidence in support of weak PPP. Weak PPP does not imply a specific value of the cointegrating vector, just that relative prices and exchange rates be cointegrated. Future work will focus on the
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specific values of the estimated cointegrating vectors for the country pairs and panels analyzed in this study to see if there is support for the strong version of PPP within any of these panels. We also find differences in our results that appear to be systematically related to the periodicity of the data. The general trend in our results is that as we move from monthly to annual data, we are more likely to reject the null hypothesis of no cointegration in our panels. The trade that drives PPP takes time to occur and thus we are not surprised to find more evidence in support of PPP in the quarterly and annual data. However, systematic differences remain between the results for panels of price data for traded goods versus panels of price data for non-traded goods.
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