Evidence of purchasing power parity for the floating regime period

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Journal of International Money and Finance 27 (2008) 156e164 www.elsevier.com/locate/jimf

Evidence of purchasing power parity for the floating regime period Claude Lopez* Department of Economics, University of Cincinnati, 1209 Crosley Tower, Cincinnati, OH 45221-0371, United States

Abstract This paper investigates the PPP hypothesis within industrialized countries for the post-Bretton Woods period via two panel unit root tests, the DFeGLSeSUR and the ADFeSUR tests, respectively developed by Lopez [A panel unit root with good power in small samples. Econometric Reviews, in press] and Levin et al. [2002. Unit root tests in panel data: asymptotic and finite-sample properties. Journal of Econometrics 108 (1), 1e24]. Both approaches allow for data specific serial and contemporaneous correlation. While both tests provide PPP evidence for the post-1973 period, the more powerful DFeGLSeSUR test demonstrates consistently stronger results, especially for the 1973e1998 period. Ó 2007 Published by Elsevier Ltd. JEL classification: F3; C3 Keywords: PPP; Panel unit root test

1. Introduction The purchasing power parity (PPP) hypothesis is a fundamental assumption for many open economy and international trade models. The PPP hypothesis stipulates a proportional relationship between nominal exchange rates and relative national prices, implying constant real exchange rates over time. This facilitates in the prediction of exchange rates as well as in

* Tel.: þ1 513 556 2346; fax: þ1 513 556 2669. E-mail address: [email protected] 0261-5606/$ - see front matter Ó 2007 Published by Elsevier Ltd. doi:10.1016/j.jimonfin.2007.09.005

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comparisons of macroeconomics outcomes among various countries. Despite being a fundamental assumption in most relevant open economy models, the empirical validity of the PPP hypothesis remains unclear, especially for the post-Bretton Woods period. Several authors, such as O’Connell (1998), Papell (2004) and Taylor (2003), strongly question the validity of the PPP evidence proposed by the literature for this period. They show the inadequacy of the testing techniques used and its impact on the results accuracy. The objective of the present paper is to reinvestigate the empirical validity of the PPP hypothesis for the flexible regime period (1973e1998) within industrialized countries via a more accurate test developed by Lopez (in press). Research in the 1980s does not confirm the empirical validity of the PPP hypothesis. Hence, several authors question the reliability of the testing methods used when applied to short spans of data. Among them, Frankel (1986) and Lothian and Taylor (1996) show that data extensions to a minimum of one century lead to PPP evidence. Frankel (1986) considers annual data from 1869 to 1984 for the dollar-sterling real exchange rate while Lothian and Taylor (1996) focus on two-centuries data for dollar-sterling and franc-sterling real exchange rates. While the latter study discriminates between fixed (prior to 1973) and flexible (after 1973) regime periods, it cannot analyze the post-1973 period due to a lack of observations (only 17 points).1 Thus, it is unclear whether the PPP hypothesis holds specifically for the flexible regime period. Additional drawbacks of using long data spans are pointed out by Hegwood and Papell (1998) and Engel (2000). These studies, respectively, show that traditional unit root tests cannot account for the existing structural shifts, and that such tests have a tendency to over accept the stationarity hypothesis when applied to extended data.2 An alternative approach to test the PPP hypothesis is to increase the number of real exchange rates considered at the estimation level. Panel unit root tests, notably, Levin et al. (2002), Im et al. (2003) and Maddala and Wu (1999), combine time-series and cross-sectional information in order to improve the power of standard unit root tests. Numerous studies, such as Frankel and Rose (1996), Jorion and Sweeney (1996), MacDonald (1996), Oh (1996), Wu (1996), Papell (1997) and Papell and Theodoridis (2001) use these new techniques and find the evidence of PPP. Yet, these results strongly depend on the amount of data considered (panels width and length). Instead of extending the data, Elliott et al. (ERS) (1996) increase the accuracy of the standard unit root test by transforming the data and then testing it. Using this new procedure, Cheung and Lai (2000) and Taylor (2002) find some evidence of PPP. Then again, the strength of the results depends on the data length. While these techniques provide significant power improvements, they still have major difficulties in studying the real exchange rate behavior for the flexible period. Indeed, these data have limited lengths and are highly persistent. In a recent work, Lopez (in press) proposes a new panel unit root test, the DFeGLSeSUR test, which performs well, especially when applied to highly persistent data with a small number of observations. In this paper, the PPP evidence is investigated for the post-Bretton Woods period via two approaches testing for the entire panel stationarity: Lopez (in press) and Levin et al. (2002). Considering several real exchange rates, all need to be stationary for the PPP hypothesis to hold. Furthermore, we allow for data specific serial and contemporaneous correlation and calculate data specific critical values. 1 Using Monte Carlo simulations, Lothian and Taylor (1997) show the lack of power of the standard unit root test when dealing with the 1973e1990 yearly data. 2 Hegwood and Papell (1998) find strong rejections of the unit root and of the non-structural change hypotheses.

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The results demonstrate a strong correlation between PPP evidence and test power. Indeed, using the more powerful DFeGLSeSUR test, we find the strongest panel evidence in support of PPP for the floating period, that is 1973e1998. Next section presents the model and test procedure used while Section 3 focuses on the empirical investigation. Finally, Section 4 summarizes our findings. 2. Model and test procedure The PPP hypothesis considers a proportional relationship between the nominal exchange rate and the relative price ratio, which implies that the real exchange rate is constant over time. Hence, a common way to test for evidence of long-run PPP is to test for the real exchange rate stationarity. The real (dollar) exchange rate for the jth country at time t, qjt (in logarithm), is defined as qjt ¼ ejt þ pUSt  pjt

ð1Þ

where ejt, pjt and pUSt are the logarithm of the nominal exchange rate (US dollar as numeraire), the foreign CPI and the US CPI, respectively. The real exchange rate, qjt, is said to be stationary if it follows a pth order autoregressive process such that Dqjt ¼ mj þ aj qj;t1 þ

kj X

jji Dqj;ti þ ujt

ð2Þ

i¼1

where aj < 0, ujt is a white noise process, Dqj;ti ¼ qj;ti  qj;ti1 , and kj, the number of lagged first difference, is selected using the general to specific procedure as suggested by Hall (1994). The stationarity of qjt is commonly tested using the augmented DickeyeFuller (ADF) test, that is, testing via Eq. (2) the null hypothesis H0: aj ¼ 0 versus the alternative H1: aj < 0.3 This paper focuses on testing the PPP hypothesis using the panel method. Hence, in this case, the entire panel needs to be stationary to conclude that PPP holds. Therefore, we concentrate our analysis on testing the hypotheses H0: aj ¼ a ¼ 0 versus H1: aj ¼ a < 0, and consider the tests proposed by Lopez (in press) and Levin et al. (2002).4 Lopez (in press) develops a panel extension of the ERS test. The DFeGLSeSUR test combines the power improvements provided by the ERS data transformation and by the cross-sectional information. It estimates Dqmjt ¼ aqmj;t1 þ

kj X

jji Dq mj;ti þ ujt

ð3Þ

i¼1

~j zjt is the locally demeaned data, ujt is a white noise process, where qmjt ¼ qjt  b m m m Dqj;ti ¼ qj;ti  qj;ti1 , and kj is selected using the modified Akaike information criteria lag 3 Long-run PPP implies that the real exchange rate has a mean-reverting behavior, which explains the absence of trend in the equation. 4 By assuming an homogeneous rate of convergence across the panels, we follow Papell and Theodoridis’ (2001) rationale: for the periods considered (from 1973(1)e1988(1) to 1973(1)e2001(4), the univariate analysis of the real exchange rates shows that the as are negative but it cannot, generally, conclude that they are significantly different from zero (the analysis for the period 1973(1)e1998(2) is reported in Table 1). Hence, ‘‘it is not clear why they should be significantly different from one another’’.

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selection, as suggested by Ng and Perron (2001).5 If the unit root null hypothesis is rejected then the entire panel is stationary and long-run PPP holds for all the real exchange rates considered. In order to allow for data specific serial and contemporaneous correlation, the system of Eq. (3) is estimated via seemingly unrelated regressions (SUR), fixing a equal across series, then the unit root null hypothesis is tested. As a benchmark, we use a version of the Levin et al. (2002) test, which we called the ADFe SUR test. The ADFeSUR test is the panel extension of the ADF test, allowing for serial and contemporaneous correlation. Following the same procedure than for the DFeGLSeSUR test, we estimate the system of Eq. (2) via SUR, fixing a equal across series, and test the null hypothesis H0: a ¼ 0. Lopez (in press) discusses and compares the finite-sample power properties of both the tests. The most relevant outcomes for our analysis stand in two points. First, the DFe GLSeSUR test is uniformly and considerably more powerful than the ADFeSUR test, especially for highly persistent time-series with a limited number of observations. For the panels considered in Section 3, the DFeGLSeSUR test rejects correctly the unit root null hypothesis at least 70% of the time while, for the ADFeSUR test, it is only 15%. Second, the DFeGLSeSUR test demonstrates high power when the data analyzed include only stationary series, even if they converge at different rates, and low power in the presence of at least one unit root in the panel.6 In summary, the DFeGLSeSUR test provides a better unit root identification than the ADFeSUR test as well as a more accurate recognition of the panel stationarity. For both the tests, we calculate data specific critical values using Monte Carlo methods. We first generate data specific empirical distributions, run univariate estimations, and consider the estimates to be the true values defining the data generating process for the errors of each series. Then, we construct real exchange rate innovations, calculate the covariance matrix S, and produce pseudo samples based on the estimated process with iid N(0, S) innovations. By taking partial sums we generate real exchange rates with a unit root. Finally, we estimate the systems of Eqs. (2) and (3) 5000 times, sort the resultant t-statistics and deduce the critical values for each panel and for each time period considered. 3. Empirical investigation 3.1. Data We consider quarterly CPIs and nominal exchange rates in dollars, from 1973, first quarter, to 2001, fourth quarter (Source IFS, CD-Rom for 03/2002), for 21 industrialized countries: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Japan, Netherlands, Norway, New Zealand, Portugal, Spain, Sweden, Switzerland, the UK, and the US. For the European countries switching to the Euro, we collect the nominal ~j ¼ ðP ~q2 Þ1 P ~zjt ~qjt . ~qjt and ~zjt are the quasi~j is the least-squares estimate of the regression of ~zj on ~qj , i.e. b b jt differences of qjt and zjt, respectively, i.e. ~qjt ¼ ðqj1 ; ðqj2  aqj1 Þ; .; ðqjT  aqj;T1 ÞÞ0 and ~zjt ¼ ð1; ð1  aÞ; pffiffiffi 0 .; ð1  aÞÞ . a ¼ 1 þ ðc= nTÞ represents the local alternative, with c ¼ 7, n cross-sections and T periods. 6 Bowman (1999) and Lopez (in press) show that there is a trade-off between the constraint of homogeneity and the power of the test. On one hand, fixing a across the series increases the power of the test, when applied to stationary data. On the other hand, such constraint leads to an acute loss in size-adjusted power in presence of some non-stationary series in the data. We view these results as advantages as we are only interested in rejecting the null hypothesis when the panel is stationary. 5

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Table 1 Univariate unit root tests, 1973(1)e2001(4) ADF test

Australia Austria Belgium Canada Denmark Finland France Germany Greece Ireland Italy Japan Netherlands Norway New Zealand Portugal Spain Sweden Switzerland UK

DFeGLS test

a

ta

kGS

a

ta

kMAIC

0.0610 0.0619 0.0590 0.0262 0.0670 0.0874 0.0682 0.0610 0.0714 0.0974 0.0865 0.0383 0.0624 0.0824 0.0712 0.0556 0.0495 0.0515 0.0685 0.0854

2.01 1.92 2.12 1.47 2.22 2.53 2.23 1.97 2.34 2.49 2.47 1.75 2.02 2.25 2.26 2.04 1.86 1.80 2.14 1.96

1 3 3 3 3 3 1 1 4 1 3 1 1 1 1 4 1 1 0 5

0.0344 0.0230 0.0477 0.0052 0.0427 0.0375 0.0662 0.0598 0.0550 0.0660 0.0737 0.0147 0.0528 0.0560 0.0720 0.0406 0.0273 0.0490 0.0281 0.0477

1.45 0.76 1.80 0.34 1.68* 1.58 2.24** 1.98** 1.89* 2.04** 2.2** 0.96 1.89* 1.89* 2.28** 1.62 1.35 1.74 1.33 1.46

1 0 1 4 1 1 1 1 5 1 1 1 1 1 1 5 1 1 1 0

*, ** represent the significance level at 10% and 5%, respectively.

exchange rate currency by US dollar from 1973(1) to 1998(4), then Euro by US dollar and use the official rate to convert into currency by US dollar.7 The data are grouped into several panels. The panel of the 20 US real exchange rates (All20) includes Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Japan, Netherlands, Norway, New Zealand, Portugal, Spain, Sweden, Switzerland, and the UK. The other panels considered are the European Community (EC), the European Monetary System (EMS), the six and 10 most industrialized countries (G6 and G10), the Euro area as of 1999 (E10), the Euro area as of 2001 (E11), and the OECD countries (13).8

3.2. PPP evidence For each panel, we estimate the initial period 1973(1)e1988(1). We then add observations quarter-by-quarter, ending with the period 1973(1)e2001(4). The critical values for the tests 7 Euro countries are Austria, Belgium, Finland, France, Germany, Italy, Ireland, the Netherlands, Portugal, and Spain. For Greece, the period is from 1973(1) to 1999(4). 8 EC includes Belgium, Denmark, France, Germany, Greece, Ireland, Italy, the Netherlands, Portugal, Spain, and the UK. EMS includes Belgium, Denmark, France, Germany, Ireland, Italy, and the Netherlands. G6 includes Canada, France, Germany, Italy, Japan, and the UK. For G10, Belgium, the Netherlands, Sweden, and Switzerland are added, and 13 includes Australia, Belgium, Canada, Denmark, Finland, France, Germany, Italy, Japan, the Netherlands, Norway, Sweden, and the UK.

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13

AII20 0.08 0.20 0.06 0.15 0.04 0.10 0.02 0.05 0.00

0.00 1988 1990 1992 1994 1996 1998 2000

1988 1990 1992 1994 1996 1998 2000

EC

EMS

0.30

0.5

0.25

0.4

0.20 0.3

0.15

0.2

0.10

0.1

0.05 0.00

0.0 1988 1990 1992 1994 1996 1998 2000 DF-GLS-SUR Test

1988 1990 1992 1994 1996 1998 2000 ADF-SUR Test

Fig. 1. Multivariate unit root tests, p-values. Note that the p-values axis starts at 0.01. Some of the results are too close to 0 to be seen otherwise.

reflect the increasing span of the data. For both the DFeGLSeSUR and the ADFeSUR tests, the p-values from panels ending between 1988 and 2001 are graphed in Figs. 1 and 2. The p-values of the DFeGLSeSUR test are uniformly lower than their ADFeSUR counterparts. Ultimately, the unit root null hypothesis is always rejected via the DFeGLSeSUR test, while the ADFeSUR test presents results varying from no rejection for G6 to a rejection at 1% for EC. As shown in Lopez (in press), the DFeGLSeSUR test demonstrates an overall better power than the ADFeSUR test. Hence, the remaining analysis focuses on its outcomes. Considering the post-Bretton Woods period, 1973(1)e2001(4), the results demonstrate overall strong PPP evidence. The unit root null hypothesis is rejected at 1% for EC, EMS, and G10, at 5% for All20, 13, E10 and E11 and at 10% for G6. Note the relation between the US dollar and the Euro zone currencies presents a slower convergence, providing PPP evidence only starting in 1993. The 1973(1)e1998(2) period allows us to narrow the question from whether or not PPP holds for the post-1973 period to does it hold under the flexible nominal exchange rate regime period, since the flexible regime period ends with the advent of the Euro. Interestingly, while we shorten the period length, the PPP evidence appears stronger with rejections of the unit root hypothesis at 1% for all panels except E11, which rejects at 5%.

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G6

G10

0.25 0.20

0.20

0.15

0.15

0.10

0.10 0.05

0.05

0.00

0.00 1988 1990 1992 1994 1996 1998 2000

1988 1990 1992 1994 1996 1998 2000

E10

E11

0.3

0.3

0.2

0.2

0.1

0.1

0.0

0.0 1988 1990 1992 1994 1996 1998 2000

1988 1990 1992 1994 1996 1998 2000

DF-GLS-SUR Test

ADF-SUR Test

Fig. 2. Multivariate unit root tests, p-values. Note that the p-values axis starts at 0.01. Some of the results are too close to 0 to be seen otherwise.

Finally, we investigate the impact of a change in numeraire on the results. Table 2 reports the p-values for both the DFeGLSeSUR and ADFeSUR tests when four different numeraires are considered: the US dollar, the Deutchemark, the British Pound and the Japanese Yen. We focus our study on panels with similar cross-sections throughout the changes, that is: All20, 13, G10 and G6. Similarly to Papell and Theodoridis (2001) and Lopez and Papell (2007), our results are numeraire specific: they are the strongest with the US dollar for the DFeGLSeSUR test

Table 2 Change in numeraire, 1973(1)e1998(2) Numeraire

US dollar m

All20 13 G10 G6

Deutchemark m

British Pound m

Japanese Yen

p

p

p

p

p

p

pm

p

0.010 0.004 0.001 0.028

0.012 0.012 0.024 0.140

0.073 0.009 0.014 0.062

0.078 0.091 0.062 0.089

0.044 0.019 0.026 0.096

0.244 0.186 0.055 0.010

0.181 0.046 0.041 0.125

0.279 0.405 0.617 0.788

pm: p-values for the DFeGLSeSUR test and p: p-values for ADFeSUR test.

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and with the Deutschemark for the ADFeSUR test.9 A closer look at the DFeGLSeSUR results shows that their weakening depends on the panels considered: both 13 and G10 reject the null hypothesis of no PPP at, at least, 5% for all the numeraires while the outcomes for All20 and G6 vary from a rejection at 1% for the US dollar to no rejection for the Japanese Yen. 4. Conclusion The standard unit root tests show strong limitations in the context of highly persistent series with limited number of observations. Hence, most of the unit root tests are inadequate to investigate the purchasing power parity hypothesis under the floating exchange rate regime period (1973e1998). In this paper, we propose to test the PPP hypothesis among industrialized countries for the post-Bretton Woods period via two relevant panel unit root tests: the DFeGLSe SUR test and the ADFeSUR test, respectively, developed by Lopez (in press) and Levin et al. (2002). Our findings are consistent with the commonly accepted idea of positive correlation between the test power and the strength of PPP evidence. Indeed, the DFeGLSeSUR test, which consistently demonstrates higher power than the ADFeSUR test, shows stronger PPP evidence. Focusing on the floating regime period, that is 1973e1998, the DFeGLSeSUR test provides strong evidence of the mean-reverting behavior of real exchange rates. The convergence toward PPP within the industrialized countries appears reliably strong from the period 1973e1988 to the period starting in 1973 and ending within the past 10 years, when the US dollar is used as numeraire.

Acknowledgements I am grateful to Chris Murray and David Papell for helpful discussions and comments. I thank Jeff Mills, Debashis Pal and the seminar participants at the University of Houston and at the University of Cincinnati for helpful suggestions, and the Charles Phelps Taft Research Center for its financial support.

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As previously noticed, the DFeGLSeSUR test demonstrates overall stronger rejections of the null hypothesis than the ADFeSUR test.

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