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Persistence in real exchange rate convergence

Thanasis Stengos and M. Ege Yazgan


In this paper we use a long memory framework to examine the validity of the Purchasing Power Parity (PPP) hypothesis using both monthly and quarterly data for a panel of 47 countries over a 50 year period (1957–2009). The analysis focuses on the long memory parameter d that allows us to obtain different convergence classifications depending on its value. Our analysis allows for the presence of smooth structural breaks and it does not rely on the use of a benchmark. Overall the evidence strongly points to the presence of a long memory process, where 0.5<d<1. The implication of our results is that we find long memory mean reverting convergence, something that is also consistent with Pesaran, M. H., R. P. Smith, T. Yamagata, and L. Hvozdyk. 2009. “Pairwise Tests of Purchasing Power Parity.” Econometric Reviews 28: 495–521. In explaining the speed of convergence as captured by the estimated long memory parameter d we find impediments to trade such as distance between neighboring countries and sticky prices to be mainly responsible for the slow adjustment of real exchange rates to PPP rather than nominal rates for all country groups but Asia, where the opposite is true.

Corresponding author: Thanasis Stengos, Department of Economics, University of Guelph, Ontario, Canada, e-mail:

We would like to thank an anonymous referee for very useful comments that helped improve the substance and personation of the paper. We would like to also thank seminar participants of Koc University and the 5th Annual Methods in International Finance Network Workshop.

  1. 1

    The definition of convergence, in this literature, hinges on the time series concept of stationarity. In this literature, stationarity is assumed to imply convergence irrespective of whether the underlying specification used in testing contains an intercept or a linear trend. This issue has attracted attention in the context of absolute or conditional convergence in the growth literature where the issue of convergence has been extensively analyzed, see Dufrénot, Mignon, and Naccache (2009) and Stengos and Yazgan (2013) for a discussion of the different definitions of convergence.

  2. 2

    This can be explained by the following example (see De Grauwe 1996, 97). Let us suppose an improvement in the terms of trade of the home country following a shift in world preferences in favor of the products of that country. As a result, the country will experience an improvement in its current account position causing a need for real appreciation to re-equilibrate the current account. In this case, the nominal exchange rates and domestic prices may even move in opposite directions, whereas in a PPP framework they move in the same proportion.

  3. 3

    The source and the description of the data used and the countries covered in the study are given in Appendix B.

  4. 4

    Although these estimators are consistent for

    asymptotically normally distributed for
    they are also known to exhibit nonstandard behavior when
    For instance, they have a non-normal limit distribution for
    and they converge to unity in probability and are inconsistent for d>1 (see Shimotsu and Phillips 2005, 2006)

  5. 5

    Hence, FEWL estimators cannot be used under the null hypothesis of test 3 below. Nevertheless we still used them for this case also for completeness as they yielded similar results to the others.

  6. 6

    The results remain qualitatively same across different choices of υ such as υ=T0.50, 0.55, 0.60, 0.7

  7. 7

    It becomes clear from the table that the quantiles of the reported distributions converge to those of the standard normal as T increases, but slowly and show significant differences across estimators. The graphics and some summary statistics of these distributions are available upon request.

  8. 8

    These countries are: Brazil, China, Hong Kong, Costa Rica, Hungary, Iran, Ireland, Saudia Arabia.

  9. 9

    Although, the underlying individual tests are not cross-sectionally independent, under the null, the fraction of rejections is expected to converge to α, as N and T→∞, where α is the size of the underlying test.

  10. 10

    To conserve space we only report the results of the FELW, FELWd, 2FELW and the 2FELWd estimators as the other two estimators give very similar results. We also do not report the results for the 10% significance level for the same reason. These results are available upon request. As mentioned above, FELWd and 2FELWd apply (linear) prior detrending the data. Therefore we also control for linear trends that may be present in the data via these estimators.

  11. 11

    We use T=500 critical values.

  12. 12

    The reported results were obtained by using 2FELW estimator of d. However we obtained qualitatively similar results with other 3 estimators (FELW,FELWd, 2FELWd) of d. The 780 pairs are obtained from 40 countries by excluding Colombia, Costa Rica, Egypt, Pakistan, Sri Lanka, Trinidad, and Uruguay from 47 countries which can be found in Appendix B. These countries are excluded because of the unavailability of trade data.

  13. 13

    This result may due to the problems in constructing the trade data as explained in Appendix B.

  14. 14

    Following the suggestion of Charles Engel we also included the real exchange rate volatility among our regressors which did not turn out to be significant. These results are available upon request

  15. 15

    TRADE becomes significant in Asia and Europe with the unexpected sign. One should be cautious about this result since this may also due the data problems as mentioned in Appendix B.

Appendix A

Table A1

Critical values of Test1–4, for T=100, 200, and 500.

Test 1Test 2aTest 2bTest 3Test 4
(a) At 5% level of significance
(b) At 10% level of significance

FELW: Feasible Exact Local Whittle estimator, FELWd: Feasible Exact Local Whittle estimator with detrending, 2FELW: 2-Stage Feasible Exact Local Whittle estimator, 2FELWd: 2-Stage Feasible Exact Local Whittle estimator with detrending, CV: critical value, T: sample size.

Test 1:


Test 2a:


Test 2b:


Test 3:


Test 4:


Appendix B

Data and sources

Monthly data contains the data on following 47 countries: Argentina, Austria, Belgium, Brazil, Canada, Chile, China, HongKong, Colombia, Costa Rica, Denmark, Egypt, Finland, France, Germany, Greece, Hungary, India, Indonesia, Iran, Ireland, Israel, Italy, Japan, Korea, Malaysia, Mexico, Netherlands, Norway, Pakistan, Peru, Philippines, Portugal, Saudi Arabia, Singapore, South Africa, Spain, Sri Lanka, Sweden, Switzerland, Thailand, Trinidad and Tobago, Turkey, UK, US, Uruguay, Venezuela.

Quarterly data (1957Q1–2008Q4) belong to 42 countries. It excludes Colombia, Costa Rica, Egypt, Pakistan, Sri Lanka, Trinidad and Tobago, Uruguay from the country set in monthly data, but also includes two new countries Australia (AU) and New Zealand (NZ). The variables used in the analysis are as follows:

Consumer price index (P): The data source for all counties was the IFS (International Financial Statistics) CPI (period averages). For China, 1986 M12 CPI value was taken from Dees et al. (2007), the remaining data were completed by using the growth rates of CPI published by IFS. For the period before German unification, in 1990M12, West German CPI (available up to 1991M12 in IFS) is used to obtain a common index.

Exchange rate (E): The data source for all counties was the IFS exchange rate (period averages). For the construction of euro area exchange rate each of the country members’ exchange rate was converted to an index with 2000 as the base year using the euro conversion rate of the corresponding currency and the euro/dollar rate for that year.

Real exchange rate: Computed as EPUS/P. All series are available between 1957M1–2009M12 except Argentina (1962M5–2009M12), Brazil (1996M1–2009M12), China (1986M12–2009M12), Costa Rica (1974M10–2009M12), Hong Kong (1980M10–2009M12), Denmark (1967M1–2009M12), Egypt (1957M1–2009M6), Hungary (1976M1–2009M12), India (1957M1–2009M11), Indonesia (1968M1–2009M12), Iran (1989M4–2009M12), Ireland (1997M1–2009M12), Korea (1970M1–2009M12), Peru (1960M1–2009M12), Saudia Arabia (1980M1–2009M12), Singapore (1961M1–2009M12), Thailand (1965M1–2009M12), Turkey (1969M1–2009M12) due to lack of data either in E or P.

Trade Data: To construct trade data, IFS DOT (Direction of Trade) statistics were used. The exports and imports (c.i.f.) available at the annual frequency were downloaded for all the countries under consideration. The sum of imports of country i from j and exports of country i to j, i.e., the trade flow of ij country pair was calculated for each year for each country. Although, in principle, the trade flow data should be symmetrical in the sense that the trade flow of ij country pair should be the identical irrespective of whether the data is reported by country i or j, in practice a wide diversity exists among countries due to differences in definitions used and in methods of obtaining value information (see, Guide to DOT Statistics). Therefore, the trade data used in the above regression analysis were constructed as the time average of the following quantitities.

where all quantities are measured in terms of current US dollars. GDP figures of the countries were obtained from IFS.


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Published Online: 2013-06-01
Published in Print: 2014-02-01

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