Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Studies in Nonlinear Dynamics & Econometrics

Ed. by Mizrach, Bruce

IMPACT FACTOR 2018: 0.448
5-years IMPACT FACTOR: 0.877

CiteScore 2018: 0.85

SCImago Journal Rank (SJR) 2018: 0.552
Source Normalized Impact per Paper (SNIP) 2018: 0.561

Mathematical Citation Quotient (MCQ) 2018: 0.07

See all formats and pricing
More options …
Volume 18, Issue 1


Volume 24 (2020)

Persistence in real exchange rate convergence

Thanasis Stengos / M. Ege Yazgan
Published Online: 2013-06-01 | DOI: https://doi.org/10.1515/snde-2012-0039


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.

This article offers supplementary material which is provided at the end of the article.

Keywords: purchasing power parity; convergence; long memory; pair-wise approach


  • Abadir, K., W. Distaso, and L. Giraitis. 2007. “Nonstationarity-Extended Local Whittle Estimation.” Journal of Econometrics 141: 1353–1384.Web of ScienceGoogle Scholar

  • Becker, R., W. Enders, and S. Hurn. 2004. “A General Test for Time Dependence in Parameters.” Journal of Applied Econometrics 19: 899–906.CrossrefGoogle Scholar

  • Becker, R., W. Enders, and S. Hurn. 2006. “A Stationary Test in the Presence of an Unknown Number of Smooth Breaks.” Journal of Time Series Analysis 27: 381–409.CrossrefGoogle Scholar

  • Cecchetti, S. G., C. M. Nelson, and J. S. Robert. 2002. “Price Index Convergence among United States Cities.” International Economic Review 43: 1081–1099.CrossrefGoogle Scholar

  • Choi, C. Y., N. C. Mark, and D. Sul. 2006. “Unbiased Estimation of the Half-life to PPP Convergence in Panel Data.” Journal of Money, Credit and Banking 38: 921–938.Web of ScienceCrossrefGoogle Scholar

  • Crucini, M. J., and M. Shintani. 2008. “Persistence in Law of One Price Deviations: Evidence from Micro-Data.” Journal of Monetary Economics 55: 629–644.CrossrefWeb of ScienceGoogle Scholar

  • Dees, S. D., F. DiMauro, M. H. Pesaran, and V. Smith. 2007. “Exploring the International Linkages of the Euro Area: A Global VAR Analysis.” Journal of Applied Econometrics 22: 1–38.CrossrefGoogle Scholar

  • De Grauwe, P. 1996. International Money. 2nd ed. Oxford, UK: Oxford University Press.Google Scholar

  • Dornbusch, R. 1976. “Expectations and Exchange Rate Dynamics.” Journal of Political Economy 84: 1161–1176CrossrefGoogle Scholar

  • Dufrénot, G., V. Mignon, and T. Naccache. 2009. “The Slow Convergence of Per Capita Income Between the Developing Countries: Growth Resistance and Sometimes Growth Tragedy.” Discussion Papers, University of Nottingham, CREDIT.Google Scholar

  • Frankel, J. A., and A. K. Rose. 1996. “A Panel Project on Purchasing Power Parity: Mean Reversion Within and Between Countries.” Journal of International Economics 40: 209–224.CrossrefGoogle Scholar

  • Kuensch, H. 1987. “Statistical Aspects of Self-Similar Processes.” In Proceedings of the First World Congress of the Bernoulli Society, edited by Y. Prokhorov and V. V.Sazanov. Utrecht: VNU Science Press.Google Scholar

  • Levin, A., C. F. Lin, and C. S. Lu. 2002. “Unit Root Tests in Panel Data: Asymptotic and Finite-Sample Properties.” Journal of Econometrics 108: 1–24CrossrefGoogle Scholar

  • Ludlow, J., and W. Enders. 2000. “Estimating Non-Linear ARMA models Using Fourier Coefficients.” International Journal of Forecasting 16: 333–347.CrossrefGoogle Scholar

  • Murray, C. J., and D. H. Papell. 2005. “Do Panels Help Solve the Purchasing Power Parity Puzzle?” Journal of Business and Economic Statistics 23: 410–415.CrossrefGoogle Scholar

  • Perron, P. 1989. “The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis.” Econometrica 57: 1361–1401.CrossrefGoogle Scholar

  • Pesaran, M. H. 2007. “A Pair-Wise Approach for Testing Output and Growth Convergence.” Journal of Econometrics 138: 312–355.Web of ScienceCrossrefGoogle Scholar

  • Pesaran, M. H., R. P. Smith, T. Yamagata, and L. Hvozdyk. 2009. “Pairwise Tests of Purchasing Power Parity.” Econometric Reviews 28: 495–521.Web of ScienceCrossrefGoogle Scholar

  • Robinson, P. M. 1995. “Gaussian Semiparametric Estimation of Long Range Dependence.” Annals of Statistics 23: 1630–1661.CrossrefGoogle Scholar

  • Rogoff, K. 1996. “The Purchasing Power Parity Puzzle.” Journal of Economic Literature 34: 647–668.Google Scholar

  • Shimotsu, K. 2010. “Exact Local Whittle Estimation of Fractional Integration with Unknown Mean and Time Trend.” Econometric Theory 26: 501–540.CrossrefWeb of ScienceGoogle Scholar

  • Shimotsu, K., and P. C. B. Phillips. 2005. “Exact Local Whittle Estimation of Fractional Integration.” Annals of Statistics 33: 1890–1933.CrossrefGoogle Scholar

  • Shimotsu, K., and P. C. B. Phillips. 2006. “Local Whittle Estimation of Fractional Integration and Some of its Variants.” Journal of Econometrics 130: 209–233.CrossrefGoogle Scholar

  • Stengos, T., and M. E. Yazgan. 2013. “Persistence in Convergence.” Macroeconomic Dynamics. Forthcoming.Google Scholar

  • Taylor, A. M., and M. P. Taylor. 2004. “The Purchasing Power Parity Debate.” Journal of Economic Perspectives 18: 135–158.CrossrefGoogle Scholar

  • Velasco, C. 1999. “Gaussian Semiparametric Estimation of Non-Stationary Time Series,” Journal of Time Series Analysis 20: 87–127.CrossrefGoogle Scholar

  • Yazgan, M. E., and H. Yilmazkuday. 2011. “Price Level Convergence: New Evidence from U.S. Cities.” Economics Letters 110: 76–78.CrossrefWeb of ScienceGoogle Scholar

About the article

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

Published Online: 2013-06-01

Published in Print: 2014-02-01

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.

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.

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

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)

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.

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

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.

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

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.

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.

We use T=500 critical values.

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.

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

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

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.

Citation Information: Studies in Nonlinear Dynamics and Econometrics, Volume 18, Issue 1, Pages 73–88, ISSN (Online) 1558-3708, ISSN (Print) 1081-1826, DOI: https://doi.org/10.1515/snde-2012-0039.

Export Citation

©2014 by Walter de Gruyter Berlin Boston.Get Permission

Supplementary Article Materials

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Mustafa Ege Yazgan and Hakan Yilmazkuday
SSRN Electronic Journal, 2010

Comments (0)

Please log in or register to comment.
Log in