On the performance of a nonparametric measure of convergence towards purchasing power parity in the presence of linearity

Abstract

In this study, we have assessed the performance of the nonparametric measure of convergence towards purchasing power parity, as previously suggested by Shintani (2006). While the measure, which is also applicable to nonlinear processes, should correspond to the exact half-life of a linear process when the true data-generating process is linear, we find, in practice, that it is too far off the mark and thus should not be employed. We recommend testing linearity first, before applying the measure of convergence.

Acknowledgements

This work was supported by Research Program 2014 of Kookmin University in Korea. I thank Mototusgu Shintani and Deockhyun Ryu for their helpful and kind comments. All remaining errors are mine.

Notes

¹Taylor (2001) also reports that the greater the degree of temporal aggregation, the larger grows the bias in half-life estimation.

²The application of this measure of convergence is not necessarily limited to PPP; see Giles and Stroomer (2006) for an application to the convergence in output across countries.

³For a linear process, Potter (2000, footnote 10) notes that the Lyapunov exponent does not make much sense as a measure of dependence; ‘in the case of linear time series the Lyapunov exponent does not produce the traditional measures of persistence’. I thank Mototsugu Shintani for this point.

⁴El-Gamal and Ryu (2006) claim that Equation 6(6) is not an average half-life but the half-life of the average estimator; see their footnote 7.

⁵I thank Mototsugu Shintani for this point.

⁶To estimate , I use, in this study, the GAUSS program, which is available from the data archive of the Journal of Applied Econometrics: http://qed.econ.queensu.ca/jae/2006-v21.5/shintani/.

⁷With the Regression Specification Error Test (RESET) of Ramsey (1969), Shintani (2006) reports that linearity is rejected for three (six) countries at the 5% (10%) significance level for the quarterly data set with 20 countries.