Abstract
This paper brings four new insights into the Purchasing Power Parity (PPP) debate. First, we show that a half-life PPP (HL) model is able to forecast real exchange rates better than the random walk (RW) model at both short and long-term horizons. Second, we find that this result holds if the speed of adjustment to the sample mean is calibrated at reasonable values rather than estimated. Third, we find that it is preferable to calibrate, rather than to elicit as a prior, the parameter determining the speed of adjustment to PPP. Fourth, for most currencies in our sample, the HL model outperforms the RW also in terms of nominal exchange rate forecasting.
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Notes
In the sensitivity analysis we will check the forecasting accuracy of different calibrations for (\(\bar {\rho }\))
Diebold (2012) states that if the aim is to test the null of equal forecast accuracy between two models the best choice is to use the Diebold Mariano (DM) statistic, especially as for rolling forecasting schemes its distribution is asymptotically normal. We however also calculated bootstrapped DM test p-values using the algorithm of Kilian (1999) to evaluate whether it is possible to reject the null that RW is the true DGP. The results, available upon request, suggest that at five year horizon the null against the alternative of the HL model is rejected for six out of nine currencies at the 5 % significance level. The Clark and West test cannot be used to evaluate RW against HL because they are not-nested models.
Pippenger and Goering (1998) present a similar application of this criterion to exchange rate forecasts generated by non-linear models.
All the results have also been cross-checked with Monte Carlo simulations.
Results for the case of recursive estimation are available upon request and would not change the overall assessment of this paper.
Zumaquero and Urrea (2002) similarly find, using cointegration techniques, that the adjustment to PPP takes place mainly via the exchange rate rather the relative price channel.
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We have benefited from helpful comments by G. Amisano, G. Benigno, L. Dedola, J. Nosal, L. Sarno and an anonymous referee. The paper has been presented at internal seminars of the ECB and NBP and at the MMF (London 2013), Macromodels (Warsaw 2013) and IWH-CIREQ Macroeconometric Workshop (Halle 2013) conferences. The views in this paper are those of the authors and do not necessarily reflect the views of the European Central Bank and the National Bank of Poland. All remaining errors are the sole responsibility of the authors.
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Ca’ Zorzi, M., Muck, J. & Rubaszek, M. Real Exchange Rate Forecasting and PPP: This Time the Random Walk Loses. Open Econ Rev 27, 585–609 (2016). https://doi.org/10.1007/s11079-015-9386-4
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DOI: https://doi.org/10.1007/s11079-015-9386-4