Purchasing power parity revisited: evidence from old and new tests for an organisation for economic co-operation and development panel

Abstract

The objective of this article is to study long-run Purchasing Power Parity (PPP) for a panel of 21 Organisation for Economic Co-operation and Development (OECD) countries from the end of the Bretton Woods era by applying a wide range of the econometric techniques available. This will allow us to present a comprehensive up to date examination of the empirical validity of PPP, covering the weak and strong versions of the hypothesis with individual and panel analysis, including the absence or presence of cross-dependency, the linear or nonlinear behaviour of the real exchange rates and the degree of persistence. Overall, the results provide evidence in favour of PPP.

Acknowledgement

The authors gratefully acknowledge financial help from the Institute for Fiscal Studies (Treasury Ministry, Spain) and from project SEJ2006-12392.

Notes

¹ See, for example, Taylor and Taylor (2004), Sarno (2005), Taylor (2008) or the forthcoming entry on PPP for the New Palgrave Dictionary of Economics (Sarno, 2008).

² We should point out several relevant caveats. First, our analysis is inevitably incomplete because all types of tests are not included, particularly the nonparametric and the Bayesian approaches. We are aware of this limitation but, similarly to the bulk of the literature, we rely on the parametric or semiparametric approaches in our empirical work. Secondly, most of the assumptions underpinning these tests are not mutually independent. For instance, nonlinearity and temporal aggregation reinforce each other, fractionally integrated processes may have some cross-sectional dependence or cointegration may happen in the presence of nonlinearities. Due to the complex nature of these questions, we do not attempt to resolve the econometric problems surrounding the above issues leaving such ambitious aim for future work.

³ The most recent literature labels the panel tests that take into account the cross-dependency problem as ‘second generation tests’ (see the surveys of, among others, Hurlin and Mignon, 2004; Breitung and Pesaran, 2005). Among the second generation tests, we have decided to use those suggested by Pesaran and Bai–Ng based on the results of Gengenbach et al. (2004), Baltagi et al. (2005), Gutierrez (2006) and Moon and Perron (2005) who, through Monte Carlo simulations, have shown that both tests keep good size and power properties under different specifications of the underlying model.

⁴ For a general revision of these models see, among others, van Dijk et al. (2002) or Teräsvirta (2004).

⁵ We started with a maximum value of two for p and q and we chose the final model according to the Akaike Information Criteria (AIC) and Schwarz Information Criteria (SBC). In all cases, we obtained models of the type ARFIMA(1,d,1) or inferior, which justifies that in columns 8 and 9, we only present the results of the estimation of the first-order model for the exchange rates. All estimations are available from the authors upon request.

⁶ If nonlinear behaviour is present in some time series (as indeed we have shown in Section III) the statistical properties (mainly size and power) of the linear tests used in this section will be affected, given that nonlinear tests would be appropriate in this case. The extension of panel tests that have been designed for the linear case to the nonlinear case would be an original and interesting contribution to the existing literature, but it is beyond the scope of this article. See the recent work of Sarno and Valente (2006) for an attempt to take into consideration simultaneously the issues of nonlinearity and regime shifts within the cointegrating VAR approach.

⁷ We also investigated the presence of a second unit root in the series and in all cases it was rejected. Further, we also applied alternative tests, such as those of Table 1 (Panel A) for real exchange rates, and in all cases the conclusions were similar to those of the ADF and KPSS. These complementary results are available from the authors upon request.

⁸ See Gutierrez (2003) for a Monte Carlo analysis of the statistical properties of some of the cointegration tests proposed in the literature.

⁹ Recently, Breitung (2005) has extended the approach of Larsson et al. (2001) to more general cases. In particular, deterministic components in the underlying VAR model are allowed (this is why in our empirical analysis we use the tabulated critical values given in Breitung's article) and a new estimator for the cointegrating vector(s) is proposed, which can be modified in case of contemporaneous cross correlation.

¹⁰ It might seem very restrictive to impose homogeneity of the effect of the domestic and foreign prices amongst all the members of the panel, but for our data, both the individual likelihood ratio tests for the domestic and foreign prices (χ_LR² = 14.44 and χ_LR² = 20.60) and the joint hypothesis of homogeneity of the price effect among countries (χ_LR² = 29.91) do not reject the corresponding null hypothesis.

¹¹ We obtain similar results using the DGLS estimation procedure for SUR cointegration regression models recently proposed in Moon and Perron (2004). On the other hand, our estimates under the homogeneity hypothesis are very similar to those obtained by Breitung (2005) using the fully modified least squares estimator (FM-OLS) method and the new two-stage estimator proposed in his work. Further, his Wald statistics do not reject in both cases the null hypothesis of β ₁ = −1 and β ₂ = 1.