Linear and Nonlinear Cointegration of Purchasing Power Parity: Further Evidence from Developing Countries

Abstract

In this study, we search for evidence of empirical validity of long-run purchasing power parity (PPP) in case of eight developing countries. We consider both a linear and non-linear model of PPP based on cointegration analysis and apply firstly Johansen's linear approach and then conduct Breitung's rank and score tests to search for any non-linear cointegrating relationship. The results obtained from Breitung's rank test suggest that once the sources of non-linearities are taken into account, the results provide stronger evidence on the empirical fulfillment of PPP.

Keywords:

• Purchasing power parity
• non-linear cointegration
• non-linearities
• rank tests
• developing countries

Keywords:

• C22
• F31

Acknowledgements

We would like to thank anonymous referees for their helpful comments and suggestions. These all make this article more valuable and readable. Any errors that remain are our own.

Notes

1. Price equalizing effect of international trade is prevalent only for tradeables. The inclusion of non-tradable goods, whose prices are determined by productivity levels to some extent, in price indices may lead to deviations from PPP. Price differentials resulting from inter-country differences in the relative productivity of tradable and non-tradable sectors are discussed independently by Harrod (1933), Balassa (1964) and Samuelson (1964), which is also known as the Harrod-Balassa-Samuelson Effect in the literature.

2. Krugman (1987) refers to this practice of firms selling the same good for different prices in different markets as “pricing-to-market”.

3. For an extensive view of empirical literature about PPP, see also Taylor (2003), Taylor and Taylor (2004) and Taylor (2006).

4. Since there are three variables in the cointegration test, it would be possible to find two cointegrating vector and this does not cause any problem for our analysis. In this article, we are interested in applying a liberal version of PPP, thus, relax all restrictions on the coefficients so that the parameters β, β ₁ and β ₂ can assume different values. Our tests concentrate on the existence of any linear combination(s) of the variables that is stationary. Cheung and Lai (1993) argued that the imposition of symmetry and proportionality conditions in the analysis can cause the restricted model to ignore possible interactions in the determination of exchange rates and prices that are allowed in the unrestricted model.

5. As stated by Hong and Phillips (2010) neglecting non-linearity in a long-run relationship can be particularly crucial in non-stationary time series. For stationary time series, linear models may be sufficient to obtain workable approximations at least locally to non-linear models. In contrast to mean-reverting stationary processes, non-stationary time series have no tendency to turn fixed mean or locality in the sample space and, like random walks. In such cases, local linear approximations can only poorly represent the global characteristics of the process, producing a high risk of faulty inference about a misspecified long-run equilibrium.

6. We apply the Schwarz Bayesian Information Criterion to select appropriate leads and lags for DOLS.

7. Pippenger and Goering (1993), Balke and Fomby (1997) and Enders and Granger (1998) argues that commonly used tests consider only for linear cointegration and have power problems when especially there is non-linear dynamics in the long-run equilibrium relation. In addition, KIlIç (2011) states that the studies examining the non-linear adjustment in deviations from long-run equilibrium relations, in fact, subject to Davies (1987) problem; that is parameter(s) can be unidentified under the null hypothesis of no unit root, no-cointegration or no-non-linear adjustment.