Revisiting purchasing power parity for African countries: with nonlinear panel unit-root tests

Abstract

This study applies Panel Seemingly Unrelated Regressions (SUR) Kapetanios et al. (Kapetanios–Shin–Snell (KSS), SURKSS) tests, proposed by Wu and Lee (2009), to investigate the properties of long-run Purchasing Power Parity (PPP) in 15 African countries. The empirical results from the univariate unit root and panel based unit root tests indicate that PPP does not hold for these 15 countries under study. However, Panel SURKSS tests indicate that PPP is valid for four of these 15 countries. These results have important policy implications for these 15 African countries under study.

Keywords:

• purchasing power parity
• panel SURKSS test

JEL Classification::

• C23
• F31

Notes

¹ PPP also states that the exchange rates between currencies are in equilibrium when their purchasing power is the same in each of the two countries. This means that the exchange rate between any two countries should equal the ratio of two currencies’ price level of a fixed basket of goods and services. The basic idea behind the PPP hypothesis is that since any international goods market arbitrage should be traded away over time, we should expect the real exchange rate to return to a constant equilibrium value in the long-run. This means that the real exchange rate should be the I(0) stationary process, for which PPP to be hold. If the real exchange rate is I(1) process, this means that the real exchange rate will not return to a constant equilibrium value in the long-run, which is a violation of the long-run PPP.

² According to Holmes (2001) and Sarno (2005), PPP is important to policymakers for several reasons. First, it can be used to predict the exchange rate and determine whether a currency is over- or under-valued, which is particularly important for less developed countries and countries experiencing large differences between domestic and foreign inflation rates. Second, the notion of PPP is used as the foundation on which many theories of exchange rate determination are built. Consequently, the validity is important to policymakers in developing countries who base their adjustments on PPP. Third, from a theoretical perspective, if PPP is not a valid long-run international parity condition, this casts doubts on the predictions of open-economy macroeconomics, which are based on the assumption of long-run PPP. Indeed, the implications of open-economy dynamic models are sensitive to the presence or absence of a unit root in the real exchange rate. Finally, estimates of PPP exchange rates are often used for practical purposes, such as determining the degree of misalignment of the nominal exchange rate and the appropriate policy response, the setting of exchange rate parities, and the international comparison of national income levels.

³ Enders and Granger (1998) show that the standard tests for unit root and cointegration all have lower power in the presence of misspecified dynamics. This is important since the linear relationship is inappropriate if prices are sticky in the downward, but not in the upward direction. Madsen and Yang (1998) have provided evidence that prices are sticky in the downward direction and that such stickiness means that real exchange rate adjustments are asymmetric. Other reasons for the asymmetric adjustment are the presence of transactions costs that inhibit international goods arbitrage and official intervention in the foreign exchange market may be such that nominal exchange rate movements are asymmetric (Obstfeld and Taylor, 1997; Taylor and Peel, 2000; Taylor and Sarno, 2001; Sarno et al., 2004; Taylor, 2004; Juvenal and Taylor, 2008). Kilian and Taylor (2003) also suggest that nonlinearity may arise from the heterogeneity of opinion in the foreign exchange market concerning the equilibrium level of the nominal exchange rate: as the nominal rate takes on more extreme values, a great degree of consensus develops concerning the appropriate direction of exchange rate movements, and traders act as accordingly.

⁴ The COMESA was formed in December 1994, replacing a Preferential Trade Area which had existed since 1981.

⁵ The SADCC which was the forerunner of the socio-economic cooperation leg of today's SADC was transformed into SADC on 17 August 1992, with the adoption by the founding members of SADCC and the newly independent Namibia of the Windhoek declaration and treaty establishing SADC.

⁶ In our study, we only consider a specification with a constant but without a time trend because time trend in real exchange rates is not consistent with the long-run PPP, therefore, we only estimate equations without the trend in our study. In fact, we have found that the results are very sensitive to whether the time trend is incorporated into the model.

⁷ The procedure poses several advantages. First, by exploiting the information from the error covariances and allowing for an autoregressive process, it produces more efficient estimators than the single equation methods. Second, the testing procedure allows for heterogeneity lag structure across the panel members. Third, the SURKSS panel integration test allows us to identify which members of the panel contain a unit root. Put differently, the advantage of the test is that it is based on an individual rather than a joint null hypothesis as in earlier versions of the panel unit root tests (Breuer et al., 2001). In our view this is very important in the present context as the COMESA and/or SADC countries under investigation have varying degrees of integration with global capital markets.

⁸ As this test has nonstandard distributions, the Critical Values (CVs) of the SURKSS test must be obtained through Monte Carlo simulations. In the simulations, the intercepts, the coefficients on the lagged values for each series were set equal to zero. In what follows, we obtain the lagged differences and the covariances matrix from the SUR estimation on the actual exchange rate data. The SURKSS test-statistic for each of the 15 series was computed as the t-statistic calculated individually for the coefficient on the lagged level. To obtain the CVs, the experiments were replicated 10 000 times and the CVs of 1%, 5% and 10% are tailored to each of the 15 panel members.

⁹ A similar study done by Chang et al. (2010b) using Panel SURADF test of Breuer et al. (2001) also provide weak evidence of favouring PPP in these 15 African countries. Chang et al. (2010b) find that the long-run PPP only holds true for Botswana, Madagascar and Malawi.

¹⁰ Compared to other countries, Botswana (11%), Burundi (14%), Madagascar (17%) and Malawi (31%) all recorded double-digit annual rates of inflation and higher than average of the group of (9.82% during this sample period).

¹¹ Recently, we have worked on a model called panel SURKSS with a Fourier function to capture the structural breaks. The models have been proved to be more powerful than that of panel SURKSS without a Fourier function. We have developed the programme codes and the codes are available from the authors upon request.