International Business & Economics Research Journal – December 2011 Volume 10, Number 12 © 2011 The Clute Institute 97 Testing For The Purchasing Power Parity Hypothesis In A Small Open Economy: A VAR-X Approach Lumengo Bonga-Bonga, University of Johannesburg, South Africa ABSTRACT This paper tests the purchasing power parity (PPP) hypothesis for the rand-US dollar exchange rate by making use of the cointegrating VAR-X approach. Given that the test of PPP hypothesis conducted in this paper involves variables of a small economy, South Africa, compared to a big economy, the US, the paper contends that traditional cointegrating VAR approach that considers all variables in a given vector as endogenous is not suitable. The results of the paper show that the restriction applied in the cointegrating vector for the VAR-X model supports the weak-form PPP hypothesis. The same restrictions are rejected in the case of traditional cointegrating VAR model. The paper concludes that it is essential to distinguish between weakly exogenous and endogenous variables in tests of the PPP hypothesis that involve small and big economies. Keywords: Purchasing Power Parity; Cointegrating VAR-X; Exchange Rates 1. INTRODUCTION he purchasing power parity (PPP) is probably the most debated theory of exchange rate determination. The theory holds that the nominal exchange rate between two currencies should be equal to the ratio of aggregate price levels between the two countries. Moreover, the PPP expression is used to derive the real exchange rate – that is, the nominal exchange rate multiplied by the ratio of foreign and domestic price levels. The link between the PPP expression and the real exchange rate is instrumental for testing the PPP hypothesis. Thus, if PPP holds, the real exchange rate should be equal to unity or stationary. The stationarity of the real exchange rate, which implies support for the PPP hypothesis, also entails that the nominal exchange rate and relative prices are cointegrated, or, equivalently, have a common stochastic trend. This reality implies that testing the PPP hypothesis can be carried out by testing the stationarity of the real exchange rate or by assessing the possibility of a common stochastic trend between the nominal exchange rate and the relative prices between two countries. The rationale behind the PPP is related to the principle of arbitrage opportunity or riskless profit. That is, if two identical products are traded at different prices in different countries, a profitable arbitrage opportunity arises if the arbitrageurs can buy the good cheaply in one location and sell it at a higher price in the other given the nominal bilateral exchange rate. If arbitrage opportunity is then precluded, this process leads to the convergence of the deviations from PPP towards zero, or the long-term equilibrium is established between bilateral nominal exchange rate and relative prices in the two locations. Studies that have used cointegration techniques to test the PPP hypothesis make a distinction between the weak and strict form. The weak form of PPP assumes that exchange rates are in equilibrium and that there is a long- term relationship between exchange rates and relative prices. However, in its strict form, the PPP holds that there is a one-on-one equilibrium relationship between nominal exchange rates and relative prices. Moreover, a number of studies in developed and developing economies alike recommend the use of a non- linear model rather than a linear model when testing for the PPP. For example, Taylor and Taylor (2004) suggest T