Facing up to the polysemy of purchasing power parity: New international evidence
Introduction
An ideal world without transaction costs never exists and a static world shifting to a dynamic and globalized one make it difficult to test for the purchasing power parity (PPP) hypothesis without considering structural changes and rapid dynamic changes in the economic system. Conventional PPP empirical literature, including PPP and TPPP (trend PPP), does not consider such a complex economic system. Unlike PPP and TPPP, the QPPP (qualified PPP) and TQPP (trend qualified PPP) allow for one-time or two-time permanent mean/trend breaks in the real exchange rate. However, many researchers do not distinguish the difference between PPP versus QPPP, and TPPP versus TQPPP when they attempt to test for the PPP hypothesis (see Section 2 for details).
The purposes of this paper are twofold. First, this study makes an effort to provide new comprehensive evidence of the four versions of the PPP hypothesis. Second, since the number of valid PPP hypothesis in each country may be different, we will explore the determinants of this difference. When testing for the four types of PPP, the temporary and permanent breaks as well as abrupt and smooth breaks are classified. Furthermore, one-time and two-time structural breaks are identified. Additionally, the symmetric and asymmetric dynamic adjustments of the real exchange rates are also taken into account, which reflect the transaction costs and government's intervention in the exchange rate market. Put simply, the first major contribution of this paper is our attempts to comprehensively consider those aforementioned situations to test for the validity of four concepts of the PPP hypothesis by using the real effective exchange rates (REERs) of 23 OECD countries plus the euro area.
To achieve the first goal, we adopt a variety of the state-of-the-art unit root tests. In the first step we examine the PPP and TPPP propositions by using a battery of powerful unit root tests without structural breaks, including the methods of the Augmented Dickey-Fuller (1979, ADF), the Elliott et al. (1996, ADF-GLS), the Kwiatkowski et al. (1992, KPSS), and the Schmidt and Phillips (1992). In the second step, in order to test for the QPPP and TQPPP, based on the idea of Papell and Pordan (2006), we employ the unit root tests with permanent structural breaks to account for possible structural breaks in the real exchange rate. In the case of abrupt structural changes, we adopt the Zivot and Andrew (1992), Lumsdaine and Papell (1997), and Lee and Strazicich (2003, 2013) unit root tests with one-break and two-break models. The structural change could be more gradual rather than instantaneous, therefore, we use the methods of Leybourne et al. (1998) and Harvey and Mills (2002) to capture single and double smooth breaks in the real exchange rate. In the third step, we test for the PPP and TPPP propositions under the assumption of temporary smooth structural breaks. That is, we consider testing for the nonstationarity of real exchange rate in the presence of infrequent smooth temporary structural breaks under the alternative hypothesis. To this end, we adopt the methods of Sollis (2005) and Enders and Lee (2012).1 In the fourth step, we consider using three popular nonlinear unit root tests to detect the PPP and TPPP. We apply two types of the exponential smooth transition autoregressive (ESTAR) models proposed by Park and Shintani (2005, 2016) and Kilic (2011). The nonlinear property characterized by the ESTAR models is coined size nonlinearity in the literature. We adopt the momentum threshold autoregressive (MTAR) model, proposed by Enders and Granger (1998), to examine the role of sign asymmetry in testing for the PPP and TPPP.2
After applying the tests listed above, our main findings offer strong evidence in favor of TPPP. The PPP and TQPPP are moderately approved and there is weak evidence in support of the QPPP. The validity of the TPPP and TQPPP is in line with the Balassa-Samuelson effect and the trended measurement errors in the prices.
The second major purpose of this study is that we try to explore why one or more versions of the PPP hold for a specific country? To accomplish this important second goal, we estimate the ordered probit model by considering some possible factors such as the size of gross domestic product (hereafter GDP), the membership of the euro area, the trade-to-GDP ratio and the government debt-to-GDP ratio. The findings are that, first, more versions of PPP hypothesis hold for countries with smaller GDP. Second, if the country is a member of the European Union and uses the euro as its currency, then the number of valid PPP hypotheses is inclined to increase. Third, the trad-to-GDP ratio has no effect on the validity of the PPP hypothesis, but the effect of the government debt-to-GDP ratio on the validity of the PPP hypothesis is significantly negative.
The remainder of this paper is organized as follows. Section 2 reviews recent empirical studies of the PPP. Section 3 describes the data. Section 4 reports the results of each test employed in this paper. Section 5 presents the discussion of the validity of four PPP propositions. We make a conclusion in Section 6.
Section snippets
Literature review
Testing the empirical validity of PPP hypothesis has long been in the interest of academics due to the fact that, for example, it is an indispensable premise of many theoretical economic models (Rogoff, 1996). Many researchers have devoted their efforts to this topic. We do not intend to review each of them since there are many good surveys of the PPP in the literature. Readers are referred to Breuer (1994), Froot and Rogoff (1995), Taylor (1995, 2006), Rogoff (1996), Sarno and Taylor (2002a, b)
Data description
We use the monthly real effective exchange rates of the following 23 OECD countries, i.e., Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Japan, Luxembourg, the Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, the UK, and the US, plus the euro area in this study. For all of the countries, the data start in 1994m1 and end in 2019m12, totally 312 observations. We download the data of REERs from the website of the
Empirical results
This section covers all of the empirical results of each test we adopt for the four versions of the PPP hypothesis. For readers’ information, we draw a flowchart in Fig. 1. We only report the final results of each test used in this paper and omit the technical part. Readers are referred to the original papers for details.
Discussion
In order to test for the PPP (TPPP) hypothesis while allowing for temporary smooth structural breaks, we employ the Sollis (2005) test and the Fourier unit root test of Christopoulos and León-Ledesma (2010) and Enders and Lee (2012). These tests account for structural breaks, but still maintain the long-run PPP or TPPP hypothesis. Likewise, to test for the QPPP (TQPPP) hypothesis by allowing the permanent smooth structural breaks, we use the unit root test model that allows one-time structural
Concluding remarks
The purposes of this paper are twofold. First, we provide new comprehensive evidence for the validity of four concepts of purchasing power parity hypothesis for 23 OECD countries plus the euro area. We point out that some previous studies misused the test statistics and misinterpreted their results concerning the PPP hypothesis. We demonstrate how to test for different versions of the PPP hypothesis by using a battery of newly-developed unit root tests. In a nutshell, our results provide more
Declaration of competing interest
The authors report no potential conflict of interest.
Acknowledgements
We would like to thank the Editor, Professor Sushanta Mallick, the Associate Editor and two anonymous referees of this journal for helpful comments and suggestions. We thank Professor Gotcher for proofreading this paper. The authors report no potential conflict of interest. The usual disclaimer applies.
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