The Purchasing Power Parity Approach: Theory, Literature, and Evidence from the ADF-Based and KPSS-Based Tests for the Case of Turkiye
Fatih ÇiftciThe main aim of this study is to test, by using alternative tools, the validity of the absolute version of the purchasing power parity (PPP) hypothesis within the context of the Turkish economy for the post-February-2001-period of floating exchange rate regime. Additional aims pursued by the present study are to introduce briefly the PPP approach and review the relevant econometric literature. Using an array of ADF- and KPSS-based traditional and modern test techniques, the econometric implementation part of this paper has primarily been devoted to investigate whether the real TL/USD exchange rate variable is stationary at its level. To that end, four different types of the real exchange rate variable have been constructed, in which two alternate nominal TL/USD exchange rate series measured by the period-average and end-of-period values and two alternate average price series defined in terms of the consumer and producer price indexes were used. The two alternate real exchange rates that use the consumer (producer) price index were calculated by means of the quarterly data that comprise the period of 2001Q2-2022Q2 (2001Q2-2020Q1). Based on the unit-root and stationarity tests, it has been found that the absolute PPP hypothesis is valid only when the possibility of structural breaks is taken into account by using some particular methods. Otherwise, it has been found to be invalid. The secondary empirical analyses of this paper have questioned if there is a cointegration relationship between the variables of nominal TL/USD exchange rate and relative price, again, by using the alternate versions of the two variables and a number of ADF- and KPSS-based techniques. In doing so, the same data-set as above was utilized. Accordingly, the absolute PPP hypothesis has been supported strongly when the potential of a structural break in the model is taken into account, while the support has been found to be weak when the other way is the case. The KPSS-based tests used in the current study have provided more evidence in favor of the validity of the PPP relationship, both in its restricted and unrestricted forms, relative to the ADF-based tests. One of the conclusions implied by the findings of the econometric analyses is that the equilibrium value of the nominal TL/USD exchange rate in Turkiye can be determined more accurately by utilizing the qualified-PPP approach, rather than its standard version.
Satınalma Gücü Paritesi Yaklaşımı: Teori, Literatür ve Türkiye Örneği İçin ADF-Temelli ve KPSS-Temelli Testlerden Kanıtlar
Fatih ÇiftciBu çalışmanın temel amacı, satınalma gücü paritesi (PPP) hipotezinin mutlak versiyonunun geçerliliğini, Türkiye ekonomisi bağlamında, Şubat 2001 sonrası dalgalı döviz kuru rejimi dönemi için ve alternatif araçlar kullanarak test etmektir. Bu çalışmayla ulaşılmak istenen tali amaçlar ise, PPP yaklaşımını kısaca tanıtmak ve konuya dair ekonometrik literatürü gözden geçirmektir. Çalışmanın ekonometrik uygulama kısmında, esas olarak, reel TL/USD kuru değişkeninin düzey-değerinde durağan olup olmadığı, ADF- ve KPSS-temelli birtakım geleneksel ve modern test teknikleri kullanılarak incelenmiştir. Bunun için, dönem-ortalaması ve dönem-sonu değerleri itibariyle ölçümlenmiş 2 alternatif nominal TL/USD kuru serisi ile tüketici ve üretici fiyat endeksleri cinsinden tanımlanmış 2 alternatif ortalama fiyat serisinin kullanıldığı 4 farklı türde reel döviz kuru değişkeni oluşturulmuştur. Tüketici (üretici) fiyat endeksinin kullanıldığı 2 alternatif reel döviz kuru, 2001Q2-2022Q2 (2001Q2-2020Q1) dönemini kapsayan çeyreklik verilerle hesaplanmıştır. Birim-kök ve durağanlık testleri sonucunda, mutlak PPP hipotezinin, sadece yapısal kırılma olasılığının belirli bazı yöntemlerle dikkate alınması halinde geçerli olduğu, aksi halde geçerli olmadığı anlaşılmıştır. Bu çalışmada, ikincil olarak, nominal TL/USD kuru ve nispi fiyat değişkenleri arasında bir eşbütünleşme ilişkisi olup olmadığı, yine bu 2 değişkenin alternatif versiyonları ve ADF- ve KPSS-temelli birkaç teknik kullanılarak, aynı veri-seti yardımıyla sorgulanmıştır. Buna göre, mutlak PPP hipotezi, modelde yapısal kırılma potansiyelinin dikkate alınması halinde güçlü, dikkate alınmaması halinde ise zayıf bir destek bulmuştur. Çalışmada kullanılan KPSS-temelli testler, ADF-temelli testlere nispetle, PPP ilişkisinin hem kısıtlı hem de kısıtsız formdaki geçerliliği lehine daha fazla kanıt sunmuştur. Ekonometrik analiz bulgularının ima ettiği sonuçlardan birisi, Türkiye’de nominal TL/USD kurunun denge değerinin, standart-PPP yaklaşımından ziyade, sınırlı-PPP yaklaşımı kullanılarak daha doğru bir biçimde belirlenebileceğidir
One of the topics that have intensively been examined and discussed in international economics literature, particularly since the 1980s, is whether the purchasing power parity (PPP) hypothesis is valid in reality. It is a well-known fact that the PPP doctrine that has a special place among different theories of exchange rates is built around a sound theoretical base, i.e., the notion of the law of one-price. However, when the studies testing the validity of the PPP approach, especially of its absolute version, through time-series techniques are reviewed generally, it can easily be inferred that no widespread evidence favoring the hypothesis has surfaced as yet. One may even go on to conclude that the findings obtained against it outweigh those of the opposite case when it comes to developing economies. The mixed evidence appeared in the literature can partly be attributed to the limitations of the traditional econometric methodologies and/or to the shortness of the time-spans that have been made use of in some of the studies. Indeed, the analyses taking account of potential structural breaks or non-linear developments in the relevant series or models have, in general, yielded more evidence in favor of the PPP approach relative to those making use of traditional methods. Besides, the studies utilizing time-spans that are relatively longer in terms of the number of years have typically provided more support to the PPP hypothesis than otherwise, probably because it is, in essence, a long-term phenomenon.
The fact that there has generally been a noticeable disagreement between the PPP doctrine and empirical evidence has motivated many researchers to carry out new studies on the subject, especially for developing countries. Recent advancements in econometrics and the increasing numbers of observations emerging during the era of floating exchange rate regime have facilitated carrying out more reliable tests for the PPP hypothesis. Using a battery of alternative econometric techniques, this study attempts to uncover if the absolute PPP hypothesis holds good in the Turkish economy for the period in which the floating regime is effectively adopted. Specifically, during the political and economic crises that had begun towards the 20th of February, 2001, the Turkish exchange rate regime was, once and for all, switched from a type of crawling-peg regime to a floating one on the 22nd of the same month of 2001. The empirical investigations of the current study cover the time-periods spanning from just after this latest major change in the regime to the most recent available time-points that varied according to which one of the two average price indicators, i.e., the CPI and PPI series, was considered. The nominal exchange rate variables were measured based on two different types, i.e., the period-average and end-of-period rates. Therefore, four alternate real exchange rate variables or long-run regression models were made use of in testing the hypothesis. Those nominal and real exchange rate variables are defined in terms of the direct quotation between the Turkish Lira (TL) and the US Dollar (USD). The data employed here are of quarterly frequency.
The analyses of central interest in the current study were conducted by using the ADF-based unit-root tests and KPSS-based stationarity tests. Traditional versions of those tests, which do not take control of potential structural breaks, have all shown that each of the four alternate real exchange rate series has a unit-root at its level. Based on this incomplete picture, one might conclude that deviations from the equilibrium exchange rate implied by the PPP relationship are permanent. Secondary analyses conducted here within the same context relate to the question of whether there is a cointegration relationship between the variables of nominal exchange rate and relative price, for each model composed of alternate variables. Doing so has made it possible to determine whether the results of the unit-root and stationarity tests are sensitive to relaxing the restriction of “proportionality”. The findings from the traditional ADF-type cointegration tests have indicated that, with one exceptional case, there is no long-run equilibrium relationship between those two variables while the traditional KPSS-type cointegration tests have, in general, yielded findings showing that there does exist such a relationship. An important implication derived from these two types of tests is the lack of an unambiguous confirmatory evidence supporting the existence of a long-run relationship. Taking into consideration the results of these KPSS-type cointegration tests, I went ahead and estimated the long-run models by means of the dynamic OLS (DOLS) and fully-modified OLS (FMOLS) techniques. Those models have revealed that the coefficient estimates are significantly different from zero and the condition of proportionality is, as expected, not satisfied. To evaluate the findings obtained by using, and based on, the traditional cointegration tests shortly, one can say that the weak form of the absolute PPP hypothesis has been supported for the Turkish economy only weakly.
This study also contains some analyses in which a series of modern test procedures taking into account the possibility of structural breaks in the relevant real exchange rate variables are used. Among four different types of ADF-based tests that control for the structural break(s) in the variables of interest by way of the standard “dummy variable” approach, one type, which controls for two breaks, has produced strong evidence in favor of the PPP hypothesis. The other three, however, have returned findings indicating otherwise for almost all the alternative cases. Nevertheless, the KPSS-based tests used in this very context have unequivocally supported the validity of the hypothesis. What seemed intriguing based on these modern tests is that the findings obtained by using the one-break version of the ADF unit-root test are clearly at odds with those of the one-break version of the KPSS stationarity test. Because of this contradiction, the ADF- and KPSS-based cointegration tests that control for one-break in the relevant model were also carried out in this study. The results obtained therefrom have shown that the contradictory findings just mentioned were, to a certain extent, resolved as a result of relaxing the restriction of proportionality. The long-run models estimated based on those tests by employing the DOLS and FMOLS estimators have provided robust evidence indicating the validity of the absolute PPP hypothesis with a break in its weak form. This study, on the other hand, benefited from a newer strand of unit-root and stationarity tests in which potential structural breaks in the relevant series are taken into account with the aid of a Fourier-function. The Fourier-ADF tests employed in this regard have unanimously shown that the PPP hypothesis is valid when the frequencies contained in the relevant Fourier-expansions are taken fractionally, and invalid when they are defined by integer values. Finally, the Fourier-KPSS tests with integer frequencies have, to a large extent, yielded evidence indicating the validity of the hypothesis.
Based upon the econometric analyses carried out in this study, one can derive a few “generalized” results. First, according to the findings from the traditional unit-root and stationarity tests, the absolute PPP hypothesis does not seem to hold in its restricted (or strong) form in Turkiye for the particular time-periods studied. It has, however, been found to hold true when a number of modern tests with higher performance are employed. Second, the KPSS-based modern tests with the null hypothesis of stationarity have provided more evidence favoring the PPP hypothesis, compared to the ADF-based modern tests taking the presence of a unit-root as their null hypothesis. Third, traditional cointegration tests that were used to determine whether the absolute PPP hypothesis is valid in its unrestricted (or weak) form have not yielded convincing evidence in its favor. Nonetheless, the cointegration tests taking the possibility of a break into account have returned some affirmative and confirmed findings in that regard. Fourth, it has been seen that the findings obtained both in favor of and against the hypothesis are not fragile to changing the measurement type of the exchange rate variable. Unlike this, the variables or models constructed with the PPI indicator have, in some cases, led to achieving more pronounced evidence in support of the PPP relationship, relative to those constructed with the CPI. Fifth, the findings obtained here have generally supported the qualified-PPP hypothesis, rather than its standard (Casselian) version. The reason for this is that the affirmative evidence that is mutually confirmed, to a certain degree, by two different types of tests has only come from the cases with structural breaks. Overall, the empirical analyses conducted in this paper reveal the non-trivial dependence of the results pertaining to the PPP hypothesis on the techniques and methods employed. They also imply that the equilibrium bilateral exchange rate between the TL and the USD can best be calculated by using the PPP models that take account of the possibility of structural breaks. It may nevertheless need to be emphasized that all the results presented herein should be approached with some caution because of the boundaries involved.
