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DOI :10.26650/B/SS10.2021.013.21   IUP :10.26650/B/SS10.2021.013.21    Full Text (PDF)

Are Inflation Rates Stationary in OECD Countries? Evidence From a Fourier Quantile Unit Root Test

Oktay Kızılkaya

Given the assumptions specific to the unit root hypothesis regarding inflation rates, if inflation rates are nonstationary, the shocks affecting a series will have permanent effect. In this case, policy action is required to return inflation to its original level. If inflation rates have a unit root, it can be concluded that the accelerationist hypothesis is valid. It is also generally acknowledged that nominal interest rates contain a unit root. Therefore, if inflation and interest rate series are integrated as order one, the existence of the Fisher effect can be tested. Conversely, if inflation rates are stationary, the shocks affecting the series will have a transitory effect. In this case, the need for policy action will become less mandatory as inflation will eventually return to its equilibrium level.

This study examines the stationarity of inflation rate series of 20 OECD countries using quarterly observations for the period 1956Q2–2019Q2. These countries include Australia, Belgium, Canada, Finland, France, Germany, Greece, Italy, Japan, Korea, Luxembourg, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, Turkey, the United Kingdom, and the United States. The inflation series used are obtained with the following equation:

where CPI indicates consumer price indices.

Becker et al. (2006) asserted that the actual nature of breaks is completely unknown. Accordingly, there is no specific guide to indicate where or how many breaks there are for a unit root/stationarity test. To overcome this challenge, we apply a flexible Fourier form. The Fourier approximation can be used in the existence of an unknown number of smooth breaks. The methodology of this study depends on the Fourier quantile unit root test, developed by Bahmani-Oskooee et al. (2017). First, we estimate the following equation by ordinary least squares (OLS) for k = 0.1,0.2,…,4.9,5.

We select the optimum frequency (k*) when the sum of squared residuals is minimized. We then compute the OLS residuals:

In the second stage, the null hypothesis of a unit root in conditional quantile of is tested by estimating the quantile regression:

where denotes the quantile of conditional on the past information set. is the conditional quantile of , and its estimated values capture the magnitude of Real Exchange Rate (RER) shock in each quantile. measures the speed of the mean reversion of in each quantile. As with the standard Augmented Dickey–Fuller (ADF) test, we use the t-ratio statistic:

where f(.) indicates the probability and F(.) denotes cumulative density functions of is the vector of the lagged dependent variables and is the projection matrix onto the space orthogonal to . Furthermore, is a consistent estimator of . Koenker and Xiao (2004) suggested quantile regression-based Kolmogorov–Smirnov (QKS) statistics for testing the null hypothesis of a unit root:

This study investigates the mean-reverting properties of inflation series using three different unit root/stationarity tests: (a) Conventional unit root tests, including ADF and Kwiatkowski et al. (KPSS). (b) Fourier-type unit root tests, which include the Fourier–KPSS (Becker et al. 2006), and the Fourier–ADF (Christopoulos and León-Ledesma 2010). Finally, (c) the Fourier quantile unit root test, developed by Bahmani-Oskooee et al. (2017).

Conventional and Fourier unit root/stationarity tests indicate mixed results. Fourier quantile unit root test results indicate that the inflation rate series is stationary for 17 of the 20 OECD countries (except Luxembourg, Norway, and Spain). It would be less costly for the monetary authorities to implement a disinflationary policy in those 17 OECD countries with stationary inflation than those countries with nonstationary inflation. It is concluded that the accelerationist hypothesis is valid for Luxembourg, Norway, and Spain. In addition, the dynamic behavior of the inflation rates is asymmetric.

DOI :10.26650/B/SS10.2021.013.21   IUP :10.26650/B/SS10.2021.013.21    Full Text (PDF)

OECD Ülkelerinde Enflasyon Oranı Durağan mı? Fourier Kantil Birim Kök Testinden Bulgular

Oktay Kızılkaya

Enflasyon konusu ülkeler için en önemli sorunlardan biri haline gelmiştir. Enflasyon oranının durağanlık özelliklerinin bilinmesi para politikasını yürütmekle görevli organlar için enflasyonla mücadele politikalarının uygulanmasında oldukça önemlidir. Bu çalışmada, 20 OECD ülkesinin enflasyon oranı serisinin durağanlık özellikleri Fourier kantil birim kök testi kullanılarak araştırılmıştır. Geleneksel ve Fourier birim kök/durağanlık testleri karmaşık sonuçlara işaret etmektedir. Fourier kantil birim kök testi sonuçları ise 20 OECD ülkesinin 17’si (Lüksemburg, Norveç ve İspanya hariç) için enflasyon oranı serisinin durağan olduğu göstermektedir. Enflasyon oranı serileri durağan olan 17 ülkenin para otoriteleri için enflasyonla mücadele politikalarını uygulamak, durağan olmayan enflasyonu olan ülkelere kıyasla daha az maliyetli olacaktır. Lüksemburg, Norveç ve İspanya için ise hızlandırmacı hipotezinin geçerli olduğu sonucuna ulaşılmıştır. Ayrıca, elde edilen sonuçlar çoğu OECD ülkesi için enflasyon oranlarının dinamik davranışlarının asimetrik olduğunu, yani bazı kantillerde durağan olduğunu, bazı kantillerde ise birim kök içerdiğini göstermektedir. Kanada, Fransa, İtalya, Yeni Zelanda, Portekiz, İsveç, Türkiye, Birleşik Krallık ve ABD’nin enflasyon oranları büyük kantillerde birim köklü iken küçük kantillerde durağan davranış göstermektedir. Bu sonuç, söz konusu ülkelerin enflasyon oranlarının düşük seviyelerdeyken durağan olduğunu, ancak göreceli olarak yüksek seviyelerde kaldıklarında ise birim kök içerdiğini göstermektedir. Bu durum, hükümetin yüksek enflasyon oranına müdahale etmek için gerekli önlemleri alabileceği anlamına gelmektedir.

References

• Bahmani-Oskooee, M., Chang T., & Ranjbar O. (2017). The Fourier quantile unit root test with an application to the PPP hypothesis in the OECD. AppliedEconomics Quarterly, 63(3), 295-317. doi: 10.3790/aeq.63.3.295. google scholar
• Basher, S. A., & Westerlund, J. (2008). Is there really a unit root in the inflation rate? More evidence from panel data models. Applied Economics Letters, 15(3), 161-164. google scholar
• Becker, R., Enders W., & Lee J. (2006). A stationarity test in the presence of an unknown number of smooth breaks. Journal of Time Series Analysis, 27(3), 381-409. doi:10.1111/j.1467-9892.2006.00478.x. google scholar
• Chang, T., Ranjbar, O., & Tang, D. P. (2013). Revisiting the mean reversion of inflation rates for 22 OECD countries. Economic Modelling, 30, 245-252. google scholar
• Charemza, W. W., Hristova, D., & Burridge, P. (2005). Is inflation stationary? Applied Economics, 37(8), 901-903. google scholar
• Chen, S. W., & Hsu, C. S. (2016). Threshold, smooth transition and mean reversion in inflation: New evidence from European countries. Economic Modelling, 53, 23-36. google scholar
• Christopoulos, D. K., & Leon-Ledesma, M. A. (2010). Smooth breaks and non-linear mean reversion: Post-Bretton Woods real exchange rates. Journal of International Money and Finance, 29(6), 1076-1093. google scholar
• Enders, W., & Lee, J. (2012). The flexible Fourier form and Dickey-Fuller type unit root tests. Economics Letters, 117(1), 196-199. google scholar
• Herve, D. B. G. (2018). Re-examining the mean reversion of inflation rate in ECOWAS. Asian Economic and Financial Review, 8(5), 653. google scholar
• Ho, T. W. (2009). The inflation rates may accelerate after all: panel evidence from 19 OECD economies. Empirical Economics, 36(1), 55-64. google scholar
• Kapetanios, G., Shin, Y., & Snell, A. (2003). Testing for a unit root in the nonlinear STAR framework. Journal of Econometrics, 112(2), 359-379. google scholar
• Koenker, R., & Xiao Z. (2004). Unit Root Quantile Autoregression Inference”. Journal of the American Statistical Association, 99(467), 775-787. doi: 10.1198/016214504000001114. google scholar
• Lee, C. F., & Tsong, C. C. (2009). Bootstrapping covariate stationarity tests for inflation rates. Economic Modelling, 26(6), 1443-1448. google scholar
• Lee, H. Y., & Wu, J. L. (2001). Mean reversion of inflation rates: evidence from 13 OECD countries. Journal of Macroeconomics, 23(3), 477-487. google scholar
• Lee, J., & Strazicich, M. C. (2003). Minimum Lagrange multiplier unit root test with two structural breaks. Review of Economics and Statistics, 85(4), 1082-1089. google scholar
• Lee, J., & Strazicich, M. C. (2004). Minimum LM unit root test with one structural break. Manuscript, Department of Economics, Appalachian State University, 1-16. google scholar
• Leybourne, S., Newbold, P., & Vougas, D. (1998). Unit roots and smooth transitions. Journal of time series analysis, 19(1), 83-97. google scholar
• Narayan, P. K., & Popp, S. (2010). A new unit root test with two structural breaks in level and slope at unknown time. Journal of Applied Statistics, 37(9), 1425-1438. google scholar
• Ozcan, B. (2013). Are inflation rates stationary in 11 Mediterranean countries? Evidence from univariate and panel unit root tests. Eurasian Journal of Business and Economics, 6(12), 79-96. google scholar
• Perron, P. (1989). The great crash, the oil price shock, and the unit root hypothesis. Econometrica: Journal of the Econometric Society, 57(6), 1361-1401. google scholar
• Tsong, C. C., & Lee, C. F. (2011). Asymmetric inflation dynamics: evidence from quantile regression analysis. Journal of Macroeconomics, 33(4), 668-680. google scholar
• Tsong, C.-C., Lee, C.-F., Tsai, L.-J., & T.-C. Hu (2016). The Fourier approximation and testing for the null of cointegration. Empirical Economics, 51(3), 1085-1113. doi: 10.1007/s00181-015-1028-6. google scholar
• Yaya, O. S. (2018). Another look at the stationarity of inflation rates in OECD countries. Statistics in Transition. New Series, 19(3), 477-493. google scholar
• Zhou, S. (2010). Nonlinearity and stationarity of inflation rates: evidence from the euro-zone countries. University of Texas at San Antonio Working Paper Series, 0006ECO-106-2010, 849-856. google scholar
• Zivot, E., & Andrews, D. W. K. (2002). Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis. Journal of Business & Economic Statistics, 20(1), 25-44. google scholar