Extended Enders and Siklos test for threshold cointegration

Magdalena Osińska; Maciej Gałecki

doi:10.5604/01.3001.0015.8669

Magdalena Osińska Nicolaus Copernicus University in Toruń, Faculty of Economic Sciences and Management, ul. Gagarina 13a, 87-100 Toruń ORCID:https://orcid.org/0000-0002-9796-2892 , Maciej Gałecki University of Łódź, Faculty of Economics and Sociology, Chair of Econometric Models and Forecasts, ul. Rewolucji 1905 r. 37/39, 90-214 Łódź ORCID:https://orcid.org/0000-0002-6402-8489 Przegląd Statystyczny. Statistical Review, vol. 69, 2022, 1, pages: 1-20 Published online: 30 June 2022 DOI 10.5604/01.3001.0015.8669 Citation: Osińska, M., & Gałecki, M. (2022). Extended Enders and Siklos test for threshold cointegration. Przegląd Statystyczny. Statistical Review, 69(1), 1–20. https://doi.org/10.5604/01.3001.0015.8669.

820 Views 84 Downloads

ARTICLE

(English) PDF

ABSTRACT

In our previous studies, we modified the Enders and Siklos test for threshold error correction to a version allowing the individual threshold variable to be responsible for the asymmetric mechanism of the system. The idea was to learn about the threshold mechanism both in the long and short run. In this paper, we tested for the asymmetry of the adjustment of the error correction mechanism towards the long-run path. The subsamples within regimes differ in size with respect to the threshold value. The novelty lies in the division of both short and long-run variables according to a threshold variable with a given threshold value (assumed or estimated). We named the test extended Enders and Siklos test (exE-S). The present study focuses on the power and size of the modified procedure. A simulation study was designed, computed and conducted. The results are favourable for the proposed approach, although they strongly depend on the difference in values between the adjustment parameters in the regimes.

KEYWORDS

threshold error correction test, power, size, Monte Carlo, economic growth

JEL

C22, O47

REFERENCES

Aharoni, Y. (2014). The Israeli Economy. Dreams and Realities. Routledge. https://doi.org/10.4324/9781315863160.

Balke, N. S., & Fomby, T. B. (1997). Threshold cointegration. International Economic Review, 38(3), 627–645. https://doi.org/10.2307/2527284.

Boehlke, J., Faldzinski, M., Galecki, M., & Osinska, M. (2017). Dynamics of Economic Growth in Ireland in 1980–2014. St. Petersburg State Polytechnical University Journal. Economics, 10(2), 7–20. https://doi.org/10.18721/JE.10201.

Boehlke, J., Fałdziński, M., Gałecki, M., & Osińska, M. (2018). Economic growth in Ireland in 1980–2014. A threshold cointegration approach. Argumenta Oeconomica, (2), 157–188. https://doi.org/10.15611/aoe.2018.2.07.

Boehlke, J., Fałdziński, M., Gałecki, M., & Osińska, M. (2019). Econometric Analysis of Economic Miracles in Selected Economies Using TECM Approach. In M. Osińska (Ed.), Economic Miracles in the European Economies (pp. 175–230). Springer. https://doi.org/10.1007/978-3-030-05606-3_9.

Bruzda, J. (2007). Procesy nieliniowe i zależności długookresowe w ekonomii. Analiza kointegracji nieliniowej. Wydawnictwo Naukowe Uniwersytetu Mikołaja Kopernika.

Chan, K. S. (1993). Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model. The Annals of Statistics, 21(1), 520–533. https://doi.org/10.1214/aos/1176349040.

Chorev, S., & Anderson, A. R. (2006). Success in Israeli high-tech start-ups; Critical factors and process. Technovation, 26(2), 162–174. https://doi.org/10.1016/j.technovation.2005.06.014.

Enders, W., & Siklos, P. L. (2001). Cointegration and Threshold Adjustment. Journal of Business & Economic Statistics, 19(2), 166–176. https://doi.org/10.1198/073500101316970395.

Engle, R. F., & Granger, C. W. J. (1987). Co-Integration and Error Correction: Representation, Estimation, and Testing. Econometrica, 55(2), 251–276. https://doi.org/10.2307/1913236.

Frey, G., & Manera, M. (2007). Econometric Models of Asymmetric Price Transmission. Journal of Economic Surveys, 21(2), 349–415. https://doi.org/10.1111/j.1467-6419.2007.00507.x.

Gałecki, M., & Osińska, M. (2019). Threshold Error Correction Model: A Methodological Overview. In M. Osińska (Ed.), Economic Miracles in the European Economies (pp. 151–173). Springer. https://doi.org/10.1007/978-3-030-05606-3_8.

Ghassan, H. B., & Banerjee, P. K. (2015). A Threshold Cointegration Analysis of Asymmetric Adjustment of OPEC and non-OPEC Monthly Crude Oil Prices. Empirical Economics, 49(1), 305–323. https://doi.org/10.1007/s00181-014-0848-0.

Gosińska, E., Leszkiewicz-Kędzior, K., & Welfe, A. (2020). Who is responsible for asymmetric fuel price adjustments? An application of the threshold cointegrated VAR model. Baltic Journal of Economics, 20(1), 59–73. https://doi.org/10.1080/1406099X.2020.1746114.

Granger, C. W. J., & Lee, T. H. (1989). Investigation of Production, Sales and Inventory Relationships Using Multicointegration and Non-Symmetric Error Correction Models. Journal of Applied Econometrics, 4(S1), 145–159. https://doi.org/10.1002/jae.3950040508.

Hansen, B. E., & Seo, B. (2002). Testing for two-regime threshold cointegration in vector errorcorrection models. Journal of Econometrics, 110(2), 293–318. https://doi.org/10.1016/S0304-4076(02)00097-0.

Hassouneh, I., Serra, T., Bojnec, Š., & Gil, J. M. (2017). Modelling price transmission and volatility spillover in the Slovenian wheat market. Applied Economics, 49(41), 4116–4126. https://doi.org/10.1080/00036846.2016.1276273.

Hogg, R. V., McKean, J. W., & Craig, A. T. (2005). Introduction to Mathematical Statistics (6th edition). Upper Saddle River, Pearson Education.

Kapetanios, G., Shin, Y., & Snall, A. (2006). Testing for Cointegration in Nonlinear Smooth Transition Error Correction Models. Econometric Theory, 22(2), 279–303. https://doi.org/10.1017/S0266466606060129.

Leszkiewicz-Kędzior, K., & Welfe, A. (2014). Asymmetric Price Adjustments in the Fuel Market. Central European Journal of Economic Modelling and Econometrics, (2), 105–127. https://doi.org/10.24425/cejeme.2014.119235.

Lichtenberg, F. R. (1995). The output contributions of computer equipment and personnel: A firm-level analysis. Economics of Innovation and New Technology, 3(3–4), 201–218. https://doi.org/10.1080/10438599500000003.

Lloyd, C. J. (2006). Estimating test power adjusted for size. Journal of Statistical Computation and Simulation, 75(11), 921–933. https://doi.org/10.1080/00949650412331321160.

Martens, M., Kofman, P., & Vorst, T. C. F. (1998). A threshold error-correction model for intraday futures and index returns. Journal of Applied Econometrics, 13(3), 245–263. https://doi.org /10.1002/(SICI)1099-1255(199805/06)13:3%3C245::AID-JAE480%3E3.0.CO;2-E.

Piłatowska, M., & Włodarczyk, A. (2017). The Environmental Kuznets Curve in the CEE Countries – the Threshold Cointegration Approach. Argumenta Oeconomica, (2), 307–340. http://dx.doi.org/10.15611/aoe.2017.2.13.

Quandt, R. E. (1958). The Estimation of the Parameters of a Linear Regression System Obeying Two Separate Regimes. Journal of the American Statistical Association, 53(284), 873–880. https://doi.org/10.2307/2281957.

Stigler, M. (2010, January 10). Threshold cointegration: overview and implementation in R. https://cran.r-project.org/web/packages/tsDyn/vignettes/ThCointOverview.pdf.

Tong, H. (1990). Non-linear Time Series: A Dynamical System Approach. Oxford University Press.

Trajtenberg, M. (2001). R&D Policy in Israel. In M. P. Feldman, & A. N. Link (Eds.), Innovation policy in the knowledge-based economy (pp. 409–454). Springer. https://doi.org/10.1007/978-1-4615-1689-7_18.

Tsay, R. S. (1998). Testing and Modeling Multivariate Threshold Models. Journal of the American Statistical Association, 93(443), 1188–1202. https://doi.org/10.1080/01621459.1998.10473779.

Zilberfarb, B-Z. (2006). From Boom to Bust: The Israeli Economy 1990–2003. Israel Affairs, 12(2), 221–233. https://doi.org/10.1080/13537120500535126.