Revisiting non-linearities in business cycles around the world

Silva Lopes, Artur C. and Florin Zsurkis, Gabriel (2015): Revisiting non-linearities in business cycles around the world.

Abstract

We use first differenced logged quarterly series for the GDP of 29 countries and the euro area to (re)assess the need to use nonlinear models to describe business cycle dynamic behaviour. Our approach is model (estimation)-free, based on testing only. We aim to maximize power to detect non-linearities and, simultaneously, we purport avoiding the pitfalls of data mining. We find evidence supporting the presence of significant non-linearities in 2/3 of the cases only. Hence, it does not provide full support to some descriptions. Linear models cannot be simply dismissed as they are sometimes useful and in many cases they do not seem to leave a substantial fraction of variation to be explained by nonlinear rivals. Nonlinear business cycle variation does not seem to be an universal, undisputable and clearly dominant stylized fact. Therefore, our evidence broadly agrees with the one that has recently emerged from the ``features approach''. Some support for nonlinear dynamics for some further countries is obtained indirectly, through unit root tests, but this marginal to our study, based on indirect methods only and can hardly be invoked to support nonlinearity in classical business cycles. However, it is relevant from the output gap perspective.

• Item Type: MPRA Paper
• Language: English
• Keywords: business cycles; nonlinear time series models; testing.
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles

References

Addo, P. M., Billio, M. and Guégan, D. (2014), The univariate MT-STAR model and a new linearity and unit root test procedure, Computational Statistics and Data Analysis, 76(C), 4-19.

Beaudry, P. and Koop, G. (1993), Do recessions permanently change output?, Journal of Monetary Economics, 31, 149-64.

Bec, F., Guay, A. and Guerre, E. (2008), Adaptive consistent unit-root tests based on autoregressive threshold model, Journal of Econometrics 142, 94--133.

Bec, F., Bouabdallah, O. and Ferrara, L. (2015), Comparing the shape of recoveries: France, the UK and the US, Economic Modelling, 44, 327-34.

Blanchard, O. (2014), Where danger lurks, Finance and Development, IMF, 51(3), available at www.imf.org/external/pubs/ft/fandd/2014/09/blanchard.htm.

Bradley, M. D. and Jansen, D. W. (1997), Nonlinear business cycle dynamics: cross-country evidence on the persistence of aggregate shocks, Economic Inquiry, 35, 495-509.

Bradley, M. D. and Jansen, D. W. (2000), Are business cycle dynamics the same across countries? Testing linearity around the globe, Studies in Nonlinear Dynamics and Econometrics, 4(2), 51-71.

Choi, C.-Y. and Moh, Y.-K. (2007), How useful are tests for unit-root in distinguishing unit-root processes from stationary but non-linear processes? Econometrics Journal, 10, 82-112.

Clements, M. P. and Krolzig, H.-M., (2003), Business cycle asymmetries: characterization and testing based on Markov-switching autoregressions, Journal of Business & Economic Statistics, 21 (1), 196-211.

Crowley, P., Garcia, H. and Quah, C. H. (2008), Is Europe growing together or growing apart? Research Discussion Papers 33/2013, Bank of Finland.

DeLong, J. B. and Summers, L. H. (1984), Are business cycles symmetric?, NBER Working Paper No. 1444.

Elliot, G., Rothenberg, T. J. and Stock, J. H. (1996), Efficient tests for an autoregressive unit root, Econometrica, 64 (4), 813-36.

Enders, W. and Granger, C. W. J. (1998), Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates, Journal of Business & Economic Statistics, 16, 304-11.

Engel, J., Haugh, D. and Pagan, A., (2005), Some methods for assessing the need for non-linear models in business cycle analysis, International Journal of Forecasting, 21 (4), 651-62.

Galvão, A. B. C. (2002), Can non-linear time series models generate US business cycle asymmetric shape? Economics Letters, 77, 187-94.

Granger, C. W. J. and Lee, T.-H. (1999), Effect of aggregation on nonlinearity, Econometric Reviews, 18, 259-69.

Granger, C. W. J. and Teräsvirta, T. (1993), Modelling Nonlinear Economic Relationships, Oxford University Press.

Hamilton, J. (1989), A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica, 57, 357-84.

Harding, D. and Pagan, A. R., (2002), Dissecting the cycle: a methodological investigation, Journal of Monetary Economics, 49, 365-81.

Harvey, D. I., Leybourne, S. J. and Xiao, B., (2008), A powerful test for linearity when the order of integration is unknown, Studies in Nonlinear Dynamics & Econometrics, 12 (3), article 2.

Hess, G. D. and Iwata, S., (1997), Measuring and comparing business-cycle features, Journal of Business & Economic Statistics, 15, 432-44.

Kapetanios, G. and Shin, Y. (2008), GLS detrending-based unit root tests in nonlinear STAR and SETAR models, Economics Letters, 100, 377-80.

Kapetanios, G., Shin, Y. and Snell, A. (2003), Testing for a unit root in the nonlinear STAR framework, Journal of Econometrics, 112, 359-79.

Kiani, K. M. and Bidarkota, P. V. (2004), On business cycle asymmetries in G7 countries, Oxford Bulletin of Economics and Statistics, 66 (3), 333-51.

Kiliç, R. (2004), Linearity tests and stationarity, Econometrics Journal, 7, 55-62.

Kiliç, R. (2011), Testing for a unit root in a stationary ESTAR process, Econometric Reviews, 30 (3), 274-302.

Kose, M. A., Otrok, C. and Prasad, E. (2008), Global business cycles: convergence or decoupling?, IZA Discussion Paper no. 3442

Lee, T.-H., White, H. and Granger, C. W. J. (1993), Testing for neglected nonlinearity in time series models: a comparison of neural network methods and alternative testes, Journal of Econometrics, 56, 269-90.

Leybourne, S.J., Newbold, P. and Vougas, D. (1998), Unit roots and smooth transitions, Journal of Time Series Analysis, 19, 83-97.

Lim, T.-H., Leybourne, S. and Newbold, P. (2002), Unit root tests with a break in innovation variance, Journal of Econometrics, 109, 365-387.

Lütkepohl, H. (2004), Univariate time series models, in Lütkepohl, H. and Krätzig, M. (eds.), Applied Time Series Econometrics, Cambridge University Press, 8-85.

Luukonen, R., Saikkonen, P. and Teräsvirta, T. (1988), Testing linearity against smooth transition autoregressive models, Biometrika, 75, 491-99.

Morley, J. and Piger, J. (2006), The importance of nonlinearity in reproducing business cycle features, in Milas, C., Rothman, P. and van Dijk, D. (eds.), Nonlinear Time Series Analysis of Business Cycles, Elsevier, 75- 94.

Morley, J. and Piger, J. (2012), The asymmetric business cycle, The Review of Economics and Statistics, 94 (1), 208-21.

Neftçi, S. N. (1984), Are economic time series asymmetric over the business cycle?, Journal of Political Economy, 92, 307-28.

Park, J. Y. and Shintani, M. (2005), Testing for a unit root against transitional autoregressive models, Working Paper, Vanderbilt University.

Pippenger, M. K. and Goering, G. E. (1993), A note on the empirical power of unit root tests under threshold processes, Oxford Bulletin of Economics and Statistics, 55, 473-81.

Psaradakis, Z. and Spagnolo, N. (2002), Power properties of nonlinearity tests for time series with Markov regimes, Studies in Nonlinear Dynamics & Econometrics, 6(3), article 2.

Shintani, M. (2013), The inf-t test for a unit root against asymmetric exponential smooth transition autoregressive models, Japanese Economic Review, 64(1), 3-15.

Sichel, D. E. (1993), Business cycle asymmetry: a deeper look, Economic Inquiry, 31, 224-36.

Sollis, R. (2009), A simple unit root test against asymmetric STAR nonlinearity with an application to real exchange rates in Nordic countries, Economic Modelling, 26, 118-25.

Sollis, R. (2011), Testing the unit root hypothesis against TAR nonlinearity using STAR-based tests, Economics Letters, 112, 19--22.

Su, J.-J. and Nguyen, J. K. (2013), GLS detrending in Sollis nonlinear unit root tests, Applied Economics Letters, 20 (13), 1259-62.

Teräsvirta, T. (1994), Specification, estimation, and evaluation of smooth transition autoregressive models, Journal of the American Statistical Association, 89, 208-18.

Teräsvirta, T. (2004), Smooth transition regression modelling, in Lütkepohl, H. and Krätzig, M. (eds.), Applied Time Series Econometrics, Cambridge university Press, 222-41.

Teräsvirta, T. and Anderson, H. A. (1992), Characterising non-linearities in business cycles using smooth transition autoregressive models, Journal of Applied Econometrics, 7, S119-S136.

Tsay, R. S. (1989), Testing and modeling threshold autoregressive models, Journal of the American Statistical Association, 84, 231-40.