Abstract
The aim of this article is to provide additional evidence about the order of integration of constant price GDP per capita in a selection of countries. It does so by taking into account the possibility of non-linear deterministic trends and of asymmetric adjustment towards equilibrium. We find evidence of a global stationary ESTAR process around a nonlinear deterministic trend in almost half of the selected countries. These results show that nonlinearities affect real GDP series. By neglecting them, one can draw misleading conclusions from unit root tests. Specifically, the article questions the so-called stylised fact of a near unit root which has so influenced macroeconomic thought over the past two decades.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abadir KM, Distaso W (2007) Testing joint hypotheses when one of the alternatives is one-sided. J Econom 140: 695–718
Beechy M, Österholm P (2008) Revisiting the uncertain unit root in GDP and CPI: testing for non-linear trend reversion. Econ Lett 100: 221–223
Ben-David D, Papell DH (1995) The great wars, the great crash, and the steady state growth: some new evidence about an old stylized fact. J Monet Econ 36: 453–475
Bhargava A (1986) On the theory of testing for unit roots in observed time series. Rev Econ Stud 53: 369–384
Bierens HJ (1997) Testing the unit root with drift hypothesis against nonlinear trend stationarity, with an application to the U.S. price level and interest rate. J Econom 81: 29–64
Caner M, Hansen B (2001) Threshold autoregressive with a unit root. Econometrica 69: 1555–1596
Chang T, Nieh C-C, Wei C-C (2005) Is per capita real GDP stationary? evidence from selected African countries based on more powerful nonlinear (logistic) unit root tests. Econ Bull 3: 1–9
Christopoulos DK (2006) Does a non-linear mean reverting process characterize real GDP movements. Empir Econ 31: 601–611
Durlauf SN (1989) Output persistence, economic structure, and the choice of stabilization policy. Brook Pap Econ Activity 2: 69–136
Elliot G, Rothenberg TJ, Stock JH (1996) Efficient tests for an autoregressive unit root. Econometrica 64: 813–836
Enders W, Ludlow J (2002) Tests for non-linear decay using a fourier approximation. Working Paper WP01-02-02. The university of Alabama
Evans GW (1989) Output and employment dynamics in the united states. J Appl Econom 4: 213–237
Harvey DI, Leybourne SJ (2007) Testing for time series linearity. Econom J 10: 149–165
Harvey DI, Leybourne SJ, Xiao B (2008) A powerful test for linearity when the order of integration is unknown. Stud Nonlinear Dyn Econom, vol 12, article 2
Kapetanios G, Shin Y, Snell A (2003) Testing for a unit root in the nonlinear STAR framework. J Econom 112: 359–379
Kruse R (2010) A new unit root test against ESTAR based on a class of modified statistics. Stat Pap (forthcoming)
Leybourne SJ, Mills TC, Newbold P (1998) Spurious rejections by Dickey–Fuller tests in the presence of a break under the null. J Econom 87(1): 191–203
Li X-M (2000) The great leap forward, economic reforms, and the unit root hypothesis: testing for breaking trend functions in China’s GDP data. J Comp Econ 28: 814–827
Ludlow J, Enders W (2000) Estimating non-linear arma models using fourier coefficients. Int J Forecast 16: 333–347
Michael P, Nobay A, Peel D (1997) Transaction costs and nonlinear adjustment in real exchange rates: An empirical investigation. J Political Econ 105: 862–879
Murray CJ, Nelson CR (2000) The uncertain trend in U.S. GDP. J Monet Econ 46: 79–95
Nelson CR, Plosser CI (1982) Trends and random walks in macroeconomic time series. J Monet Econ 10: 139–162
Ng S, Perron P (2001) Lag selection and the construction of unit root tests with good size and power. Econometrica 69: 1519–1554
Perron P (1989) The great crash, the oil price shock and the unit root hypothesis. Econometrica 57: 1361–1401
Perron P (1990) Testing for a unit root in a time series with a changing mean. J Bus Econ Stat 8: 153–162
Perron P, Phillips PCB (1987) Does GNP have a unit root? A reevaluation. Econ Lett 23: 139–145
Phillips PCB (1987) Time series regression with a unit root. Econometrica 55: 311–340
Phillips PCB, Perron P (1988) Testing for a unit root in time series regression. Biometrica 75: 335–346
Vougas DV (2007) Is the trend in post-WW II US real gdp uncertain or non-linear?. Econ Lett 94: 348–355
West KD (1988) Asymptotic normality when regressors have a unit root. Econometrica 56: 1397–1418
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cuestas, J.C., Garratt, D. Is real GDP per capita a stationary process? Smooth transitions, nonlinear trends and unit root testing. Empir Econ 41, 555–563 (2011). https://doi.org/10.1007/s00181-010-0389-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00181-010-0389-0