Unit Roots, Level Shifts and Trend Breaks in Per Capita Output: A Robust Evaluation

Kejriwal, Mohitosh and Lopez, Claude (2010): Unit Roots, Level Shifts and Trend Breaks in Per Capita Output: A Robust Evaluation.

Abstract

Determining whether per capita output can be characterized by a stochastic trend is complicated by the fact that infrequent breaks in trend can bias standard unit root tests towards non-rejection of the unit root hypothesis. The bulk of the existing literature has focused on the application of unit root tests allowing for structural breaks in the trend function under the trend stationary alternative but not under the unit root null. These tests, however, provide little information regarding the existence and number of trend breaks. Moreover, these tests su¤er from serious power and size distortions due to the asymmetric treatment of breaks under the null and alternative hypotheses. This paper estimates the number of breaks in trend employing procedures that are robust to the unit root/stationarity properties of the data. Our analysis of the per-capita GDP for OECD countries thereby permits a robust classi�cation of countries according to the "growth shift", "level shift" and "linear trend" hypotheses. In contrast to the extant literature, unit root tests conditional on the presence or absence of breaks do not provide evidence against the unit root hypothesis.

• Item Type: MPRA Paper
• Language: English
• Keywords: growth shift, level shift, structural change, trend breaks, unit root
• Subjects: E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes

References

Andrews, D.W.K. (1993), Tests for Parameter Instability and Structural Change with Unknown Change Point, Econometrica 61, 821-856.

Andrews, D.W.K. and W. Ploberger (1994), Optimal Tests when a Nuisance Parameter is present only under the Alternative Econometrica 62, 1383-1414.

Bai, J. (1994), Least Squares Estimation of a Shift in Linear Processes, Journal of Time Series Analysis 15, 453-472.

Bai, J. (1997), Estimation of a Change Point in Multiple Regression Models, The Review of Economics and Statistics 79, 551-563.

Bai, J. and P. Perron (1998), Estimating and Testing Linear Models with Multiple Structural Changes, Econometrica 66, 47-78.

Balke, N.S. and T.B Fomby (1991), Shifting Trends, Segmented Trends, and Infrequent Permanent Shocks, Journal of Monetary Economics 28, 61-85.

Banerjee, A., J. Dolado, and J.W. Galbraith (1990), Recursive Tests for Unit Roots and Structural Breaks in Long Annual GNP Series, Manuscript, University of Florida.

Banerjee, A., R.L. Lumsdaine and J. H. Stock (1992), Recursive and Sequential Tests of the Unit Root and Trend-Break Hypotheses: Theory and International Evidence, Journal of Business and Economic Statistics 10, 271-287.

Ben-David, D. and D.H. Papell (1995), The Great Wars, the Great Crash, and steady state growth: Some new Evidence about an Old Stylized Fact, Journal of Monetary Economics 36, 453—475.

Ben-David, D. and D.H. Papell (2000), Some Evidence on the Continuity of the Growth Process among the G7 Countries, Economic Inquiry 38, 320—330.

Ben-David, D., R.L. Lumsdaine, and D.H. Papell (2003), Unit Roots, Postwar Slowdowns and Long-run Growth: Evidence from two Structural Breaks, Empirical Economics 28, 303—319.

Bradley, M.D. and D.W. Jansen (1995), Unit Roots and Infrequent Large Shocks: New International Evidence on Output Growth, Journal of Money, Credit, and Banking 27, 876—893.

Carrion-i-Silvestre, J.L., D. Kim and P. Perron (2009), GLS-based Unit Root Tests with Multiple Structural Breaks both Under the Null and the Alternative Hypotheses, Econometric Theory 25, 1754-1792.

Campbell, J.Y. and P. Perron (1991), Pitfalls and Opportunities: What Macroeconomists should know about Unit Roots, NBER Macroeconomics Annual 6, 141-201.

Chong, T.T. (1995), Partial Parameter Consistency in a Misspecified Structural Change Model, Economics Letters 49, 351-357.

Christiano, L.J. (1992), Searching for a Break in GNP, Journal of Business and Economic Statistics 10, 237—250.

Darne, O. and C. Diebolt (2004), Unit Roots and Infrequent Large Shocks: New International Evidence on Output, Journal of Monetary Economics 51, 1449-1465.

Dickey, D.A. andW.A. Fuller (1979), Distribution of the Estimators for Autoregressive Time Series with a Unit Root, Journal of the American Statistical Association 74, 427-431.

Elliott, G., Rothenberg, T., and J.H. Stock (1996), Efficient Tests for an Autoregressive Unit Root, Econometrica 64, 813-836.

Harris, D., D.I. Harvey, S.J. Leybourne and A.M.R. Taylor (2009), Testing for a Unit Root in the Presence of a Possible Break in Trend, Econometric Theory 25, 1545-1588.

Harvey, D. I., Leybourne, S. J. and A.M.R Taylor (2007), A Simple, Robust and Powerful Test of the Trend Hypothesis, Journal of Econometrics 141, 1302-1330.

Harvey, D.I., S.J. Leybourne, and A.M.R. Taylor (2009), Simple, Robust and Powerful Tests of the Breaking Trend Hypothesis, Econometric Theory 25, 995-1029.

Harvey, D.I., S.J. Leybourne, and A.M.R. Taylor (2010), Robust Methods for Detecting Multiple Level Breaks in Autocorrelated Time Series, Journal of Econometrics 157, 342-358.

Hatanaka, M. and K. Yamada (1999), A Unit Root Test in the Presence of Structural Changes in I(1) and I(0) models, in R.F. Engle and H. White (eds.), Cointegration, Causality and Forecasting, Oxford University Press.

Kejriwal, M. and P. Perron (2010), A Sequential Procedure to Determine the Number of Breaks in Trend with an Integrated or Stationary Noise Component, Journal of Time Series Analysis 31, 305-328.

Kilian, L. and L. Ohanian (2002), Unit Roots, Trend Breaks, and Transitory Dynamics: A Macroeconomic Perspective, Macroeconomic Dynamics 6, 614-631.

Kim, D. and P. Perron (2009), Unit Root TestsAllowing for a Break in theTrend Function at an Unknown Time under Both the Null and Alternative Hypotheses, Journal of Econometrics 148, 1-13.

Kuznets, S. (1963), Notes on the Take-off, inW.W. Rostow (ed.), The Economics of Take-Off into Sustained Growth, Macmillan.

Lee, J., and M.C. Strazicich (2001), Break Point Estimation and Spurious Rejections with Endogenous Unit Roots, Oxford Bulletin of Economics and Statistics 63, 535-558.

Lee, J., and M.C. Strazicich (2003), Minimum Lagrange Multiplier Unit Root Test with Two Structural Breaks, The Review of Economics and Statistics 85, 1082-1089.

Lumsdaine, R.L. and D.H. Papell (1997), Multiple Trend Breaks and the Unit Root Hypothesis, Review of Economics and Statistics 79, 212—218.

Maddison, A. (2009), Statistics on World Population, GDP and Per Capita GDP,http://www.ggdc.net/maddison/.

Murray, C.J. and C.R. Nelson (2000), The Uncertain Trend in U.S. GDP, Journal of Monetary Economics 46, 79—95.

Ng, S. and P. Perron (2001), Lag Length Selection and the Construction of Unit Root Tests With Good Size and Power, Econometrica 69, 1519-1554.

Olson, M. (1982), The Rise and Decline of Nations: Economic Growth, Stagflation and Social Rigidities, Yale University Press, 1982.

Nunes, L.C., P. Newbold, and C.-M. Kuan (1997), Testing for Unit Roots with Breaks: Evidence on the Great Crash and the Unit Root Hypothesis Reconsidered, Oxford Bulletin of Economics and Statistics 59, 435—448.

Papell, D.H. and R. Prodan (2004), The Uncertain Unit Root in U.S. Real GDP: Evidence with Restricted and Unrestricted Structural Change, Journal of Money, Credit and Banking 36, 423-427.

Papell D.H. and R. Prodan (2009), Time Series Tests of Constant Steady-State Growth, Working Paper, University of Houston.

Perron, P. (1989), The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis, Econometrica 57, 1361—1401.

Perron, P. (1997), Further Evidence on Breaking Trend Functions in Macroeconomic Variables, Journal of Econometrics 80, 355—386.

Perron, P. and T. Yabu (2009a), Testing for Shifts in Trend with an Integrated or Stationary Noise Component, Journal of Business and Economic Statistics 27, 369-396.

Perron, P. and T. Yabu (2009b), Estimating Deterministic Trends with an Integrated or Stationary Noise Component, Journal of Econometrics 151, 56-69.

Perron, P. and X. Zhu (2005), Structural Breaks with Deterministic and Stochastic Trends, Journal of Econometrics 129, 65-119.

Prodan, R. (2008), Potential Pitfalls in Determining Multiple Structural Changes with an Application to Purchasing Power Parity, Journal of Business and Economic Statistics 26, 50-65.

Raj, B. (1992), International Evidence on Persistence in Output in the Presence of an Episodic Change, Journal of Applied Econometrics 7, 281—293.

Romer, P.M. (1986), Increasing Returns and Long-Run Growth, Journal of Political Economy 98, 71-102.

Rosenstein-Rodan, P.N. (1943), Problems of Industrialization of Eastern and South-Eastern Europe, The Economic Journal 53, 202-211.

Rostow, W.W. (1961), The Stages of Economic Growth: A Non-Communist Manifesto, Cambridge University Press.

Roy, A. and W.A. Fuller (2001), Estimation for Autoregressive Time Series With a Root Near 1, Journal of Business and Economic Statistics 19, 482-493.

Vogelsang, T.J. (1998), Trend Function Hypothesis Testing in the Presence of Serial Correlation, Econometrica 66, 123-148.

Vogelsang, T.J. (2001), Tests for a Shift in trend when Serial Correlation is of Unknown Form, Unpublished Manuscript, Department of Economics, Cornell University.

Vogelsang, T.J and P. Perron (1998), Additional Tests for a Unit Root Allowing the Possibility of Breaks in the Trend Function, International Economic Review 39, 1073-1100.

Zelhorst, D. and J. De Haan (1995), Testing for a Break in Output: New International Evidence, Oxford Economic Papers 47, 357—362.

Zivot, E. and D.W.K. Andrews (1992), Further Evidence on the Great Crash, the Oil-price Shock, and the Unit-root Hypothesis, Journal of Business and Economic Statistics 10, 251—270.