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Testing for a Deterministic Trend when there is Evidence of Unit-Root

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  • Gómez, Manuel
  • Ventosa-Santaulària, Daniel

Abstract

Whilst the existence of a unit root implies that current shocks have permanent effects, in the long run, the simultaneous presence of a deterministic trend obliterates that consequence. As such, the long-run level of macroeconomic series depends upon the existence of a deterministic trend. This paper proposes a formal statistical procedure to distinguish between the null hypothesis of unit root and that of unit root with drift. Our procedure is asymptotically robust with regard to autocorrelation and takes into account a potential single structural break. Empirical results show that most of the macroeconomic time series originally analysed by Nelson and Plosser (1982) are characterized by their containing both a deterministic and a stochastic trend.

Suggested Citation

  • Gómez, Manuel & Ventosa-Santaulària, Daniel, 2010. "Testing for a Deterministic Trend when there is Evidence of Unit-Root," MPRA Paper 58780, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:58780
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    References listed on IDEAS

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    1. Carrion-i-Silvestre, Josep Lluís & Kim, Dukpa & Perron, Pierre, 2009. "Gls-Based Unit Root Tests With Multiple Structural Breaks Under Both The Null And The Alternative Hypotheses," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1754-1792, December.
    2. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    3. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
    4. Christiano, Lawrence J, 1992. "Searching for a Break in GNP," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 237-250, July.
    5. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    6. Manuel Gomez-Zaldivar & Daniel Ventosa-Santaularia, 2010. "Per Capita Output Convergence : The Dickey-Fuller Test Under the Simultaneous Presence of Stochastic and Deterministic Trends," Annals of Economics and Statistics, GENES, issue 99-100, pages 429-445.
    7. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    8. Gómez, Manuel & Ventosa-Santaulària, Daniel, 2007. "Income convergence: the Dickey-Fuller test under the simultaneous presence of stochastic and deterministic trends," MPRA Paper 58778, University Library of Munich, Germany.
    9. Kim, Dukpa & Perron, Pierre, 2009. "Unit root tests allowing for a break in the trend function at an unknown time under both the null and alternative hypotheses," Journal of Econometrics, Elsevier, vol. 148(1), pages 1-13, January.
    10. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 473-495.
    11. Josep Lluís Carrion-i-Silvestre & Andreu Sansó, 2006. "Joint hypothesis specification for unit root tests with a structural break *," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 196-224, July.
    12. Vogelsang, Timothy J & Perron, Pierre, 1998. "Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1073-1100, November.
    13. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    14. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119.
    15. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
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    Cited by:

    1. Gomez Zaldivar, M. & Ventosa-Santaularia, D., 2009. "Bilateral Relationship between Consumption and GDP in Mexico and the USA: A Comment," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 9(1).
    2. Antón, Arturo & Hernández-Trillo, Fausto & Ventosa-Santaulària, Daniel, 2021. "(In)Effective tax enforcement and demand for cash," Journal of Macroeconomics, Elsevier, vol. 70(C).
    3. de Jesús Fonseca, Felipe & Gómez-Zaldívar, Manuel & Ventosa-Santaulària, Daniel, 2020. "Public investment and economic activity in Mexico, 1925-1981," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 14, pages 1-24.
    4. Felipe J. Fonseca & Daniel Ventosa-Santaulària, 2011. "Revenue Elasticity of the Main federal Taxes in Mexico," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 48(1), pages 89-111.
    5. Daniel Ventosa-santaulària & Manuel Gómez-zaldívar & Lizet A Pérez, 2013. "Long-run relationship with shifts between Mexican current account revenues and expenditures," Economics Bulletin, AccessEcon, vol. 33(2), pages 1317-1327.
    6. Alfonso Mendoza-Velázquez & Daniel Ventosa-Santaulària & Vicente Germán-Soto, 2019. "Mexico’s inter-regional inequality: a convergent process?," Empirical Economics, Springer, vol. 56(5), pages 1683-1705, May.
    7. Rodríguez-Caballero, Carlos Vladimir & Ventosa-Santaulària, Daniel, 2017. "Energy-growth long-term relationship under structural breaks. Evidence from Canada, 17 Latin American economies and the USA," Energy Economics, Elsevier, vol. 61(C), pages 121-134.
    8. Víctor-Hugo Alcalá Ríos & Manuel Gómez Zaldívar & Daniel Ventosa-Santaulà ria, 2011. "Paradoja Feldstein-Horioka: el caso de México (1950-2007)," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 26(2), pages 293-313.

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    More about this item

    Keywords

    Unit Root; Deterministic Trend; Trend Regression; R2.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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