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Testing Linearity in Cointegrating Relations With an Application to Purchasing Power Parity

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  • Hong, Seung Hyun
  • Phillips, Peter C. B.

Abstract

This paper develops a linearity test that can be applied to cointegrating relations. We consider the widely used RESET specification test and show that when this test is applied to nonstationary time series its asymptotic distribution involves a mixture of noncentral chi^2 distributions, which leads to severe size distortions in conventional testing based on the central chi^2. Nonstationarity is shown to introduce two bias terms in the limit distribution, which are the source of the size distortion in testing. Appropriate corrections for this asymptotic bias leads to a modified version of the RESET test which has a central chi^2 limit distribution under linearity. The modified test has power not only against nonlinear cointegration but also against the absence of cointegration. Simulation results reveal that the modified test has good size infinite samples and reasonable power against many nonlinear models as well as models with no cointegration, confirming the analytic results. In an empirical illustration, the linear purchasing power parity (PPP) specification is tested using US, Japan, and Canada monthly data after Bretton Woods. While commonly used ADF and PP cointegration tests give mixed results on the presence of linear cointegration in the series, the modified test rejects the null of linear PPP cointegration.
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  • Hong, Seung Hyun & Phillips, Peter C. B., 2010. "Testing Linearity in Cointegrating Relations With an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 96-114.
    • Handle: RePEc:bes:jnlbes:v:28:i:1:y:2010:p:96-114
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    1. Philip Hans Franses & Dick van Dijk, 2006. "A simple test for PPP among traded goods," Applied Financial Economics, Taylor & Francis Journals, vol. 16(1-2), pages 19-27.
    2. Joon Y. Park & Peter C. B. Phillips, 2000. "Nonstationary Binary Choice," Econometrica, Econometric Society, vol. 68(5), pages 1249-1280, September.
    3. Moshiri, Saeed & Cameron, Norman E & Scuse, David, 1999. "Static, Dynamic, and Hybrid Neural Networks in Forecasting Inflation," Computational Economics, Springer;Society for Computational Economics, vol. 14(3), pages 219-235, December.
    4. Michael, Panos & Nobay, A Robert & Peel, David A, 1997. "Transactions Costs and Nonlinear Adjustment in Real Exchange Rates: An Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 105(4), pages 862-879, August.
    5. Linda F. DeBenedictis, & David E. A. Giles, 1998. "Robust Specification Testing in Regression: The FRESET Test and Autocorrelated Disturbances," Econometrics Working Papers 9806, Department of Economics, University of Victoria.
    6. Thursby, Jerry G, 1981. "A Test Strategy for Discriminating between Autocorrelation and Misspecification in Regression Analysis," The Review of Economics and Statistics, MIT Press, vol. 63(1), pages 117-123, February.
    7. Breitung, Jorg, 2001. "Rank Tests for Nonlinear Cointegration," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(3), pages 331-340, July.
    8. Jeffrey A. Frankel & Andrew K. Rose, 1994. "A Survey of Empirical Research on Nominal Exchange Rates," NBER Working Papers 4865, National Bureau of Economic Research, Inc.
    9. Kenneth Rogoff, 1996. "The Purchasing Power Parity Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 647-668, June.
    10. Serena Ng & Pierre Perron, 2002. "PPP May not Hold Afterall: A Further Investigation," Annals of Economics and Finance, Society for AEF, vol. 3(1), pages 43-64, May.
    11. Phillips, Peter C B, 1983. "ERAs: A New Approach to Small Sample Theory," Econometrica, Econometric Society, vol. 51(5), pages 1505-1525, September.
    12. Baghestani, Hamd, 1991. "Application of the RESET test to the original Andersen-Jordan equation," Journal of Macroeconomics, Elsevier, vol. 13(1), pages 157-169.
    13. Peter C. B. Phillips, 2001. "Descriptive econometrics for non-stationary time series with empirical illustrations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 389-413.
    14. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(1), pages 99-125.
    15. Lo, Ming Chien & Zivot, Eric, 2001. "Threshold Cointegration And Nonlinear Adjustment To The Law Of One Price," Macroeconomic Dynamics, Cambridge University Press, vol. 5(4), pages 533-576, September.
    16. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(3), pages 269-298, June.
    17. Vitaliano, Donald F., 1987. "On the estimation of hospital cost functions," Journal of Health Economics, Elsevier, vol. 6(4), pages 305-318, December.
    18. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-1078, September.
    19. Alan M. Taylor, 2002. "A Century Of Purchasing-Power Parity," The Review of Economics and Statistics, MIT Press, vol. 84(1), pages 139-150, February.
    20. repec:bla:scandj:v:78:y:1976:i:2:p:229-48 is not listed on IDEAS
    21. Lothian, James R & Taylor, Mark P, 1996. "Real Exchange Rate Behavior: The Recent Float from the Perspective of the Past Two Centuries," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 488-509, June.
    22. Ermini, Luigi & Granger, Clive W. J., 1993. "Some generalizations on the algebra of I(1) processes," Journal of Econometrics, Elsevier, vol. 58(3), pages 369-384, August.
    23. Peter C. B. Phillips, 2005. "Econometric Analysis of Fisher's Equation," American Journal of Economics and Sociology, Wiley Blackwell, vol. 64(1), pages 125-168, January.
    24. Andrew P. Blake & George Kapetanios, 2003. "A radial basis function artificial neural network test for neglected nonlinearity," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 357-373, December.
    25. Rudiger Dornbusch, 1985. "Purchasing Power Parity," NBER Working Papers 1591, National Bureau of Economic Research, Inc.
    26. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    27. Siu Fai Leung & Shihti Yu, 2001. "The sensitivity of the RESET tests to disturbance autocorrelation in regression analysis," Empirical Economics, Springer, vol. 26(4), pages 721-726.
    28. Grilli, Vittorio & Kaminsky, Graciela, 1991. "Nominal exchange rate regimes and the real exchange rate : Evidence from the United States and Great Britain, 1885-1986," Journal of Monetary Economics, Elsevier, vol. 27(2), pages 191-212, April.
    29. Yoosoon Chang & Joon Y. Park & Peter C. B. Phillips, 2001. "Nonlinear econometric models with cointegrated and deterministically trending regressors," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-36.
    30. Dumas, Bernard, 1992. "Dynamic Equilibrium and the Real Exchange Rate in a Spatially Separated World," The Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 153-180.
    31. Simon Peters, 2000. "On the use of the RESET test in microeconometric models," Applied Economics Letters, Taylor & Francis Journals, vol. 7(6), pages 361-365.
    32. O'Connell, Paul G. J., 1998. "The overvaluation of purchasing power parity," Journal of International Economics, Elsevier, vol. 44(1), pages 1-19, February.
    33. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
    34. Porter, Richard D. & Kashyap, Anil K., 1984. "Autocorrelation and the sensitivity of reset," Economics Letters, Elsevier, vol. 14(2-3), pages 229-233.
    35. repec:cup:macdyn:v:5:y:2001:i:4:p:533-76 is not listed on IDEAS
    36. Hamilton, James D, 2001. "A Parametric Approach to Flexible Nonlinear Inference," Econometrica, Econometric Society, vol. 69(3), pages 537-573, May.
    37. Lee, Tae-Hwy & White, Halbert & Granger, Clive W. J., 1993. "Testing for neglected nonlinearity in time series models : A comparison of neural network methods and alternative tests," Journal of Econometrics, Elsevier, vol. 56(3), pages 269-290, April.
    38. Froot, Kenneth A. & Rogoff, Kenneth, 1995. "Perspectives on PPP and long-run real exchange rates," Handbook of International Economics, in: G. M. Grossman & K. Rogoff (ed.), Handbook of International Economics, edition 1, volume 3, chapter 32, pages 1647-1688, Elsevier.
    39. Ibragimov, Rustam & Phillips, Peter C.B., 2008. "Regression Asymptotics Using Martingale Convergence Methods," Econometric Theory, Cambridge University Press, vol. 24(4), pages 888-947, August.
    40. N. R. Swanson, 1999. "Finite sample properties of a simple LM test for neglected nonlinearity in error‐correcting regression equations," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 53(1), pages 76-95, March.
    41. Peter Pedroni, 2001. "Purchasing Power Parity Tests In Cointegrated Panels," The Review of Economics and Statistics, MIT Press, vol. 83(4), pages 727-731, November.
    42. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation for Research in Economics, Yale University.
    43. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    44. Xiao, Zhijie & Phillips, Peter C. B., 2002. "A CUSUM test for cointegration using regression residuals," Journal of Econometrics, Elsevier, vol. 108(1), pages 43-61, May.
    45. G. M. Grossman & K. Rogoff (ed.), 1995. "Handbook of International Economics," Handbook of International Economics, Elsevier, edition 1, volume 3, number 3.
    46. Kapetanios George, 2003. "Bootstrap Neural Network Cointegration Tests Against Nonlinear Alternative Hypotheses," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 7(2), pages 1-16, July.
    47. Meese, Richard A. & Rogoff, Kenneth, 1983. "Empirical exchange rate models of the seventies : Do they fit out of sample?," Journal of International Economics, Elsevier, vol. 14(1-2), pages 3-24, February.
    48. Blake, Andrew P. & Kapetanios, George, 2000. "A radial basis function artificial neural network test for ARCH," Economics Letters, Elsevier, vol. 69(1), pages 15-23, October.
    49. Robert de Jong, 2004. "Nonlinear estimators with integrated regressors but without exogeneity," Econometric Society 2004 North American Winter Meetings 324, Econometric Society.
    50. Granger, Clive W J, 1995. "Modelling Nonlinear Relationships between Extended-Memory Variables," Econometrica, Econometric Society, vol. 63(2), pages 265-279, March.
    51. Saikkonen, Pentti & Choi, In, 2004. "Cointegrating Smooth Transition Regressions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 301-340, April.
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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: 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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