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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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Bibliographic Info

Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

Volume (Year): 28 (2010)
Issue (Month): 1 ()
Pages: 96-114

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Handle: RePEc:bes:jnlbes:v:28:i:1:y:2010:p:96-114

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References

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Citations

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Cited by:
  1. Vadim Marmer, 2005. "Nonlinearity, Nonstationarity and Spurious Forecasts," Econometrics 0503002, EconWPA, revised 15 Dec 2005.
  2. Derek Bond & Michael J. Harrison & Edward J. O'Brien, 2006. "Purchasing Power Parity: The Irish Experience Re-visited," Trinity Economics Papers tep200615, Trinity College Dublin, Department of Economics.
  3. Liew, Venus Khim-Sen & Ling, Tai-Hu & Chia, Ricky Chee-Jiun & Yoon, Gawon, 2012. "On the application of the rank tests for nonlinear cointegration to PPP: The case of Papua New Guinea," Economic Modelling, Elsevier, vol. 29(2), pages 326-332.
  4. Haiqiang Chen & Ying Fang & Yingxing Li, 2013. "Estimation and Inference for Varying-coefficient Models with Nonstationary Regressors using Penalized Splines," SFB 649 Discussion Papers SFB649DP2013-033, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  5. Qiying Wang & Peter C.B. Phillips, 2006. "Asymptotic Theory for Local Time Density Estimation and Nonparametric Cointegrating Regression," Cowles Foundation Discussion Papers 1594, Cowles Foundation for Research in Economics, Yale University.
  6. repec:wyi:journl:002195 is not listed on IDEAS
  7. Chaohua Dong & Jiti Gao & Dag Tjostheim & Jiying Yin, 2014. "Specification Testing for Nonlinear Multivariate Cointegrating Regressions," Monash Econometrics and Business Statistics Working Papers 8/14, Monash University, Department of Econometrics and Business Statistics.
  8. Chaohua Dong & Jiti Gao, 2014. "Specification Testing in Structural Nonparametric Cointegration," Monash Econometrics and Business Statistics Working Papers 2/14, Monash University, Department of Econometrics and Business Statistics.

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