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Nonlinear Cointegrating Regression under Weak Identification

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Abstract

An asymptotic theory is developed for a weakly identified cointegrating regression model in which the regressor is a nonlinear transformation of an integrated process. Weak identification arises from the presence of a loading coefficient for the nonlinear function that may be close to zero. In that case, standard nonlinear cointegrating limit theory does not provide good approximations to the finite sample distributions of nonlinear least squares estimators, resulting in potentially misleading inference. A new local limit theory is developed that approximates the finite sample distributions of the estimators uniformly well irrespective of the strength of the identification. An important technical component of this theory involves new results showing the uniform weak convergence of sample covariances involving nonlinear functions to mixed normal and stochastic integral limits. Based on these asymptotics, we construct confidence intervals for the loading coefficient and the nonlinear transformation parameter and show that these confidence intervals have correct asymptotic size. As in other cases of nonlinear estimation with integrated processes and unlike stationary process asymptotics, the properties of the nonlinear transformations affect the asymptotics and, in particular, give rise to parameter dependent rates of convergence and differences between the limit results for integrable and asymptotically homogeneous functions.

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File URL: http://cowles.econ.yale.edu/P/cd/d17b/d1768.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1768.

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Length: 46 pages
Date of creation: Sep 2010
Date of revision:
Publication status: Published in Econometric Theory (June 2012), 28(3): 509-547
Handle: RePEc:cwl:cwldpp:1768

Note: CFP 1355.
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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Integrated process; Local time; Nonlinear regression; Uniform weak convergence; Weak identification;

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References

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  1. Raffaella Giacomini & Clive W.J. Granger, 2002. "Aggregation of Space-Time Processes," Boston College Working Papers in Economics 582, Boston College Department of Economics.
  2. Robert de Jong, 2004. "Nonlinear estimators with integrated regressors but without exogeneity," Econometric Society 2004 North American Winter Meetings 324, Econometric Society.
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Cited by:
  1. Donald W.K. Andrews & Xu Cheng, 2011. "GMM Estimation and Uniform Subvector Inference with Possible Identification Failure," Cowles Foundation Discussion Papers 1828, Cowles Foundation for Research in Economics, Yale University, revised Jan 2013.
  2. 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.
  3. Xu Cheng, 2014. "Uniform Inference in Nonlinear Models with Mixed Identification Strength," PIER Working Paper Archive 14-018, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  4. Yae In Baek & Jin Seo Cho & Peter C.B. Phillips, 2013. "Testing Linearity Using Power Transforms of Regressors," Cowles Foundation Discussion Papers 1917, Cowles Foundation for Research in Economics, Yale University.
  5. repec:wyi:journl:002195 is not listed on IDEAS

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