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Nonlinear Cointegrating Regression under Weak Identification

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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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.
Contact details of provider: Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/

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Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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  1. Giacomini, Raffaella & Granger, Clive W.J., 2001. "Aggregationn of Space-Time Processes," University of California at San Diego, Economics Working Paper Series qt77f76455, Department of Economics, UC San Diego.
  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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