Nonlinear estimators with integrated regressors but without exogeneity
This paper analyzes nonlinear cointegrating regressions as have been recently analyzed in a paper by Park and Phillips in Econometrica. I analyze the consequences of removing Park and Phillips' exogeneity assumption, which for the special case of a linear model would imply the asymptotic validity of the least squares estimator for linear cointegrating regressions. For the linear model, the unlikeliness of such an exogeneity assumption to hold in practice has inspired the `fully modified' technique, the `leads and lags' technique, and Park's `canonical regressions'. In this paper, a `fully modified' type technique is proposed for nonlinear cointegrating regressions. The mathematical tool for proving this result is a new so-called `convergence to stochastic integrals' result. This result is proven for objects that are summations of a stationary random variable times an asymptotically homogeneous function of an integrated process. The increments of the integrated process are allowed to be correlated with the stationary random variable. This result is derived by extending a line of proof pioneered in work by Chan and Wei
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- Joon Y. Park & Peter C.B. Phillips, 1998.
"Nonlinear Regressions with Integrated Time Series,"
Cowles Foundation Discussion Papers
1190, Cowles Foundation for Research in Economics, Yale University.
- Peter C.B. Phillips, 1985.
"Understanding Spurious Regressions in Econometrics,"
Cowles Foundation Discussion Papers
757, Cowles Foundation for Research in Economics, Yale University.
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- Davidson, James & de Jong, Robert M., 2000.
"The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals Ii,"
Cambridge University Press, vol. 16(05), pages 643-666, October.
- de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(05), pages 621-642, October.
- Park, Joon Y. & Phillips, Peter C.B., 1999.
"Asymptotics For Nonlinear Transformations Of Integrated Time Series,"
Cambridge University Press, vol. 15(03), pages 269-298, June.
- Peter C.B. Phillips & Joon Y. Park, 1998. "Asymptotics for Nonlinear Transformations of Integrated Time Series," Cowles Foundation Discussion Papers 1182, Cowles Foundation for Research in Economics, Yale University.
- Joon Y. Park & Peter C. B. Phillips, 1999.
"Nonstationary Binary Choice,"
Working Paper Series
no5, Institute of Economic Research, Seoul National University.
- Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-43, January.
- Peter C.B. Phillips & Bruce E. Hansen, 1988. "Statistical Inference in Instrumental Variables," Cowles Foundation Discussion Papers 869R, Cowles Foundation for Research in Economics, Yale University, revised Apr 1989.
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