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Nonparametric Structural Estimation via Continuous Location Shifts in an Endogenous Regressor

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Abstract

Recent work by Wang and Phillips (2009b, c) has shown that ill posed inverse problems do not arise in nonstationary nonparametric regression and there is no need for nonparametric instrumental variable estimation. Instead, simple Nadaraya Watson nonparametric estimation of a (possibly nonlinear) cointegrating regression equation is consistent with a limiting (mixed) normal distribution irrespective of the endogeneity in the regressor, near integration as well as integration in the regressor, and serial dependence in the regression equation. The present paper shows that some closely related results apply in the case of structural nonparametric regression with independent data when there are continuous location shifts in the regressor. In such cases, location shifts serve as an instrumental variable in tracing out the regression line similar to the random wandering nature of the regressor in a cointegrating regression. Asymptotic theory is given for local level and local linear nonparametric estimators, links with nonstationary cointegrating regression theory and nonparametric IV regression are explored, and extensions to the stationary strong mixing case are given. In contrast to standard nonparametric limit theory, local level and local linear estimators have identical limit distributions, so the local linear approach has no apparent advantage in the present context. Some interesting cases are discovered, which appear to be new in the literature, where nonparametric estimation is consistent whereas parametric regression is inconsistent even when the true (parametric) regression function is known. The methods are further applied to establish a limit theory for nonparametric estimation of structural panel data models with endogenous regressors and individual effects. Some simulation evidence is reported.

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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 1702.

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Length: 42 pages
Date of creation: Jun 2009
Date of revision:
Publication status: Published in Econometrics Journal (October 2011), 14(3): 457-486
Handle: RePEc:cwl:cwldpp:1702

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Keywords: Fixed effects; Kernel regression; Location shift; Mixing; Nonparametric IV; Nonstationarity; Panel model; Structural estimation;

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References

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  1. 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.
  2. Whitney K. Newey & James L. Powell & Francis Vella, 1998. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Working papers 98-6, Massachusetts Institute of Technology (MIT), Department of Economics.
  3. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
  4. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77 Elsevier.
  5. Richard Blundell & James Powell, 2001. "Endogeneity in nonparametric and semiparametric regression models," CeMMAP working papers CWP09/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
  7. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76 Elsevier.
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Cited by:
  1. Peter C.B. Phillips & Liangjun Su, 2009. "A Paradox of Inconsistent Parametric and Consistent Nonparametric Regression," Cowles Foundation Discussion Papers 1704, Cowles Foundation for Research in Economics, Yale University.

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