A Paradox of Inconsistent Parametric and Consistent Nonparametric Regression

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A Paradox of Inconsistent Parametric and Consistent Nonparametric Regression

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Peter C.B. Phillips () (Cowles Foundation, Yale University)
Liangjun Su (School of Economics, Singapore Management University)

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Abstract

This paper explores a paradox discovered in recent work by Phillips and Su (2009). That paper gave an example in which nonparametric regression is consistent whereas parametric regression is inconsistent even when the true regression functional form is known and used in regression. This appears to be a paradox, as knowing the true functional form should not in general be detrimental in regression. In the present case, local regression methods turn out to have a distinct advantage because of endogeneity in the regressor. The paradox arises because additional correct information is not necessarily advantageous when information is incomplete. In the present case, endogeneity in the regressor introduces bias when the true functional form is known, but interestingly does not do so in local nonparametric regression. We examine this example in detail and propose two new consistent estimators for the parametric regression, which address the endogeneity in the regressor by means of spatial bounding and bias correction using nonparametric estimation. Some simulations are reported illustrating the paradox and the new procedures.

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Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1704.

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Length: 31 pages
Date of creation: Jun 2009
Date of revision:
Handle: RePEc:cwl:cwldpp:1704

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods

This paper has been announced in the following NEP Reports:

NEP-ALL-2009-06-17 (All new papers)
NEP-ECM-2009-06-17 (Econometrics)
NEP-ETS-2009-06-17 (Econometric Time Series)

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Peter C.B. Phillips & Liangjun Su, 2009. "Nonparametric Structural Estimation via Continuous Location Shifts in an Endogenous Regressor," Cowles Foundation Discussion Papers 1702, Cowles Foundation, Yale University. [Downloadable!]

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This page was last updated on 2009-11-12.

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