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A Paradox of Inconsistent Parametric and Consistent Nonparametric Regression

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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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  • 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.
  • Handle: RePEc:cwl:cwldpp:1704
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d17/d1704.pdf
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    1. 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 for Research in Economics, Yale University.
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    Keywords

    Bias-correction; Endogeneity; Kernel regression; L_{2} regression; Location shift; Nonparametric IV; Nonstationarity; Paradox; Spatial regression; Structural Estimation;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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