Non-parametric Regression under Location Shifts
Recent work by Wang and Phillips (2009b, 2011) has shown that ill-posed inverse problems do not arise in non-stationary non-parametric regression and there is no need for non-parametric instrumental variable estimation. Instead, simple Nadaraya–Watson non-parametric estimation of a cointegrating reg...
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sg-smu-ink.soe_research-23632017-08-05T00:10:51Z Non-parametric Regression under Location Shifts PHILLIPS, Peter C. B. SU, Liangjun Recent work by Wang and Phillips (2009b, 2011) has shown that ill-posed inverse problems do not arise in non-stationary non-parametric regression and there is no need for non-parametric instrumental variable estimation. Instead, simple Nadaraya–Watson non-parametric estimation of a cointegrating regression equation is consistent irrespective of the endogeneity in the regressor. The present paper shows that some closely related results apply in the case of structural non-parametric regression with independent data when there are continuous location shifts in the regressor. Some interesting cases are discovered where non-parametric 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. The paradox arises because additional correct information is not necessarily advantageous when information is incomplete. In this case, endogeneity in the regressor introduces bias when the true functional form is known, but interestingly does not do so in local non-parametric regression. We 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 non-parametric estimation. 2011-10-01T07:00:00Z text application/pdf https://ink.library.smu.edu.sg/soe_research/1364 info:doi/10.1111/j.1368-423X.2011.00344.x https://ink.library.smu.edu.sg/context/soe_research/article/2363/viewcontent/Nonparametric_Regression_under_Location_Shifts_2010_pp.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection School Of Economics eng Institutional Knowledge at Singapore Management University Biascorrection Endogeneity Kernel regression Location shift Nonparametric IV Nonstationarity Paradox Spatial regression Structural estimation Econometrics |
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Biascorrection Endogeneity Kernel regression Location shift Nonparametric IV Nonstationarity Paradox Spatial regression Structural estimation Econometrics PHILLIPS, Peter C. B. SU, Liangjun Non-parametric Regression under Location Shifts |
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Recent work by Wang and Phillips (2009b, 2011) has shown that ill-posed inverse problems do not arise in non-stationary non-parametric regression and there is no need for non-parametric instrumental variable estimation. Instead, simple Nadaraya–Watson non-parametric estimation of a cointegrating regression equation is consistent irrespective of the endogeneity in the regressor. The present paper shows that some closely related results apply in the case of structural non-parametric regression with independent data when there are continuous location shifts in the regressor. Some interesting cases are discovered where non-parametric 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. The paradox arises because additional correct information is not necessarily advantageous when information is incomplete. In this case, endogeneity in the regressor introduces bias when the true functional form is known, but interestingly does not do so in local non-parametric regression. We 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 non-parametric estimation. |
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PHILLIPS, Peter C. B. SU, Liangjun |
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PHILLIPS, Peter C. B. SU, Liangjun |
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PHILLIPS, Peter C. B. |
title |
Non-parametric Regression under Location Shifts |
title_short |
Non-parametric Regression under Location Shifts |
title_full |
Non-parametric Regression under Location Shifts |
title_fullStr |
Non-parametric Regression under Location Shifts |
title_full_unstemmed |
Non-parametric Regression under Location Shifts |
title_sort |
non-parametric regression under location shifts |
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Institutional Knowledge at Singapore Management University |
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2011 |
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https://ink.library.smu.edu.sg/soe_research/1364 https://ink.library.smu.edu.sg/context/soe_research/article/2363/viewcontent/Nonparametric_Regression_under_Location_Shifts_2010_pp.pdf |
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