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Non-parametric regression under location shifts

机译:位置偏移下的非参数回归

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摘要

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.
机译:Wang and Phillips(2009b,2011)的最新工作表明,在非平稳非参数回归中不会出现不适定的逆问题,并且不需要非参数工具变量估计。取而代之的是,与回归变量的内生性无关,对协整回归方程的简单Nadaraya-Watson非参数估计是一致的。本文表明,当回归变量中存在连续的位置偏移时,在具有独立数据的结构非参数回归中,一些紧密相关的结果适用。发现了一些有趣的情况,其中非参数回归是一致的,而参数回归却是不一致的,即使知道了真正的回归函数形式并将其用于回归中也是如此。这似乎是一个悖论,因为知道真正的功能形式通常不会对回归产生不利影响。之所以出现这种矛盾,是因为当信息不完整时,附加的正确信息并不一定是有利的。在这种情况下,当已知真正的函数形式时,回归函数中的内生性会引入偏差,但有趣的是,在局部非参数回归中不会这样做。我们为参数回归提出了两个新的一致估计量,它们通过空间限制和使用非参数估计的偏差校正来解决回归变量的内生性。

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