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摘要翻译：
我们在一个非参数框架中考虑了具有选择性观察协变量的回归问题。我们的方法依赖于解释潜在协变量变化的工具变量，但对选择没有直接影响。所关注的回归函数被证明是观察到的条件期望的加权版本，其中加权函数是选择概率的一个分数。通过部分完备性假设，实现了分数概率权函数的非参数辨识。我们提供了部分完备性成立的本原函数形式假设。辨识结果对FPW级数估计器具有建设性。我们导出了收敛速度和逐点渐近分布。在这两种情况下，FPW级数估计器的渐近性能都不存在由非参数工具变量方法导出的反问题。在Monte Carlo研究中，我们分析了我们的估计量的有限样本性质，并将我们的方法与逆概率加权方法进行了比较，这两种方法可以交替用于无条件矩估计。在实证应用中，我们重点研究了两种不同的应用。我们使用来自份额调查和行政养恤金信息的相关数据，并使用养恤金权利作为工具，估计收入和健康之间的联系。在第二个应用中，我们基于德国社会经济小组研究(SOEP)的数据，重新讨论了收入如何影响住房需求的问题。在这个应用中，我们使用住宅街区层面的地区收入信息作为工具。在这两个应用中，我们证明了收入是选择性缺失的，并且我们证明了不考虑非随机选择过程的标准方法会导致对低收入个人的显著偏差估计。
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英文标题：
《Nonparametric Regression with Selectively Missing Covariates》
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作者：
Christoph Breunig and Peter Haan
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最新提交年份：
2020
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分类信息：
一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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英文摘要：
We consider the problem of regression with selectively observed covariates in a nonparametric framework. Our approach relies on instrumental variables that explain variation in the latent covariates but have no direct effect on selection. The regression function of interest is shown to be a weighted version of observed conditional expectation where the weighting function is a fraction of selection probabilities. Nonparametric identification of the fractional probability weight (FPW) function is achieved via a partial completeness assumption. We provide primitive functional form assumptions for partial completeness to hold. The identification result is constructive for the FPW series estimator. We derive the rate of convergence and also the pointwise asymptotic distribution. In both cases, the asymptotic performance of the FPW series estimator does not suffer from the inverse problem which derives from the nonparametric instrumental variable approach. In a Monte Carlo study, we analyze the finite sample properties of our estimator and we compare our approach to inverse probability weighting, which can be used alternatively for unconditional moment estimation. In the empirical application, we focus on two different applications. We estimate the association between income and health using linked data from the SHARE survey and administrative pension information and use pension entitlements as an instrument. In the second application we revisit the question how income affects the demand for housing based on data from the German Socio-Economic Panel Study (SOEP). In this application we use regional income information on the residential block level as an instrument. In both applications we show that income is selectively missing and we demonstrate that standard methods that do not account for the nonrandom selection process lead to significantly biased estimates for individuals with low income.
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PDF链接：
https://arxiv.org/pdf/1810.00411
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