Inference for best linear approximations to set identified functions
Inference for best linear approximations to set identified functions
复制标题
推断最佳线性近似以设置识别的函数
DOI：
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发表时间：
2012
期刊：
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通讯作者：
Paul Schrimpf
中科院分区：
文献类型：
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作者：
Arun G. Chandrasekhar;V. Chernozhukov;Francesca Molinari;Paul Schrimpf
本文提供了已知在一个频带内的函数的最佳线性逼近的推理方法。它扩展了部分辨识文献，允许定义带的上下函数是任何函数，包括带一个可以参数或非参数估计的指标的函数。通过支持函数对最佳线性逼近参数的识别区域进行表征，并对最佳线性逼近参数的识别区域建立了极限理论。证明了支持函数近似收敛于高斯过程，并证明了贝叶斯自举的有效性。本文将文献中的典型例子：区间值结果数据均值回归和区间值回归数据均值回归作为特例。由于边界可以带一个指标，本文涵盖了均值回归以外的问题；该框架非常通用。应用包括区间值数据的分位数和分布回归，样本选择问题，以及均值，分位数和分布处理效果。此外，该框架可以说明工具的可用性。运用Mulligan和Rubinstein（2008）的方法研究女性劳动力参与。
This paper provides inference methods for best linear approximations to functions which are known to lie within a band. It extends the partial identification literature by allowing the upper and lower functions defining the band to be any functions, including ones carrying an index, which can be estimated parametrically or non-parametrically. The identification region of the parameters of the best linear approximation is characterised via its support function, and limit theory is developed for the latter. We prove that the support function approximately converges to a Gaussian process, and validity of the Bayesian bootstrap is established. The paper nests as special cases the canonical examples in the literature: mean regression with interval valued outcome data and interval valued regressor data. Because the bounds may carry an index, the paper covers problems beyond mean regression; the framework is extremely versatile. Applications include quantile and distribution regression with interval valued data, sample selection problems, as well as mean, quantile and distribution treatment effects. Moreover, the framework can account for the availability of instruments. An application is carried out, studying female labor force participation along the lines of Mulligan and Rubinstein (2008).