Inference in High-Dimensional Panel Models With an Application to Gun Control
Inference in High-Dimensional Panel Models With an Application to Gun Control
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DOI：
10.1080/07350015.2015.1102733
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发表时间：
2016-10-01
影响因子：
3
通讯作者：
Kozbur, Damian
中科院分区：
文献类型：
--
作者：
Belloni, Alexandre;Chernozhukov, Victor;Kozbur, Damian
我们考虑在高维环境中具有附加的未观察到的个体特定异质性的面板数据模型中的估计和推断。该设置允许时变回归量的数量大于样本大小。为了使信息估计和推断变得可行，我们要求消除个体特定异质性后的时变变量的总体贡献可以由相对较少的身份未知的可用变量来捕获。这一限制允许估计问题作为变量选择问题进行。重要的是，我们将个体特定的异质性视为固定效应，这允许这种异质性以未指定的方式与观察到的时变变量相关，并且允许这种异质性对于所有个体来说可能不同。在此框架内，我们提供的程序可以对规范线性固定效应模型中的固定参数子集以及具有固定效应和多种工具的面板数据工具变量模型中的内生变量固定向量的系数进行一致有效的推断。我们提出了模拟结果来支持理论发展，并说明了这些方法在旨在估计枪支流行率对犯罪率影响的应用中的使用。
We consider estimation and inference in panel data models with additive unobserved individual specific heterogeneity in a high-dimensional setting. The setting allows the number of time-varying regressors to be larger than the sample size. To make informative estimation and inference feasible, we require that the overall contribution of the time-varying variables after eliminating the individual specific heterogeneity can be captured by a relatively small number of the available variables whose identities are unknown. This restriction allows the problem-of estimation to proceed as a variable selection problem. Importantly, we treat the individual specific heterogeneity as fixed effects which allows this heterogeneity to be related to the observed time-varying variables in an unspecified way and allows that this heterogeneity may differ for all individuals. Within this framework, we provide procedures that give uniformly valid inference over a fixed subset of parameters in the canonical linear fixed effects model and over coefficients on a fixed vector of endogenous variables in panel data instrumental variable models with fixed effects and many instruments. We present simulation results in support of the theoretical developments and illustrate the use of the methods in an application aimed at estimating the effect of gun prevalence on crime rates.