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摘要翻译：
在高维背景下，我们考虑了具有加性、未观察到的个体特异异质性的面板数据模型的估计和推理。该设置允许时变回归数大于样本量。为了使信息估计和推理可行，我们要求在消除个体特定异质性后，时变变量的总体贡献能够被相对较少的恒等式未知的可用变量所捕获。这种限制允许估计问题作为变量选择问题进行。重要的是，我们把个体的特异性异质性视为固定效应，从而允许这种异质性以一种未指定的方式与观察到的时变变量相关，并允许这种异质性对所有个体来说都是非零的。在这个框架内，我们给出了在标准线性固定效应模型中的固定参数子集上的一致有效的推论，以及在具有固定效应和许多工具的面板数据工具变量模型中的固定内生变量向量上的系数上的一致有效的推论。发展我们提出的过程的特性的一个输入是使用Lasso估计器的一个变体，它允许分组数据结构，其中跨组的数据是独立的，组内的依赖是不受限制的。在此结构中，我们给出了所提出的Lasso变体选择具有良好逼近性质的稀疏模型的形式条件。我们给出了支持理论发展的模拟结果，并说明了这些方法在一个应用中的使用，该应用旨在估计枪支流行对犯罪率的影响。
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英文标题：
《Inference in High Dimensional Panel Models with an Application to Gun
Control》
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作者：
Alexandre Belloni and Victor Chernozhukov and Christian Hansen and
Damian Kozbur
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最新提交年份：
2014
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分类信息：
一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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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 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 be non-zero 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 variables models with fixed effects and many instruments. An input to developing the properties of our proposed procedures is the use of a variant of the Lasso estimator that allows for a grouped data structure where data across groups are independent and dependence within groups is unrestricted. We provide formal conditions within this structure under which the proposed Lasso variant selects a sparse model with good approximation properties. 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.
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PDF链接：
https://arxiv.org/pdf/1411.6507
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