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摘要翻译：
本文讨论了通过工具变量识别的高维参数向量$\beta^0$的低维分量的推论。我们允许包含和排除协变量的期望外积的特征值，以$M$表示，随着样本量的增加收缩到零。我们提出了一种新的基于工具变量Lasso估计器的解派生估计器，它是2SLS的一个正则化版本，带有一个额外的校正项。此估计器收敛到$\beta^0$的速率取决于稀疏链接条件捕获的$M$的映射属性。证明了$\beta^0$估计的线性组合是渐近正态分布的。基于一致协方差估计，我们的方法允许构造可信区间和对$\beta^0$的单维或低维分量的统计检验。在Monte-Carlo模拟中，我们分析了估计量的有限样本行为。
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英文标题：
《Ill-posed Estimation in High-Dimensional Models with Instrumental
Variables》
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作者：
Christoph Breunig, Enno Mammen, Anna Simoni
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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：
This paper is concerned with inference about low-dimensional components of a high-dimensional parameter vector $\beta^0$ which is identified through instrumental variables. We allow for eigenvalues of the expected outer product of included and excluded covariates, denoted by $M$, to shrink to zero as the sample size increases. We propose a novel estimator based on desparsification of an instrumental variable Lasso estimator, which is a regularized version of 2SLS with an additional correction term. This estimator converges to $\beta^0$ at a rate depending on the mapping properties of $M$ captured by a sparse link condition. Linear combinations of our estimator of $\beta^0$ are shown to be asymptotically normally distributed. Based on consistent covariance estimation, our method allows for constructing confidence intervals and statistical tests for single or low-dimensional components of $\beta^0$. In Monte-Carlo simulations we analyze the finite sample behavior of our estimator.
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PDF链接：
https://arxiv.org/pdf/1806.00666
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