分位数模型的平滑GMM

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摘要翻译：
本文在比文献中更弱的假设下，发展了由一般条件分位数限制识别的有限维参数的可行估计的理论。这包括工具变量，非线性分位数回归作为一个特例。更具体地说，我们考虑了一组由条件分位数限制所隐含的无条件矩，为局部识别提供了条件。由于基于样本矩的估计在实际应用中一般无法进行数值计算，本文研究了基于平滑样本矩的可行估计。对于精确辨识的模型，我们提出了一种矩估计方法；对于过辨识的模型，我们提出了一种广义矩估计方法。在弱相关数据和非线性结构模型的一般条件下，我们建立了两种估计量的相合性和渐近正态性。仿真结果表明了该方法的有限样本特性。我们深入的经验应用涉及从分位数效用最大化导出的消费欧拉方程。分位数欧拉方程的优点包括对胖尾的鲁棒性、风险态度与跨期替代弹性的解耦以及无任何逼近误差的对数线性化。对于我们所考察的四个国家，贴现因子和跨期替代弹性的分位数估计对于高于中位数的分位数范围在经济上是合理的，即使两阶段最小二乘估计是不合理的。
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英文标题：
《Smoothed GMM for quantile models》
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作者：
Luciano de Castro (1), Antonio F. Galvao (2), David M. Kaplan (3), Xin
  Liu (3) ((1) University of Iowa, (2) University of Arizona, (3) University of
  Missouri)
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最新提交年份：
2018
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
--
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。
--
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
--
一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
--

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英文摘要：
  This paper develops theory for feasible estimators of finite-dimensional parameters identified by general conditional quantile restrictions, under much weaker assumptions than previously seen in the literature. This includes instrumental variables nonlinear quantile regression as a special case. More specifically, we consider a set of unconditional moments implied by the conditional quantile restrictions, providing conditions for local identification. Since estimators based on the sample moments are generally impossible to compute numerically in practice, we study feasible estimators based on smoothed sample moments. We propose a method of moments estimator for exactly identified models, as well as a generalized method of moments estimator for over-identified models. We establish consistency and asymptotic normality of both estimators under general conditions that allow for weakly dependent data and nonlinear structural models. Simulations illustrate the finite-sample properties of the methods. Our in-depth empirical application concerns the consumption Euler equation derived from quantile utility maximization. Advantages of the quantile Euler equation include robustness to fat tails, decoupling of risk attitude from the elasticity of intertemporal substitution, and log-linearization without any approximation error. For the four countries we examine, the quantile estimates of discount factor and elasticity of intertemporal substitution are economically reasonable for a range of quantiles above the median, even when two-stage least squares estimates are not reasonable.
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PDF链接：
https://arxiv.org/pdf/1707.03436

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关键词：GMM 分位数 econometrics Multivariate Restrictions 限制 GMM models conditions 包括