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摘要翻译：
具有不可加分、不可观测的异质性的三角系统为复杂结构关系的建模提供了一个理论上有吸引力的框架。然而，由于需要具有较大支持度的外生变量，估计中的维数问题，以及缺乏推理工具等原因，它们在实际应用中并不常用。本文介绍了两类半参数不可分三角模型。它们是基于内生变量的条件分布的简化形式的分布和分位数回归模型。我们通过一种不需要很大支持度条件的控制函数方法证明了在这些系统中的平均、分布和分位数结构函数。我们提出了一个计算上有吸引力的三阶段过程来估计结构函数，其中前两个阶段由分位数或分布回归组成。我们给出了每个阶段的渐近理论和统一的推理方法。特别地，我们给出了结构函数的分布回归估计的泛函中心极限定理和bootstrap泛函中心极限定理。这些结果证明了bootstrap对结构函数的三阶段估计的有效性，并导致了简单的推理算法。我们用数值模拟和需求分析的经验应用来说明我们所有方法的实施和适用性。
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英文标题：
《Semiparametric Estimation of Structural Functions in Nonseparable
Triangular Models》
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作者：
Victor Chernozhukov, Iv\'an Fern\'andez-Val, Whitney Newey, Sami
Stouli and Francis Vella
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最新提交年份：
2019
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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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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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英文摘要：
Triangular systems with nonadditively separable unobserved heterogeneity provide a theoretically appealing framework for the modelling of complex structural relationships. However, they are not commonly used in practice due to the need for exogenous variables with large support for identification, the curse of dimensionality in estimation, and the lack of inferential tools. This paper introduces two classes of semiparametric nonseparable triangular models that address these limitations. They are based on distribution and quantile regression modelling of the reduced form conditional distributions of the endogenous variables. We show that average, distribution and quantile structural functions are identified in these systems through a control function approach that does not require a large support condition. We propose a computationally attractive three-stage procedure to estimate the structural functions where the first two stages consist of quantile or distribution regressions. We provide asymptotic theory and uniform inference methods for each stage. In particular, we derive functional central limit theorems and bootstrap functional central limit theorems for the distribution regression estimators of the structural functions. These results establish the validity of the bootstrap for three-stage estimators of structural functions, and lead to simple inference algorithms. We illustrate the implementation and applicability of all our methods with numerical simulations and an empirical application to demand analysis.
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PDF链接：
https://arxiv.org/pdf/1711.02184
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