Semiparametric estimation of structural functions in nonseparable triangular models
Semiparametric estimation of structural functions in nonseparable triangular models
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DOI：
10.3982/qe1239
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发表时间：
2020-05-01
影响因子：
1.8
通讯作者：
Vella, Francis
中科院分区：
文献类型：
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作者：
Chernozhukov, Victor;Fernandez-Val, Ivan;Vella, Francis
具有不可加性可分离的不可观测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，由于需要大量支持识别的外生变量，估计中的维数灾难以及缺乏推理工具，它们在实践中并不常用。本文介绍了两类半参数不可分三角模型，解决这些限制。它们是基于内生变量的简化形式条件分布的分布和分位数回归建模。我们发现，平均，分布和分位数结构功能，确定在这些系统中，通过控制功能的方法，不需要一个大的支持条件。我们提出了一个计算上有吸引力的三阶段的过程来估计的结构功能，其中前两个阶段包括分位数或分布回归。我们为每个阶段提供了渐进理论和一致推理方法。特别地，我们得到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。这些结果建立了结构函数的三阶段估计的自举的有效性，并导致简单的推理算法。我们用数值模拟和需求分析的实证应用说明了我们所有方法的实施和适用性。
Triangular systems with nonadditively separable unobserved heterogeneity provide a theoretically appealing framework for the modeling 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 modeling 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 uniforminference 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.