Semiparametric Efficiency Bound for Models of Sequential Moment Restrictions Containing Unknown Functions
Semiparametric Efficiency Bound for Models of Sequential Moment Restrictions Containing Unknown Functions
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DOI：
10.2139/ssrn.1484713
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发表时间：
2009-10
期刊：
影响因子：
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通讯作者：
C. Ai;Xiaohong Chen
中科院分区：
文献类型：
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作者：
C. Ai;Xiaohong Chen
本文计算了由含有未知函数的序列矩约束模型识别的有限维参数的半参数有效界。我们的结果将Chamberlain（1992 b）和Ai and Chen（2003）关于具有相同信息集的半参数条件矩约束模型的结果推广到嵌套信息集的情况，将Chamberlain（1992 a）和Brown and Newey（1998）关于不含未知函数的序列矩约束模型的结果推广到含有可能内生变量的未知函数的情况。我们的结果适用于半参数面板数据模型和半参数两阶段插入问题。作为一个例子，我们计算了一个非参数工具变量（IV）回归的加权平均导数的效率界，并发现简单的插件估计是无效的。最后，我们提出了一个最佳加权，正交化，筛最小距离估计，达到半参数效率界。
This paper computes the semiparametric efficiency bound for finite dimensional parameters identified by models of sequential moment restrictions containing unknown functions. Our results extend those of Chamberlain (1992b) and Ai and Chen (2003) for semiparametric conditional moment restriction models with identical information sets to the case of nested information sets, and those of Chamberlain (1992a) and Brown and Newey (1998) for models of sequential moment restrictions without unknown functions to cases with unknown functions of possibly endogenous variables. Our bound results are applicable to semiparametric panel data models and semiparametric two stage plug-in problems. As an example, we compute the efficiency bound for a weighted average derivative of a nonparametric instrumental variables (IV) regression, and find that the simple plug-in estimator is not efficient. Finally, we present an optimally weighted, orthogonalized, sieve minimum distance estimator that achieves the semiparametric efficiency bound.