具有辅助数据的GMM模型的半参数有效性
Semiparametric efficiency in GMM models with auxiliary data
摘要：
本文研究了缺失数据下一般矩约束下参数的半参数有效界和有效估计。识别依赖于辅助数据，其中包含关于缺失变量分布的信息，条件是在主要数据库和辅助数据库中观察到的代理变量，如果这种分布对两个数据集是共同的。辅助样本可以独立于主样本，也可以是主样本的子集。对于这两种情况，当给定代理变量的缺失数据的概率未知，或已知，或属于正确指定的参数族时，我们推导出边界。我们发现当两个样本独立时，条件概率不是辅助的。对于所有的情况，我们讨论有效的半参数估计。基于条件期望投影的估计比基于逆概率加权的估计需要更温和的正则性条件。
英文摘要：
We study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data. Identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are observed in both the primary and the auxiliary database, when such distribution is common to the two data sets. The auxiliary sample can be independent of the primary sample, or can be a subset of it. For both cases, we derive bounds when the probability of missing data given the proxy variables is unknown, or known, or belongs to a correctly specified parametric family. We find that the conditional probability is not ancillary when the two samples are independent. For all cases, we discuss efficient semiparametric estimators. An estimator based on a conditional expectation projection is shown to require milder regularity conditions than one based on inverse probability weighting.
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