有意使用无效工具：用于GMM的聚焦时刻选择和平均
Using Invalid Instruments on Purpose: Focused Moment Selection and Averaging for GMM
AI总结：
本文提出聚焦矩选择准则（FMSC）用于GMM，通过选择具有更低MSE的矩条件来提高估计精度，并展示其在推断和实证分析中的应用。
摘要：
在有限样本中，使用略微内生但高度相关的工具可以减少均方误差（MSE）。基于这一观察，我提出了一种新的GMM矩选择程序——聚焦矩选择准则（FMSC），其中矩条件的选择不是基于其有效性，而是基于其关联估计目标参数的MSE。FMSC模拟了应用研究人员在一组相对温和的“基线”假设下开始，并必须决定是否引入一组更强但更争议的“可疑”假设的情况。当（正确规范的）基线矩条件识别模型时，FMSC提供了一个渐近无偏的渐近MSE估计，使我们能够在可疑矩条件下进行选择。我进一步展示了用于推导FMSC的框架如何解决在矩选择后的推断问题。将后选择估计器视为矩平均的特殊案例，其中基于不同矩集的估计器给予数据依赖的权重，我提出了一种基于模拟的推断程序，可以应用于各种正式和非正式的矩选择和平均程序。FMSC和置信区间程序在模拟中表现良好。最后，我通过一个经验例子研究了工具选择对疟疾与人均收入估计关系的影响。
英文摘要：
In finite samples, the use of a slightly endogenous but highly relevant instrument can reduce mean-squared error (MSE). Building on this observation, I propose a novel moment selection procedure for GMM -- the Focused Moment Selection Criterion (FMSC) -- in which moment conditions are chosen not based on their validity but on the MSE of their associated estimator of a user-specified target parameter. The FMSC mimics the situation faced by an applied researcher who begins with a set of relatively mild "baseline" assumptions and must decide whether to impose any of a collection of stronger but more controversial "suspect" assumptions. When the (correctly specified) baseline moment conditions identify the model, the FMSC provides an asymptotically unbiased estimator of asymptotic MSE, allowing us to select over the suspect moment conditions. I go on to show how the framework used to derive the FMSC can address the problem of inference post-moment selection. Treating post-selection estimators as a special case of moment-averaging, in which estimators based on different moment sets are given data-dependent weights, I propose simulation-based procedures for inference that can be applied to a variety of formal and informal moment-selection and averaging procedures. Both the FMSC and confidence interval procedures perform well in simulations. I conclude with an empirical example examining the effect of instrument selection on the estimated relationship between malaria and income per capita.
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