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英文文献：On Bootstrap Validity for Specification Tests with Weak Instruments-弱仪器规格测试的Bootstrap有效性研究
英文文献作者：Firmin Doko Tchatoka
英文文献摘要：
We investigate the asymptotic validity of the bootstrap for Durbin-Wu-Hausman (DWH) tests of exogeneity in linear IV regressions, with or without identification. Our analysis of the properties (size and power) of the proposed bootstrap tests provides some new insights and extensions of earlier studies. More precisely, we show that when identification is strong, the bootstrap: (1) provides an asymptotic refinement of the size of the DWH tests under exogeneity, and (2) is consistent under the alternative hypothesis if the endogeneity parameter is fixed. However, the bootstrap only provides a first-order approximation of the asymptotic distributions of these statistics when instruments are weak. Moreover, we characterize the necessary and sufficient condition under which the proposed bootstrap DWH tests exhibit power under fixed endogeneity and weak instruments. The latter condition may still hold over a wide range of cases, provided that at least one instrument is not irrelevant. But all bootstrap tests have low power when all instruments are irrelevant, a case of little interest in empirical work. We present a Monte Carlo experiment that confirms our theoretical findings.
我们研究了在线性IV回归中包含所有解释变量的Durbin-Wu-Hausman (DWH)检验的bootstrap的渐近有效性，是否有识别。我们对所提出的bootstrap测试的特性(大小和功率)的分析提供了一些新的见解和对早期研究的扩展。更准确地说，我们发现当识别性较强时，bootstrap:(1)提供了外生性变量下DWH检验规模的渐近细化，且(2)在备选假设下，如果内生性参数固定，则是一致的。然而，bootstrap仅在工具较弱时提供这些统计量的渐近分布的一阶近似值。此外，我们还刻画了自举DWH检验在固定内存和弱仪器条件下显示有效的充必要条件。后一项条件在许多情况下仍然适用，只要至少有一项文书并非无关紧要。但是，当所有工具都不相关时，所有的bootstrap测试都是低功率的，这是一个对实证工作兴趣不大的情况。我们提出了一个蒙特卡罗实验来证实我们的理论发现。
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