Efficient two-sided nonsimilar invariant tests in IV regression with weak instruments
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弱工具变量回归中的有效双侧非相似不变检验
- 研究问题
- 弱工具变量回归中，对单个内生解释变量系数的双侧检验，扩大到非相似不变检验后能否获得明显更高的功效？
- 方法与思路
- 作者理论刻画对工具变量旋转不变的双侧非相似检验功效包络，在五个工具变量情形数值评估，并提出新的P*检验。
- 材料陈述的贡献
- 摘要称两类功效包络数值上非常接近，条件似然比检验近乎达到非相似包络；P*检验仅涉及初等函数且在强工具下渐近有效。
- 阅读关注点
- 应核对相似性、不变性与功效包络的定义，理论分析的模型条件，以及数值近优结论和P*临界值构造的适用范围。
- 阅读边界
- 仅据所给出版社摘要，数值上近乎最优不等于一般设定下严格统一最优；摘要未说明完整分布条件、临界值形式或数值差距。
原文摘要
As Nelson and Startz [Nelson, C.R., Startz, R., 1990a. The distribution of the instrumental variable estimator and its t ratio when the instrument is a poor one. Journal of Business 63, S125-S140; Nelson, C.R., Startz, R., 1990b. Some further results on the exact small sample properties of the instrumental variables estimator. Econometrica 58, 967-976] dramatically demonstrated, standard hypothesis tests and confidence intervals in instrumental variables regression are invalid when instruments are weak. Recent work on hypothesis tests for the coefficient on a single included endogenous regressor when instruments may be weak has focused on similar tests. This paper extends that work to nonsimilar tests, of which similar tests are a subset. The power envelope for two-sided invariant (to rotations of the instruments) nonsimilar tests is characterized theoretically, then evaluated numerically for five IVs. The power envelopes for similar and nonsimilar tests differ theoretically, but are found to be very close numerically. The nonsimilar test power envelope is effectively achieved by the Moreira [Moreira, M.J., 2003. A conditional likelihood ratio test for structural models. Econometrica 71, 1027-1048] conditional likelihood ratio test, so that test is effectively uniformly most powerful invariant (UMPI). We also provide a new nonsimilar test, P*, which has critical values, is asymptotically efficient under strong instruments, involves only elementary functions, and is very nearly UMPI.