THE IMPACT OF A HAUSMAN PRETEST ON THE ASYMPTOTIC SIZE OF A HYPOTHESIS TEST
THE IMPACT OF A HAUSMAN PRETEST ON THE ASYMPTOTIC SIZE OF A HYPOTHESIS TEST
复制标题
豪斯曼预检验对假设检验渐近规模的影响
DOI：
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发表时间：
2009
影响因子：
0.8
通讯作者：
Patrik Guggenberger
中科院分区：
文献类型：
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作者：
Patrik Guggenberger
本文研究了线性工具变量模型中两阶段检验的渐近大小性质，其中第一阶段使用 Hausman (1978) 规范检验作为回归量外生性的预检验。在第二阶段，使用基于普通最小二乘 (OLS) 或两阶段最小二乘估计 (2SLS) 的 t 统计量来测试有关结构参数向量分量的简单假设，具体取决于 Hausman 预测试的结果。两阶段检验的渐近大小是在模型中导出的，其中通过对工具强度施加正下限来排除弱工具。对于参数空间的经验相关选择，渐近大小等于 1。尺寸失真是由结构误差项和简化形式误差项之间的相关参数中的检验统计量的渐近分布的不连续性引起的。 Hausman 预检验对于局部为零的相关性没有足够的功效，而基于 OLS 的 t 统计量对于此类非零相关性采用较大的值。建议不要使用两阶段程序，而是使用基于 2SLS 估计量的 t 统计量，或者如果担心工具较弱，则使用 Moreira (2003) 的条件似然比检验。
This paper investigates the asymptotic size properties of a two-stage test in the linear instrumental variables model when in the first stage a Hausman (1978) specification test is used as a pretest of exogeneity of a regressor. In the second stage, a simple hypothesis about a component of the structural parameter vector is tested, using a t-statistic that is based on either the ordinary least squares (OLS) or the two-stage least squares estimator (2SLS), depending on the outcome of the Hausman pretest. The asymptotic size of the two-stage test is derived in a model where weak instruments are ruled out by imposing a positive lower bound on the strength of the instruments. The asymptotic size equals 1 for empirically relevant choices of the parameter space. The size distortion is caused by a discontinuity of the asymptotic distribution of the test statistic in the correlation parameter between the structural and reduced form error terms. The Hausman pretest does not have sufficient power against correlations that are local to zero while the OLS-based t-statistic takes on large values for such nonzero correlations. Instead of using the two-stage procedure, the recommendation then is to use a t-statistic based on the 2SLS estimator or, if weak instruments are a concern, the conditional likelihood ratio test by Moreira (2003).