Weak identification is a well-known issue in the context of linear structural models. However, for probit models with endogenous explanatory variables, this problem has been little explored. In this paper, we study by simulating the behavior of the usual z-test and the LR test in the presence of weak identification. We find that the usual asymptotic z-test exhibits large level distortions (over-rejections under the null hypothesis). The magnitude of the level distortions depends heavily on the parameter value tested. In contrast, asymptotic LR tests do not over-reject and appear to be robust to weak identification.

中文翻译：

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具有内生协变量的概率模型中的弱识别

在线性结构模型的背景下，弱识别是一个众所周知的问题。但是，对于具有内生解释变量的概率模型，这个问题很少被探讨。在本文中，我们通过在弱识别条件下模拟常规z检验和LR检验的行为进行研究。我们发现，通常的渐近z检验表现出较大的水平失真（在原假设下过度拒绝）。电平失真的幅度在很大程度上取决于测试的参数值。相比之下，渐近LR测试不会过分拒绝，并且对于弱识别具有明显的鲁棒性。