We provide a Copula-based approach to test the exogeneity of instrumental variables in linear regression models. We show that the exogeneity of instrumental variables is equivalent to the exogeneity of their standard normal transformations with the same CDF value. Then, we establish a Wald test for the exogeneity of the instrumental variables. We demonstrate the performance of our test using simulation studies. Our simulations show that if the instruments are actually endogenous, our test rejects the exogeneity hypothesis approximately 93% of the time at the 5% significance level. Conversely, when instruments are truly exogenous, it dismisses the exogeneity assumption less than 30% of the time on average for data with 200 observations and less than 2% of the time for data with 1,000 observations. Our results demonstrate our test's effectiveness, offering significant value to applied econometricians.

翻译：本文提出一种基于Copula的方法，用于检验线性回归模型中工具变量的外生性。我们证明，工具变量的外生性等价于其具有相同累积分布函数值的标准正态变换的外生性。随后，我们构建了工具变量外生性的Wald检验。通过模拟研究展示了该检验的表现。模拟结果表明：当工具变量实际为内生时，在5%显著性水平下，我们的检验拒绝外生性假设的概率约为93%；反之，当工具变量真实外生时，对于200个观测值的数据，检验错误拒绝外生性假设的平均概率低于30%，而对于1000个观测值的数据，该概率低于2%。研究结果验证了该检验的有效性，为应用计量经济学家提供了重要价值。