Testing identifying assumptions in bivariate probit models
针对双变量Probit模型的识别假设（线性指标、联合正态性、工具外生性和相关性）提出可检验的等式和易于实施的检验程序，并在模型被拒绝时给出放宽正态性假设的平均处理效应边界。
Summary This paper considers the bivariate probit model's identifying assumptions: linear index specification, joint normality of errors, instrument exogeneity, and relevance. First, we develop sharp testable equalities that detect all possible observable violations of the assumptions. Second, we propose an easy‐to‐implement testing procedure for the model's validity using existing inference methods for intersection bounds. The test achieves correct empirical size and performs well in detecting violations of the conditions in simulations. Finally, we provide a road map on what to do when the bivariate probit model is rejected, including novel bounds for the average treatment effect that relax the normality assumption.