Testing Conditional Mean Independence Under Symmetry
提出一个Kolmogorov–Smirnov型统计量，在对称性条件下检验条件均值独立性，并通过自助法获取p值和临界值；模拟显示小样本表现良好，并应用于中国大学教育回报数据集验证假设。
Conditional mean independence (CMI) is one of the most widely used assumptions in the treatment effect literature to achieve model identification. We propose a Kolmogorov–Smirnov-type statistic to test CMI under a specific symmetry condition. We also propose a bootstrap procedure to obtain the p-values and critical values that are required to carry out the test. Results from a simulation study suggest that our test can work very well even in small to moderately sized samples. As an empirical illustration, we apply our test to a dataset that has been used in the literature to estimate the return on college education in China, to check whether the assumption of CMI is supported by the dataset and show the plausibility of the extra symmetry condition that is necessary for this new test.