分位数样本选择测试
Testing for Quantile Sample Selection
摘要：
本文提供了用于检测非参数条件分位数函数中样本选择的测试。第一个检验是省略的预测检验，其中倾向分数作为省略的变量。与任何综合测试一样，在拒绝的情况下，我们无法区分拒绝是由于真正的选择还是由于错误的说明。因此，我们建议进行第二次测试，以提供支持性证据，证明在第一阶段拒绝的原因是否完全是由于选择。仅使用倾向分数接近1的个人，这第二个测试依赖于“无限认同”的论点，但也适用于不规则认同的情况。重要的是，这两个测试都不需要对选择方程进行参数假设，也不需要连续排除限制。数据驱动的带宽程序提出，和蒙特卡罗证据表明，一个良好的有限样本性能，特别是第一次测试。最后，我们还推导出一个扩展的第一个测试的非参数条件均值函数，并应用我们的程序来测试选择在对数小时工资使用英国家庭支出调查数据\citet{AB2017}。
英文摘要：
This paper provides tests for detecting sample selection in nonparametric conditional quantile functions. The first test is an omitted predictor test with the propensity score as the omitted variable. As with any omnibus test, in the case of rejection we cannot distinguish between rejection due to genuine selection or to misspecification. Thus, we suggest a second test to provide supporting evidence whether the cause for rejection at the first stage was solely due to selection or not. Using only individuals with propensity score close to one, this second test relies on an `identification at infinity' argument, but accommodates cases of irregular identification. Importantly, neither of the two tests requires parametric assumptions on the selection equation nor a continuous exclusion restriction. Data-driven bandwidth procedures are proposed, and Monte Carlo evidence suggests a good finite sample performance in particular of the first test. Finally, we also derive an extension of the first test to nonparametric conditional mean functions, and apply our procedure to test for selection in log hourly wages using UK Family Expenditure Survey data as \citet{AB2017}.
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