A Unified Framework for Specification Tests of Continuous Treatment Effect Models
提出一个检验连续处理效应模型设定的通用框架，通过估计权重函数构造检验统计量，能比真实权重函数更高效地检测模型偏差，适用于平均和分位数处理效应模型。
We propose a general framework for the specification testing of continuous treatment effect models. We assume a general residual function, which includes the average and quantile treatment effect models as special cases. The null models are identified under the unconfoundedness condition and contain a nonparametric weighting function. We propose a test statistic for the null model in which the weighting function is estimated by solving an expanding set of moment equations. We establish the asymptotic distributions of our test statistic under the null hypothesis and under fixed and local alternatives. The proposed test statistic is shown to be more efficient than that constructed from the true weighting function and can detect local alternatives deviated from the null models at the rate of O(N−1/2). A simulation method is provided to approximate the null distribution of the test statistic. Monte-Carlo simulations show that our test exhibits a satisfactory finite-sample performance, and an application shows its practical value.