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A Unified Framework for Specification Tests of Continuous Treatment Effect Models

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Huang, Wei 
Zhang, Zheng 


We propose a general framework for the specification testing of continuous treat- ment 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 func- tion. 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 alterna- tives 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.



Journal Title

Journal of Business and Economic Statistics

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American Statistical Association


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