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A Unified Framework for Specification Tests of Continuous Treatment Effect Models

Author

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  • Huang, W.
  • Linton, O.
  • Zhang, Z.
Abstract
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 confoundedness 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 Op (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.

Suggested Citation

  • Huang, W. & Linton, O. & Zhang, Z., 2021. "A Unified Framework for Specification Tests of Continuous Treatment Effect Models," Cambridge Working Papers in Economics 2113, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:2113
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    More about this item

    Keywords

    Consistent tests; Continuous treatment effect; Series estimation; Bootstrap;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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