A Unified Framework for Specification Tests of Continuous Treatment Effect Models

TL;DR

This paper introduces a comprehensive framework for testing the correctness of continuous treatment effect models, including a new test statistic with improved efficiency and ability to detect subtle deviations.

Contribution

It develops a unified testing approach for continuous treatment models with a novel statistic that outperforms existing methods in efficiency and sensitivity.

Findings

The test statistic is asymptotically normal under the null hypothesis.

The proposed test can detect local alternatives at a rate of O(N^{-1/2}).

Simulation results demonstrate good finite-sample performance.

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 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.