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Semiparametric Single-Index Estimation for Average Treatment Effects

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  • Difang Huang
  • Jiti Gao
  • Tatsushi Oka

Abstract

We propose a semiparametric method to estimate the average treatment effect under the assumption of unconfoundedness given observational data. Our estimation method alleviates misspecification issues of the propensity score function by estimating the single-index link function involved through Hermite polynomials. Our approach is computationally tractable and allows for moderately large dimension covariates. We provide the large sample properties of the estimator and show its validity. Also, the average treatment effect estimator achieves the parametric rate and asymptotic normality. Our extensive Monte Carlo study shows that the proposed estimator is valid in finite samples. We also provide an empirical analysis on the effect of maternal smoking on babies' birth weight and the effect of job training program on future earnings.

Suggested Citation

  • Difang Huang & Jiti Gao & Tatsushi Oka, 2022. "Semiparametric Single-Index Estimation for Average Treatment Effects," Monash Econometrics and Business Statistics Working Papers 10/22, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2022-10
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    More about this item

    Keywords

    Average treatment effects; causal inference; Hermite series expansion; propensity score;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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