Estimating Counterfactual Distribution Functions via Optimal Distribution Balancing with Applications

Zongwu Cai, Ying Fang, Ming Lin and Yaqian Wu
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Zongwu Cai: Department of Economics, The University of Kansas, Lawrence, KS 66045, USA
Ying Fang: The Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, Fujian 361005, China and Department of Statistics & Data Science, School of Economics, Xiamen University, Xiamen, Fujian 361005, China
Ming Lin: The Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, Fujian 361005, China and Department of Statistics and Data Science, School of Economics, Xiamen University, Xiamen, Fujian 361005, China
Yaqian Wu: School of Economics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China

No 202415, WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS from University of Kansas, Department of Economics

Abstract: In this paper, we propose a new method to estimate counterfactual distribution functions via the optimal distribution balancing weights, to avoid estimating the inverse propensity weights, which is sensitive to model specification and easily causes unstable estimates as well as often fails to adequately balance covariates. First, we demonstrate that the estimated weights exactly balance the estimated conditional distributions among the treated, untreated, and combined groups via a well-defined convex optimization problem. Secondly, we show that the resulting estimator of counterfactual distribution function converges weakly to a mean-zero Gaussian process at the parametric rate of the squared root n. Additionally, we show that a properly designed Bootstrap method can be used to obtain confidence intervals for conducting statistical inferences, together with its theoretical justification. Furthermore, with the estimates of counterfactual distribution functions, we provide methods to estimate the quantile treatment effects and test the stochastic dominance relationship between the potential outcome distributions. Moreover, Monte Carlo simulations are conducted to illustrate that the finite sample performance for the proposed estimator is better than the inverse propensity score weighted estimators in many scenarios. Finally, our empirical study revisits the effect of maternal smoking on infant birth weight.

Keywords: Counterfactual distribution function; Covariate balance; Quantile treatment effect; Stochastic dominance; Weighting scheme. (search for similar items in EconPapers)
JEL-codes: C01 C14 C54 (search for similar items in EconPapers)
Date: 2024-10
New Economics Papers: this item is included in nep-ecm
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