Regression-adjusted average treatment effect estimates in stratified randomized experiments

Liu, Hanzhong; Yang, Yuehan

doi:10.1093/biomet/asaa038

Cited by 45 publications

(68 citation statements)

References 18 publications

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“…Although the Wald estimator exhibits good asymptotic properties, it does not use covariate information. If these baseline covariates can predict the potential outcomes, covariate adjustment tends to reduce the variance of the estimated treatment effect (Lin, 2013;Bloniarz et al, 2016;Fogarty, 2018;Yue et al, 2019;Liu and Yang, 2020;Li and Ding, 2020). In this section, we propose three model-assisted CATE estimators and study their asymptotic properties under the finite-population and randomization-based inference framework.…”

Section: Model-assisted Cate Estimatorsmentioning

confidence: 99%

“…In randomized experiments with perfect compliance, researchers have proposed regression adjustment methods with treatment assignment by covariate interactions to estimate the average treatment effect, and showed that the resulting estimator is generally more efficient than the simple difference-in-means estimator (Lin, 2013;Bloniarz et al, 2016;Fogarty, 2018;Yue et al, 2019;Liu and Yang, 2020;Li and Ding, 2020). Motivated by these ideas and considering non-compliance, we propose an indirect least squares (ILS) method that includes the treatment assignment by covariate interactions in the two linear (working) models.…”

Section: Introductionmentioning

confidence: 99%

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Model-assisted complier average treatment effect estimates in randomized experiments with non-compliance and a binary outcome

Ren¹,

Liu²

2021

Preprint

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In randomized experiments, the actual treatments received by some experimental units may differ from their treatment assignments. This noncompliance issue often occurs in clinical trials, social experiments, and the applications of randomized experiments in many other fields. Under certain assumptions, the average treatment effect for the compliers is identifiable and equal to the ratio of the intention-to-treat effects of the potential outcomes to that of the potential treatment received. To improve the estimation efficiency, we propose three model-assisted estimators for the complier average treatment effect in randomized experiments with a binary outcome. We study their asymptotic properties, compare their efficiencies with that of the Wald estimator, and propose the Neyman-type conservative variance estimators to facilitate valid inferences. Moreover, we extend our methods and theory to estimate the multiplicative complier average treatment effect. Our analysis is randomization-based, allowing the working models to be misspecified. Finally, we conduct simulation studies to illustrate the advantages of the model-assisted methods and apply these analysis methods in a randomized experiment to evaluate the effect of academic services or incentives on academic performance.

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Section: Model-assisted Cate Estimatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Model-assisted complier average treatment effect estimates in randomized experiments with non-compliance and a binary outcome

Ren¹,

Liu²

2021

Preprint

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“…The robustness test of DID ensures that all effects are indeed caused by the implementation of the policy [ 18 – 20 ]. Besides, the effect is mainly manifested in the following two aspects.…”

Section: Research Model On the Impact Of Utcp On Female Employmentmentioning

confidence: 99%

Influence of UTCP on the employment of female workers and the supply of labor force

Wang

2021

PLoS ONE

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In recent years, China has introduced the Universal Two-Child Policy (UTCP), which means that a couple can have two children. The implementation of this policy may affect female employment. Based on this background, this work aims to the impact of UTCP on the number and employment of Chinese women workers, and find out the countermeasures for the adverse impact of the policy. Firstly, the role of the Propensity Score Matching-Differences in Differences model is introduced, and the average and dynamic effects of UTCP on women’s employment are discussed by using the Propensity Score Matching model. Secondly, the survey data on issues related to female employment after the implementation of UTCP from 2016 to 2020 is analyzed. Finally, a conclusion is drawn according to the survey data. The results demonstrate that the implementation of UTCP widens the income gap between men and women. Meanwhile, the younger the couple, the greater the income gap. Besides, the unemployment rate changes slightly after the introduction of the policy. As the growth rate of female income is significantly lower than that of men of the same age, UTCP has little impact on the employment of Chinese female workers, but has a great impact on the quality of employment. Among all the respondents, the proportion of employed men is higher than employed women, which is about 64% ~ 65%. However, it is still unknown whether age, education, family characteristics, nationality, occupations, and economic development of the province have a certain impact on female income, which is worth noting by follow-up research. On the whole, the full liberalization of the second child has little impact on the employment of female workers in China, but has a great impact on the quality of employment. The present work lays a foundation for the study of the impact of UTCT on female employment in future, and offers a certain reference for the further study of the impact of the policy on employment in the future.

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“…In particular, Theorem 3.3 gives the asymptotic distribution of our regression adjusted rank-based estimator. Previously, the asymptotic distributions of regression adjusted difference-inmeans type estimators were derived under different randomization strategies (Fogarty, 2018;Li and Ding, 2020;Liu and Yang, 2020;Su and Ding, 2021;Zhao and Ding, 2021b). These results build on the results of Li and Ding (2017) and do not apply to rank-based estimators, as already discussed above.…”

Section: Summary Of Our Contributionsmentioning

confidence: 99%

“…Lin (2013) proposed a regression adjusted estimator by modifying the ANCOVA model to include the interactions of the treatment and covariates that is asymptotically at least as efficient as the unadjusted difference-in-means estimator. Recently, regression adjusted or model assisted estimators have been developed for different study designs (Fogarty, 2018;Li and Ding, 2020;Liu and Yang, 2020;Su and Ding, 2021;Zhao and Ding, 2021b). But, these regression adjustment methods based on linear models which typically use robust standard errors from the classical literature (Huber, 1967;White, 1980) are still sensitive to heavy-tailed distributions, extreme values or outliers in the potential outcomes (MacKinnon and White, 1985;Young, 2018).…”

Section: Introductionmentioning

confidence: 99%

Efficiency of Regression (Un)-Adjusted Rosenbaum's Rank-based Estimator in Randomized Experiments

Ghosh¹,

Deb²,

Karmakar³

et al. 2021

Preprint

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A completely randomized experiment allows us to estimate the causal effect by the difference in the averages of the outcome under the treatment and control. But, difference-in-means type estimators behave poorly if the potential outcomes have a heavy-tail, or contain a few extreme observations or outliers. We study an alternative estimator by Rosenbaum that estimates the causal effect by inverting a randomization test using ranks. We study the asymptotic properties of this estimator and develop a framework to compare the efficiencies of different estimators of the treatment effect in the setting of randomized experiments. In particular, we show that Rosenbaum's estimator has variance that is asymptotically, in the worst case, at most about 1.16 times the variance of the difference-in-means estimator, and can be much smaller when the potential outcomes are not light-tailed. We further derive a consistent estimator of the asymptotic standard error for Rosenbaum's estimator which immediately yields a readily computable confidence interval for the treatment effect, thereby alleviating the expensive numerical calculations needed to implement Rosenbaum's original proposal.Further, we propose a regression adjusted version of Rosenbaum's estimator to incorporate additional covariate information in randomization inference. We prove gain in efficiency by this regression adjustment method under a linear regression model. Finally, we illustrate through simulations that, unlike the difference-in-means based estimators, either unadjusted or regression adjusted, these rank-based estimators are efficient and robust against heavy-tailed distributions, contamination, and various model misspecifications.

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Regression-adjusted average treatment effect estimates in stratified randomized experiments

Cited by 45 publications

References 18 publications

Model-assisted complier average treatment effect estimates in randomized experiments with non-compliance and a binary outcome

Model-assisted complier average treatment effect estimates in randomized experiments with non-compliance and a binary outcome

Influence of UTCP on the employment of female workers and the supply of labor force

Efficiency of Regression (Un)-Adjusted Rosenbaum's Rank-based Estimator in Randomized Experiments

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