Chunrong Ai, Oliver Linton, Kaiji Motegi, Zheng Zhang
arXiv 15 Aug 2018 · Econometrics · publishedQuantitative Economics (2021) · 23 citations (OpenAlex)
arXiv:1808.04936 · PDF · DOI · OpenAlex · Extracted main text
This paper presents a weighted optimization framework that unifies the binary,multi-valued, continuous, as well as mixture of discrete and continuous treatment, under the unconfounded treatment assignment. With a general loss function, the framework includes the average, quantile and asymmetric least squares causal effect of treatment as special cases. For this general framework, we first derive the semiparametric efficiency bound for the causal effect of treatment, extending the existing bound results to a wider class of models. We then propose a generalized optimization estimation for the causal effect with weights estimated by solving an expanding set of equations. Under some sufficient conditions, we establish consistency and asymptotic normality of the proposed estimator of the causal effect and show that the estimator attains our semiparametric efficiency bound, thereby extending the existing literature on efficient estimation of causal effect to a wider class of applications. Finally, we discuss etimation of some causal effect functionals such as the treatment effect curve and the average outcome. To evaluate the finite sample performance of the proposed procedure, we conduct a small scale simulation study and find that the proposed estimation has practical value. To illustrate the applicability of the procedure, we revisit the literature on campaign advertise and campaign contributions. Unlike the existing procedures which produce mixed results, we find no evidence of campaign advertise on campaign contribution.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Fong, Hazlett, and Imai (2018) Covariate Balancing Propensity Score for a Continuous Treatment: Application to the Efficacy of Political Advertisements | 0.693 | 17 | 1 | 100% |
| 2 | Ai, Linton, Motegi, and Zhang (2018) A Unified Framework for Efficient Estimation of Binary, Multi-level, Continuous and Mixture of Discrete and Continuous Treatment… | 0.644 | 4 | 1 | 100% |
| 3 | Firpo (2007) Efficient Semiparametric Estimation of Quantile Treatment Effects | 0.585 | 3 | 1 | 100% |
| 4 | Cattaneo (2010) Efficient semiparametric estimation of multi-valued treatment effects under ignorability | 0.585 | 3 | 1 | 100% |
| 5 | Hahn (1998) On the role of the propensity score in efficient semiparametric estimation of average treatment effects | 0.511 | 2 | 1 | 100% |
| 6 | Masry (1996) Multivariate local polynomial regression for time series: uniform strong consistency and rates | 0.511 | 2 | 1 | 100% |
| 7 | Robins, Rotnitzky, and Zhao (1994) Estimation of regression coefficients when some regressors are not always observed | 0.511 | 2 | 1 | 100% |
| 8 | Bickel, Klaassen, Ritov, and Wellner (1993) Efficient and Adaptive Estimation for Semiparametric Models | 0.405 | 1 | 1 | 100% |
| 9 | Andrews (1994) Empirical process methods in econometrics | 0.405 | 1 | 1 | 100% |
| 10 | Chan, Yam, and Zhang (2016) Globally efficient non-parametric inference of average treatment effects by empirical balancing calibration weighting self | 0.405 | 1 | 1 | 100% |
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