skip to content

Faculty of Economics

Journal Cover

Ai, C., Linton, O., Motegi, K. and Zhang, Z.

A Unified Framework for Efficient Estimation of General Treatment Models

Quantitative Economics, forthcoming


Abstract: This paper presents a weighted optimization framework that unifies the binary, multivalued, 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 estimation 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.

Keywords: Treatment effect, Semiparametric efficiency, Stabilized Weights

Author links: Oliver Linton  

Publisher's Link:

Open Data link:

Cambridge Working Paper in Economics Version of Paper: A Unified Framework for Efficient Estimation of General Treatment Models, Ai, C., Linton, O., Motegi, K., Zhang, Z., (2019)

Papers and Publications

Recent Publications

Onatski, A. and Wang, C. Spurious Factor Analysis Econometrica [2021]

Elliott, M. and Golub, B. A Network Approach to Public Goods Journal of Political Economy [2019]

Cantore, C. and Freund, L. B. Workers, Capitalists, and the Government: Fiscal Policy and Income (Re)Distribution Journal of Monetary Economics [2021]

Cavalcanti, T. and Santos, M. (Mis)Allocation Effects of an Overpaid Public Sector Journal of the European Economic Association [2020]