Hostname: page-component-74656f9884-j7cmm Total loading time: 0 Render date: 2026-11-10T21:30:56.182Z Has data issue: false hasContentIssue false
  • English
  • Français

COMBINING ESTIMATES OF CONDITIONAL TREATMENT EFFECTS

Published online by Cambridge University Press:  06 November 2018

Craig A. Rolling ,
Yuhong Yang  and
Dagmar Velez
Craig A. Rolling*
Affiliation:
Saint Louis University
Yuhong Yang
Affiliation:
University of Minnesota
Dagmar Velez
Affiliation:
Saint Louis University
*
*Address correspondence to Craig A. Rolling, Department of Epidemiology and Biostatistics, Saint Louis University, St. Louis, Missouri, USA; e-mail: craig.rolling@slu.edu.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Estimating a treatment’s effect on an outcome conditional on covariates is a primary goal of many empirical investigations. Accurate estimation of the treatment effect given covariates can enable the optimal treatment to be applied to each unit or guide the deployment of limited treatment resources for maximum program benefit. Applications of conditional treatment effect estimation are found in direct marketing, economic policy, and personalized medicine. When estimating conditional treatment effects, the typical practice is to select a statistical model or procedure based on sample data. However, combining estimates from the candidate procedures often provides a more accurate estimate than the selection of a single procedure. This article proposes a method of model combination that targets accurate estimation of the treatment effect conditional on covariates. We provide a risk bound for the resulting estimator under squared error loss and illustrate the method using data from a labor skills training program.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 35 , Issue 6 , December 2019 , pp. 1089 - 1110
Copyright
Copyright © Cambridge University Press 2018 

Footnotes

The authors would like to thank Arthur Lewbel and four anonymous referees for their helpful comments and suggestions that have improved the article.

References

REFERENCES

Abadie, A. & Imbens, G.W. (2006) Large sample properties of matching estimators for average treatment effects. Econometrica 74, 235–267.CrossRefGoogle Scholar
Abadie, A. & Imbens, G.W. (2011) Bias-corrected matching estimators for average treatment effects. Journal of Business and Economic Statistics 29, 1–11.CrossRefGoogle Scholar
Abrevaya, J., Hsu, Y.-C., & Lieli, R.P. (2015) Estimating conditional average treatment effects. Journal of Business & Economic Statistics 33, 485–505.CrossRefGoogle Scholar
Akaike, H. (1974) A new look at the statistical model identification. IEEE Transactions on Automatic Control 19, 716–723.CrossRefGoogle Scholar
Althauser, R.P. & Rubin, D. (1970) The computerized construction of a matched sample. American Journal of Sociology 76, 325–346.CrossRefGoogle Scholar
Bhattacharya, D. & Dupas, P. (2012) Inferring welfare maximizing treatment assignment under budget constraints. Journal of Econometrics 167, 168–196.CrossRefGoogle Scholar
Buckland, S., Burnham, K., & Augustin, N. (1997) Model selection: An integral part of inference. Biometrics 53, 603–618.CrossRefGoogle Scholar
Cai, T., Tian, L., Wong, P.H., & Wei, L. (2011) Analysis of randomized comparative clinical trial data for personalized treatment selections. Biostatistics 12, 270–282.CrossRefGoogle ScholarPubMed
Chang, M., Lee, S., & Whang, Y.-J. (2015) Nonparametric tests of conditional treatment effects with an application to single-sex schooling on academic achievements. The Econometrics Journal 18, 307–346.CrossRefGoogle Scholar
Claeskens, G. & Hjort, N.L. (2008) Minimizing average risk in regression models. Econometric Theory 24, 493–527.CrossRefGoogle Scholar
Claeskens, G., Magnus, J.R., Vasnev, A.L., & Wang, W. (2016) The forecast combination puzzle: A simple theoretical explanation. International Journal of Forecasting 32, 754–762.CrossRefGoogle Scholar
Cook, R.D. (1998) Regression Graphics. Wiley.CrossRefGoogle Scholar
Cook, R.D. & Li, B. (2002) Dimension reduction for conditional mean in regression. The Annals of Statistics 30, 455–474.CrossRefGoogle Scholar
Dehejia, R.H. & Wahba, S. (1999) Causal effects in nonexperimental studies: Reevaluating the evaluation of training programs. Journal of the American Statistical Association 94, 1053–1062.CrossRefGoogle Scholar
Green, D.P. & Kern, H.L. (2012) Modeling heterogeneous treatment effects in survey experiments with Bayesian additive regression trees. Public Opinion Quarterly 76, 491–511.CrossRefGoogle Scholar
Hirano, K. & Porter, J.R. (2009) Asymptotics for statistical treatment rules. Econometrica 77, 1683–1701.Google Scholar
Holland, P.W. (1986) Statistics and causal inference. Journal of the American Statistical Association 81, 945–960.CrossRefGoogle Scholar
Hsu, Y.-C. (2017) Consistent tests for conditional treatment effects. The Econometrics Journal 20, 1–22.CrossRefGoogle Scholar
Imai, K. & Ratkovic, M. (2013) Estimating treatment effect heterogeneity in randomized program evaluation. The Annals of Applied Statistics 7, 443–470.CrossRefGoogle Scholar
Imbens, G.W. (2004) Nonparametric estimation of average treatment effects under exogeneity: A review. Review of Economics and Statistics 86, 4–29.CrossRefGoogle Scholar
Imbens, G.W. & Wooldridge, J.M. (2009) Recent developments in the econometrics of program evaluation. Journal of Economic Literature 47, 5–86.CrossRefGoogle Scholar
Kitagawa, T. & Tetenov, A. (2015) Who Should be Treated? Empirical Welfare Maximization Methods for Treatment Choice. Cemmap Working paper, CWP10/15.Google Scholar
LaLonde, R.J. (1986) Evaluating the econometric evaluations of training programs with experimental data. The American Economic Review 76, 604–620.Google Scholar
Li, K.-C. (1991) Sliced inverse regression for dimension reduction. Journal of the American Statistical Association 86, 316–327.CrossRefGoogle Scholar
Li, K.-C., Lue, H.-H., & Chen, C.-H. (2000) Interactive tree-structured regression via principal Hessian directions. Journal of the American Statistical Association 95, 547–560.CrossRefGoogle Scholar
Li, L. (2007) Sparse sufficient dimension reduction. Biometrika 94, 603–613.CrossRefGoogle Scholar
Li, L. & Yin, X. (2008) Sliced inverse regression with regularizations. Biometrics 64, 124–131.CrossRefGoogle ScholarPubMed
Qian, M. & Murphy, S.A. (2011) Performance guarantees for individualized treatment rules. The Annals of Statistics 39, 1180–1210.CrossRefGoogle ScholarPubMed
Qian, W., Rolling, C.A., Cheng, G., & Yang, Y. (2017) On the forecast combination puzzle. Preprint. Available at https://arxiv.org/abs/1505.00475v1.Google Scholar
Raftery, A.E. (1995) Bayesian model selection in social research. Sociological Methodology 25, 111–163.CrossRefGoogle Scholar
Rolling, C.A. & Yang, Y. (2014) Model selection for estimating treatment effects. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 76, 749–769.CrossRefGoogle Scholar
Schwarz, G. (1978) Estimating the dimension of a model. The Annals of Statistics 6, 461–464.CrossRefGoogle Scholar
Smith, J. & Wallis, K. (2009) A simple explanation of the forecast combination puzzle. Oxford Bulletin of Economics and Statistics 71, 331–355.CrossRefGoogle Scholar
Stoye, J. (2009) Minimax regret treatment choice with finite samples. Journal of Econometrics 151, 70–81.CrossRefGoogle Scholar
Taddy, M., Gardner, M., Chen, L., & Draper, D. (2016) A nonparametric Bayesian analysis of heterogenous treatment effects in digital experimentation. Journal of Business & Economic Statistics 34, 661–672.CrossRefGoogle Scholar
Wood, S.N. (2006) Generalized Additive Models: An Introduction with R. Chapman and Hall/CRC.CrossRefGoogle Scholar
Yang, Y. (2001) Adaptive regression by mixing. Journal of the American Statistical Association 96, 574–588.CrossRefGoogle Scholar
Yang, Y. (2003) Regression with multiple candidate models: Selecting or mixing? Statistica Sinica 13, 783–809.Google Scholar
Yang, Y. (2004) Combining forecasting procedures: Some theoretical results. Econometric Theory 20, 176–222.CrossRefGoogle Scholar
Zhang, B. (2016) Empirical likelihood in causal inference. Econometric Reviews 35, 201–231.CrossRefGoogle Scholar
Supplementary material: PDF

Rolling et al. supplementary material

Rolling et al. supplementary material
Download Rolling et al. supplementary material(PDF)
PDF 315.9 KB