Endogenous treatment effect estimation using high-dimensional instruments and double selection. (English) Zbl 1456.62032

Summary: We propose a double selection instrumental variable estimator for the endogenous treatment effects using both high-dimensional control variables and instrumental variables. It deals with the endogeneity of the treatment variable and reduces omitted variable bias due to imperfect model selection.


62F07 Statistical ranking and selection procedures
62D20 Causal inference from observational studies
62P25 Applications of statistics to social sciences


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[1] Amemiya, T., The non-linear two-stage least squares estimator, J. Econometrics, 2, 105-110 (1974) · Zbl 0282.62089
[2] Belloni, A.; Chen, D.; Chernozhukov, V.; Hansen, C., Sparse models and methods for optimal instruments with an application to eminent domain, Econometrica, 80, 2369-2429 (2012) · Zbl 1274.62464
[3] Belloni, A.; Chernozhukov, V.; Hansen, C., Inference on treatment effects after selection amongst high-dimensional controls, Rev. Econom. Stud., 81, 608-650 (2014) · Zbl 1409.62142
[4] Castro, M.; Expósito-Casas, E.; López-Martín, E.; Lizasoain, L.; Navarro-Asencio, E.; Gaviria, J. L., Parental involvement on student academic achievement: A meta-analysis, Educ. Res. Rev., 14, 33-46 (2015)
[5] Chernozhukov, V.; Hansen, C.; Spindler, M., Post-selection and post-regularization inference in linear models with many controls and instruments, Amer. Econ. Rev.: Pap. Proc., 105, 486-490 (2015)
[6] Dohl, G.; Lochner, L., The impact of family income on child achievement: Evidence from the earned income tax credit, Amer. Econ. Rev., 102, 1927-1956 (2012)
[7] Donohue III, J. J.; Levitt, S. D., The impact of legalized abortion on crime, Q. J. Econ., 116, 379-420 (2001)
[8] Fan, Q.; He, K.; Zhong, W., R package naivereg: Nonparametric additive instrumental variable estimator and related IV methods (2020), Version 1.0.5. Published on 2020-03-18. https://cran.r-project.org/web/packages/naivereg/index.html
[9] Fan, J.; Li, R., Variable selection via nonconcave penalized likelihood and its oracle properties, J. Amer. Statist. Assoc., 96, 1348-1360 (2001) · Zbl 1073.62547
[10] Fan, Q.; Zhong, W., Nonparametric additive instrumental variable estimator: A group shrinkage estimation perspective, J. Bus. Econom. Statist., 36, 388-399 (2018)
[11] Farrell, M. H., Robust inference on average treatment effects with possibly more covariates than observations, J. Econometrics, 189, 1-23 (2015) · Zbl 1337.62113
[12] Heckman, J.; Ichimura, H.; Smith, J.; Todd, P., Characterizing selection bias using experimental data, Econometrica, 66, 1017-1098 (1998) · Zbl 1055.62573
[13] Imbens, G. W., Nonparametric estimation of average treatment effects under exogeneity: A review, Rev. Econ. Stat., 86, 4-29 (2004)
[14] Imbens, G. W.; Rubin, D. B., Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction (2015), Cambridge University Press: Cambridge University Press New York · Zbl 1355.62002
[15] Kang, H.; Zhang, A.; Cai, T. T.; Small, D. S., Instrumental variables estimation with some invalid instruments and its application to mendelian randomization, J. Amer. Statist. Assoc., 111, 132-144 (2016)
[16] Lin, W.; Feng, R.; Li, H., Regularization methods for high-dimensional instrumental variables regression with an application to genetical genomics, J. Amer. Statist. Assoc., 110, 270-288 (2015) · Zbl 1373.62371
[17] Tibshirani, R., Regression shrinkage and selection via lasso, J. R. Statist. Soc. Ser. B-Statist. Methodol., 58, 267-288 (1996) · Zbl 0850.62538
[18] Van De Geer, S.; Bühlmann, P.; Zhou, S., The adaptive and the thresholded lasso for potentially misspecified models, Electron. J. Stat., 5, 688-749 (2011) · Zbl 1274.62471
[19] Wang, H.; Li, R.; Tsai, C., Tuning parameter selectors for the smoothly clipped absolute deviation method, Biometrika, 94, 553-568 (2007) · Zbl 1135.62058
[20] Zhong, W.; Zhou, W.; Fan, Q.; Gao, Y., Dummy Endogenous Treatment Effect Estimation using High-Dimensional Instrumental VariablesWorking paper (2020)
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