This paper studies non-separable models with a continuous treatment when the dimension of the control variables is high and potentially larger than the effective sample size. We propose a three-step estimation procedure to estimate the average, quantile, and marginal treatment effects. In the first stage we estimate the conditional mean, distribution, and density objects by penalized local least squares, penalized local maximum likelihood estimation, and penalized conditional density estimation, respectively, where control variables are selected via a localized method of L1-penalization at each value of the continuous treatment. In the second stage we estimate the average and the marginal distribution of the potential outcome via the plug-in principle. In the third stage, we estimate the quantile and marginal treatment effects by inverting the estimated distribution function and using the local linear regression, respectively. We study the asymptotic properties of these estimators and propose a weighted-bootstrap method for inference. Using simulated and real datasets, we demonstrate the proposed estimators perform well infinite samples.
Average treatment effect, High dimension, Least absolute shrinkage and selection operator (Lasso), Nonparametric quantile regression, Nonseparable models, Quantile treatment effect, Unconditional average structural derivative.
SU, Liangjun; URA, Takuya; and ZHANG, Yichong.
Non-separable models with high-dimensional data. (2017). 1-85. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/2105
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