Inference for Nonlinear Endogenous Treatment Effects Accounting for High-Dimensional Covariate Complexity
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913396213940224 |
|---|---|
| author | Fan, Qingliang Guo, Zijian Mei, Ziwei Zhang, Cun-Hui |
| author_facet | Fan, Qingliang Guo, Zijian Mei, Ziwei Zhang, Cun-Hui |
| contents | Nonlinearity and endogeneity are prevalent challenges in causal analysis using observational data. This paper proposes an inference procedure for a nonlinear and endogenous marginal effect function, defined as the derivative of the nonparametric treatment function, with a primary focus on an additive model that includes high-dimensional covariates. Using the control function approach for identification, we implement a regularized nonparametric estimation to obtain an initial estimator of the model. Such an initial estimator suffers from two biases: the bias in estimating the control function and the regularization bias for the high-dimensional outcome model. Our key innovation is to devise the double bias correction procedure that corrects these two biases simultaneously. Building on this debiased estimator, we further provide a confidence band of the marginal effect function. Simulations and an empirical study of air pollution and migration demonstrate the validity of our procedures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_08063 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Inference for Nonlinear Endogenous Treatment Effects Accounting for High-Dimensional Covariate Complexity Fan, Qingliang Guo, Zijian Mei, Ziwei Zhang, Cun-Hui Econometrics Nonlinearity and endogeneity are prevalent challenges in causal analysis using observational data. This paper proposes an inference procedure for a nonlinear and endogenous marginal effect function, defined as the derivative of the nonparametric treatment function, with a primary focus on an additive model that includes high-dimensional covariates. Using the control function approach for identification, we implement a regularized nonparametric estimation to obtain an initial estimator of the model. Such an initial estimator suffers from two biases: the bias in estimating the control function and the regularization bias for the high-dimensional outcome model. Our key innovation is to devise the double bias correction procedure that corrects these two biases simultaneously. Building on this debiased estimator, we further provide a confidence band of the marginal effect function. Simulations and an empirical study of air pollution and migration demonstrate the validity of our procedures. |
| title | Inference for Nonlinear Endogenous Treatment Effects Accounting for High-Dimensional Covariate Complexity |
| topic | Econometrics |
| url | https://arxiv.org/abs/2310.08063 |