Qingliang Fan, Zijian Guo, Ziwei Mei, Cun-Hui Zhang
arXiv 12 Oct 2023 · Econometrics · 1 citations (OpenAlex)
arXiv:2310.08063 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Chernozhukov, V., Chetverikov, D., and Kato, K (2014) Anti-concentration and honest, adaptive confidence bands | 1.000 | 5 | 4 | 100% |
| 2 | Chernozhukov, V., Chetverikov, D., and Kato, K (2014) Gaussian approximation of suprema of empirical processes | 1.000 | 5 | 4 | 100% |
| 3 | Chen, X. and Christensen, T. M (2018) Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric IV regression | 1.000 | 5 | 3 | 100% |
| 4 | Lu, J., Kolar, M., and Liu, H (2020) Kernel meets sieve: Post-regularization confidence bands for sparse additive model | 1.000 | 5 | 3 | 100% |
| 5 | Newey, W. K., Powell, J., and Vella, F (1999) Nonparametric estimation of triangular simultaneous equations models | 1.000 | 5 | 3 | 100% |
| 6 | Javanmard, A. and Montanari, A (2014) Confidence intervals and hypothesis testing for high-dimensional regression | 0.928 | 4 | 4 | 100% |
| 7 | Ozabaci, D., Henderson, D. J., and Su, L (2014) Additive nonparametric regression in the presence of endogenous regressors | 0.928 | 4 | 3 | 100% |
| 8 | Chen, S., Oliva, P., and Zhang, P (2022) The effect of air pollution on migration: Evidence from China | 0.874 | 5 | 2 | 100% |
| 9 | Su, L. and Ullah, A (2008) Local polynomial estimation of nonparametric simultaneous equations models | 0.843 | 3 | 3 | 100% |
| 10 | Schumaker, L (2007) Spline functions: basic theory | 0.811 | 4 | 2 | 100% |
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