Xiduo Chen, Xingdong Feng, Antonio F. Galvao, Yeheng Ge
arXiv 26 Mar 2025 · Econometrics
arXiv:2503.20149 · PDF · DOI · OpenAlex · Extracted main text
Obtaining valid treatment effect inferences remains a challenging problem when dealing with numerous instruments and non-sparse control variables. In this paper, we propose a novel ridge regularization-based instrumental variables method for estimation and inference in the presence of both high-dimensional instrumental variables and high-dimensional control variables. These methods are applicable both with and without sparsity assumptions. To address the bias caused by high-dimensional instruments, we introduce a two-step procedure incorporating a data-splitting strategy. We establish statistical properties of the estimator, including consistency and asymptotic normality. Furthermore, we develop statistical inference procedures by providing a consistent estimator for the asymptotic variance of the estimator. The finite sample performance of the proposed method is evaluated through numerical simulations. Results indicate that the new estimator consistently outperforms existing sparsity-based approaches across various settings, offering valuable insights for more complex scenarios. Finally, we provide an empirical application estimating the causal effect of schooling on earnings by addressing potential endogeneity through the use of high-dimensional instrumental variables and high-dimensional covariates.
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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 | Hansen, C. and D. Kozbur (2014) Instrumental variables estimation with many weak instruments using regularized jive | 1.000 | 15 | 5 | 100% |
| 2 | Chernozhukov, V., C. Hansen, and M. Spindler (2015) Post-selection and post-regularization inference in linear models with many controls and instruments | 1.000 | 8 | 4 | 100% |
| 3 | Liu, X., S. Zheng, and X. Feng (2020) Estimation of error variance via ridge regression | 0.874 | 6 | 4 | 67% |
| 4 | Angrist, J. D. and A. B. Krueger (1991) Does compulsory school attendance affect schooling and earnings? | 0.811 | 4 | 2 | 100% |
| 5 | Chernozhukov, V., D. Chetverikov, M. Demirer, E. Duflo, C. Hansen, W… (2018) Double/debiased machine learning for treatment and structural parameters | 0.644 | 2 | 2 | 100% |
| 6 | Hausman, J. A., W. K. Newey, T. Woutersen, J. C. Chao, and N. R. Swa… (2012) Instrumental variable estimation with heteroskedasticity and many instruments | 0.644 | 2 | 2 | 100% |
| 7 | Chao, J. C., N. R. Swanson, J. A. Hausman, W. K. Newey, and T. Woute… (2012) Asymptotic distribution of jive in a heteroskedastic iv regression with many instruments | 0.585 | 3 | 1 | 100% |
| 8 | Belloni, A., D. Chen, V. Chernozhukov, and C. Hansen (2012) Sparse models and methods for optimal instruments with an application to eminent domain | 0.585 | 3 | 1 | 100% |
| 9 | He, X. and Q.-M. Shao (2000) On parameters of increasing dimensions | 0.511 | 2 | 2 | 50% |
| 10 | Liu, Y. and J. Xie (2020) Cauchy combination test: a powerful test with analytic p-value calculation under arbitrary dependency structures | 0.511 | 2 | 1 | 100% |
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