arXiv 8 Oct 2021 · Econometrics
arXiv:2110.03973 · PDF · DOI · OpenAlex · Extracted main text
A recent literature considers causal inference using noisy proxies for unobserved confounding factors. The proxies are divided into two sets that are independent conditional on the confounders. One set of proxies are `negative control treatments' and the other are `negative control outcomes'. Existing work applies to low-dimensional settings with a fixed number of proxies and confounders. In this work we consider linear models with many proxy controls and possibly many confounders. A key insight is that if each group of proxies is strictly larger than the number of confounding factors, then a matrix of nuisance parameters has a low-rank structure and a vector of nuisance parameters has a sparse structure. We can exploit the rank-restriction and sparsity to reduce the number of free parameters to be estimated. The number of unobserved confounders is not known a priori but we show that it is identified, and we apply penalization methods to adapt to this quantity. We provide an estimator with a closed-form as well as a doubly-robust estimator that must be evaluated using numerical methods. We provide conditions under which our doubly-robust estimator is uniformly root-$n$ consistent, asymptotically centered normal, and our suggested confidence intervals have asymptotically correct coverage. We provide simulation evidence that our methods achieve better performance than existing approaches in high dimensions, particularly when the number of proxies is substantially larger than the number of confounders.
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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 | Griliches, Zvi (1977) Estimating the Returns to Schooling: Some Econometric Problems | 0.928 | 4 | 3 | 100% |
| 2 | Miao, Wang, Shi, Xu, & Tchetgen, Eric Tchetgen (2018) A Confounding Bridge Approach for Double Negative Control Inference on Causal Effects | 0.874 | 9 | 2 | 100% |
| 3 | Chernozhukov, Victor, Chetverikov, Denis, Demirer, Mert, Duflo, Esth… (2018) Double/debiased machine learning for treatment and structural parameters | 0.863 | 14 | 4 | 64% |
| 4 | Deaner, Ben (2021) Proxy Controls and Panel Data self | 0.693 | 6 | 1 | 100% |
| 5 | Bunea, Florentina, She, Yiyuan, & Wegkamp, Marten H (2011) Optimal selection of reduced rank estimators of high-dimensional matrices | 0.511 | 2 | 1 | 100% |
| 6 | Chernozhukov, Victor, Escanciano, Juan Carlos, Ichimura, Hidehiko, N… (2016) Locally Robust Semiparametric Estimation | 0.511 | 2 | 1 | 100% |
| 7 | Deaner, Ben (2019) Proxy Controls and Panel Data self | 0.511 | 2 | 1 | 100% |
| 8 | Miao, Wang, Geng, Zhi, & Tchetgen, Eric J. Tchetgen (2018) Identifying causal effects with proxy variables of an unmeasured confounder | 0.511 | 2 | 1 | 100% |
| 9 | Pearl, Judea (2009) Causality: Models, Reasoning, and Inference (Second Edition) | 0.511 | 2 | 1 | 100% |
| 10 | Tchetgen, Eric J. Tchetgen, Ying, Andrew, Cui, Yifan, Shi, Xu, & Mia… (2020) An Introduction to Proximal Causal Learning | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 20 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Proxy Controls and Panel Data | 0.405 | 1 | 1 |
| 2 | Instrumented Common Confounding | 0.405 | 1 | 1 |
| 3 | Causal Models for Longitudinal and Panel Data: A Survey | 0.405 | 1 | 1 |
| 4 | Fast and Adaptive Rates for Regularized DeepIV | 0.405 | 1 | 1 |
| 5 | An Introduction to Double/Debiased Machine Learning | 0.405 | 1 | 1 |