Andrew Bennett, Nathan Kallus, Xiaojie Mao, Whitney Newey, Vasilis Syrgkanis, Masatoshi Uehara
arXiv 10 Feb 2023 · Statistics — Machine Learning
arXiv:2302.05404 · PDF · DOI · OpenAlex · Extracted main text
In this paper, we study nonparametric estimation of instrumental variable (IV) regressions. Recently, many flexible machine learning methods have been developed for instrumental variable estimation. However, these methods have at least one of the following limitations: (1) restricting the IV regression to be uniquely identified; (2) only obtaining estimation error rates in terms of pseudometrics (e.g., projected norm) rather than valid metrics (e.g., $L_2$ norm); or (3) imposing the so-called closedness condition that requires a certain conditional expectation operator to be sufficiently smooth. In this paper, we present the first method and analysis that can avoid all three limitations, while still permitting general function approximation. Specifically, we propose a new penalized minimax estimator that can converge to a fixed IV solution even when there are multiple solutions, and we derive a strong $L_2$ error rate for our estimator under lax conditions. Notably, this guarantee only needs a widely-used source condition and realizability assumptions, but not the so-called closedness condition. We argue that the source condition and the closedness condition are inherently conflicting, so relaxing the latter significantly improves upon the existing literature that requires both conditions. Our estimator can achieve this improvement because it builds on a novel formulation of the IV estimation problem as a constrained optimization problem.
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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 | Dikkala, N., G. Lewis, L. Mackey, and V. Syrgkanis (2020) Minimax estimation of conditional moment models | 1.000 | 20 | 3 | 100% |
| 2 | Bennett, A., N. Kallus, X. Mao, W. Newey, V. Syrgkanis, and M. Uehara (2022) Inference on strongly identified functionals of weakly identified functions self | 1.000 | 13 | 3 | 100% |
| 3 | Carrasco, M., J.-P. Florens, and E. Renault (2007) Linear inverse problems in structural econometrics estimation based on spectral decomposition and regularization | 1.000 | 8 | 3 | 100% |
| 4 | Cavalier, L (2011) Inverse problems in statistics | 1.000 | 5 | 3 | 100% |
| 5 | Florens, J.-P., J. Johannes, and S. Van Bellegem (2011) Identification and estimation by penalization in nonparametric instrumental regression | 1.000 | 5 | 3 | 100% |
| 6 | Chen, X. and M. Reiss (2011) On rate optimality for ill-posed inverse problems in econometrics | 0.928 | 4 | 3 | 100% |
| 7 | Liao, L., Y.-L. Chen, Z. Yang, B. Dai, M. Kolar, and Z. Wang (2020) Provably efficient neural estimation of structural equation models: An adversarial approach | 0.874 | 12 | 2 | 100% |
| 8 | Kallus, N., X. Mao, and M. Uehara (2021) Causal inference under unmeasured confounding with negative controls: A minimax learning approach self | 0.843 | 4 | 3 | 75% |
| 9 | Ito, K. and B. Jin (2014) Inverse problems: Tikhonov theory and algorithms, Volume 22 | 0.843 | 3 | 3 | 100% |
| 10 | Chen, Q (2021) Robust and optimal estimation for partially linear instrumental variables models with partial identification | 0.811 | 4 | 2 | 100% |
Showing the top 10 of 55 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Penalized GMM Framework for Inference on Functionals of Nonparametric Instrumental Variable Estimators | 0.644 | 2 | 2 |
| 2 | Long-term Causal Inference Under Persistent Confounding via Data Combination | 0.585 | 3 | 1 |