arXiv 26 Aug 2024 · Econometrics
arXiv:2408.14671 · PDF · DOI · OpenAlex · Extracted main text
We develop an estimator for treatment effects in high-dimensional settings with additive measurement error, a prevalent challenge in modern econometrics. We introduce the Double/Debiased Convex Conditioned LASSO (Double/Debiased CoCoLASSO), which extends the double/debiased machine learning framework to accommodate mismeasured covariates. Our principal contributions are threefold. (1) We construct a Neyman-orthogonal score function that remains valid under measurement error, incorporating a bias correction term to account for error-induced correlations. (2) We propose a method of moments estimator for the measurement error variance, enabling implementation without prior knowledge of the error covariance structure. (3) We establish the $\sqrt{N}$-consistency and asymptotic normality of our estimator under general conditions, allowing for both the number of covariates and the magnitude of measurement error to increase with the sample size. Our theoretical results demonstrate the estimator's efficiency within the class of regularized high-dimensional estimators accounting for measurement error. Monte Carlo simulations corroborate our asymptotic theory and illustrate the estimator's robust performance across various levels of measurement error. Notably, our covariance-oblivious approach nearly matches the efficiency of methods that assume known error variance.
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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 | Datta, Abhirup, Zou, Hui (2017) Cocolasso for high-dimensional error-in-variables regression | 0.956 | 8 | 6 | 88% |
| 2 | Chernozhukov, Victor, Chetverikov, Denis, Demirer, Mert, Duflo, Esth… (2018) Double/debiased machine learning for treatment and structural parameters | 0.874 | 6 | 5 | 67% |
| 3 | Loh, Po-Ling, Wainwright, Martin J (2011) High-dimensional regression with noisy and missing data: Provable guarantees with non-convexity | 0.644 | 2 | 2 | 100% |
| 4 | Belloni, Alexandre, Chernozhukov, Victor, Hansen, Christian (2014) High-dimensional methods and inference on structural and treatment effects | 0.405 | 1 | 1 | 100% |
| 5 | Belloni, Alexandre, Chernozhukov, Victor, Hansen, Christian (2014) Inference on treatment effects after selection among high-dimensional controls | 0.405 | 1 | 1 | 100% |
| 6 | Belloni, Alexandre, Chernozhukov, Victor, Fernandez-Val, Ivan, Hanse… (2017) Program evaluation and causal inference with high-dimensional data | 0.405 | 1 | 1 | 100% |
| 7 | Caner, Mehmet, Kock, Anders Bredahl (2018) Asymptotically honest confidence regions for high dimensional parameters by the desparsified conservative lasso | 0.405 | 1 | 1 | 100% |
| 8 | Carroll, Raymond J, Ruppert, David, Stefanski, Leonard A (1995) Measurement error in nonlinear models | 0.405 | 1 | 1 | 100% |
| 9 | Chernozhukov, Victor, Hansen, Christian, Spindler, Martin (2015) Valid post-selection and post-regularization inference: An elementary, general approach | 0.405 | 1 | 1 | 100% |
| 10 | Chernozhukov, Victor, Newey, Whitney K, Singh, Rahul (2022) Automatic debiased machine learning of causal and structural effects | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 24 scored citations.