Christoph Breunig, Enno Mammen, Anna Simoni
arXiv 2 Jun 2018 · Econometrics · publishedJournal of Econometrics (2020) · 3 citations (OpenAlex)
arXiv:1806.00666 · PDF · DOI · OpenAlex · Extracted main text
This paper is concerned with inference about low-dimensional components of a high-dimensional parameter vector $\beta^0$ which is identified through instrumental variables. We allow for eigenvalues of the expected outer product of included and excluded covariates, denoted by $M$, to shrink to zero as the sample size increases. We propose a novel estimator based on desparsification of an instrumental variable Lasso estimator, which is a regularized version of 2SLS with an additional correction term. This estimator converges to $\beta^0$ at a rate depending on the mapping properties of $M$ captured by a sparse link condition. Linear combinations of our estimator of $\beta^0$ are shown to be asymptotically normally distributed. Based on consistent covariance estimation, our method allows for constructing confidence intervals and statistical tests for single or low-dimensional components of $\beta^0$. In Monte-Carlo simulations we analyze the finite sample behavior of our estimator.
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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 | V. Chernozhukov, C. Hansen, and M. Spindler (2015) Post-selection and post-regularization inference in linear models with many controls and instruments | 0.874 | 6 | 2 | 100% |
| 2 | N. Meinshausen and P. Bühlmann (2006) High-dimensional graphs and variable selection with the lasso | 0.811 | 4 | 2 | 100% |
| 3 | S. van de Geer, P. Bühlmann, Y. Ritov, and R. Dezeure (2014) On asymptotically optimal confidence regions and tests for high-dimensional models | 0.747 | 12 | 5 | 42% |
| 4 | E. Gautier, A. Tsybakov, and C. Rose (2011) High-dimensional instrumental variables regression and confidence sets | 0.737 | 3 | 2 | 100% |
| 5 | X. Chen and D. Pouzo (2012) Estimation of nonparametric conditional moment models with possibly nonsmooth moments | 0.644 | 2 | 2 | 100% |
| 6 | D. W. Andrews and X. Cheng (2012) Estimation and inference with weak, semi-strong, and strong identification | 0.644 | 2 | 2 | 100% |
| 7 | X. Chen and T. M. Christensen (2018) Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric iv regression | 0.585 | 3 | 1 | 100% |
| 8 | P. Bühlmann and S. Van De Geer (2011) Statistics for high-dimensional data: methods, theory and applications | 0.511 | 2 | 2 | 50% |
| 9 | S. Berry, J. Levinsohn, and A. Pakes (1995) Automobile prices in market equilibrium | 0.511 | 2 | 1 | 100% |
| 10 | V. Chernozhukov, D. Chetverikov, M. Demirer, E. Duflo, C. Hansen, W.… (2018) Double/debiased machine learning for treatment and structural parameters | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 41 scored citations.
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| Citing paper | Intensity | Mentions | Sections | |
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| 1 | Functional Spatial Autoregressive Models | 0.405 | 1 | 1 |
| 2 | Ill-Conditioned Orthogonal Scores in Double Machine Learning | 0.405 | 1 | 1 |