Alexandre Belloni, Victor Chernozhukov, Christian Hansen
arXiv 6 Dec 2010 · Statistics — Methodology · 81 citations (OpenAlex)
arXiv:1012.1297 · PDF · DOI · OpenAlex · Extracted main text
In this note, we propose to use sparse methods (e.g. LASSO, Post-LASSO, sqrt-LASSO, and Post-sqrt-LASSO) to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments in the canonical Gaussian case. The methods apply even when the number of instruments is much larger than the sample size. We derive asymptotic distributions for the resulting IV estimators and provide conditions under which these sparsity-based IV estimators are asymptotically oracle-efficient. In simulation experiments, a sparsity-based IV estimator with a data-driven penalty performs well compared to recently advocated many-instrument-robust procedures. We illustrate the procedure in an empirical example using the Angrist and Krueger (1991) schooling data.
appendix boundary found by appendix_command · 74% of the source is main text. Read the extracted text to check this.
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 | P. J. Bickel, Y. Ritov, and A. B. Tsybakov (2009) Simultaneous analysis of Lasso and Dantzig selector | 0.894 | 7 | 4 | 71% |
| 2 | Christian Hansen, Jerry Hausman, and Whitney K. Newey (2008) Estimation with many instrumental variables self | 0.811 | 4 | 2 | 100% |
| 3 | A. Belloni, V. Chernozhukov, and L. Wang (2010) Square-root-lasso: Pivotal recovery of sparse signals via conic programming | 0.737 | 3 | 3 | 67% |
| 4 | A. Belloni and V. Chernozhukov (2009) Post-$_1$-penalized estimators in high-dimensional linear regression models | 0.659 | 7 | 4 | 29% |
| 5 | J. D. Angrist and A. B. Krueger (1991) Does compulsory school attendance affect schooling and earnings? | 0.644 | 4 | 1 | 100% |
| 6 | Wayne A. Fuller (1977) Some properties of a modification of the limited information estimator | 0.644 | 2 | 2 | 100% |
| 7 | Paul A. Bekker (1994) Alternative approximations to the distributions of instrumental variables estimators | 0.511 | 2 | 1 | 100% |
| 8 | Whitney K. Newey (1990) Efficient instrumental variables estimation of nonlinear models | 0.511 | 2 | 1 | 100% |
| 9 | J. D. Angrist, G. W. Imbens, and D. B. Rubin (2006) Identification of causal effects using instrumental variables | 0.405 | 1 | 1 | 100% |
| 10 | J. D. Angrist and A. Krueger (2001) Instrumental variables and the search for identification: From supply and demand to natural experiments | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 30 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.