Helmut Farbmacher, Rebecca Groh, Michael Mühlegger, Gabriel Vollert
arXiv 16 Aug 2024 · Econometrics
arXiv:2408.08580 · PDF · DOI · OpenAlex · Extracted main text
Instrumental variables estimation with many instruments is biased. Traditional bias-adjustments are closely connected to the Silverstein equation. Based on the theory of random matrices, we show that Ridge estimation of the first-stage parameters reduces the implicit price of bias-adjustments. This leads to a trade-off, allowing for less costly estimation of the causal effect, which comes along with improved asymptotic properties. Our theoretical results nest existing ones on bias approximation and adjustment with ordinary least-squares in the first-stage regression and, moreover, generalize them to settings with more instruments than observations. Finally, we derive the optimal tuning parameter of Ridge regressions in simultaneous equations models, which comprises the well-known result for single equation models as a special case with uncorrelated error terms.
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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 | Hahn, J. and J. Hausman (2002) Notes on bias in estimators for simultaneous equation models | 1.000 | 5 | 3 | 100% |
| 2 | Dobriban, E. and S. Wager (2018) High-dimensional asymptotics of prediction: Ridge regression and classification | 0.928 | 5 | 4 | 80% |
| 3 | Chao, J. C. and N. R. Swanson (2005) Consistent estimation with a large number of weak instruments | 0.874 | 5 | 2 | 100% |
| 4 | Chamberlain, G. and G. Imbens (2004) Random effects estimators with many instrumental variables | 0.737 | 3 | 2 | 100% |
| 5 | Hahn, J. and J. Hausman (2002) A new specification test for the validity of instrumental variables | 0.737 | 3 | 2 | 100% |
| 6 | Hansen, C. and D. Kozbur (2014) Instrumental variables estimation with many weak instruments using regularized JIVE | 0.737 | 3 | 2 | 100% |
| 7 | Nagar, A. L (1959) The bias and moment matrix of the general k-class estimators of the parameters in simultaneous equations | 0.737 | 3 | 2 | 100% |
| 8 | Donald, S. G. and W. K. Newey (2001) Choosing the number of instruments | 0.644 | 2 | 2 | 100% |
| 9 | Hastie, T., A. Montanari, S. Rosset, and R. J. Tibshirani (2022) Surprises in high-dimensional ridgeless least squares interpolation | 0.644 | 2 | 2 | 100% |
| 10 | Dobriban, E. and S. Wager (2018) High-dimensional asymptotics of prediction: Ridge regression and classification | 0.585 | 4 | 4 | 25% |
Showing the top 10 of 30 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Robust Inference with High-Dimensional Instruments | 0.405 | 1 | 1 |