arXiv 21 Aug 2017 · Mathematics — Statistics Theory · 1 citations (OpenAlex)
arXiv:1708.06443 · PDF · DOI · OpenAlex · Extracted main text
The two-stage least-squares (2SLS) estimator is known to be biased when its first-stage fit is poor. I show that better first-stage prediction can alleviate this bias. In a two-stage linear regression model with Normal noise, I consider shrinkage in the estimation of the first-stage instrumental variable coefficients. For at least four instrumental variables and a single endogenous regressor, I establish that the standard 2SLS estimator is dominated with respect to bias. The dominating IV estimator applies James-Stein type shrinkage in a first-stage high-dimensional Normal-means problem followed by a control-function approach in the second stage. It preserves invariances of the structural instrumental variable equations.
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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 | Chamberlain, G (2007) Decision Theory Applied to an Instrumental Variables Model | 0.843 | 3 | 3 | 100% |
| 2 | James, W. and Stein, C (1961) Estimation with quadratic loss | 0.811 | 4 | 2 | 100% |
| 3 | Stein, C. M (1981) Estimation of the Mean of a Multivariate Normal Distribution | 0.511 | 2 | 1 | 100% |
| 4 | Spiess, J (2017) Unbiased Shrinkage Estimation self | 0.405 | 1 | 1 | 100% |
| 5 | Piegorsch, W. W. and Casella, G (1985) The existence of the first negative moment | 0.405 | 1 | 1 | 100% |
| 6 | Hansen, B. E (2017) Stein-like 2SLS estimator | 0.405 | 1 | 1 | 100% |
| 7 | Moser, S. M (2008) Expectations of a noncentral chi-square distribution with application to IID MIMO Gaussian fading | 0.405 | 1 | 1 | 100% |
Showing the top 7 of 7 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Unbiased Shrinkage Estimation | 0.405 | 1 | 1 |
| 2 | Revisiting the Many Instruments Problem using Random Matrix Theory | 0.405 | 1 | 1 |