arXiv 20 Nov 2018 · Econometrics · publishedEconometrics Journal (2020)
arXiv:1811.08083 · PDF · DOI · OpenAlex · Extracted main text
We propose a two-stage least squares (2SLS) estimator whose first stage is the equal-weighted average over a complete subset with $k$ instruments among $K$ available, which we call the complete subset averaging (CSA) 2SLS. The approximate mean squared error (MSE) is derived as a function of the subset size $k$ by the Nagar (1959) expansion. The subset size is chosen by minimizing the sample counterpart of the approximate MSE. We show that this method achieves the asymptotic optimality among the class of estimators with different subset sizes. To deal with averaging over a growing set of irrelevant instruments, we generalize the approximate MSE to find that the optimal $k$ is larger than otherwise. An extensive simulation experiment shows that the CSA-2SLS estimator outperforms the alternative estimators when instruments are correlated. As an empirical illustration, we estimate the logistic demand function in Berry, Levinsohn, and Pakes (1995) and find the CSA-2SLS estimate is better supported by economic theory than the alternative estimates.
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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 | Berry, S., J. Levinsohn, and A. Pakes (1995) Automobile prices in market equilibrium | 1.000 | 6 | 3 | 100% |
| 2 | Kuersteiner, G. and R. Okui (2010) Constructing optimal instruments by first-stage prediction averaging | 0.953 | 15 | 6 | 87% |
| 3 | Donald, S. G. and W. K. Newey (2001) Choosing the number of instruments | 0.902 | 30 | 6 | 73% |
| 4 | Nagar, A. L (1959) The bias and moment matrix of the general k-class estimators of the parameters in simultaneous equations | 0.843 | 3 | 3 | 100% |
| 5 | Hansen, B. E (2007) Least squares model averaging | 0.811 | 4 | 2 | 100% |
| 6 | Li, K.-C (1987) Asymptotic optimality for $C_p$, $C_L$, cross-validation and generalized cross-validation: discrete index set | 0.811 | 4 | 2 | 100% |
| 7 | Carrasco, M (2012) A regularization approach to the many instruments problem | 0.737 | 3 | 2 | 100% |
| 8 | Chao, J. C. and N. R. Swanson (2005) Consistent estimation with a large number of weak instruments | 0.644 | 2 | 2 | 100% |
| 9 | Lee, Y. and Y. Zhou (2015) Averaged instrumental variables estimators | 0.644 | 2 | 2 | 100% |
| 10 | Angrist, J. D. and A. B. Krueger (1991) Does compulsory school attendance affect schooling and earnings? | 0.585 | 3 | 1 | 100% |
Showing the top 10 of 53 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | csa2sls: A complete subset approach for many instruments using Stata | 1.000 | 7 | 5 |
| 2 | Complete Subset Averaging for Quantile Regressions | 0.405 | 1 | 1 |