arXiv 9 Oct 2019 · Econometrics · publishedOxford Bulletin of Economics and Statistics (2024) · 1 citations (OpenAlex)
arXiv:1910.04245 · PDF · DOI · OpenAlex · Extracted main text
This paper proposes averaging estimation methods to improve the finite-sample efficiency of the instrumental variables quantile regression (IVQR) estimation. First, I apply Cheng, Liao, Shi's (2019) averaging GMM framework to the IVQR model. I propose using the usual quantile regression moments for averaging to take advantage of cases when endogeneity is not too strong. I also propose using two-stage least squares slope moments to take advantage of cases when heterogeneity is not too strong. The empirical optimal weight formula of Cheng et al. (2019) helps optimize the bias-variance tradeoff, ensuring uniformly better (asymptotic) risk of the averaging estimator over the standard IVQR estimator under certain conditions. My implementation involves many computational considerations and builds on recent developments in the quantile literature. Second, I propose a bootstrap method that directly averages among IVQR, quantile regression, and two-stage least squares estimators. More specifically, I find the optimal weights in the bootstrap world and then apply the bootstrap-optimal weights to the original sample. The bootstrap method is simpler to compute and generally performs better in simulations, but it lacks the formal uniform dominance results of Cheng et al. (2019). Simulation results demonstrate that in the multiple-regressors/instruments case, both the GMM averaging and bootstrap estimators have uniformly smaller risk than the IVQR estimator across data-generating processes (DGPs) with all kinds of combinations of different endogeneity levels and heterogeneity levels. In DGPs with a single endogenous regressor and instrument, where averaging estimation is known to have least opportunity for improvement, the proposed averaging estimators outperform the IVQR estimator in some cases but not others.
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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 | Chernozhukov, V. and C. Hansen (2005) An IV model of quantile treatment effects | 1.000 | 8 | 3 | 100% |
| 2 | Cheng, X., Z. Liao, and R. Shi (2019) On uniform asymptotic risk of averaging GMM estimators | 0.972 | 37 | 6 | 92% |
| 3 | de Castro, L., A. F. Galvao, D. M. Kaplan, and X. Liu (2019) Smoothed GMM for quantile models | 0.965 | 10 | 4 | 90% |
| 4 | Kaplan, D. M. and Y. Sun (2017) Smoothed estimating equations for instrumental variables quantile regression | 0.920 | 9 | 5 | 78% |
| 5 | Kato, K (2012) Asymptotic normality of Powell's kernel estimator | 0.794 | 10 | 3 | 50% |
| 6 | Abadie, A., J. Angrist, and G. Imbens (2002) Instrumental variables estimates of the effect of subsidized training on the quantiles of trainee earnings | 0.511 | 2 | 2 | 50% |
| 7 | Hansen, B. E (2017) A Stein-like 2SLS estimator | 0.511 | 2 | 2 | 50% |
| Chernozhukov and Hansen | unmatched citation key Chernozhukov and Hansen | 0.511 | 2 | 1 | 100% |
| 9 | Chernozhukov, V. and C. Hansen (2006) Instrumental quantile regression inference for structural and treatment effect models | 0.511 | 2 | 1 | 100% |
| 10 | Koenker, R. and G. Bassett, Jr (1978) Regression quantiles | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 44 scored citations. 1 of these could not be matched to a bibliography entry, so only the citation key is shown.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Smoothed instrumental variables quantile regression | 0.644 | 2 | 2 |
| 2 | Confidence intervals for intentionally biased estimators | 0.405 | 1 | 1 |