arXiv 28 Sep 2016 · Statistics — Methodology · 1 citations (OpenAlex)
arXiv:1609.09033 · PDF · DOI · OpenAlex · Extracted main text
The moment conditions or estimating equations for instrumental variables quantile regression involve the discontinuous indicator function. We instead use smoothed estimating equations (SEE), with bandwidth $h$. We show that the mean squared error (MSE) of the vector of the SEE is minimized for some $h>0$, leading to smaller asymptotic MSE of the estimating equations and associated parameter estimators. The same MSE-optimal $h$ also minimizes the higher-order type I error of a SEE-based $χ^2$ test and increases size-adjusted power in large samples. Computation of the SEE estimator also becomes simpler and more reliable, especially with (more) endogenous regressors. Monte Carlo simulations demonstrate all of these superior properties in finite samples, and we apply our estimator to JTPA data. Smoothing the estimating equations is not just a technical operation for establishing Edgeworth expansions and bootstrap refinements; it also brings the real benefits of having more precise estimators and more powerful tests. Code for the estimator, simulations, and empirical examples is available from the first author's website.
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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. & C. B. Hansen (2006) Instrumental quantile regress… Journal of Econometrics\/ 132, 491–525 | 1.000 | 11 | 5 | 100% |
| 2 | Horowitz, J. L. (1998) Bootstrap methods for median regression models Econometrica\/ 66, 1327–1351 | 0.977 | 15 | 6 | 93% |
| 3 | Whang, Y.-J. (2006) Smoothed empirical likelihood methods for quanti… Econometric Theory\/ 22, 173–205 | 0.956 | 8 | 6 | 88% |
| 4 | Chen, X. & D. Pouzo (2009) Efficient estimation of semiparametric co… Journal of Econometrics\/ 152, 46–60 | 0.843 | 3 | 3 | 100% |
| 5 | Chen, X. & D. Pouzo (2012) Estimation of nonparametric conditional m… Econometrica\/ 80, 277–322 | 0.843 | 3 | 3 | 100% |
| 6 | Abadie, A., J. Angrist, & G. Imbens (2002) Instrumental variables es… Econometrica\/ 70, 91–117 | 0.811 | 4 | 2 | 100% |
| 7 | Huber, P. J. (1964) Robust estimation of a location parameter The Annals of Mathematical Statistics\/ 35, 73–101 | 0.737 | 3 | 2 | 100% |
| Chernozhukov and Hansen | unmatched citation key Chernozhukov and Hansen | 0.644 | 4 | 1 | 100% |
| 9 | Chernozhukov, V., C. Hansen, & M. Jansson (2009) Finite sample infer… Journal of Econometrics\/ 152, 93–103 | 0.644 | 2 | 2 | 100% |
| Horowitz | unmatched citation key Horowitz | 0.585 | 3 | 1 | 100% |
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