arXiv 20 May 2026 · Econometrics
arXiv:2605.20601 · PDF · DOI · OpenAlex · Extracted main text
This paper studies quantile regression with an endogenous regressor and measurement error in the dependent variable. Standard quantile regression estimators ignoring these two elements can induce substantial bias. We adopt a control-function approach in a triangular system and show that the conditional quantile coefficient functions, together with all other distributional parameters, are nonparametrically identifiable. Building on this constructive identification result, we propose a two-step sieve ML estimator. The first step estimates the control function. The second step performs a sieve likelihood maximization that incorporates the generated control variable through copula weights. When the number of quantile grid knots grows at an appropriate speed, the estimator is consistent and asymptotically normal, permitting inference via bootstrap. Monte Carlo simulations demonstrate that the estimator markedly reduces bias relative to existing methods, confirming its effectiveness in settings with endogeneity and additive measurement error in the outcome.
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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 | Imbens, G. W. and W. K. Newey (2009) Identification and estimation of triangular simultaneous equations models without additivity | 0.923 | 14 | 5 | 79% |
| 2 | Hausman, J., H. Liu, Y. Luo, and C. Palmer (2021) Errors in the dependent variable of quantile regression models | 0.879 | 28 | 6 | 68% |
| 3 | Lee, S (2007) Endogeneity in quantile regression models: A control function approach | 0.693 | 8 | 2 | 50% |
| 4 | Blundell, R., X. Chen, and D. Kristensen (2007) Semi-nonparametric iv estimation of shape-invariant engel curves | 0.644 | 2 | 2 | 100% |
| 5 | Chernozhukov, V. and C. Hansen (2005) An iv model of quantile treatment effects | 0.644 | 2 | 2 | 100% |
| 6 | Callaway, B., T. Li, and I. Murtazashvili (2021) Distributional effects with two-sided measurement error: An application to intergenerational income mobility | 0.511 | 2 | 1 | 100% |
| 7 | Doty, J. and S. Song (2023) Nonparametric identification and estimation of quantile production functions | 0.405 | 1 | 1 | 100% |
| 8 | Song, S (2026) Identification and estimation of nonseparable triangular models with measurement error | 0.405 | 1 | 1 | 100% |
| 9 | Abrevaya, J. and J. A. Hausman (1999) Semiparametric estimation with mismeasured dependent variables: an application to duration models for unemployment spells | 0.405 | 1 | 1 | 100% |
| 10 | Blundell, R. and J. L. Powell (2007) Censored regression quantiles with endogenous regressors | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 43 scored citations.