arXiv 25 Dec 2020 · Econometrics
arXiv:2012.13614 · PDF · DOI · OpenAlex · Extracted main text
We study linear quantile regression models when regressors and/or dependent variable are not directly observed but estimated in an initial first step and used in the second step quantile regression for estimating the quantile parameters. This general class of generated quantile regression (GQR) covers various statistical applications, for instance, estimation of endogenous quantile regression models and triangular structural equation models, and some new relevant applications are discussed. We study the asymptotic distribution of the two-step estimator, which is challenging because of the presence of generated covariates and/or dependent variable in the non-smooth quantile regression estimator. We employ techniques from empirical process theory to find uniform Bahadur expansion for the two step estimator, which is used to establish the asymptotic results. We illustrate the performance of the GQR estimator through simulations and an empirical application based on auctions.
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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 | Zou, H. & Yuan, M (2008) Composite quantile regression and the oracle model selection theory | 1.000 | 5 | 3 | 100% |
| 2 | Koenker, R (2005) Quantile Regression | 0.874 | 5 | 2 | 100% |
| 3 | Gimenes, N. & Guerre, E (2020) Quantile regression methods for first-price auctions | 0.843 | 3 | 3 | 100% |
| 4 | Koenker, R. & Bassett, G (1978) Regression quantiles | 0.843 | 3 | 3 | 100% |
| 5 | Buchinsky, M (1995) Quantile regression, Box–Cox transformation model, and the US wage structure, 1963–1987 | 0.811 | 4 | 2 | 100% |
| 6 | Amemiya, T (1974) The nonlinear two-stage least-squares estimator | 0.644 | 2 | 2 | 100% |
| 7 | Chen, X., Linton, O., & Van Keilegom, I (2003) Estimation of semiparametric models when the criterion function is not smooth | 0.644 | 2 | 2 | 100% |
| 8 | Newey, W. K. & McFadden, D (1994) Large sample estimation and hypothesis testing | 0.644 | 2 | 2 | 100% |
| 9 | Massart, P (2007) Concentration inequalities and model selection, volume 6 | 0.585 | 3 | 3 | 33% |
| 10 | Buchinsky, M (1994) Changes in the US wage structure 1963-1987: Application of quantile regression | 0.585 | 3 | 1 | 100% |
Showing the top 10 of 55 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Estimating Conditional Value-at-Risk with Nonstationary Quantile Predictive Regression Models | 0.606 | 9 | 3 |
| 2 | Quantile Time Series Regression Models Revisited | 0.405 | 1 | 1 |