Quantile regression with censoring and endogeneity
In this paper we develop a new censored quantile instrumental variable (CQIV) estimator and describe its properties and computation. The CQIV estimator combines Powell (1986) censored quantile regression (CQR) to deal with censoring, with a control variable approach to incorporate endogenous regress...
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| Format: | Article |
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Elsevier BV
2018
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| Online Access: | http://hdl.handle.net/1721.1/114834 https://orcid.org/0000-0002-3250-6714 |
| _version_ | 1826217933708197888 |
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| author | Fernández-Val, Iván Kowalski, Amanda E. Chernozhukov, Victor V |
| author2 | Massachusetts Institute of Technology. Department of Economics |
| author_facet | Massachusetts Institute of Technology. Department of Economics Fernández-Val, Iván Kowalski, Amanda E. Chernozhukov, Victor V |
| author_sort | Fernández-Val, Iván |
| collection | MIT |
| description | In this paper we develop a new censored quantile instrumental variable (CQIV) estimator and describe its properties and computation. The CQIV estimator combines Powell (1986) censored quantile regression (CQR) to deal with censoring, with a control variable approach to incorporate endogenous regressors. The CQIV estimator is obtained in two stages that are nonadditive in the unobservables. The first stage estimates a nonadditive model with infinite dimensional parameters for the control variable, such as a quantile or distribution regression model. The second stage estimates a nonadditive censored quantile regression model for the response variable of interest, including the estimated control variable to deal with endogeneity. For computation, we extend the algorithm for CQR developed by Chernozhukov and Hong (2002) to incorporate the estimation of the control variable. We give generic regularity conditions for asymptotic normality of the CQIV estimator and for the validity of resampling methods to approximate its asymptotic distribution. We verify these conditions for quantile and distribution regression estimation of the control variable. Our analysis covers two-stage (uncensored) quantile regression with nonadditive first stage as an important special case. We illustrate the computation and applicability of the CQIV estimator with a Monte-Carlo numerical example and an empirical application on estimation of Engel curves for alcohol. |
| first_indexed | 2024-09-23T17:11:02Z |
| format | Article |
| id | mit-1721.1/114834 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T17:11:02Z |
| publishDate | 2018 |
| publisher | Elsevier BV |
| record_format | dspace |
| spelling | mit-1721.1/1148342022-09-30T00:18:20Z Quantile regression with censoring and endogeneity Fernández-Val, Iván Kowalski, Amanda E. Chernozhukov, Victor V Massachusetts Institute of Technology. Department of Economics Chernozhukov, Victor V In this paper we develop a new censored quantile instrumental variable (CQIV) estimator and describe its properties and computation. The CQIV estimator combines Powell (1986) censored quantile regression (CQR) to deal with censoring, with a control variable approach to incorporate endogenous regressors. The CQIV estimator is obtained in two stages that are nonadditive in the unobservables. The first stage estimates a nonadditive model with infinite dimensional parameters for the control variable, such as a quantile or distribution regression model. The second stage estimates a nonadditive censored quantile regression model for the response variable of interest, including the estimated control variable to deal with endogeneity. For computation, we extend the algorithm for CQR developed by Chernozhukov and Hong (2002) to incorporate the estimation of the control variable. We give generic regularity conditions for asymptotic normality of the CQIV estimator and for the validity of resampling methods to approximate its asymptotic distribution. We verify these conditions for quantile and distribution regression estimation of the control variable. Our analysis covers two-stage (uncensored) quantile regression with nonadditive first stage as an important special case. We illustrate the computation and applicability of the CQIV estimator with a Monte-Carlo numerical example and an empirical application on estimation of Engel curves for alcohol. 2018-04-20T20:30:41Z 2018-04-20T20:30:41Z 2014-07 2014-03 2018-04-19T19:09:13Z Article http://purl.org/eprint/type/JournalArticle 0304-4076 http://hdl.handle.net/1721.1/114834 Chernozhukov, Victor, et al. “Quantile Regression with Censoring and Endogeneity.” Journal of Econometrics 186, 1 (May 2015): 201–221 © 2014 Elsevier B.V. https://orcid.org/0000-0002-3250-6714 http://dx.doi.org/10.1016/J.JECONOM.2014.06.017 Journal of Econometrics Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier BV arXiv |
| spellingShingle | Fernández-Val, Iván Kowalski, Amanda E. Chernozhukov, Victor V Quantile regression with censoring and endogeneity |
| title | Quantile regression with censoring and endogeneity |
| title_full | Quantile regression with censoring and endogeneity |
| title_fullStr | Quantile regression with censoring and endogeneity |
| title_full_unstemmed | Quantile regression with censoring and endogeneity |
| title_short | Quantile regression with censoring and endogeneity |
| title_sort | quantile regression with censoring and endogeneity |
| url | http://hdl.handle.net/1721.1/114834 https://orcid.org/0000-0002-3250-6714 |
| work_keys_str_mv | AT fernandezvalivan quantileregressionwithcensoringandendogeneity AT kowalskiamandae quantileregressionwithcensoringandendogeneity AT chernozhukovvictorv quantileregressionwithcensoringandendogeneity |