Hostname: page-component-8448b6f56d-wq2xx Total loading time: 0 Render date: 2024-04-24T16:30:45.469Z Has data issue: false hasContentIssue false
  • English
  • Français

INSTRUMENTAL VARIABLE QUANTILE REGRESSION WITH MISCLASSIFICATION

Published online by Cambridge University Press:  13 March 2020

Takuya Ura
Takuya Ura*
Affiliation:
University of California, Davis
*
Address correspondence to Takuya Ura, Department of Economics, University of California, Davis, One Shields Avenue, Davis, CA 95616-5270, USA; e-mail: takura@ucdavis.edu.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This article investigates the instrumental variable quantile regression model (Chernozhukov and Hansen, 2005, Econometrica 73, 245–261; 2013, Annual Review of Economics, 5, 57–81) with a binary endogenous treatment. It offers two identification results when the treatment status is not directly observed. The first result is that, remarkably, the reduced-form quantile regression of the outcome variable on the instrumental variable provides a lower bound on the structural quantile treatment effect under the stochastic monotonicity condition. This result is relevant, not only when the treatment variable is subject to misclassification, but also when any measurement of the treatment variable is not available. The second result is for the structural quantile function when the treatment status is measured with error; the sharp identified set is characterized by a set of moment conditions under widely used assumptions on the measurement error. Furthermore, an inference method is provided in the presence of other covariates.

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 1 , February 2021 , pp. 169 - 204
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© Cambridge University Press 2020

Footnotes

First version: October, 2016. I am grateful to Peter C.B. Phillips, Arthur Lewbel, and four anonymous referees for comments and suggestions that have significantly improved this article. I would like to thank Alexandre Belloni, Stéphane Bonhomme, Federico A. Bugni, A. Colin Cameron, V. Joseph Hotz, Shakeeb Khan, Jia Li, Matthew A. Masten, Arnaud Maurel, Adam M. Rosen, and seminar participants at Duke, UC Berkeley, Shanghai University of Finance and Economics, Hakodate Conference in Econometrics, IAAE Annual Conference, Econometric Society North American Summer Meeting, and Econometric Society Asian Meeting for very helpful comments. The usual disclaimer applies.

References

REFERENCES

Abadie, A., Angrist, J., & Imbens, G. (2002) Instrumental variables estimates of the effect of subsidized training on the quantiles of trainee earnings. Econometrica 70, 91–117.CrossRefGoogle Scholar
Angrist, J.D., Imbens, G.W., & Rubin, D.B. (1996) Identification of causal effects using instrumental variables. Journal of the American Statistical Association 91, 444–455.CrossRefGoogle Scholar
Benjamin, D.J. (2003) Does 401(k) eligibility increase saving? Evidence from propensity score subclassification. Journal of Public Economics 87, 1259–1290.CrossRefGoogle Scholar
Bitler, M.P., Hoynes, H.W., & Domina, T. (2016) Experimental Evidence on Distributional Effects of Head Start, Working paper.Google Scholar
Bound, J., Brown, C., & Mathiowetz, N. (2001) Measurement error in survey data. In Heckman, J. and Leamerin, E. (eds.) Handbook of Econometrics, vol. 5, chap. 59, pp. 3705–3843. Elsevier.CrossRefGoogle Scholar
Buchinsky, M. & Hahn, J. (1998) An alternative estimator for the censored quantile regression model. Econometrica 66, 653.CrossRefGoogle Scholar
Calvi, R., Lewbel, A., & Tommasi, D. (2017) LATE with Mismeasured or Misspecified Treatment: An Application To Women’s Empowerment in India, Working paper.CrossRefGoogle Scholar
Chernozhukov, V. & Hansen, C. (2004) The effects of 401(K) participation on the wealth distribution: An instrumental quantile regression analysis. Review of Economics and Statistics 86, 735–751.CrossRefGoogle Scholar
Chernozhukov, V. & Hansen, C. (2005) An IV model of quantile treatment effects. Econometrica 73, 245–261.CrossRefGoogle Scholar
Chernozhukov, V. & Hansen, C. (2008) Instrumental variable quantile regression: A robust inference approach. Journal of Econometrics 142, 379–398.CrossRefGoogle Scholar
Chernozhukov, V. & Hansen, C. (2013) Quantile models with endogeneity. Annual Review of Economics 5, 57–81.CrossRefGoogle Scholar
Chesher, A. (1991) The effect of measurement error. Biometrika 78, 451–462.CrossRefGoogle Scholar
Chesher, A. (2003) Identification in nonseparable models. Econometrica 71, 1405–1441.CrossRefGoogle Scholar
Chesher, A. (2017) Understanding the effect of measurement error on quantile regressions. Journal of Econometrics 200, 223–237.CrossRefGoogle Scholar
DiNardo, J. & Lee, D.S. (2011) Program evaluation and research designs. In Ashenfelter, O. and Card, D. (eds.) Handbook of Labor Economics, vol. 4, part A, chap. 5, pp. 463–536, Elsevier.CrossRefGoogle Scholar
DiTraglia, F.J. & García-Jimeno, C. (2019) On mis-measured binary regressors: New results and some comments on the literature. Journal of Econometrics 209, 376–390.CrossRefGoogle Scholar
Doksum, K. (1974) Empirical probability plots and statistical inference for nonlinear models in the two-sample case. Annals of Statistics 2, 267–277.CrossRefGoogle Scholar
Dong, Y. & Shen, S. (2018) Testing for rank invariance or similarity in program Evaluation. Review of Economics and Statistics 100, 78–85.CrossRefGoogle Scholar
Firpo, S., Galvao, A.F., & Song, S. (2017) Measurement Errors in Quantile Regression Models. Journal of Econometrics 198, 146–164.CrossRefGoogle Scholar
Frandsen, B.R. & Lefgren, L.J. (2018) Testing rank similarity. Review of Economics and Statistics 100, 86–91.CrossRefGoogle Scholar
Frazis, H. & Loewenstein, M.A. (2003) Estimating linear regressions with mismeasured, possibly endogenous, binary explanatory variables. Journal of Econometrics 117, 151–178.CrossRefGoogle Scholar
Galvao, A.F. & Montes-Rojas, G. (2009) Instrumental Variables Quantile Regression for Panel Data with Measurement Errors, Working paper.Google Scholar
Gustman, A.L., Steinmeier, T., & Tabatabai, N. (2008) Do workers know about their pension plan type? Comparing workers’ and employers’ pension information. In Lusardi, A. (ed.) Overcoming the Saving Slump; How to Increase the Effectiveness of Financial Education and Saving Programs. University of Chicago Press, Chicago, IL, pp. 47–81.Google Scholar
Hausman, J.A., Abrevaya, J., & Scott-Morton, F.M. (1998) Misclassification of the dependent variable in a discrete-response setting. Journal of Econometrics 87, 239–269.CrossRefGoogle Scholar
Heckman, J.J., Smith, J., & Clements, N. (1997) Making the most out of programme evaluations and social experiments: Accounting for heterogeneity in programme impacts. The Review of Economic Studies 64, 487–535.CrossRefGoogle Scholar
Henry, M., Kitamura, Y., & Salanié, B. (2014) Partial identification of finite mixtures in econometric models. Quantitative Economics 5, 123–144.CrossRefGoogle Scholar
Hu, Y. (2008) Identification and estimation of nonlinear models with misclassification error using instrumental variables: A general solution. Journal of Econometrics 144, 27–61.CrossRefGoogle Scholar
Imbens, G.W. & Angrist, J.D. (1994) Identification and estimation of local average treatment effects. Econometrica 62, 467–75.CrossRefGoogle Scholar
Kim, J.H. & Park, B. (2018) Testing Rank Similarity in the Local Average Treatment Effect Model, Working paper.Google Scholar
Lewbel, A. (2007) Estimation of average treatment effects with misclassification. Econometrica 75, 537–551.CrossRefGoogle Scholar
Mahajan, A. (2006) Identification and estimation of regression models with misclassification. Econometrica 74, 631–665.CrossRefGoogle Scholar
Newey, W.K. & McFadden, D. (1994) Large sample estimation and hypothesis testing. In Engle, R. F. and McFadden, D. L. (eds.) Handbook of Econometrics, vol. 4, chap. 36, pp. 2111–2245. Elsevier.Google Scholar
Nguimkeu, P., Denteh, A., & Tchernis, R. (2019) On the estimation of treatment effects with endogenous misreporting. Journal of Econometrics 208, 487–506.CrossRefGoogle Scholar
Pollard, D. (1991) Asymptotics for least absolute deviation regression estimators. Econometric Theory 7, 186–199.CrossRefGoogle Scholar
Schennach, S.M. (2008) Quantile regression with mismeasured covariates. Econometric Theory 24, 1010–1043.CrossRefGoogle Scholar
Small, D.S. & Tan, Z. (2007) A Stochastic Monotonicity Assumption for the Instrumental Variables Method, Working paper.Google Scholar
Song, S. (2018) Nonseparable Triangular Models with Errors in Endogenous Variables, Working paper.Google Scholar
Ura, T. (2018) Heterogeneous treatment effects with mismeasured endogenous treatment. Quantitative Economics 9, 1335–1370.CrossRefGoogle Scholar
Wei, Y. & Carroll, R.J. (2009) Quantile regression with measurement error. Journal of the American Statistical Association 104, 1129–1143.CrossRefGoogle ScholarPubMed
Wüthrich, K. (2019) A comparison of two quantile models with endogeneity. Journal of Business and Economic Statistics, forthcoming, https://doi.org/10.1080/07350015.2018.1514307.CrossRefGoogle Scholar
Yanagi, T. (2019) Inference on local average treatment effects for misclassified treatment. Econometric Reviews 38, 938–959.CrossRefGoogle Scholar
Yu, P. (2017) Testing Conditional Rank Similarity With and Without Covariates, Working paper.Google Scholar
Supplementary material: PDF

Ura supplementary material

Ura supplementary material

Download Ura supplementary material(PDF)
PDF 106.2 KB