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Penalized Quantile Regression with Semiparametric Correlated Effects: Applications with Heterogeneous Preferences

Author

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  • Harding, Matthew

    () (Stanford University)

  • Lamarche, Carlos

    () (University of Kentucky)

Abstract

This paper proposes new ?1-penalized quantile regression estimators for panel data, which explicitly allows for individual heterogeneity associated with covariates. We conduct Monte Carlo simulations to assess the small sample performance of the new estimators and provide comparisons of new and existing penalized estimators in terms of quadratic loss. We apply the techniques to two empirical studies. First, the new method is applied to the estimation of labor supply elasticities and we find evidence that positive substitution effects dominate negative wealth effects at the middle of the conditional distribution of hours. The overall effect tends to be larger at the lower tail, which suggests that changes in taxes have different effects across the response distribution. Second, we estimate consumer preferences for nutrients from a demand model using a large scanner dataset of household food purchases. We show that preferences for nutrients vary across the conditional distribution of expenditure and across genders, and emphasize the importance of fully capturing consumer heterogeneity in demand modeling. Both applications highlight the importance of estimating individual heterogeneity when designing economic policy.

Suggested Citation

  • Harding, Matthew & Lamarche, Carlos, 2013. "Penalized Quantile Regression with Semiparametric Correlated Effects: Applications with Heterogeneous Preferences," IZA Discussion Papers 7741, Institute of Labor Economics (IZA).
  • Handle: RePEc:iza:izadps:dp7741
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    References listed on IDEAS

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    1. Kato, Kengo & F. Galvao, Antonio & Montes-Rojas, Gabriel V., 2012. "Asymptotics for panel quantile regression models with individual effects," Journal of Econometrics, Elsevier, vol. 170(1), pages 76-91.
    2. Burtless, Gary & Hausman, Jerry A, 1978. "The Effect of Taxation on Labor Supply: Evaluating the Gary Negative Income Tax Experiments," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 1103-1130, December.
    3. He, Xuming & Shi, Peide, 1996. "Bivariate Tensor-Product B-Splines in a Partly Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 58(2), pages 162-181, August.
    4. repec:wly:japmet:v:1:y:1986:i:1:p:55-80 is not listed on IDEAS
    5. Harding, Matthew & Lamarche, Carlos, 2009. "A quantile regression approach for estimating panel data models using instrumental variables," Economics Letters, Elsevier, vol. 104(3), pages 133-135, September.
    6. van Soest, Arthur & Das, Marcel & Gong, Xiaodong, 2002. "A structural labour supply model with flexible preferences," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 345-374, March.
    7. MaCurdy, Thomas E, 1981. "An Empirical Model of Labor Supply in a Life-Cycle Setting," Journal of Political Economy, University of Chicago Press, vol. 89(6), pages 1059-1085, December.
    8. Anil Kumar, 2012. "Nonparametric estimation of the impact of taxes on female labor supply," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(3), pages 415-439, April.
    9. Ivan A. Canay, 2011. "A simple approach to quantile regression for panel data," Econometrics Journal, Royal Economic Society, vol. 14(3), pages 368-386, October.
    10. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    11. Yanlin Tang & Huixia Wang & Xuming He & Zhongyi Zhu, 2012. "An informative subset-based estimator for censored quantile regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 635-655, December.
    12. Richard Blundell & Costas Meghir, 1986. "Selection criteria for a microeconometric model of labour supply," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 1(1), pages 55-80, January.
    13. Rosen, Adam M., 2012. "Set identification via quantile restrictions in short panels," Journal of Econometrics, Elsevier, vol. 166(1), pages 127-137.
    14. Muellbauer, John, 1974. "Household Production Theory, Quality, and the "Hedonic Technique."," American Economic Review, American Economic Association, vol. 64(6), pages 977-994, December.
    15. Antonio F. Galvao & Carlos Lamarche & Luiz Renato Lima, 2013. "Estimation of Censored Quantile Regression for Panel Data With Fixed Effects," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 1075-1089, September.
    16. Graham, Bryan S. & Hahn, Jinyong & Powell, James L., 2009. "The incidental parameter problem in a non-differentiable panel data model," Economics Letters, Elsevier, vol. 105(2), pages 181-182, November.
    17. Chamberlain, Gary, 1982. "Multivariate regression models for panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 5-46, January.
    18. Lamarche, Carlos, 2010. "Robust penalized quantile regression estimation for panel data," Journal of Econometrics, Elsevier, vol. 157(2), pages 396-408, August.
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    Cited by:

    1. repec:eee:econom:v:211:y:2019:i:1:p:61-82 is not listed on IDEAS
    2. Hartley, Robert Paul & Lamarche, Carlos, 2018. "Behavioral responses and welfare reform: Evidence from a randomized experiment," Labour Economics, Elsevier, vol. 54(C), pages 135-151.
    3. Harding, Matthew & Lamarche, Carlos, 2019. "A panel quantile approach to attrition bias in Big Data: Evidence from a randomized experiment," Journal of Econometrics, Elsevier, vol. 211(1), pages 61-82.
    4. Jiaying Gu & Stanislav Volgushev, 2018. "Panel Data Quantile Regression with Grouped Fixed Effects," Papers 1801.05041, arXiv.org, revised Aug 2018.

    More about this item

    Keywords

    labor supply; quantile regression; panel data; shrinkage; scanner data;

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • J22 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Time Allocation and Labor Supply

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