IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v188y2015i2p421-434.html
   My bibliography  Save this article

Binary response correlated random coefficient panel data models

Author

Listed:
  • Gao, Yichen
  • Li, Cong
  • Liang, Zhongwen

Abstract

In this paper, we consider binary response correlated random coefficient (CRC) panel data models which are frequently used in the analysis of treatment effects and demand of products. We focus on the nonparametric identification and estimation of panel data models under unobserved heterogeneity which is captured by random coefficients and when these random coefficients are correlated with regressors. Our identification conditions and estimation are based on the framework of the model with a special regressor, which is a novel approach proposed by Lewbel (1998, 2000) to solve the heterogeneity and endogeneity problem in the binary response models. With the help of the additional information on the special regressor, we can transform a binary response CRC model to a linear moment relation. We also construct a semiparametric estimator for the average slopes and derive the n-normality result. Further, we propose a nonparametric method to test the correlations between random coefficients and regressors. Simulations are given to show the finite sample performance of our estimators and test statistics.

Suggested Citation

  • Gao, Yichen & Li, Cong & Liang, Zhongwen, 2015. "Binary response correlated random coefficient panel data models," Journal of Econometrics, Elsevier, vol. 188(2), pages 421-434.
    • Handle: RePEc:eee:econom:v:188:y:2015:i:2:p:421-434
    DOI: 10.1016/j.jeconom.2015.03.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407615000779
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2015.03.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Khan, Shakeeb & Lewbel, Arthur, 2007. "Weighted And Two-Stage Least Squares Estimation Of Semiparametric Truncated Regression Models," Econometric Theory, Cambridge University Press, vol. 23(2), pages 309-347, April.
    2. Hoderlein, Stefan & Klemelä, Jussi & Mammen, Enno, 2010. "Analyzing The Random Coefficient Model Nonparametrically," Econometric Theory, Cambridge University Press, vol. 26(3), pages 804-837, June.
    3. Hahn, Jinyong, 2001. "Comment: Binary Regressors in Nonlinear Panel-Data Models with Fixed Effects," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 16-17, January.
    4. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
    5. Heckman, James J. & Schmierer, Daniel & Urzua, Sergio, 2010. "Testing the correlated random coefficient model," Journal of Econometrics, Elsevier, vol. 158(2), pages 177-203, October.
    6. Fox, Jeremy T. & Kim, Kyoo il & Ryan, Stephen P. & Bajari, Patrick, 2012. "The random coefficients logit model is identified," Journal of Econometrics, Elsevier, vol. 166(2), pages 204-212.
    7. Bo E. Honore & Arthur Lewbel, 2002. "Semiparametric Binary Choice Panel Data Models Without Strictly Exogeneous Regressors," Econometrica, Econometric Society, vol. 70(5), pages 2053-2063, September.
    8. Jeremy T. Fox & Kyoo il Kim & Stephen P. Ryan & Patrick Bajari, 2011. "A simple estimator for the distribution of random coefficients," Quantitative Economics, Econometric Society, vol. 2(3), pages 381-418, November.
    9. Yingying Dong & Arthur Lewbel, 2015. "A Simple Estimator for Binary Choice Models with Endogenous Regressors," Econometric Reviews, Taylor & Francis Journals, vol. 34(1-2), pages 82-105, February.
    10. Andrews,Donald W. K. & Stock,James H. (ed.), 2005. "Identification and Inference for Econometric Models," Cambridge Books, Cambridge University Press, number 9780521844413, September.
    11. Hoderlein, Stefan & White, Halbert, 2012. "Nonparametric identification in nonseparable panel data models with generalized fixed effects," Journal of Econometrics, Elsevier, vol. 168(2), pages 300-314.
    12. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871532, September.
    13. Shakeeb Khan & Elie Tamer, 2010. "Irregular Identification, Support Conditions, and Inverse Weight Estimation," Econometrica, Econometric Society, vol. 78(6), pages 2021-2042, November.
    14. Angrist, Joshua D, 2001. "Estimations of Limited Dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 2-16, January.
    15. Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July.
    16. Manuel Arellano & Stéphane Bonhomme, 2012. "Identifying Distributional Characteristics in Random Coefficients Panel Data Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(3), pages 987-1020.
    17. Gayle, Wayne-Roy, 2013. "Identification and N-consistent estimation of a nonlinear panel data model with correlated unobserved effects," Journal of Econometrics, Elsevier, vol. 175(2), pages 71-83.
    18. Heckman, James J. & Schmierer, Daniel, 2010. "Tests of hypotheses arising in the correlated random coefficient model," Economic Modelling, Elsevier, vol. 27(6), pages 1355-1367, November.
    19. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692106, September.
    20. Jeffrey M. Wooldridge, 2005. "Fixed-Effects and Related Estimators for Correlated Random-Coefficient and Treatment-Effect Panel Data Models," The Review of Economics and Statistics, MIT Press, vol. 87(2), pages 385-390, May.
    21. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
    22. László Mátyás & Patrick Sevestre (ed.), 2008. "The Econometrics of Panel Data," Advanced Studies in Theoretical and Applied Econometrics, Springer, number 978-3-540-75892-1.
    23. Bryan S. Graham & James L. Powell, 2012. "Identification and Estimation of Average Partial Effects in “Irregular” Correlated Random Coefficient Panel Data Models," Econometrica, Econometric Society, vol. 80(5), pages 2105-2152, September.
    24. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291.
    25. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692090, September.
    26. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(3), pages 726-748, June.
    27. Li, Qi, et al, 2002. "Semiparametric Smooth Coefficient Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 412-422, July.
    28. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    29. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    30. V. Chernozhukov & Ivan Fernandez-Val, "undated". "Quantile and Average Effects in Nonseparable Panel Models," Boston University - Department of Economics - Working Papers Series wp2009-011, Boston University - Department of Economics.
    31. Stéphane Bonhomme, 2012. "Functional Differencing," Econometrica, Econometric Society, vol. 80(4), pages 1337-1385, July.
    32. Eric Gautier & Yuichi Kitamura, 2013. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Econometrica, Econometric Society, vol. 81(2), pages 581-607, March.
    33. Victor Chernozhukov & Iván Fernández‐Val & Jinyong Hahn & Whitney Newey, 2013. "Average and Quantile Effects in Nonseparable Panel Models," Econometrica, Econometric Society, vol. 81(2), pages 535-580, March.
    34. Gary Chamberlain, 2010. "Binary Response Models for Panel Data: Identification and Information," Econometrica, Econometric Society, vol. 78(1), pages 159-168, January.
    35. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    36. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871549, September.
    37. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    38. Angrist, Joshua D, 2001. "Estimations of Limited Dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 27-28, January.
    39. Elias Masry, 1996. "Multivariate Local Polynomial Regression For Time Series:Uniform Strong Consistency And Rates," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(6), pages 571-599, November.
    40. Martin Browning & Jesus Carro, 2006. "Heterogeneity and Microeconometrics Modelling," CAM Working Papers 2006-03, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xue, Sen & Yang, Thomas Tao & Zhou, Qiankun, 2018. "Binary choice model with interactive effects," Economic Modelling, Elsevier, vol. 70(C), pages 338-350.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Arthur Lewbel, 2012. "An Overview of the Special Regressor Method," Boston College Working Papers in Economics 810, Boston College Department of Economics.
    2. Matzkin, Rosa L., 2019. "Constructive identification in some nonseparable discrete choice models," Journal of Econometrics, Elsevier, vol. 211(1), pages 83-103.
    3. Arthur Lewbel, 2019. "The Identification Zoo: Meanings of Identification in Econometrics," Journal of Economic Literature, American Economic Association, vol. 57(4), pages 835-903, December.
    4. Botosaru, Irene & Muris, Chris & Pendakur, Krishna, 2023. "Identification of time-varying transformation models with fixed effects, with an application to unobserved heterogeneity in resource shares," Journal of Econometrics, Elsevier, vol. 232(2), pages 576-597.
    5. Yingying Dong & Arthur Lewbel, 2015. "A Simple Estimator for Binary Choice Models with Endogenous Regressors," Econometric Reviews, Taylor & Francis Journals, vol. 34(1-2), pages 82-105, February.
    6. Matzkin, Rosa L., 2012. "Identification in nonparametric limited dependent variable models with simultaneity and unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 166(1), pages 106-115.
    7. Irene Botosaru & Chris Muris, 2017. "Binarization for panel models with fixed effects," CeMMAP working papers 31/17, Institute for Fiscal Studies.
    8. Williams, Benjamin, 2020. "Nonparametric identification of discrete choice models with lagged dependent variables," Journal of Econometrics, Elsevier, vol. 215(1), pages 286-304.
    9. Irene Botosaru & Chris Muris & Krishna Pendakur, 2020. "Intertemporal Collective Household Models: Identification in Short Panels with Unobserved Heterogeneity in Resource Shares," Department of Economics Working Papers 2020-09, McMaster University.
    10. Arthur Lewbel & Krishna Pendakur, 2017. "Unobserved Preference Heterogeneity in Demand Using Generalized Random Coefficients," Journal of Political Economy, University of Chicago Press, vol. 125(4), pages 1100-1148.
    11. Khan, Shakeeb & Ponomareva, Maria & Tamer, Elie, 2016. "Identification of panel data models with endogenous censoring," Journal of Econometrics, Elsevier, vol. 194(1), pages 57-75.
    12. Fernández-Val, Iván, 2009. "Fixed effects estimation of structural parameters and marginal effects in panel probit models," Journal of Econometrics, Elsevier, vol. 150(1), pages 71-85, May.
    13. Hoderlein, Stefan & Sherman, Robert, 2015. "Identification and estimation in a correlated random coefficients binary response model," Journal of Econometrics, Elsevier, vol. 188(1), pages 135-149.
    14. Valentin Verdier, 2020. "Average treatment effects for stayers with correlated random coefficient models of panel data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(7), pages 917-939, November.
    15. Escanciano, Juan Carlos, 2023. "Irregular identification of structural models with nonparametric unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 234(1), pages 106-127.
    16. Sadikoglu, Serhan, 2019. "Essays in econometric theory," Other publications TiSEM 99d83644-f9dc-49e3-a4e1-5, Tilburg University, School of Economics and Management.
    17. Hoderlein, Stefan & White, Halbert, 2012. "Nonparametric identification in nonseparable panel data models with generalized fixed effects," Journal of Econometrics, Elsevier, vol. 168(2), pages 300-314.
    18. Santiago Pereda-Fernández, 2021. "Copula-Based Random Effects Models for Clustered Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 575-588, March.
    19. Geert Dhaene & Koen Jochmans, 2015. "Split-panel Jackknife Estimation of Fixed-effect Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(3), pages 991-1030.
    20. Centorrino, Samuele & Florens, Jean-Pierre, 2021. "Nonparametric Instrumental Variable Estimation of Binary Response Models with Continuous Endogenous Regressors," Econometrics and Statistics, Elsevier, vol. 17(C), pages 35-63.

    More about this item

    Keywords

    Random coefficient; Binary choice; Nonparametric; Panel data; Specification test;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:188:y:2015:i:2:p:421-434. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.