IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v190y2016i2p233-251.html
   My bibliography  Save this article

Varying coefficient panel data model in the presence of endogenous selectivity and fixed effects

Author

Listed:
  • Malikov, Emir
  • Kumbhakar, Subal C.
  • Sun, Yiguo

Abstract

This paper considers a flexible panel data sample selection model in which (i) the outcome equation is permitted to take a semiparametric, varying coefficient form to capture potential parameter heterogeneity in the relationship of interest, (ii) both the outcome and (parametric) selection equations contain unobserved fixed effects and (iii) selection is generalized to a polychotomous case. We propose a two-stage estimator. Given consistent parameter estimates from the selection equation obtained in the first stage, we estimate the semiparametric outcome equation using data for the observed individuals whose likelihood of being selected into the sample stays approximately the same over time. The selection bias term is then “asymptotically” removed from the equation along with fixed effects using kernel-based weights. The proposed estimator is consistent and asymptotically normal. We showcase our estimator by applying it to study production technologies of US retail credit unions from 2002 to 2006.

Suggested Citation

  • Malikov, Emir & Kumbhakar, Subal C. & Sun, Yiguo, 2016. "Varying coefficient panel data model in the presence of endogenous selectivity and fixed effects," Journal of Econometrics, Elsevier, vol. 190(2), pages 233-251.
  • Handle: RePEc:eee:econom:v:190:y:2016:i:2:p:233-251
    DOI: 10.1016/j.jeconom.2015.06.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407615001761
    Download Restriction: Full text for ScienceDirect subscribers only

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. Cai, Zongwu & Li, Qi, 2008. "Nonparametric Estimation Of Varying Coefficient Dynamic Panel Data Models," Econometric Theory, Cambridge University Press, vol. 24(05), pages 1321-1342, October.
    2. Zongwu Cai & Huaiyu Xiong, 2012. "Partially varying coefficient instrumental variables models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(2), pages 85-110, May.
    3. David C. Wheelock & Paul W. Wilson, 2011. "Are Credit Unions Too Small?," The Review of Economics and Statistics, MIT Press, vol. 93(4), pages 1343-1359, November.
    4. Hughes, Joseph P. & Mester, Loretta J., 2013. "Who said large banks don’t experience scale economies? Evidence from a risk-return-driven cost function," Journal of Financial Intermediation, Elsevier, vol. 22(4), pages 559-585.
    5. Bo Honore & Ekaterini Kyriazidou & J. L. Powell, 2000. "Estimation of tobit-type models with individual specific effects," Econometric Reviews, Taylor & Francis Journals, vol. 19(3), pages 341-366.
    6. Li, Qi, et al, 2002. "Semiparametric Smooth Coefficient Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 412-422, July.
    7. James A. Wilcox, 2006. "Performance divergence of large and small credit unions," FRBSF Economic Letter, Federal Reserve Bank of San Francisco, issue aug4.
    8. Fried, Harold O. & Lovell, C. A. Knox & Yaisawarng, Suthathip, 1999. "The impact of mergers on credit union service provision," Journal of Banking & Finance, Elsevier, vol. 23(2-4), pages 367-386, February.
    9. Jeremy T. Fox, 2007. "Semiparametric estimation of multinomial discrete-choice models using a subset of choices," RAND Journal of Economics, RAND Corporation, vol. 38(4), pages 1002-1019, December.
    10. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 3-29, July.
    11. Charlier, Erwin & Melenberg, Bertrand & van Soest, Arthur, 2001. "An analysis of housing expenditure using semiparametric models and panel data," Journal of Econometrics, Elsevier, vol. 101(1), pages 71-107, March.
    12. James A. Wilcox, 2005. "Economies of scale and continuing consolidation of credit unions," FRBSF Economic Letter, Federal Reserve Bank of San Francisco, issue nov4.
    13. Smith, Donald J, 1984. " A Theoretic Framework for the Analysis of Credit Union Decision Making," Journal of Finance, American Finance Association, vol. 39(4), pages 1155-1168, September.
    14. Henderson, Daniel J. & Ullah, Aman, 2005. "A nonparametric random effects estimator," Economics Letters, Elsevier, vol. 88(3), pages 403-407, September.
    15. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 31(3), pages 129-137.
    16. Scott Frame, W. & Karels, Gordon V. & McClatchey, Christine A., 2003. "Do credit unions use their tax advantage to benefit members? Evidence from a cost function," Review of Financial Economics, Elsevier, vol. 12(1), pages 35-47.
    17. Henderson, Daniel J. & Carroll, Raymond J. & Li, Qi, 2008. "Nonparametric estimation and testing of fixed effects panel data models," Journal of Econometrics, Elsevier, vol. 144(1), pages 257-275, May.
    18. Goddard, John & McKillop, Donal & Wilson, John O.S., 2008. "The diversification and financial performance of US credit unions," Journal of Banking & Finance, Elsevier, vol. 32(9), pages 1836-1849, September.
    19. Li, Qi, 1996. "On the root-N-consistent semiparametric estimation of partially linear models," Economics Letters, Elsevier, vol. 51(3), pages 277-285, June.
    20. Das, M., 2003. "Identification and sequential estimation of panel data models with insufficient exclusion restrictions," Journal of Econometrics, Elsevier, vol. 114(2), pages 297-328, June.
    21. Malikov, Emir & Kumbhakar, Subal C., 2014. "A generalized panel data switching regression model," Economics Letters, Elsevier, vol. 124(3), pages 353-357.
    22. Wooldridge, Jeffrey M., 1995. "Selection corrections for panel data models under conditional mean independence assumptions," Journal of Econometrics, Elsevier, vol. 68(1), pages 115-132, July.
    23. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-694, July.
    24. Cai, Zongwu, 2007. "Trending time-varying coefficient time series models with serially correlated errors," Journal of Econometrics, Elsevier, vol. 136(1), pages 163-188, January.
    25. Ekaterini Kyriazidou, 1997. "Estimation of a Panel Data Sample Selection Model," Econometrica, Econometric Society, vol. 65(6), pages 1335-1364, November.
    26. Goddard, John A. & McKillop, Donal G. & Wilson, John O. S., 2002. "The growth of US credit unions," Journal of Banking & Finance, Elsevier, vol. 26(12), pages 2327-2356.
    27. Das, M., 2005. "Instrumental variables estimators of nonparametric models with discrete endogenous regressors," Journal of Econometrics, Elsevier, vol. 124(2), pages 335-361, February.
    28. Li, Qi & Stengos, Thanasis, 1996. "Semiparametric estimation of partially linear panel data models," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 389-397.
    29. Bauer, Keldon J. & Miles, Linda L. & Nishikawa, Takeshi, 2009. "The effect of mergers on credit union performance," Journal of Banking & Finance, Elsevier, vol. 33(12), pages 2267-2274, December.
    30. Manski, Charles F, 1987. "Semiparametric Analysis of Random Effects Linear Models from Binary Panel Data," Econometrica, Econometric Society, vol. 55(2), pages 357-362, March.
    31. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    32. Malikov, Emir & Restrepo-Tobon, Diego A & Kumbhakar, Subal C., 2014. "Are All U.S. Credit Unions Alike? A Generalized Model of Heterogeneous Technologies with Endogenous Switching and Correlated Effects," MPRA Paper 55994, University Library of Munich, Germany.
    33. Christian Dustmann & María Engracia Rochina-Barrachina, 2007. "Selection correction in panel data models: An application to the estimation of females' wage equations," Econometrics Journal, Royal Economic Society, vol. 10(2), pages 263-293, July.
    34. Su, Liangjun & Ullah, Aman, 2006. "Profile likelihood estimation of partially linear panel data models with fixed effects," Economics Letters, Elsevier, vol. 92(1), pages 75-81, July.
    35. Wheelock, David C. & Wilson, Paul W., 2013. "The evolution of cost-productivity and efficiency among US credit unions," Journal of Banking & Finance, Elsevier, vol. 37(1), pages 75-88.
    36. Cai, Zongwu & Das, Mitali & Xiong, Huaiyu & Wu, Xizhi, 2006. "Functional coefficient instrumental variables models," Journal of Econometrics, Elsevier, vol. 133(1), pages 207-241, July.
    37. Mitali Das & Whitney K. Newey & Francis Vella, 2003. "Nonparametric Estimation of Sample Selection Models," Review of Economic Studies, Oxford University Press, vol. 70(1), pages 33-58.
    38. repec:adr:anecst:y:1999:i:55-56:p:06 is not listed on IDEAS
    39. Bauer, Keldon, 2008. "Detecting abnormal credit union performance," Journal of Banking & Finance, Elsevier, vol. 32(4), pages 573-586, April.
    40. Gary Chamberlain, 1980. "Analysis of Covariance with Qualitative Data," Review of Economic Studies, Oxford University Press, vol. 47(1), pages 225-238.
    41. Ekaterini Kyriazidou, 2001. "Estimation of Dynamic Panel Data Sample Selection Models," Review of Economic Studies, Oxford University Press, vol. 68(3), pages 543-572.
    42. Xihong Lin & Raymond J. Carroll, 2006. "Semiparametric estimation in general repeated measures problems," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 69-88.
    43. repec:adr:anecst:y:1999:i:55-56 is not listed on IDEAS
    44. Das, M., 2004. "Simple estimators for nonparametric panel data models with sample attrition," Journal of Econometrics, Elsevier, vol. 120(1), pages 159-180, May.
    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. Malikov, Emir & Hartarska, Valentina, 2018. "Endogenous scope economies in microfinance institutions," Journal of Banking & Finance, Elsevier, vol. 93(C), pages 162-182.
    2. repec:taf:emetrv:v:36:y:2017:i:6-9:p:988-1006 is not listed on IDEAS
    3. repec:taf:emetrv:v:37:y:2018:i:10:p:1095-1119 is not listed on IDEAS
    4. Chirok Han & Goeun Lee, 2017. "Efficient Estimation of Linear Panel Data Models with Sample Selection and Fixed Effects," Discussion Paper Series 1707, Institute of Economic Research, Korea University.
    5. Emir Malikov & Diego A. Restrepo-Tobón & Subal C. Kumbhakar, 2018. "Heterogeneous credit union production technologies with endogenous switching and correlated effects," Econometric Reviews, Taylor & Francis Journals, vol. 37(10), pages 1095-1119, November.
    6. Sun, Yiguo & Malikov, Emir, 2018. "Estimation and inference in functional-coefficient spatial autoregressive panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 203(2), pages 359-378.

    More about this item

    Keywords

    Credit union; Fixed effects; Selection; Semiparametric; Smooth coefficient; Switching regression; Varying coefficient;

    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
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages

    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:190:y:2016:i:2:p:233-251. See general information about how to correct material in RePEc.

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

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.