IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v163y2011i2p144-162.html
   My bibliography  Save this article

Bias corrections for two-step fixed effects panel data estimators

Author

Listed:
  • Fernández-Val, Iván
  • Vella, Francis

Abstract

This paper introduces large-T bias-corrected estimators for nonlinear panel data models with both time invariant and time varying heterogeneity. These models include systems of equations with limited dependent variables and unobserved individual effects, and sample selection models with unobserved individual effects. Our two-step approach first estimates the reduced form by fixed effects procedures to obtain estimates of the time varying heterogeneity underlying the endogeneity/selection bias. We then estimate the primary equation by fixed effects including an appropriately constructed control variable from the reduced form estimates as an additional explanatory variable. The fixed effects approach in this second step captures the time invariant heterogeneity while the control variable accounts for the time varying heterogeneity. Since either or both steps might employ nonlinear fixed effects procedures it is necessary to bias adjust the estimates due to the incidental parameters problem. This problem is exacerbated by the two-step nature of the procedure. As these two-step approaches are not covered in the existing literature we derive the appropriate correction thereby extending the use of large-T bias adjustments to an important class of models. Simulation evidence indicates our approach works well in finite samples and an empirical example illustrates the applicability of our estimator.

Suggested Citation

  • Fernández-Val, Iván & Vella, Francis, 2011. "Bias corrections for two-step fixed effects panel data estimators," Journal of Econometrics, Elsevier, vol. 163(2), pages 144-162, August.
  • Handle: RePEc:eee:econom:v:163:y:2011:i:2:p:144-162
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407611000649
    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. Gayle, George-Levi & Viauroux, Christelle, 2007. "Root-N consistent semiparametric estimators of a dynamic panel-sample-selection model," Journal of Econometrics, Elsevier, vol. 141(1), pages 179-212, November.
    2. Porter,Jack, 2002. "Efficiency of Covariance Matrix Estimators for Maximum Likelihood Estimation," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 431-440, July.
    3. Rilstone, Paul & Srivastava, V. K. & Ullah, Aman, 1996. "The second-order bias and mean squared error of nonlinear estimators," Journal of Econometrics, Elsevier, vol. 75(2), pages 369-395, December.
    4. Luojia Hu, 2002. "Estimation of a Censored Dynamic Panel Data Model," Econometrica, Econometric Society, vol. 70(6), pages 2499-2517, November.
    5. Manuel Arellano, 2003. "Discrete choices with panel data," Investigaciones Economicas, Fundación SEPI, vol. 27(3), pages 423-458, September.
    6. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters,in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492 National Bureau of Economic Research, Inc.
    7. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    8. Geert Dhaene & Koen Jochmans, 2015. "Split-panel Jackknife Estimation of Fixed-effect Models," Review of Economic Studies, Oxford University Press, vol. 82(3), pages 991-1030.
    9. Peter C. B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Econometrica, Econometric Society, vol. 67(5), pages 1057-1112, September.
    10. 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.
    11. Lee, Lung-fei & Maddala, G S & Trost, R P, 1980. "Asymptotic Covariance Matrices of Two-Stage Probit and Two-Stage Tobit Methods for Simultaneous Equations Models with Selectivity," Econometrica, Econometric Society, vol. 48(2), pages 491-503, March.
    12. Wooldridge, Jeffrey M., 2000. "A framework for estimating dynamic, unobserved effects panel data models with possible feedback to future explanatory variables," Economics Letters, Elsevier, vol. 68(3), pages 245-250, September.
    13. Angrist, Joshua D & Evans, William N, 1998. "Children and Their Parents' Labor Supply: Evidence from Exogenous Variation in Family Size," American Economic Review, American Economic Association, vol. 88(3), pages 450-477, June.
    14. Verbeek, Marno & Nijman, Theo, 1992. "Testing for Selectivity Bias in Panel Data Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(3), pages 681-703, August.
    15. Card, David & Sullivan, Daniel G, 1988. "Measuring the Effect of Subsidized Training Programs on Movements in and out of Employment," Econometrica, Econometric Society, vol. 56(3), pages 497-530, May.
    16. Gourieroux, Christian & Monfort, Alain & Renault, Eric & Trognon, Alain, 1987. "Generalised residuals," Journal of Econometrics, Elsevier, vol. 34(1-2), pages 5-32.
    17. Moon, Choon-Geol & Stotsky, Janet G, 1993. "The Effect of Rent Control on Housing Quality Change: A Longitudinal Analysis," Journal of Political Economy, University of Chicago Press, vol. 101(6), pages 1114-1148, December.
    18. Chesher, Andrew & Jewitt, Ian, 1987. "The Bias of a Heteroskedasticity Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 55(5), pages 1217-1222, September.
    19. Blundell, Richard & Smith, Richard J., 1994. "Coherency and estimation in simultaneous models with censored or qualitative dependent variables," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 355-373.
    20. 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.
    21. Vella, Francis, 1993. "A Simple Estimator for Simultaneous Models with Censored Endogenous Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(2), pages 441-457, May.
    22. Javier Alvarez & Manuel Arellano, 2003. "The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators," Econometrica, Econometric Society, vol. 71(4), pages 1121-1159, July.
    23. 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.
    24. Mundlak, Yair, 1978. "On the Pooling of Time Series and Cross Section Data," Econometrica, Econometric Society, vol. 46(1), pages 69-85, January.
    25. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, July.
    26. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 31(3), pages 129-137.
    27. Ivan Fernandez-Val, 2005. "Estimation of Structural Parameters and Marginal Effects in Binary Choice Panel Data Models with Fixed Effects," Boston University - Department of Economics - Working Papers Series WP2005-38, Boston University - Department of Economics.
    28. Newey, Whitney K., 1984. "A method of moments interpretation of sequential estimators," Economics Letters, Elsevier, vol. 14(2-3), pages 201-206.
    29. Honore, Bo E., 1993. "Orthogonality conditions for Tobit models with fixed effects and lagged dependent variables," Journal of Econometrics, Elsevier, vol. 59(1-2), pages 35-61, September.
    30. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-959, July.
    31. Ivan Fernandez-Val, 2005. "Bias Correction in Panel Data Models with Individual Specific Parameters," Boston University - Department of Economics - Working Papers Series WP2005-041, Boston University - Department of Economics.
    32. Nickell, Stephen J, 1981. "Biases in Dynamic Models with Fixed Effects," Econometrica, Econometric Society, vol. 49(6), pages 1417-1426, November.
    33. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245 Elsevier.
    34. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
    35. Nijman, T.E. & Verbeek, M.J.C.M., 1992. "Testing for selectivity in panel data models," Other publications TiSEM 7ec34a6c-1d84-4052-971c-d, Tilburg University, School of Economics and Management.
    36. Dean R. Hyslop, 1999. "State Dependence, Serial Correlation and Heterogeneity in Intertemporal Labor Force Participation of Married Women," Econometrica, Econometric Society, vol. 67(6), pages 1255-1294, November.
    37. Vella, Francis & Verbeek, Marno, 1999. "Two-step estimation of panel data models with censored endogenous variables and selection bias," Journal of Econometrics, Elsevier, vol. 90(2), pages 239-263, June.
    38. Smith, Richard J & Blundell, Richard W, 1986. "An Exogeneity Test for a Simultaneous Equation Tobit Model with an Application to Labor Supply," Econometrica, Econometric Society, vol. 54(3), pages 679-685, May.
    39. 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.
    40. Richard W. Blundell & Richard J. Smith, 1989. "Estimation in a Class of Simultaneous Equation Limited Dependent Variable Models," Review of Economic Studies, Oxford University Press, vol. 56(1), pages 37-57.
    41. Arthur Lewbel, 2005. "Simple Endogenous Binary Choice and Selection Panel Model Estimators," Boston College Working Papers in Economics 613, Boston College Department of Economics, revised 04 Sep 2006.
    42. William Greene, 2004. "Fixed Effects and Bias Due to the Incidental Parameters Problem in the Tobit Model," Econometric Reviews, Taylor & Francis Journals, vol. 23(2), pages 125-147.
    43. Francis Vella & Marno Verbeek, 1998. "Whose wages do unions raise? A dynamic model of unionism and wage rate determination for young men," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(2), pages 163-183.
    44. Ekaterini Kyriazidou, 1997. "Estimation of a Panel Data Sample Selection Model," Econometrica, Econometric Society, vol. 65(6), pages 1335-1364, November.
    45. Roberts, Mark J & Tybout, James R, 1997. "The Decision to Export in Colombia: An Empirical Model of Entry with Sunk Costs," American Economic Review, American Economic Association, vol. 87(4), pages 545-564, September.
    46. Cameron,A. Colin & Trivedi,Pravin K., 2008. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9787111235767.
    47. Jinyong Hahn & Guido Kuersteiner, 2002. "Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects when Both "n" and "T" Are Large," Econometrica, Econometric Society, vol. 70(4), pages 1639-1657, July.
    48. Carrasco, Raquel, 2001. "Binary Choice with Binary Endogenous Regressors in Panel Data: Estimating the Effect of Fertility on Female Labor Participation," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 385-394, October.
    49. 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.
    50. Chamberlain, Gary, 1984. "Panel data," Handbook of Econometrics,in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 22, pages 1247-1318 Elsevier.
    51. James J. Heckman & Thomas MaCurdy, 1982. "Corrigendum on A Life Cycle Model of Female Labour Supply," Review of Economic Studies, Oxford University Press, vol. 49(4), pages 659-660.
    52. Hahn, Jinyong & Kuersteiner, Guido, 2011. "Bias Reduction For Dynamic Nonlinear Panel Models With Fixed Effects," Econometric Theory, Cambridge University Press, vol. 27(06), pages 1152-1191, December.
    53. Arellano, Manuel & Carrasco, Raquel, 2003. "Binary choice panel data models with predetermined variables," Journal of Econometrics, Elsevier, vol. 115(1), pages 125-157, July.
    54. Amemiya, Takeshi, 1981. "Qualitative Response Models: A Survey," Journal of Economic Literature, American Economic Association, vol. 19(4), pages 1483-1536, December.
    55. Nerlove, Marc, 1971. "Further Evidence on the Estimation of Dynamic Economic Relations from a Time Series of Cross Sections," Econometrica, Econometric Society, vol. 39(2), pages 359-382, March.
    56. Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, vol. 54(6), pages 1461-1481, November.
    57. Yatchew, Adonis & Griliches, Zvi, 1985. "Specification Error in Probit Models," The Review of Economics and Statistics, MIT Press, vol. 67(1), pages 134-139, February.
    58. Manuel Arellano & Jinyong Hahn, 2005. "Understanding Bias In Nonlinear Panel Models: Some Recent Developments," Working Papers wp2005_0507, CEMFI.
    59. Bo E. Honoré & Ekaterini Kyriazidou, 2000. "Panel Data Discrete Choice Models with Lagged Dependent Variables," Econometrica, Econometric Society, vol. 68(4), pages 839-874, July.
    60. Tiemen Woutersen, 2002. "Robustness against Incidental Parameters," UWO Department of Economics Working Papers 20028, University of Western Ontario, Department of Economics.
    61. Gary Chamberlain, 1980. "Analysis of Covariance with Qualitative Data," Review of Economic Studies, Oxford University Press, vol. 47(1), pages 225-238.
    62. Ekaterini Kyriazidou, 2001. "Estimation of Dynamic Panel Data Sample Selection Models," Review of Economic Studies, Oxford University Press, vol. 68(3), pages 543-572.
    63. Rivers, Douglas & Vuong, Quang H., 1988. "Limited information estimators and exogeneity tests for simultaneous probit models," Journal of Econometrics, Elsevier, vol. 39(3), pages 347-366, November.
    64. Tony Lancaster, 2002. "Orthogonal Parameters and Panel Data," Review of Economic Studies, Oxford University Press, vol. 69(3), pages 647-666.
    65. Lancaster, Tony, 2000. "The incidental parameter problem since 1948," Journal of Econometrics, Elsevier, vol. 95(2), pages 391-413, April.
    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. Fernández-Val, Iván & Weidner, Martin, 2016. "Individual and time effects in nonlinear panel models with large N, T," Journal of Econometrics, Elsevier, vol. 192(1), pages 291-312.
    2. Alderighi, Marco & Gaggero, Alberto A. & Piga, Claudio A., 2015. "The effect of code-share agreements on the temporal profile of airline fares," Transportation Research Part A: Policy and Practice, Elsevier, vol. 79(C), pages 42-54.
    3. Elizabeth Schroeder, 2016. "Dynamic labor supply adjustment with bias correction," Empirical Economics, Springer, vol. 51(4), pages 1623-1640, December.
    4. Beckmann, Michael & Cornelissen, Thomas & Kräkel, Matthias, 2017. "Self-managed working time and employee effort: Theory and evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 133(C), pages 285-302.
    5. Chrysanthou, Georgios Marios, 2008. "Estimating union wage effects in Great Britain during 1991-2003," UC3M Working papers. Economics we082214, Universidad Carlos III de Madrid. Departamento de Economía.
    6. Geert Dhaene & Koen Jochmans, 2015. "Split-panel Jackknife Estimation of Fixed-effect Models," Review of Economic Studies, Oxford University Press, vol. 82(3), pages 991-1030.
    7. Michael J. Hicks & Michael LaFaive & Srikant Devaraj, 2016. "New Evidence on the Effect of Right-to-Work Laws on Productivity and Population Growth," Cato Journal, Cato Journal, Cato Institute, vol. 36(1), pages 101-120, Winter.
    8. Michael Beckmann & Thomas Cornelissen, 2014. "Self-Managed Working Time and Employee Effort: Microeconometric Evidence," SOEPpapers on Multidisciplinary Panel Data Research 636, DIW Berlin, The German Socio-Economic Panel (SOEP).
    9. Harrison Fell & Daniel T. Kaffine, 2014. "A one-two punch: Joint effects of natural gas abundance and renewables on coal-fired power plants," Working Papers 2014-10, Colorado School of Mines, Division of Economics and Business.
    10. Jochmans, Koen, 2015. "Multiplicative-error models with sample selection," Journal of Econometrics, Elsevier, vol. 184(2), pages 315-327.
    11. Aysen Isaoglu, 2010. "Worker Reallocation across Occupations in Western Germany," SOEPpapers on Multidisciplinary Panel Data Research 319, DIW Berlin, The German Socio-Economic Panel (SOEP).
    12. Chrysanthou, Georgios Marios, 2014. "Heterogeneity, Endogeneity, Measurement Error and Identification of the Union Wage Impact," QM&ET Working Papers 14-4, University of Alicante, D. Quantitative Methods and Economic Theory, revised 05 Nov 2014.
    13. Ramon Cobo-Reyes & Gabriel Katz & Simone Meraglia?, 2017. "Endogenous Sanctioning Institutions and Migration Patterns: Experimental Evidence," Discussion Papers 1702, Exeter University, Department of Economics.
    14. Panutat Satchachai & Peter Schmidt, 2010. "Estimates of technical inefficiency in stochastic frontier models with panel data: generalized panel jackknife estimation," Journal of Productivity Analysis, Springer, vol. 34(2), pages 83-97, October.
    15. Mingli Chen & Ivan Fernandez-Val & Martin Weidner, 2014. "Nonlinear Panel Models with Interactive Effects," Papers 1412.5647, arXiv.org.
    16. Almer, Christian & Laurent-Lucchetti, Jérémy & oechslin, Manuel, 2011. "Income shocks and social unrest: theory and evidence," MPRA Paper 34426, University Library of Munich, Germany.
    17. Kufenko, Vadmin & Prettner, Klaus, 2017. "You can't always get what you want? A Monte Carlo analysis of the bias and the efficiency of dynamic panel data estimators," ECON WPS - Vienna University of Technology Working Papers in Economic Theory and Policy 07/2017, Vienna University of Technology, Institute for Mathematical Methods in Economics, Research Group Economics (ECON).
    18. Christian Almer & Stefan Boes, 2012. "Climate (change) and conflict: resolving a puzzle of association and causation," Diskussionsschriften dp1203, Universitaet Bern, Departement Volkswirtschaft.

    More about this item

    Keywords

    Panel data Two-step estimation Endogenous regressors Fixed effects Sample selection bias Union premium;

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials
    • J51 - Labor and Demographic Economics - - Labor-Management Relations, Trade Unions, and Collective Bargaining - - - Trade Unions: Objectives, Structure, and Effects

    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:163:y:2011:i:2:p:144-162. 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.