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On the role of time in nonseparable panel data models

Author

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  • Stefan Hoderlein

    () (Institute for Fiscal Studies and Boston College)

  • Yuya Sasaki

    (Institute for Fiscal Studies)

Abstract

This paper contributes to the understanding of the source of identification in panel data models. Recent research has established that few time periods suffice to identify interesting structural effects in nonseparable panel data models even in the presence of complex correlated unobservables, provided these unobservables are time invariant. A communality of all of these approaches is that they point identify effects only for subpopulations. In this paper we focus on average partial derivatives and continuous explanatory variables. We elaborate on the parallel between time in panels and instrumental variables in cross sections and establish that point identification is generically only possible in specific subpopulations, for finite T . Moreover, for general subpopulations, we provide sharp bounds. Finally, we show that these bounds converge to point identification as T tends to infinity only. We systematize this behavior by comparing it to increasing the number of support points of an instrument. Finally, we apply all of these concepts to the semiparametric panel binary choice model and establish that these issues determine the rates of convergence of estimators for the slope coefficient.

Suggested Citation

  • Stefan Hoderlein & Yuya Sasaki, 2011. "On the role of time in nonseparable panel data models," CeMMAP working papers CWP15/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:15/11
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    File URL: http://cemmap.ifs.org.uk/wps/cwp1511.pdf
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    References listed on IDEAS

    as
    1. Joseph G. Altonji & Rosa L. Matzkin, 2001. "Panel Data Estimators for Nonseparable Models with Endogenous Regressors," NBER Technical Working Papers 0267, National Bureau of Economic Research, Inc.
    2. repec:oup:restud:v:79:y::i:3:p:987-1020 is not listed on IDEAS
    3. Myoung-jae Lee, 1999. "A Root-N Consistent Semiparametric Estimator for Related-Effect Binary Response Panel Data," Econometrica, Econometric Society, vol. 67(2), pages 427-434, March.
    4. 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.
    5. Azeem M. Shaikh & Edward J. Vytlacil, 2011. "Partial Identification in Triangular Systems of Equations With Binary Dependent Variables," Econometrica, Econometric Society, vol. 79(3), pages 949-955, May.
    6. Manuel Arellano & Stéphane Bonhomme, 2012. "Identifying Distributional Characteristics in Random Coefficients Panel Data Models," Review of Economic Studies, Oxford University Press, vol. 79(3), pages 987-1020.
    7. Andrew Chesher, 2005. "Nonparametric Identification under Discrete Variation," Econometrica, Econometric Society, vol. 73(5), pages 1525-1550, September.
    8. Bryan S. Graham & James Powell, 2008. "Identification and Estimation of 'Irregular' Correlated Random Coefficient Models," NBER Working Papers 14469, National Bureau of Economic Research, Inc.
    9. Richard Blundell & James L. Powell, 2001. "Endogeneity in nonparametric and semiparametric regression models," CeMMAP working papers CWP09/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. 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.
    11. Bester, C. Alan & Hansen, Christian, 2009. "Identification of Marginal Effects in a Nonparametric Correlated Random Effects Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 235-250.
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