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Panel Data Estimators for Nonseparable Models with Endogenous Regressors

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  • Joseph G. Altonji
  • Rosa L. Matzkin

Abstract

We propose two new estimators for a wide class of panel data models with nonseparable error terms and endogenous explanatory variables. The first estimator covers qualitative choice models and both estimators cover models with continuous dependent variables. The first estimator requires the existence of a vector z such that the density of the error term does not depend on the explanatory variables once one conditions on z. In some panel data cases we may find z by making the assumption that the distribution of the error term conditional on the vector of the explanatory variables for each cross-section' unit in the panel is exchangeable in the values of those explanatory variables. This situation may be realistic, in particular, when each unit is a group of individuals, so that the observations are across groups and for different individuals in each group. The basic idea is to first estimate the slope of the mean of the dependent variable conditional on both the explanatory variable and z and then undo the effect of conditioning on z by taking the average of the slope over the distribution of z conditional on a particular value of the explanatory variable. We also extend the procedure to the case in which the explanatory variable is endogenous conditional on z but an instrumental variable is available. The second estimator is based on the assumption that the error distribution is exchangeable in the explanatory variables of each unit. It applies to models that are monotone in the error term. A shift in the value of an explanatory variable for member 1 of a group has both a direct effect on the distribution of the dependent variable for member 1 and an indirect effect through the distribution of the error. A shift in the explanatory variable has an indirect effect on the dependent variable for other members of the panel but no direct effect. We isolate the direct effect by comparing the effect of the explanatory variable on the distribution of the dependent variable for member 1 to its effect on the distribution for the other panel members.

Suggested Citation

  • 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.
  • Handle: RePEc:nbr:nberte:0267
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    References listed on IDEAS

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    Cited by:

    1. Woocheol Kim, 2004. "Identification And Estimation Of Nonparametric Structural," Econometric Society 2004 Far Eastern Meetings 733, Econometric Society.
    2. Schennach, Susanne & White, Halbert & Chalak, Karim, 2012. "Local indirect least squares and average marginal effects in nonseparable structural systems," Journal of Econometrics, Elsevier, vol. 166(2), pages 282-302.
    3. Browning, Martin & Carro, Jesus M., 2014. "Dynamic binary outcome models with maximal heterogeneity," Journal of Econometrics, Elsevier, vol. 178(2), pages 805-823.
    4. Susan Athey & Guido W. Imbens, 2006. "Identification and Inference in Nonlinear Difference-in-Differences Models," Econometrica, Econometric Society, vol. 74(2), pages 431-497, March.
    5. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
    6. Nese Yildiz, 2012. "Estimation of Binary Choice Models with Linear Index and Dummy Endogenous Variables," Koç University-TUSIAD Economic Research Forum Working Papers 1202, Koc University-TUSIAD Economic Research Forum.
    7. Joseph G. Altonji & Ulrich Doraszelski, 2005. "The Role of Permanent Income and Demographics in Black/White Differences in Wealth," Journal of Human Resources, University of Wisconsin Press, vol. 40(1).
    8. 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.
    9. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, September.
    10. 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.
    11. Joseph G. Altonji & Hidehiko Ichimura & Taisuke Otsu, 2012. "Estimating Derivatives in Nonseparable Models With Limited Dependent Variables," Econometrica, Econometric Society, vol. 80(4), pages 1701-1719, July.
    12. Steven T. Berry & Philip A. Haile, 2014. "Identification in Differentiated Products Markets Using Market Level Data," Econometrica, Econometric Society, vol. 82, pages 1749-1797, September.
    13. Steven T. Berry & Philip A. Haile, 2009. "Identification of a Heterogeneous Generalized Regression Model with Group Effects," Cowles Foundation Discussion Papers 1732, Cowles Foundation for Research in Economics, Yale University.
    14. Victor Chernozhukov & Roberto Rigobon & Thomas M. Stoker, 2009. "Set identification with Tobin regressors," CeMMAP working papers CWP12/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    15. Susanne Schennach & Halbert White & Karim Chalak, 2007. "Local Indirect Least Squares and Average Marginal Effects in Nonseparable Structural Systems," Boston College Working Papers in Economics 680, Boston College Department of Economics, revised 26 Dec 2009.
    16. 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.
    17. Chesher, Andrew, 2007. "Instrumental values," Journal of Econometrics, Elsevier, vol. 139(1), pages 15-34, July.
    18. Jeremy T. Fox & Amit Gandhi, 2011. "Identifying Demand with Multidimensional Unobservables: A Random Functions Approach," NBER Working Papers 17557, National Bureau of Economic Research, Inc.
    19. Joseph G. Altonji & Todd E. Elder & Christopher R. Taber, 2002. "An Evaluation of Instrumental Variable Strategies for Estimating the Effects of Catholic Schools," NBER Working Papers 9358, National Bureau of Economic Research, Inc.
    20. Carro, Jesus M., 2007. "Estimating dynamic panel data discrete choice models with fixed effects," Journal of Econometrics, Elsevier, vol. 140(2), pages 503-528, October.
    21. Steven T. Berry & Philip A. Haile, 2009. "Nonparametric Identification of Multinomial Choice Demand Models with Heterogeneous Consumers," NBER Working Papers 15276, National Bureau of Economic Research, Inc.
    22. Rosa L. Matzkin & James Heckman & Lars Nesheim, 2002. "Nonparametric Estimation and Nonadditive Hedonic Models," Working Papers 51, Universidad de San Andres, Departamento de Economia, revised Jun 2002.
    23. Diego Ubfal & Alessandro Maffioli, 2010. "The Impact of Funding on Research Collaboration: Evidence from Argentina," IDB Publications (Working Papers) 9395, Inter-American Development Bank.
    24. 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.

    More about this item

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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