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Panel Data Estimators for Nonseparable Models with Endogenous Regressors

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Author Info
Joseph G. Altonji
Rosa L. Matzkin

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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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0267.

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Date of creation: Mar 2001
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Handle: RePEc:nbr:nberte:0267

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Find related papers by 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

References listed on IDEAS
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  1. Currie, Janet & Thomas, Duncan, 1995. "Does Head Start Make a Difference?," American Economic Review, American Economic Association, vol. 85(3), pages 341-64, June. [Downloadable!] (restricted)
    Other versions:
  2. 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.
  3. Joseph G. Altonji & Hidehiko Ichimura & Taisuke Otsu, 2008. "Estimating Derivatives in Nonseparable Models with Limited Dependent Variables," Cowles Foundation Discussion Papers 1668, Cowles Foundation, Yale University. [Downloadable!]
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  4. Joseph G. Altonji & Fumio Hayashi & Laurence Kotlikoff, . "The Effects of Income and Wealth on Time and MOney Transfers Between Parents and Children," IPR working papers 96-5, Institute for Policy Resarch at Northwestern University.
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  5. Donald J. Brown & Rosa L. Matzkin, 1998. "Estimation of Nonparametric Functions in Simultaneous Equations Models, with an Application to Consumer Demand," Cowles Foundation Discussion Papers 1175, Cowles Foundation, Yale University. [Downloadable!]
  6. Chamberlain, Gary, 1980. "Analysis of Covariance with Qualitative Data," Review of Economic Studies, Blackwell Publishing, vol. 47(1), pages 225-38, January. [Downloadable!] (restricted)
  7. Honore, Bo E, 1992. "Trimmed LAD and Least Squares Estimation of Truncated and Censored Regression Models with Fixed Effects," Econometrica, Econometric Society, vol. 60(3), pages 533-65, May. [Downloadable!] (restricted)
  8. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May. [Downloadable!] (restricted)
  9. 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. [Downloadable!] (restricted)
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  11. Abrevaya, Jason, 2000. "Rank estimation of a generalized fixed-effects regression model," Journal of Econometrics, Elsevier, vol. 95(1), pages 1-23, March. [Downloadable!] (restricted)
  12. Geronimus, Arline T & Korenman, Sanders, 1992. "The Socioeconomic Consequences of Teen Childbearing Reconsidered," The Quarterly Journal of Economics, MIT Press, vol. 107(4), pages 1187-214, November. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!] (restricted)
  2. Woocheol Kim, 2004. "Identification And Estimation Of Nonparametric Structural," Econometric Society 2004 Far Eastern Meetings 733, Econometric Society. [Downloadable!]
  3. Susan Athey & Guido W. Imbens, 2002. "Identification and Inference in Nonlinear Difference-In-Differences Models," NBER Technical Working Papers 0280, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  4. Guido W. Imbens & Whitney K. Newey, 2002. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," NBER Technical Working Papers 0285, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  5. Joseph G. Altonji & Ulrich Doraszelski, 2000. "The Role of Permanent Income and Demographics in Black/White Differences in Wealth," Working Papers 850, Economic Growth Center, Yale University. [Downloadable!]
    Other versions:
  6. Andrew Chesher, 2002. "Instrumental Values," CeMMAP working papers CWP17/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
    Other versions:
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