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Modeling Heterogeneity

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  • Arthur Lewbel

    (Boston College)

Abstract

My goal here is to provide some synthesis of recent results regarding unobserved heterogeneity in nonlinear and semiparametric models, using as a context Matzkin (2005a) and Browning and Carro (2005), which were the papers presented in the Modeling Heterogeneity session of the 2005 Econometric Society World Meetings in London. These papers themselves consist of enormously heterogeneous content, ranging from high theory to Danish milk, which I will attempt to homogenize. The overall theme of this literature is that, in models of individual economic agents, errors at least partly reflect unexplained heterogeneity in behavior, and hence in tastes, technologies, etc.,. Economic theory can imply restrictions on the structure of these errors, and in particular can generate nonadditive or nonseparable errors, which has profound implications for model specification, identification, estimation, and policy analysis.

Suggested Citation

  • Arthur Lewbel, 2006. "Modeling Heterogeneity," Boston College Working Papers in Economics 650, Boston College Department of Economics.
    • Handle: RePEc:boc:bocoec:650
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    References listed on IDEAS

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    1. Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 655-679.
    2. Martin Browning & Jesus M. Carro, 2010. "Heterogeneity in dynamic discrete choice models," Econometrics Journal, Royal Economic Society, vol. 13(1), pages 1-39, February.
    3. Brown, Bryan W, 1983. "The Identification Problem in Systems Nonlinear in the Variables," Econometrica, Econometric Society, vol. 51(1), pages 175-196, January.
    4. Soest, Arthur van & Kapteyn, Arie & Kooreman, Peter, 1993. "Coherency and regularity of demand systems with equality and inequality constraints," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 161-188.
    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 for Research in Economics, Yale University.
    6. Arthur Lewbel, 2007. "Coherency And Completeness Of Structural Models Containing A Dummy Endogenous Variable," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1379-1392, November.
    7. Ivar Ekeland & James J. Heckman & Lars Nesheim, 2002. "Identifying Hedonic Models," American Economic Review, American Economic Association, vol. 92(2), pages 304-309, May.
    8. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(1), pages 147-165.
    9. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, July.
    10. Lewbel, Arthur & McFadden, Daniel & Linton, Oliver, 2011. "Estimating features of a distribution from binomial data," Journal of Econometrics, Elsevier, vol. 162(2), pages 170-188, June.
    11. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-959, July.
    12. Gourieroux, C & Laffont, J J & Monfort, A, 1980. "Coherency Conditions in Simultaneous Linear Equation Models with Endogenous Switching Regimes," Econometrica, Econometric Society, vol. 48(3), pages 675-695, April.
    13. Daniel McFadden, 2005. "Revealed stochastic preference: a synthesis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 245-264, August.
    14. Bresnahan, Timothy F. & Reiss, Peter C., 1991. "Empirical models of discrete games," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 57-81.
    15. 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.
    16. Arthur Lewbel, 2001. "Demand Systems with and without Errors," American Economic Review, American Economic Association, vol. 91(3), pages 611-618, June.
    17. Muellbauer, John, 1974. "Household composition, Engel curves and welfare comparisons between households : A duality approach," European Economic Review, Elsevier, vol. 5(2), pages 103-122, August.
    18. Roehrig, Charles S, 1988. "Conditions for Identification in Nonparametric and Parametic Models," Econometrica, Econometric Society, vol. 56(2), pages 433-447, March.
    19. Joseph G. Altonji & Rosa L. Matzkin, 2005. "Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 73(4), pages 1053-1102, July.
    20. Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July.
    21. Walter Beckert & Richard Blundell, 2004. "Invertibility of Nonparametric Stochastic Demand Functions," Birkbeck Working Papers in Economics and Finance 0406, Birkbeck, Department of Economics, Mathematics & Statistics.
    22. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, September.
    23. 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.
    24. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-730, May.
    25. Arthur Lewbel, 1989. "Identification and Estimation of Equivalence Scales under Weak Separability," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(2), pages 311-316.
    26. Tiemen Woutersen, 2002. "Robustness against Incidental Parameters," University of Western Ontario, Departmental Research Report Series 20028, University of Western Ontario, Department of Economics.
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    Cited by:

    1. Yingying Dong & Arthur Lewbel, 2015. "A Simple Estimator for Binary Choice Models with Endogenous Regressors," Econometric Reviews, Taylor & Francis Journals, vol. 34(1-2), pages 82-105, February.
    2. Jean-Michel Grandmont, 2017. "Behavioral Heterogeneity : Pareto Distributions of Homothetic Preference Scales and Aggregate Expenditures Income Elasticities," Working Papers 2017-11, Center for Research in Economics and Statistics.

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    Keywords

    unobserved heterogeneity; nonlinear models; semiparametric models;
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