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Estimation of Nonparametric Functions in Simultaneous Equations Models, with an Application to Consumer Demand

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Abstract

We present a method for consistently estimating nonparametric functions and distributions in simultaneous equations models. This method is used to identify and estimate a random utility model of consumer demand. Our identification conditions for this particular model extend the results of Houthakker (1950), Uzawa (1971) and Mas-Colell (1977), where a deterministic utility function is uniquely recovered from its deterministic demand function.

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  • 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.
  • Handle: RePEc:cwl:cwldpp:1175
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    1. Roehrig, Charles S, 1988. "Conditions for Identification in Nonparametric and Parametic Models," Econometrica, Econometric Society, vol. 56(2), pages 433-447, March.
    2. Manski, Charles F, 1983. "Closest Empirical Distribution Estimation," Econometrica, Econometric Society, vol. 51(2), pages 305-319, March.
    3. Mas-Colell, Andreu, 1977. "The Recoverability of Consumers' Preferences from Market Demand Behavior," Econometrica, Econometric Society, vol. 45(6), pages 1409-1430, September.
    4. Brown, Bryan W, 1983. "The Identification Problem in Systems Nonlinear in the Variables," Econometrica, Econometric Society, vol. 51(1), pages 175-196, January.
    5. Foster, Andrew & Hahn, Jinyong, 2000. "A consistent semiparametric estimation of the consumer surplus distribution," Economics Letters, Elsevier, vol. 69(3), pages 245-251, December.
    6. Brown, Bryan W & Walker, Mary Beth, 1989. "The Random Utility Hypothesis and Inference in Demand Systems," Econometrica, Econometric Society, vol. 57(4), pages 815-829, July.
    7. McElroy, Marjorie B, 1987. "Additive General Error Models for Production, Cost, and Derived Demand or Share Systems," Journal of Political Economy, University of Chicago Press, vol. 95(4), pages 737-757, August.
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    Cited by:

    1. Tsunao Okumura, 2011. "Nonparametric Estimation of Labor Supply and Demand Factors," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 174-185, January.
    2. Martin Browning & Pierre-André Chiappori & Valérie Lechene, 2006. "Collective and Unitary Models: A Clarification," Review of Economics of the Household, Springer, vol. 4(1), pages 5-14, March.
    3. Steven T. Berry & Philip A. Haile, 2011. "Identification in a Class of Nonparametric Simultaneous Equations Models," Cowles Foundation Discussion Papers 1787, Cowles Foundation for Research in Economics, Yale University.
    4. Woocheol Kim, 2004. "Identification And Estimation Of Nonparametric Structural," Econometric Society 2004 Far Eastern Meetings 733, Econometric Society.
    5. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, September.
    6. Richard W. Blundell & Martin Browning & Ian A. Crawford, 2003. "Nonparametric Engel Curves and Revealed Preference," Econometrica, Econometric Society, vol. 71(1), pages 205-240, January.
    7. Daniel McFadden, 2001. "Economic Choices," American Economic Review, American Economic Association, vol. 91(3), pages 351-378, June.
    8. Liangjun Su & Yundong Tu & Aman Ullah, 2015. "Testing Additive Separability of Error Term in Nonparametric Structural Models," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 1057-1088, December.
    9. Arthur Lewbel, 2006. "Modeling Heterogeneity," Boston College Working Papers in Economics 650, Boston College Department of Economics.
    10. Brown, Donald J & Matzkin, Rosa L, 1996. "Testable Restrictions on the Equilibrium Manifold," Econometrica, Econometric Society, vol. 64(6), pages 1249-1262, November.
    11. Halbert White & Karim Chalak, 2008. "Identifying Structural Effects in Nonseparable Systems Using Covariates," Boston College Working Papers in Economics 734, Boston College Department of Economics.
    12. Mette Lunde Christensen, 2002. "Heterogeneity in consumer demands and the income effect: evidence from panel data," 10th International Conference on Panel Data, Berlin, July 5-6, 2002 C4-1, International Conferences on Panel Data.
    13. Carvajal, Andres & Ray, Indrajit & Snyder, Susan, 2004. "Equilibrium behavior in markets and games: testable restrictions and identification," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 1-40, February.
    14. Sher, Itai & Kim, Kyoo il, 2014. "Identifying combinatorial valuations from aggregate demand," Journal of Economic Theory, Elsevier, vol. 153(C), pages 428-458.
    15. C. Lanier Benkard & Steven Berry, "undated". "On the Nonparametric Identification of Nonlinear Simultaneous Equations Models: comment on B. Brown (1983) and Roehrig (1988)," Cowles Foundation Discussion Papers 1482, Cowles Foundation for Research in Economics, Yale University.
    16. McAleer, Michael & Medeiros, Marcelo C. & Slottje, Daniel, 2008. "A neural network demand system with heteroskedastic errors," Journal of Econometrics, Elsevier, vol. 147(2), pages 359-371, December.
    17. 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.
    18. 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.
    19. Arthur Lewbel, 2001. "Demand Systems with and without Errors," American Economic Review, American Economic Association, vol. 91(3), pages 611-618, June.
    20. Su, Liangjun & Ullah, Aman, 2008. "Local polynomial estimation of nonparametric simultaneous equations models," Journal of Econometrics, Elsevier, vol. 144(1), pages 193-218, May.
    21. C. Lanier Benkard & Steven Berry, 2006. "On the Nonparametric Identification of Nonlinear Simultaneous Equations Models: Comment on Brown (1983) and Roehrig (1988)," Econometrica, Econometric Society, vol. 74(5), pages 1429-1440, September.
    22. Arthur Lewbel & Krishna Pendakur, 2009. "Tricks with Hicks: The EASI Demand System," American Economic Review, American Economic Association, vol. 99(3), pages 827-863, June.
    23. Donald J. Brown & Caterina Calsamiglia, 2003. "Rationalizing and Curve-Fitting Demand Data with Quasilinear Utilities," Cowles Foundation Discussion Papers 1399R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2004.
    24. repec:eee:econom:v:199:y:2017:i:1:p:35-48 is not listed on IDEAS
    25. Walter Beckert, 2007. "Specification and Identification of Stochastic Demand Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(6), pages 669-683.

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