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Semiparametric Estimation of Monotone and Concave Utility Functions for Polychotomous Choice Models

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  • Matzkin, Rosa L

Abstract

This paper introduces a semiparametric estimation method for Polychotomous Choice models. The method does not require a parametric structure for the systematic subutility of observable exogenous variables. The distribution of the random terms is assumed to be known up to a finite-dimensional parameter vector. In contrast, previous semiparametric methods of estimating discrete choice models have concentrated on relaxing parametric subutility parametrically specified. The systematic subutility is assumed to possess properties such as monotonicity and concavity that are typically assumed in microeconomic theory. The estimator for the systematic subutility and the parameter vector of the distribution is shown to be strongly consistent. A computational technique to calculate the estimators is developed. Copyright 1991 by The Econometric Society.

Suggested Citation

  • Matzkin, Rosa L, 1991. "Semiparametric Estimation of Monotone and Concave Utility Functions for Polychotomous Choice Models," Econometrica, Econometric Society, vol. 59(5), pages 1315-1327, September.
  • Handle: RePEc:ecm:emetrp:v:59:y:1991:i:5:p:1315-27
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    Cited by:

    1. John Quah, 2014. "A test for weakly separable preferences," Economics Series Working Papers 708, University of Oxford, Department of Economics.
    2. Lee, Lung-fei, 1995. "Semiparametric maximum likelihood estimation of polychotomous and sequential choice models," Journal of Econometrics, Elsevier, vol. 65(2), pages 381-428, February.
    3. Jeremy T. Fox, 2010. "Identification in matching games," Quantitative Economics, Econometric Society, vol. 1(2), pages 203-254, November.
    4. Hazelton, Martin L. & Turlach, Berwin A., 2011. "Semiparametric regression with shape-constrained penalized splines," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2871-2879, October.
    5. Yining Chen & Richard J. Samworth, 2016. "Generalized additive and index models with shape constraints," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 729-754, September.
    6. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
    7. Steffen Andersen & Glenn Harrison & Arne Hole & Morten Lau & E. Rutström, 2012. "Non-linear mixed logit," Theory and Decision, Springer, vol. 73(1), pages 77-96, July.
    8. Le-Yu Chen, 2009. "Identification of structural dynamic discrete choice models," CeMMAP working papers CWP08/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Henderson, Daniel J. & Parmeter, Christopher F., 2009. "Imposing Economic Constraints in Nonparametric Regression: Survey, Implementation and Extension," IZA Discussion Papers 4103, Institute for the Study of Labor (IZA).
    10. John Rust, 2014. "The Limits of Inference with Theory: A Review of Wolpin (2013)," Journal of Economic Literature, American Economic Association, vol. 52(3), pages 820-850, September.
    11. Gad Allon & Michael Beenstock & Steven Hackman & Ury Passy & Alexander Shapiro, 2007. "Nonparametric estimation of concave production technologies by entropic methods," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(4), pages 795-816.
    12. Samuele Centorrino & Jean-Pierre Florens, 2014. "Nonparametric Instrumental Variable Estimation of Binary Response Models," Department of Economics Working Papers 14-07, Stony Brook University, Department of Economics.
    13. Brian Blackburn & Aprajit Mahajan & Alessandro Tarozzi & Joanne Yoong, 2009. "Bednets, Information and Malaria in Orissa," Discussion Papers 08-025, Stanford Institute for Economic Policy Research.
    14. Pang Du & Christopher F. Parmeter & Jeffrey S. Racine, 2012. "Nonparametric Kernel Regression with Multiple Predictors and Multiple Shape Constraints," Department of Economics Working Papers 2012-08, McMaster University.
    15. Rosa L. Matzkin, 1988. "Nonparametric and Distribution-Free Estimation of the Binary Choice and the Threshold-Crossing Models," Cowles Foundation Discussion Papers 889, Cowles Foundation for Research in Economics, Yale University.
    16. Huang, J u-Chin & Nychka, Douglas W., 2000. "A nonparametric multiple choice method within the random utility framework," Journal of Econometrics, Elsevier, vol. 97(2), pages 207-225, August.
    17. Levon Barseghyan & Francesca Molinari & Ted O'Donoghue & Joshua C. Teitelbaum, 2013. "The Nature of Risk Preferences: Evidence from Insurance Choices," American Economic Review, American Economic Association, vol. 103(6), pages 2499-2529, October.
    18. Jeremy T. Fox, 2008. "Estimating Matching Games with Transfers," NBER Working Papers 14382, National Bureau of Economic Research, Inc.
    19. Stephen V. Cameron & James J. Heckman, 1998. "Life Cycle Schooling and Dynamic Selection Bias: Models and Evidence for Five Cohorts of American Males," Journal of Political Economy, University of Chicago Press, vol. 106(2), pages 262-333, April.
    20. 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.
    21. Maxim Engers & Monica Hartmann & Steven Stern, 2009. "Annual miles drive used car prices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(1), pages 1-33.
    22. Fabio A. Miessi Sanches & Daniel Silva Junior, Sorawoot Srisuma, 2014. "Ordinary Least Squares Estimation for a Dynamic Game," Working Papers, Department of Economics 2014_19, University of São Paulo (FEA-USP), revised 23 Feb 2015.
    23. Pablo M Garcia, 2005. "Una Aproximación Microeconométrica a los Determinantes de la Elección del Modo de Transporte. (A Microeconometric Approach to the Determinants of Travel Mode Choice)," Urban/Regional 0504005, EconWPA.
    24. Stephen V. Cameron & James J. Heckman, 1998. "Life Cycle Schooling and Dynamic Selection Bias: Models and Evidence for Five Cohorts," NBER Working Papers 6385, National Bureau of Economic Research, Inc.

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