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Using penalized likelihood to select parameters in a random coefficients multinomial logit model

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  • Horowitz, Joel L.
  • Nesheim, Lars

Abstract

This paper is about estimating a random coefficients logit model in which the distribution of each coefficient is characterized by finitely many parameters, some of which may be zero. The paper gives conditions under which, with probability approaching 1 as the sample size increases, penalized maximum likelihood (PML) estimation with the adaptive LASSO (AL) penalty distinguishes correctly between zero and non-zero parameters. The paper also gives conditions under which PML reduces the asymptotic mean-square estimation error of any continuously differentiable function of the model’s parameters. The paper describes a method for computing PML estimates and presents the results of Monte Carlo experiments that illustrate their performance. It also presents the results of PML estimation of a random coefficients logit model of choice among brands of butter and margarine in the British groceries market.

Suggested Citation

  • Horowitz, Joel L. & Nesheim, Lars, 2021. "Using penalized likelihood to select parameters in a random coefficients multinomial logit model," Journal of Econometrics, Elsevier, vol. 222(1), pages 44-55.
    • Handle: RePEc:eee:econom:v:222:y:2021:i:1:p:44-55
    DOI: 10.1016/j.jeconom.2019.11.008
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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. McFadden, Daniel & Ruud, Paul A, 1994. "Estimation by Simulation," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 591-608, November.
    3. Heiss, Florian & Winschel, Viktor, 2008. "Likelihood approximation by numerical integration on sparse grids," Journal of Econometrics, Elsevier, vol. 144(1), pages 62-80, May.
    4. Geweke, John & Keane, Michael P & Runkle, David, 1994. "Alternative Computational Approaches to Inference in the Multinomial Probit Model," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 609-632, November.
    5. Small, Kenneth A & Rosen, Harvey S, 1981. "Applied Welfare Economics with Discrete Choice Models," Econometrica, Econometric Society, vol. 49(1), pages 105-130, January.
    6. Ackerberg, Daniel & Lanier Benkard, C. & Berry, Steven & Pakes, Ariel, 2007. "Econometric Tools for Analyzing Market Outcomes," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 63, Elsevier.
    7. Rachel Griffith & Lars Nesheim & Martin O'Connell, 2018. "Income effects and the welfare consequences of tax in differentiated product oligopoly," Quantitative Economics, Econometric Society, vol. 9(1), pages 305-341, March.
    8. Joel L. Horowitz, 2015. "Variable selection and estimation in high‐dimensional models," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 48(2), pages 389-407, May.
    9. Christopher R. Knittel & Konstantinos Metaxoglou, 2014. "Estimation of Random-Coefficient Demand Models: Two Empiricists' Perspective," The Review of Economics and Statistics, MIT Press, vol. 96(1), pages 34-59, March.
    10. Hajivassiliou, Vassilis & McFadden, Daniel & Ruud, Paul, 1996. "Simulation of multivariate normal rectangle probabilities and their derivatives theoretical and computational results," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 85-134.
    11. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
    12. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    13. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387, September.
    14. Hansheng Wang & Bo Li & Chenlei Leng, 2009. "Shrinkage tuning parameter selection with a diverging number of parameters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 671-683, June.
    15. Geweke, John & Keane, Michael, 2001. "Computationally intensive methods for integration in econometrics," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 56, pages 3463-3568, Elsevier.
    16. Joel L. Horowitz, 2015. "Variable selection and estimation in high-dimensional models," Canadian Journal of Economics, Canadian Economics Association, vol. 48(2), pages 389-407, May.
    17. Jianqing Fan & Jinchi Lv & Lei Qi, 2011. "Sparse High-Dimensional Models in Economics," Annual Review of Economics, Annual Reviews, vol. 3(1), pages 291-317, September.
    18. Joel L. Horowitz, 2015. "Variable selection and estimation in high-dimensional models," CeMMAP working papers CWP35/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    19. Kenneth L. Judd & Ben Skrainka, 2011. "High performance quadrature rules: how numerical integration affects a popular model of product differentiation," CeMMAP working papers CWP03/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    20. Michael Keane & Nada Wasi, 2013. "Comparing Alternative Models Of Heterogeneity In Consumer Choice Behavior," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(6), pages 1018-1045, September.
    21. Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Biometrika Trust, vol. 94(3), pages 553-568.
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    More about this item

    Keywords

    Penalized estimation; Adaptive LASSO; Random coefficients; Logit model;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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