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Random Utility Models with Skewed Random Components: the Smallest versus Largest Extreme Value Distribution

Author

Listed:
  • Richard T. Carson
  • Derrick H. Sun
  • Yixiao Sun
Abstract
At the core of most random utility models (RUMs) is an individual agent with a random utility component following a largest extreme value Type I (LEVI) distribution. What if, instead, the random component follows its mirror image -- the smallest extreme value Type I (SEVI) distribution? Differences between these specifications, closely tied to the random component's skewness, can be quite profound. For the same preference parameters, the two RUMs, equivalent with only two choice alternatives, diverge progressively as the number of alternatives increases, resulting in substantially different estimates and predictions for key measures, such as elasticities and market shares. The LEVI model imposes the well-known independence-of-irrelevant-alternatives property, while SEVI does not. Instead, the SEVI choice probability for a particular option involves enumerating all subsets that contain this option. The SEVI model, though more complex to estimate, is shown to have computationally tractable closed-form choice probabilities. Much of the paper delves into explicating the properties of the SEVI model and exploring implications of the random component's skewness. Conceptually, the difference between the LEVI and SEVI models centers on whether information, known only to the agent, is more likely to increase or decrease the systematic utility parameterized using observed attributes. LEVI does the former; SEVI the latter. An immediate implication is that if choice is characterized by SEVI random components, then the observed choice is more likely to correspond to the systematic-utility-maximizing choice than if characterized by LEVI. Examining standard empirical examples from different applied areas, we find that the SEVI model outperforms the LEVI model, suggesting the relevance of its inclusion in applied researchers' toolkits.

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  • Richard T. Carson & Derrick H. Sun & Yixiao Sun, 2024. "Random Utility Models with Skewed Random Components: the Smallest versus Largest Extreme Value Distribution," Papers 2405.08222, arXiv.org, revised May 2024.
    • Handle: RePEc:arx:papers:2405.08222
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    References listed on IDEAS

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    1. Ruud, Paul A., 1986. "Consistent estimation of limited dependent variable models despite misspecification of distribution," Journal of Econometrics, Elsevier, vol. 32(1), pages 157-187, June.
    2. Hausman, Jerry A & Wise, David A, 1977. "Social Experimentation, Truncated Distributions, and Efficient Estimation," Econometrica, Econometric Society, vol. 45(4), pages 919-938, May.
    3. Denzil G. Fiebig & Michael P. Keane & Jordan Louviere & Nada Wasi, 2010. "The Generalized Multinomial Logit Model: Accounting for Scale and Coefficient Heterogeneity," Marketing Science, INFORMS, vol. 29(3), pages 393-421, 05-06.
    4. Richard Paap & Philip Hans Franses, 2000. "A dynamic multinomial probit model for brand choice with different long-run and short-run effects of marketing-mix variables," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(6), pages 717-744.
    5. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555.
    6. Brownstone, David & Train, Kenneth, 1999. "Forecasting new product penetration with flexible substitution patterns," Department of Economics, Working Paper Series qt1j6814b3, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    7. Brownstone, David & Train, Kenneth, 1999. "Forecasting new product penetration with flexible substitution patterns," Department of Economics, Working Paper Series qt3tb6j874, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    8. Keane, Michael P & Wolpin, Kenneth I, 1994. "The Solution and Estimation of Discrete Choice Dynamic Programming Models by Simulation and Interpolation: Monte Carlo Evidence," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 648-672, November.
    9. Hahn, Jinyong & Hausman, Jerry & Lustig, Josh, 2020. "Specification test on mixed logit models," Journal of Econometrics, Elsevier, vol. 219(1), pages 19-37.
    10. Hausman, Jerry & McFadden, Daniel, 1984. "Specification Tests for the Multinomial Logit Model," Econometrica, Econometric Society, vol. 52(5), pages 1219-1240, September.
    11. Brownstone, David & Bunch, David S & Golob, Thomas F & Ren, Weiping, 1996. "A Transactions Choice Model for Forecasting Demand for Alternative-Fuel Vehicles," University of California Transportation Center, Working Papers qt3sm7w9zk, University of California Transportation Center.
    12. Jiang, Zhengyang & Peng, Cameron & Yan, Hongjun, 2024. "Personality differences and investment decision-making," Journal of Financial Economics, Elsevier, vol. 153(C).
    13. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    14. Jain, Dipak C & Vilcassim, Naufel J & Chintagunta, Pradeep K, 1994. "A Random-Coefficients Logit Brand-Choice Model Applied to Panel Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 317-328, July.
    15. Vassilis A. Hajivassiliou & Daniel L. McFadden, 1998. "The Method of Simulated Scores for the Estimation of LDV Models," Econometrica, Econometric Society, vol. 66(4), pages 863-896, July.
    16. Mai, Tien & Bastin, Fabian & Frejinger, Emma, 2017. "On the similarities between random regret minimization and mother logit: The case of recursive route choice models," Journal of choice modelling, Elsevier, vol. 23(C), pages 21-33.
    17. Barbera, Salvador & Pattanaik, Prasanta K, 1986. "Falmagne and the Rationalizability of Stochastic Choices in Terms of Random Orderings," Econometrica, Econometric Society, vol. 54(3), pages 707-715, May.
    18. Cramer,J. S., 2011. "Logit Models from Economics and Other Fields," Cambridge Books, Cambridge University Press, number 9780521188036, September.
    19. Jiang, Zhengyang & Peng, Cameron & Yan, Hongjun, 2024. "Personality differences and investment decision-making," LSE Research Online Documents on Economics 121634, London School of Economics and Political Science, LSE Library.
    20. Wuyang Hu, 2005. "Logit models: smallest versus largest extreme value error distributions," Applied Economics Letters, Taylor & Francis Journals, vol. 12(12), pages 741-744.
    21. Joseph A. Herriges & Catherine L. Kling, 1999. "Nonlinear Income Effects in Random Utility Models," The Review of Economics and Statistics, MIT Press, vol. 81(1), pages 62-72, February.
    22. Sørensen, Jesper R.-V. & Fosgerau, Mogens, 2022. "How McFadden met Rockafellar and learned to do more with less," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    23. Brownstone, David & Train, Kenneth, 1998. "Forecasting new product penetration with flexible substitution patterns," Journal of Econometrics, Elsevier, vol. 89(1-2), pages 109-129, November.
    24. Tomáš Jagelka, 2024. "Are Economists’ Preferences Psychologists’ Personality Traits? A Structural Approach," Journal of Political Economy, University of Chicago Press, vol. 132(3), pages 910-970.
    25. Brownstone, David & Train, Kenneth, 1998. "Forecasting new product penetration with flexible substitution patterns," Journal of Econometrics, Elsevier, vol. 89(1-2), pages 109-129, November.
    26. John K. Dagsvik, 2016. "What independent random utility representations are equivalent to the IIA assumption?," Theory and Decision, Springer, vol. 80(3), pages 495-499, March.
    27. 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.
    28. Meredith Fowlie, 2010. "Emissions Trading, Electricity Restructuring, and Investment in Pollution Abatement," American Economic Review, American Economic Association, vol. 100(3), pages 837-869, June.
    29. P. O. Lindberg & Tony E. Smith, 2017. "A note on a recent paper by Dagsvik on IIA and random utilities," Theory and Decision, Springer, vol. 82(2), pages 305-307, February.
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