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Mixed MNL models for discrete response

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  • Daniel McFadden

    (Department of Economics, University of California, Berkeley, CA, 94720-3880, USA)

  • Kenneth Train

    (Department of Economics, University of California, Berkeley, CA, 94720-3880, USA)

Abstract

This paper considers mixed, or random coefficients, multinomial logit (MMNL) models for discrete response, and establishes the following results. Under mild regularity conditions, any discrete choice model derived from random utility maximization has choice probabilities that can be approximated as closely as one pleases by a MMNL model. Practical estimation of a parametric mixing family can be carried out by Maximum Simulated Likelihood Estimation or Method of Simulated Moments, and easily computed instruments are provided that make the latter procedure fairly efficient. The adequacy of a mixing specification can be tested simply as an omitted variable test with appropriately defined artificial variables. An application to a problem of demand for alternative vehicles shows that MMNL provides a flexible and computationally practical approach to discrete response analysis. Copyright © 2000 John Wiley & Sons, Ltd.

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Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 15 (2000)
Issue (Month): 5 ()
Pages: 447-470

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Handle: RePEc:jae:japmet:v:15:y:2000:i:5:p:447-470

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  1. Kenneth E. Train, 1998. "Recreation Demand Models with Taste Differences over People," Land Economics, University of Wisconsin Press, vol. 74(2), pages 230-239.
  2. Hajivassiliou, Vassilis A & Ruud, Paul A., 1993. "Classical Estimation Methods for LDV Models Using Simulation," Department of Economics, Working Paper Series qt3cg196fr, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  3. Beggs, John J., 1988. "A simple model for heterogeneity in binary logit models," Economics Letters, Elsevier, vol. 27(3), pages 245-249.
  4. Steven Stern, 1994. "Two Dynamic Discrete Choice Estimation Problems and Simulation Method Solutions," Virginia Economics Online Papers 389, University of Virginia, Department of Economics.
  5. Heckman, James J. & Singer, Burton, 1986. "Econometric analysis of longitudinal data," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 3, chapter 29, pages 1689-1763 Elsevier.
  6. Brownstone, David & Train, Kenneth, 1999. "Forecasting new product penetration with flexible substitution patterns," University of California Transportation Center, Working Papers qt3tb6j874, University of California Transportation Center.
  7. James Heckman & Lance Lochner & Christopher Taber, 1998. "Explaining Rising Wage Inequality: Explanations With A Dynamic General Equilibrium Model of Labor Earnings With Heterogeneous Agents," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 1(1), pages 1-58, January.
  8. Westin, Richard B., 1974. "Predictions from binary choice models," Journal of Econometrics, Elsevier, vol. 2(1), pages 1-16, May.
  9. McFadden, Daniel L., 1984. "Econometric analysis of qualitative response models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 24, pages 1395-1457 Elsevier.
  10. Enberg, John & Gottschalk, Peter & Wolf, Douglas, 1990. "A random-effects logit model of work-welfare transitions," Journal of Econometrics, Elsevier, vol. 43(1-2), pages 63-75.
  11. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245 Elsevier.
  12. Westin, Richard B. & Gillen, David W., 1978. "Parking location and transit demand : A case study of endogenous attributes in disaggregate mode choice models," Journal of Econometrics, Elsevier, vol. 8(1), pages 75-101, August.
  13. Dagsvik, John K, 1994. "Discrete and Continuous Choice, Max-Stable Processes, and Independence from Irrelevant Attributes," Econometrica, Econometric Society, vol. 62(5), pages 1179-1205, September.
  14. Steckel, Joel H & Vanhonacker, Wilfried R, 1988. "A Heterogeneous Conditional Logit Model of Choice," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(3), pages 391-98, July.
  15. Daniel McFadden, 1987. "A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration," Working papers 464, Massachusetts Institute of Technology (MIT), Department of Economics.
  16. McFadden, Daniel & Ruud, Paul A, 1994. "Estimation by Simulation," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 591-608, November.
  17. 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.
  18. Chesher, Andrew & Santos Silva, J M C, 2002. "Taste Variation in Discrete Choice Models," Review of Economic Studies, Wiley Blackwell, vol. 69(1), pages 147-68, January.
  19. S Reader, 1993. "Unobserved heterogeneity in dynamic discrete choice models," Environment and Planning A, Pion Ltd, London, vol. 25(4), pages 495-519, April.
  20. Train, Kenneth E & McFadden, Daniel L & Goett, Andrew A, 1987. "Consumer Attitudes and Voluntary Rate Schedules for Public Utilities," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 383-91, August.
  21. Brownstone, David & Bunch, David S. & Golob, Thomas F. & Ren, Weiping, 1996. "A Transaction Choice Model for Forecasting Demand for Alternative-Fuel Vehicles," University of California Transportation Center, Working Papers qt0244r8g2, University of California Transportation Center.
  22. V A Hajivassiliou & DL McFadden, 1997. "The Method of Simulated Scores for the Estimation of LDV Models," STICERD - Econometrics Paper Series /1997/328, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  23. Kenneth Train, . "Simulation Methods for Probit and Related Models Based on Convenient Error Partitioning," Working Papers _009, University of California at Berkeley, Econometrics Laboratory Software Archive.
  24. David Revelt & Kenneth Train, 1998. "Mixed Logit With Repeated Choices: Households' Choices Of Appliance Efficiency Level," The Review of Economics and Statistics, MIT Press, vol. 80(4), pages 647-657, November.
  25. Heckman, James & Singer, Burton, 1984. "A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data," Econometrica, Econometric Society, vol. 52(2), pages 271-320, March.
  26. Lee, Lung-Fei & Chesher, Andrew, 1986. "Specification testing when score test statistics are identically zero," Journal of Econometrics, Elsevier, vol. 31(2), pages 121-149, March.
  27. Chavas, Jean-Paul & Segerson, Kathleen, 1986. "Singularity and Auotregressive Disturbances in Linear Logit Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(2), pages 161-69, April.
  28. 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 317-28, July.
  29. McFadden, Daniel, 1987. "Regression-based specification tests for the multinomial logit model," Journal of Econometrics, Elsevier, vol. 34(1-2), pages 63-82.
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