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Using A Laplace Approximation To Estimate The Random Coefficients Logit Model By Nonlinear Least Squares

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  • Matthew C. Harding
  • Jerry Hausman

Abstract

Current methods of estimating the random coefficients logit model employ simulations of the distribution of the taste parameters through pseudo-random sequences. These methods suffer from difficulties in estimating correlations between parameters and computational limitations such as the curse of dimensionality. This article provides a solution to these problems by approximating the integral expression of the expected choice probability using a multivariate extension of the Laplace approximation. Simulation results reveal that our method performs very well, in terms of both accuracy and computational time. Copyright 2007 by the Economics Department Of The University Of Pennsylvania And Osaka University Institute Of Social And Economic Research Association.

Suggested Citation

  • Matthew C. Harding & Jerry Hausman, 2007. "Using A Laplace Approximation To Estimate The Random Coefficients Logit Model By Nonlinear Least Squares," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1311-1328, November.
  • Handle: RePEc:ier:iecrev:v:48:y:2007:i:4:p:1311-1328
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    References listed on IDEAS

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    1. Hausman, Jerry A & Wise, David A, 1978. "A Conditional Probit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences," Econometrica, Econometric Society, vol. 46(2), pages 403-426, March.
    2. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    3. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387, March.
    4. Patrick Bajari & Han Hong & Stephen Ryan, 2004. "Identification and Estimation of Discrete Games of Complete Information," NBER Technical Working Papers 0301, National Bureau of Economic Research, Inc.
    5. 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.
    6. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    7. Beggs, S. & Cardell, S. & Hausman, J., 1981. "Assessing the potential demand for electric cars," Journal of Econometrics, Elsevier, vol. 17(1), pages 1-19, September.
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    Cited by:

    1. Bordley, Robert F., 2011. "An anti-ideal point representation of economic discrete choice models," Economics Letters, Elsevier, vol. 110(1), pages 60-63, January.
    2. Cherchi, Elisabetta & Guevara, Cristian Angelo, 2012. "A Monte Carlo experiment to analyze the curse of dimensionality in estimating random coefficients models with a full variance–covariance matrix," Transportation Research Part B: Methodological, Elsevier, vol. 46(2), pages 321-332.
    3. Bhat, Chandra R., 2012. "Recent developments in discrete choice model formulation, estimation, and inference," Transportation Research Part B: Methodological, Elsevier, vol. 46(2), pages 273-275.
    4. Burda, Martin & Harding, Matthew & Hausman, Jerry, 2008. "A Bayesian mixed logit-probit model for multinomial choice," Journal of Econometrics, Elsevier, vol. 147(2), pages 232-246, December.
    5. Matzkin, Rosa L., 2012. "Identification in nonparametric limited dependent variable models with simultaneity and unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 166(1), pages 106-115.

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