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Using a Laplace approximation to estimate the random coefficients logit model by non-linear least squares

Author

Listed:
  • Matthew C. Harding

    (Institute for Fiscal Studies and Stanford University)

  • Jerry Hausman

    () (Institute for Fiscal Studies and MIT)

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 paper 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, both in terms of accuracy and computational time.

Suggested Citation

  • Matthew C. Harding & Jerry Hausman, 2006. "Using a Laplace approximation to estimate the random coefficients logit model by non-linear least squares," CeMMAP working papers CWP01/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:01/06
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    File URL: http://cemmap.ifs.org.uk/wps/cwp0601.pdf
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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, April.
    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. 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.
    3. 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.
    4. 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.
    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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