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Generalized Indirect Inference for Discrete Choice Models


  • Marianne Bruins

    () (Nuffield College and Dept of Economics, Univesity of Oxford)

  • James A. Duffy

    () (Nuffield College, Dept of Economics and Institute for New Economic Thinking at the Oxford Martin School, Univesity of Oxford)

  • Michael P. Keane

    () (Nuffield College and Dept of Economics, Univesity of Oxford)

  • Anthony A. Smith, Jr

    (Yale University)


This paper develops and implements a practical simulation-based method for estimating dynamic discrete choice models. The method, which can accommodate lagged dependent variables, serially correlated errors, unobserved variables, and many alternatives, builds on the ideas of indirect inference. The main difficulty in implementing indirect inference in discrete choice models is that the objective surface is a step function, rendering gradientbased optimization methods useless. To overcome this obstacle, this paper shows how to smooth the objective surface. The key idea is to use a smoothed function of the latent utilities as the dependent variable in the auxiliary model. As the smoothing parameter goes to zero, this function delivers the discrete choice implied by the latent utilities, thereby guaranteeing consistency. We establish conditions on the smoothing such that our estimator enjoys the same limiting distribution as the indirect inference estimator, while at the same time ensuring that the smoothing facilitates the convergence of gradient-based optimization methods. A set of Monte Carlo experiments shows that the method is fast, robust, and nearly as efficient as maximum likelihood when the auxiliary model is sufficiently rich.

Suggested Citation

  • Marianne Bruins & James A. Duffy & Michael P. Keane & Anthony A. Smith, Jr, 2015. "Generalized Indirect Inference for Discrete Choice Models," Economics Papers 2015-W08, Economics Group, Nuffield College, University of Oxford.
  • Handle: RePEc:nuf:econwp:1508

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    References listed on IDEAS

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    6. Cristina Lopez-Mayan, 2014. "Microeconometric Analysis of Residential Water Demand," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 59(1), pages 137-166, September.
    7. Magnac, Thierry & Robin, Jean-Marc & Visser, Michael, 1995. "Analysing Incomplete Individual Employment Histories Using Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(S), pages 153-169, Suppl. De.
    8. Otsu, Taisuke, 2008. "Conditional empirical likelihood estimation and inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 142(1), pages 508-538, January.
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    10. Lee, Lung-Fei, 1997. "Simulated maximum likelihood estimation of dynamic discrete choice statistical models some Monte Carlo results," Journal of Econometrics, Elsevier, vol. 82(1), pages 1-35.
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    Cited by:

    1. Joseph G. Altonji & Anthony A. Smith Jr. & Ivan Vidangos, 2013. "Modeling Earnings Dynamics," Econometrica, Econometric Society, vol. 81(4), pages 1395-1454, July.
    2. José Mustre-del-Río, 2011. "The aggregate implications of individual labor supply heterogeneity," Research Working Paper RWP 11-09, Federal Reserve Bank of Kansas City.
    3. Shintaro Yamaguchi, 2010. "Job Search, Bargaining, and Wage Dynamics," Journal of Labor Economics, University of Chicago Press, vol. 28(3), pages 595-631, July.
    4. Gouriéroux, Christian & Phillips, Peter C.B. & Yu, Jun, 2010. "Indirect inference for dynamic panel models," Journal of Econometrics, Elsevier, vol. 157(1), pages 68-77, July.
    5. Ivan Vidangos, 2009. "Household welfare, precautionary saving, and social insurance under multiple sources of risk," Finance and Economics Discussion Series 2009-14, Board of Governors of the Federal Reserve System (U.S.).
    6. Li Gan & Guan Gong, 2007. "Estimating Interdependence Between Health and Education in a Dynamic Model," NBER Working Papers 12830, National Bureau of Economic Research, Inc.
    7. Matteo Barigozzi & Roxana Halbleib & David Veredas, "undated". "Which model to match?," ULB Institutional Repository 2013/136240, ULB -- Universite Libre de Bruxelles.
    8. repec:eee:econom:v:198:y:2017:i:2:p:189-208 is not listed on IDEAS
    9. Melanie Morten, 2016. "Temporary Migration and Endogenous Risk Sharing in Village India," NBER Working Papers 22159, National Bureau of Economic Research, Inc.
    10. Cristina Lopez-Mayan, 2014. "Microeconometric Analysis of Residential Water Demand," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 59(1), pages 137-166, September.
    11. Kristensen, Dennis & Salanié, Bernard, 2017. "Higher-order properties of approximate estimators," Journal of Econometrics, Elsevier, vol. 198(2), pages 189-208.

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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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