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Likelihood approximation by numerical integration on sparse grids

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  • Heiss, Florian
  • Winschel, Viktor

Abstract

The calculation of likelihood functions of many econometric models requires the evaluation of integrals without analytical solutions. Approaches for extending Gaussian quadrature to multiple dimensions discussed in the literature are either very specific or suffer from exponentially rising computational costs in the number of dimensions. We propose an extension that is very general and easily implemented, and does not suffer from the curse of dimensionality. Monte Carlo experiments for the mixed logit model indicate the superior performance of the proposed method over simulation techniques.

Suggested Citation

  • Heiss, Florian & Winschel, Viktor, 2008. "Likelihood approximation by numerical integration on sparse grids," Journal of Econometrics, Elsevier, vol. 144(1), pages 62-80, May.
    • Handle: RePEc:eee:econom:v:144:y:2008:i:1:p:62-80
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    Cited by:

    1. Reynaert, Mathias & Verboven, Frank, 2014. "Improving the performance of random coefficients demand models: The role of optimal instruments," Journal of Econometrics, Elsevier, vol. 179(1), pages 83-98.
    2. Christian Bayer & Markus Siebenmorgen & Raul Tempone, 2016. "Smoothing the payoff for efficient computation of Basket option prices," Papers 1607.05572, arXiv.org, revised Feb 2017.
    3. Jean-Francois Richard, 2016. "Finite Gaussian Mixture Approximations to Analytically Intractable Density Kerkels," Working Paper 5980, Department of Economics, University of Pittsburgh.
    4. Bhat, Chandra R., 2011. "The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models," Transportation Research Part B: Methodological, Elsevier, vol. 45(7), pages 923-939, August.
    5. Michael Chen & Sanjay Mehrotra & Dávid Papp, 2015. "Scenario generation for stochastic optimization problems via the sparse grid method," Computational Optimization and Applications, Springer, vol. 62(3), pages 669-692, December.
    6. Matthew Gentzkow & Jesse M. Shapiro & Michael Sinkinson, 2014. "Competition and Ideological Diversity: Historical Evidence from US Newspapers," American Economic Review, American Economic Association, vol. 104(10), pages 3073-3114, October.
    7. Florian Heiss, 2011. "Dynamics of self-rated health and selective mortality," Empirical Economics, Springer, vol. 40(1), pages 119-140, February.
    8. Maria Polyakova, 2016. "Regulation of Insurance with Adverse Selection and Switching Costs: Evidence from Medicare Part D," American Economic Journal: Applied Economics, American Economic Association, vol. 8(3), pages 165-195, July.
    9. Fox, Jeremy T. & Kim, Kyoo il & Yang, Chenyu, 2016. "A simple nonparametric approach to estimating the distribution of random coefficients in structural models," Journal of Econometrics, Elsevier, vol. 195(2), pages 236-254.
    10. Santiago Pereda Fernández, 2016. "Copula-based random effects models for clustered data," Temi di discussione (Economic working papers) 1092, Bank of Italy, Economic Research and International Relations Area.
    11. Silvia Cagnone & Francesco Bartolucci, 2017. "Adaptive Quadrature for Maximum Likelihood Estimation of a Class of Dynamic Latent Variable Models," Computational Economics, Springer;Society for Computational Economics, vol. 49(4), pages 599-622, April.
    12. Daniel Gerhard & Melanie Bremer & Christian Ritz, 2014. "Estimating marginal properties of quantitative real-time PCR data using nonlinear mixed models," Biometrics, The International Biometric Society, vol. 70(1), pages 247-254, March.
    13. repec:eee:eejocm:v:23:y:2017:i:c:p:9-20 is not listed on IDEAS
    14. Paleti, Rajesh & Bhat, Chandra R., 2013. "The composite marginal likelihood (CML) estimation of panel ordered-response models," Journal of choice modelling, Elsevier, vol. 7(C), pages 24-43.
    15. Florian Heiss & Daniel McFadden & Joachim Winter & Amelie Wuppermann & Bo Zhou, 2016. "Inattention and Switching Costs as Sources of Inertia in Medicare Part D," NBER Working Papers 22765, National Bureau of Economic Research, Inc.
    16. Sándor Zsolt, 2013. "Monte Carlo Simulation in Random Coefficient Logit Models Involving Large Sums," Acta Universitatis Sapientiae, Economics and Business, De Gruyter Open, vol. 1(1), pages 85-108, July.
    17. Eggleston, Jonathan, 2016. "An efficient decomposition of the expectation of the maximum for the multivariate normal and related distributions," Journal of Econometrics, Elsevier, vol. 195(1), pages 120-133.
    18. Abay, Kibrom A., 2015. "Evaluating simulation-based approaches and multivariate quadrature on sparse grids in estimating multivariate binary probit models," Economics Letters, Elsevier, vol. 126(C), pages 51-56.
    19. Justine Hastings & Jesse M. Shapiro, 2012. "Mental Accounting and Consumer Choice: Evidence from Commodity Price Shocks," NBER Working Papers 18248, National Bureau of Economic Research, Inc.
    20. Florian Heiss & Steven F. Venti & David A. Wise, 2014. "The Persistence and Heterogeneity of Health among Older Americans," NBER Working Papers 20306, National Bureau of Economic Research, Inc.
    21. repec:gam:jrisks:v:5:y:2017:i:4:p:57-:d:117091 is not listed on IDEAS
    22. Gerstner, Thomas & Griebel, Michael & Holtz, Markus, 2009. "Efficient deterministic numerical simulation of stochastic asset-liability management models in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 434-446, June.

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