Advanced Search
MyIDEAS: Login

Likelihood approximation by numerical integration on sparse grids

Contents:

Author Info

  • 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.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.sciencedirect.com/science/article/B6VC0-4RJYVBD-1/1/7b5d8472f6a7afdc291825c393a2710e
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 144 (2008)
Issue (Month): 1 (May)
Pages: 62-80

as in new window
Handle: RePEc:eee:econom:v:144:y:2008:i:1:p:62-80

Contact details of provider:
Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Hess, Stephane & Train, Kenneth E. & Polak, John W., 2006. "On the use of a Modified Latin Hypercube Sampling (MLHS) method in the estimation of a Mixed Logit Model for vehicle choice," Transportation Research Part B: Methodological, Elsevier, vol. 40(2), pages 147-163, February.
  2. Lee, L.F., 1994. "Simulated Maximum Likelihood Estimation of Dynamic Discrete Choice Statistical Models--Some Monte Carlo Results," Papers 94-06, Michigan - Center for Research on Economic & Social Theory.
  3. Sandor, Zsolt & Andras, P.Peter, 2004. "Alternative sampling methods for estimating multivariate normal probabilities," Journal of Econometrics, Elsevier, vol. 120(2), pages 207-234, June.
  4. Naylor, J. C. & Smith, A. F. M., 1988. "Econometric illustrations of novel numerical integration strategies for Bayesian inference," Journal of Econometrics, Elsevier, vol. 38(1-2), pages 103-125.
  5. Lee, Lung-fei, 2000. "A numerically stable quadrature procedure for the one-factor random-component discrete choice model," Journal of Econometrics, Elsevier, vol. 95(1), pages 117-129, March.
  6. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
  7. Brownstone, David & Train, Kenneth, 1999. "Forecasting new product penetration with flexible substitution patterns," University of California Transportation Center, Working Papers qt1j6814b3, University of California Transportation Center.
  8. Jean-Francois Richard, 2007. "Efficient High-Dimensional Importance Sampling," Working Papers 321, University of Pittsburgh, Department of Economics, revised Jan 2007.
  9. Vassilis A. Hajivassiliou & Axel Borsch-Supan, 1990. "Smooth Unbiased Multivariate Probability Simulators for Maximum Likelihood Estimation of Limited Dependent Variable Models," Cowles Foundation Discussion Papers 960, Cowles Foundation for Research in Economics, Yale University.
  10. Rabe-Hesketh, Sophia & Skrondal, Anders & Pickles, Andrew, 2005. "Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects," Journal of Econometrics, Elsevier, vol. 128(2), pages 301-323, October.
  11. Chiou, Lesley & Walker, Joan L., 2007. "Masking identification of discrete choice models under simulation methods," Journal of Econometrics, Elsevier, vol. 141(2), pages 683-703, December.
  12. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
  13. Viktor Winschel, 2005. "Solving, Estimating and Selecting Nonlinear Dynamic Economic Models without the Curse of Dimensionality," GE, Growth, Math methods 0507014, EconWPA.
  14. Stern, Steven, 1992. "A Method for Smoothing Simulated Moments of Discrete Probabilities in Multinomial Probit Models," Econometrica, Econometric Society, vol. 60(4), pages 943-52, July.
  15. John F. Geweke & Michael P. Keane & David E. Runkle, 1994. "Statistical inference in the multinomial multiperiod probit model," Staff Report 177, Federal Reserve Bank of Minneapolis.
  16. John Geweke, 1995. "Monte Carlo simulation and numerical integration," Staff Report 192, Federal Reserve Bank of Minneapolis.
  17. Butler, J S & Moffitt, Robert, 1982. "A Computationally Efficient Quadrature Procedure for the One-Factor Multinomial Probit Model," Econometrica, Econometric Society, vol. 50(3), pages 761-64, May.
  18. Bhat, Chandra R., 2001. "Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model," Transportation Research Part B: Methodological, Elsevier, vol. 35(7), pages 677-693, August.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Florian Heiss, 2011. "Dynamics of self-rated health and selective mortality," Empirical Economics, Springer, vol. 40(1), pages 119-140, February.
  2. REYNAERT, Mathias & VERBOVEN, Frank, 2012. "Improving the performance of random coefficients demand models: The role of optimal instruments," Working Papers 2012011, University of Antwerp, Faculty of Applied Economics.
  3. 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.
  4. 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.
  5. 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.
  6. Matthew Gentzkow & Jesse M. Shapiro & Michael Sinkinson, 2012. "Competition and Ideological Diversity: Historical Evidence from US Newspapers," NBER Working Papers 18234, National Bureau of Economic Research, Inc.
  7. 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.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:144:y:2008:i:1:p:62-80. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.