IDEAS home Printed from https://ideas.repec.org/a/wly/japmet/v40y2025i2p237-245.html

A Reassessment of Likelihood Approximation by Integration on Sparse Grids

Author

Listed:
  • Szilárd Madaras
  • Zsolt Sándor

Abstract

This paper revisits sparse grid integration proposed in the literature for approximating integrals that occur as choice probabilities in random coefficient discrete choice models. First, we successfully replicate their main findings for the panel mixed logit. Second, for higher variances and for a different structure of the variances of the random coefficients, in certain cases, we fail to replicate the original results. Third, for the important special case of cross‐sectional mixed logit, replication of the original results is successful when the number of alternatives is moderate but fails otherwise.

Suggested Citation

  • Szilárd Madaras & Zsolt Sándor, 2025. "A Reassessment of Likelihood Approximation by Integration on Sparse Grids," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 40(2), pages 237-245, March.
    • Handle: RePEc:wly:japmet:v:40:y:2025:i:2:p:237-245
    DOI: 10.1002/jae.3108
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/jae.3108
    Download Restriction: no
    File URL: https://libkey.io/10.1002/jae.3108?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Prateek Bansal & Vahid Keshavarzzadeh & Angelo Guevara & Shanjun Li & Ricardo A Daziano, 2022. "Designed quadrature to approximate integrals in maximum simulated likelihood estimation [Evaluating simulation-based approaches and multivariate quadrature on sparse grids in estimating multivariate binary probit models]," The Econometrics Journal, Royal Economic Society, vol. 25(2), pages 301-321.
    2. Heiss, Florian & Winschel, Viktor, 2008. "Likelihood approximation by numerical integration on sparse grids," Journal of Econometrics, Elsevier, vol. 144(1), pages 62-80, May.
    3. 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.
    4. Sun, Yutec & Ishihara, Masakazu, 2019. "A computationally efficient fixed point approach to dynamic structural demand estimation," Journal of Econometrics, Elsevier, vol. 208(2), pages 563-584.
    5. 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.
    6. Kenneth L. Judd & Ben Skrainka, 2011. "High performance quadrature rules: how numerical integration affects a popular model of product differentiation," CeMMAP working papers CWP03/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Mathias Reynaert, 2021. "Abatement Strategies and the Cost of Environmental Regulation: Emission Standards on the European Car Market," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(1), pages 454-488.
    8. Christopher Conlon & Jeff Gortmaker, 2020. "Best practices for differentiated products demand estimation with PyBLP," RAND Journal of Economics, RAND Corporation, vol. 51(4), pages 1108-1161, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Brunner, Daniel & Heiss, Florian & Romahn, André & Weiser, Constantin, 2025. "Simulation error and numerical instability in estimating random coefficient logit demand models," Journal of Econometrics, Elsevier, vol. 247(C).
    2. Pál, László & Sándor, Zsolt, 2023. "Comparing procedures for estimating random coefficient logit demand models with a special focus on obtaining global optima," International Journal of Industrial Organization, Elsevier, vol. 88(C).
    3. Büscher, Sebastian & Bauer, Dietmar, 2024. "Weighting strategies for pairwise composite marginal likelihood estimation in case of unbalanced panels and unaccounted autoregressive structure of the errors," Transportation Research Part B: Methodological, Elsevier, vol. 181(C).
    4. Christopher Conlon & Jeff Gortmaker, 2020. "Best practices for differentiated products demand estimation with PyBLP," RAND Journal of Economics, RAND Corporation, vol. 51(4), pages 1108-1161, December.
    5. Greg Lewis & Bora Ozaltun & Georgios Zervas, 2021. "Maximum Likelihood Estimation of Differentiated Products Demand Systems," Papers 2111.12397, arXiv.org.
    6. Sándor Zsolt, 2013. "Monte Carlo Simulation in Random Coefficient Logit Models Involving Large Sums," Acta Universitatis Sapientiae, Economics and Business, Sciendo, vol. 1(1), pages 85-108, July.
    7. 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.
    8. Kandelhardt, Johannes, 2023. "Flexible estimation of random coefficient logit models of differentiated product demand," DICE Discussion Papers 399, Heinrich Heine University Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).
    9. Santiago Pereda-Fernández, 2021. "Copula-Based Random Effects Models for Clustered Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 575-588, March.
    10. Takeshi Fukasawa, 2024. "Fast and simple inner-loop algorithms of static / dynamic BLP estimations," Papers 2404.04494, arXiv.org, revised Apr 2025.
    11. Reynaert, Mathias & Ale-Chilet, Jorge & Chen, Cuicui & Li, Jing, 2021. "Colluding Against Environmental Regulation," CEPR Discussion Papers 16038, C.E.P.R. Discussion Papers.
    12. Joel L. Horowitz & Lars Nesheim, 2018. "Using penalized likelihood to select parameters in a random coefficients multinomial logit model," CeMMAP working papers CWP29/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    13. Sun, Yutec & Ishihara, Masakazu, 2019. "A computationally efficient fixed point approach to dynamic structural demand estimation," Journal of Econometrics, Elsevier, vol. 208(2), pages 563-584.
    14. Heiss, Florian & Winschel, Viktor, 2008. "Likelihood approximation by numerical integration on sparse grids," Journal of Econometrics, Elsevier, vol. 144(1), pages 62-80, May.
    15. Fournel, Jean-François, 2023. "Electric Vehicle Subsidies: Cost-Effectiveness and Emission Reductions," TSE Working Papers 23-1465, Toulouse School of Economics (TSE), revised Jun 2024.
    16. Augustus Smith, 2025. "The consequences of a British combustion engine ban," Economics Series Working Papers 1083, University of Oxford, Department of Economics.
    17. Takeshi Fukasawa, 2022. "The Biases in Applying Static Demand Models under Dynamic Demand," Discussion Paper Series DP2022-18, Research Institute for Economics & Business Administration, Kobe University, revised Jul 2022.
    18. 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.
    19. Horowitz, Joel L. & Nesheim, Lars, 2021. "Using penalized likelihood to select parameters in a random coefficients multinomial logit model," Journal of Econometrics, Elsevier, vol. 222(1), pages 44-55.
    20. Mabit, Stefan E., 2026. "Mixed logit applications in travel behaviour research," Transportation Research Part A: Policy and Practice, Elsevier, vol. 203(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:japmet:v:40:y:2025:i:2:p:237-245. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.interscience.wiley.com/jpages/0883-7252/ .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.