IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2402.02303.html
   My bibliography  Save this paper

Bootstrapping Fisher Market Equilibrium and First-Price Pacing Equilibrium

Author

Listed:
  • Luofeng Liao
  • Christian Kroer

Abstract

The linear Fisher market (LFM) is a basic equilibrium model from economics, which also has applications in fair and efficient resource allocation. First-price pacing equilibrium (FPPE) is a model capturing budget-management mechanisms in first-price auctions. In certain practical settings such as advertising auctions, there is an interest in performing statistical inference over these models. A popular methodology for general statistical inference is the bootstrap procedure. Yet, for LFM and FPPE there is no existing theory for the valid application of bootstrap procedures. In this paper, we introduce and devise several statistically valid bootstrap inference procedures for LFM and FPPE. The most challenging part is to bootstrap general FPPE, which reduces to bootstrapping constrained M-estimators, a largely unexplored problem. We devise a bootstrap procedure for FPPE under mild degeneracy conditions by using the powerful tool of epi-convergence theory. Experiments with synthetic and semi-real data verify our theory.

Suggested Citation

  • Luofeng Liao & Christian Kroer, 2024. "Bootstrapping Fisher Market Equilibrium and First-Price Pacing Equilibrium," Papers 2402.02303, arXiv.org, revised Mar 2025.
    • Handle: RePEc:arx:papers:2402.02303
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2402.02303
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ramesh Johari & Hannah Li & Inessa Liskovich & Gabriel Y. Weintraub, 2022. "Experimental Design in Two-Sided Platforms: An Analysis of Bias," Management Science, INFORMS, vol. 68(10), pages 7069-7089, October.
    2. Ma, Shuangge & Kosorok, Michael R., 2005. "Robust semiparametric M-estimation and the weighted bootstrap," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 190-217, September.
    3. Matias D. Cattaneo & Michael Jansson & Kenichi Nagasawa, 2020. "Bootstrap‐Based Inference for Cube Root Asymptotics," Econometrica, Econometric Society, vol. 88(5), pages 2203-2219, September.
    4. Bucher, Axel & Segers, Johan & Volgushev, Stanislav, 2014. "When uniform weak convergence fails: empirical processes for dependence functions via epi- and hypographs," LIDAM Reprints ISBA 2014018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Parker, Thomas, 2019. "Asymptotic inference for the constrained quantile regression process," Journal of Econometrics, Elsevier, vol. 213(1), pages 174-189.
    6. Stefan Wager & Kuang Xu, 2021. "Experimenting in Equilibrium," Management Science, INFORMS, vol. 67(11), pages 6694-6715, November.
    7. Hsieh, Yu-Wei & Shi, Xiaoxia & Shum, Matthew, 2022. "Inference on estimators defined by mathematical programming," Journal of Econometrics, Elsevier, vol. 226(2), pages 248-268.
    8. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, September.
    9. Vincent Conitzer & Christian Kroer & Debmalya Panigrahi & Okke Schrijvers & Nicolas E. Stier-Moses & Eric Sodomka & Christopher A. Wilkens, 2022. "Pacing Equilibrium in First Price Auction Markets," Management Science, INFORMS, vol. 68(12), pages 8515-8535, December.
    10. Bose, Arup & Chatterjee, Snigdhansu, 2001. "Generalised bootstrap in non-regular M-estimation problems," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 319-328, December.
    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


    Cited by:

    1. Luofeng Liao & Christian Kroer, 2024. "Statistical Inference and A/B Testing in Fisher Markets and Paced Auctions," Papers 2406.15522, arXiv.org, revised Mar 2025.

    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. Salim Bouzebda & Issam Elhattab & Anouar Abdeldjaoued Ferfache, 2022. "General M-Estimator Processes and their m out of n Bootstrap with Functional Nuisance Parameters," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2961-3005, December.
    2. Luofeng Liao & Christian Kroer, 2024. "Statistical Inference and A/B Testing in Fisher Markets and Paced Auctions," Papers 2406.15522, arXiv.org, revised Mar 2025.
    3. Jinglong Zhao, 2024. "Experimental Design For Causal Inference Through An Optimization Lens," Papers 2408.09607, arXiv.org, revised Aug 2024.
    4. repec:osf:socarx:bwxfz_v1 is not listed on IDEAS
    5. Luo, Shikai & Yang, Ying & Shi, Chengchun & Yao, Fang & Ye, Jieping & Zhu, Hongtu, 2024. "Policy evaluation for temporal and/or spatial dependent experiments," LSE Research Online Documents on Economics 122741, London School of Economics and Political Science, LSE Library.
    6. Shuze Chen & David Simchi-Levi & Chonghuan Wang, 2024. "Improving the Estimation of Lifetime Effects in A/B Testing via Treatment Locality," Papers 2407.19618, arXiv.org, revised Sep 2025.
    7. Firpo, Sergio & Galvao, Antonio F. & Parker, Thomas, 2023. "Uniform inference for value functions," Journal of Econometrics, Elsevier, vol. 235(2), pages 1680-1699.
    8. Yifan Wu & Ramesh Johari & Vasilis Syrgkanis & Gabriel Y. Weintraub, 2024. "Switchback Price Experiments with Forward-Looking Demand," Papers 2410.14904, arXiv.org.
    9. Isaiah Andrews & Jonathan Roth & Ariel Pakes, 2023. "Inference for Linear Conditional Moment Inequalities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(6), pages 2763-2791.
    10. Wenlong Ji & Lihua Lei & Asher Spector, 2023. "Model-Agnostic Covariate-Assisted Inference on Partially Identified Causal Effects," Papers 2310.08115, arXiv.org, revised Nov 2024.
    11. Ozan Candogan & Chen Chen & Rad Niazadeh, 2024. "Correlated Cluster-Based Randomized Experiments: Robust Variance Minimization," Management Science, INFORMS, vol. 70(6), pages 4069-4086, June.
    12. Zach Flynn, 2020. "Identifying productivity when it is a factor of production," RAND Journal of Economics, RAND Corporation, vol. 51(2), pages 496-530, June.
    13. Luofeng Liao & Christian Kroer, 2023. "Statistical Inference and A/B Testing for First-Price Pacing Equilibria," Papers 2301.02276, arXiv.org, revised Jun 2023.
    14. Jizhou Liu & Azeem M. Shaikh & Panos Toulis, 2025. "Randomization Inference in Two-Sided Market Experiments," Papers 2504.06215, arXiv.org.
    15. Jun, Sung Jae & Pinkse, Joris, 2024. "An information–Theoretic approach to partially identified auction models," Journal of Econometrics, Elsevier, vol. 238(2).
    16. Mohsen Bayati & Yuwei Luo & William Overman & Sadegh Shirani & Ruoxuan Xiong, 2024. "Higher-Order Causal Message Passing for Experimentation with Complex Interference," Papers 2411.00945, arXiv.org, revised Feb 2025.
    17. Ruoxuan Xiong & Alex Chin & Sean J. Taylor, 2024. "Data-Driven Switchback Experiments: Theoretical Tradeoffs and Empirical Bayes Designs," Papers 2406.06768, arXiv.org.
    18. Kaido, Hiroaki, 2017. "Asymptotically Efficient Estimation Of Weighted Average Derivatives With An Interval Censored Variable," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1218-1241, October.
    19. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2013. "Testing Many Moment Inequalities," CeMMAP working papers 65/13, Institute for Fiscal Studies.
    20. Patrick Bajari & Jeremy Fox & Stephen Ryan, 2008. "Evaluating wireless carrier consolidation using semiparametric demand estimation," Quantitative Marketing and Economics (QME), Springer, vol. 6(4), pages 299-338, December.
    21. Yuichi Kitamura & Jörg Stoye, 2013. "Nonparametric analysis of random utility models: testing," CeMMAP working papers 36/13, Institute for Fiscal Studies.

    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:arx:papers:2402.02303. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.