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Penalization methods with group-wise sparsity: econometric applications to eBay Motors online auctions

Author

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  • Qing Wang

    (Wellesley College)

  • Dan Zhao

    (Yale University)

Abstract

This paper investigates several recent developments in statistical penalization methods with applications to econometric models and economic data. When the set of covariate variables can be categorized into groups, we propose to use the Group Lasso (Yuan and Lin in J R Stat Soc Ser B 68(1):49–67, 2006) and Sparse Group Lasso (Simon et al. in J Comput Graph Stat 22(2):231–245, 2013) techniques to achieve group-wise sparsity. When estimating a structural model in empirical auctions work, these methods can flexibly control for observable heterogeneity by producing better, simpler first-stage fits for the approaches as proposed by Haile et al. (in: NBER working paper no. 10105, 2003) and Athey and Haile (in: Chapter 60 in handbook of econometrics, Elsevier, Amsterdam, 2007). In applying these methods to eBay Motors auction data, the models with group-wise sparsity are compared to the benchmark models and commonly used penalization methods with only parameter-wise regularization. Empirical results show that the Sparse Group Lasso method yields comparable or even better prediction performance than its counterparts in both linear regression and binary classification. Furthermore, it can drastically reduce the complexity of the model and produce a much more parsimonious model.

Suggested Citation

  • Qing Wang & Dan Zhao, 2019. "Penalization methods with group-wise sparsity: econometric applications to eBay Motors online auctions," Empirical Economics, Springer, vol. 57(2), pages 683-704, August.
  • Handle: RePEc:spr:empeco:v:57:y:2019:i:2:d:10.1007_s00181-018-1460-5
    DOI: 10.1007/s00181-018-1460-5
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    References listed on IDEAS

    as
    1. Philip A. Haile & Han Hong & Matthew Shum, 2003. "Nonparametric Tests for Common Values at First-Price Sealed-Bid Auctions," NBER Working Papers 10105, National Bureau of Economic Research, Inc.
    2. John Asker, 2010. "A Study of the Internal Organization of a Bidding Cartel," American Economic Review, American Economic Association, vol. 100(3), pages 724-762, June.
    3. Vincent, Martin & Hansen, Niels Richard, 2014. "Sparse group lasso and high dimensional multinomial classification," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 771-786.
    4. Elena Krasnokutskaya, 2011. "Identification and Estimation of Auction Models with Unobserved Heterogeneity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(1), pages 293-327.
    5. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    6. Nicola Lacetera & Bradley J. Larsen & Devin G. Pope & Justin R. Sydnor, 2016. "Bid Takers or Market Makers? The Effect of Auctioneers on Auction Outcome," American Economic Journal: Microeconomics, American Economic Association, vol. 8(4), pages 195-229, November.
    7. Gregory Lewis, 2011. "Asymmetric Information, Adverse Selection and Online Disclosure: The Case of eBay Motors," American Economic Review, American Economic Association, vol. 101(4), pages 1535-1546, June.
    8. Matt Shum & Phil Haile & Han Hong, 2003. "Nonparametric Tests for Common Values in First-Price Auctions," Economics Working Paper Archive 501, The Johns Hopkins University,Department of Economics.
    9. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    10. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    11. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    12. Athey, Susan & Haile, Philip A., 2007. "Nonparametric Approaches to Auctions," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 60, Elsevier.
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    Cited by:

    1. Wen Lin, 2023. "The effect of product quantity on willingness to pay: A meta‐regression analysis of beef valuation studies," Agribusiness, John Wiley & Sons, Ltd., vol. 39(3), pages 646-663, July.

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    More about this item

    Keywords

    eBay Motors; Group Lasso; Group-wise sparsity; Penalization; Sparse Group Lasso;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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