Empirical Economics

, Volume 57, Issue 2, pp 683–704 | Cite as

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

  • Qing WangEmail author
  • Dan Zhao


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.


eBay Motors Group Lasso Group-wise sparsity Penalization Sparse Group Lasso 

JEL Classification

C13 C40 C55 



The authors would like to thank Yao Luo for his help with data collection, Stephen Sheppard and David Salant for their valuable comments. The authors are also grateful for the constructive suggestions from the two anonymous referees that helped improve the manuscript significantly.


  1. Asker J (2010) A study of the internal organization of a bidding cartel. Am Econ Rev 100:724–762Google Scholar
  2. Athey S, Haile PA (2007) Nonparametric approaches to auctions. In: Chapter 60 in handbook of econometrics. Elsevier, AmsterdamGoogle Scholar
  3. Box GEP, Cox DR (1964) An analysis of transformations. J R Stat Soc Ser B 26(2):211–252Google Scholar
  4. Breiman L (1996) Heuristics of instability and stabilization in model selection. Ann Stat 24(6):2350–2383Google Scholar
  5. Cuneo AZ (2003) eBay bids to remake $372B used-car biz; Ads pitch service that “nationalize” local industry. Advert Age 74(19):1Google Scholar
  6. Friedman J, Hastie T, Tibshirani R (2010) Regularization paths for generalized linear models via coordinate descent. J Stat Softw 33(1):1–22Google Scholar
  7. Fu WJ (1998) Penalized regressions: the bridge versus the lasso. J Comput Graph Stat 7(3):397–416Google Scholar
  8. Guerre E, Perrigne I, Vuong Q (2012) Optimal nonparametric estimation of first-price auctions. Econometrica 68(3):525–574Google Scholar
  9. Haile PA, Hong H, Shum M (2003) Nonparametric tests for common values in first-price sealed-bid auctions. In: NBER working paper no. 10105Google Scholar
  10. Hoerl AE, Kennard RW (1970) Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12(1):55–67Google Scholar
  11. Krasnokutskaya E (2011) Identification and estimation of auction models with unobserved heterogeneity. Rev Econ Stud 78(1):293–327Google Scholar
  12. Lacetera N, Larsen BJ, Pope DG, Sydnor JR (2016) Bid takers or market makers? The effect of auctioneers on auction outcome. Am Econ J Microecon 8(4):195–229Google Scholar
  13. Lewis G (2011) Asymmetric information, adverse selection and online disclosure: the case of eBay Motors. Am Econ Rev 101:1535–1546Google Scholar
  14. Lokhorst J (1999) The lasso and generalized linear models. Technical report. University of Adelaide, AdelaideGoogle Scholar
  15. Meier L, van de Geer S, Bhlmann P (2008) The grouped lasso for logistic regression. J R Stat Soc Ser B 70(1):53–71Google Scholar
  16. Piszczalski M (2003) eBay and autos: A new model? Information: technology update. Automot Des Prod 115(3):16–17Google Scholar
  17. R Core Team (2017) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna.
  18. Roth V (2004) The generalized LASSO. IEEE Trans Neural Netw 15(1):16–28Google Scholar
  19. Simon N, Friedman J, Hastie T, Tibshirani R (2013) A sparse-group lasso. J Comput Graph Stat 22(2):231–245Google Scholar
  20. Tibshirani R (1996) Regression shrinkage and selection via the LASSO. J R Stat Soc Ser B 58(1):267–288Google Scholar
  21. Tibshirani R (1997) The LASSO method for variable selection in the Cox model. Stat Med 16:385–395Google Scholar
  22. Vincent M, Hansen NR (2014) Sparse group lasso and high dimensional multinomial classification. Comput Stat Data Anal 71:771–786Google Scholar
  23. Wingfield N, Lundegaard K (2003) Improbably, eBay emerges as a giant in used-car sales. Wall Str J 7:1–5Google Scholar
  24. Xu H, Caramanis C, Mannor S (2012) Sparse algorithms are not stable: a no-free-lunch theorem. IEEE Trans Pattern Anal Mach Intell 34(1):187–93Google Scholar
  25. Yuan M, Lin Y (2006) Model selection and estimation in regression with grouped variables. J R Stat Soc Ser B 68(1):49–67Google Scholar
  26. Zou H, Hastie T (2005) Regularization and variable selection via the elastic net. J R Stat Soc Ser B 67(2):301–320Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics (Science Center)Wellesley CollegeWellesleyUSA
  2. 2.Department of EconomicsYale UniversityNew HavenUSA

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