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 (Simonetal.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 Haileetal.(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.