A new procedure for variable selection in presence of rare events

Abstract

This paper proposes a new method to select the most relevant covariates for predicting bank defaults. In particular, as bank failure is a rare event, we estimate the probability of default of financial institutions using Generalized Extreme Value regression and implement a variable selection procedure, suitable when the binary dependent variable has a smaller number of ones than zeros. The proposed procedure has some advantages. First, it does not use any penalized function, and consequently, the estimation of regularization parameters is not required. Second, it is very easy to implement, and thus, it is efficient from a computational perspective. Third, it deals with the dependence structure and works well in the presence of strong correlation in the data. We validate the variable selection procedure by a simulation study. Moreover, we apply the procedure to a dataset of Italian banks and evaluate its performance to identify the most relevant covariates that influence the failure probability. The results of both the simulation study and empirical analysis show that our proposal outperforms other variable selection approaches, such as the forward stepwise method.

Keywords:

• Rare events
• GEV models
• screening
• subsampling
• variable selection

Disclosure statement

No potential conflict of interest was reported by the authors.

Acknowledgements

The authors would like to thank the anonymous referees and the associate editor. Their suggestions and valuable comments considerably helped to improve the paper.

Notes

1 The sample ${\mathbf{Y}}_m^{\left(i\right)}$ needs to have an adequate number of 1’s, as clarified in Section 5.2