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We propose a nonparametric method to study which characteristics provide incremental information for the cross-section of expected returns. We use the adaptive group LASSO to select characteristics and to estimate how selected characteristics affect expected returns nonparametrically. Our method can handle a large number of characteristics and allows for a flexible functional form. Our implementation is insensitive to outliers. Many of the previously identified return predictors don’t provide incremental information for expected returns, and nonlinearities are important. We study our method’s properties in simulations and find large improvements in both model selection and prediction compared to alternative selection methods. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

This article studies non-parametric panel data models with multidimensional, unobserved individual effects when the number of time periods is fixed. I focus on models where the unobservables have a factor structure and enter an unknown structural function non-additively. The setup allows the individual effects to impact outcomes differently in different time periods and it allows for heterogeneous marginal effects. I provide sufficient conditions for point identification of all parameters of the model. Furthermore, I present a non-parametric sieve maximum likelihood estimator as well as flexible semiparametric and parametric estimators. Monte Carlo experiments demonstrate that the estimators perform well in finite samples. Finally, in an empirical application, I use these estimators to investigate the relationship between teaching practice and student achievement. The results differ considerably from those obtained with commonly used panel data methods.

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