Estimation of Panel Models with Group Structures in Fixed Effects: Extending the Standard Linear

Recent contributions to the econometrics literature present new estimation approaches to panel models with group fixed effects, which use a machine learning step to group individual fixed effects for dimension reduction. We focus on the approach with unsupervised non-parametric density based clustering with unknown number of groups and unknown group location. Only similar units are estimated to belong to the same group, while the non-clustered remain atomic units. This paper extends this approach beyond the standard linear fixed-effects model. We first allow for additional endogeneities due to correlation between the covariates and the time-varying error term. Our simulations confirm that the approach is applicable in the context of instrumental variable estimation. We then introduce an adapted estimation approach for non-linear models with group fixed effects. Simulations for the fixed effects Poisson and fixed effects fractional regression show desirable finite sample performance and demonstrate an effective solution to the incidental parameter problem of non-linear models with individual fixed effects. We demonstrate the practicality of the approaches with real data applications.