Fixed Effects Models

In recent years the massive emergence of multi-dimensional panels has led to an increasing demand for more sophisticated model formulations with respect to the well known two-dimensional ones to address properly the additional heterogeneity in the data. This chapter deals with the most relevant three-dimensional fixed effects model specifications and derives appropriate Least Squares Dummy Variables and Within estimators for them. The main results of the chapter are also generalized for unbalanced panels, cross-sectional dependence in the error terms, and higher dimensional data. Some thoughts on models with varying slope coefficients are also presented.