What do we compare when we run a fixed effects (FE) model on time-series cross-sectional data? If we place the FEs on the cases, then the coefficients compare one time point to another for the same case. If we place the FEs on the time points, then the coefficients compare one case to another at the same point in time. If we place the FEs on both the cases and time points in the same model — two-way FEs — then this model removes confounders that are fixed over time or across cases, but at a cost: the coefficients combine cross-sectional and temporal variance in a way that does not clearly describe how cases differ from one another or how these cases change over time. We urge researchers to avoid employing two-way FEs and instead to focus on choosing a model that directly speaks to the research question of interest.
Link to paper here.