I show that, even with the assumptions required for them to have a causal interpretation, high dimensional fixed effects estimators, do not recover the average effects of firms or workers on wages if there is heterogeneity or dynamic effects of either firms or workers on wages. This is well-known in the context of differences-in-differences estimation, where two-way fixed effects (TWFE) models do not identify the causal estimands that are typically of interest. Here, I point out that these issues extend to high-dimensional fixed effects estimation, and that these biases are salient in the context of labor economics. Heterogeneous treatment effects correspond to match effects between firms and workers and dynamic treatment effects correspond to firm- and worker-specific tenure-earnings profiles. Typical estimation of match effects in an AKM model (Woodcock, 2015) rely on TWFE estimation that does not identify the average effect in the presence of match effects. I define a notion of average effects that is relevant here, show examples of the bias of TWFE relative to this notion of average effects, and sketch an alternative estimator. The estimator I propose cannot be implemented, and it’s not clear that it would identify the average effect even if it could be. I hope to extend this work to find a better estimator, as well as to implement it on matched employer-employee data and test whether it makes a substantial difference in the conclusions relative to previous work.