Many
researchers use unit fixed effects regression models as their
default methods for causal inference with longitudinal data. We
show that the ability of these models to adjust for unobserved
time-invariant confounders comes at the expense of dynamic causal
relationships, which are permitted under an alternative
selection-on-observables approach. Using the nonparametric directed
acyclic graph, we highlight two key causal identification
assumptions of unit fixed effects models: past treatments do not
directly influence current outcome, and past outcomes do not affect
current treatment. Furthermore, we introduce a new nonparametric
matching framework that elucidates how various unit fixed effects
models implicitly compare treated and control observations to draw
causal inference. By establishing the equivalence between matching
and weighted unit fixed effects estimators, this framework enables a
diverse set of identification strategies to adjust for unobservables
in the absence of dynamic causal relationships between treatment and
outcome variables. We illustrate the proposed methodology through its
application to the estimation of GATT membership effects on dyadic
trade volume. The
open-source software is
available for implementing the proposed methodology.