The two-way linear fixed effects
regression (2FE) has become a default method for estimating causal
effects from panel data. Many applied researchers use the 2FE
estimator to adjust for unobserved unit-specific and time-specific
confounders at the same time. Unfortunately, we demonstrate that
the ability of the 2FE model to simultaneously adjust for these
two types of unobserved confounders critically relies upon the
assumption of linear additive effects. Another common justification
for the use of the 2FE estimator is based on its equivalence to
the difference-in-differences estimator under the simplest setting
with two groups and two time periods. We show that this equivalence
does not hold under more general settings commonly encountered in
applied research. Instead, we prove that the multi-period
difference-in-differences estimator is equivalent to the weighted
2FE estimator but with some observations having negative weights.
These analytical results imply that in contrast to the popular
belief, the 2FE estimator does not represent a design-based,
nonparametric estimation strategy for causal inference. Instead,
its validity fundamentally rests on the modeling assumptions. |