  This paper shows that a two-way fixed effects (TWFE) estimator is a weighted
average of first-difference (FD) estimators with different gaps between
periods, generalizing a well-known equivalence theorem in a two-period panel.
Exploiting the identity, I clarify required conditions for the causal
interpretation of the TWFE estimator. I highlight its several limitations and
propose a generalized estimator that overcomes the limitations. An empirical
application on the estimates of the minimum wage effects illustrates that
recognizing the numerical equivalence and making use of the generalized
estimator enable more transparent understanding of what we get from the TWFE
estimator.
