  Difference-in-differences is one of the most used identification strategies
in empirical work in economics. This chapter reviews a number of important,
recent developments related to difference-in-differences. First, this chapter
reviews recent work pointing out limitations of two way fixed effects
regressions (these are panel data regressions that have been the dominant
approach to implementing difference-in-differences identification strategies)
that arise in empirically relevant settings where there are more than two time
periods, variation in treatment timing across units, and treatment effect
heterogeneity. Second, this chapter reviews recently proposed alternative
approaches that are able to circumvent these issues without being substantially
more complicated to implement. Third, this chapter covers a number of
extensions to these results, paying particular attention to (i) parallel trends
assumptions that hold only after conditioning on observed covariates and (ii)
strategies to partially identify causal effect parameters in
difference-in-differences applications in cases where the parallel trends
assumption may be violated.

Econometrics