Glossary

R: Difference-in-Differences with fixed effects

A quasi-experimental research design that estimates a causal effect by comparing changes over time between a treatment group and a control group. The key identifying assumption — the parallel trends assumption — requires that, absent treatment, both groups would have followed ...

title: Difference-in-Differences (DiD)

slug: did

Definition

Why It Matters

Randomized experiments are often infeasible in economics and public policy. DiD provides a credible path to causal inference by leveraging natural variation in treatment timing across groups. When the parallel trends assumption holds, the design difference-in-differences estimator removes both time-invariant group differences and common time shocks, isolating the treatment effect. Violations of parallel trends, however, produce biased estimates, making pre-trend testing and sensitivity analysis essential.

Example

A state raises its minimum wage while a neighboring state does not. Employment changes in both states are observed before and after the policy. The DiD estimate — the change in employment in the treatment state minus the change in the control state — identifies the causal effect of the minimum wage increase, provided both states would have followed parallel employment trends absent the policy change.

```r

library(fixest)

model <- feols(employment ~ treated * post | state + year, data = df)

```

Related Terms

Software Notes

R: Use fixest for fast twoway fixed-effects DiD; did package for staggered adoption designs with heterogeneous treatment effects (Callaway and Sant'Anna, 2021). Stata: Use reghdfe for twoway FE DiD; csdid for staggered adoption. Python: Use linearmodels for panel DiD; custom implementations for heterogeneous-treatment-effect estimators.