Difference-in-Differences (DiD)

Card and Krueger (1994): NJ minimum wage hike from $4.25 to $5.05 yielded +2.75 FTE by DiD. This refuted classical elasticity theory and triggered a revolution in political economy.

• **Policy:** DiD is the evidentiary standard for minimum wage, tax reform, and lockdown studies in AER and QJE.
• **Tech:** Meta, Airbnb use DiD for geographic feature rollout evaluation without A/B tests.
• **Medicine:** DiD estimates vaccine effectiveness when randomization is unethical.

Classical DiD

Card and Krueger (1994) estimated the impact of New Jersey's minimum wage increase from $4.25 to $5.05 on employment: they compared fast-food restaurants in NJ (treatment) and Pennsylvania (control) before and after. DiD estimate: +2.75 FTE workers -- contrary to classical theory.

Staggered DiD and Heterogeneous Effects

Callaway and Sant'Anna (2021) showed that classical TWFE under staggered adoption yields biased estimates due to 'negative weights'. Meta used this insight to audit A/B rollout tests: old TWFE estimates were biased by up to 40%.

Key ideas

• **DiD:** (Y_T,post - Y_T,pre) - (Y_C,post - Y_C,pre). Removes common trends. Requires parallel trends.
• **TWFE:** Y_it=alpha_i+gamma_t+delta D_it+eps_it. OLS is consistent under parallel trends.
• **Staggered adoption:** classical TWFE is biased with heterogeneous effects -- Callaway-Sant'Anna correction needed.