How does difference-in-differences identify causal effects?

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AcadiFi · Accepted Answer

Difference-in-differences (DiD) compares the change in outcomes over time between a treatment group (affected by policy) and a control group (unaffected), under the parallel trends assumption: absent treatment, both groups would have followed the same trend. The canonical 2x2 DiD estimator: delta = (Y_T,post - Y_T,pre) - (Y_C,post - Y_C,pre), where T is treated and C is control. Equivalent regression: Y_{i,t} = alpha + beta_1 * Treat_i + beta_2 * Post_t + beta_3 * (Treat_i * Post_t) + e_{i,t}. The coefficient beta_3 is the DiD estimate. For Beacon's study: Oregon (treatment) and Washington (control), employment before and after the $15/hour increase. If Oregon employment dropped 2% and Washington rose 1%, DiD = -2% - 1% = -3% attributable to the policy. ```mermaid flowchart LR T1[Treated
pre] --> T2[Treated
post] C1[Control
pre] --> C2[Control
post] T2 --> D[DiD
effect] C2 --> D ``` Key assumptions: (1) parallel trends—pre-treatment trends should match; test by plotting trends or including group-specific time trends; (2) no spillovers from treated to control; (3) treatment timing is exogenous (not chosen in response to anticipated outcomes). Extensions: event study designs allow dynamic treatment effects (leads and lags); staggered DiD with multiple treatment timings uses recent methods (Callaway-Sant'Anna, de Chaisemartin) to avoid two-way FE bias identified by Goodman-Bacon. DiD is the workhorse for policy evaluation in finance (e.g., regulatory changes) and labor economics.

How does difference-in-differences identify causal effects?

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