Difference-in-Differences (DID) Skill

This skill guides complete DID analysis: from assumption validation and model specification to staggered treatment designs and event study regressions. Designed for policy evaluation and natural experiment settings.

Core DID Logic

DID compares the change in outcomes for a treatment group before and after treatment to the change for a control group over the same period.

DID Estimator = (Ȳ_treat,post − Ȳ_treat,pre) − (Ȳ_ctrl,post − Ȳ_ctrl,pre)

Key Assumption (Parallel Trends): In the absence of treatment, the treatment group's outcome would have evolved in parallel with the control group.

DID Workflow

1. Design check: Confirm treatment/control assignment and timing
2. Parallel trends: Test with pre-treatment event study regression
3. Baseline regression: 2×2 DID or TWFE regression
4. Staggered design check: If adoption dates vary, use robust estimators
5. Robustness: Placebo treatment, alternative control groups, callaway-santanna

Basic 2×2 DID Model

Y_it = β₀ + β₁·Treat_i + β₂·Post_t + β₃·(Treat_i × Post_t) + ε_it

β₃ = DID estimate (ATT)

Code Templates

# Python — 2×2 DID with TWFE
import statsmodels.formula.api as smf

# Simple 2x2
model = smf.ols('y ~ treat + post + treat_post', data=df).fit(cov_type='HC3')

# TWFE with entity and time FE (preferred)
from linearmodels.panel import PanelOLS
df_panel = df.set_index(['entity_id', 'year'])
twfe = PanelOLS(df_panel['y'], df_panel[['treat_post']],
                entity_effects=True, time_effects=True)
result = twfe.fit(cov_type='clustered', cluster_entity=True)
print(result.summary)

# R — TWFE
library(plm); library(lmtest); library(sandwich)
panel_df <- pdata.frame(df, index = c("entity_id", "year"))
twfe <- plm(y ~ treat_post, data = panel_df, model = "within", effect = "twoways")
coeftest(twfe, vcov = vcovHC(twfe, cluster = "group"))

* Stata — TWFE with clustered SE
xtset entity_id year
xtreg y treat_post i.year, fe cluster(entity_id)
* Or equivalently:
reghdfe y treat_post, absorb(entity_id year) cluster(entity_id)

Parallel Trends: Event Study Regression

Replace the single treat_post dummy with relative-time dummies to visualize pre-trends:

* Stata — event study
reghdfe y ib(-1).rel_time, absorb(entity_id year) cluster(entity_id)
coefplot, vertical yline(0) xline(0) ///
    title("Event Study: Pre/Post Treatment Effects") ///
    xlabel(, angle(45))

# R — event study
library(fixest)
es_model <- feols(y ~ i(rel_time, treat, ref = -1) | entity_id + year,
                  data = df, cluster = ~entity_id)
iplot(es_model, xlab = "Periods relative to treatment")

Interpreting the event study plot:

• Pre-treatment coefficients ≈ 0 → parallel trends assumption holds
• Pre-trend test: joint F-test for all pre-treatment coefficients = 0
• Post-treatment coefficients show dynamic treatment effects

Staggered DID

When units adopt treatment at different times, standard TWFE can be biased (Callaway-Sant'Anna, Sun-Abraham).

# R — Callaway-Sant'Anna estimator (csdid)
library(did)
cs_result <- att_gt(yname = "y",
                    gname = "cohort_year",   # year of first treatment (0 if never treated)
                    idname = "entity_id",
                    tname  = "year",
                    xformla = ~x1 + x2,
                    data = df)

# Aggregate to average ATT
aggte(cs_result, type = "simple")   # Overall ATT
aggte(cs_result, type = "dynamic")  # Dynamic effects
ggdid(cs_result)

# R — Sun-Abraham (fixest)
library(fixest)
sa_model <- feols(y ~ sunab(cohort_year, year) | entity_id + year,
                  data = df, cluster = ~entity_id)
iplot(sa_model)

* Stata — Callaway-Sant'Anna (csdid from SSC)
csdid y x1 x2, ivar(entity_id) time(year) gvar(cohort_year)
csdid_plot

Robustness Checks for DID

1. Placebo treatment dates: assign fake treatment 1–2 periods before actual treatment
2. Placebo treatment groups: run DID using only control units with a fake treatment
3. Alternative control groups: restrict to more comparable controls
4. Continuous treatment intensity: use dose-response DID

Reporting Standards

• Report event study plot as Figure (essential for credibility)
• State the parallel trends assumption and supporting evidence
• Report DID coefficient with clustered SE (cluster at entity level)
• Discuss potential violations: anticipation effects, Ashenfelter's dip, spillovers
• For staggered designs, always use CS or SA estimators and explain why

See references/did-reference.md for heterogeneous treatment effects, triple-difference models, synthetic control comparison, Borusyak-Jaravel-Spiess imputation estimator, de Chaisemartin-D'Haultfoeuille estimator, and Roth (2022) pre-trends power analysis.

Common Pitfalls

• Using TWFE with staggered treatment and heterogeneous effects: Standard TWFE is biased — use Callaway-Sant'Anna, Sun-Abraham, or Borusyak-Jaravel-Spiess
• Clustering at the treatment level: Don't cluster at the individual level if treatment varies at the state level — cluster at the state level
• Failing to reject pre-trends ≠ parallel trends hold: Low power is common; use Roth (2022) power analysis to assess
• Ignoring anticipation effects: If agents anticipate treatment, pre-treatment coefficients may be non-zero even with parallel trends
• Not showing the event study plot: Reviewers expect to see pre-trends visually — always include the event study figure