Contamination Weights for TWFE Event-Study Coefficients (Sun-Abraham 2021)

Estimates the contamination weights $\omega^{\ell''}_{e,\ell}$ that decompose each TWFE event-study coefficient $\hat\mu_{\ell''}$ into a linear combination of cohort-specific ATTs (CATTs): $$\hat\mu_{\ell''} = \sum_{(e,\ell)} \omega^{\ell''}_{e,\ell} \cdot \widehat{CATT}_{e,\ell}$$ (Sun and Abraham 2021, Equation 20).

The weights are obtained via the OVB auxiliary regression (Eq. 12): for each cohort-period CATT cell $(e, \ell)$, regress the cohort-specific indicator $1\{E_i = e\}\cdot 1\{t-E_i = \ell\}$ on all cohort-aggregated relative-time indicators $D^{\ell''}_{i,t}$ and two-way fixed effects. The resulting regression coefficient on $D^{\ell''}_{i,t}$ is $\omega^{\ell''}_{e,\ell}$.

Usage

compute_contamination_weights(
  data,
  time,
  timing,
  unit,
  fe = NULL,
  baseline = -1L
)

Arguments

data: A data.frame with one row per unit-period (balanced panel).
time: Unquoted name of the calendar time variable (numeric).
timing: Unquoted name of the first-treatment-period variable; NA marks never-treated units.
unit: Unquoted name of the unit identifier.
fe: One-sided fixed-effects formula, e.g. ~ id + year. When NULL (default), falls back to ~ <unit> + <time> with a warning.
baseline: Integer reference (baseline) period excluded from the TWFE specification (default -1L). Must match the baseline argument used in run_es().

Value

An object of class c("sa_contamination_weights", "data.frame") with one row per (catt_cohort, catt_period, twfe_period) triple, and columns:

catt_cohort: Cohort $e$ (first treatment period).
catt_period: Relative event time $\ell$ of the CATT.
twfe_period: Relative event time $\ell''$ of the TWFE coefficient being decomposed.
weight: Contamination weight $\omega^{\ell''}_{e,\ell}$.
is_own: Logical; TRUE when catt_period == twfe_period.

Attributes: baseline, cohorts, cohort_sizes, incl_periods.

Interpretation

Own-period cell (catt_period == twfe_period): $\omega^{\ell}_{{e,\ell}}$ represents the weight the TWFE estimator places on $CATT_{e,\ell}$. Under the SA IW estimator these equal the cohort-size weights $n_e / \sum n_{e'}$.
Cross-period cell (catt_period != twfe_period): Any non-zero weight indicates contamination: the TWFE coefficient $\hat\mu_{\ell''}$ also picks up treatment effects from period $\ell \ne \ell''$.
Verification: the OVB identity (property iii) holds exactly, so $\hat\mu_{\ell''} = \sum_{(e,\ell)} \omega^{\ell''}_{e,\ell} \cdot \widehat{CATT}_{e,\ell}$ up to floating-point precision.

References

Sun, L. and Abraham, S. (2021). Estimating dynamic treatment effects in event studies with heterogeneous treatment effects. Journal of Econometrics, 225(2), 175–199.

Examples

if (FALSE) { # \dontrun{
# Estimate contamination weights
cw <- compute_contamination_weights(
  data     = panel_data,
  time     = year,
  timing   = first_treat,
  unit     = id,
  fe       = ~ id + year,
  baseline = -1L
)
print(cw)
plot_contamination_weights(cw)
} # }