2.1 Within-unit serial correlation beyond the random effect

The unit random effect $c_i$ in F1 absorbs a single, time-constant deviation per unit. It does not model serial correlation in the idiosyncratic shocks: under F1, $u_{it}$ and $u_{i,t-1}$ are uncorrelated once $c_i$ is conditioned on. In practice, panel outcomes often exhibit residual time-series structure (mean reversion, lagged shocks, sticky deviations) that the random effect alone cannot explain. Bertrand, Duflo, and Mullainathan (2004) is the classic warning that ignoring within-unit serial correlation can drastically understate DiD standard errors.

2.2 Heteroskedasticity across units

F1 imposes a single $\sigma_\varepsilon^2$ across all units. If the residual variance differs across, say, large vs. small states, or volatile vs. stable industries, the model-based variance can be off in either direction relative to a heteroskedasticity-robust alternative.

2.3 Higher-level clustering

F1 treats units as i.i.d. If observations within a state-year, industry-year, or other higher-level grouping share unobserved shocks across multiple sampled units, the variance estimated under F1 will understate the true sampling variability. The package’s current data model does not target this case directly: the natural opt-in cluster level (which is the level the experimental option below uses) is the unit itself.

In all three cases, a textbook fix is to replace the model-based variance with a sandwich estimator that does not rely on the compound-symmetric covariance structure.

3.1 The formula

Let $\widehat{S}$ be the support selected by the bridge regression, $X_{\widehat{S}}$ the corresponding design matrix in the coordinate system the regression was solved in (GLS-transformed for ETWFE/twfeCovs, fusion-then-GLS-transformed for FETWFE/BETWFE), and $\widehat\varepsilon$ the residuals from OLS on that selected support. The cluster-robust variance is

$$V_{\text{CR}} \;=\; \frac{N}{N-1}\; (X_{\widehat{S}}^\top X_{\widehat{S}})^{-1}\; \left(\sum_{i=1}^N X_{i\cdot\widehat{S}}^\top \widehat\varepsilon_{i\cdot} \widehat\varepsilon_{i\cdot}^\top X_{i\cdot\widehat{S}}\right)\; (X_{\widehat{S}}^\top X_{\widehat{S}})^{-1},$$

with units $i = 1, \dots, N$ as clusters and an $N/(N-1)$ small-sample adjustment (matching sandwich::vcovCL(cadjust = TRUE, type = "HC0")). The CATT SE for cohort $r$ is $\sqrt{\psi_r^\top V_{\text{CR}} \psi_r}$ (using a zero-padded $\psi_r$ on the full selected support); the ATT regression-coefficient variance is $\psi_{\text{att}}^\top V_{\text{CR}} \psi_{\text{att}}$, replacing $\mathrm{Var}_1$ above. The second variance term $\mathrm{Var}_2$ (from estimating cohort probabilities) is unchanged because it depends on empirical cohort proportions, not regression residuals; the conservative-vs-asymptotically-exact combination logic also carries through unchanged.

For FETWFE and BETWFE, se_type = "cluster" is only meaningful when q < 1 (the bridge oracle property is required); for q >= 1 the cluster path returns NA just like the default. ETWFE and twfeCovs have no q argument, so the cluster path always runs when the Gram matrix is invertible.

3.2 Why we call this experimental

The CR1 sandwich is a textbook estimator and the package’s implementation matches sandwich::vcovCL() to numerical precision on a clean panel without selection. What is not yet covered by the paper’s theory is:

• Verification that the bridge oracle property of Theorem 6.2 still holds under the relaxed covariance structure that motivates cluster-robust SEs in the first place.
• Sandwich consistency after model selection, i.e., that the CR1 sandwich evaluated at the bridge-selected support is a consistent estimator of the true asymptotic variance.

These extensions are mechanically routine but conceptually non-trivial, and they are explicitly outside the package’s current scope. Until they land, se_type = "cluster" is exposed as an opt-in, clearly-labelled experimental feature.

Recommendation. Until the theory lands, treat se_type = "cluster" as a sensitivity check: report both se_type = "default" and se_type = "cluster" in applied work, comment on the gap, and lean on the default for headline numbers.

3.3 Worked example

set.seed(2026)
sim_coefs <- genCoefs(R = 3, T = 6, d = 2, density = 0.5, eff_size = 2)
sim_data  <- simulateData(
  sim_coefs,
  N = 120,
  sig_eps_sq = 1,
  sig_eps_c_sq = 0.5
)

res_default <- fetwfeWithSimulatedData(sim_data)
res_cluster <- fetwfeWithSimulatedData(sim_data, se_type = "cluster")

c(
  default = res_default$att_se,
  cluster = res_cluster$att_se
)
#>    default    cluster 
#> 0.03444904 0.03576436

On this F1-conforming simulated panel the two SEs are similar by construction: the data-generating process satisfies F1, so the model-based SE is already valid and the cluster-robust SE estimates the same underlying variance. Under a deliberately serially-correlated DGP (or under heteroskedasticity, or higher-level clustering) the cluster-robust SE will typically be larger.

The print() and summary() methods label the SE so it is clear which one was used:

print(res_cluster)
#> Fused Extended Two-Way Fixed Effects Results
#> ===========================================
#> 
#> Overall Average Treatment Effect (ATT):
#>   Estimate:   -0.2148
#>   Std. Error (cluster-robust): 0.0358
#>   P-value:    1.894e-09
#>   Selected:   TRUE
#>   95% CI:    [-0.2849, -0.1447]
#> 
#> Cohort Average Treatment Effects (CATT):
#>  Cohort Estimated TE         SE ConfIntLow ConfIntHigh     P_value selected
#>       2    0.0000000 0.00000000  0.0000000   0.0000000          NA    FALSE
#>       3   -0.5370618 0.05389132 -0.6426869  -0.4314368 2.15468e-23     TRUE
#>       4    0.0000000 0.00000000  0.0000000   0.0000000          NA    FALSE
#> 
#> Model Details:
#>   Units (N)           : 120
#>   Time periods (T)    : 6
#>   Treated cohorts (R) : 3
#>   Covariates (d)      : 2
#>   Features (p)        : 62
#>   Selected size       : 16
#>   Lambda*             : 0.0925

The CATT SEs and confidence intervals in catt_df are recomputed from the same cluster-robust sandwich; the CATT p-values follow accordingly.