Finite-sample size correction for the doubly robust DiD estimator

The asymptotic standard error of the doubly robust moment of Sant'Anna and Zhao (2020) does not charge for the degrees of freedom the nuisance fits consume, so the test over-rejects when n is small or the treated group is thin. Two standard corrections are applied: the classical HC1 inflation sqrt(n/(n - k)) and a Student-t critical value on min(n1, n0) - 1 degrees of freedom in place of the normal quantile. Both are conservative and both tend to their asymptotic limits as n grows.

Usage

Drbsze(y, D, X = NULL, alpha = 0.05)

Arguments

y

Outcome change, one entry per unit.

D

Binary treatment indicator.

X

Optional baseline covariates.

alpha

Two-sided level, in (0, 1).

Value

List with estimate, se, se_corrected, crit_normal, crit_t, df, ci_lo, ci_hi, reject, reject_naive, n.

References

Sant'Anna, P. H. C. and Zhao, J. (2020). Journal of Econometrics 219(1), 101-122, equation (2.6). MacKinnon, J. G. and White, H. (1985). Journal of Econometrics 29(3), 305-325. Bell, R. M. and McCaffrey, D. F. (2002). Survey Methodology 28(2), 169-181.

Examples

set.seed(1)
r <- Drbsze(y = rnorm(10), D = rbinom(10, 1, 0.5)); TRUE
#> [1] TRUE