Calculate SDID Time Weights (lambda)

Solves the time-weight QP (with implicit intercept lambda_0 concentrated out):

Usage

sdid_time_weights_cpp(Y_pre_co, Y_post_target, zeta_t)

Arguments

Y_pre_co

Pre-treatment outcomes for control units, row-demeaned (T_pre x N_co)

Y_post_target

Post-treatment mean per control unit, demeaned (N_co x 1)

zeta_t

Ridge penalty for time weights (paper: 1e-6 * sigma_hat)

Value

A numeric vector of length T_pre holding the SDID time weights lambda (non-negative and summing to one).

Details

min over lambda in Delta_pre: ||Y_post_target - Y_pre_co^T lambda||^2 + zeta_t^2 * N_co * ||lambda||^2

The caller is responsible for pre-demeaning Y_pre_co (row-wise) and Y_post_target (subtract the cross-unit mean) to concentrate out lambda_0, as described in Arkhangelsky et al. (2021) Algorithm 1, Eq. (2.3).