SDID defaults are shown throughout. The tighter-optimization reference is added only if its largest period difference exceeds 0.001 or total variation exceeds 0.005; every vector remains in the downloads. “Optimized” holds SDID's penalty fixed—it is not penalty retuning.
All mathematically positive TROP factors are retained, including extremely small values. Calendar/source periods appear on hover and in the exact-value tables; the plotted horizontal axis counts observed pre-periods, which may not be evenly spaced in calendar time. Restricted samples and original design labels are retained. These selected examples do not characterize the whole corpus.
Estimation, tuning, validation and reproducibility
TROP implementation: author package 0.1.11, pinned commit 43738cd. Its weighted untreated-cell least-squares loss includes free unit/time effects and a nuclear-norm penalty. A memory-efficient proximal solver targets this same convex objective without subsampling. It is validated against direct author calls; the largest example has over 100,000 units.
Outcomes are centered at the control pre-period mean and divided by the standard deviation of control pre-period first differences. Three fixed, seeded folds of controls are each assigned placebo treatment over the actual post window. Tuning minimizes the root mean squared placebo treatment effect; actual treated post outcomes are not used.
Coordinate search starts at no localization and no low-rank adjustment. Unit-decay grid: 0, 0.5, 2 in scaled units. Time half-lives: ∞, T₀, T₀/5, T₀/20. Nuclear penalties: ∞ or {1, 0.1, 0.01, 0.001} × twice the spectral norm of the demeaned control matrix. The search updates unit, time and nuclear parameters in that order, reuses the same folds, and stops at an unchanged triplet (six-cycle cap). This is an exploratory grid—not a universal author default or a guarantee of globally optimal tuning. Boundary selections are labeled.
CV fits require relative primal–dual gap ≤10⁻⁶; final fits require ≤10⁻⁸, relative to the weighted additive baseline loss. Final TROP estimates are in the original outcome units, without confidence intervals. When the selected low-rank matrix is zero, a separate four-cell weighted-DiD identity checks the estimate. The original published results and all previous SDID files remain unchanged.