Population and sample construction
This extension covers the 14 papers classified as possible balanced-sample or earlier-cohort rescues in the preceding inventory. The frozen roster has 418 cohort–outcome blocks across 64 prepared specifications. Each block uses the source outcome and treatment definition; outcomes are not imputed, and no new treatment threshold is introduced. The original collection and previously reported fits remain unchanged.
A deterministic rule is applied before fitting: use complete treated-cohort and control units over the entire prepared window when that yields at least two controls and one treated unit. Otherwise, end immediately before the next adoption cohort, add later adopters while they remain untreated, and retain complete units in that window. The start of the prepared pre-period is unchanged. The resulting split is 315 full-window and 103 shortened-window blocks.
These choices change the sample or horizon. Retention, source specification, window, later-adopter donor counts and earlier preparation steps are exported. Raw treatment indicators were checked within each selected window: no exposed donor or treated-unit reversal remains in those windows. This does not make reversing treatments globally absorbing or remove concerns about anticipation, spillovers, sample selection, or the causal interpretation of the original design. Fiscal Capacity retains its existing mixed-IV classification; E-governance retains its pending classification. These computations do not decide eligibility.
Estimation target
The target is the SDID time-weight component. In the no-covariate author implementation this is separable from unit-weight fitting. This extension does not calculate new effect estimates, unit weights, or bootstrap intervals. The author time solver and its defaults (including sparsification) are used, with an independent quadratic-program comparison at the same default penalty. “Optimized” refers to numerical optimization, not penalty selection.
Let A be the donor pre-outcome matrix and b its mean post-outcome vector, both centered across donors to profile out the free intercept and divided by the default noise scale. The objective is mean squared prediction error plus 10^-12 times the squared Euclidean norm of the time weights, on the simplex. A gap of at most 10^-8 and raw feasibility violation of at most 10^-8 are the numerical objective checks. Such weak regularization can leave weights poorly determined even when the objective gap is small. Both QP initializations and rank diagnostics are retained; high-precision follow-up is reported separately.
Large donor panels
For tall donor matrices, a QR reduction preserves the complete time objective. If the centered, unscaled matrix D = [A, b] has QR factor R with r rows, use sqrt(r/N0) R as the input to the same author solver, with the intercept already profiled out. Its mean-square loss, ridge penalty, Frank–Wolfe step, sparsification and stopping criterion are unchanged in exact arithmetic. No donor is subsampled. Twenty direct-author steps are compared with reduced steps for every reduced block, and a full direct-author fit is checked for each preselected example. Floating-point differences and checks are exported.
Numerical results
| default |
36 |
43 |
| qp_default_start |
360 |
0 |
| qp_uniform |
360 |
0 |
| 7 |
aeraej-105-source–y__d–c157 |
1.94192384 |
0.74611239 |
0 |
| 15 |
aeraej-120-source–y__d–c017 |
1.76260268 |
0.63180531 |
0 |
| 6 |
aeraej-105-source–y__d–c148 |
1.46241904 |
0.33399328 |
0 |
| 14 |
aeraej-120-source–y__d–c012 |
0.48627137 |
0.13732353 |
0 |
| 296 |
S18-P010–y__d–c282 |
0.10393027 |
0.05196514 |
0 |
| 289 |
S18-P010–y__d–c148 |
0.00163422 |
0.00081711 |
0 |
| 77 |
S04-P001–y__d–c005 |
0.00000000 |
0.00000000 |
0 |
| 1 |
AEJ159-T5A1–l_subsidy_rate__cgvo–c005 |
0.00000000 |
0.00000000 |
0 |
| 2 |
AEJ159-T5A1–l_subsidy_rate__cgvo–c008 |
0.00000000 |
0.00000000 |
0 |
| 3 |
AEJ159-T5A1–l_subsidy_rate__cgvo–c009 |
0.00000000 |
0.00000000 |
0 |
| 4 |
AEJ159-T5A1–l_subsidy_rate__cgvo–c010 |
0.00000000 |
0.00000000 |
0 |
| 5 |
AEJ159-T5A1–l_subsidy_rate__cgvo–c012 |
0.00000000 |
0.00000000 |
0 |
The CSVs retain all zeros and small weights. Support thresholds are diagnostic; no thresholded vector is substituted for a fitted vector. Multiple outcomes and cohorts share data and donor pools, so the blocks are dependent examples.