=== ITEM LEVEL === item n share_present coef_P_main_z se_P_main_z coef_D_pc1_z se_D_pc1_z coef_K_mean_z se_K_mean_z decline 93 0.409 1.114 0.364 0.593 0.287 0.101 0.260 collapse 126 0.016 5.697 2.605 -0.489 0.479 -0.994 0.393 downward_mobility 123 0.447 0.281 0.180 0.199 0.188 0.045 0.196 extermination 122 0.139 0.321 0.336 0.545 0.284 0.460 0.240 uprising 123 0.455 0.153 0.191 0.466 0.227 0.515 0.239 revolution 117 0.171 0.497 0.254 0.659 0.407 0.566 0.383 successful_revolution 121 0.099 0.586 0.273 1.100 0.576 1.437 0.937 civil_war 124 0.540 0.307 0.212 0.449 0.191 0.350 0.199 century_plus 126 0.056 -0.726 0.360 -0.871 0.378 -0.521 0.318 fragmentation 127 0.346 0.207 0.192 0.122 0.197 -0.003 0.190 capital 116 0.181 0.059 0.233 0.121 0.228 0.127 0.234 conquest 124 0.395 -0.117 0.189 -0.055 0.194 0.027 0.189 assassination 115 0.400 0.519 0.206 0.659 0.238 0.387 0.249 depose 113 0.496 0.223 0.198 0.544 0.207 0.561 0.232 {'mean_interitem_corr': 0.07944663342813164, 'median_interitem_corr': 0.066622495165543, 'first_eigen_share': 0.18913552099018466, 'n_items': 14} corr(K_mean, polities per NGA) = 0.292 === PRIMARY (Y1 fractional logit, cluster region) === model term coef se p n A1 primary: Y1 ~ P + FE P_main_z 0.196 0.056 0.000 127 A2: Y1 ~ P + X + FE P_main_z 0.243 0.086 0.004 93 A3: Y1 ~ P + complexity PC1 + X + FE P_main_z 0.243 0.087 0.005 93 B1 baseline D only D_pc1_z 0.416 0.173 0.016 93 B2 baseline K only K_mean_z 0.041 0.248 0.870 93 B3 baseline complexity PC1 complexity_pc1_z 0.078 0.313 0.803 93 B4 baseline persistence prior_crisis_nga 0.373 0.202 0.065 93 B5 D and K separately D_pc1_z 0.440 0.170 0.010 93 B5 D and K separately K_mean_z -0.126 0.188 0.503 93 B5 Wald test of beta_D + beta_K = 0 (restriction implied by P) D+K 0.314 0.257 0.222 93 Placebo: P built with production infrastructure instead of K (X = warfare only) P_placebo 0.192 0.166 0.247 93 Placebo comparison: P with the same controls (X = warfare only) P_main_z 0.290 0.079 0.000 93 A1b: Y1b ~ P + region FE (logit, HC1; era FE dropped: separation) P_main_z -0.178 0.203 0.381 123 A2b: Y1b ~ P + X + region FE (logit, HC1) P_main_z 0.254 0.316 0.422 91 A3b: Y1b ~ P (logit, HC1, no FE) P_main_z -0.068 0.180 0.703 123 Exploratory: reform consequences ~ P + X + FE P_main_z -0.013 0.164 0.937 91 === ROBUSTNESS === model term coef se p n R: K = IRT latent _P 0.175 0.082 0.032 100 R: D = log population only _P 0.279 0.109 0.010 76 R: K = PC1 of blocks _P 0.247 0.084 0.003 93 R: D at lower bounds _P 0.237 0.087 0.007 93 R: D at upper bounds _P 0.244 0.085 0.004 93 R: inferred codes dropped _P 0.131 0.060 0.029 77 R: standardized within era _P 0.265 0.091 0.004 93 R: standardized within macro-region _P 0.224 0.085 0.008 93 R: rank-based P _P 0.185 0.076 0.016 93 R: D without settlement hierarchy _P 0.249 0.074 0.001 84 R: K without administrative levels _P 0.250 0.088 0.005 94 R: both hierarchy indicators removed _P 0.247 0.068 0.000 85 R: quasi-polities dropped P_main_z 0.205 0.101 0.042 87 R: crises starting ≥25 years after polity start P_main_z 0.305 0.095 0.001 79 R: ≥12 of 14 items coded P_main_z 0.250 0.091 0.006 88 R: no era FE P_main_z 0.296 0.111 0.008 93 R: no region FE P_main_z 0.277 0.079 0.000 93 R: no FE P_main_z 0.288 0.095 0.002 93 R: SE clustered by NGA P_main_z 0.243 0.074 0.001 93 R: SE clustered by polity P_main_z 0.243 0.088 0.006 93 === OOS wins of A2 over baselines === model baseline folds win_share mean_diff scheme A2 P B0 FE only 10 1.00 0.016 loro A2 P B1 D only 10 0.20 -0.004 loro A2 P B2 K only 10 1.00 0.017 loro A2 P B3 complexity 10 1.00 0.017 loro A2 P B4 persistence 10 0.70 0.011 loro A2 P B5 D+K 10 0.20 -0.004 loro A2 P B0 FE only 50 0.86 0.008 kfold A2 P B1 D only 50 0.42 -0.001 kfold A2 P B2 K only 50 0.84 0.011 kfold A2 P B3 complexity 50 0.84 0.011 kfold A2 P B4 persistence 50 0.78 0.005 kfold A2 P B5 D+K 50 0.44 0.001 kfold === Y1b OOS summary === model oos_loglik auc brier A2 P -1.192 0.702 0.219 B0 FE only -1.172 0.716 0.214 B1 D only -1.196 0.703 0.218 B2 K only -1.191 0.708 0.218 B3 complexity -1.194 0.703 0.220 B4 persistence -1.206 0.702 0.224 B5 D+K -1.216 0.693 0.223 === H4 === { "folds": 50, "hinge_beats_linear_share": 0.1, "spline_beats_linear_share": 0.08, "mean_ll_linear": -0.5997872195502219, "mean_ll_hinge": -0.6046239254037978, "mean_ll_spline": -0.6014858334143698, "median_knot": 0.202378235149079, "insample_knot": 0.920093143962066, "insample_hinge_coef": -0.3443603832338329, "insample_P_coef": 0.30680452291054316 } === H5 === model coef se p n held_out_n within_block_coef within_block_se H5 leave-region-out: Central_Asia 0.275 0.080 0.001 89 13 NaN NaN H5 leave-region-out: East_Asia 0.269 0.103 0.009 70 30 0.362 0.083 H5 leave-region-out: Europe 0.366 0.096 0.000 78 39 0.187 0.164 H5 leave-region-out: North_Africa 0.281 0.080 0.000 83 12 NaN NaN H5 leave-region-out: North_America 0.266 0.088 0.002 89 13 NaN NaN H5 leave-region-out: South_America 0.285 0.085 0.001 90 6 NaN NaN H5 leave-region-out: South_Asia 0.269 0.078 0.001 88 5 NaN NaN H5 leave-region-out: Southeast_Asia_Oceania 0.255 0.090 0.005 86 13 NaN NaN H5 leave-region-out: Southwest_Asia 0.264 0.087 0.002 75 29 0.437 0.234 H5 leave-region-out: Sub_Saharan_Africa 0.236 0.065 0.000 89 6 NaN NaN H5 leave-era-out: 1-1000 0.336 0.130 0.010 71 40 0.193 0.182 H5 leave-era-out: 1000BCE-0 0.255 0.146 0.081 73 28 0.390 0.145 H5 leave-era-out: 1001-1500 0.310 0.112 0.006 70 43 0.316 0.152 H5 leave-era-out: 1501-1800 0.267 0.084 0.001 79 31 0.325 0.483 H5 leave-era-out: post-1800 0.287 0.121 0.018 86 16 0.208 0.264 H5 leave-era-out: pre-1000BCE 0.293 0.114 0.010 86 8 NaN NaN H5 leave-sphere-out: Andes_Amazonia 0.285 0.085 0.001 90 6 NaN NaN H5 leave-sphere-out: East_Asia 0.269 0.103 0.009 70 30 0.362 0.083 H5 leave-sphere-out: Europe 0.366 0.096 0.000 78 38 0.187 0.164 H5 leave-sphere-out: Mesoamerica_North_America 0.266 0.088 0.002 89 13 NaN NaN H5 leave-sphere-out: Oceania 0.278 0.091 0.002 91 6 NaN NaN H5 leave-sphere-out: South_Asia 0.269 0.078 0.001 88 5 NaN NaN H5 leave-sphere-out: Southeast_Asia 0.272 0.077 0.000 88 7 NaN NaN H5 leave-sphere-out: Steppe_Central_Asia 0.279 0.079 0.000 91 12 NaN NaN H5 leave-sphere-out: Sub_Saharan_Africa 0.236 0.065 0.000 89 6 NaN NaN H5 leave-sphere-out: West_Asia_North_Africa 0.274 0.089 0.002 63 43 0.401 0.393 === Y2 Cox / Y3 === model term coef se p n events hr schoenfeld_p_P Y2-1 Cox: P + strata(macro-region) P_z 0.031 0.060 0.600 317 302 1.032 NaN Y2-2 Cox: P + X + midpoint + strata P_z 0.000 0.068 0.995 208 201 1.000 0.983 Y2-3 Cox: D + K + X + midpoint + strata D_pc1_z 0.128 0.133 0.336 208 201 1.136 NaN Y2-3 Cox: D + K + X + midpoint + strata K_mean_z 0.559 0.200 0.005 208 201 1.749 NaN Y2-4 Cox: complexity PC1 + X + strata complexity_pc1_z 0.399 0.291 0.171 208 201 1.490 NaN Y2-5 Cox: D + K + X + midpoint + polities per NGA (periodization) + strata D_pc1_z 0.082 0.135 0.544 206 200 1.086 NaN Y2-5 Cox: D + K + X + midpoint + polities per NGA (periodization) + strata K_mean_z 0.535 0.203 0.009 206 200 1.707 NaN Y2-5 Cox: D + K + X + midpoint + polities per NGA (periodization) + strata n_polities_in_nga_z 0.317 0.140 0.023 206 200 1.373 NaN Y3-1 logit: discontinuous succession ~ P + FE P_z 0.018 0.393 0.964 145 24 NaN NaN Y3-2 logit: + X P_z 0.239 0.325 0.461 117 18 NaN NaN