12=== ITEM LEVEL ===3 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_z4 decline 93 0.409 1.114 0.364 0.593 0.287 0.101 0.2605 collapse 126 0.016 5.697 2.605 -0.489 0.479 -0.994 0.3936 downward_mobility 123 0.447 0.281 0.180 0.199 0.188 0.045 0.1967 extermination 122 0.139 0.321 0.336 0.545 0.284 0.460 0.2408 uprising 123 0.455 0.153 0.191 0.466 0.227 0.515 0.2399 revolution 117 0.171 0.497 0.254 0.659 0.407 0.566 0.38310successful_revolution 121 0.099 0.586 0.273 1.100 0.576 1.437 0.93711 civil_war 124 0.540 0.307 0.212 0.449 0.191 0.350 0.19912 century_plus 126 0.056 -0.726 0.360 -0.871 0.378 -0.521 0.31813 fragmentation 127 0.346 0.207 0.192 0.122 0.197 -0.003 0.19014 capital 116 0.181 0.059 0.233 0.121 0.228 0.127 0.23415 conquest 124 0.395 -0.117 0.189 -0.055 0.194 0.027 0.18916 assassination 115 0.400 0.519 0.206 0.659 0.238 0.387 0.24917 depose 113 0.496 0.223 0.198 0.544 0.207 0.561 0.232 18 {'mean_interitem_corr': 0.07944663342813164, 'median_interitem_corr': 0.066622495165543, 'first_eigen_share': 0.18913552099018466, 'n_items': 14}19corr(K_mean, polities per NGA) = 0.29220=== PRIMARY (Y1 fractional logit, cluster region) ===21 model term coef se p n22 A1 primary: Y1 ~ P + FE P_main_z 0.196 0.056 0.000 12723 A2: Y1 ~ P + X + FE P_main_z 0.243 0.086 0.004 9324 A3: Y1 ~ P + complexity PC1 + X + FE P_main_z 0.243 0.087 0.005 9325 B1 baseline D only D_pc1_z 0.416 0.173 0.016 9326 B2 baseline K only K_mean_z 0.041 0.248 0.870 9327 B3 baseline complexity PC1 complexity_pc1_z 0.078 0.313 0.803 9328 B4 baseline persistence prior_crisis_nga 0.373 0.202 0.065 9329 B5 D and K separately D_pc1_z 0.440 0.170 0.010 9330 B5 D and K separately K_mean_z -0.126 0.188 0.503 9331 B5 Wald test of beta_D + beta_K = 0 (restriction implied by P) D+K 0.314 0.257 0.222 9332Placebo: P built with production infrastructure instead of K (X = warfare only) P_placebo 0.192 0.166 0.247 9333 Placebo comparison: P with the same controls (X = warfare only) P_main_z 0.290 0.079 0.000 9334 A1b: Y1b ~ P + region FE (logit, HC1; era FE dropped: separation) P_main_z -0.178 0.203 0.381 12335 A2b: Y1b ~ P + X + region FE (logit, HC1) P_main_z 0.254 0.316 0.422 9136 A3b: Y1b ~ P (logit, HC1, no FE) P_main_z -0.068 0.180 0.703 12337 Exploratory: reform consequences ~ P + X + FE P_main_z -0.013 0.164 0.937 913839=== ROBUSTNESS ===40 model term coef se p n41 R: K = IRT latent _P 0.175 0.082 0.032 10042 R: D = log population only _P 0.279 0.109 0.010 7643 R: K = PC1 of blocks _P 0.247 0.084 0.003 9344 R: D at lower bounds _P 0.237 0.087 0.007 9345 R: D at upper bounds _P 0.244 0.085 0.004 9346 R: inferred codes dropped _P 0.131 0.060 0.029 7747 R: standardized within era _P 0.265 0.091 0.004 9348 R: standardized within macro-region _P 0.224 0.085 0.008 9349 R: rank-based P _P 0.185 0.076 0.016 9350 R: D without settlement hierarchy _P 0.249 0.074 0.001 8451 R: K without administrative levels _P 0.250 0.088 0.005 9452 R: both hierarchy indicators removed _P 0.247 0.068 0.000 8553 R: quasi-polities dropped P_main_z 0.205 0.101 0.042 8754R: crises starting ≥25 years after polity start P_main_z 0.305 0.095 0.001 7955 R: ≥12 of 14 items coded P_main_z 0.250 0.091 0.006 8856 R: no era FE P_main_z 0.296 0.111 0.008 9357 R: no region FE P_main_z 0.277 0.079 0.000 9358 R: no FE P_main_z 0.288 0.095 0.002 9359 R: SE clustered by NGA P_main_z 0.243 0.074 0.001 9360 R: SE clustered by polity P_main_z 0.243 0.088 0.006 936162=== OOS wins of A2 over baselines ===63 model baseline folds win_share mean_diff scheme64 A2 P B0 FE only 10 1.00 0.016 loro65 A2 P B1 D only 10 0.20 -0.004 loro66 A2 P B2 K only 10 1.00 0.017 loro67 A2 P B3 complexity 10 1.00 0.017 loro68 A2 P B4 persistence 10 0.70 0.011 loro69 A2 P B5 D+K 10 0.20 -0.004 loro70 A2 P B0 FE only 50 0.86 0.008 kfold71 A2 P B1 D only 50 0.42 -0.001 kfold72 A2 P B2 K only 50 0.84 0.011 kfold73 A2 P B3 complexity 50 0.84 0.011 kfold74 A2 P B4 persistence 50 0.78 0.005 kfold75 A2 P B5 D+K 50 0.44 0.001 kfold7677=== Y1b OOS summary ===78 model oos_loglik auc brier79 A2 P -1.192 0.702 0.21980 B0 FE only -1.172 0.716 0.21481 B1 D only -1.196 0.703 0.21882 B2 K only -1.191 0.708 0.21883 B3 complexity -1.194 0.703 0.22084B4 persistence -1.206 0.702 0.22485 B5 D+K -1.216 0.693 0.2238687=== H4 === {88 "folds": 50,89 "hinge_beats_linear_share": 0.1,90 "spline_beats_linear_share": 0.08,91 "mean_ll_linear": -0.5997872195502219,92 "mean_ll_hinge": -0.6046239254037978,93 "mean_ll_spline": -0.6014858334143698,94 "median_knot": 0.202378235149079,95 "insample_knot": 0.920093143962066,96 "insample_hinge_coef": -0.3443603832338329,97 "insample_P_coef": 0.3068045229105431698}99100=== H5 ===101 model coef se p n held_out_n within_block_coef within_block_se102 H5 leave-region-out: Central_Asia 0.275 0.080 0.001 89 13 NaN NaN103 H5 leave-region-out: East_Asia 0.269 0.103 0.009 70 30 0.362 0.083104 H5 leave-region-out: Europe 0.366 0.096 0.000 78 39 0.187 0.164105 H5 leave-region-out: North_Africa 0.281 0.080 0.000 83 12 NaN NaN106 H5 leave-region-out: North_America 0.266 0.088 0.002 89 13 NaN NaN107 H5 leave-region-out: South_America 0.285 0.085 0.001 90 6 NaN NaN108 H5 leave-region-out: South_Asia 0.269 0.078 0.001 88 5 NaN NaN109 H5 leave-region-out: Southeast_Asia_Oceania 0.255 0.090 0.005 86 13 NaN NaN110 H5 leave-region-out: Southwest_Asia 0.264 0.087 0.002 75 29 0.437 0.234111 H5 leave-region-out: Sub_Saharan_Africa 0.236 0.065 0.000 89 6 NaN NaN112 H5 leave-era-out: 1-1000 0.336 0.130 0.010 71 40 0.193 0.182113 H5 leave-era-out: 1000BCE-0 0.255 0.146 0.081 73 28 0.390 0.145114 H5 leave-era-out: 1001-1500 0.310 0.112 0.006 70 43 0.316 0.152115 H5 leave-era-out: 1501-1800 0.267 0.084 0.001 79 31 0.325 0.483116 H5 leave-era-out: post-1800 0.287 0.121 0.018 86 16 0.208 0.264117 H5 leave-era-out: pre-1000BCE 0.293 0.114 0.010 86 8 NaN NaN118 H5 leave-sphere-out: Andes_Amazonia 0.285 0.085 0.001 90 6 NaN NaN119 H5 leave-sphere-out: East_Asia 0.269 0.103 0.009 70 30 0.362 0.083120 H5 leave-sphere-out: Europe 0.366 0.096 0.000 78 38 0.187 0.164121H5 leave-sphere-out: Mesoamerica_North_America 0.266 0.088 0.002 89 13 NaN NaN122 H5 leave-sphere-out: Oceania 0.278 0.091 0.002 91 6 NaN NaN123 H5 leave-sphere-out: South_Asia 0.269 0.078 0.001 88 5 NaN NaN124 H5 leave-sphere-out: Southeast_Asia 0.272 0.077 0.000 88 7 NaN NaN125 H5 leave-sphere-out: Steppe_Central_Asia 0.279 0.079 0.000 91 12 NaN NaN126 H5 leave-sphere-out: Sub_Saharan_Africa 0.236 0.065 0.000 89 6 NaN NaN127 H5 leave-sphere-out: West_Asia_North_Africa 0.274 0.089 0.002 63 43 0.401 0.393128129=== Y2 Cox / Y3 ===130 model term coef se p n events hr schoenfeld_p_P131 Y2-1 Cox: P + strata(macro-region) P_z 0.031 0.060 0.600 317 302 1.032 NaN132 Y2-2 Cox: P + X + midpoint + strata P_z 0.000 0.068 0.995 208 201 1.000 0.983133 Y2-3 Cox: D + K + X + midpoint + strata D_pc1_z 0.128 0.133 0.336 208 201 1.136 NaN134 Y2-3 Cox: D + K + X + midpoint + strata K_mean_z 0.559 0.200 0.005 208 201 1.749 NaN135 Y2-4 Cox: complexity PC1 + X + strata complexity_pc1_z 0.399 0.291 0.171 208 201 1.490 NaN136Y2-5 Cox: D + K + X + midpoint + polities per NGA (periodization) + strata D_pc1_z 0.082 0.135 0.544 206 200 1.086 NaN137Y2-5 Cox: D + K + X + midpoint + polities per NGA (periodization) + strata K_mean_z 0.535 0.203 0.009 206 200 1.707 NaN138Y2-5 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 NaN139 Y3-1 logit: discontinuous succession ~ P + FE P_z 0.018 0.393 0.964 145 24 NaN NaN140 Y3-2 logit: + X P_z 0.239 0.325 0.461 117 18 NaN NaN141