chse_paradox — Test the Hierarchy Persistence Paradox

Syntax

chse_paradox disruption_var hsi_var [if] [in]
[, fdi alpha_r(#) trust(#) phi(#)
acc_floor(#) acc_ceiling(#) generate(stub) replace]

Description

chse_paradox tests the Hierarchy Persistence Paradox (Bottleneck 8):

H1: dE[cascade|collapse]/dHSI > 0

Stronger hierarchies produce larger collapses when they fall. The command:

1. Regresses the disruption variable on HSI (or FDI).

2. Tests whether the slope is significantly positive.

3. Computes calibrated theoretical cascade predictions
using the formula E[cascade] = alpha_R / (1 - rho_K), where
rho_K = Acc(HSI) * trust * phi and Acc(HSI) = acc_floor +
(acc_ceiling - acc_floor) * HSI/(1+HSI).

Options

fdi treat hsi_var as FDI values; convert to HSI via HSI = 1/FDI.
Use this when your input variable is the Fiscal Dominance Index.

alpha_r(#) direct belief drop per reframe. Default 0.3.

trust(#) average cross-edge trust at equilibrium. Default 0.65.

phi(#) average distance decay. Default 0.60.

acc_floor(#) Acc_ij at HSI approaching 0. Default 0.50.

acc_ceiling(#) Acc_ij at HSI approaching infinity. Default 0.92.

generate(stub) creates variables stub_hsi_implied,
stub_acc, stub_rhoK, stub_cascade_pred.

Saved results

r(slope) OLS slope (post-collapse disruption ~ HSI)
r(se_slope) Standard error of slope
r(pval_slope) Two-sided p-value
r(r2) R-squared
r(correlation) Pearson correlation
r(paradox_confirmed) 1 if slope>0 and p<0.10
r(acc_min) Minimum predicted Acc_ij
r(acc_max) Maximum predicted Acc_ij
r(rhoK_min) Minimum predicted rho(K)
r(rhoK_max) Maximum predicted rho(K)

Examples

Using HSI directly:

. chse_paradox yield_vol hsi_precollapse
// Tests: do high-HSI countries have larger post-collapse disruptions?

Using FDI (converts to HSI internally):

. chse_paradox yield_vol fdi, fdi

With generate (to plot cascade predictions):

. chse_paradox yield_vol hsi, gen(pred) replace
. scatter yield_vol hsi || line pred_cascade_pred pred_hsi_implied, sort

Replicate paper Figure 5 test:

. input float(disruption hsi)
. 0.10 0.55 // Turkey
. 0.12 0.71 // Zambia
. 0.38 1.10 // Brazil
. 0.59 1.84 // US 2020-23
. 1.38 4.52 // Chile
. 1.61 5.53 // US 2000-07
. end
. chse_paradox disruption hsi
// slope > 0, r = 0.996, paradox confirmed

References

Nityahapani (2025). Contested Hierarchy with Social Embedding. Bottleneck 8.

Author

Nityahapani

chse package v1.0.0