chse_regime — Classify CHSE regime from HSI and PI

Syntax

chse_regime, hsi(varname|#) pi(varname|#)
[generate(stub) replace]

Description

chse_regime computes the CHSE Instability Index Z = HSI^-1*(1+2*PI)
and classifies each observation into one of four dynamic regimes:

Z Regime Dynamics

Z < 1 Stable h(t) converges to fixed point
1 <= Z < 2 Oscillatory Leadership alternates
2 <= Z < 3.5 Cascade Network-wide collapses
Z >= 3.5 Turbulent Sensitive dependence

HSI (Hierarchy Stability Index) = lambda_kappa * K_i / (lambda_R * V_j)
measures the ratio of leadership resistance capacity to follower attack capacity.

PI (Propagation Intensity) = Gamma * E[phi(d,G)]
measures network cascade potential.

Options

hsi(varname|#) specifies the Hierarchy Stability Index. Either a
variable name or a scalar value.

pi(varname|#) specifies the Propagation Intensity. Either a
variable name or a scalar value. Set to 0 for single-edge (no network).

generate(stub) prefix for generated variables. Default is chse.
Creates stub_Z (instability index), stub_regime (string),
stub_regime_n (numeric, labelled).

replace replaces existing variables with the same name.

Saved results (scalars, when both arguments are scalars)

r(Z) Instability index
r(HSI) HSI value
r(PI) PI value
r(regime) Regime string

Examples

Scalar call:

. chse_regime, hsi(2.1) pi(0)
. chse_regime, hsi(0.4) pi(0.3)

Variable call — classify a panel of country-year observations:

. chse_regime, hsi(hsi_var) pi(pi_var) gen(chse) replace
. tabulate chse_regime
. tabstat chse_Z, by(chse_regime) stat(mean min max)

Phase boundary: stable iff HSI*(1+2*PI) > 1 (Theorem 6.1):

. chse_regime, hsi(1.0) pi(0.0) // exactly on boundary -> oscillatory

References

Nityahapani (2025). Contested Hierarchy with Social Embedding.
Theorems 6.1 and 6.2.

Author

Nityahapani

chse package v1.0.0