chse_hoe — Estimate HOE statistics from observed h(t) series

Syntax

chse_hoe varname [if] [in]
[, burnin(#) windows(#) alpha_r(#) tol(#)]

Description

chse_hoe estimates the three empirical statistics that characterise
the Hierarchy Orbit Equilibrium (Definition 10.2):

tau_hat — leadership turnover frequency (flips per period)

Var(h) — variance of h in the stationary distribution

E[cascade size] — expected cascade size (via rho(K) proxy)

The variable varname should contain an observed h(t) time series where
h ∈ [0,1] is the hierarchy belief at each period. In the central bank
application, h(t) can be proxied by:

Yield spread response to CB announcements (normalised to [0,1])

CB forecast dominance share in professional surveys

Policy divergence index between CB and Treasury

Stationarity is tested by comparing window means across the post-burn-in
trajectory. Convergence is declared if max window-mean difference < tol.

Options

burnin(#) number of initial observations to discard. Default 0.

windows(#) number of windows for stationarity test. Default 4.

alpha_r(#) direct belief drop per successful reframe, used for the
cascade size calculation. Default 0.3.

tol(#) stationarity tolerance (max window-mean difference for
declaring convergence). Default 0.05.

Saved results

r(tau_hat) Turnover frequency
r(var_h) Variance of h (post burn-in)
r(mean_h) Mean of h
r(min_h) Minimum h
r(max_h) Maximum h
r(frac_above) Fraction of periods h > 0.5
r(n_flips) Total number of leadership flips
r(N_post_burnin) Observations used
r(rho_K_proxy) Proxy for spectral radius rho(K)
r(exp_cascade) Expected cascade size bound
r(max_win_diff) Max window-mean difference
r(converged) 1 if stationarity test passed

Examples

Stable HOE — central bank with high independence:

. use cb_yield_data.dta, clear
. chse_hoe h_proxy, burnin(20)
// expect: tau_hat≈0, mean_h≈0.8, converged=1

Oscillatory HOE — contested CB period:

. chse_hoe h_proxy if contested==1, burnin(12) windows(6)
// expect: tau_hat>0.1, mean_h≈0.5

Time series panel — one group per country:

. xtset country year
. by country: chse_hoe h_proxy, burnin(5)

References

Nityahapani (2025). Contested Hierarchy with Social Embedding.
Section 10, Definitions 10.1 and 10.2.

Author

Nityahapani

chse package v1.0.0