CHSE: Stata module implementing Contested Hierarchy with Social Embedding

We develop a theory of hierarchical authority in which leadership is contested, not structural. Hierarchy beliefs (the probability that player i leads player j) evolve through four coupled mechanisms: Bayesian anticipation, role ambiguity, retroactive reframing, and network propagation via an endogenous kernel. The solution concept is the Hierarchy Orbit Equilibrium (HOE), an invariant measure of the induced Markov process, nesting Nash and Stackelberg as degenerate special cases. We show that a 15-parameter system compresses into two indices: the Hierarchy Stability Index and Propagation Intensity, whose ratio partitions parameter space into four dynamic regimes. We prove existence, ergodicity, and Lyapunov stability, and characterise three welfare distortions endemic to interior equilibria. A central result is the Hierarchy Persistence Paradox: stronger hierarchies produce larger cascades when they fall, because accumulated anticipation accuracy inflates the spectral radius of the propagation kernel. Applied to central bank independence, the framework correctly classifies six country-period episodes from robust monetary dominance to fiscal dominance.