chse_welfare — Compute the three CHSE welfare distortions

Syntax

chse_welfare [varname] [if] [in],
eta(#) kappa(#) gamma(#)
[beta_r(#) zeta_ii(#) c_mu(#) c_kappa2(#)
avg_spillover(#) avg_ambiguity(#) avg_degree(#)
n_edges(#)]

Description

chse_welfare computes the three welfare distortions present in any
interior HOE relative to the social optimum (Bottleneck 6):

Distortion 1 (over-investment in reframing):
Excess = eta_eq * beta_R * Gamma / (1-Gamma).
Policy fix: legal estoppel, institutional precedent.

Distortion 2 (over-investment in commitment resistance):
Excess = kappa_eq * avg_network_spillover.
Policy fix: legibility subsidies, transparent announcements.

Distortion 3 (under-investment in hierarchy clarity):
Deficit = zeta_II * avg_degree * avg_ambiguity, where ambiguity =
1 - |2*h - 1| (equals 1 at h=0.5, 0 at h=0 or h=1).
Policy fix: public commitment requirements, board resolutions.

Total welfare loss = D1*c_mu*n_edges + D2*c_kappa*n_edges + D3.

If varname is supplied, it is treated as a variable of observed h values
(one per edge), and avg_ambiguity is computed directly from the data.
Otherwise supply avg_ambiguity() and avg_degree() as scalars.

Options

eta(#) equilibrium reframing investment eta_eq.

kappa(#) equilibrium credibility investment kappa_eq.

gamma(#) propagation factor Gamma in [0,1).

beta_r(#) reframing network spillover. Default 0.1.

zeta_ii(#) ambiguity spillover rate. Default 0.3.

c_mu(#) cost of reframing investment. Default 0.5.

c_kappa2(#) cost of credibility investment. Default 0.5.

avg_spillover(#) average network spillover for D2. Default 0.5.

avg_ambiguity(#) average 1-|2h-1| over edges (if no varname). Default 0.5.

avg_degree(#) average node degree (if no varname). Default 2.0.

n_edges(#) number of edges. Default 1.

Saved results

r(excess_1) Distortion 1 magnitude
r(eta_SO) Social optimum eta
r(excess_2) Distortion 2 magnitude
r(deficit_3) Distortion 3 magnitude
r(welfare_loss) Total monetised welfare loss
r(excess_factor) beta_R*Gamma/(1-Gamma)

Examples

Scalar (3-player complete network, h=0.65, calibrated params):

. chse_welfare, eta(0.5) kappa(0.6) gamma(0.4) beta_r(0.15)
. zeta_ii(0.3) c_mu(0.3) c_kappa2(0.3)
. avg_ambiguity(0.35) avg_degree(2) n_edges(3)
// Welfare loss = 1.4043

From edge-level h data:

. chse_welfare h_edge if wave==2, eta(0.5) kappa(0.6) gamma(0.4)

References

Nityahapani (2025). Contested Hierarchy with Social Embedding. Bottleneck 6.