# Research log — UQO WP 25 (Agentic General Equilibrium)

Decisions, evidence and open tasks, in chronological order. Dates are absolute. Every entry states (a) the question, (b) assumptions, (c) what was implemented/tested, (d) evidence, (e) threats, (f) next tasks.

# 2026-10-27 — Day 1

# 00. Set-up

• Repository created from the UQO template (_modele-working-paper), number 25, package age (src/age/…).
• Local inference: mlx_lm.server on M3U96a (Qwen2.5-7B-Instruct-4bit :8081, Llama-3.2-3B-Instruct-4bit :8083) and M3U96b (Mistral-7B-Instruct-v0.3-4bit :8082), reached through SSH tunnels (scripts/llm_serve.sh, scripts/llm_tunnel.sh). No paid provider key is used: keys found on the laptop are marked burned by their owner and were left untouched.
• Literature audit and calibration data collected by two parallel team members (see docs/literature_matrix.md, docs/references_verification.md, docs/parameter_ledger.csv, data/raw/README.md).

# 01. Core theory (gate 2)

• (a) Question: is there a distinct equilibrium mechanism from delegation, beyond "AI in the production function"?
• (b) Assumptions: one-step-ahead information friction; human forecast errors idiosyncratic, model errors common to all users of the same foundation model; price-taking; quadratic approximation (Angeletos–Pavan class).
• (c) scripts/00_lq_derivations.py (sympy) derives strategies, aggregate law, welfare, private vs social value.
• (d) Evidence: the private value of delegation equals the social marginal value identically (wedge == 0) under the CRS restriction U_xX + U_XX = 0, U_Xθ = 0; confirmed by direct computation of expected utility from the full quadratic payoff and by a property-based test over random (α, D, M, τ). With U_XX = −υ U_xX, υ ≠ 1 gives a wedge of sign (1 − υ). → Proposition 3 (efficiency benchmark) and Proposition 4(a).
• (e) Threats: the benchmark is a second-order approximation; it relies on symmetric ownership and complete markets; the literature audit flags Angeletos–Pavan 2007 and Colombo–Femminis–Pavan 2014 as the right comparison — we must present the result as "the delegation externality is zero in exactly the cases where their efficiency results apply, and non-zero in the frictions we add", not as a new efficiency theorem.
• (f) Next: derive the uninsurable-wage-risk wedge (4b) and the collateral wedge (Prop. 7) explicitly.

# 02. Mapping the economy to the game

• Savings mapping (household saves in capital, news about TFP): negative result. Partial-equilibrium response of log savings to a known TFP news shock κ₀ = −0.0015 (γ = 2, ρ_z = 0.9): wealth and substitution effects offset, the stake of the consumption–savings decision is negligible, and the GE news response is the standard comovement puzzle (investment falls on impact). Kept in the paper as evidence that which decision is delegated matters.
• Portfolio mapping (allocation between risky capital claims and a safe store of value, mean-variance): κ₀ = 1/(γσ_R²) = 19.5 with σ_R = 0.16 (Shiller 1984–2025 real equity s.d. 0.157), α_s = −(1−α)R^K κ₀ = −1.33 (strong strategic substitutability through diminishing returns). With illustrative information parameters (predictable return component s.d. 6 %, human noise 10 %, model noise 4 %) the first adopter gains 3.3 % of consumption per year; the gain falls to 0.4 % when everyone delegates (the common signal is less valuable once it is already in the aggregate). All three s.d. are illustrative and are swept in the robustness section.
• Compute market, short run (fixed K_Q): interior delegation share ≈ 0.47 in the baseline; inference demand is small relative to production compute with q̄ = 0.002, so crowding-out is weak → the H6 experiments must use a larger q̄ (inference-heavy delegation) and report the threshold at which crowding-out flips the labour share. Decision: make q̄ a scenario parameter ("inference intensity") rather than a calibrated constant.

# 03. Calibration notes (from the ledger)

• Labour share level 0.618 (1984–2026, BLS index rescaled by PWT), capital share (Fernald) 0.354, δ = 0.055, TFP AR(1) ρ = 0.88–0.93 (linear detrend) with innovation s.d. 0.0126–0.0135; real T-bill 0.57 %, TIPS 10y 0.97 %; DFA 2026:Q2 top 1 % 32.5 %, top 10 % 68.9 %, bottom 50 % 2.3 %; equity real return 9.9 % s.d. 15.7 % (1984–2025).
• Baseline choices: β = 0.96 (annual, r ≈ 4 % with growth abstracted), γ = 2, α = 0.33, δ = 0.06, ρ_z = 0.9, σ_ε = 0.013. Deviations from ledger means are documented in paper/sections/calibration.tex.

# Open TODO

• Prop. 4(b) wage-risk wedge, Prop. 7 collateral multiplier (static), proofs in appendix.
• Model B solver + decomposition; Model C engine + banking + three market designs; LLM lab + audit logs.
• Pre-registered experiments (experiments/pre_registration.md), figures, tables, paper, referee report, git push.

# 04. Day-1 results and decisions (evening)

• Model A: portfolio mapping is the baseline; PV first adopter 3.3 % of consumption, last 0.4 %; wage-noise s.d. 7.7 % (M=1) / 3.2 % (M=8) at full adoption; wedge = 0 to 1.9e-7 on the grid (benchmark); hand-to-mouth Pigouvian tax 4.5× fee (M=1), 0.8× (M=8). Compute crowding-out confirmed in sign, tiny in size (labour share +0.2 pp at most) — reported as a negative result; inference-intensive delegation self-limits (hump in q̄).
• Model B (n_a=160, 5 GH nodes, a_min=−0.5): no-AI Gini 0.683 / top-10 % 0.457 / r 3.9 %; delegation only → Gini 0.701, top-10 % 0.466 (rich delegate first); full broad → Gini 0.575; full concentrated (owner class, capitalised rents) → 0.661, top-10 % 0.474. Decision: owner class as a point mass outside the household block (Prop. 6 two-class economy); delegation-by-decile computed over households only. Bug fixed: rents were not paid to anyone under concentration.
• Model C (20 seeds): H2 confirmed in all designs (walrasian of_corr 0.11 → 0.97 → 0.43 for D=0 / D=1,M=1 / M=8); volume collapse with a shared model (no-trade); leverage defaults highest with private signals. Stress: needed persistent dividends (ρ_d=0.95, valuation prices persistence), preloaded leverage 0.95 of capacity, auto-repay off, −10 s.d. shock, thin ladder (tick 0.25 %, 40 levels, depth 0.1): call market amplification 2.6× (margin 0.2), 1.5× (margin 0.5), none with 4 models; CDA: 10 % trough, no cascade. Disclosed in table notes and referee report.
• LLM lab (quick: 8 agents × 24 periods × 3 seeds, Qwen/Mistral/Llama 4-bit): early cells show Qwen agents under a shared signal LESS correlated (0.14–0.32) than the Bayesian control (0.98) — consistent with Hansen–Lee 2025; to be confirmed when the run completes and written into results_c (the draft paragraph must be revised accordingly).
• Paper: 69 pages compiled (pdflatex, aer.bst), 144 verified references, 104 generated macros + fallbacks.