1# Research log — UQO WP 24 "From Labor to Capital"23Chronological record of completed steps, assumptions taken, residuals, unresolved problems and next actions4(required by CLAUDE.md). Dates are 2026-10-27 unless stated.56## Stage A — Source audit (done)7* Downloaded the NBER conference PDF (20 pp., July 4 2025 draft) and wrote `docs/source_audit.md` with page8 references for every primitive, definition and proposition (P1–P11). Observations: no proofs in the source,9 compute is an endowment, no capital/prices/ownership; P6's own caveat (p. 11) identifies scarce resources as10 the point of failure of the wage result.11* Literature matrix and 118 verified references delivered by the bibliography task (`docs/literature_matrix.md`,12 `docs/references_verification.md`); 6 entries flagged PARTIAL, none invented.1314## Stage B — Smallest exact benchmark (done)15* `tasks.py` reproduces Restrepo's static economy with 4 bottleneck + 2 accessory task classes and CES σ_B = 0.5.16 On a grid Q ∈ {0,…,1e5}: A constant from Q = 5 on, Y linear in Q (slope = A to 1e-6), w_H = A·CEU(H) = 8A,17 w_L = 2A < 3A = A·CEU(L) (the accessory task with the highest α is not worth automating: the skill is in18 Restrepo's group 𝒩 and gets the discounted \widetilde{CEU}), labor share 1 → 4e-4, compute share → 1,19 total wages higher than pre-AGI. Tests in `tests/test_static.py` (P1–P6).20* A nuance not in the source: the "discount" of P4 arises whenever the max-α task of a skill is not automated,21 even if nobody works in it (accessory output abandoned entirely because its marginal value Zγ_a is below the22 wage available in bottleneck tasks).23* Observation on definitions: with a CES aggregator every task is a bottleneck unless the elasticity is infinite;24 accessory work in the sense of Definition 2 requires asymptotically linear entry.2526## Stage C/D — Two-class, four-capital model and solver (done, with lessons)27* Static block: SLSQP on scaled variables + Newton polish of the KKT equalities on the active set; the polished28 solution is independent of the warm start (banded FD Jacobian matches a dense one to 6e-10). Accepting the29 polish on its residual rather than on fsolve's status flag was necessary (10 % of calls were rejected with30 residuals of 1e-18).31* Accounting identity GDP = factor payments holds to 1e-8 and a deliberately broken version (compute services32 counted as final output) is caught by `test_income_identity_fails_when_accounting_is_broken`.33* Harrod-neutral trend growth on labor, land and the energy resource (TFP constant) gives an exact frozen-AI BGP34 (residual 2.5e-8 at the BGP guess). A first version with Hicks-neutral Z growing at g produced rentals growing35 at 1.5 %/yr — not a BGP — and was corrected.36* **Lesson 1 (calibration must match the scenario's anticipated prices).** Calibrating the 2026 compute rental37 with the user cost of a *declining* price (g_pQ = 0.15) and then solving a scenario with a different g_pQ38 creates a jump at t = 0 (compute Euler off by 60 %), the task block switches regime (task 1 fully automated)39 and the Newton system becomes nearly singular along the (K_Q, r) direction. With the base point re-calibrated40 for each scenario's technology rates (`calibrate(overrides=…)`), the frozen case converges in 5 iterations to41 1.8e-10.42* **Lesson 2 (accessory tasks and energy).** With a linear accessory block and an energy constraint, the marginal43 value of compute is bounded below by Zγ_a/α_a while the marginal value of energy in the core (σ_T < 1) is44 bounded above; as ε_t → 0 compute would absorb all energy to produce accessory output and core output would45 collapse. Accessory tasks are therefore kept in the analytical replication only.46* **Lesson 3 (scenario magnitudes).** g_pQ = 0.28 with a floor at 1e-5 and g_alpha = 0.2 produce compute stocks47 growing by e^40 within the horizon and no terminal state close to a BGP; the solver cannot find a 30-year path.48 The baseline uses g_pQ = 0.15 (floor 1e-3, Moore's law ends ≈ 2072), g_eps = 0.10, g_alpha = 0.15; the Epoch49 value (0.34) is a scenario.50* Solver: banded Newton (colored FD Jacobian, band 2) with backtracking; homotopy in the size of the shock on51 T = 40; horizon continuation 40 → 80 → 140 → 200 → 275; truncation check with 50 extra years.52 A trust-region least-squares alternative (`solve_trf`) was tried and found much slower.5354## Stage E — Asset pricing (implemented in `transition.py`)55* Tobin's q per capital type, ex-dividend equity values, net payouts (negative = issuance), land prices by56 backward recursion with a Gordon terminal value, aggregate wealth = sum of claims. Decompositions in57 `analysis.py` (to do: Campbell–Shiller exact under perfect foresight).5859## Stage F — Propositions (in progress)60* Regime theorem drafted (see `paper/sections/theory.tex`): labor share → 0 is robust; wage level and the61 destination of income depend on whether compute is an endowment or a priced reproducible capital good and on62 the elasticity between the task composite and scarce complements.6364## Stage G — Heterogeneous agents (implemented, GE loop to do)65* `households.py`: EGM with housing-inclusive price index, Rouwenhorst(5), 3 discount types × 2 skills, 300-point66 grid; stationary solution in ≈ 1 s. At the reference prices β = (0.93, 0.97, 0.993) with masses (0.5, 0.3, 0.2)67 give wealth 8.3 × GDP, Gini 0.80, top-10 % share 65 %, top-1 % 13 % (data 32.5 %: not reachable without return68 heterogeneity — reported as an untargeted moment).6970## Stage H — Data (done)71* 162 targets retrieved (`data/processed/calibration_targets.csv`), all with URLs, vintages and sha256; FRED72 reached through a browser-fetch fallback (Akamai timeouts), documented in `data/raw/fred/_RETRIEVAL_NOTE.md`.7374## Open problems / next actions751. Run the scenario catalogue on the cluster; check horizon truncation for the explosive scenarios.762. HA general-equilibrium loop (relaxation on the interest-rate path) for baseline + 3 scenarios.773. Stochastic AGI-arrival extension (risk premia) in a two-regime version.784. Empirical design section (industry exposure × margins/valuation) — design only.7980## Stage I–K — Scenarios, figures, paper (2026-10-27, afternoon)8182* 26 scenarios solved directly at λ = 1 on the full horizon (275 years) from the partial-equilibrium guess; 6–1083 Newton iterations, 7–15 minutes each on one core (12 in parallel). The short-horizon homotopy was abandoned:84 mid-transition terminal conditions made the Newton stall at the last period.85* **Lesson 4 (reference scenario).** "Capability frozen" with Moore's law continuing still automates three task86 classes by 2060 (2026 compute requirements are finite). The clean reference is everything frozen (exact BGP);87 the capability-only freeze is reported as its own scenario (`no_capability`).88* **Lesson 5 (utilization margin cost).** The energy-constrained scenarios spend most of their time in the89 utilization bisection (200 iterations to 1e-13 in log u); reduced to 60 iterations / 1e-11, which is still90 far below the Newton tolerance.91* **Lesson 6 (welfare metric).** Infinite-horizon CEVs of hand-to-mouth workers whose consumption goes to zero92 are dominated by the far future (thousands of percent); CEVs are reported over 2026–2065.93* **Lesson 7 (HA general equilibrium).** Relaxation with λ = 0.3 on log excess demand diverged at the first step94 (gap of 4 log points; r driven negative; singular production Jacobian). Replaced by a damped quasi-Newton using95 the finite-difference Jacobian of household log demand with respect to the return path (275 household solves,96 ≈ 7 min, terminal policy cached), a crude diagonal for the supply response, steps bounded by 0.2, checkpoints.97 Gap 4.0 → 1.0 in five iterations.98* Baseline facts (two-class): tasks automated 2029/2043/2045/2057; labor share 0.56 → 0.28 (2050) → 3e-5 (2100);99 w_H transitory premium ×3.5 in 2050; GDP ×3.7 (2050), ×233 (2100); r peaks 40.5 % (2060); W/GDP 4.1 → 2.7100 (2042) → 31 (2100); land share 0.60 in 2100; compute value ≤ 0.2 GDP; P/E compute ≈ 2 in the 2040s.101* Paper compiles (54 pp.), slides (28 pp., to be extended), 0 undefined references; wide tables wrapped in102 resizebox; `scripts/55_fallbacks.py` lists macros not yet generated (HA ones until `make ha`).103104## Final state (2026-10-27, evening)105106* 22 of 26 scenarios solved to 1e-9; 4 not (Cobb–Douglas, substitutes, energy-constrained, Moore without end):107 Newton stalls on utilization kinks / explosive compute stocks; documented in Appendix C and the referee report.108* HA GE: baseline gap 2.5e-3, citizen fund 4.0e-3, frozen 9e-5 (quasi-Newton stops improving near 1e-3; reported109 as such). **Lesson 8:** the asset grid must scale with aggregate wealth (fixed grid → everyone at the cap → Gini110 → 0, a pure artifact). **Lesson 9:** with a citizen fund, households hold (1−θ_F) of the claims; counting all111 claims double-counts the fund's payout.112* HA result: wealth Gini non-monotonic (0.74 → 0.60 in 2050 → 0.73 in 2100 → 0.80 in 2150): the boom is113 equalizing (premium of the last-automated skill + high returns on small savings), the limit is a rentier economy.114* Paper 55 pp. (0 errors, no missing macro), slides 33 pp., 35 tests pass, README, referee report, pushed to115 spbgit `wp24_uqo.git`.116