# Research log — UQO WP 24 "From Labor to Capital"

Chronological record of completed steps, assumptions taken, residuals, unresolved problems and next actions
(required by CLAUDE.md). Dates are 2026-10-27 unless stated.

## Stage A — Source audit (done)
* Downloaded the NBER conference PDF (20 pp., July 4 2025 draft) and wrote `docs/source_audit.md` with page
  references for every primitive, definition and proposition (P1–P11). Observations: no proofs in the source,
  compute is an endowment, no capital/prices/ownership; P6's own caveat (p. 11) identifies scarce resources as
  the point of failure of the wage result.
* Literature matrix and 118 verified references delivered by the bibliography task (`docs/literature_matrix.md`,
  `docs/references_verification.md`); 6 entries flagged PARTIAL, none invented.

## Stage B — Smallest exact benchmark (done)
* `tasks.py` reproduces Restrepo's static economy with 4 bottleneck + 2 accessory task classes and CES σ_B = 0.5.
  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,
  w_L = 2A < 3A = A·CEU(L) (the accessory task with the highest α is not worth automating: the skill is in
  Restrepo's group 𝒩 and gets the discounted \widetilde{CEU}), labor share 1 → 4e-4, compute share → 1,
  total wages higher than pre-AGI. Tests in `tests/test_static.py` (P1–P6).
* A nuance not in the source: the "discount" of P4 arises whenever the max-α task of a skill is not automated,
  even if nobody works in it (accessory output abandoned entirely because its marginal value Zγ_a is below the
  wage available in bottleneck tasks).
* Observation on definitions: with a CES aggregator every task is a bottleneck unless the elasticity is infinite;
  accessory work in the sense of Definition 2 requires asymptotically linear entry.

## Stage C/D — Two-class, four-capital model and solver (done, with lessons)
* Static block: SLSQP on scaled variables + Newton polish of the KKT equalities on the active set; the polished
  solution is independent of the warm start (banded FD Jacobian matches a dense one to 6e-10). Accepting the
  polish on its residual rather than on fsolve's status flag was necessary (10 % of calls were rejected with
  residuals of 1e-18).
* Accounting identity GDP = factor payments holds to 1e-8 and a deliberately broken version (compute services
  counted as final output) is caught by `test_income_identity_fails_when_accounting_is_broken`.
* Harrod-neutral trend growth on labor, land and the energy resource (TFP constant) gives an exact frozen-AI BGP
  (residual 2.5e-8 at the BGP guess). A first version with Hicks-neutral Z growing at g produced rentals growing
  at 1.5 %/yr — not a BGP — and was corrected.
* **Lesson 1 (calibration must match the scenario's anticipated prices).** Calibrating the 2026 compute rental
  with the user cost of a *declining* price (g_pQ = 0.15) and then solving a scenario with a different g_pQ
  creates a jump at t = 0 (compute Euler off by 60 %), the task block switches regime (task 1 fully automated)
  and the Newton system becomes nearly singular along the (K_Q, r) direction. With the base point re-calibrated
  for each scenario's technology rates (`calibrate(overrides=…)`), the frozen case converges in 5 iterations to
  1.8e-10.
* **Lesson 2 (accessory tasks and energy).** With a linear accessory block and an energy constraint, the marginal
  value of compute is bounded below by Zγ_a/α_a while the marginal value of energy in the core (σ_T < 1) is
  bounded above; as ε_t → 0 compute would absorb all energy to produce accessory output and core output would
  collapse. Accessory tasks are therefore kept in the analytical replication only.
* **Lesson 3 (scenario magnitudes).** g_pQ = 0.28 with a floor at 1e-5 and g_alpha = 0.2 produce compute stocks
  growing by e^40 within the horizon and no terminal state close to a BGP; the solver cannot find a 30-year path.
  The baseline uses g_pQ = 0.15 (floor 1e-3, Moore's law ends ≈ 2072), g_eps = 0.10, g_alpha = 0.15; the Epoch
  value (0.34) is a scenario.
* Solver: banded Newton (colored FD Jacobian, band 2) with backtracking; homotopy in the size of the shock on
  T = 40; horizon continuation 40 → 80 → 140 → 200 → 275; truncation check with 50 extra years.
  A trust-region least-squares alternative (`solve_trf`) was tried and found much slower.

## Stage E — Asset pricing (implemented in `transition.py`)
* Tobin's q per capital type, ex-dividend equity values, net payouts (negative = issuance), land prices by
  backward recursion with a Gordon terminal value, aggregate wealth = sum of claims. Decompositions in
  `analysis.py` (to do: Campbell–Shiller exact under perfect foresight).

## Stage F — Propositions (in progress)
* Regime theorem drafted (see `paper/sections/theory.tex`): labor share → 0 is robust; wage level and the
  destination of income depend on whether compute is an endowment or a priced reproducible capital good and on
  the elasticity between the task composite and scarce complements.

## Stage G — Heterogeneous agents (implemented, GE loop to do)
* `households.py`: EGM with housing-inclusive price index, Rouwenhorst(5), 3 discount types × 2 skills, 300-point
  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)
  give wealth 8.3 × GDP, Gini 0.80, top-10 % share 65 %, top-1 % 13 % (data 32.5 %: not reachable without return
  heterogeneity — reported as an untargeted moment).

## Stage H — Data (done)
* 162 targets retrieved (`data/processed/calibration_targets.csv`), all with URLs, vintages and sha256; FRED
  reached through a browser-fetch fallback (Akamai timeouts), documented in `data/raw/fred/_RETRIEVAL_NOTE.md`.

## Open problems / next actions
1. Run the scenario catalogue on the cluster; check horizon truncation for the explosive scenarios.
2. HA general-equilibrium loop (relaxation on the interest-rate path) for baseline + 3 scenarios.
3. Stochastic AGI-arrival extension (risk premia) in a two-regime version.
4. Empirical design section (industry exposure × margins/valuation) — design only.

## Stage I–K — Scenarios, figures, paper (2026-10-27, afternoon)

* 26 scenarios solved directly at λ = 1 on the full horizon (275 years) from the partial-equilibrium guess; 6–10
  Newton iterations, 7–15 minutes each on one core (12 in parallel). The short-horizon homotopy was abandoned:
  mid-transition terminal conditions made the Newton stall at the last period.
* **Lesson 4 (reference scenario).** "Capability frozen" with Moore's law continuing still automates three task
  classes by 2060 (2026 compute requirements are finite). The clean reference is everything frozen (exact BGP);
  the capability-only freeze is reported as its own scenario (`no_capability`).
* **Lesson 5 (utilization margin cost).** The energy-constrained scenarios spend most of their time in the
  utilization bisection (200 iterations to 1e-13 in log u); reduced to 60 iterations / 1e-11, which is still
  far below the Newton tolerance.
* **Lesson 6 (welfare metric).** Infinite-horizon CEVs of hand-to-mouth workers whose consumption goes to zero
  are dominated by the far future (thousands of percent); CEVs are reported over 2026–2065.
* **Lesson 7 (HA general equilibrium).** Relaxation with λ = 0.3 on log excess demand diverged at the first step
  (gap of 4 log points; r driven negative; singular production Jacobian). Replaced by a damped quasi-Newton using
  the finite-difference Jacobian of household log demand with respect to the return path (275 household solves,
  ≈ 7 min, terminal policy cached), a crude diagonal for the supply response, steps bounded by 0.2, checkpoints.
  Gap 4.0 → 1.0 in five iterations.
* Baseline facts (two-class): tasks automated 2029/2043/2045/2057; labor share 0.56 → 0.28 (2050) → 3e-5 (2100);
  w_H transitory premium ×3.5 in 2050; GDP ×3.7 (2050), ×233 (2100); r peaks 40.5 % (2060); W/GDP 4.1 → 2.7
  (2042) → 31 (2100); land share 0.60 in 2100; compute value ≤ 0.2 GDP; P/E compute ≈ 2 in the 2040s.
* Paper compiles (54 pp.), slides (28 pp., to be extended), 0 undefined references; wide tables wrapped in
  resizebox; `scripts/55_fallbacks.py` lists macros not yet generated (HA ones until `make ha`).

## Final state (2026-10-27, evening)

* 22 of 26 scenarios solved to 1e-9; 4 not (Cobb–Douglas, substitutes, energy-constrained, Moore without end):
  Newton stalls on utilization kinks / explosive compute stocks; documented in Appendix C and the referee report.
* HA GE: baseline gap 2.5e-3, citizen fund 4.0e-3, frozen 9e-5 (quasi-Newton stops improving near 1e-3; reported
  as such). **Lesson 8:** the asset grid must scale with aggregate wealth (fixed grid → everyone at the cap → Gini
  → 0, a pure artifact). **Lesson 9:** with a citizen fund, households hold (1−θ_F) of the claims; counting all
  claims double-counts the fund's payout.
* HA result: wealth Gini non-monotonic (0.74 → 0.60 in 2050 → 0.73 in 2100 → 0.80 in 2150): the boom is
  equalizing (premium of the last-automated skill + high returns on small savings), the limit is a rentier economy.
* Paper 55 pp. (0 errors, no missing macro), slides 33 pp., 35 tests pass, README, referee report, pushed to
  spbgit `wp24_uqo.git`.