# 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.