Identification: what pins each parameter, and what cannot be identified
Classification used in results/data/parameters.json (source field) and in Table 2 of the paper:
data (read from data/processed/calibration_targets.csv), data-derived (arithmetic on retrieved
series), calibrated (implied by base-point shares and the model's steady-state conditions),
literature (elasticities and preference parameters from cited estimates), assumed (documented
assumption, no series retrieved), scenario (forward-looking input; not identified by any data).
1. Base point (2026, frozen-technology balanced growth path)
| Parameter | Pinned by | Status | Identification limit |
|---|---|---|---|
| Labor share 0.568 | PWT 11 labsh 2023 |
data | definitional choice (PWT vs NIPA) moves it by ±0.04 |
| $K^H_0$ = 1.17, $\delta_H$ = 0.023 | BEA fixed assets (total − nonresidential) | data-derived | current-cost valuation |
| $\delta_N$ = 0.089 | BEA nonresidential depreciation / net stock | data | |
| $K^N_0$ = 1.71 | residual of the income identity given shares and $r^*$ | calibrated | not a target (data 1.22); absorbs the inconsistency between income shares and $r^*$ |
| $p^Q_0K^Q_0$ = 0.062 | info-processing-equipment investment / GDP capitalized at $\delta_Q+g_Z+g_{pQ}$ | data-derived | IPE includes non-AI computers; software excluded |
| $\delta_Q$ = 0.25 | accounting lives of servers/accelerators (4–6 years) | assumed | |
| $\alpha_{1,0}$ (= 14.9 in the baseline) | compute Euler + task-1 tie $A=w_L/\alpha_1$ | calibrated | depends on $g_{pQ}$ through the user cost (hence re-calibrated per scenario) |
| compute share of task-1 input (0.22) | implied | implied | not targeted; a check of plausibility |
| data-center energy share 0.044 | LBNL 2024 | data | electricity only |
| energy share 0.04, $K^E_0$ = 0.30, $\eta$ = 0.35 | assumption, assumption, energy Euler | assumed / calibrated | |
| land rent share 0.03, housing VA 0.12, $\nu_H$ = 0.42, $\theta_H$ = 0.16 | assumptions; housing Euler; base-point accounting | assumed / calibrated | land rent share is the least documented input; the scarce_land scenario doubles it |
| $r^*$ = 0.035, $g_Z$ = 0.015, $\gamma$ = 2 → $\beta$ = 0.9954 | assumption / literature | assumed / literature | $r^*$ between TIPS (1.96 %) and returns on wealth |
| $H_L$ = 0.6, premium 1.7, task wage shares | assumptions | assumed | |
| $\nu_i$ (task weights), $\nu_N,\nu_T,\nu_E$, $Z_0$ | base-point cost shares (CES normalization) | calibrated | exact given shares and elasticities |
2. Elasticities
$\sigma_B$ = 0.5 (across tasks), $\sigma_N$ = 0.7 (tasks vs structures), $\sigma_T$ = 0.6 (top nest): literature values. They are partially identified at best in the relevant region: no historical episode has compute intensities comparable to the scenarios, so $\sigma_N$ and $\sigma_T$ are reported across {0.4, 0.7/0.6, 1, 1.5}. The sign of every asymptotic statement in Section 7 of the paper depends on whether $\sigma_T$ is above or below one; the paper reports both.
3. Scenario inputs (not identified)
$g_{pQ}$ (0.15 baseline; 0.34 Epoch GPU trend), floor $\underline p/p_0$ (0.01 baseline; 0.12, 0.001, 1e-6), $g_\varepsilon$ (0.10; 0.25, 0), floor $\underline\varepsilon/\varepsilon_0$ (0.01), $g_\alpha$ (0.10; 0.05, 0.20), $\alpha_i^\infty$ = (1, 2, 4, 8), rapid-AGI date (2032). None of these is a forecast; the paper's results are conditional on them and reported across the catalogue. The level of wages in the AGI limit is proportional to the product of the two floors, $(r+\delta_Q)\underline p,\alpha^\infty_i$ plus energy; this is the parameter combination that would need external evidence (future compute cost per human-equivalent).
4. Heterogeneous-agent block
Productivity process ($\rho_e$ = 0.95, $\sigma_e$ = 0.20): literature (Aiyagari-type calibrations). Discount types: $\beta_1, \beta_2$ assumed (0.93, 0.97); $\beta_3$ calibrated so that stationary savings equal the two-class wealth $W_0$ — hence the wealth-to-income ratio is matched by construction and the Gini / top-10 % share are untargeted checks. The top-1 % share is not reachable without return heterogeneity and is reported as a known miss.
5. Partial identification and sensitivity (what the paper reports)
- automation elasticities: $\sigma_B$ ∈ {0.3, 0.5, 0.8} changes the timing of displacement and the size of the transitory wage premium of the last-automated skill, not the limits;
- future compute costs: Table 4 of the paper spans $g_{pQ}$ and floors; the wage level in 2100 moves one-for-one with the floor;
- the pre-AGI sample cannot identify post-AGI parameters; validation is limited to base-point shares and to the 2026–2030 co-movements listed in Section 11 of the paper.