# Phase 74 — capital, productivity and employment feedback

This is a theoretical mechanism experiment, not an empirical estimate or a solved general equilibrium. Base snapshot: `8f88bd9c5894f44a5474f8b4ee772aa455390a0b`. Phase 71/72 inputs and phase 73 financial rules remain the reference. The only change to phase 73 is an optional beginning-capital feedback callback and additional diagnostics; default calculations retain their original behavior.

## Equations and timing

Let barred variables be the original phase 71 annual paths. Initial real productive capital K0=200, workforce=1, consumer price P=bar P. For each year t>0, beginning capital K[t-1] affects production before current saving and asset trades:

    r = K[t-1]/200
    L[t] = min(1, max(0.8, bar L[t] * r^eta))
    Yreal[t] = bar Yreal[t] * r^alpha * (L[t]/bar L[t])^(1-alpha)
    Ynom[t] = P[t] * Yreal[t]
    W[t] = bar W[t] * L[t]/bar L[t]
    productivity[t] = Yreal[t]/L[t]
    profits[t] = Ynom[t] - W[t]

This is a Cobb-Douglas-shaped **reduced-form net-output** response around the imposed technology path. The employment equation is an explicit behavioral closure, not the first-order condition of the production function. Wages per employed person and consumer prices stay on their original paths. Tax rates and accessible base fractions retain the original time paths; cash profit tax is recomputed on max(profits,0), wage tax on actual wages. Dividends, fiscal benefits, interest, saving, repayments and asset trades are then recalculated, not copied from the baseline.

    Inet[t] = Ynom[t] - C[t] - G[t]
    K[t] = K[t-1] + Inet[t]/P[t]
    corporate_cash[t] - corporate_cash[t-1] = net_equity_cash[t] - Inet[t]
    household_cash + corporate_cash + Treasury_cash = 50
    Delta(bonds - Treasury_cash) = G + benefits + public_interest - tax_revenue
    Delta(private_loan) = unpaid_private_interest - principal_repaid

The investment good and consumption good have the same price. As in phase 73, output and investment are treated net of capital consumption; depreciation is not separately estimated. Applying a gross-GDP production function plus a new depreciation subtraction would change the accounting convention and is outside this comparison. Net disinvestment reduces capital. Year 0 is an initialization/reference observation, not a settled flow year.

| Mode | alpha | eta | Interpretation |
|---|---:|---:|---|
| external | 0 | 0 | Unmodified phase 73 production path |
| capital_only | .30 | 0 | Capital raises net production, employment unchanged |
| complement | .30 | .10 | Capital also expands labor demand |
| substitute | .30 | -.10 | Capital reduces labor demand, subject to cohort floor |

The 80% employment floor is essential: fixed four-cohort definitions allow only the two 10% displacement cohorts to lose jobs; workers70% and owners10% stay employed. Thus substitution effects are censored at 20% unemployment. This experiment cannot infer unemployment above20%, entry, occupation changes or actual deciles. The positive eta case can re-employ displaced cohorts. Neither sign nor magnitude is fitted to data. Acemoglu & Restrepo (2019), https://doi.org/10.1257/jep.33.2.3, motivates distinguishing productivity, displacement and reinstatement channels; it does **not** validate these elasticities or this financial closure.

## Design and financing interpretation

384 paths = 3 macro cases (reference, strong productivity, limited tax capture) x 2 ownership systems x 2 saving rules x 4 valuation rules x 4 mechanisms x transition/no-automation. Each control sets automation unemployment and efficiency changes to zero but retains the same feedback, fiscal tax path, saving and valuation rules. A strong-productivity no-automation control therefore retains its tax-rate change; the comparison isolates the jointly removed unemployment/efficiency transition, not every policy difference from year0.

The original16 transition scenarios and16 matched controls are preserved inside the reference/external subset. No random seed is needed. Source hashes appear in the generated full JSON. Elasticities are illustrative point assumptions rather than a comprehensive robustness region.

Only117 of384 paths complete20 years: external48/96, capital_only24/96, complement13/96, substitute32/96. These chosen-grid counts are not probabilities. Partial paths retain their last settled year and a separate attempted failure year/reason. Comparisons are missing unless all required paths reach20; a partial year19 observation must never be labeled year20.

Financing feasibility means feasibility **under the retained fixed-money closure**. Higher production can fail because firms lack cash while Treasury accumulates it. There is no bank credit creation, new public deficit borrowing, external finance or monetary accommodation. Such failure does not establish that the real economy could not finance investment. Household consumption shortfalls do not automatically stop a path; unpaid private interest capitalizes at par, without recognizing lender credit losses.

## Reference example: concentrated ownership, income-share saving, constant real equity quote

All monetary/real quantities are normalized, not NIS. Consumption indices are relative to each cohort's own initial90%-of-disposable-income consumption, not equal absolute living standards.

| Year20 measure | external | capital_only | substitute |
|---|---:|---:|---:|
| Real output (initial100) |120.00|151.73|151.25|
| Real capital (initial200) |392.25|456.37|451.37|
| Unemployment % |20.00|20.00|20.00|
| Private loan (nominal aggregate, initial20) |16.76|15.78|15.97|
| Government bonds (nominal, initial60) |60.00|27.83|31.01|
| Treasury cash |0.00|0.00|0.00|
| Workers consumption index |150.60|162.47|162.73|
| Displaced debt-free consumption index |69.07|100.00|100.00|
| Displaced indebted consumption index |56.52|100.00|100.00|
| Owners consumption index |116.64|164.37|163.72|
| Workers share of aggregate net current income % |50.70|43.72|43.84|
| Displaced debt-free income share % |3.32|3.84|3.85|
| Displaced indebted income share % |2.27|3.20|3.21|
| Owners income share % |43.71|49.23|49.10|

Income shares use population-weighted real current income after contractual private interest, including transfers and interest received; exclude capital gains, principal repayments and bond redemptions. They are neither wage shares nor wealth shares. The machine-readable files also contain each cohort's real wealth, income index and equity share.

The complement path stops at attempted year20: firm cash would be -7.04 while real capital would be532.24. Last settled year19 output165.56, unemployment12.73%, Treasury cash18.90. These are **not year20 results**.

## What survives and what changes

- The original56.52 observation reproduces. Its interpretation as an inevitable consumption loss does not survive the capital_only or substitute specification: both reach100 in this example. Higher profit tax receipts permit the original reference-consumption benefit target to be financed. This is a fiscal consequence of imposed extra production, not an empirically identified effect.
- Higher output need not reduce concentration: in the example, owners' net-income share rises from43.71% to49.23% under capital_only, even while displaced consumption improves.
- In this example all three completed paths retain positive private debt and government bonds at20. Nominal debt is never erased simply by marking equity up; gains remain distinct from current income.
- A matched-control sign reversal occurs for **broad ownership / income-share saving / drawdown valuation / capital_only / indebted displaced**: automation-minus-control consumption-index difference is +1.48 points versus -20.06 in external. This is the only strict sign reversal in the defined valid group comparisons, not evidence that the mechanism generally benefits borrowers. Raw index100 versus56.52 is a different comparison.
- Some comparisons become infeasible rather than reversing. Excluding failures and averaging survivors would create selection bias. Full completion flags and failure records are retained in summary outputs.

## Reproduce and validate

From repository root with Python3 (standard library only):

    python scripts/capital_feedback_v74.py
    python -m unittest discover -s calibration -p 'test_*v7*.py' -v

Outputs: `data/processed/capital_feedback_v74.json` (full annual paths, generated locally), `capital_feedback_v74_summary.csv` (flattened all-path endpoint metrics and failure fields), and `capital_feedback_v74_comparisons.json` (valid matched-control consumption effects and reversals). The full10MB JSON is regenerated rather than committed. Incomplete summary endpoints are explicitly last_year, not terminal estimates.

Tests verify preservation of phase73 defaults and56.52, neutral feedback, beginning-capital timing, labor-channel signs, accounting and cash conservation, fiscal and corporate counterparts, cohort bounds and explicit financing failure. Existing phase73 private-loan/equity tests remain active. No empirical coefficient estimation has been added. A subsequent empirical step needs investment/capital-stock and sectoral employment data, depreciation definitions, estimation of labor responses, and comparison of alternative monetary/fiscal closures before policy claims.