System-Welfare-Adjusted GDP and the welfare ledger

GDP counts transactions while leaving system welfare off the ledger

The paper argues that national income accounting omits the system-welfare coordinate by construction. System-Welfare-Adjusted GDP adds that missing account using the SAPM damage term rather than folding the correction into official GDP.

• Correction: aggregate β_W^cause × Π across productive domains
• β_W^cause = −dW/dΠ, the causal damage derivative of system welfare with respect to industry revenue
• Π is annual industry revenue

The measurable object is sign and rank, not one welfare-cost total

The paper rejects the common move of estimating separate deadweight losses for pollution, fishery depletion, financial instability, antibiotic resistance, and other domains, then summing them into a single annual number.

• Aggregate dollar cost is a planner-relative calibration band
• The sign of β_W^cause says whether revenue destroys system welfare
• The rank of β_W^cause says which domains sit above others under stated prices

Shadow prices can move the aggregate without erasing the ordering

The aggregate level depends on choices such as VSL, SCC, morbidity prices, and ecosystem prices. Those choices are vulnerable to planner assumptions and capture, so the paper makes the price vector visible rather than treating the total as market-identified.

• Level: shadow-price dependent
• Sign and rank: the capture-robust claims when sensitivity checks support them
• Dollar aggregates and cost-of-capital understatement are labeled conditional

Rank holds when damage terms rise monotonically and channel mixes do not cross-invert

The source-note sign-and-rank condition is the paper’s identification discipline. If each domain’s β_W^cause is monotone increasing over the published shadow-price range, and channel mixes do not cross-invert, the rank-ordering survives even though the level changes.

• Shadow-price vector: π = VSL, SCC, and other published prices
• Monotone β_W^cause prevents sign reversal within the range
• No cross-inversion means domains do not swap ordering through channel mix changes

A 59-domain grid keeps high rank stability across VSL and SCC ranges

Corollary T.1 reports the demonstrated robustness check: VSL from 3.0M to 15.0M crossed with SCC from 1 to 190 per ton. The 59-domain ordering remains highly stable, with limited movement only in adversarial low-VSL cases.

• Kendall’s τ ≥ 0.78
• Spearman ρ ≥ 0.89
• Top tier is mostly stable; strict invariance is not claimed

The ledger identifies which activities are worst before claiming a dollar total

The paper’s policy use is ordering. Where the aggregate welfare figure is calibrated, the ranking of β_W^cause can still identify priority domains when the robustness condition and sensitivity grid support it.

• Policy-priority ordering is the rank of β_W^cause
• The honest claim is high rank stability plus β_W sign
• If rank moves, the ledger must show that movement

P1–P3 need β_W^cause > 0 and rank, not cardinal magnitude

Corollary T.2 says the framework’s predictions do not require a precise dollar damage coefficient. They require the activity to have positive causal system-welfare damage and a cross-sectional position relative to other domains.

• Sign-only sufficiency: β_W^cause > 0
• Cross-sectional rank carries the empirical content
• Cardinal level is not needed for P1–P3

C is reported as a separate shadow-price-sensitive account

The formal contribution is an accounting architecture. The paper says to report system-welfare costs separately, mark the price vector used, and preserve only the sign and rank claims that survive sensitivity analysis.

• Do not collapse C into GDP silently
• Show the shadow-price vector
• Report sensitivity instead of a false single total

Students change VSL, SCC, morbidity, and ecosystem prices to test what survives

The teaching exercise is a sensitivity-grid exercise. Students start with the central ledger, change the price vector, and separate level movement from rank and sign stability.

• Environmental economics: shadow pricing
• Public finance: national accounts
• Policy: transparent uncertainty

This is a draft theory ledger, not a calibrated domain tile

The paper positions System-Welfare-Adjusted GDP above applied β_W domain ranking as measurement theory. It does not replace official national accounts, does not claim a permanently correct shadow price, and does not fabricate new channel values.

• Target journal: JEEM
• Status: draft manuscript; peer review pending
• No empirical β_W tile