Calculating Externalities: From Indicators to Monetized Costs

This page explains the operational mechanics of calculating $C_2$, $C_3$, and $C_4$: which indicators to use, how to monetize them, and how to handle upper bounds for unknown data.

General Structure

For each product/service $p$ in a defined functional unit $u$ (e.g., 1 kg, 1 meal, 1 service unit):

$C_k={\sum }_i(I_{k,i}\times F_{k,i})$

Where:

• $I_{k,i}$: midpoint indicator (physical or categorical)
• $F_{k,i}$: monetization factor (€/unit of indicator)

$C_2$: Social Externality

Footprint Indicators

Indicator Category	Midpoint Indicator	Unit
Child labour	Hazardous child labour hours	hours
	Non-hazardous child labour hours	hours
	Labour force to audit	FTE
Forced labour	Forced workers (least severe)	FTE
	Forced workers (medium severe)	FTE
	Forced workers (most severe)	FTE
	Debt bondage cases	FTE
	Abuse victims	FTE
Gender discrimination	Female workers without maternity	FTE
	Maternity leave value denied	€
	Gender wage gap	€
	Unequal opportunities wage gap	€
Underpayment	Below minimum wage gap	€
	Below living wage gap	€
Social security	Workers without social security	FTE
	Denied paid leave value	€
Overtime	Workers performing illegal overtime	FTE
	Underpaid overtime	FTE
	Overtime pay gap	€
Living income	Living income gap	€
Harassment	Non-physical, non-sexual	worker
	Non-physical, sexual	worker
	Physical, non-sexual	worker
	Physical, sexual (non-severe)	worker
	Physical, sexual (severe)	worker
Freedom of association	Denied freedom violations	violation
Occupational health	DALYs lost to OHS incidents	DALY

Cost Factors (TPF v4.0.2, EUR2024)

Indicator	Monetization Factor	Components
Hazardous child labour	€42.0/hour	CO + PR + RT
Non-hazardous child labour	€15.3/hour	CO + PR + RT
Audit requirement	€8.75/FTE	PR
Forced labour (least severe)	€14,000/FTE	RS + CO + PR + RT
Forced labour (medium severe)	€76,600/FTE	RS + CO + PR + RT
Forced labour (most severe)	€139,000/FTE	RS + CO + PR + RT
Debt bondage	€20,600/FTE	RS + PR + RT
Abuse victims	€43,400/FTE	CO + RS + RT
Maternity provision	€2,000/FTE	RS + PR + RT
Wage/income gaps	€1.03/€1.00 gap	CO (+ PR + RT)
Social security lack	€2,650/FTE	CO + PR + RT
Illegal/underpaid overtime	€125/FTE	CO + PR + RT
Harassment (non-physical)	€27,800/worker	RS + CO + PR + RT
Harassment (physical, non-sexual)	€68,500/worker	RS + CO + PR + RT
Harassment (severe sexual)	€86,100/worker	RS + CO + PR + RT
Freedom of association denial	€430/violation	PR + RT only
OHS (health impacts)	€129,000/DALY	Health valuation

Component codes:

• RS: Restoration
• CO: Compensation
• PR: Prevention
• RT: Retribution

Calculation Example: Coffee Supply Chain

For 1 kg coffee beans from specific origin:

Child labour (hazardous): 0.5 hours × €42.0/hour = €21.0
Living income gap: €0.30 × €1.03/€ = €0.31
OHS impacts: 0.0002 DALY × €129,000/DALY = €25.8
Gender wage gap: €0.15 × €1.03/€ = €0.15
---
C_2 = €47.26/kg

Upper Bound for Unknown (95th Percentile)

When origin, supplier practices, or audit data is missing:

1. Identify sector-country combination (e.g., “Coffee production, Colombia”)
2. Query MRIO database (Eora, EXIOBASE) or sector studies for intensity distribution
3. Use 95th percentile value as conservative default
4. Example: If Colombia coffee sector shows child labour intensity distribution with 95th percentile = 1.2 hours/kg, use that value

Rationale: Penalizes opacity while remaining defensible (not worst-case, but conservative).

$C_3$: Environmental Externality

Footprint Indicators

Indicator Category	Midpoint Indicator	Unit
Climate change	Greenhouse gas emissions	kg CO₂e
Water use	Water consumed (scarcity-adjusted)	m³
Biodiversity	Land use impact	ha·year
	Mean Species Abundance loss	MSA·ha·year
Soil degradation	Nutrient depletion (NPK)	kg N/P/K
	Soil organic carbon loss	kg SOC
Air pollution	Particulate matter precursors	kg PM2.5
	NOx, SOx emissions	kg
Water pollution	Eutrophication potential	kg N-eq
	Acidification potential	kg SO₂-eq
	Ecotoxicity	CTUe

Cost Factors (TPF v4.0.2, EUR2024)

Indicator	Monetization Factor	Logic
CO₂e	€0.312/kg CO₂e	Social cost of carbon (long-term damage)
Water (scarce region)	€2.50-15/m³ (region-dependent)	Restoration/replacement cost in water-stressed areas
Biodiversity (MSA)	€8,000-25,000/ha·year	Ecosystem restoration or lost services
Soil nutrients (N)	€1.50/kg N	Replacement fertilizer cost
Soil organic carbon	€0.25/kg SOC	Carbon sequestration value
PM2.5 (health)	See $C_4$ below	Through respiratory disease burden
Eutrophication	~€5-10/kg N-eq	Water treatment cost

Note: Some environmental impacts also create health externalities (e.g., air pollution causes respiratory disease). To avoid double-counting:

• Environmental component ($C_3$): remediation/cleanup cost
• Health component ($C_4$): DALY burden on exposed populations

Calculation Example: Beef Production

For 1 kg beef (conventional, feedlot):

Climate: 27 kg CO₂e × €0.312/kg = €8.42
Water: 15 m³ × €5/m³ = €75 (scarce region)
Land use: 20 m²·year × (€10,000/ha·year ÷ 10,000 m²/ha) = €20
Eutrophication: 0.5 kg N-eq × €7/kg = €3.50
---
C_3 = €106.92/kg

Upper Bound for Unknown

When production method, origin, or supply chain data missing:

1. Map to sector-country (e.g., “Cattle ranching, Brazil”)
2. Query LCA databases (Agri-footprint, ecoinvent) or MRIO environmental extensions
3. Use 95th percentile intensities for:
   • Carbon intensity (kg CO₂e/kg product or per €)
   • Water consumption (m³/kg or per €)
   • Land use (ha·year/kg or per €)
4. For Brazil cattle with unknown practices: 95th percentile might be 50 kg CO₂e/kg (vs. 27 kg for verified lower-impact)

Effect: Products with missing LCA data receive penalty until supply chain is verified.

$C_4$: Consumer/Public Health Externality

Footprint Indicators (Food Products)

Indicator Category	Midpoint Indicator	Unit
Nutritional quality	Nutri-Score	A/B/C/D/E
Processing level	NOVA classification	1/2/3/4
Added sugar	Grams per 100g	g
Salt	Grams per 100g	g
Trans fats	Grams per 100g	g
Consumer exposure	Air pollution (PM2.5)	kg PM2.5 (population-weighted)
	Water contaminants	DALYs from exposure

Cost Factors: DALY Mapping

Core valuation: €129,000/DALY (consistent with occupational health)

Nutri-Score to DALY proxy (conservative estimates):

Nutri-Score	DALY risk proxy per 1000 kcal/year	Rationale
A	0.0001 DALY	Minimal diet-related disease risk
B	0.0003 DALY	Slightly elevated risk
C	0.0006 DALY	Moderate risk (standard Western diet)
D	0.0012 DALY	High risk (poor nutrition)
E	0.0025 DALY	Very high risk (ultra-poor nutrition)

NOVA to DALY multiplier (processing penalty):

NOVA	Multiplier	Rationale
1 (Unprocessed)	1.0×	Baseline
2 (Processed ingredients)	1.1×	Minimal processing impact
3 (Processed foods)	1.3×	Added preservatives, processing artifacts
4 (Ultra-processed)	1.8×	High disease association (meta-analyses)

Combined formula:

${\text{DALY}}_{\text{diet}}=\text{kcal consumed/year}\times \text{NutriScore proxy}\times \text{NOVA multiplier}\times (1/1000)$

Air pollution (consumer exposure):

${\text{DALY}}_{\text{pollution}}=\text{population-weighted PM2.5}\times \text{exposure duration}\times \text{dose-response factor}$

Standard dose-response: ~0.001 DALY per person per µg/m³ per year of PM2.5 exposure.

Calculation Example: Ultra-Processed Snack

For 100g snack (Nutri-Score E, NOVA 4):

Annual consumption assumption: 10 kg (average consumer)
Energy: 500 kcal/100g → 50,000 kcal/year for this product

DALY_diet = 50,000 kcal × 0.0025 DALY/1000 kcal × 1.8 (NOVA) = 0.225 DALY/year per regular consumer

Per 100g unit:
DALY per 100g = 0.225 DALY/year ÷ 100 units/year = 0.00225 DALY/100g

C_4 = 0.00225 DALY × €129,000/DALY = €290.25 per 100g unit

Note: This appears high, which is intentional—reflects true public health burden of ultra-processed, nutrient-poor foods when consumed regularly.

Upper Bound for Unknown

When nutritional data or processing method unknown:

1. Nutri-Score missing: Assign “E” (worst category)
2. NOVA missing: Assign “4” (ultra-processed) for packaged goods
3. Ingredients unknown: Use product category 95th percentile for sugar/salt/fat
4. Effect: Incentivizes nutritional transparency and disclosure

Example: Generic “snack bar” with no data receives:

• Nutri-Score E (0.0025 DALY/1000 kcal)
• NOVA 4 (1.8× multiplier)
• Total: Conservative high estimate until verified

Calculation Workflow

1. Product characterization:

   • Functional unit (kg, meal, service)
   • Supply chain map (materials, processes, locations)
   • Available primary data (audits, certifications, measurements)

2. Indicator population:

   • For known data: use measured/verified values
   • For unknown data: query sector-country distribution → extract 95th percentile (see Data Sources)

3. Monetization:

   • Apply TPF factors to each indicator
   • Sum within component ($C_2$, $C_3$, $C_4$)

4. Aggregation:

   • Compute externality norm: $N_{ext}(C)=\sqrt{w_2{C}_2^2+w_3{C}_3^2+w_4{C}_4^2}$
   • Consumer signal: $P_{signal}=C_1+N_{ext}(C)$

5. Tax application:

   • At each supply chain stage: tax on incremental EV
   • Final consumer: tax on total EV (with input credits for intermediate stages)

For detailed information on data sources, verification tiers, and sector-country priors, see Data Sources.

Upper Bound Philosophy

The unknown penalty is not punitive by design; it is conservative realism:

• Unknown supply chains carry real risk
• 95th percentile represents plausible high-impact scenario
• Penalty declines with verification
• Creates market for traceability and auditing services
• Prevents “ignorance is bliss” strategy

Key principle: The burden of proof shifts to the producer. Opacity is expensive; transparency is valuable.

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Next: Data Sources
Parent: TCA