Measuring Sustainable Development

The three measurement approaches

Remember:

• Composite monetary measures (genuine savings, inclusive/comprehensive wealth, World Bank CWON — Changing Wealth of Nations): monetise market and non-market goods into one unit (€/$). Need shadow prices for non-market capital.
• Dashboards (the SDGs — Sustainable Development Goals: 17 goals / 231 indicators; Switzerland's MONET 2030, >100 indicators): transparent, multidimensional — but no single comparable score.
• Composite unit-free indices (HDI — Human Development Index; SDG Index; OHI — Ocean Health Index; EPI — Environmental Performance Index): collapse the dashboard into one number (0–1 or 0–100). Comparable, but sensitive to normalization, weighting, and aggregation.

Monetary wealth measures

Capital-management framing (Hotelling, ~100 years ago)

What: Capital = a stock delivering a flow of services over time — manufactured, human, natural, knowledge/ideas. One stock can deliver many services (a forest = timber, recreation, climate regulation, water/air purification, erosion control, nutrient cycling, biodiversity).

Why: To value a stock you need non-market valuation across its services and a discounted sum of all future services. So discounting, projections of future relevance, and uncertainty all matter. The SCC is often an input (valuing the climate-regulation service).

Comprehensive (inclusive) wealth

$$W = \sum_i p_i \cdot K_i$$

What: Sum of all capital stocks valued at shadow prices ($p_i$).

Remember: A necessary but not sufficient condition for sustainability is that per-capita $W$ does not decline (a minimal intergenerational-justice idea; sustainability also needs intra-generational distribution etc.).

Weak vs. strong sustainability

Remember: Weak = all capitals are substitutes (deplete natural capital if offset by gains in other capital). Strong = capitals must be maintained intact, are mainly complementary, with critical thresholds for natural capital. Today's lecture explores the middle ground via the elasticity of substitution. With current shadow-pricing, inclusive wealth is effectively a weak-sustainability measure (but could in principle be extended toward strong).

Hartwick / Solow–Hartwick rule

Remember: Invest the rents from exhaustible resources into reproducible capital → solves the ethical problem of the current generation short-changing the future by over-consuming. Norway's oil/wealth fund is the textbook-style success. Extends beyond oil: the value of investment in human capital should equal the value of natural-capital extraction/destruction — needs shadow prices (WTP for biodiversity; SCC for climate). Requires sufficient substitutability or regeneration — not always true.

Arrow et al. — are we consuming too much?

Remember: Evaluate consumption against (1) maximising the discounted PV of utility and (2) a positive change in the intertemporal social-welfare function = genuine/comprehensive investment. Conclusion: the consumption share of output is likely too high; several nations fail the sustainability criterion — investments in human/produced capital don't offset natural-capital depletion. Most acute in some of the poorest countries.

Empirical inclusive wealth (UNEP / UNDP / World Bank)

Remember: ~1990s–2010, inclusive wealth per capita rose ~2%/yr, but natural capital per capita fell ~2%/yr — income rising while environment degraded; the rise in human-made capital out-values the fall in natural capital. But very few facets of natural capital are even counted (fossil fuels, minerals, agricultural land, timber forest resources; CWON adds non-timber forest resources + ecosystem services + carbon damages — the only proper non-market service). Most natural capital is implicitly valued at zero.

Shadow prices — the Achilles' heel

Remember: A shadow price is forward-looking — the contribution of current investment to future utility. It depends on current capital stocks, resource-allocation mechanisms (often inefficient, esp. for public goods), and exogenous factors (institutions, technology, preferences). This estimation is the "Achilles' heel" of inclusive wealth, and ties back to the weak/strong (substitutability + relative-price) debate: lower elasticity of substitution → higher SCC and higher WTP for environmental quality.

Adjusting CWON for relative prices (Drupp et al. 2025)

The fix

What: Take the World Bank CWON's only public natural-capital stock — non-wood forest benefits (per-hectare monetary values from a 2018 meta-analysis) — and ask how limited substitutability + relative price changes should adjust it.

Remember (the load-bearing CWON assumptions — why it understates natural capital): CWON appraises the per-hectare value for one year, holds it constant over time (only inflation-adjusted via country GDP deflators), and capitalises it as the present value over a 100-year horizon at a 4% discount rate — and applies no relative-price adjustment despite a positive GDP-elasticity of WTP. (So implicitly: no service after 100 years; 4% discount; constant real value.)

Relative price change of environmental goods

$$\text{RPC} = \eta \cdot (g_C - g_E)$$

where $\eta$ = inverse of the elasticity of substitution (degree of complementarity).

Remember: Meta-analysis of contingent-valuation studies (~750 WTP–income pairs): income elasticity of WTP $\eta \approx 0.59$ (full sample), $\approx 0.66$ (forest ES); implied complementarity elasticity ≈ 0.6. With market consumption $g_C \approx 1.82\%/\text{yr}$ (GDP/cap) and forest $g_E \approx -0.11\%$ (slight degrowth, assumed to continue), RPC ≈ 1.3%/yr — by how much the per-hectare shadow price should rise each year.

Result

Remember: Adjusting for limited substitutability + RPC raises the value of non-wood forest natural capital by ~40% in CWON. But because forest stocks are declining, the revised CWON shows less sustainability, not more. Caveat: non-wood forest benefits are "a small drop on a hot stone" — only a sliver of public natural capital is counted; most is still implicitly zero.

Dashboards

The 17 SDGs and Switzerland's MONET 2030

Remember: SDGs = "the world's most important to-do list" — 17 goals, many indicators each, placed side by side. MONET 2030 is the Swiss version: >100 indicators (environmental/social/economic), each a time profile with quality flags and a good/neutral/bad color.

Why dashboards struggle: Transparent and rich for a specific indicator, but with 100 differently-colored time profiles you can't see the forest for the trees — hard for the public or policymakers to judge overall progress. This motivates collapsing into a single index, at the cost of transparency.

Composite indices: normalization, weighting, aggregation

Normalization embeds value judgments

What: Indicators come in different units → must be normalized to a common 0–1 / 0–100 scale by setting a minimum threshold (the "zero") and a maximum ceiling.

Remember: Setting that min (often not a pure zero but a subsistence / basic-needs floor) and max already bakes in ethical choices "people don't discuss enough." The lecture takes these as given and focuses on weighting + aggregation.

HDI — a warm-up

Remember: Three dimensions — health (life expectancy), education, income — extending Amartya Sen's broader human-development concept beyond income. Until 2010: arithmetic mean (1/3 weights, summed) → poor performance in one dimension easily compensated by another. Since 2010: geometric mean (product, then root) — in response to that critique.

The generalized mean (= CES — Constant Elasticity of Substitution)

$$M_r(x) = \left(\sum_i w_i\, x_i^{\,r}\right)^{1/r}$$

What: Arithmetic, geometric, harmonic means are all special cases — which economists call the CES function. It maps the whole spectrum from weak (perfect substitution) to strong (no substitution) sustainability. With the complementarity parameter $\eta$:

• $r=1,\ \eta=0$ → arithmetic mean — perfect substitutability (HDI pre-2010; SDG Index).
• $r\to 0,\ \eta=1$ → geometric mean — Cobb-Douglas (HDI post-2010).
• $r=-1,\ \eta=2$ → harmonic mean — stronger complementarity (US EPA used it for allowable water-toxicity levels).
• $r\to-\infty,\ \eta\to\infty$ → minimum — Leontief, strong sustainability (Rawlsian flavour).

Remember (Trap 13): arithmetic > geometric > harmonic > minimum in decreasing substitutability ($r = 1, 0, -1, -\infty$; $\eta = 0, 1, 2, \infty$). Key question: how much extra good performance in one dimension is needed to compensate poor performance in another? Worked example (SDG index, target score 50, two goals): arithmetic mean allows poverty 65 / climate 35 → mean 50; you can even have 0 in one dimension and still score well. The geometric mean needs more compensation and every indicator becomes essential — a 0 in any → whole index 0; harmonic needs ≥33.

Substitutability drives rankings

Remember: Jeffrey Sachs et al. compute the SDG Index for the UN with the arithmetic mean (perfect substitutability). Germany scores ~83; Norway ranks 4th, Germany 6th — but Norway scores poorly on SDG 13 because it pumps too much oil. Moving away from perfect substitutability, every country's score falls, and Norway's crashes: at the harmonic mean ($\eta=2$) Norway falls below Thailand. So "Norway above Germany" is highly sensitive to the substitutability assumption. There is no right answer — it's an ethical/social choice.

The CES/OHI experiment (eliciting public preferences)

Setup

Remember: Estimate public preferences for the substitutability parameter using the OHI (Ocean Health Index) — which aggregates 10 ocean goals (water quality, biodiversity, "sense of place"/cultural services, recreation/tourism, fishers' economic livelihoods…) with the arithmetic mean, just like the SDG Index. >6,000 participants in 12 major coastal countries; after info + comprehension checks + training, each saw 3 random goal-pairs (of 45 possible) × 20 rounds of allocation choices.

Generalized Dictator Game

What: The standard Dictator Game elicits fairness/equity-efficiency preferences (split 100 francs). The generalized version varies the efficiency of giving — 1 franc given might cost the giver 2 (the budget line / rate of transformation tilts). Here participants allocate between two goals along varying budget lines; the varying "price" of giving identifies their substitutability/complementarity.

Remember (3 archetypes): always-choose-corners + switch at price 1 → perfect substitutes, $\eta=0$; "messy" choices that normalise to a smooth curve → Cobb-Douglas, $\eta\approx1$; always-split-equally regardless of price → perfect complements.

Results

Remember: Aggregating 45 goal-pairs → one $\eta$ + goal weights. Weights differ only mildly from 1/N (clean water, food provisioning weighted a bit higher; tourism lower) → reweighting alone changes the OHI by only ~−1% (insignificant). But substitutability: only <20% of people are in the substitutes domain; most see goals as complements. Median $\eta = 3$ — even beyond the harmonic mean (harmonic = 2) in the complements space. Recomputing the OHI at median preferences drops the index ~−20% (same ~−20% for the SDG version). Implication: the arithmetic-mean shortcut paints too rosy a picture — oceans should be assessed as less healthy than portrayed.

Why it matters — policy focus

Remember: Two reasons. (1) Cross-country rankings (the prof finds this the less important use). (2) Policy focus — switching the objective from arithmetic to a complementarity-respecting generalised mean means we should shift policy effort toward the worst-performing dimensions, because under complementarity the laggard goals are decisive.

Dashboards vs. a single number: Stiglitz–Sen–Fitoussi

The car-dashboard analogy

Remember: In 2009 the French president convened the Stiglitz–Sen–Fitoussi Commission (Commission on the Measurement of Economic Performance and Social Progress). Their analogy: a single meter that fused current speed + remaining fuel into one number would be useless to a driver — both are critical and must sit in distinct areas of the dashboard. → there is no silver bullet; keep a dashboard with ≥1 index per primary dimension (e.g. within-generation vs. across-generation). An argument for dashboards (with light aggregation) over single composites.

Closing

Remember: No single right way to measure sustainable development — people disagree on indicators, weights, and substitutability. A limited dashboard with at least one index per primary dimension may be the way forward. "The more you know, the more you know that you don't know" → take away some humility.

Key formulas & one-line takeaways

Key formulas

Comprehensive wealth: $W=\sum_i p_i K_i$; sustainability necessary but not sufficient: per-capita $W$ non-declining.

Relative price change of environmental goods: $\text{RPC} = \eta\,(g_C - g_E)$, $\eta = 1/\sigma$ = degree of complementarity.

Generalized mean (CES): $M_r(x)=\left(\sum_i w_i x_i^{\,r}\right)^{1/r}$; $r=1$ arithmetic ($\eta=0$), $r\to0$ geometric ($\eta=1$), $r=-1$ harmonic ($\eta=2$), $r\to-\infty$ minimum ($\eta\to\infty$).

CES utility in the OHI experiment: $U=\left(\sum_i\alpha_i x_i^{\rho}\right)^{1/\rho}$, with $\sigma = 1/(1-\rho) = 1/\eta$; median elicited $\eta\approx3$.

One-line takeaways

• Three approaches: monetary composites (need shadow prices), dashboards (transparent, no single score), composite indices (one number, sensitive to normalization/weighting/aggregation).
• Comprehensive wealth non-decline (Hartwick) is necessary but not sufficient; with current shadow prices it's a weak-sustainability measure.
• 1990s–2010: inclusive wealth/cap +~2%/yr while natural capital/cap −~2%/yr; most natural capital is implicitly valued at zero.
• Shadow pricing is forward-looking and the "Achilles' heel"; lower substitutability → higher SCC and WTP for environmental quality.
• Drupp et al. (2025): adjusting CWON for limited substitutability + RPC (~1.3%/yr) raises non-wood forest value ~40%, but declining stocks → less sustainability. Load-bearing CWON assumptions: 100-yr horizon, 4% discount, constant real value, no RPC.
• Normalization (setting the min/zero and max) already embeds ethical choices.
• HDI: arithmetic mean pre-2010, geometric since 2010; the generalized mean (= CES) spans arithmetic→geometric→harmonic→minimum, i.e. weak→strong sustainability.
• Norway-above-Germany in the SDG Index is fragile: under the harmonic mean Norway falls below Thailand; less substitutability lowers every score.
• OHI experiment (>6,000 people, 12 countries, generalized Dictator Game): median $\eta=3$ (complements, beyond harmonic) → recomputed OHI −20%, "too rosy" arithmetic-mean picture; policy should shift toward worst-performing dimensions.
• Stiglitz–Sen–Fitoussi (2009): a speed+fuel single number is useless → keep a dashboard with ≥1 index per dimension; there is no silver bullet.