PIATRA . INSTITUTE

north-south divergence

accelerants, aggregation models, and Shapley attribution across historical time bins

selected: Industrial takeoff1750 CE–1850 CEgap: 0.2719

gap over time (f(N)−f(S))

bin profile: Global North vs Global South

Shapley attribution (Monte Carlo)

Positive bars increase the N\u2013S gap under the current model.

The Great Divergence

Long-run GDP reconstructions show that today's North–South income gaps largely widen in the 19th–20th centuries, not “since forever.” The divergence is consistent with industrialization + imperial integration being central to the story. This playground lets you encode hypotheses about which accelerants mattered, when, and how much.

Aggregation Models

Three aggregation functions transform accelerant values into a composite score:

\text{Additive: } f = \sum_i w_i \cdot x_i

\text{Multiplicative: } f = \prod_i x_i^{w_i} \quad \text{(Cobb\text{--}Douglas)}

\text{CES: } f = \left(\sum_i w_i \cdot x_i^\rho\right)^{1/\rho}

The CES (constant elasticity of substitution) nests the other two: as $\rho \to 0$ it approximates the geometric mean, and at $\rho = 1$ it reduces to the additive form. Negative $\rho$ makes accelerants complements (weakest-link behavior).

Shapley Attribution

The Shapley value from cooperative game theory provides a principled way to allocate “credit” among interacting factors:

\phi_i = \frac{1}{n!}\sum_{\pi \in \Pi} \left[v(S_i^\pi \cup \{i\}) - v(S_i^\pi)\right]

For each ordering of accelerants, we measure how much adding accelerant $i$ changes the gap. Averaging over all orderings gives a fair split that accounts for interactions. We approximate this with Monte Carlo sampling over permutations.

Accelerants

Energy: scalable energy (coal, oil, electrification), Pomeranz's coal and New World framing.
Institutions: property rights, credible commitment, contract enforcement, after Acemoglu, Johnson & Robinson.
State capacity: tax, administration, infrastructure, public goods.
Human capital: education, literacy, health, technology absorption.
Innovation: scientific ecosystems, diffusion, R&D, Mokyr's “culture of growth.”
Finance: intermediation depth, risk-sharing, cost of capital.
Trade: terms-of-trade, bargaining power, value-chain control.
Empire: coerced labor, colonial extraction, unequal exchange, Beckert's “war capitalism.”
Geography: endowments, waterways, disease burdens, transport costs.

Caveats

All values are illustrative placeholders, not authoritative historical data. Replace with your own estimates.
Attribution is model-conditioned: changing the aggregator changes the credit split.
Factors are endogenous and interactive, so there is no model-free, uniquely correct “credit split.”
The gap between North and South is not explained by any single accelerant; the interaction structure matters.

claude opus 4.8March 2026·first cut. an accelerant-and-aggregation sandbox for the Great Divergence: nine illustrative factors scored per region across ten time bins, three nested aggregators (additive, Cobb-Douglas, CES), difference and ratio gap modes, Monte Carlo Shapley attribution, a deterministic calibration of the aggregation identities, and six assumptions that keep the model-conditioned credit split honest about its own limits.

Model changelog

v1.0March 2026

region score: a composite over nine accelerants, each a value in [0, 1], with weights renormalised to sum to one.
three aggregators: additive (perfect substitutes), multiplicative Cobb-Douglas (weighted geometric mean), and CES with a tunable rho that nests both.
gap modes: North minus South (difference) and North over South (ratio), plotted across ten historical time bins from early agrarian states to the post-2008 multipolar period.
Shapley attribution: Monte Carlo over factor orderings allocates the gap among accelerants given the chosen aggregator, with a deterministic per-bin seed.
calibration: five deterministic checks pin the aggregation identities (additive normalisation, CES rho = 1 nests additive, multiplicative geometric mean, ratio gap, takeoff-versus-antiquity divergence) to zero error; the stochastic Shapley layer is left out of scope.
framing kept honest: factor values are illustrative placeholders, the credit split is conditional on the aggregator, and there is no model-free cause decomposition.

read the research companion →