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Project Overview

13,298Synthetic Firms
150Countries
0.823Panel Correlation vs Real CCDI
0.84ln(t) Slope Ratio (Emergent)

Dependency theory described how the core-periphery hierarchy reproduces itself, but never specified the generative process that produces it. This project supplies that missing mechanism. It builds an agent-based model in which thousands of firms make decentralized investment decisions, deploying capital into host economies and withdrawing it under instability or saturation, with no country-level dependency rule and no time trend written into the model. From these firm-level choices alone, country dependency, measured by the Core Capital Dependency Index, emerges and accumulates.

The central result is an emergence finding. Real dependency grows logarithmically over time, following the form y = a + b·ln(t). The model contains no time variable, yet it reproduces that same logarithmic functional form and very nearly its rate, with an emergent ln(t) slope of 0.0098 against an observed 0.0117 (a ratio of 0.84). The model is built with Mesa in Python, seeded to reconstruct the real 2009 bilateral FDI network at r = 0.999, and validated across 30 random seeds against the observed CCDI panel for 150 countries from 2009 to 2023 at a correlation of 0.823.

A Two-Process Firm Model

The model represents the world economy as a population of capital-holding firms distributed across 150 countries, seeded proportional to GDP and sized log-normally so that a few large firms hold most of the investable capital. Each firm acts through two decoupled processes. There is no equation that sets a country's dependency directly; dependency is recomputed each year from the net pattern of firm flows, exactly as the Core Capital Dependency Index is computed from real bilateral data.

The Two Processes

1
Inflow (deployment). Firms holding capital choose destinations through a softmax over an attractiveness score built from market size, the coreness gap between home and host, incumbency in existing positions, and host institutions (political stability, rule of law, control of corruption, democracy, trade openness, resource rents). Capital flows from more-core toward less-core economies.
Pullᵢⱼ = f(market size, coreness gap, incumbency, institutions)
2
Outflow (withdrawal). Existing positions are withdrawn under instability shocks, host saturation, host maturation as domestic firms grow, and baseline churn. Because firms accumulate capital over time, fast-growing economies build their own outward positions, which net against inflows and allow gradual ascent.
Pushᵢⱼ = g(instability, saturation, maturation, churn)
3
Dependency, recomputed. Each year the model recomputes every country's CCDI from the resulting bilateral network: composition (how core-like its senders are), reliance (inflows over total flows), and the country's own coreness. Dependency is an outcome of firm behavior, never an input.
Dependencyᵢₜ = Composition × Reliance × (1 − Coreness)

This architecture reproduces the empirical asymmetry documented in the panel work: because firm capital accumulates slowly and compounds, ascent through the maturation channel is gradual and rare, while descent through inward flooding under instability can happen quickly. The descent-fast, ascent-slow pattern is not imposed; it falls out of the mechanism.

The Generative Experiment

The analysis has the structure of a generative experiment: a world is built from observed data, a population of firms is endowed with empirically grounded behavior, the world is run forward through time, and the macro pattern it produces is held against the macro pattern that actually occurred. The schematic below lays out this architecture. Hover over each stage for detail.

Model Architecture: From 2009 Network to Validated Trajectory
The model is seeded with the observed 2009 bilateral FDI network, populated with 13,298 firms following fixed behavioral rules, run forward to 2023, and validated against the independently measured Core Capital Dependency Index.

Validation: Predicted vs. Observed Dependency

The full validation cloud plots each country-year's model-predicted dependency against its observed value, shaded by year. The cloud tracks the 45-degree line of perfect prediction across the full range of the index, with an overall correlation of 0.828 and a fitted slope of 0.89. The mild attenuation, slightly over-predicting the least dependent and under-predicting the most dependent, is the signature of a probabilistic allocation mechanism. Hover for country and year.

Model-Predicted vs. Observed Core Capital Dependency
2,189 country-year observations across 2009 to 2023, shaded by year. Overall correlation 0.828; fitted slope 0.89, intercept 0.06. The 45-degree dashed line marks perfect prediction.

The Fit Is Broad, Not Average

Aggregate correlations can conceal a model that succeeds on average while failing for many individual cases. The distribution below shows the model's accuracy across all 150 countries: each is summarized by its mean absolute error between predicted and observed dependency over 2009 to 2023. The mass concentrates at low error, with a median country predicted within 0.063 on the zero-to-one index. The fit is broad rather than carried by a handful of well-captured cases. The best-fit countries include the Netherlands, the United States, the United Kingdom, Switzerland, and Spain; the weakest fits fall on small or volatile economies such as Grenada, Senegal, Tonga, Iraq, and the Central African Republic.

Distribution of Model Fit Across All 150 Countries
Median per-country MAE = 0.063; 41 percent of countries predicted within 0.05 and 68 percent within 0.10 across 2009 to 2023. The dashed line marks the median.

The Emergence Result

This is the central contribution. Observed global mean dependency rises logarithmically over time, following y = a + b·ln(t). The model contains no time variable and no logarithmic rule. Yet the dependency it generates, plotted as the mean over 30 seeds with a 95 percent band, follows the same logarithmic form at an emergent slope of 0.0098, within the immediate neighborhood of the observed 0.0117. A logarithmic growth law emerges from decentralized firm behavior alone.

Logarithmic Time Fit vs Generative ABM Prediction
Observed ln(t) slope 0.0117; emergent ABM slope 0.0098. The model reproduces both the logarithmic form and approximately the rate of dependency growth without time as an input.

Institutional and Structural Features

Each firm's decision to deploy capital into a host economy is governed by an attractiveness function built from observed institutional and structural features. The table lists each feature, how it is measured, its source, its theoretical role, the mechanism through which it operates in the model, and its expected direction of association with inward investment. Institutional attractors follow meta-analytic evidence that political stability, rule of law, and democracy attract foreign direct investment while corruption deters it.

Features Driving Firm Investment Decisions
FeatureMeasureSourceTheoretical roleMechanism in modelSign
WDI = World Bank World Development Indicators; WGI = Worldwide Governance Indicators; CCDI = Core Capital Dependency Index. All features enter the firm-level attractiveness function. Expected sign indicates the direction of association with inward investment.

Key Findings

A logarithmic growth law for dependency emerges from a model that contains no time variable. The emergent ln(t) slope of 0.0098 matches the observed 0.0117 closely (ratio 0.84), and the model reproduces the full cross-national panel of dependency at a correlation of 0.823 across 30 seeds. This is the methodological payoff: dependency theory long asserted that the hierarchy reproduces itself, but the reproduction was never derived from a generative process. Here it is.

The model also reproduces the asymmetry between rising and falling without being told to. Because firm capital compounds slowly, ascent is gradual and rare; because inward flooding under instability is fast, descent is quick and structured. The same descent-fast, ascent-slow pattern documented in the discrete-time mobility models falls out of the firm mechanism endogenously, which is stronger evidence for the mechanism than fitting the pattern directly would be.

Seeded to reconstruct the real 2009 bilateral FDI network at r = 0.999 and validated against the observed CCDI panel, the model offers a defensible generative account of dependency reproduction. Because the central result is an emergent property rather than a fitted coefficient, it is robust to the common critique that critical models bake their conclusions into their assumptions.