Project Overview
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
Pullᵢⱼ = f(market size, coreness gap, incumbency, institutions)
Pushᵢⱼ = g(instability, saturation, maturation, churn)
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.
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.
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.
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.
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.
| Feature | Measure | Source | Theoretical role | Mechanism in model | Sign |
|---|
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.