Why Complex Industries May Favor Economies That Already Have a Head Start

Why should the same industry expand quickly in one economy and slowly in another? In the preprint The Dynamic Theory of Economic Complexity, César A. Hidalgo and Viktor Stojkoski propose an explanation built around specialized inputs, investment and bottlenecks. Their central claim is that the capabilities an activity requires help determine which economies can accumulate productive capacity fastest.

The authors compare predictions from their model with international trade and regional industry data. They report broadly consistent patterns, while acknowledging that the empirical exercise is an indirect test of the mechanism.

Growth depends on combinations

A capability, in this framework, is an input that cannot readily substitute for something else: specialized expertise, particular equipment or an institution supporting certain activities. Industries require different combinations of these inputs, and economies possess them to different degrees.

The model uses a “weak-link” production function. Output depends on the combination of required capabilities, so a shortage of one can constrain what the others achieve. More intensely required inputs create stronger constraints.

The dynamic ingredient is reinvestment. A share of output finances activities that build the capabilities those activities use—a learning-by-doing mechanism. Capability accumulation slows as stocks approach an assumed ceiling.

Investment also faces knowledge and information frictions. Entrepreneurs may understand their own industry better than distant sectors, making investment elsewhere less effective. Their modeled choice weighs these losses against the future value of the capabilities an investment would build. Under strong frictions, investment remains in the originating sector.

When catching up becomes conditional

The model asks where capability accumulation is fastest along the path from scarcity to abundance.

In a simplified version allowing some production even without an initial capability stock, undemanding activities generate the fastest accumulation in the least-endowed economies. This resembles unconditional convergence: those starting behind catch up faster.

As average capability requirements rise, the peak shifts toward economies that already possess a positive stock. Catch-up becomes conditional on existing capabilities. In this particular single-capability case, with a specified saturation rule, the transition occurs when average requirement intensity exceeds one-half. That is a model-specific threshold, not an observed cutoff for real industries.

When production instead requires an initial foothold in the relevant capability, the model produces a tunable conditional-convergence pattern. More demanding activities favor higher stocks at the point of fastest accumulation.

Comparing the mechanism with data

The researchers examine exports by country and product from 2002–2022, payroll by industry in U.S. metropolitan areas from 2003–2022, and formal employment by sector in Brazilian microregions from 2013–2023.

Because capabilities are not directly observed, they use the Economic Complexity Index as a proxy for economy-level endowments and the Product Complexity Index as a proxy for activity requirements. They identify the three fastest-growing economies in each activity and examine their mean economic complexity.

Here, “growth” means the increase in a bounded transformation of revealed comparative advantage, a measure of relative specialization—not percentage growth in exports, wages or jobs. To separate the estimation of the two complexity indices, the authors use repeated random splits of economies into distinct estimation groups.

Across all three datasets, more complex activities have their fastest growers in more complex economies. The theory-based curves achieve R² values of 0.157 for trade, 0.306 for U.S. metropolitan areas and 0.396 for Brazilian microregions. The best alternative benchmark curves fit somewhat better. The authors emphasize their curve’s interpretation through a capability-building mechanism rather than superior predictive performance.

Why related industries matter

Shared capabilities create another prediction: investment supporting one industry can build inputs useful to another. This generates “relatedness,” the tendency for activities to grow where related activities are already present.

The model further predicts that relatedness matters less as capability stocks rise and more as an activity’s requirements intensify. Five-year panel regressions using a bounded specialization measure show the predicted coefficient signs across all three datasets. These are associations consistent with the model, not direct observations of capability transfers.

What remains unresolved

The distinction between theory and measurement is consequential. The fitted theoretical curve locates maximum capability accumulation, whereas the empirical outcome measures changes in normalized specialization. The paper explicitly notes this mismatch; its appendix also shows that capability accumulation, output increases and proportional output growth need not peak at the same stock.

The framework leaves demand-side considerations outside its main analysis and does not model sectors competing for a limited pool of skilled workers. Its baseline capability stocks have fixed ceilings; conditional on production across all activities, economies eventually approach a common frontier and growth stops. The highlighted convergence differences therefore concern transition paths, not permanently different growth rates.

The preprint offers a mechanism connecting existing productive structure to subsequent development. Its evidence supports the direction of several predictions, without establishing that this mechanism alone explains the observed patterns.