Economic complexity at subnational level: A consistency analysis

Subnational Economic Complexity Measures Found Inconsistent with Global Data

Researchers have long used "economic complexity" to measure a region's productive capabilities. This essentially quantifies the specialized knowledge and skills embedded in an economy. While these network-based tools work well for entire countries, many researchers apply them to smaller areas like cities or provinces. This helps guide local development. However, a new study from Wenli Du and Andrea Zaccaria suggests that these local measurements may be fundamentally unreliable.

The researchers found that measuring the economic complexity of small areas using only local data produces results that do not match global standards. This discrepancy means local measurements might be misleading. They could provide a distorted view of a region's actual industrial sophistication. The study proposes a shift in methodology. Instead of relying on local data alone, researchers should use "exogenous" measures. These combine local production patterns with complexity values derived from the global trade network.

The breakdown of scale invariance

The core premise of economic complexity is that the "know-how" required to produce a specific item should be a constant property of that product. Whether a semiconductor is made in a small province or a massive nation, its inherent complexity should remain the same.

However, the authors report that this assumption fails in practice. By analyzing product-level complexity across Brazil, China, and Italy, the study finds a pronounced lack of correlation between global (country-level) and local (subnational) estimates. As shown in, different algorithms might agree with each other when applied to the same geographical scale.

Yet, they diverge sharply when compared to the global benchmark.

This creates a theoretical crisis. If complexity traces underlying capabilities, those capabilities should not change just because you change the zoom level of your map. The authors demonstrate this mismatch in .

They compare complexity measures computed from international trade data (the y-axis) against those computed from subnational data (the x-axis). The lack of correlation is stark. Global measures align with established benchmarks like PRODY (a metric based on the GDP of exporting countries). Local ones do not. This suggests that applying these algorithms "endogenously"—using only the local data available—yields inconsistent results.

Moving from endogenous to exogenous computation

To fix this, the authors propose moving from endogenous to exogenous models. In an endogenous approach, the algorithm treats the subnational territory as a closed system. It calculates complexity based solely on the internal relationships within that specific area. In an exogenous approach, the algorithm treats the local territory as a participant in a much larger global network.

The authors' proposed mechanism follows these logical steps:

1. Global Benchmarking: First, the complexity of every product is calculated using the full international trade network. This anchors the "value" of a product to global reality.
2. Local Mapping: The researcher identifies the specific products produced or exported by a subnational unit.
3. Exogenous Weighting: Instead of running a new iterative algorithm on the local matrix, the researcher calculates the territory's complexity. They do this by taking a weighted sum or average of pre-determined global complexity values.

The authors highlight a distinction in how these weights are applied. They compare "summation" methods against "averaging" methods. Summation methods reward territories that are more diversified (producing a wider variety of goods). They also advocate for "extensive" measures. These use market shares—the relative contribution of a territory to a product's total volume—rather than simple binary indicators. Binary indicators only record whether a territory produces a product or not. This is akin to weighing a student's grade not just by whether they passed a class, but by the credit weight of that course.

Identifying the most robust indicators

The paper evaluates which of these new exogenous metrics actually aligns with real-world economic health. The authors measure success by how strongly these complexity scores correlate with standard macroeconomic indicators. These include GDP per capita and employment rates.

The results favor the "extensive" measures. The study finds that metrics based on weighted sums of global complexities show the strongest associations with local economic development. In contrast, the traditional Economic Complexity Index (ECI) performs poorly when applied locally.

The authors report a striking failure mode in Brazil. There, the correlation between ECI and GDP per capita is actually negative at the subnational level .

This contradicts the theoretical expectation that complexity should track development. The authors note that ECI is essentially a clustering algorithm. In Brazil, the differences in diversification across regions are relatively small. This makes the arbitrary sign of the ECI index behave inconsistently with economic growth.

The most successful metric identified is "Job-Based Extensive Fitness" (JBEF). This approach maps the complexity of specific occupations to the industries they inhabit. It then weights them by market share. According to the authors, JBEF maintains a consistently high correlation with GDP per capita across all studied countries and all administrative scales . This suggests that looking at the "hidden" complexity of the workforce provides a more stable signal of regional prosperity than looking at raw export volumes alone.

Limitations of the consistency analysis

While the study provides a clear path forward, it is not a complete solution for all economic modeling. The authors explicitly state that their work is a consistency analysis. It is not a study designed to establish causal links. They demonstrate that current tools are mathematically inconsistent across scales. However, they do not prove that complexity causes GDP growth.

There are two main caveats for practitioners to consider:

• Data Granularity Dependencies: The reliability of these measures depends heavily on product classifications. As seen in the Italian examples in, the level of detail changes how closely different metrics correlate.
• Aggregation Sensitivity: The choice between a summation approach and an averaging approach significantly alters the results. Summation yields stronger correlations with economic indicators. This choice requires careful methodological justification.

Professional recommendations for subnational analysis

If you are using economic complexity to inform regional policy or investment, the study suggests a change in approach. Researchers should avoid applying endogenous subnational algorithms. Applying the Method of Reflections or EFC directly to a local matrix produces results disconnected from global economic reality.

Instead, consider an exogenous approach. Use global product complexity as your foundation. Weight these values by local market shares. If you need a single, robust metric that survives different levels of geographical granularity, the "Job-Based Extensive Fitness" approach appears to be the most reliable candidate. Transitioning from asking "what is being produced here?" to "how does this production fit into the global hierarchy of skill?" may make subnational complexity measurements truly meaningful.

Figures from the paper