Economic Complexity Index and Product Complexity Index

Method

Build the binary country-product matrix M from Balassa RCA on export values: M[c][p] = 1 when RCA >= 1.0, else 0. The threshold is inclusive. BACI export values are thousands of USD, and the units cancel in RCA.

ECI is the second eigenvector of the country-country projection Dc^-1 M Dp^-1 M^T, where Dc = diag(k_c) is diversity (row sums of M) and Dp = diag(k_p) is ubiquity (column sums). PCI is the second eigenvector of the product-product projection of the same M. The hidalgo crate (external) solves bundle_from_rca(mat, threshold=1.0) with defaults max_iters=100000 and tol=1e-12.

This is the eigenvector construction of the Atlas of Economic Complexity (Hausmann et al. 2011), equivalent to the converged method of reflections of Hidalgo and Hausmann (2009) per Mealy, Farmer and Teytelboym (2019). No reflections iteration exists in this repository.

Standardisation is per year, over that year's kept set, with population standard deviation (ddof = 0). Sign is pinned by convention: ECI is negated if it correlates negatively with diversity, PCI if it correlates positively with ubiquity. These conventions are implemented in the hidalgo crate (external).

Countries with zero RCA products and products no country specialises in are dropped that year (k_c > 0, k_p > 0). This is the only filter: there is no minimum population, GDP or trade filter, unlike the Harvard Atlas.

Values are rounded to 4 decimals. Ranks are dense 1..N descending with ties broken by code ascending, so no rank is tied.

PCI is a hybrid. Core HS96 codes carry the eigenvector value. Extended codes (HS02/07/12/17/22 codes absent from the HS96 catalogue) instead get the unweighted mean ECI of the countries with extended RCA >= 1 in that product, and the rank column is recomputed over the union. In 2024 that is 4,762 eigenvector codes and 1,504 mean-ECI codes in one 6,266-row ranking. Extended rows exist only for 2002 onward.

Equations

Validation

• Cross-vintage Spearman, V202601 rebuild against the previous V202501 estate on shared codes: ECI 0.9964 to 0.9994 for 2000-2024, and 0.947 in 1996 (the HS96 coverage ramp year). PCI grouped overlap in 2024: 0.9985 core, 0.9995 extended, 0.9942 for codes that moved between the two (docs/CODEBASE_LEDGER.md and data/parquet/MANIFEST.json ext_notes).
• Top-11 ECI membership for 2024 is identical across the two vintages (FIN and NIU swap ranks 10 and 11).
• scripts/integrity/test_parquet_integrity.py asserts every year has at least one negative PCI and that ECI and PCI ranks are contiguous 1..N with no gaps or ties.
• scripts/quality/check-gate.sh Check 3 asserts at least 7 of the latest year's ECI top 10 are canonical complexity leaders.
• There is no benchmark against the Harvard Atlas or OEC in this repository. All validation is internal.

Limitations

• The panel holds 226 reporters in 2024, not 238. It is 213 in 1996-1998 and peaks at 227 in 2013. Any "238 countries" claim elsewhere on the site refers to the countries.parquet row count, not the ECI panel.
• Standardisation is per year, so ECI and PCI levels are not comparable across years. Only the position in that year's distribution is.
• One PCI ranking mixes two estimators. Core PCI is a z-score with unit standard deviation (2024 range -3.5389 to 3.0693); extended PCI is an unstandardised mean of z-scores and is mechanically compressed (2024 range -0.9973 to 2.1903). Ranking them together is not like for like.
• 1996-1999 sit on the CEPII HS96 classification coverage ramp: world totals are 6.03% lower in 1996 than the HS92 estate, and the ECI cross-vintage Spearman falls to 0.947 there. Read those four years with caution.
• /api/rankings/pci joins products.parquet and therefore silently drops all 1,504 extended codes, while /api/v1/rankings/pci joins products_all.parquet and keeps them. The two endpoints return different universes for the same year.
• /api/rankings/eci deduplicates countries.parquet with MIN(code), which drops 2 reporters in 1996-1998 and 1 in 1999-2011 (BEL, DEU and SDN each carry two codes). 2012 onward is unaffected.
• PCI is zero-centred and routinely negative. Negatives are signal and are never filtered.

References

• Hidalgo and Hausmann (2009), The Building Blocks of Economic Complexity, PNAS 106(26): 10570-10575.
• Hausmann, Hidalgo et al. (2011), The Atlas of Economic Complexity.
• Mealy, Farmer and Teytelboym (2019), Interpreting economic complexity, Science Advances 5(1).
• Balassa (1965), Trade Liberalisation and Revealed Comparative Advantage.

Endpoints