Product proximity and the product space

Method

Proximity is the minimum of the two conditional co-export probabilities between products, computed on the same binary M matrix as ECI, with RCA threshold 1.0. Implemented as phi(a,b) = co(a,b) / max(k_p(a), k_p(b)), which is algebraically the minimum form.

Computed independently per year, 1996-2024. Not pooled and not a single-year snapshot.

Stored as the strict upper triangle: one row per unordered pair with product_a < product_b, diagonal excluded, rounded to 4 decimals, kept only where proximity >= 0.2. Any consumer must symmetrise (union both orientations) before grouping.

Density around a product is the share of that product's proximity mass that runs to products the country already exports competitively.

Live counts, measured 2026-08-27: 96,376,841 rows over 1996-2024; 2024 holds 3,005,162 rows over 4,762 distinct product nodes. The table is core HS96 only: the 1,521 extended codes in the catalogue (products_all.parquet 6,636 rows minus products.parquet 5,115) carry no edge and therefore have no density. 1,504 of those 1,521 carry a 2024 PCI row, which is the figure card 1 uses.

Equations

Validation

• All 3,005,162 rows of the 2024 partition satisfy product_a < product_b, confirming the upper-triangle convention (measured 2026-08-27).
• Row count matches data/parquet/MANIFEST.json derived_row_counts.product_proximity exactly.
• The hidalgo Rust implementation is the same external crate that produces ECI and PCI, so proximity and complexity are built from one binarisation of one matrix.
• scripts/check/product-space-density.ts verifies the shared density implementation against a hand-computed four-product fixture and checks every call site.

Limitations

• The published density is not the textbook Hidalgo-Klinger-Barabasi-Hausmann density. The stored table is thresholded at 0.2 and excludes the diagonal, so the denominator is sum over p' != p with phi >= 0.2 rather than the full row sum. Densities on this site are therefore systematically higher than the textbook value.
• /api/product-space defaults minProximity to 0.55 for browser performance, which leaves 9,554 of the 3,005,162 available 2024 edges. The rendered network is a thin slice of the space.
• All four call sites, /api/product-space/opportunities, /api/product-space/summary, /api/countries/[iso3]/opportunities and the analyst growth_opportunities tool through src/lib/country-brief.ts, now compute density with densityMap in src/lib/product-space/density.ts, symmetrising the stored upper triangle. Until 2026-08-27 the country-detail endpoint returned a filtered mean proximity instead, and the BGD 2024 top 20 rankings shared no product.
• 353 of the 5,115 core HS6 codes carry no 2024 edge above the 0.2 threshold, so no density is defined for them.
• /api/product-space/summary resolves the country with a single code, so BEL and SDN are truncated.
• PCI enters the opportunity score signed. Negative PCI is never filtered.

References

• Hidalgo, Klinger, Barabasi and Hausmann (2007), The Product Space Conditions the Development of Nations, Science 317(5837): 482-487.

Endpoints