ECI and income: the 2009 PNAS scatter, redrawn for 2022

Hidalgo & Hausmann argue that the knowledge embedded in a country’s export basket predicts its income level and future growth. The headline figure: a monotone scatter of the Economic Complexity Index against log GDP per capita. Our re-estimate using 2022 BACI-derived ECI and World Bank GDP per capita reproduces the correlation within a few hundredths.

Published result

Hidalgo & Hausmann (2009, PNAS) introduce the Economic Complexity Index (ECI) via the method of reflections on the binary country-product RCA matrix M_cp(= 1 if country c has RCA > 1 in product p). Iterating k_c,N = (1/k_c,0) Σ_p M_cp k_p,N−1 and k_p,N = (1/k_p,0) Σ_c M_cp k_c,N−1 — where k_c,0 = diversity (row sum) and k_p,0 = ubiquity (column sum) — produces a sequence of increasingly refined complexity rankings. The limit is equivalent to the second eigenvector of the transformed M̃_cc′ = Σ_p M_cpM_c′p / (k_c,0 k_p,0). Their Figure 2 plots ECI against log GDP per capita for roughly 128 countries on the 1985 baseline basket. The reported Pearson correlation is r ≈ 0.78, and they argue that ECI predictsfuture income growth beyond current income and capital-labour inputs — a panel result their Table 1 reports with a coefficient on ΔECI significant at 1%.

Our re-estimate

ECI is recomputed annually on the TradeWeave BACI 202501 release using the same Hausmann-Hidalgo spectral recipe. We cross the 2022 country-level ECI against the World Bank WDI series NY.GDP.PCAP.CD (GDP per capita, current US$). The scatter covers 201 country-year rows — BACI includes some sub-jurisdictions (Hong Kong, Macao, Curaçao) that WDI also reports — and yields a Pearson correlation of r = 0.76, with a fitted OLS line of ln(GDPpc) = 9.02 + 1.09 · ECI. The slope says a one-σ rise in ECI is associated with a 109% higher GDP per capita, at the 2022 cross-section.

How fast does the method of reflections converge?

The recipe behind ECI is iterative: start from diversity/ubiquity, then each step the country (product) rank is updated as the mean of its partners’ previous-step rank. Hidalgo & Hausmann (2009) prove the rankings stabilise as n grows, but the paper does not plot the convergence rate. We re-run the reflections on the 2022 binary M_cp matrix (226 countries × 6445 HS6 products where RCA ≥ 1) and track the Spearman rank correlation between iterations. product rankings take a handful more iterations because the ubiquity distribution has a longer right tail than the diversity distribution.

Spectral scree of the country-similarity matrix

The method of reflections converges geometrically at rate |λ₂/λ₁|, where λ₁ and λ₂ are the top two eigenvalues of the symmetric country-similarity matrix M̃_cc′ = Σ_p M_cpM_c′p / (k_c,0 k_c′,0 k_p,0). The dominant eigenvector of M̃ is (up to sign) the uniform vector; the secondeigenvector is the ECI itself (Hausmann & Hidalgo 2009, SI equations 4-6). We power-iterate the top 10 eigenvalues on the 2022 M̃ and plot them as a scree. The top-two spectral gap is |λ₂| / |λ₁| = 0.271, which pins the per-iteration contraction rate of the reflections recipe in Figure 2.

Does 2010 ECI predict 2010-2020 growth?

Hidalgo & Hausmann’s headline claim is not descriptive but predictive: countries with higher ECI than their current income “deserves” should grow faster over the following decade, as income catches up to knowledge. We re-run this test with a fresh out-of-sample window: 2010 ECI plus 2010 log GDPpc projecting onto annualised 2010-2020 income growth. If the conditional ECI coefficient is positive and economically meaningful, the complexity-predicts-growth mechanism that the 2009 paper proposed for 1985-1995 should still be operating two decades later. On 200 countries with valid ECI and WDI GDPpc at both endpoints, the OLS coefficient on ECI₂₀₁₀ is +0.0078 with the log-GDPpc convergence control at -0.0119 and R² = 0.11. A one-σ rise in ECI is associated with a 0.78-pp higher annualised decadal growth rate, conditional on starting income.

Who climbed and who fell on the ECI ladder, 2000 → 2022?

The cross-section of Figure 1 is a snapshot. The HH (2009) framework also implies something about ranks over time: a country’s ECI rank should drift in line with its productive-knowledge accumulation, not its income. By cross-tabulating the ECI rank in 2000 against the ECI rank in 2022 (filtering to countries with at least USD 5 billion in 2022 exports to drop the noisy small-territory tail), we recover the “climbers” (sectoral upgraders that pulled themselves up the complexity ladder) and the “fallers” (typically commodity-exporters whose basket structure regressed as the resource intensification of the 2000s hardened their specialisation pattern). The biggest single climb on the BACI panel is BRN (rank 221 → 108, +113 positions); the biggest fall is LBY (rank 89 → 207, -118 positions).

Numerical comparison

What’s the same, what differs

Same: spectral-reflections construction of ECI from the binary M_cpmatrix; cross-sectional regression ln(GDPpc) = α + β · ECI + ε; reported Pearson r near 0.78. Differs: 2022 cross-section vs 1985 baseline; BACI HS6 (201 economies) vs SITC-based 1985 sample (~128); WDI current-US$ GDPpc vs PWT 6.2 constant-dollar.

Why the correlation differs

The 0.02 gap between our r and the paper’s is unsurprising given (i) a 37-year vintage difference (1985 baseline vs 2022 cross-section), (ii) BACI’s wider country coverage (201 vs 128 in the original), which adds small economies with noisier RCA matrices and thus more measurement error in ECI, and (iii) a different GDP deflator — Hidalgo-Hausmann used constant-dollar GDPpc from Penn World Tables 6.2, while we use current-dollar WDI, which introduces a modest level-shift but leaves the correlation nearly intact. The point estimate also picks up countries that have moved along the complexity ladder since 1985: China’s ECI was barely positive in 1985 and is near the South Korean level in 2022, which densifies the middle of the scatter.

The qualitative claim — that ECI is a strong cross-sectional predictor of income — survives at essentially the same strength in 2022 as in 1985. This is the paper’s long-run stability test, passed.

BibTeX

@article{hidalgo_hausmann_2009,
  author  = {Hidalgo, C{\'e}sar A. and Hausmann, Ricardo},
  title   = {The Building Blocks of Economic Complexity},
  journal = {Proceedings of the National Academy of Sciences},
  volume  = {106},
  number  = {26},
  pages   = {10570--10575},
  year    = {2009},
  doi     = {10.1073/pnas.0900943106}
}

More on this method at /complexity and in the methods notes. Return to the replication gallery.