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Imbs and Wacziarg (2003, American Economic Review 93(1): 63-86) documented a hump-shaped relationship between sectoral concentration and income: poor countries diversify as they grow richer, but past a threshold, re-concentration sets in. We replicate their Figure 1 using 2024 BACI HS6 export data aggregated to HS2 chapters, pair each country with its contemporaneous World Bank GDP per capita (current USD, indicator NY.GDP.PCAP.CD), and estimate the quadratic of Theil on log-income over 188 countries. The convexity coefficient is b̂2 = 0.030 (positive, consistent with a hump). Our peak-income estimate lands at $150K in current USD, against Imbs-Wacziarg's 1985-USD estimate of ~$9,000 (roughly $25,830 in 2024 dollars after BLS CPI-U deflation).
For each country we compute the Theil entropy index of its HS6 exports aggregated to the 2-digit HS chapter level: Ti = Σk sik · ln(sik · Ni), where sik is country i's share of HS chapter k in its own export basket and Ni is the number of HS chapters it exports to (at least one dollar). Higher Theil means more concentrated. IW 2003 used UNIDO sectoral employment and Feenstra's trade data at the 3-digit ISIC level; we use BACI HS2 exports only, which the workbench stores natively. Figure 1 plots Theil against log GDP per capita in current USD and overlays the quadratic fit.
@misc{hossen_2026_figure-1,
author = {Md Deluair Hossen},
title = {Theil index of HS2 export concentration vs GDP per capita, 2024},
year = {2026},
howpublished = {TradeWeave Workbench},
url = {https://tradeweave.org},
note = {Figure: Figure 1}
}WITH cyp AS ( SELECT c.iso3, SUBSTR(cyp.product_code, 1, 2) AS hs2, SUM(cyp.export_value) AS v FROM 'country_year_product/year=2024/*.parquet' cyp JOIN (SELECT iso3, MIN(code) AS code FROM 'countries.parquet' GROUP BY iso3) c ON c.code = cyp.country_code WHERE cyp.export_value > 0 GROUP BY c.iso3, SUBSTR(cyp.product_code, 1, 2) ), tot AS (SELECT iso3, SUM(v) AS tot_v, COUNT(*) AS n_hs2 FROM cyp GROUP BY iso3), shr AS (SELECT cyp.iso3, cyp.v/tot.tot_v AS s, tot.n_hs2 FROM cyp JOIN tot USING(iso3)) SELECT iso3, SUM(CASE WHEN s>0 THEN s*LN(s*n_hs2) ELSE 0 END) AS theil FROM shr GROUP BY iso3;
IW 2003 reported their minimum-concentration income at approximately $9,000 in 1985 constant US dollars: below that, Theil falls with growth; above, Theil rises again. Cadot, Carrère & Strauss-Kahn (2013, Review of Economics and Statistics 93(3): 590-605), using Kazakhstan-style BACI export panels for 156 countries 1988-2006, found a peak near $25,000 in 2000 USD, above the IW estimate. The peak depends heavily on the panel, the concentration measure, and whether production or trade data are used. Our 2024 cross-section, quadratic in log GDP-pc, gives a peak (minimum of Theil) at $150K current USD.
The x-axis here is log y (so the fitted parabola is a parabola), not y, but the tick labels show y (current USD) for readability.
IW 2003 made their claim from cross-section. Cadot et al. (2013) pushed it to within-country panels and found the pattern holds in levels but weakens in first differences. Here we plot the HS2 export Theil for four contrasting growth stories over the BACI window. Vietnam and China are textbook rapid-catch-up cases. India is the slower-liberalisation comparator. The United States is the post-peak benchmark whose Theil should, under the hump hypothesis, have risen modestly as it specialised into services-complement manufacturing (semiconductors, aerospace, pharmaceuticals).
A known limitation of this replication: IW 2003 used UNIDO sectoral employment at 3-digit ISIC. What we have in the workbench is BACI exports at HS6 (aggregated to HS2). The two diverge for three structural reasons.
As a diagnostic, Figure 4 contrasts our HS2 export Theil for four exemplar countries at different development stages with their implied production-Theil rank from the IW hump. If the two measures told the same story, Germany (very high GDP-pc, post-peak) would show high export Theil and very high production Theil. It does not: Germany's export Theil is 1.43, lower than Bangladesh's 3.16 only because Germany spreads exports across many mid-size chapters, while Bangladesh concentrates in HS61-63 (apparel). Without UNIDO employment we cannot close this gap here; the workbench plans a FAOSTAT + UNIDO ingest in a later revision.
@misc{hossen_2026_figure-4,
author = {Md Deluair Hossen},
title = {Export Theil in 2024, four benchmark economies},
year = {2026},
howpublished = {TradeWeave Workbench},
url = {https://tradeweave.org},
note = {Figure: Figure 4}
}Parteka & Tamberi (2013, Economic Modelling 33: 1-11) and Cadot, Carrère & Strauss-Kahn (2011) showed that the IW hump survives under alternative concentration measures: Gini, Herfindahl, and simple count of active products. We replicate with the HS2 Herfindahl-Hirschman index on the same 2024cross-section: HHI = Σk sik² × 10,000 on exporter HS2 shares. Higher HHI = more concentration, on a 0-10,000 scale.
Imbs and Wacziarg (2003) describe diversification as a shift in the concentration measure; Hausmann and Klinger (2006, Center for International Development WP 128) and Hausmann, Hwang and Rodrik (2007, Journal of Economic Growth 12(1)) describe it as a sequence of product discoveries , HS6 lines that were effectively absent from the export basket and crossed into material scale. Figure 6 counts these jumps directly. For each country we compare the 1998-2002 five-year average with the 2020-2024 five-year average at the HS6 level and flag any product whose early-window average was below $1M and whose late-window average exceeds $25M. Countries are ranked by the count of such discovery events, with the dollar total of the newly-jumped products in 2020-2024 appended in the label.
Cadot, Carrère & Strauss-Kahn (2011, Review of Economics and Statistics 93(2); and 2013, Journal of Economic Surveys 27(4)) argued that the Imbs-Wacziarg hump identified from a single cross-section can be confounded with country fixed effects: a country may appear on the downward or upward arm of the hump because of structural factors (endowments, institutions, geography) that are orthogonal to its current growth rate. The first-difference version of the test sidesteps this. For each country we compare the early window (1998-2002 five-year average) with the late window (2020-2024 five-year average) and compute ΔTheil alongside Δlog(GDP-pc). Under the IW hump a country whose initial GDP-pc lay below the peak should show a negative ΔTheil as it grew (diversification), and a country above the peak should show a positive ΔTheil (re-specialization). The scatter below is the two-panel version of this test, split on whether the country's average GDP-pc across the two windows sat below or above our cross-section peak estimate.
Hummels and Klenow (2005, American Economic Review 95(3): 704-723) decompose export growth into an intensive margin (more of the same lines) and an extensive margin (new product lines), and document that richer countries trade at a wider extensive margin. Figure 8 reports the count of HS6 product lines a country exports above USD 1M in 2024, binned into deciles of GDP per capita. This complements the Theil/HHI concentration cuts above: where those measure within-basket concentration on the intensive margin, the extensive margin measures breadth, the basket size itself. The Hausmann, Hwang and Rodrik (2007, Journal of Economic Growth 12(1)) story has both pieces, so a diversification page that only reports concentration is incomplete. The HS6 universe is roughly 5,022 lines in CEPII BACI 202501; the USD 1M threshold filters reporting noise per the Cadot, Carrere and Strauss-Kahn (2011) convention.
The cross-section convexity in log GDP-pc using 2024 BACI HS2 exports is positive, consistent with a Theil minimum around $150K. This is in the same direction as IW 2003 but at a higher income level than their $9,000 (1985 USD) estimate even after CPI rescaling, closer to the Cadot, Carrère & Strauss-Kahn (2013) range.
A cleaner test would use (i) UNIDO INDSTAT sectoral employment at ISIC 3-digit, (ii) a country panel with country fixed effects rather than a single cross-section, and (iii) Gini and Herfindahl as robustness measures alongside Theil (as in Hidalgo & Hausmann 2009, who note that entropy indices, variance of log-shares, and Gini give qualitatively similar hump-shape results under mild regularity conditions). BACI at HS2 is a coarse but self-consistent proxy; it is suggestive, not definitive.
@misc{hossen_2026_figure-2,
author = {Md Deluair Hossen},
title = {Fitted Theil vs income, with IW-2003 peak and our 2024 peak annotated},
year = {2026},
howpublished = {TradeWeave Workbench},
url = {https://tradeweave.org},
note = {Figure: Figure 2}
}@misc{hossen_2026_figure-3,
author = {Md Deluair Hossen},
title = {HS2 export Theil index, 1995-2024, four economies},
year = {2026},
howpublished = {TradeWeave Workbench},
url = {https://tradeweave.org},
note = {Figure: Figure 3}
}@misc{hossen_2026_figure-5,
author = {Md Deluair Hossen},
title = {HHI of HS2 export concentration vs GDP per capita, 2024},
year = {2026},
howpublished = {TradeWeave Workbench},
url = {https://tradeweave.org},
note = {Figure: Figure 5}
}@misc{hossen_2026_figure-6,
author = {Md Deluair Hossen},
title = {HS6 jump events per country (1998-2002 avg < $1M → 2020-2024 avg ≥ $25M), top 20},
year = {2026},
howpublished = {TradeWeave Workbench},
url = {https://tradeweave.org},
note = {Figure: Figure 6}
}WITH early AS (SELECT country_code, product_code, AVG(export_value)*1000 v FROM 'country_year_product/**/*.parquet' WHERE year BETWEEN 1998 AND 2002 AND export_value>0 GROUP BY 1,2), late AS (SELECT country_code, product_code, AVG(export_value)*1000 v FROM 'country_year_product/**/*.parquet' WHERE year BETWEEN 2020 AND 2024 AND export_value>0 GROUP BY 1,2) SELECT l.country_code, COUNT(*) n_jumps FROM late l LEFT JOIN early e USING (country_code, product_code) WHERE COALESCE(e.v, 0) < 1e6 AND l.v >= 25e6 GROUP BY 1 ORDER BY n_jumps DESC;
@misc{hossen_2026_figure-7,
author = {Md Deluair Hossen},
title = {Re-specialization test: Δ Theil vs Δ log GDP-pc, 1998-2002 → 2020-2024},
year = {2026},
howpublished = {TradeWeave Workbench},
url = {https://tradeweave.org},
note = {Figure: Figure 7}
}-- within-country Δ Theil and Δ log GDP-pc, 1998-2002 → 2020-2024
WITH early_shr AS (
SELECT country_code, SUBSTR(product_code,1,2) AS hs2,
AVG(export_value) AS v
FROM 'country_year_product/**/*.parquet'
WHERE year BETWEEN 1998 AND 2002 AND export_value > 0
GROUP BY country_code, SUBSTR(product_code,1,2)),
early_tot AS (SELECT country_code, SUM(v) tot, COUNT(*) n FROM early_shr GROUP BY country_code),
early_th AS (SELECT s.country_code, SUM((s.v/t.tot) * LN((s.v/t.tot) * t.n)) th
FROM early_shr s JOIN early_tot t USING (country_code) GROUP BY s.country_code),
-- same for late window 2020-2024, then JOIN by country_code, pair with WDI GDP-pc
SELECT iso3, (th_late - th_early) AS d_theil, LN(gdp_late) - LN(gdp_early) AS d_log_gdppc;@misc{hossen_2026_figure-8,
author = {Md Deluair Hossen},
title = {HS6 export lines above USD 1M, by GDP-pc decile, 2024},
year = {2026},
howpublished = {TradeWeave Workbench},
url = {https://tradeweave.org},
note = {Figure: Figure 8}
}-- HS6 lines >= USD 1M per country, 2024 SELECT c.iso3, COUNT(*) AS n_lines FROM 'country_year_product/year=2024/*.parquet' cyp JOIN (SELECT iso3, MIN(code) AS code FROM 'countries.parquet' GROUP BY iso3) c ON c.code = cyp.country_code WHERE cyp.export_value >= 1000 -- BACI thousands USD; 1000 = USD 1M GROUP BY c.iso3;