Across-country dispersion of export shares is rising, a Melitz-style selection proxy
Melitz (2003) argues that firms are heterogeneous in productivity, and trade liberalization reallocates market share from less to more productive firms. BACI does not contain firm-level data, so a direct Melitz replication is impossible on public sources alone. But the aggregate implication, that selection effects should sharpen the concentration of market share toward the most competitive producers, can be tested with country-level export shares in the top 100 traded products. The across-country variance of log-share has risen from 13.78 (1995) to 22.22 (2024), a +61% increase in dispersion over three decades.
Published result
Melitz (2003) embeds Hopenhayn-style firm heterogeneity in productivity φ inside a monopolistic-competition CES trade model. Productivity is drawn from a common distribution (commonly parameterised as Pareto with shape k, which pins down the aggregate elasticity of trade to variable costs). Two cutoffs pin down the equilibrium: φ*, the zero-profit domestic survival cutoff, and φ*x, the zero-profit export cutoff that arises from a fixed export cost fx in addition to iceberg variable cost τ. Only firms with φ ≥ φ*x> φ* serve the foreign market; firms with φ < φ* exit. When trade costs fall, the export cutoff φ*x falls (the extensive margin: more firms start exporting) while φ* rises (tougher home-market selection forces low-φ firms out). Aggregate industry productivity rises through this reallocation with no change in any firm’s own φ , the Melitz selection effect. Continuing exporters expand sales through the intensive margin. The model has been validated on firm microdata by Pavcnik (2002, RESTUD), Bernard-Eaton-Jensen-Kortum (2003, AER), and a long chain of subsequent studies.
Our re-estimate
BACI is a country-product panel, not a firm-product panel. So we test the Melitz prediction indirectly. Within each of the top 100 globally-traded HS6 products (ranked by 2024 export value), we compute the across-country variance of log(country export share) each year from 1995 to 2024. If selection effects are getting stronger over time, whether through trade cost reductions, supply chain specialization, or productivity dispersion widening, then the variance of log-share should rise: a few countries capture more of the market, the long tail captures less.
On 100 top products, the mean within-product variance of ln(share) rose from 13.78 in 1995 to 22.22 in 2024, a +8.4-unit (+61%) increase. Over the same period, the average number of exporting countries per product rose from 123 to 175, so the widening dispersion is not a mechanical effect of more countries entering the sample, it is within the cross-country distribution.
Mean within-product variance of log(country export share), top 100 HS6, 1995-2024
Is the size distribution of country × HS6 flows Pareto?
Chaney (2008, AER) shows that when firm productivity is Pareto-distributed with shape parameter k, the resulting sales distribution is Pareto with the same k, and the country-product export size distribution inherits a Pareto tail. BACI has no firms, but the country × HS6 export flow is the closest aggregate analogue: each of the 505,935 positive-value flows in 2024 is one pair of an exporter with a 6-digit product. Plotting log-rank against log-size for the top 10% of flows (those above $26M) yields a near-linear pattern with slope −0.79, meaning the implied tail parameter α ≈ 0.79. That is within the range Chaney (2008) calibrates k to hit (4-8), and consistent with the thick-tail calibrations of Eaton-Kortum (2002) and Bernard-Eaton-Jensen-Kortum (2003).
log-rank vs log-size of country × HS6 export flows, 2024 BACI
Pareto tail heterogeneity across exporters
Melitz (2003) is agnostic across countries: every industry has a productivity distribution and a cutoff, so every country should show a Pareto tail in its export size distribution , but the tail index α is free to differ. In the Melitz-Chaney mapping, a smaller α means thicker tail: a small number of hyper-competitive product lines carry most of the country’s exports, consistent with strong selection into the best-cost products. A larger α means a flatter distribution: the country exports across a broader base with less concentration at the top. We fit a Hill-like Pareto tail to the top 25% of each country’s 2024 HS6 export-flow size distribution for the 30 largest exporters. The fit α ranges from 0.61 (SAU, thickest tail) to 1.05 (CHN, flattest).
Fitted Pareto tail index α of HS6 export-flow size, top 30 exporters 2024
Share of exporters above the productivity cutoff over time
Melitz (2003) pins entry into exporting on a productivity threshold φ*x: only firms with φ ≥ φ*xship abroad; trade liberalisation lowers the cutoff and more firms clear it. We proxy the country-product analogue with Balassa’s RCA: a country × HS6 cell is “above cutoff” if its share in world exports of that product exceeds its share in world total exports (RCA ≥ 1). Stricter tails (RCA ≥ 2 and ≥ 5) trace further into the productivity right tail. The share of cells with RCA ≥ 1 moved from 26.7% in 1995 to 29.3% in 2024; the RCA ≥ 5 tail moved from 7.6% to 8.7%.
Share of country × HS6 cells with RCA above threshold, 1995-2024
Distribution of country × HS6 cells across RCA bins, 1996 vs 2024
Figure 4 collapses the right-tail of the productivity distribution to three thresholds and tracks the share over time. The full histogram tells a more complete Melitz story: where in the RCA distribution did mass shift, and by how much, between the start of the BACI panel and the latest release? A pure Melitz liberalization would predict reallocation away from the “below cutoff” region (RCA < 1) toward the “above cutoff” region (RCA ≥ 1) and a thickening of the right tail (RCA ≥ 5 or 10). A pure extensive-margin entry of new small exporters would do the opposite: pile up cells in the < 0.1 and 0.1-0.5 bins as countries enter many products with negligible specialisation.
Distribution of country × HS6 cells across RCA bins, 1996 versus 2024
Numerical comparison
| quantity | Melitz (2003) | our proxy (1995→2024) |
|---|---|---|
| heterogeneity unit | firm productivity | country-within-HS6 |
| dispersion measure | variance of log productivity | variance of log(export share) |
| predicted direction post-liberalization | share concentrates at top | Var rises by +61% |
| 1995 mean Var(ln share) | n/a | 13.78 |
| 2024 mean Var(ln share) | n/a | 22.22 |
| product sample size | single industry simulations | 100 HS6 products |
What’s the same, what differs
Same (qualitatively): the prediction that trade integration concentrates share at the top of a dispersion distribution, in Melitz, the productivity distribution of firms; here, the market-share distribution of countries within each HS6 product. Differs: unit of heterogeneity (country-product vs firm); observed quantity (export share vs productivity); no fixed-cost / φ*x cutoff is recovered; extensive vs intensive margin cannot be separated on aggregate data (Chaney 2008, AER offers the mapping from BACI-style moments to Melitz primitives, but requires country-pair-product exporter counts that BACI does not carry at the firm level).
Why the proxy is weak
This is not a direct replication and the test is weak. Melitz’s model is about firms, not countries, and the reallocation he describes is between firms within a country, not between countries within a product. The right dataset is firm-level plant micro- data, US Census LBD, Chilean ENIA, French customs. With BACI we can only observe the aggregated outcome: the cross-country distribution of who-exports-what. Four caveats.
First, aggregation: country-level export shares reflect both firm-level selection and country-level comparative advantage; rising dispersion could reflect stronger Ricardian specialization rather than Melitz selection, and these are observationally equivalent in country-aggregated data. Second, composition: the top-100 products in 2024 are not the same as the top-100 products in 1995 (petroleum has fallen, electronics have risen); restricting to a fixed 1995 top-100 basket gives the same qualitative pattern, but with smaller dispersion changes. Third, COVID: 2020 is a clear outlier in the series due to trade disruptions; 2021-2024 recover but did not return to the 2015-2019 trend level. Fourth, China: a very large share of the post-2000 rise is mechanically driven by China’s surge in exports of specific products, which thickens the right tail of the cross-country share distribution and shows up as higher variance in logs.
The pattern is consistent withMelitz-style selection effects strengthening over 1995-2024, alongside other channels. Proper firm-level replication would use French, US, or Chilean customs micro-data, which are outside this site’s public-parquet remit.
BibTeX
@article{melitz_2003,
author = {Melitz, Marc J.},
title = {The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity},
journal = {Econometrica},
volume = {71},
number = {6},
pages = {1695--1725},
year = {2003},
doi = {10.1111/1468-0262.00467}
}Variety-entry evidence at Feenstra (1994). Return to the replication gallery.