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 f_x 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.

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 (5.5-8), and consistent with the thick-tail calibrations of Eaton-Kortum (2002) and Bernard-Eaton-Jensen-Kortum (2003).

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).

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*_x ship 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%.

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.

Numerical comparison

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 with Melitz-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.