Project Frontier Jorge Menéndez-Pidal

TH-001 · Revised Master’s Thesis · October 2026

The Exporter Hump

Trade, Firm Premia and the Wage Distribution across Spanish Regions, 2006–2022

Jorge Menéndez-Pidal

Abstract

With heterogeneous firms, trade raises wage inequality where few firms export and lowers it where most do. I show that the variance of log wages in a local labour market is hump-shaped in the employment share of exporters for any productivity distribution, and that the shape of the hump carries information about the tail of the productivity distribution that can be read from wage data alone: with a Pareto tail, wage dispersion among exporters does not vary with the exporter share, and the peak lies between 1/e and 1/2. Foreign demand raises inequality up to and beyond that peak. Using five waves of Spain’s Wage Structure Survey (2006–2022), which record whether each worker’s employer sells mainly abroad, I find the hump across region–sector cells, with a peak at 0.35 (95% interval 0.29–0.43). Within-exporter wage dispersion does not vary with the exporter share, as a Pareto tail implies. Most Spanish employment lies on the rising side of the hump. Three instruments (EU demand for each sector’s products, the regional product mix and exposure to the construction bust) have weak first stages, so the causal effect of exporting is not identified. Model-based counterfactuals bound it: a five-point rise in the exporter share raises the variance of log wages by about 2 points (×1000) according to within-cell estimates and an exact accounting, and by 13 according to the cross-section, against an observed fall of 34 points over 2006–2022. The 2008 bust raised measured inequality through the loss of mid-wage construction jobs but compressed the wage structure more. The 2019 minimum-wage increase compressed the lower tail in proportion to its regional bite.

Keywords trade and inequality, exporter wage premium, firm heterogeneity, composition effects, minimum wage, Spain

No.
TH-001
Date
08.10.2026
Status
Draft v1.2
Area
Inequality
Fields
International trade · Labor economics
Method
Theory · survey microdata · shift-share · bounds
Data
Spanish Wage Structure Survey, 5 waves, 2006–2022
JEL
F16 · F14 · J31 · J38 · R23

01The question

Exporters pay more. So when trade expands exporting, it widens the gap between the firms that export and those that do not. But that cannot go on forever: when every firm exports, the gap disappears.

Where does trade raise wage inequality, where does it lower it, and which side of that line is Spain on?

The object is the variance of log wages in a local labour market, a region–sector cell. The paper asks how three margins move it: which firms export, how much more exporters pay, and which jobs exist at all. It replaces the author's 2021 master's thesis on the same question.

02The exporter hump

Wages combine a worker component, a firm premium that rises with productivity, and an extra premium \(\varphi\) for exporting. Firms export when their productivity clears a threshold, and a share \(\rho\) of employment ends up in exporters. For any productivity distribution,

\[V(\rho)=\sigma_a^2+\lambda^2\operatorname{Var}(x)+\rho(1-\rho)\big[\varphi^2+2\lambda\varphi\,\Delta(\rho)\big]\]

where \(\Delta\) is the productivity gap between exporters and non-exporters. The bracketed term is positive and vanishes when nobody or everybody exports: inequality is hump-shaped in the exporter share. The hump has two sources. One is the exporter premium itself. The other, and larger, is the covariance between productivity and exporting: exporters are the most productive firms, so they would pay more even without the export premium.

03The peak and the tail

With Pareto productivity the covariance term is \(-\rho\ln\rho\), steep where exporters are scarce, and the peak lies between \(1/e\approx0.37\) and \(1/2\). With log-normal productivity it sits at exactly \(1/2\); with a Pareto tail above a log-normal body, its location also depends on the body. If exporters occupy a Pareto tail above a log-normal body, wage dispersion among exporters should not vary with \(\rho\), while dispersion among non-exporters should. These are two tests of the tail of the productivity distribution that do not require observing productivity.

04Foreign demand

More foreign demand lowers the export threshold (\(\rho\) rises) and raises the exporter premium (\(\varphi\) rises). The premium margin always raises inequality, so

\[\frac{dV}{d\ln A^*}=\zeta\rho\,G(\rho)+\Lambda\,\partial_\varphi V,\qquad \partial_\varphi V>0\]

and any turning point, above which trade compresses wages, lies beyond the peak of the hump. With a Pareto tail the turning point is unique, and the effect of a shock is itself a hump in the initial exporter share: zero where no firm exports, largest at intermediate exposure.

05Evidence

Spain's Wage Structure Survey records, for about 200,000 workers per wave, both the hourly wage and whether the employer's main market is domestic, the EU or the world. Five waves, 2006–2022, give 543 region–sector–year cells.

  • The hump is there. Wage inequality is concave in the exporter share, with a peak at 0.35 (95% interval 0.29–0.43). It survives sector-by-year and region fixed effects and controls for worker characteristics, and it disappears in a placebo that classifies firms by whether they sell beyond their region rather than abroad.
  • The covariance drives it. The exporter premium alone generates a tenth of the curvature.
  • The tail looks Pareto. Residual dispersion among exporters is flat in \(\rho\) (\(p=0.27\)); among non-exporters it is not (\(p=0.03\)). The peak points the same way, but the survey understates exporting, which could produce that on its own.
  • Spain is on the rising side. 90% of private employment is in cells whose measured exporter share lies below the lower end of the confidence interval for the peak.
  • But the causal effect is not identified. EU demand for a sector's products does not predict Spain's sectoral exports, consistent with exports having been pushed out by the domestic slump rather than pulled by foreign demand. A regional design using customs data by province has the right sign but a weak first stage, and a design based on exposure to the construction bust has none.
  • The effect is bounded. A five-point rise in the exporter share, the size of Spain's rise in 2006–2014, raises the variance of log wages by about 2 points (×1000) with within-cell estimates and the exact accounting, and by 13 with the cross-section, against an observed fall of 34 points over 2006–2022.

06What happened to Spanish wages

Hourly wage inequality in the private sector fell between 2006 and 2022. The 2008 bust destroyed construction jobs that were homogeneous and paid near the median, which widened measured inequality through composition. But the wage structure compressed more. The 2019 minimum-wage increase compressed the lower tail in proportion to its bite: 10 more percentage points of workers below the new floor meant 6.6 log points more compression of P50/P10, with no change in the upper tail. An exact accounting puts the contribution of exporting at 1 to 1.5 points of variance (out of about 200) per four-year period.

07Results

Trade raises wage inequality in most of Spain, but it was not what moved Spanish wages.

MarginEffect on wage inequality, 2006–2022
Exporting (extensive + premium)Positive, small: 1–1.5 points of variance per period; 2–13 points per 5 pp rise in the exporter share (model bounds)
Composition of employment, 2006–10Positive: +19 points (loss of mid-wage construction jobs)
Wage structure, 2006–10Negative: −34 points
Minimum wage, 2018–22Lower tail compressed in proportion to the bite; upper tail unchanged
CaveatThe hump is a cross-sectional regularity; within cells over time the data are uninformative. Three instruments are weak, so the effect of exporting on inequality is not causally identified; the paper bounds it with the model instead. The survey records a firm's main market, not whether it exports, and regions are NUTS-1 aggregates.

08Status

LevelWhere it stands
ModelSix propositions, proved and verified symbolically and by Monte Carlo under five productivity distributions.
DataEES microdata 2006–2022; Eurostat Comext; Spanish customs records by province, 2016–2022.
NextSocial Security employer–employee data linked to firm-level exporter status, to run the venting-out design at the level of firms and provinces; destination-specific shocks (Brexit, the 2018 US tariffs, the 2014 Russian embargo); the size distribution of Spanish firms to test the peak. Draft v1.2.

WP-001 shows that Spain's housing-supply elasticity collapsed after 2008. Appendix C of this paper shows why that matters here: the real-wage gains from a regional trade shock shrink when housing supply cannot respond.

Citation

Menéndez-Pidal, J. (2026). “The Exporter Hump: Trade, Firm Premia and the Wage Distribution across Spanish Regions, 2006–2022.” Project Frontier Revised Master’s Thesis No. 001, Madrid.

BibTeX 
techreport{menendezpidal2026hump,
  author      = {Men{\'e}ndez-Pidal, Jorge},
  title       = {The Exporter Hump: Trade, Firm Premia and the Wage Distribution across Spanish Regions, 2006–2022},
  institution = {Project Frontier},
  type        = {Revised Master’s Thesis},
  number      = {001},
  address     = {Madrid},
  year        = {2026},
  month       = {oct}
}

Preliminary draft. Comments welcome; please do not cite without permission.