**Caveats** The main limitation of this study is the lack of data on wages in the Tunisian labor force survey (ENPE). The joint prediction of the theoretical model described in this paper is that foreign demand shocks that concentrate on male-intensive industries should decrease both the female-tomale employment ratio and the female relative wage. There is quite extensive documentation in the literature that is indeed happened in other contexts<sup>5</sup> . Therefore, it would be surprising if male wages did not increase relative to female wages after a male-intensive positive foreign demand sock. Furthermore, the fact that we were able to identify that, in Tunisia, the changes in the female-tomale employment ratio work primarily through changes in the behavior of married women serves as an additional check on the theoretical mechanism, since it suggests that the mechanism operates through joint household decisions.

Another caveat relates to aggregation. The empirical strategy developed here relies on exploiting differential regional variation in exposure to exports. However, as documented by Chodorow-Reich (2020), strategies that rely on this kind of cross-sectional variation only capture the effect of additional exposure to exports relative to other regions<sup>6</sup> . One cannot extrapolate from the cross-sectional to the aggregate effect without imposing additional assumptions. In this case, one variable that could make aggregation harder is migration. If households move across provinces in response to negative (positive) shocks, they could make relative estimates larger (smaller) than aggregate estimates.

The empirical specification above only captures short-run effects, since it was limited to using the previous period as the base period. In that context, unless there are no mobility costs, the migration channel is likely more muted. If one thinks of labor as immobile, spillovers are a function of domestic trade patterns. Intuitively, if the provincial consumption basket of a province exposed to a foreign demand shock to its male-intensive sector is tilted towards the male-intensive sector, this will exacerbate the aggregate effect with respect to our estimates. Conversely, if their consumption basket is tilted towards the female-intensive sector, then the aggregate effect will be attenuated with respect to the relative effect.

Therefore, the relative effect could be either a lower bar or an upper bar to the aggregate effect. One cannot put bounds without knowing the consumption patterns at the regional level. Exploring these second-order effects that happen through the production network would be a fruitful avenue for future research.

# **5 Conclusion**

This paper focuses on how gender segmentation in labor markets shapes the local effects of international trade. We first develop a theoretical framework that embeds trade and gender-segmented labor markets to show that foreign demand shocks may either increase or decrease the female-to-male employment ratio. The key theoretical result shows formally that the effects of trade on gendersegmented labor markets depend crucially on (a) the sectors that face the foreign demand shock; and (b) the domestic relevance of the foreign countries in which the demand shocks originate from. If the foreign demand shock from a relevant market happens in a female-intensive (male-intensive) sector, the model predicts that the female-to-male employment ratio should increase (decrease).

> 5This is true both in theory and empirics. Dhyne et al. (2022) shows that in a large class of models there is a positive pass-through of foreign demand shocks to labor (except when labor is fixed by assumption). Aguayo-Tellez, Airola, and Juhn (2010) shows that access to liberalized markets through NAFTA in Mexico led to an increase in relative female wages due to positive shocks to the clothing sector. Similarly, De Hoyos, Bussolo, and N ́u ̃nez (2012) shows that the expansion of the maquilas in Honduras led to an increase of female relative earnings.

> 6In fact, Chodorow-Reich (2020) shows that this estimator is analogous to a differences-in-differences estimator with an additional term that captures spill-overs across regions (SUTVA violations). For instance, Caliendo, Dvorkin, and Parro (2019) show that the negative relative effect captured from the China Trade Shock estimated by Autor, Dorn, and Hanson (2013) may be positive in general equilibrium. Ad ̃ao, Arkolakis, and Esposito (2019) develop a similar argument and show that spill-overs can have a non-negligible effect of attenuation or amplification of the relative effect.

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