This thesis comprises four self-contained papers that rely on applied micro-econometric methods to understand which factors are important in shaping the gender wage gap in globalized firms and how firms innovate when exposed to trade-induced shocks.

In the first paper, we study how the within-firm gender wage gap in Sweden is affected by the degree of gender inequality in the home country of foreign investors. The results suggest that gender norms of the home country matter-the wage gap between men and women in foreign-owned subsidiaries appears to increase with the degree of gender inequality prevailing in the investors' home market.

The second paper aims to improve our understanding of how exports and the associated need for communication with foreign partners affect the gender wage gap. Our key finding is that exports of goods that are intensive in interpersonal contacts widen the gender wage gap. The negative wage effect is robust across various specifications and is most pronounced for domestic exporting firms, which mainly deal with external contractors. We ascribe this result to a male comparative advantage in bargaining-a skill that is especially needed and rewarded when serving foreign markets, where contracting problems manifest themselves.

In the third paper, we examine whether exposure to gender inequality at export destinations (in the form of customer discrimination) impacts the gender wage gap in exporting firms. Relying on high-quality matched employer-employee data from Sweden, we demonstrate that exports to gender-unequal destinations increase the within-firm gender wage gap. We find the most pronounced negative wage impacts for female managers, who appear to be particularly exposed to the gender inequality of export partners.

In the fourth paper, I explore how exposure to import competition across different geographical aggregations alters the innovation activity of firms in the manufacturing sector. Using detailed geographical information on the location of manufacturing producers in Sweden, I analyze whether increased competitive pressure from abroad triggers a different response in innovation at the national, local labor market, and municipality levels. By exploiting exogenous shocks in the foreign export supply of intermediate manufacturing goods, I find the most pronounced effects at the lowest levels of geographical aggregation, which are consistently negative across different innovation metrics.