especially in markets characterized by low competition among firms in which monopolistic employers can afford to pay male workers higher wages than their productivity would suggest. Trade‐induced competition, however, makes taste‐based discrimination more costly. Oostendorp (2009) studies the role of globalization on the gender wage gap for a large cross‐section of countries and finds that gender wage discrimination falls with more economic development and trade. Evidence for a positive role of trade liberalization in lowering the gender wage gap and increasing female labor demand via reduced discrimination has also been found for Uruguay (Ben Yahmed 2017) and Colombia (Ederington et al. 2009).

But trading could also re‐enforce female discrimination through at least three channels: (i) Trading can increase firm profits through better access to inputs and markets or higher productivity and allows firms to maintain their discriminatory practices (see, e.g., Bernard and Jensen 1999; Ben Yahmed 2017). (ii) Trade‐induced competition could also reduce women’s bargaining power in the labor market (Darity and Williams 1985, and Williams 1987), adding further downward pressure on their wages. Support for this theory has been found in Chinese Taipei, the Republic of Korea, India and China (Berik 2000, Berik et al. 2004, Menon and Van der Meulen Rodgers 2008, and Chen et al. 2012). (iii) A recent study suggests that exporting firms demand highly flexible employees (for working peculiar hours, taking late night phone calls and engaging in international travel arranged at short notice) and therefore discriminate against women as they are perceived to be less flexible. This theory is confirmed in a study on Norway using matched employer‐employee data where the gender wage gap is higher in exporting compared to non‐ exporting firms, but only for higher‐skilled jobs (Bøler et al. 2018). It is not clear if this channel also applies to a developing country context abundant in unskilled workers.

Our paper contributes to the strand of literature linking trade and labor in the following ways: (i) We modify the cost share functions that have been introduced by Feenstra and Hanson (1996) to assess the impacts of trade on different worker types. Rather than focusing on high‐ versus low‐skill workers, our emphasis is on female versus male workers. (ii) We use a rich harmonized micro‐level dataset that covers a large number of developing and emerging countries, while many studies on trade and female labor participation in a developing country context are performed at a more aggregate level.<sup>5</sup> (iii) Finally, we also assess the role of female entrepreneurship, specifically female ownership and management, for the female labor share premium of trading firms.<sup>6</sup> Our paper is closest in spirit to Juhn et al. (2013, 2014) who focus on the relationship between trade liberalization, rather than trading status, and female labor

> 5 Exceptions include Ederington et al. (2009) for Colombia, Chen et al. (2012) for China, and Juhn et al. (2013, 2014) for Mexico.

> 6 For an overview of female entrepreneurship and a discussion of different drivers, see, e.g., Carranza et al. (2018).

3