The Impact of Migration on the Gender Wage Gap

I am currently adding new material to my paper on: "The Impact of Migration on the Gender Wage Gap". Most of the previous work on changes in the gender wage gap over time have focused on the educational attainment and work experience of women. Furthermore, in using the Oxaca decomposition, these studies assume that men and women are perfect substitutes in production, which is inconsistent with on other work on gender discrimination. If men and women are imperfect substitutes in production, then changes in the labour participation of women will affect the gender wage gap not only truncating the wage distribution for women (who opt out of the market), but also by affecting the relative supply of women.
I directly estimate the elasticity of substitutions between men and women using a production function approach and simulate the impact of changes in the gender composition of migration on the relative wage of men and women. To the best of my knowledge this is the first paper to directly do so. In order to control for reverse causality I instrument for the change in the ratio of male to female workers in urban areas with rural-urban migrants (driven by rainfall shocks in rural areas and changes in transportation costs between rural and urban areas).
I find an elasticity of substitution between men and women of 1.78, far from being perfect substitutes. I use this result to simulate the impact of migration on the gender wage gap and find that the 5% decrease in the gender wage gap between 1991 and 2000 was in spite of the increase in the share of female migrants during this period, which, if everything else remained the same, would have increased the gender wage gap by 4%.