On the Origins of Gender Roles: Women and the Plough

A new paper by Alesina, et al, claims:

We have provided empirical evidence suggesting that contemporary cultural differences in attitudes about the role of women in society have been shaped by historical forces. Specifically, we have shown that individuals, ethnicities and societies whose ancestors used plough agriculture today have more “traditional” beliefs about the role of women in society. 

The authors do not mention war as a determinant of gender roles: say for example men go to war and women stay home. I wonder what is the relative importance of the historical use of plough agriculture vs the historical frequency of war to determine gender roles.