Given the obviously crucial role of endogeneity issues in this debate, we carefully consider the causal nature of the relationship. More specifically, we exploit relatively exogenous variation of (migration adjusted) lactose tolerance and pasture suitability as instrumental variables for female autonomy.My translation: women do better with dairy cows than plowing ground for grain, and if women do better, the overall economy does better.
The idea is that a high lactose tolerance increased the demand for dairy farming, whereas similarly, a high share of land suitable for pasture farming allowed more supply. In dairy farming, women traditionally had a strong role; this allowed them to participate substantially in income generation during the late medieval and early modern period (Voigtländer and Voth, 2013).
A similar logic could apply to chickens. You don't need a lot of strength to manage a flock of hens. The one advantage dairy has over chickens is it's easier to store dairy products--cheese specifically, than it is eggs.
I suspect this may be over-simplified. I vaguely remember that the development of plows which could handle the soils of northwest Europe, soils which were heavier than the soils of southern Europe, was a big deal, at least in history as it was taught 60 years ago.