Ok, so by "gender equality", you merely mean "statistically similar representation of women in assorted reference classes" rather than "equal treatment". (The latter is what I originally thought you meant.)
Of course, I'd be rather hard pressed to see what that has to do with fertility. I'd suggest maybe that there is a simpler explanation for the phenomenon you observed - the countries with gender equality also seem to have lots of subsidies for parenthood. Most likely the subsidies are the cause of fertility.
If the subsidies are the actual cause, we could probably get higher fertility by subsidizing parenthood together with higher societal expectations of maternal activities from women. The carrot of free money for the fertile life path, and the stick of lower social status for the less fertile path.
(Not that I advocate this course of action, but I'm not in favor of encouraging fertility in any case.)
Of course, I'd be rather hard pressed to see what that has to do with fertility. I'd suggest maybe that there is a simpler explanation for the phenomenon you observed - the countries with gender equality also seem to have lots of subsidies for parenthood. Most likely the subsidies are the cause of fertility.
If the subsidies are the actual cause, we could probably get higher fertility by subsidizing parenthood together with higher societal expectations of maternal activities from women. The carrot of free money for the fertile life path, and the stick of lower social status for the less fertile path.
(Not that I advocate this course of action, but I'm not in favor of encouraging fertility in any case.)