Which hormone is largely responsible for women having wider hips than men?

Estrogen 

Estrogens are hormones also referred to as female sex hormones because these hormones are primary in women. They are produced in the ovaries, adrenal glands, and fat tissues.  The function of estrogen in the body is complex—it is essential in the growth and development of female breasts, pubic and armpit hair, and the regulation of the menstrual cycle and reproductive system. It also prepares the reproductive organs for conception and pregnancy. Women have wider hips because of estrogen, too.  

The answer to your question is

Estrogen

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