1. Allergy
2. Nutrient deficiency
3. Magne (Disease causing Hair fall and itchy skin)
I think yours is having the third problem, Magne. Magne is also of two types,
1. Pododermatitis magne (only affecting paws)
2. Demodectic mange, which harms the whole skin, resulting in patchy fur or scaly skin.
This is a contagious disease, even humans can get affected by it, so keep a little distance and take your dog to a vet. The dog suffering from this disease needs vaccination and proper medication.