According to a report published by the Children's Hospital of Philadelphia, keeping a pet in the house can improve the sense of confidence and self esteem in your children. The report also mentions that children feel emotionally more secure when they have a pet of their own.

Having a pet in the house has numerous advantages for your young ones, some of them are:
They are exposed to the cycle of life through their pets by coming to know about issues like birth, sickness, accidents, and grief.
By taking care of a pet, children learn how to be responsible and caring.
They learn important lessons in patience and respect for other living creatures.
Most importantly, they learn how to share, love, and be loved in return.
Via: Y!News