Why a parrot lives long as compared to a crow ?

Parrots are the longest lived order of birds:
cockatoos & Amazonian parrots can reach the age of 75 or older.Even budgerigars live 15-25 years,which is an exceptionally long life for such small animals.The reason for this is that they have few predators & are often colonial,so their chances of finding food are better.

Species with lots of predators(crow & other birds) can't expect to escape being eaten for more than a few years.So they evolve to reproduce as qucikly as possible,& in large number.This takes a lot of metabolic resources out of the adults,& they are more likely to die shortly after breeding.Even more importantly,genetic mutation that might cause disability or disease later in life don't have any effect on natural selection(i.e. Parrot)because those individuals have already reproduced.This means mutations of this sort tend to accumulate in the species,& so its maximum natural life span will tend to shorten.
In the absent of parrot predators,natural selection has weeded out most of those mutation from their gene pool.