The Curious Tale of the Nativity

Our nativity story is primarily based on the accounts in Matthew's Gospel and Luke's Gospel. But the accounts are contradictory. In Matthew, Joseph and Mary appear to start the story in Bethlehem and only live in Nazareth after the return from Egypt. In Luke, the story starts and ends in Nazareth. So is there any historical basis to the story? One way to approach this question is to look at the context of the writing of the two source gospels...