In the book, "Inventing Christmas" we find the following quote:
No one knows the time of year, much less the day, of Christ's birth. In fact, we don't know the year Jesus was born. It must have been at least four or five years earlier than the date we customarily recognize.
In the Gospel according to Matthew, we find "Now when Jesus was born in Bethlehem of Judea in the days of Herod the king, behold, wise men from the East came to Jerusalem... " The Gospel according go Luke also placed the birth in the time of Herod, and we know that Herod died in 4 B.C.
Another explanation of the dating discrepancy: Our modern calendar is a modification of the Roman calendar introduced by Julius Caesar in 45 B.C. Caesar based his dating from the foundation of Rome. Well and good. In the sixth century a monk, Dionysius Exiguus, proposed that the Christian Era should date from the year of Christ's birth. Well and good again. However, the monk made a mistake in tallying up Roman history; he forgot the four-year reign of Emperor Octavian. Nobody's perfect.
Christmas Origin - Inventing Christmas - How our Holiday came to be
One more bit of evidence: Tertullian, the great Christian lawyer of the early third century, reported that the birth of Jesus occurred seven or eight years before the supposed date. Censuses took place every fourteen years - A.D. 20, 34 and 48. Counting backward, previous censuses would have been in A.D. 6 and 8 B.C. So when Luke wrote: "In those days a decree went out from Caesar Augustus that all the world should be counted," the census in which the Holy Family was included would have been in 8 B.C., agreeing with Tertullian's estimate.
Now you know more about the date of Christ's birth than most people, which should come in handy at dinner parties, if not in church.
Yes Virginia there is a Santa Claus. He exists as certainly as love and generosity and devotion exist and you know that they abound and give to your life its highest beauty and joy. Alas! how dreary would be the world if there were no Santa Claus! It would be as dreary as if there were no Virginias. There would be no childlike faith then no poetry no romance to make tolerable this existence.' (Excerpt from Chapter 1)