Quote from one article, dealing with the issue ...
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Luke went on to say that, “all were proceeding to register for the census, everyone to his own city.” (Luke 2:3) It has seemed a problem that the Jewish method of returning to one’s own tribal headquarters to be “numbered” was used for a census under Herod.14 The Romans usually took a census in one’s home town.15 However, in a census for inheritance taxation it would be expected that this would be conducted where the tribal records were kept, no matter who conducted the census. Joseph was a descendent of David of the tribe of Judah. David’s ancestral home was in Bethlehem, and in that town the land records and genealogies required for such a census would have been located. Or, simply, Joseph was born in Bethlehem but then lived in Nazareth. Joseph and Mary went to Bethlehem to register for this census, and there Jesus was born.
As will be seen in the following chapters, the evidence suggests a winter birth for Jesus. But, why would Joseph and Mary journey to Bethlehem in the middle of winter to register for the census? There are several possibilities. Joseph may have recently inherited some land. Since the special taxation was related to inheritances, Joseph journeyed to Bethlehem to claim his estate and settle any taxes due. He would have there registered his property for the census. Or, perhaps Joseph had recently become eighteen years of age, and as an adult was required to then register as an independent household.16 Or, they had recently married, and the registration of the family was required. Or, Joseph and Mary thought that their child might be the promised Messiah and that the Messiah was to be born in Bethlehem (Mic. 5:2). They may have timed their trip to Bethlehem for the census to ensure that Jesus was born there. Also, registration may have been required before the end of the Roman year, that is, December 31, and they were late. However, there is no need to require that Joseph’s registration occurred immediately after the census for taxation was decreed. There are other possibilities, but these are mostly speculation.
IV. Conclusion
In support of Luke’s description of the census that brought Joseph and Mary to Bethlehem, it is confirmed that Augustus did decree a 5% world wide inheritance tax to support the military. This was sometime before the second taxing in 6 CE and likely before Herod’s death in 4 BCE; it was at some point discontinued. When this census took place cannot yet be determined, and Quirinius’ official status at that time is unknown.
An alternate translation suggests that Luke was actually saying that the census was only the one before that when Quirinius was governor of Syria in 6 CE. Luke was not saying he was governor when the first census was taken.
It does not seem presently possible to establish an earliest limit for the birth of Jesus. As such the search must go elsewhere to establish the date of His birth. As will discussed in the following chapters, the conception of John the Baptist and Jesus offers a surprising answer.
http://www3.telus.net/trbrooks/firstcensus.htm
There is also a papyrus from about 80 AD in Egypt telling of a census there, in which everyone was ordered to return to their home area for counting.
We date the death of Herod at 4 BC, because Josephus says he died shortly after an eclipse of the moon. But there were a couple of partial eclipses after that, so that it is possible Herod lived past 4 BC and died later.
There is good evidence of a worldwide tax imposed by Augustus around 3 BC, in which people also pledged allegiance to him. That may very well be the census referred to by Luke (and not an early one in 7 BC, which
actually was only of Roman citizens).