One of the oddities, or perhaps it should be termed biases, I’ve noted when Luke is compared with Josephus is that Josephus must be the one who is correct, if the two differ, and Luke must be the one who is in error. Josephus never mentions a universal census in the time of Augustus Caesar; therefore, there never was such a census. Quirinius took a census of the Jewish lands cir. 6 AD, according to Josephus. Therefore, Luke is in error about Quirinius taking one of Jewish lands (and others in the Syrian province) at an earlier date, and so it goes!
I have already shown in a previous blog-post that there was, indeed, a universal or empire-wide census taken in 3 BC for the purpose of celebrating Caesar Augustus’ silver jubilee and his being awarded (formally on February 5th in the year 2 BC) the title Pater Patriae (Father of the Country / Nation) by the Senate. This award included taking an oath of loyalty from every citizen of the empire. Augustus even acknowledged his award with his final entry in the Reg Gestae, implying it was the most prestigious honor ever given him. In fact, Suetonius claims he accepted the award with tears in his eyes, saying:
“Having attained my highest hopes, Fathers of the Senate, what more have I to ask of the immortal gods than that I may retain this same unanimous approval of yours to the very end of my life.” [SUETONIUS: The Lives of the Twelve Caesars; book 2; section 58]
Although Josephus makes no mention of an empire-wide census, he does refer to the census Luke claims Quirinius conducted in 3 BC. Notice what Josephus says about the census taken in Herod’s kingdom:
041 There was also a Jewish party called Pharisees, who …could have greatly helped the king but were set on opposing and harming him. 042 When all the rest of the Jews swore allegiance to Caesar and the rule of the king, more than six thousand of these men did not swear… [JOSEPHUS; Antiquities of the Jews 17.2.4 (041-042) – emphasis mine]
The very worldwide census that Luke mentions (Luke 2:1) is recorded by Josephus above: “when all the rest of the Jews swore allegiance to Caesar…” The fact that a census of some kind was taken is very clear. Otherwise, how would Josephus or Herod have known that there were more than 6000 Pharisees who refused to take the oath? Moreover, what Josephus claims above lines up in context to what has been more recently found out through archeological finds elsewhere. Moreover, that this was the first of other such oaths and censuses that would be taken later is clear from what Orosius says in the 5th century AD:
“[Augustus] ordered that a census be taken of each province everywhere and that all men be enrolled. … This is the earliest and most famous public acknowledgment which marked Caesar as the first of all men and the Romans as lords of the world, a published list of all men entered individually… This first and greatest census was taken, since in this one name of Caesar all the peoples of the great nations took oath, and at the same time, through the participation in the census, were made a part of one society” [Orosius, VI.22 and VII.2].
And, this is again corroborated by Josephus in his own history of the Jewish people. Years later (cir. 37 AD), Vitellius, the governor of Syria, had been in Jerusalem for three days offering sacrifices at the Temple in preparation for war with Aretas, king of the Nabataeans, “…when on the fourth day letters arrived announcing the death of Tiberius, he made the people swear their loyalty to Gaius.” In other words, he took a census of the people causing them to swear their loyalty to the new emperor, just as the entire Roman world swore it’s loyalty to Augustus over 30 years earlier.
 The inscription found in Paphlagonia (north central Asia Minor). It dates to 3 BC and records an oath of obedience “taken by the inhabitants of Paphlagonia and the Roman businessmen dwelling among them.”
 JOSEPHUS: Antiquities of the Jews 18.5.3 (124).