Is there a discrepancy between Matthew and Luke for the correct date of birth for Jesus? The primary difficulty centers on the criticism of Luke’s account of Jesus’ Birth as found in his description of the census that Luke says was ordered by Caesar Augustus.
And it came to pass in those days that a decree went out from Caesar Augustus that all the world should be registered. This census first took place while Quirinius was governing Syria. So all went to be registered, everyone to his own city. ~Luke 2:1-3
Because no archeological discovery had ever previously verified that such a census took place, Luke was regarded in past history as having embellished this story. A later discovery regarding the taxes of the kingdom of the Roman government revealed that the taxpayers were enrolled every 14 years by the use of a census. Archeology has uncovered facts that verify Caesar Augustus did conduct the precise census described during the period of time Luke specified—near the birth of Jesus in Bethlehem.
Further, an inscription discovered in Antioch describes Quirinius in 7 B.C., who was the governor of Syria on two occasions—7 B.C. and 6 A.D.—a fact that is confirmed by the Jewish historian Josephus.
Herod the Great reigned from 37-4 B.C.
An archeological discovery in Egypt uncovered a Papyrus that specifically describes the details of this census spoken of by Luke, under Caesar Augustus:
“Because of the approaching census it is necessary that all those residing for any cause away from their homes should at once prepare to return to their own governments in order that they may complete the family registration of the enrollment and that the tilled lands may retain those belonging to them.”
In his book, Archeological Confirmation of the New Testament, Dr. F. F. Bruce describes a problem that was present in Luke’s description of the Tetrarch of Abilene, in Luke 3:1.
Now in the fifteenth year of the reign of Tiberius Caesar, Pontius Pilate being governor of Judea, Herod being tetrarch of Galilee, his brother Philip tetrarch of Iturea and the region of Trachonitis, and Lysanias tetrarch of Abilene… ~Luke 3:1
Previously there was no record of anyone called “Lysanias” as the tetrarch of Abilene during the time Luke specified that he was there. In recent history, an archeological discovery made in Damascus, Syria describes a person called “Freedman of Lysanias the Tetrarch.” Scholars date this inscription at between 14 A.D. and 29 A.D. This is the same period of time in which Luke had written of Lysanias.
An interesting discovery in 1910 by Sir William Ramsey debunked the secular record of Cicero of the Romans, who described Iconium as being in Lycaonia. Luke describes Lystra and Derbe as being in Lycaonia.
They became aware of it and fled to Lystra and Derbe, cities of Lycaonia, and to the surrounding region. ~Acts 14:6
The secular record has been erroneously held as more reliable and accurate than the Biblical record in past history. This continues to be a common error made today. The facts bearing witness, the Bible is always right in matters of history and the secular record is consistently wrong. This truth has been confirmed by archeological discoveries over the entire course of human history, all over the world.
Other noted scholars such as Dr. Adrian Nicholas Sherwin-White, a British historian and scholar—regarding Ancient Rome—wrote his doctoral thesis on the treatment of the New Testament from the point of view of Roman law and society.
Dr. Sherwin-White said this regarding the work of Dr. Ramsey’s conclusions on the Book of Acts:
“Any attempt to reject its (the New Testament’s) basic historicity even in matters of detail must now appear absurd. Roman historians have long taken it for granted.”
Dr. Sherwin-White examined the records of Rome, and concluded that their own history proved the narrative of the New Testament scriptures regarding the death and resurrection of Jesus Christ.
 1.John Elder, “Prophets, Idols and Diggers.” Indianapolis, New York: Bobbs-Merrill,1960. Pages 159, 160
2.Joseph Free,. “Archaeology and Bible History.” Wheaton: Scripture Press Publications, 1969, Page 285
 Elder, John. Prophets, Idols and Diggers. Indianapolis, New York: Bobbs-Merrill,1960, Page 160
 1.Elder, John. Prophets, Idols and Diggers. Indianapolis, New York: Bobbs-Merrill,1960, Pages 159, 160
2.Free, Joseph. Archaeology and Bible History. Wheaton: Scripture Press Publications, 1969, page 285.
 F. F. Bruce, “Archaeological Confirmation of the New Testament.” Revelation and the Bible. Edited by Carl Henry. Grand Rapids: Baker Book House, 1969. Page 321.
 Adrian Nicholas Sherwin-White, Roman Society and Roman Law in the New Testament, 1963, page 189.
 Tacitus’ characterization of “Christian abominations” may have been based on the rumors in Rome that during the Eucharist rituals Christians ate the body and drank the blood of their God, interpreting the symbolic ritual as cannibalism by Christians. References: Ancient Rome by William E. Dunstan 2010 ISBN 0-7425-6833-4 page 293 and An introduction to the New Testament and the origins of Christianity by Delbert Royce Burkett 2002 ISBN 0-521-00720-8 page 485