A.T. Robertson Commentary Luke 2:1

"Now it came to pass in those days, there went out a decree from Caesar Augustus, that all the world should be enrolled." — Luke 2:1 (ASV)

Decree from Caesar Augustus (δογμα παρα Καισαρος Αυγουστου). Old and common word from δοκεω, to think, form an opinion. No such decree was given by Greek or Roman historians and it was for long assumed by many scholars that Luke was in error. But papyri and inscriptions have confirmed Luke on every point in these crucial verses 2:1-7. See W.M. Ramsay's books (Was Christ Born at Bethelehem? Luke the Physician. The Bearing of Recent Discovery on the Trustworthiness of the N.T.).

The World (την οικουμενην). Literally,

the inhabited (land , γην). Inhabited by the Greeks, then by the Romans, then the whole world (Roman world, the world ruled by Rome). So Ac 11:28; 17:6.

Should be enrolled (απογραφεσθα). It was a census, not a taxing, though taxing generally followed and was based on the census. This word is very old and common. It means to write or copy off for the public records, to register.