Exegesis:

When the reading eudokias ‘favour’ in the genitive is adopted the hymn consists of two corresponding lines connected by kai; the parallelism between the various parts of each line is very close but does not strictly follow the word order: doxa ‘glory’ corresponds with eirēnē ‘peace,’ en hupsistois ‘in the highest’ with epi gēs ‘on earth,’ and theō ‘to God’ with en anthrōpois ‘among men.’ When however the reading eudokia in the nominative is adopted this parallelism is lost because eudokia is then a third predicate besides doxa and eirēnē. The reading eudokias is preferable, cf. Plummer and Schrenk, TW-NT, II, 745ff.

doxa en hupsistois theō ‘glory in the highest to God’; the form of the verb einai that is to be understood with the phrase, is either eiē ‘may be’ (optative) or estin ‘is’ (indicative); neither form however expresses the meaning of the doxology adequately because a doxology is not merely a wish (‘may glory be given to God’) nor just a statement (‘God has glory’), but rather “a statement of that which is, in terms of a praise of God” (cf. Kittel, TW-NT, II, 251); in the present context ‘that which is’ is the birth of the Saviour and the doxology expresses what this birth means in heaven and on earth.

doxa ‘glory,’ cf. on v. 9; here it does not have the connotation of ‘radiant light.’

hupsista ‘the highest,’ cf. on 1.32; en hupsistois goes with theo as indicating the place where God is (cf. Revised Standard Version, New English Bible, and others) or with the phrase as a whole, indicating the place where glory is given to God (cf. Translator’s New Testament, The Four Gospels – a New Translation); the latter seems preferable because of the place of en hupsistois before theō and of the parallelism with epi gēs ‘on earth.’

epi gēs eirene en anthrōpois eudokias ‘on earth peace among men of his favour.’

gē ‘soil,’ ‘ground,’ ‘land,’ ‘earth.’

eirēnē ‘peace,’ cf. on 1.79.

eudokia (also 10.21) ‘good will’ of men, cf. “men of good will” (The Four Gospels – a New Translation), or ‘favour,’ ‘pleasure,’ of God, cf. “men on whom his favour rests” (New English Bible); the latter interpretation is adopted by the great majority of commentators and translators and supported by the repeated occurrence of the same phrase in Hebrew in the Dead Sea Scrolls, where the possessive suffix makes clear that God is the subject of the act implied in the verbal nouns ‘favour’ or ‘pleasure.’ The genitive is qualifying. There is no reason to assume a contradiction between panti tō laō ‘all the people’ in v. 10 and en anthrōpois eudokias ‘among men of his favour’ as if the latter would impose a restriction upon the former: it only serves to express that the initiative in establishing peace on earth is not with men but with God.

Translation:

Glory to God. Often a verb must be added, ‘praise be/is-offered to God’ (Javanese), or the syntactic pattern changed, e.g. ‘most exalted (is) God’ (Balinese), or ‘honoured should God be’ (Sundanese), ‘let God be greatly praised’ (South Bolivian Quechua).

In the highest. Some versions have to add a word for ‘place’ (Telugu, Sundanese). Where the context is not sufficient to show that place to be God’s abode in heaven it is better to add ‘heaven(s).’ Balinese uses a term, ‘highest-world,’ referring to the highest of the layers of heaven, cf. also ‘upper world’ (Kannada).

On earth. The rendering must be the normal counterpart of the term chosen for “in the highest”. Thus Balinese employs ‘sphere-of-mortals’ (thought of as taking the middle position between heaven and netherworld and, as such, also called ‘middle sphere’), because this term, not ‘earth,’ is commonly used in one pair with ‘highest-world.’

Peace among men, or, ‘peace reign(s) among men,’ ‘men (may) receive peace,’ ‘men’s condition is (or, may be) peaceful.’ For peace, here used in its positive meaning, see on 1.79.

With whom he is pleased. Some versions keep closer to the Greek construction, only adding a possessive pronoun, cf. “men of his choice” (Translator’s New Testament, similarly Sinhala). Several do as Revised Standard Version does, and shift to a relative verbal clause, e.g. “men he favors” (An American Translation), ‘men he rejoices in’ (Chinese), ‘people that he accepts/approves of’ (Kituba, using a continuative present tense), ‘people He likes’ (Tboli, lit. ‘people where stays his breath’), ‘men who are-pleasing to His heart’ (Bahasa Indonesia KB), ‘people who fit God’s eye’ (Sranan Tongo). When the verb is specific, and normally used with God as agent, it is sometimes possible to omit the indication of the agent, e.g. ‘men who are elected’ (Javanese). When a relative clause is impossible one may shift to, ‘peace for men: he favours (or, is pleased with, or, loves) them.’ For pleased see references on “well pleased” in 3.22.

In some languages incongruity between the two lines of the verse in matters of word order would destroy the meaning of the whole clause, or at least impair the stylistic impression aimed at; then the word order of the two lines should be made more closely parallel. Similar considerations may make preferable the use of more closely parallel renderings of the prepositions, e.g. ‘is given to God … comes to the earth’ (Sranan Tongo), “glory to God … peace to the men” (An American Translation), ‘most exalted (is) God … very peaceful (are) the men’ (Balinese).

Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.