>ǵ-, zero-grade of *h₂eǵ- "drive, impel, lead" — more at agent

NOTE: This etymology follows G. Dunkel, "Latin verbs in -igāre and -īgāre," 125 Jahre Indogermanistik in Graz (Graz: Leykam, 2000), pp. 87-99. According to the older conventional explanation, the initial element is the adjective castus "free from, untouched (by the thing specified), pure, not sexually promiscuous" (see chaste), but semantically this is a poor fit, and does not clearly account for the long ī. On the other hand, Dunkel's hypothesis would mean that Indo-European *ḱeHs- shows up in Latin only in this presumed i-stem derivative and nowhere else, unless castus itself can be attributed to the same etymon—but again that does not fit well semantically ("instruct, reprove" > "pure"?). See also the note at chaste.