Last March I mentioned that Fr Michael Lang had written on this question in 2004 in the journal Divinitas and was intending to publish the material more widely. He has edited a collection of articles which has now been published by Nova et Vetera: Die Anaphora von Addai und Mari – Studien zu Eucharistie und Einsetzungsworten (The Anaphora of Addai and Mari - Studies on the Eucharist and the Institution Narrative).
Rorate Caeli has posted some extracts from one of the articles: "Historical and Theological Argumentation in Favour Of Anaphoras without Institution Narrative: A Critical Appraisal" by Ansgar Santogrossi OSB. This calls into question the historical and theological basis for the decision made by the Pontifical Council for Promoting Christian Unity and particularly the status of the guidelines issued. Santogrossi argues that they were not an authentic act of "magisterium" as such.
In a follow-up post, Rorate Caeli adds a further extract from the article describing Propaganda Fide's reaction to the discovery in the late 19th century that some manuscripts of the Anaphora of Addai and Mari lacked the institution narrative.
It was at this time that an instruction of the Holy See’s Congregatio de Propaganda Fide to Catholic missionaries in the Near East instructed them to uproot the “incredible abuse” of Mass without the words of consecration and to instruct about the true form of the sacrament of the Eucharist.The question of competence and magisterium is only one of the areas of research related to the Anaphora of Addai and Mari. There are versions of this Anaphora that do have the words of institution. Another area of disagreement is whether the version without the words of institution is in fact a corrupt version of an earlier prayer.