I'm not an ethnic historian by any means, but working with questions of identification in the ancient world I hope I can share a thing or two that might be useful, as well as try to streamline my thoughts on the matter a bit. This is a very virulent matter in my line of work, and here the problem is compounded by the fact that we have so little in the way of people themselves telling us to which ethnicity they thought to belong themselves.

Methodological approaches I myself have found useful come from two important inputs from anthropology and archaeology. S. Jones in The Archaeology of Ethnicity. Constructing the past and present (London - New York 1997) has defined ethnicity as the "aspect of a person's self-conceptualization which results from identification with a broader group in opposition to others on the basis of perceived cultural differentiation and/or common descen", an ethnic group being "any group ... who set themselves apart and/or are set apart by others with whom they interact or co-exist on the basis of their perceptions of cultural differentiation and/or common descent." [p. XII] For her, the concept of ethnicity focuses on how social and cultural processes intersect in the construction of an ethnic identity. In some social sciences, there is a distinction made between 'emic' and 'etic' labels, ascriptions that come from within the group ('We are Icelanders') vs. from without the group ('Those guys over there are Icelanders'). This is a bit of an inescapable conundrum, since there is no truly objective position here when those two conflict (which they often do, as you discovered).

This dichotomy is also apparent in Jones' definition, the perspective of outsiders can be as important as the perspective of insiders - there is the bonmot that 'empires create tribes' by the way they interact with foreign societies, they label them, group them together after certain criteria such as language or material culture, cutting through the way those peoples structured there relationship with each other. But in time, they may become the internalized and accepted framework by which these people view their ethnic relationships. In the words of C. Morgan (in: T. Derks - N. Roymans (eds.), Ethnic Construcs in Antiquity: The Role of Power and Tradition (Amsterdam 2009) pp. 11-36, here p. 12), "ethnic identities can arise both from insider perceptions and from the views of outsiders subsequently internalized." Opposition to the 'Other' is one of the key mechanism of ethnic self-identification ('Those guys over there are not like us and therefore no true Icelanders').

One work I found useful and which also approaches the problam from a very wide angle would be Anthony Smith (The Cultural Foundations of Nations. Hierarchy, Covenant and Republic (Oxford 2008)). He distinguished between two main uses of the concept of 'ethnicity', the first focusing on ethnic descent (factual or presumed, as f.e. the Romans in relation to Troy), the other a broader one, which he classifies into three levels:

• ethnic categories. Constructs, often from an outside perspective, by which people get grouped together by shared elements of common culture living in a certain area, but who may lack a name of their own, or even a sense of community from the emic perspective.

• ethnic networks. Ethnic networks show certain patterns of shared cultural practices, activities and relation, which have a name of their own and a myth of descent, but rarely any political union.

• ethnic communities. These he defines as "named and self-defined human populations with myths of common origins, shared historical memories, elements of common culture and a measure of ethnic solidarity" [Smith 2008, 30-33].

Thinking about ethnicity by way of these 'ethnic communities' is I think very useful. It makes us focus on these shared elements that tie a group together and define the ethnicity both among the people themselves as well as from the perspective of an outsider. Importantly, to him, ethnic community requires a clear self-definition.

It is also useful to see ethnicity as one important aspect of identity. For identification of the individual, ethnicity plays an important aspect, but it is only one of several. Furthermore, it is also a process that is contingent on a certain context. For example, an trader from the Rhine-Neckar-region in the 2nd century A.D. might identify as German when he visits his native village and offers a votive altar to a 'German' god using the native name (but, at the same time, using the very Roman practice of setting up a votive altar at all, using the Latin alphabet and the traditional Latin formulae!), but abroad, buying, say, amber in the baltic, he might view himself (and will probably be seen by the locals) as a Roman citizen. Identification is a process, and identity changes over time. Identity in that sense is not something a person has, but something she does.

If we want to approach the question of how people identify themselves, or get identified by others, we have to look at the different ways identity gets expressed, the most important categories here (in which I follow Fernandez-Götz, who does a great job of summarizing the whole problem and different schools of thought in Identity of Power (Amsterdam 2014), pp. 13-39 and which I'd really recommend) being

• Gender
• Age
• Ethnicity
• Religion
• Social Status and Power
• Profession

Of importance here is then also the concept of intersectionality, to understand how these categories intersect and influence each other. Thing about how certain ethnicities get pushed into certain professions, and in turn may associate themselves with these professions, how religion can be (lamentably still) so incredibly important in separating ethnicities and so on. [On intersectionality, see f.e. K. Davis, Intersectionality as buzzword, Feminist Theory 9, 1, 67-86] Men will express their ethnicity different from women, for example in dress, ornamentation, coiffure and so on.

Thinking of ethnicity in that way, it becomes clear that there is a variety of factors we can look at along these different axes of identity as indicators of ethnicity. From a historians perspective, some of the most useful and accessible ones are:

• Language - what language do people use, where, in which context (at home, at work? What language do they speak to each other, what language do they use when communicating with a government official? What do they write?)
• Geographic area - where do they live?
• Laws and Customs - Another important marker of ethnicity, and sometimes laws are helpful by defining who counts as an outsider.
• Dress and Ornamentation, as well as other aspects of material culture. Iconography, different styles and different ways to make stuff (this crosses over into archaeology a lot)
• Cultural practices: certain music associated with a group of people, 'ethnic' dances, plays, poems and ways of doing poetry.
• A shared place of origin - factual or imagined.

So in that sense, you can approach the question of 'ethnicity' as an outsider, but you have to consider a lot of factors. To get back to your example, it is probably more helpful not to try to shoehorn the people you are working on in pre-defined slots of 'Norwegian' and 'Icelandic', but to take a look at what techniques and practices these people used to identify themselves, or how they got identified by others, and how ethnicity played a role in that.