It depends on how many Russians flee to Ethiopia because of World War 1 and/or the Russian Civil War - I made a guess of an initial 500,000 refugees that grows to roughly 1-2 million by the late 30s-40s which is around the beginning of the Second World War. I'd assume that Ethiopia's population will be around 14-15 million by 1918 so the Russians may make up roughly 1-2% of Ethiopia's population by the time of its joining in World War 2 - by the time the early 2000s rolls around, Ethiopia's total European-descended populace might make up around 9-12% of the entire population but again, I'm not the best with estimating numbers and statistics. You'll probably see a sizable amount nobles and ministers flee to Ethiopia with the Romanovs as well as members of the intelligentsia that settle in the developed urban centers as Ethiopia accepts those fleeing the RCW. Try asking Incanian, they'll probably know more.How do you imagine the demographic transition will be in this ATL Ethiopia compared with OTL Ethiopia? Also how will different groups differ in the demographic transition and in general in Demographic trends? Groups like rich and poor, urban and rural, educated and uneducated, differing ethnicities and religious groups?
Will Ethiopia see immigration? From where will immigrants come? Africa, Middle East, Europe or somewhere else? What will be the motivation of immigrants to Ethiopia? Refuge, emplyment, studies, family reunion? What position in society will immigrants have? What will be Ethiopias position on immigration?
Will Ethiopia experience emigration? Who will emigrate from Ethiopia and why will some emigrate?
How will Ethiopias demographis look like?
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Ethiopia is most likely going to see immigration but it depends on the time period - Ethiopia could see a second wave of Russian immigration from the Soviet Union, peasants and intellectuals that are disillusioned with Lenin's Bolshevik government but the White Russo-Ethiopian government may not accept them. Immigrants from Europe is plausible in the 30s and going to be a given in WW2, especially Orthodox Christian Eastern Europeans (i.e. Greeks and Yugoslavs) which may or may not permanently settle in Ethiopia - there's also going to be the fact that the Italian population of Ethiopia is going to increase when Ethiopia has annexed Eritrea (and possibly Italian Somaliland). By the time of the 90s, there could be another wave of Russian migrants immigrating from the former Soviet Union but again, they might not be excepted. As for migrants from Africa, that could happen as Africans might not want to live in the newly independent but underdeveloped African countries and opt to immigrate to the much more developed Ethiopia and I can see white South Africans/Rhodesians/Portuguese/etc. fleeing to Ethiopia in the 90s. I doubt there are going to be many migrants from the Middle East, considering how Orthodox Christians are going to dominate Ethiopia where the Muslim populace is dwindling as the White Russians take power in 1917 and consolidate their grip. The reasons that you mention about motivation are quite enough, although I'm not sure about the position of immigrants in White Russian Ethiopia - depending on pre-war ties and whatnot, they could be quite high or low. Some Ethiopians may not like the amount of European immigrants flowing in but you could see the majority of ethnic Ethiopians supporting immigration but once again, it depends on the time period.
As for emigration, it could be White Russians who don't want to stay in a still-developing Ethiopia when they can instead opt for western Europe or the United States - same might go for other expatriates during the period of World War 2.