It is difficult to find the required numbers to answer your question as asked, but I've made an attempt. The raw data I've used is from the statistical database from "Statistics Norway". The charts and numbers are not deep-linkable but available in the sections "Immigration and immigrants", "Population", "Labour market and earnings" and "Social conditions, welfare and crime".
"Statistics Norway" offer a lot of raw data from their database, but not all numbers are broken down by citizenship. I've tried to find a few datasources, from which at least a partial conclution can be drawn (all numbers from 2010):
- Population count broken down by citizenship. These numbers do not account for immigrants, which have obtained a Norwegian citizenship.
- Number of persons charged with at least one criminal offence, broken down by citizenship. The number only includes more serious crimes and not less serious delicts. As already pointed out, these numbers may be skewed if the law enforcement tend to pursuit crimes committed by specific ethnic groups more eagerly than crimes committed by the native population. They also include criminal charges against foreigners, which are not permanent residents of Norway.
- The absolute number of unemployed persons broken down by citizenship. This is the closest I can get to a measurement of wealth, but I think it is pretty safe to assume a correlation between unemployment ratio and wealth. However, only the total number of unemployed is counted and not the fraction of the relevant labour force. I would assume that the age distribution varies between different groups of immigrants and hence also the labour force ratio may differ.
- The numbers are only available for 44 different citizenships. For the rest of the origin countries, either the population, number of criminal charges or number of unemployments is too low for these to be accounted for separately.
Based on these numbers, I've calculated the following ratios by citizenship:
- Number of charged persons per population count, scaled so that Norway = 1. In the following text, I'll refer to this number as "crime ratio".
- Number of unemployed persons per population count, scaled so that Norway = 1. In the following text, I'll refer to this number as "unemployment ratio".
6 of the 44 countries have rather extreme ratios and fall outside this diagram, but plotting the crime ratio on the X axis and the unemployment ratio on the Y axis gives the following plot:

Looking at the crime and unemployment ratios separately, there is a very large variance in the numbers. Here is a list of countries, where at least one of the ratios are >10:
crime unemployment
Romania 14 4
Algeria 54 19
Gambia 23 18
Morocco 12 21
Nigeria 35 8
Sri Lanka 3 15
Iraq 4 10
Iran 5 14
Pakistan 2 10
Vietnam 4 36
Chile 4 13
Yes, these ratios are actually correct. The number of Algerians charged with a criminal offence is relative to the population count 54 times higher than the number of charged Norwegians. 29,516 of roughly 4.5 million Norwegian citizens were charged with a criminal offence in 2010, while 128 Algerians faced the same faith of a population of 362. Likewise, 700 of the 1561 Vietnamese citizens living in Norway were reported unemployed, making the unemployment ratio 36 times higher than among the Norwegian citizens.
Worth to notice is perhaps also, that only immigrants from three countries show a crime ratio <1:
Thailand 0.75
Germany 0.90
USA 0.95
All countries show an unemployment ratio >1.
The crime ratios may also contradict the early assumption that the law enforcement may more strictly pursuit crimes committed by specific ethnic groups. The crime rates for immigrants from Sweden and UK are e.g. higher than for the immigrants from Poland, Turkey, Ukraine, Bosnia, Eritrea, Ethiopia and Pakistan - immigrant groups which undoubtedly have a reputation of being "more criminal" than other foreigners.
If I now try to correlate these ratios (crime ratio divided by unemployment ratio, Norway still being fixed to 1), we get a number where a high value indicate a high criminal ratio despite low unemployment, while a low number indicate a low criminal ratio, despite high unemployment.
Immigrants from only six countries score a crime per unemployment ratio >1.5:
Netherlands 1.52
Lithuania 1.58
Liberia 1.66
Algeria 2.83
Romania 3.47
Nigeria 4.18
I've made all the data used in these calculations available in an unfortunately rather chaotic OO Calc Spreadsheet. Source of the data: Statistisk Sentralbyrå, Statistics Norway.
Feel free to draw your own conclusions.