Migration to rich countries such as the United States of America and various European countries happens for a number of different reasons. People may move to rich countries for such things like education, just to move, and other various things. We can not blame a country because they are rich.
I do not believe rich countries are inherently responsible for migration. Migration can happen due to over-consumption of natural resources, but generally migration doesn't happen unless there are a number of factors involved. Large migration changes happen over decades and generations and I think it is impossible to say it happens simply because of consumption.
I do not think that rich countries are responsible for migration due to the over-consumption of natural resources. I think that migration is due to some countries just not being able to take care of their people and their societies. Richer countries will always be appealing to those that come from third-world places.
No, rich countries are not responsible for migration due to the over-consumption of natural resources, because it is not natural resources that make people want to move. There is no point to moving somewhere that has a big waterfall, or an oil rig that has not been developed. It is using the resources to be productive that people are attracted to.