|Per capita petroleum consumption. Source
It is relatively simple to calculate a lower-bound on the impact.
Consider that residents of Mexico consume an average of 970 liters of petroleum per capita. The average resident of the US consumes 3500 liters of petroleum per capita. The difference is 2530 liters of petroleum per capita per year.
Over the course of a decade, that translates into 1.5 million pounds of CO2 per immigrant (conversion factors HERE). Or, if one uses MIT's latest estimate of roughly 20,000,000 illegal immigrants in the US, that comes to 30,000,000,000,000 pounds of CO2. And that is just the United States!
Considering Europe: The average German uses 1700 liters of petroleum per year. The average immigrant comes from a country that uses less than 500 liters per year for a net difference of 1200 liters per year.
First time asylum applicants for the EU averaged a half million per year for the last ten years. Assuming a 2X factor to gather in those who failed to apply for asylum and for those who arrived before 2008, that suggests that there are a minimum of 10,000,000 refugees in Europe.
Going through the same math I used to calculate the US net CO2 increase, one gets 680,000,000,000 additional pounds of CO2 per decade.
Not every immigrant will achieve "average" fuel consumption.
Response: Only petroleum was considered in an attempt to have offsetting "errors". Adding in coal and natural gas would increase the carbon footprint considerably. If you want me to comprehend the effects of the lower economic status of immigrants I will include the use of coal and natural gas. Just by way of comment: I see more immigrants driving old pickup trucks and Buicks than Prius. Just saying.
Why Germany? They have the highest petroleum consumption of Europe. You are skewing the results.
Response: Germany is the number one destination of refugees because of the strong economy. Therefore I chose them as a proxy for all of Europe. It should be noted that Syria is the number one originator of refugees and they have a much higher base consumption of petroleum compared to, say, Nigeria. The "from" number is much, much closer to Syria than Nigeria.
You inflate the number by using a decade time horizon.
All time horizons are arbitrary. How long do refugees stay? A day? A week? A year? A decade? Which comes closest to the real answer?