There are many studies saying just that.

However, and bearing in mind it's got to be 15 years since I cancelled my IMechE subscription to periodicals, the studies are working with huge variables;

Steel and other metals production carbon footprint varies. Compare Germany to China for instance.

Factories and their efficiency / carbon footprint variability.

Fuel / consumables efficiency of the vehicle.

Life span of original components.

I recall one paper looking at the Old Trabant factory, bearing in mind they didn't actually use much fuel and it was estimated that over 90% of the carbon footprint was before you fired it up for the first time. I am only guessing here but my BMW, made in Bavaria with rather strict ecology laws, it had to be considerably less, especially given the estimated lifespan.