. . . 1) How much extra pollution did Volkswagen cause? Bloomberg crunched some numbers and estimated that Volkswagen's 482,000 deceitful US cars may have added between 3,000 to 12,000 additional tons of nitrogen oxide pollution (NOx) to the atmosphere each year, assuming the cars were driven an average amount.**
Extrapolating that out to 11 million cars around the world, and we get somewhere between 68,000 and 274,000 additional tons of NOx emissions each year.
Now, there are tons of assumptions and simplifications embedded in these estimates, particularly around how many miles VW's cars were actually driven. But that's ... potentially a large amount of extra NOx pollution. At the high end globally, it's 25 times what a typical coal plant without emission controls puts out in a year.
2) How many deaths might that extra pollution have caused? Now, it's harder to calculate the precise health damage from all that extra NOx. Certain types of nitrogen oxides are hazardous both both because they can irritate the lungs and because they can help form harmful particulate pollution and smog. Higher smog levels have been linked to respiratory illnesses, increased asthma attacks, and even premature deaths (especially among the sick or elderly). The tricky part is that the exact levels of smog formation can vary from place to place, depending on sunlight, temperature, local winds, and other factors.
Still, we can get ballpark figures using data from the Environmental Protection Agency, which calculates that every ton of NOx leads to somewhere between 0.00085 and 0.0019 premature deaths. (Note that this only includes impacts from particulate formation, not smog effects, which are harder to quantify; see p. 40 of this report.)
Putting this all together, the estimated extra pollution from Volkswagen's US cars could be expected to lead to an additional 3 to 23 premature deaths each year. If we extrapolated worldwide to all 11 million vehicles, that would come to somewhere between 58 and 520 premature deaths annually.
Again, this is a crude, back-of-the-envelope exercise, not a peer-reviewed scientific analysis. Keep in mind all the caveats listed above. And criticisms and refinements are welcome. But if Volkswagen's deception really was responsible for that much additional pollution, it's safe to say it did noticeable damage to public health.