You don't know the effect because the existing experiments do not vary or hold constant oxygen levels. All you see is the net average effect, without any sort of partitioning among causes.
Existing experiments do vary oxygen levels systematically, albeit usually unintentionally, by geography. Going up 100 meters from sea level gives you a 1% drop in oxygen pressure and density. If that was enough for a detectable effect on IQ, then even the 16% lower oxygen levels around Denver should leave Coloradans obviously handicapped. IIRC altitude sickness does show a strong effect on mental performance, but only at significantly lower air pressures still.
And they also vary CO2 levels systematically by geography as well; if that was enough for a detectable effect on IQ, then the lower CO2 levels around Denver should make the rest of us at lower altitudes, such as sea level, look obviously handicapped. If you believe the altitude point refutes effects of oxygen, then it must refute effects of carbon dioxide and nitrogen as well...
Which is part of my original point about implausible effect sizes: the causal effect is underidentified, but whether it's oxygen or CO2 or nitrogen, it is so large that we should be able to see its repercussions all over in things like the weather (or altitude, yes).
One or two research groups have published work on carbon dioxide and cognition. The state of the published literature is confusing.
Here is one paper on the topic. The authors investigate a proprietary cognitive benchmark, and experimentally manipulate carbon dioxide levels (without affecting other measures of air quality). They find implausibly large effects from increased carbon dioxide concentrations.
If the reported effects are real and the suggested interpretation is correct, I think it would be a big deal. To put this in perspective, carbon dioxide concentrations in my room vary between 500 and 1500 ppm depending on whether I open the windows. The experiment reports on cognitive effects for moving from 600 and 1000 ppm, and finds significant effects compared to interindividual differences.
I haven't spent much time looking into this (maybe 30 minutes, and another 30 minutes to write this post). I expect that if we spent some time looking into indoor CO2 we could have a much better sense of what was going on, by some combination of better literature review, discussion with experts, looking into the benchmark they used, and just generally thinking about it.
So, here's a proposal:
Some clarifications:
(Thanks to Andrew Critch for mentioning these results to me and Jessica Taylor for lending me a CO2 monitor so that I could see variability in indoor CO2 levels. I apologize for deliberately not doing my homework on this post.)