Using fixed-effects for each person helps model such heterogeneity, but still nothing comes out. I don't see why you would dismiss them so readily. It's just that the old-wives-tales are wrong yet again.
If you really believe that weather relationships could be so obscure and complicated and individual that there are no meaningful average effects, that casts a lot of doubt on the claim that there's a consistent average effect from CO2 and all the background studies about ventilation and air quality as well.
Using fixed-effects for each person helps model such heterogeneity, but still nothing comes out.
Feddersen et al model very particular heterogeneity, to wit the usual demographic and econometric data:
...These include age and its square, the number of household dependents aged between 0 and 24 years, and the natural logarithm of nominal household disposable income for the previous financial year in Australian dollars. Dummy variables are also included for disability status, employment status, marital status and education. These controls are typ
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.)