The answer to that question just muddies the waters further. Anti-inflammatory drugs have been shown to have some anti-depressant effect, while anti-depressant drugs have been shown to have some anti-inflammatory effect. In both cases, the effect size is fairly small.

It would be nice to find a simple cure for a complex and diffuse set of symptoms, but we haven't had any luck so far. In all likelihood there are multiple interacting factors that affect the progression of depressive disorders, with no singular cause.

http://www.nature.com/mp/journal/vaop/ncurrent/full/mp201616... https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3194072/