Let me supplement Alice's nice answer with a few more points. Regarding 

> there are antidepressants that do not enhance serotonin but suppress it.

That seems to be [tianeptine](https://en.wikipedia.org/wiki/Tianeptine); it is often brought up such discussions as *the* counterexample to SSRIs being "real" anti-depressants. More [recent research](https://www.nature.com/articles/tp201430) on tianeptine suggests it acts on the opioid receptors... and that's not a new line of antidepressant treatment, but rather an [old one](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3594542/), potentially sharing [the same addiction risks](https://psychology.stackexchange.com/questions/18685/is-tianeptine-addictive) as other opioid-acting medications (e.g. painkillers).

Which brings us to the next point

> There are some that do nothing to serotonin at all, but their therapeutic effects are all the same, according to Hirsch.

Surely there are; [bupropion](https://en.wikipedia.org/wiki/Bupropion) is a more widely used (at the least in the US) anti-depressant that is not an obvious SSRI. 

> So the effect is independent of the chemical composition. That means the chemical imbalance theory is wrong.

That's basically jumping to conclusions (and more than once). The effect is not *totally* independent of the chemical composition of the medication. An alternative conclusion is that depression, which is diagnosed based on a checklist of symptoms, is a [heterogeneous disease](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3188778/) with multiple causes producing somewhat similar symptoms (which, by the way, don't all have to be present to get a diagnostic). 

Actually almost every individual neurotransmitter that is suspect to be involved in depression, including serotonin, but also catecholamines (norepinephrine and dopamine) have been subjected to experimental manipulation typically via dietary changes (in live humans). You can read more details [in my answer on skeptics](https://skeptics.stackexchange.com/a/40311/29579), but the main pattern seems to be that while we can't cause healthy individuals to get (majorly) depressed by lowering the aforementioned neurotransmitters, in previously depressed individuals (and to a lesser extent in their relatives) such interventions that lower these neurotransmitters do produce more significant mood changes; the most significant changes are seen in patients who are taking exactly the medication that the diet intervention counteracts. (see e.g. [Kumar et al.](https://doi.org/10.1016/B978-0-12-386945-6.00012-3)).

Also current anti-depressants are only [30% to 60%](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3181893/) effective (depending who reviews the evidence and more importantly whether substituting medications [several times] counts etc.)

So what to conclude from this? The most sensible conclusion to me is that not everything is understood about the neurochemistry of depression, but surely concluding that neurotransmitters are not involved is rubbish.

Almost every researcher who works in this field has some favorite hypothesis that explains better the current non-quite-satisfactory simple explanations based on one neutrotrasmitter or antoher, e.g. a [2008 review in *Nature*](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2721780/#S2title) said:

> It is now thought that acute increases in the amount of synaptic monoamines induced by antidepressants produce secondary neuroplastic changes that are on a longer timescale and involve transcriptional and translational changes that mediate molecular and cellular plasticity.

I doubt that's the ultimate word on the topic (all such narrative reviews have their biases when it comes to the less investigated aspects, no matter how prestigious the venue or the author), but it's clear that the "brighter bulbs" keep looking for more satisfying answers than the monoamine hypothesis (this what's called in the mass media "chemical imbalance"). I think any ultimately useful answer has to account for how the current antidepressants work... which is by acting on neurotransmitters, which in turn does alleviate depression (better than placebo) in some people but alas does not in quite a few others.