I think the naive metric is this:
Cost of the good/service you are redeeming for if purchased with cash.
By this metric, we can take a typical airline mile and assign it a value of ~10 cents, as this is about the value for a premium cabin redemption. However, this is an extremely naive metric, as you presumably would not be purchasing a $10k first class ticket otherwise.

A better metric is:
Cost you would have been willing to pay for the good/service you are redeeming for if purchased with cash.
In this case, if I would be willing to pay ~$2k for a premium ticket and I instead used miles for it, I would be getting a valuation of about 2 cents or so. There is still a flaw for this metric though, as it doesn't make the miles especially fungible--we're looking at a single specific booking, which may not be representative of the actual value.

To fix this, we can go to:
Cost a typical person would be willing to pay for the goods/services they would redeem airline miles for.
I'd call this the "per capita GDP" of airline miles. If we sum up the value people received from their redemptions and divide by the number of miles, we can get an estimate of the actual value of those airline miles (sample size, etc etc). I still don't like this metric, though, as it mostly just demonstrates how inefficiently people use their miles.

I think the best we can do is something along the lines of this:
Cost a typical person would be willing to pay for the goods/services they would use their miles for if making choices informed by an expert.
This gets us to the value I think is most appropriate if you want a single number valuation. As flyertalk tends to a wealthier audience, we tend to tout premium cabin awards, but a decent percentage of fully-informed average Americans could easily set their valuation based on an economy award, as they may not be willing to "pay" the extra cost for a premium cabin. Although a small minority, some people would not be interested in air travel no matter how efficient, so they would be getting a lower-valuation merchandise award. I do think, though, the valuation of a fully-informed average American would be in the 1.5 to 2 cent range, as this is the "sweet spot" where most reasonably-efficient redemptions are going to occur.

I think you could experimentally determine this valuations, but it would certainly be a pain. Any sensible valuation is going to be within a couple standard deviations of 1.5 cents, so it's probably not even worth as much thought as I took writing this up.