I found that Bhutan created the Gross National Happiness (GNH) Index in order to evaluate the happiness of their citizens and compare that with other countries. I presume the intention of that was to do some comparative politics and be able to find out the output in terms of happiness of specific policies.
Even though, when one analyzes GNH quickly realizes it's a really subjective index. And that's not surprising at all, since happiness is something indeed pretty subjective.
Even though, I was interested if some institutions of any kind (with international repercussion) had created similar indexes, that try to find out some value of happiness in a country.
I'm aware of the existence of the Human Development Index, though I wouldn't say it falls upon the consideration of "happiness index"