Does concavity of the utility function has any bite?
This post shows clearly why in the world of "standard" ordinal utility, concavity of a utility function cannot obtain an economically meaningful interpretation, although it may be useful as a mathematical property.

But "standard" ordinal utility is not compatible with Econometrics, because Econometrics deal inherently with situations where there exists uncertainty, and in a framework with uncertainty we move from "fully ordinal utility" to Expected Utility theory, where properties like concavity have economically meaningful content -they express attitude towards risk (as well as "preference intensity", as this laborious post shows).  

The concavity assumption/restriction is made because there is universal consensus that the vast majority of people exhibit risk aversion in their economic behavior.