@BorgersTilman my answer, I had to do a thread since twitter is not designed for long answers :-). @BorgersTilman this is evidently the Achilles'' heel, so to speak of the "as if" approach. But, I think there is a way out.
In the original consumer theory program, we were trying to do it all, very ambitious, as it should be, but also I think it is cracking! I think we should break down the problem of predicting and welfare inference into two separate (obvi. related) problems.
The "as if" aggregate rationality I think has been proven to be already successful empirically for prediction and description. That's why Amazon keeps hiring IO economists :-). More formally, data tells us it works!
Economist have gotten really good at estimating price elasticities for instance. I am talking basically consumer empirics which are very effective. I don't take a stand on macro empirics.
Welfare on the other hand has to take into account the fact that consumers that generate the aggregate "as if" rational behavior, may not be rational themselves. So here we may better use robust ways to elicit welfare. The instant classic work of Bernheim and Rangel 2009 comes
to mind! Here we use robust forms of preference revelation to infer what people like. I think if you want to do welfare you have to engage seriously with the question of identification of the distribution of preferences. However, we can get good price elasticities without good
estimates of welfare. I am also a big fan of stated preferences, and incentivized willingness-to-accept and willingness-to-pay field experiments to elicit welfare without having to deal with noisy revealed preferences. Behavioral welfare is very active and I am also excited about
this. So in summary, the main issue is that the current state-of-the-art of practitioners is doing welfare analysis as if "every individual" is rational, when this is usually not supported by data, in which case it is also unclear what this means. So we need to do better. I think
that doing better requires a "divide-and-conquer" approach rather the current unified but empirically "wrong" approach.
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