People talk a lot about well-being as an objective of macro policy (together with gdp growth). So if well-being is an objective, i'm wondering if we can add well-being into macro model as an endogenous variable? and we can see the response of this variable to a shock just as we did for other endogenous variables? Thank you for all your help.
One can model anything, that's why it is a model. The real question is what the value of such a model would be.
More to the point, I think this would be a very hard thing to do sensibly because how are we going to measure well-being? It encompasses way more factors than our economic models typically capture, such as social relations, health and mental state. Even if we include all of those, the relation between all those variables among each other and well-being is often unknown. We could theorize about it, but actually finding out what the relations are would be very hard to do.
For example suppose I model well-being as a combination of health, income and social relationships. That would mean that my macro-economic model would have to contain some kind of measure how social relationships evolve. Moreover, not only are increases in my income going to improve my well-being directly, but it is also going to affect my health (positively up to a point probably) and social relationships (those I guess could go both ways depending on income inequality or the possibility to be generous or visit friends and relatives).
If one really wants to capture well-being there are so many variables affecting that, that the model essentially becomes a black box. We don't know what's driving the results anymore.
What has been done, is trying to measure these things in retrospect. There are various macro-economic/social indicators and indices that try to capture how well-being has evolved over time. These retrospective studies are then used to judge what has gone well and what has not (the latter is also a hard thing to do because we typically have no good counterfactuals)