A short memo on the state of economics

A short memo that may possibly lead to a new essay on the state of economics.

While a lot have been said about the state of economics, there has been a hole that very few, if not none, notice.

That is:

 Arrow-Debreu-Mackenzie general equilibrium theory (ADM theory), restricted to conventional understanding, cannot actually be the foundation of modern economics done so far, if not for future. This is true even when we leave out issues like behavioral economics. (It has been claimed that much of economics has, as its foundation, ADM.)

One may argue that game theory forms a more of general foundational theory for modern economics, and there is some truth to it. If this is so true, then I believe we should move away from books that focus on general equilibrium, such as MWG, to books that focus on game theory.

Even so, our misunderstanding of ADM will plague our understanding of game theory as well.

This may sound contradictory: I argued in the past that ADM should be revisited, and yet I argue that ADM cannot be the foundation of modern economics done so far. But it is not: we can start from the ADM root and its conventional understanding and formulate a new variant theory.

What is wrong about the current understanding of ADM? There technically is nothing wrong mathematically with the current understanding - the issue is more of a logical problem.

A simple question will answer this: how does ADM treat subjective expectations?

Now you may say that this has already been addressed: because ADM is timeless, equilibrium concepts, such as Radner equilibrium and modern DSGE economics, were developed, addressing shifting expectations and so on.

But even then these equilibrium concepts, while different from ADM, are still, broadly speaking, general equilibrium models, focusing on how "price" changes behaviors of agents, with "somewhat market-clearing" equilibrium forming at the right price vector.
(Monopolistically competitive models, or sometimes called Marshallian models in macroeconomics history parlance, change firm behaviors to not depend directly on the price vector, but then overall they do remain in general equilibrium spirits. A prominent example of course is New Keynesian models, or "policy models.")

And yet they are different from ADM in that they explicitly incorporate how expectations are formed.

And now think of this case: "Agents have different risk aversion, but they share the knowledge of maximum riskless interest/profit rate in the economy."

For this note, I am not going to explain directly why this turns out to be problematic, but then if one carefully examines the issue, one can say that ADM variants in use, especially in macroeconomics but of course not restricted to macro, were blessed with a somewhat ADM foundation and yet cursed with what ADM theory does not actually provide. One of these curses somewhat surprisingly to many is:

 Existence of general equilibrium.

You may say, what? We in econ classes get taught in proofs of existence of competitive equilibrium in DSGE models (or more precisely recursive competitive equilibrium) along with ADM proof of existence of general equilibrium. What are you saying?

Yes, these proofs are mathematically correct. Except, they are not what you are thinking. In fact, in book LS, one of canon books in macro, authors make clear that recursive competitive equilibrium is a partial equilibrium concept, and thus proof of existence only captures the partial equilibrium side.

Thus the only option left inside traditional understanding is: either force expectation formulation to guarantee existence of equilibrium (which really is unnatural) or simply revert to sheer subjective expectation of ADM, which guarantees existence of equilibrium.

Note that the example case involves expectation of something that cannot directly be captured into subjective utility form. ("riskless rate" equilibration/equalization is more of a direct equilibrium condition/constraint than derived inside ADM.)

That completes the memo.