Does the Real World Converge to Equilibrium?This rant was triggered by some research I am doing, some articles discussing equilibrium that I have recently read (Andrew Lainton, Peter Radford), and this question on equilibrium on the Economics Stack Exchange.
The questioner asks:
but is the model's equilibrium one that occurs naturally? Is real-life money supply equal to money demand? Is real-life investment equal to savings?This raises all kinds of questions. What is equilibrium? Is it a property of the real world? How is it possible to write a macro textbook and not answer these questions?
My question in short: why does the economy converge to these equilibriums?
Seriously, It's a SetMainstream economics is highly mathematical. One of the perceived advantages of the mathematics is that argumentation is supposed to be clearer than literary economics. However, in order for mathematics to provide this advantage, concepts have to be formally defined. From the perspective of applied mathematics, this means defining concepts in terms of set theory (yes, there are weird corner cases in mathematical logic, such as self-referential sets, where we have to go beyond set theory).
Other than very highly stylised models, most macro models are specified by three things.
- A set of economic variables, which are elements in the set of "time series."
- "Constraints" on those variables: accounting identities, production functions, etc.
- A method to find a "solution" to the system. A solution is the set of variable values (1) that satisfy constraints (2). In general, there is an infinite number of potential solutions that satisfy constraints, so some method is needed to winnow down the choices.
Based on a textual analysis of economic writing, it seems clear that "general equilibrium" (whatever it is), is a technique for choosing a solution. By itself, this is innocuous. For example, we need to calculate the solution to the system of equations of a stock-flow consistent model; if we set up the equations correctly, there will be a unique solution. What is to stop us from labelling said solution the "general equilibrium"? From an ideological perspective, that would be a big no-no (based on my reading of the literature). From a formal mathematical perspective, we would need a definition of "general equilibrium" that stops us from making that characterisation.
Economic Model Transitivity Fallacy
Before returning to general equilibrium, I want to explain (again) one of my complaints about the economic literature. Whenever I read Dynamic Stochastic General Equilibrium (DSGE) articles, there are commonly logical jumps in proofs, where assertions are made without any justification. The mathematical logic being used seems to rely on "Economic Model Transitivity."
- An "economic model" X has mathematical property A.
- Model Y is an "economic model."
- Therefore, Y has property A.
This obviously does not work from a formal mathematical perspective, unless we can validate that model Y has exactly the same characteristics as X, which allowed us to derive the result that A holds. The only way to be sure is to re-derive the proof that A holds for the new model Y.
In other words, we cannot just appeal to random theorems (or definitions) without citation; we need to explicitly list the conditions for the theorem (or definition), and then validate that the system meets those conditions.
What is General Equilibrium?
DSGE macro has its roots in optimal control theory. However, the optimal control theory mathematics has largely been obscured by economists following a publishing convention that gets further and further away from its mathematical roots. It is entirely possible to read a few dozen DSGE journal articles, texts, or lecture notes, without finding a valid formal characterisation of how to find the solution for the macro model of interest. (When I refer to a macro model, it includes both households and firms attempting to optimise their utility/profits respectively, as well as a government sector. This creates a optimisation structure that is completely unlike an optimisation problem for one sector alone.)
The implicit assumption is that the determination of "general equilibrium" was covered elsewhere. Walras? Arrow and Debreu? Intermediate microeconomics? The obvious question to ask: did that ultimate definition source solve the same macroeconomic system as the current journal article, or was the modern author relying on "Economic Model Transitivity"? That is, we can find definitions of "general equilibrium" that work for some models; the trick is to find a definition that matches macro DSGE models. At the time of writing, I still have not found anything satisfactory, but I want to underline that this is still a research in progress.*
Why Criticisms of Equilibrium do not Register
As a final note, I would suggest that this situation explains why heterodox complaints about the realism of equilibrium do not register among mainstream economists. In practice, the equilibrium assumption does not even get properly defined in papers that allegedly depend upon the assumption. Given the low level of attention to the concept, worrying about its realism is moot.
* The closest I have seen is in Section 7,3 ("Recursive competitive equilibrium") in "Recursive Economic Theory: by Lars Ljungqvist and Thomas J. Sargent. Although it appears quite formal, there were a couple of issues. One was a verbal formulation that was hard to translate into a statement about sets. (This could be viewed as a stylistic issue; in applied mathematics, it is normal to use verbal shortcuts. However, it is unclear how to resolve the ambiguity.) The second issue is more serious, as it does not take into account the differing objective functions of households and firms. I am in the process of reading the text, and I do not know whether this concern is addressed in a later section.
(c) Brian Romanchuk 2017