Claim: Mathematical models of the economy have thousands of variables

Question

A quote from the book Linear algebra done right by Axler is as follows:

"Mathematical models of the economy have thousands of variables"

I find this hard to believe. Is there any credibility to such a claim?

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Full quote: "Mathematical models of the economy have economy have thousands of variables, say $x_1,\dots,x_{5000}$, which means that we must operate in $\mathbb{R}^{5000}$. Such a space cannot be dealt with geometrically, but the algebraic approach works well. That's why our subject is called linear algebra."

Answer 1

Sure there is. In an intermediate microeconomics class, you might deal with two consumers in an exchange economy. In a first semester graduate microeconomics course, you may have to find the Nash equilibrium in a Cournot oligopoly with $n$ firms. Generally, we don't deal with $5000$ firms in a textbook problem, but generalize this in $\mathbb{R}^{n}$.

Auction theory is another area where there are a large number of variables. If you are trying to derive a bidding strategy in a largescale government auction, you are competing against thousands of others around the country. There may also be thousands of commodities, and you are concerned about certain ones. There can also be dynamic valuations on these commodities (ie., trying to form a collection of certain commodities). Auction theory is more discrete in a lot of ways, than more traditional fields in economics. Networks and graphs are cropping up more in economics, as well. These provide another instance for a large number of variables.

Answer 2

A lot of the policy people in the central banks use vector auto-regression (VAR) models of the economy as alternative to structural models that are more firmly rooted in theory. In a VAR, all variables are treated as endogenous, with each written as linear function of its own lagged lagged values and the lagged values of all the other variables. Some of the Federal Reserve's models have over 250 behavioral equations, so you can see how easily it is to get into the thousands if you count lags as a separate variable.