I want to respond with two points about this, which also relate to Smith's general views on maths, theory, and economics. First, a theory is a concept. An idea. Theories can therefore be modelled mathematically in many ways. Second, the stocks and flows of the mainstream are different, theoretically, to those of the monetary economists.

**Theories are concepts**

Evolution is a theory. It requires absolutely no maths to explain it. Cell theory, is, well, a theory. Again, no maths required. Plate tectonics. Heliocentirsm. All concepts or ideas. Not equations.

Or closer to home, game theory is a concept that has many, many, mathematical representations.

I don’t see the problem with an “economics without maths” if we are engaged in debate about which ideas have merit, and can on their face, provide useful predictions. Smith cites Minksy as an economist who explains his theory of “stability is destabilising” in words. To me that’s a great example of the usefulness of theories, even without mathematical models to accompany them. After all, many mathematical methods could be used to capture the core elements of this theory.

So to say frame “broad idea-sketching” as an alternative to “formal models” is rather naive in my view. You can’t have a formal model without big ideas underneath it. After all, every variable and parameter in a mathematical equation is meant to capture some piece of reality, and you need a theory to say that such a thing even exists.

And there are still many debates about whether measured, mathematical, things have theoretical foundations that allow them to be interpreted in particular ways. Think of the capital debates. You can have many formal models with K in them, but you need a theory to say what K is in reality.

Or more recently, there has been a debate around the meaning of the number we get when we measure multi-factor productivity. Just because we measured it, and had a formal model underpinning it, doesn’t allow for an interpretation without a theory to accompany it.

**SFC models use different concepts**

With that in mind, we can now compare the SFC approach of monetary economics with the apparent stock-flow consistency of mainstream models. As you might have guessed, the consistency is not really there once we account for the underlying theoretical concepts.

Again I will use my mud-map of economic domains to make this point. I find this a useful way to structure economic inquiry as it makes clear the point that there are different conceptual and theoretical domains in which economic analysis takes place.

The fundamental difference is this. Standard models capture a theory about real goods and services, and real capital (the physical buildings and machines). SFC models capture transactions and balances (assets and liabilities) in money, regardless of the underlying physical attributes of the goods and capital. This means that SFC models allow for credit balances between entities, which can’t be captured in the standard economics of real goods, since credits are not physical goods or services. The image below tries to show that although standard models are consistent in their treatment of stocks of physical capital and flows of investment in that physical capital, the very concept of physical capital is different to the items accounted for in money-based SFC models.

I also try to show that the way each approach deals with aggregation can be quite different. Standard models typically pick an arbitrary level and aggregate under the assumption of a representative agent, often to the level of a whole country. But SFC models are only useful when they aggregate at the levels of economic sectors, or even more finely than that. Because after all, once you have aggregated the whole economy to a single agent, the credit balances between agents within the group all cancel out, yet the whole point of SFC models it to observe the dynamics of these balances between different parts of the economy.

I have long held the view that many of the conflicts in economics stem from theoretical confusions. After all, once a bunch of equations are written down, it is very easy to see if the “solution” is correct.

Noah could use his unique position as a facilitator of economic debate in the blogosphere to help economists with different approaches begin to talk to each other, rather than past each other. But confusing formal models with theory, and holding alternative approaches to a higher standard to mainstream approaches, is not a great start.

UPDATE:

To make clear the idea of analysing different domains, I think a motor-racing analogy is useful. One racing "school of thought" measures stocks and flows in terms of the weight of each car each lap. They show that the flows of weight lost in fuel is consistently captured in declining stock of weight of the car. Another school of thought measures the length travelled by each car and its speed, noting how their stocks and flows of distance are also consistent.

Yet the two aren't directly comparable, even though they may both be independently, and jointly, useful approaches for understanding motor-racing. In economics we get confused because we use words like capital to mean multiple things. This problem is all too obvious if consider what sort of understanding of racing we would have if the two schools of thought used the name capital to mean both distance and weight.