Saturday 20 August 2016

On Maths and Models

Every now and then a debate seems to flare up about economic models. A recent one started with Noah Smith arguing (in reply to Frances Coppola), that heterodox economics does not have the tools to replace mainstream economics. Steve Keen gave an excellent point by point reply about the mathematical quality of heterodox work. Then Frances also wrote a reply and then another, which  I agree with, pointing out that an understanding of the economy does not require maths. Where maths can be used to formalise this understanding, it is very useful. But economics is not a mathematical equation.

I say this from the point of view of someone with a PhD in mathematics, but whose job is to predict the behaviour of systems, specifically financial systems. And I know that in describing a system, parsimony is king. One should use as much maths as is necessary and not a bit more. The more complex the maths, generally the worse the predictive power.

The economy is a very complex system. It is non-linear with a huge number of unknowns. For this reason prediction is difficult. This seems to have meant that any degree of poor prediction is excused on the grounds that no-one can predict the future. I recommend everyone read this excellent Noah Smith blog post from 2013 which was only let down by the somewhat cowardly conclusion.  It shows DSGE models are not useful as predictions - he points to this paper showing that DSGE models are no better than simple univariate autoregression (AR) models at predicting inflation and GDP growth. Bearing in mind AR models are just simple mean reversion models this is a pretty categorical failure. He then argues that they are neither good for policy advice nor even for communication of ideas, before concluding that we should continue with them as the are the 'only game in town'.

Saying that the economy can't be predicted because it is too complex and no-one knows the future is a big cop out for me. No-one could have predicted with any degree of certainty that the global financial crisis would happen in 2008. This is because it is impossible to predict the timing of events of this nature that depend on triggers and positive feedback loops. It also depends on policy reaction. For example, a possible crash in China early this year was averted by a large government spending programme. But what heteredox economics has done is give keys to understanding the nature of the economy.

If we know that a crash is going to come if we let private sector debt build up, then we will try to reduce the build up of private sector debt. If we know that government debt is benign, then we will use that to grow the economy rather than private credit, share buybacks and house price rises. We don't need any maths to understand this. As I said in a tweet, in my opinion the main thing maths has given macroeconomics is the ability to be more precisely completely wrong.

Defenders of the economic orthodoxy generally say that they understand that their models have not done the best in the past, but that they are flexible so can be adapted to include whatever you want. This is sort of true, but to start where they are starting from is insane.

As a builder of models I would like to humbly offer this advice to macroeconomists about building a model to describe the economy. I have made my own attempt here, and obviously I think it is a pretty good description. But in any case, I would advise the following:

How Not to Build a Macroeconomic Model

1) Microfoundations: Would a pollster make a prediction for an election based upon what they thought each rational voter should do, and building up to the whole population assuming they all think independently? Of course they wouldn't. They model it by asking people and then using known relationships between people you ask and the population as a whole. There is no reason whatsoever to model the economy as individual independent rational agents and in fact it is completely incorrect to do so. People do not behave independently and the aggregate must be modelled not the individuals.

2) Rationality: Why would you assume rationality? It is completely unnecessary and also completely false to suggest that people act rationally at all. It is certainly false to assume that rationality includes perfect knowledge of the future and that Ricardian equivalence holds. All assumptions about peoples behaviour should be testable.

3) Loanable funds: It is completely wrong to model money as if there is a finite amount of it that is simply loaned by more patient people to invest. Banks create credit, corporations and governments issue bonds. This expansion of the money supply allows growth to happen. And also can create instability. Any model that misses this out will be unable to describe the economy correctly.

4) Interest rate effects: interest rate cuts boost the economy through two main channels. First, they increases the amount of private sector debt, meaning more money in the economy. Second they boost asset prices, because lower interest rates (increasing bond prices) and reduce the discount rate for risk assets thus making their price rise.

The problem with loanable funds is that if interest rates are cut, it means all growth in spending must now come from rational agents choosing to spend more of their income rather than save - the 'rational' logic being that they will save less if they get less interest as it means future consumption is higher (and their target is to maximise their utility from consumption). As Eric Lonergan argued recently there is not even any evidence for this. One could argue that if people save for a target then the opposite is true - lower interest rates mean a rational person saves more. Any model needs to correctly account for why changes in important variables work. Being wrong about this particular one has led to a spectacular build up in private sector debt over the past 40 years.

5) No financial sector: the growth of debt has led to a huge increase in the size of the financial sector. Or maybe partly the other way around. Whichever it is, there are both distributional impacts and stability impacts. The instability is very well covered by Steve Keen with his Minsky model. The distribution impacts are looked at in my paper but involve interest payments going from those with a high marginal propensity to consume (MPC) to those with a lower MPC. Also included in this could be the increase in corporate profits as a share of GDP - something that has the same effect. The instability and inequality must be a part of the model or the economy can not be properly understood.

What does this mean? 

Yes, it may be possible to adjust the current models to include all of these things, but really why bother to try? The difficulty of trying to adapt a completely inappropriate and incorrect model to reality is much higher than simply starting again. And the starting point in my view must be a stock flow consistent money approach as pioneered by Wynne Godley.

Addendum: Noah Smith replied to a few responses to his post, including this one and he made a fair point. In criticising microfoundations, I am apparently also ruling out agent-based models. I am not meaning to do this as these types of models, where individual agents interact with each other, are excellent for studying the emergent properties of certain systems. If I could divide economic modelling into two separate themes, it would be 1) models used for short term prediction (these should be as simple as possible) and 2) models used to help understand the system. Into category 2 would fall Steve Keen's Minsky model and as well as these agent based models. I think that Smith is right that one day the type 2 models could become type 1 models. Unfortunately standard mainstream models are of neither type.

Also, he is right that the Financial sector is something that should be included so doesn't really fit under the heading. So I have changed the sub-heading to to 'No Financial Sector'.