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'.


  1. excellent post.I really don't understand frameworks provided by other more orthodox approaches,they seem so unintuitive if anything.

  2. I'm unsure about a few of your requirements:

    "There is no reason whatsoever "

    Only if you ignore a good chunk of literature showing how flawed aggregated 'hydraulic' models of the 70s and earlier can be. You need some kind of solution to ensure the behavioural rules are invariant to policy changes, microfoundations is a solution to this.

    "It is completely unnecessary" (re rationality)

    It's not unnecessary, it's far harder to make a tractable model with irrational agents which isn't uselessly chaotic, isn't Keynesian cross levels of aggregation or just arbitrary (yes ABM is having a go at it, we'll see where that goes). Secondly, if a policy works only if agents are irrational but not if they are rational, I would be very uncomfortable with that - it means certain people can game the system, it means a situation is only stable until people 'figure out' what's actually going on.

    "All assumptions about peoples behaviour should be testable."

    Sure here you go:

    Honestly, this whole anti rationality path is just wrongheaded, obviously there are behavioural irregularities that occur, which behavioural economics provides a useful role for, but to dismiss anything using rationality is absurd - even unlearningeconomics, one of the biggest economics contrarians around, will tell you it's a bad criticism.

    " This expansion of the money supply allows growth to happen. "

    The expansion of credit requires the central bank to provide base money on demand when banks need it - at a price, the interest rate. Modern DSGE models look at the interest rates, most don't care about money or available funds at all. Which leads me to:

    "if people save for a target then the opposite is true - lower interest rates mean a rational person saves more."

    It seems you're talking about consumption smoothing. Do you really not think there have been long discussions over decades about how interest rate changes affect consumption smoothing consumers? Come on now, of course economists have thought of this very problem.

    Also, I still don't see why you don't want interest effects in the model, when you just acknowledged they boost the economy through two channels (by the way, your two channels fairly require rational lenders and and investors).

    1. I don't explain things very well, and possibly put things in a way here that they are read not quite as they are intended.

      Regarding aggregation and rationality, what I am saying is that behaviour of groups of people need to be modelled as close to how they are in real life as possible and reasonable, not just as we think is rational. Because people patently obviously do not behave as rational agents. As a small example, people save less for their pension than is 'rational'.

      My real problem is that the 'rationality' used by mainstream economics about spending and saving decisions is completely wrong. Most people on low to medium incomes spend the majority of their income, those on higher incomes spend much less. Distribution of more money to richer people means that less money is spent. This is completely independent of interest rate. This means that the model is based on false reasoning.

      But worse, 'Rationality' is used to justify austerity (Ricardian equivalence) and very free market economics. It is used to create a value system which helps those with wealth against those without.

      So here, my point again is that we should model behaviour as it is, not how we think it should be.

      Regarding credit expansion and interest rates, your model is not complete. This Bank of England report gives a good explanation
      and DSGE models look at it in the wrong way.

      I will happily admit my knowledge of the economic literature is poor - I imagine many different versions of rationality have been attempted. What I am really saying is that interest rate changes have very little effect on saving/spending decisions but a large effect on borrowing decisions and hence the creation of new credit. And also on speculation decisions, so lower interest rates push the stock market higher and give a wealth effect.

      Here I am saying that of course interest rate impacts should be included in the model - but they should have the mechanism of how they work correct.

    2. I think we need to be careful with the term "rationality" or "rational agent". In this context, a rational agent is one who makes the best decision for herself based upon her own preferences and the available information (including expectations of the future). The inclusion of personal preferences and expectations of the future in this definition means that it is possible for people to behave in ways that appear irrational to others but are internally consistent to them. "Irrational" can be locally rational.

      I think the bigger problem here, Ari, is the aggregation effect. Individually rational choices can be irrational at the aggregate level. Herding, for example, is individually rational (if there is a fire in the cinema, I will run for the exit), but collectively irrational (if everyone runs for the exit at the same time, no-one will get out). Microfounded models using representative agents struggle to represent aggregation effects adequately - well, let's be honest, they don't represent them at all. Consequently, fallacy of composition is a common and serious problem in macroeconomic modelling.

    3. On the effects of interest rates, I think it is fair to say that we do not really understand the behavioural effects of interest rate changes.

      At the micro level, there is recent research showing that firms who set high hurdle rates may be indifferent to interest rates when evaluating investment opportunities.

      There is also anecdotal evidence that very low interest rates may encourage people to save more, not less. People saving for retirement target a FUTURE income, which when interest rates are very low they can only achieve at their risk preference by saving more. See Yves Mersch's comment here:

    4. Thanks Frances. The data on interest rate efects are very interesting and really so important.

      I would suspect that individuals are more likely to take out mortgages when the current monthly repayments are lower. And similarly that companies are more likely to issue debt for 'balance sheet efficiency' when interest rates are lower. Thus the more GDP unproductive sources of credit are the ones most sensitive to interest rates. If this were the case, it makes lowering interest rate an even worse way of stimulationg growth than first thought.

      I agree that aggregation is the bigger problem (but at the same time feel that the term 'rationality' is abused for free market ends). By using agent-based models it is possible to create a system that does display the aggregation effects of herding, but then I really struggle to see how any calibration of this onto the real economy is possible. Thus important economic effects can be demonstrated using better aggregation of individual agents, but the final model will be unable to predict next year's GDP growth. But then maybe this is fine.

    5. Ari,

      Yes, people are more likely to take out mortgages when interest rates are lower, though only if macroprudential regulations make this possible. Low LTV limits, for example, discourage poorer first-time buyers - as we are seeing in London. What happens then, of course, is unlicensed lenders spring up offering subprime loans at much higher rates to those who can't afford the deposit.

      Mortgage lending does have a stimulatory effect on the economy due to secondary effects (people make improvements to houses they've just bought, or even just decorate and buy new furniture). Also, pumping up the housing market increases spending due to wealth effects - think about the effect of H2B just before the 2015 election. The downside of this is that borrowing at low variable rates increases household balance sheet risk. Mark Carney has persistently warned about this.

      I agree with you that very low interest rates encourage unproductive and dysfunctional behaviour by firms - leveraged stock buybacks, for example.


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