Leon Gettler interviewed me recently on my exchange with Krugman. As you can imagine, it’s a difficult thing to explain in an interview, but I took that as a challenge – if you like to my interview ‘technique’. Just as I love doing it with columns, working over what I’m saying to try to come up with the clearest and best combination of explanation and engagement, so I love being ‘in the zone’ in an interview or on a panel. Of concentrating as hard as possible and getting into a ‘flow’ state where I’m trying to do all this in real time. If I’ve thought about an issue sufficiently, and have come to know what I think, and if I then concentrate hard and give it the right amount of energy, it often works well.

Anyway, here’s the result in this case.

I think that mathematical models are very useful. You say at one point that they are not because if we ask them what happens in we increase this variable then the answer is “it depends”. But that’s the right answer. Models can be used for predictions in specific circumstances. So for this country with this trade balance and this savings and investment and drop in interest rates will have this numerically estimated effect on GDP. Sounds useful to me.

And you can also investigate the general shape of a model using fairly simply machine learning ideas. I must say I am Krugman’s side on this one. I have been to too many conventional economics seminars where that make blindingly naïve assumptions and end up proving the bloody obvious. When they prove a counter-intuitive results (which they love to do) it is usually driven by the assumptions. Then at the other end there are good examples of the kind of economics you like, such as the market for lemons.

Thanks Chris, but I can’t make head or tail of what you’re saying.

A better source for this is my article on Krugman rather than the interview – though if you want to quote specific things I said in the interview, I’d be happy to respond – and I may have to qualify or clarify what I was trying to say.

My only claim is that mathematical modelling

of the kind Krugman is talking aboutis useful in some circumstances and not worth the trouble elsewhere – though one can’t always tell in advance. Other kinds of uses of mathematics – for instance econometric estimation of things – can be useful for investigating empirical regularities which is a different matter.I always find in these arguments that people who are comfortable using maths get uncomfortable thinking about what happens when the maths isn’t much use. Then they start thinking I’m recommending some occult form of knowledge like ‘intuition’. I’m not.

We’re using discursive reasoning here. Why? Because we’re trying to understand as much as we can about what we’re discussing and maths won’t help us – not until we’ve established some thing which maths will help us investigate. I’m arguing for a theoretically self-aware understanding of this demarcation of where maths and formalism might be expected to be useful. I have at least one example where it’s not likely to be useful – sorting out the kinds of things we’re arguing about in this thread.

Hi Nick,

I had just got off a plane with no sleep and had a spare five minutes Doha airport, which probably explains my lack of clarity. I have no familiarity with Krugman’s research apart from knowing that it involves models for trade that we more complex than when he entered the field. So, I don’t know whether you statement about his most brilliant work being useless is true.

In my experience with economics seminars, the models are just toy ones, because microeconomists insist on closed form solutions. You just cannot get published in a top journal if you can’t solve the equilibrium. The conclusions you get out of these models are suspect to me. And they could almost be achieved with a heuristic verbal argument in many cases – what I call proving the bleeding obvious. I am not sure of this would include Max Corden’s early work or not.

While I am a mathematical type, my type of math is applied so in the end I really care that it makes sense and can be interpreted. But this does not imply that we should use naïve models.

In business analytic, we pay a lot of attention to whether we need a simple and interpretable model or a complex black box one for the particular job at hand. But these days, we more often choose complex models. Multiple regression just doesn’t cut it any more, except for very special circumstances. The properties of more appropriately complex models can be summarised and simplified in various ways at the end. And this is much better than fitting a simple model in the first place. You do your simplification at the final summary stage, not at the initial modelling stage.

Complex models are unequivocally best for making direct predictions, because the truth is virtually always complex So, for instance, if you had a complex model for trade-flows you cannot easily say how relative interest rates will affect flows in general. But for a given set of conditions you could calculate the prediction under current interest rates and a changed counterfactual interest rate. This measures the effect of an interest rate increase at this point of time under the present conditions. This sounds useful to me.

Yes, we’re totally in agreement.

Krugman’s models are closed form toy models in which the ‘answer’ is what you get at equilibrium. A more or less complete waste of time if you’re trying to get more ‘realistic’. As I’ve said they do demonstrate some logical implications of scale economies which can be useful – but doesn’t require the hijinks of the new models.

But if you’re serious about looking at imperfect competition, then perfection in competition is a bit like happiness in Tolstoy’s families. Every example of imperfect competition is imperfect in its own way. There’s scale economies, there’s learning by doing there’s asymmetric information and on and on. And of course most examples are complex mixes of these things.

So you can get empirical and investigate patterns which of course could call for econometric techniques and also the kind of complex models you’re talking about. You can check out some of these phenomena and see how much you might be able to make worthwhile claims about them with other things presumed equal.

You might be interested in Keynes’ reaction to John Hicks Value and Capital (from which I extracted Hicks marvellous explanation for going with perfect competition.)

Value and Capitalis generally regarded as a classic in economics and it is grappling with important practical problems relating to the economic cycle. But much of it introduces quite a few of ideas that are now taught as foundations of microeconomics in which economics is elaborated as the logic of pure choice. I think Keynes would have thought that economics was much more than that – and that that wasn’t very interesting or likely to lead to very important insights.“…perfection in competition is a bit like happiness in Tolstoy’s families. Every example of imperfect competition is imperfect in its own way.”

Well put. Fits the point I was labouring. Reason: there are no measurement units for competition. So for theorising there’s competition or there’s not; nothing in between can be coped with.

When you walk into that milk bar what other things, apart from competition, are operating on your psychology? If economics has not improved for decades, someone, somewhere has to tackle those other things. And for them to bear fruit they’ll have to be either present or absent, without pretense of in-between measures.