OT: Osborne's equation - does it make sense - any maths gurus about here

[michael newport]

OT but possibly interesting in a strange kind of way. Warning: Risk of considerable boredom. I've just been looking at the amazing publication:-

"treasury_analysis_economic_impact_of_eu_membership_web.pdf" Available at

Osborne's eqn, has, according to BBC News hack Norman Smith, ("you'd have to be Einstein cousin's to understand it") , a spectacular equation on p 158

A couple of things about the eqn (I couldn't get further before boredom set in).

The equation has about a dozen terms (so must be complicated right!). I'm no maths guru by any means so, while not understanding the eqn's meaning, there are (to me) some strange goings on in it. So, I wonder can anyone else explain it?

1) For starters the eqn has the LHS as ln(T subscript (ijt)) =

ijt we are told denotes "Trade flows between country i and country j in time t". But what happens if country i has no trade flow with country j (time is irrelevant here), then we would have ln(0). Isn't this impossible! As is defined as (minus)infinity!

2) The terms on the RHS do not seem to pass the wildest test of basic dimensional analysis. i.e They are summing different entities! Unless of course Economics has a maths language that is based on a kind of feral gibberish.

Ah well, I look forward to a clear explanation from Mr Osborne - or anyone. I mean, it MUST be correct as Britain's future depends on it - doesn't it.

[Tim Streater]

I expect that zero never applies, but well spotted.

Do these people even understand dimensional analysis? Whoever invented the BMI clearly doesn't, f'rinstance. That has the dimension of length, when it ought to be dimensionless.

[Capitol]

I just looked at the conclusions and decided that the basic assumptions were incompetent. It is much more expensive to stay in than LEAVE.

[Chris Hogg]

Aren't you interpreting it wrongly? It's a predictive equation giving you the value of ln(T subscript (ijt)) if you know all the other stuff. If there is no trade flow between countries i and j, then there's probably a division by zero on the RHS, coupled with a minus sign somewhere, so the whole RHS becomes minus infinity.

Incidentally, I note that they haven't defined epsilon sub (ijt).

I doubt that dimensional analysis comes into it. It looks like the sort of equation obtained by a multi-parameter curve fitting routine, which fits a whole set of numerical parameters considered important by economic statisticians, to real data, and derives appropriate factors depending on their significance. Taking natural logarithms of most of them probably helps in ignoring the dimensions (what for example are the dimensions of ln(Population difference) and ln(distance between states)?). AIUI such logs are dimensionless.

You'd have to go to the reference Head and Mayer 2013 to get more details on how the equation is derived:

Good luck with that!

I doubt he'd have a clue!

[harry]

Osbourne can't predict a year ahead never mind five. The equation is bollix. Just dreamt up to look impressive.

[Chris Hogg]

In fact, skimming very fast through that link (not to be recommended BTW), they do talk about the consequences of zeros in the equations:

"5.2. Causes and consequences of zeros The structural gravity models we have considered in this paper express trade as the multiple of strictly positive variables. Hence, they do not naturally generate zero flows. Most actual trade data sets exhibit substantial fractions of zeros, which become more frequent with disaggregation at the firm or product level......"

and much more, but they're obviously well aware of the problem. One's left with the impression that it's all very erudite, but very hypothetical!

[Tim Streater]

As the Emperor Franz-Josef might have said: "Too many variables."

This is a model, and like all models it has built-in assumptions. What we don't know is whether the assumptions are valid or not.

The other thing to remember is that models don't actually *tell* you anything. They make *predictions* and that is all. When NASA sends a spacecraft off, they say that Newton predicts that it will pitch up at Mars next Tuesday fortnight. That it then does so tells us that the model is a good one.

You can form your own conclusions about Treasury or Climate Change models.

[Chris Hogg]

Climate change models also went through my mind when I was skimming that report!

[bert]

Just stick Vat on pasties and all will be well.

[newshound]

The big difference is that the Treasury has a lot of historic data. It really is a very different sort of modelling problem to climate, but I would be inclined to assume that the mathematicians in the treasury do, in fact, know what they are doing. And test their models on real data. Of course when *policy* gets in the way......

[Capitol]

Are you saying it is crap?

[Chris Hogg]

Good god no. To make such a comment you'd need to understand it, which I certainly don't. I just felt it had the air of being hypothetical, rather than being a formula for calculating exact numbers.

[Chris J Dixon]

Reminds me about the landowner who, with some visitors, calls over his man and asks him to ride a horse around the field.

"Certainly sir. Am I riding for buying or selling?"

Chris

[harry]

The main point is they can't even predict one year into the future.