Mathematical Economics, Criticisms and Defence.

Its harder to model human behaviour than it is particle behaviour in physics for instance because it is more erratic and changes over time. Particles behave now the same way they did 100 years ago but human choices, tastes etc change. So the economist always faces some challenges when trying to model mathematically.

A lot of relationships between things in economics are explained through mathematics, and they help you understand what affects what, eg if you understand the Phillips Curve equation you can understand how unemployment affects inflation, if you understand the uncovered interest parity condition you understand how interest rates affect exchange rates. General algebraic expressions are a very useful way in which maths can show you 'what affects what else, and in what way'.

However predicting human behaviour is an inexact science and there are so many unknowns that can come in, most of the models that policy makers use have a (+ random shock) part at the end of the equation. Which is why you always get growth forecasts and the like being revised, when the OBR made its growth forecasts in June 2010 it wasn't anticipating war in Libya which has affected oil prices in ways that couldn't be foreseen.

I think maths is a very useful tool but economists have to respect its limits, the problem is people who have high mathematical ability will be able to make sophisticated models on the strength of past behaviour and they start to think because the model uses very advanced maths that they have uncovered a foolproof truth, but they haven't.

In the context of internet forums, mathematics in an economics degree is a bit of a 'mines bigger than yours' thing. It's like if you go on a bodybuilding forum people judge each other by how much you squat, because they know squats are hard and thats what gets respect. Maths is hard and so people who are doing highly mathematical programmes tend to regard theirs as a superior course. It has an advantage in terms of 'signalling' high ability to employers, more than being an advantage in terms of being an economist, especially in the policy side.

Hey, thanks for replying, what are the assumptions and what does not work and what does work? Also, then why is there such a high Maths requirement for undergraduate degrees?

I think maths is a very useful tool but economists have to respect its limits, the problem is people who have high mathematical ability will be able to make sophisticated models on the strength of past behaviour and they start to think because the model uses very advanced maths that they have uncovered a foolproof truth, but they haven't.

Its harder to model human behaviour than it is particle behaviour in physics for instance because it is more erratic and changes over time. Particles behave now the same way they did 100 years ago but human choices, tastes etc change. So the economist always faces some challenges when trying to model mathematically.

A lot of relationships between things in economics are explained through mathematics, and they help you understand what affects what, eg if you understand the Phillips Curve equation you can understand how unemployment affects inflation, if you understand the uncovered interest parity condition you understand how interest rates affect exchange rates. General algebraic expressions are a very useful way in which maths can show you 'what affects what else, and in what way'.

However predicting human behaviour is an inexact science and there are so many unknowns that can come in, most of the models that policy makers use have a (+ random shock) part at the end of the equation. Which is why you always get growth forecasts and the like being revised, when the OBR made its growth forecasts in June 2010 it wasn't anticipating war in Libya which has affected oil prices in ways that couldn't be foreseen.

I think maths is a very useful tool but economists have to respect its limits, the problem is people who have high mathematical ability will be able to make sophisticated models on the strength of past behaviour and they start to think because the model uses very advanced maths that they have uncovered a foolproof truth, but they haven't.

In the context of internet forums, mathematics in an economics degree is a bit of a 'mines bigger than yours' thing. It's like if you go on a bodybuilding forum people judge each other by how much you squat, because they know squats are hard and thats what gets respect. Maths is hard and so people who are doing highly mathematical programmes tend to regard theirs as a superior course. It has an advantage in terms of 'signalling' high ability to employers, more than being an advantage in terms of being an economist, especially in the policy side.

Hey, thank you for replying, I have more questions concerning Maths in Economics which also has to do with the evolution of the subject and the historical aspect of it. Would you happen to know anything about:

Chaos in Economics (Chaos Theory, Mathematical Chaos), and if that is addressed/taught at an undergraduate level, or is it primarily studied by someone pursuing a joint degree in Mathematics and Economics or only by Mathematics students who have a flexible course structure (who aren't forced to study Mechanics/Mathematical Phsyics).
Concerning this, from a historical perspective, how Newtonian science and Equilibrium systems (Newtonian world view) contributed to an Economy as being viewed as a machine that could be engineered perfectly, and in a nutshell, the Chaotic elements of an economy and the Maths relating to that today.

Is all the essential and required mathematics covered in an Economics undergraduate degree or is there more?

Hey, thanks for replying, including danny111 and everyone else.

I'm not really interested in Finance per say, . What I am interested is Economics.

The economy is not dependable, not changeless, not predictable, is unexpected, is not mechanistic, is not controllable, is unstable, and is generally chaotic. (correct me if I'm wrong)
As you said, Chaotic behaviour will not be taught or studied in an Economics undergraduate degree programme, even if it is at LSE with all the maths options, and might come in at a later level.

Concerning, the Newtonian view, or the economy as a machine, I was referring to earlier times, around/before the invention of the modern computer. (..as a part of economics history)

Wikipedia is (sadly) not always right.

I doubt you will do chaos theory on an undergraduate economics course, I think that type of thing comes in at MSc level and is probably more part of Finance based masters. Really if you are interested in this type of quantitative modelling I would advise doing at least a joint honours with maths in it if not a straight maths undergrad degree and then a finance type masters afterwards.

Regarding your question about how the economy came to be viewed as a machine that could be engineered perfectly, I am not sure exactly, it seems to have come in recent times from US universities and the financial sector. Keynes developed the idea that the economy could be managed but he was not heavily mathematical, he was not working on the basis of precise mathematical models, more a set of tools which policy makers could use to mitigate against the effects of shocks, but not with precision. A lot of the famous economic models are quite simple ones, most of the earlier economists were more political-economists than mathematical-economists.

The recent trend has been that the subject has become very mathematical but that trend will probably change a bit in the light of the financial crisis, which has undermined general confidence in economists. There are two big problems when economics becomes very mathematical:
1 - it becomes more divorced from the 'real world' of policy, policymakers can't understand it, and it becomes more a subject that academics talk to each other about in language only they can understand and nobody with the power to make decisions, actually reads it
2 - the sector which has embraced mathematical economics is the financial sector, where they have used financial modelling to try and make informed financial decisions (hence the popularity of highly mathematical programmes amongst those who want to work in investment banking). However in recent times a lot of people have lost a lot of money because they placed too much faith in models.

For example you get 'tail risk' which is when you take a risk on an event which is supposedly 3 standard deviations away from the mean, the probability of this happening should be 0.26% or something like that. So if you are running an investment fund and without telling your investors you start offering insurance (which will bankrupt the entire fund if you have to pay out) on events which you assume will be 3 standard deviations or more away from the mean, you can be pretty confident that you will be able to just charge the premiums and make money on it and you'd have to be very unlucky for the bad state to occur where you have to pay out. It's a dodgy way to run a fund but it's how people were making money. But a few too many people took on 'tail risk' which went wrong...which suggests the models they were using had something wrong with them, and they were identifying something as being in the extreme tails of probability, when it actually wasn't. So I think there is less blanket confidence than there used to be, in mathematical models of human behaviour.

The new direction economics is headed down is behavioural economics. Economics has been influenced by philosophers, political scientists, mathematicians and the next lot will be psychologists.