Maths in economics

SLUSK

Why is there an obsession with maths in modern economics? What good does this mathematical models do? Does anyone honestly believe that human behavior can be properly described through ma thematic formulas?

The Austrians say that mathematics is not appropriate to use in economics because human action is not quantifiable in that way.

"What is the problem, then, of using math for economics, and why are Austrians opposed to such a methodology? In a word, math is not an appropriate tool to describe human action. As Mises and Rothbard often pointed out, one cannot quantify human action. This does not mean that people do not engage in activity in which mathematics is not important, but rather that we cannot accurately use math to describe how humans behave."
http://mises.org/daily/926

Thomas_S_Hunterson

"All models are wrong but some are useful"

SLUSK

Sean_K wrote: »

"All models are wrong but some are useful"

Why continue using maths in economics then?

Thomas_S_Hunterson

SLUSK wrote: »

Why continue using maths in economics then?

It's useful.

SLUSK

Sean_K wrote: »

It's useful.

Ehm... how?

Flamed Diving

SLUSK wrote: »

Ehm... how?

Because 50% of an eye sees better than no eye at all.

If you don't understand that metaphor, then this discussion ends, for me.

Time Magazine

SLUSK wrote: »

Ehm... how?

Because maths is more precise than English. You can fully trace out the implications of a model using maths. It's far easier to make mistakes or to reach mutually incompatible conclusions if you rely on English.

The reality of the situation is that the Austrians, too, have a model. They just don't want to formalise it, because depending on how you view it it's either completely falsified (data not matching the model) or completely untestable and unscientific ("ah, the data doesn't match our model now, but we're sure that at some point in the medium-term future that there will be an effect on something we're not sure of, because human behaviour can't be quantified.")

SLUSK

Time Magazine wrote: »

Because maths is more precise than English. You can fully trace out the implications of a model using maths. It's far easier to make mistakes or to reach mutually incompatible conclusions if you rely on English.

The reality of the situation is that the Austrians, too, have a model. They just don't want to formalise it, because depending on how you view it it's either completely falsified (data not matching the model) or completely untestable and unscientific ("ah, the data doesn't match our model now, but we're sure that at some point in the medium-term future that there will be an effect on something we're not sure of, because human behaviour can't be quantified.")

Are you kidding me. So economic models become "proper science" when using math? Maths becomes pretty useless when trying to describe subjective things like people's preference of one good over another and so on.

This Swedish economist Stefan MI. Karlsson seems to agree with me here.
http://stefanmikarlsson.blogspot.com/2008/04/real-problem-with-non-austrian.html

dan_d

Because maths is a universal language.

egan007

Well if the Australians did not use Maths their economic policy would look something like

You collect the chizzawaggers and add them to you annual dingdongs and bobs your transvestite auntie mate.

BESman

I can't disagree with SLUSK's reasoning here. The Austrians may not be conventional but the over reliance on maths in some economic fields is a cause of concern for me. Ultimately, economics studies human behaviour. Psychology would be no different, does anyone know how large a component mathematics is in this field? It would be interesting to know.

Economists disguise their "science" from the lay person by blanketing their models in often baffling and largely useless mathematics. Some mathematics is of course useful in economics, just as it is in any scientific field, especially areas like econometrics. However many of the modern macro models are a load of arse.

Time Magazine

SLUSK wrote: »

Are you kidding me. So economic models become "proper science" when using math?

No, many mathematical papers are nonsense. But Solow (1956), for example, is excellent science and really changed perspectives. Same can be said for Nash's PhD thesis, or Heckman (1979). They are all excellent applied scientific pieces, esssentially impossible without maths.

Maths becomes pretty useless when trying to describe subjective things like people's preference of one good over another and so on.

Why?

This Swedish economist Stefan MI. Karlsson seems to agree with me here.
http://stefanmikarlsson.blogspot.com/2008/04/real-problem-with-non-austrian.html

Ah yes, the internationally-renowned Stefan Karlsson. Who is this chap?

Look, read the first two paragraphs of this piece. Regardless of your views on Krugman, it makes the argument pretty well. You started off this asking "What good is mathematics?" and there's your answer.

Time Magazine

BESman wrote: »

Psychology would be no different, does anyone know how large a component mathematics is in this field? It would be interesting to know.

Very little. They tend to suck at statistics too, only now starting to come to terms with causality.

Economists disguise their "science" from the lay person by blanketing their models in often baffling and largely useless mathematics. Some mathematics is of course useful in economics, just as it is in any scientific field, especially areas like econometrics. However many of the modern macro models are a load of arse.

For the most part they're testable loads of arse, which is a start. And, to be fair, your problem is more that macro is crap (a reasonable claim) rather than the use of mathematics is crap.

There's definitely a problem with a focus on pretty mathematics. I don't think CAPM would have caught on as much were it not so prettily derived from mean-variance utility, etc.

However it's important to note that this is not an argument about the use of mathematics in social science. One of the most illuminating books ever I have ever read was Kahneman, Tversky and some other guy who somehow managed to get his name on there. There's still math behind it.

leninbenjamin

dan_d wrote: »

Because maths is a universal language.

It's also incredibly flawed, a fact people continuously overlook.

For example try introducing a dynamic component to the demand and supply model, very easy to end up with a chaotic model.

There's also an over-reliance on statistical and numerical software in the sciences in general. I remember been given raw data from some agricultural thinktank for the purposes of an econometrics project before and being able to prove beyond doubt that the number of cows in the country as the only statistically significant driver of the economy. Nonsensical garbage to anyone with a bit of common sense. But for issues that are less clear cut, it shows how easy it is to make utterly nonsensical inferences on the back of reliable data and statistical methods.

And funnily enough, not long after that I was given a lecture in a computer science module about animation and perception. The lecturer, good at maths but complete novice at stats basically did the exact same thing I did above, collected the data, ran the package and only then made the inferences. Because her area is a complete unknown she was able to get a published paper from it, yet it was disproven as complete ****e less than 6 months later I was told. She's not the only one mind, there are plenty of people who've made a very lucrative career in the area of perception doing that kind of ****.

Time Magazine

leninbenjamin wrote: »

There's also an over-reliance on statistical and numerical software in the sciences in general. I remember been given raw data from some agricultural thinktank for the purposes of an econometrics project before and being able to prove beyond doubt that the number of cows in the country as the only statistically significant driver of the economy. Nonsensical garbage to anyone with a bit of common sense. But for issues that are less clear cut, it shows how easy it is to make utterly nonsensical inferences on the back of reliable data and statistical methods.

I'm not sure how much econometrics you have done so apologies if this comes across as paternal, but causal analysis has long been discussed. See instrumental variables for one approach, and the subsequent debate on local area treatment effects. Here's the latest contribution.

FWIW, it's economists who are driving this scientific inquiry into causality. The scientific status of economics is a frontier research topic and causal analysis is at the heart of it. It's essentially impossible for economics to be both scientific but also mathematics-lite. In the choice between science or easy maths, I choose science.

nesf

leninbenjamin wrote: »

There's also an over-reliance on statistical and numerical software in the sciences in general. I remember been given raw data from some agricultural thinktank for the purposes of an econometrics project before and being able to prove beyond doubt that the number of cows in the country as the only statistically significant driver of the economy. Nonsensical garbage to anyone with a bit of common sense. But for issues that are less clear cut, it shows how easy it is to make utterly nonsensical inferences on the back of reliable data and statistical methods.

The software only runs the regression for you. It can't interpret it for you. One of the most basic rules of econometrics is that your model needs to make theoretical sense as well as making empirical sense. Otherwise you end up with your cows driving the economy type results.

Ostrom

I always found Elinor Ostrom's work a nice balance (although not strictly economics). Much of her recent work has involved compiling qualitative data on local governance structures - with her conceptual work on complex socioecological systems, you can see the utility of combining sustainibility outcome models with data that deal with the 'human' dimension.

If you can get it (I'm not sure if it is open source...) check this out:

Ostrom, Elinor. 2009. A General Framework for Analyzing Sustainibility of Social-Ecological Systems, Science, 325:419-422

It gives a good review of some of the difficulties in communication

You might like this too. Mostly an argument for reporting effect sizes, but does raise the issue of statistical/practical significance.

Time Magazine

efla wrote: »

You might like this too. Mostly an argument for reporting effect sizes, but does raise the issue of statistical/practical significance.

Just looking at the review, it seems to be mostly arguing about looking at the magnitude of the coefficient as well as the significance. Fair enough, but any regression output I've ever seen has something like:

1.2345**
(0.678)

No?

Ostrom

Time Magazine wrote: »

Just looking at the review, it seems to be mostly arguing about looking at the magnitude of the coefficient as well as the significance. Fair enough, but any regression output I've ever seen has something like:

1.2345**
(0.678)

No?

Yes, but there seem to be different conventions around reporting across disciplines - and you cant interpret the practical significance of the predictors from either.

I have come across many articles with linear regression graphs that don't report anything - the function or r^2

Edit: Just out of interest, is Bayesian inference used in economics?

Please show me an article published in an economic journal that only used the r^2 measure for predicting a simple linear regression.

Yes, check out some of the work done by one of my former professors: http://ideas.repec.org/e/psa95.html

Ostrom

Deleted User wrote: »

Please show me an article published in an economic journal that only used the r^2 measure for predicting a simple linear regression.

Yes, check out some of the work done by one of my former professors: http://ideas.repec.org/e/psa95.html

I can show you plenty from sociology with regression lines as illustrations - I dont know nor have I ever studied economics

Thanks for the link

efla

efla wrote: »

Yes, but there seem to be different conventions around reporting across disciplines - and you cant interpret the practical significance of the predictors from either.

I have come across many articles with linear regression graphs that don't report anything - the function or r^2

Edit: Just out of interest, is Bayesian inference used in economics?

I'm sorry, I can't really let this stand. This reads more of you not understanding the econometrics, then the econometrics 'not being useful'.

Practical significance can be drawn from practically every estimate - especially those in simple linear regressions. These might not be useful for forecasting (see my other post on this) but that is not the same as the results being useless. There are also common standards for publishing results and even if these are not adhered to, reading the paper fully (rather then say just skimming the tables) will explain the results.

Again - show me a published article where people were getting away with using r^2. I have never seen this in three years of studying 'published' econometrics work.

Bayesian Markov models have been a cornerstone of financial econometrics for many years now. They aren't taught at undergrad and not really taught in detail at graduate level (most people would only come to terms with them at PhD level) but they are used by the leading practitioners.

How much work have you done with this?

efla

efla wrote: »

I can show you plenty from sociology with regression lines as illustrations - I dont know nor have I ever studied economics

Thanks for the link

Bad statistical practice != a failure of the subject.

Ostrom

Deleted User wrote: »

I'm sorry, I can't really let this stand. This reads more of you not understanding the econometrics, then the econometrics 'not being useful'.

I dont! I know nothing of econometrics, nor did I claim to?

Deleted User wrote: »

Practical significance can be drawn from practically every estimate - especially those in simple linear regressions. These might not be useful for forecasting (see my other post on this) but that is not the same as the results being useless. There are also common standards for publishing results and even if these are not adhered to, reading the paper fully (rather then say just skimming the tables) will explain the results.

I cannot interpret the practical significance of a statistically significant difference in mean age of marriage for example without some reference to other dimensions of social structure - occupation, household/family type etc. Nor does regressing population density onto mortality for example offer anything useful without being able to describe the nature of regional occupation - if you are asking for examples.

Deleted User wrote: »

Again - show me a published article where people were getting away with using r^2. I have never seen this in three years of studying 'published' econometrics work.

I have never read anything in econometrics, I am not commenting on econometrics

I refer to Ostrom as she is the only semi-economist I am familiar with whose work I have seen cited in both qualitative and quantitative research - in response to an early query about causation and complexity

This thread refers to the use of math in economics - which is tested by econometrics. Econometrics is advanced statistics applied to testing and verifying economic theories.

Again - you seem to be quoting badly done studies. Thats a failure of behalf of sociology to come to terms with statistics rather then a failure of statistics.

Take your marriage example; correlation of variables doesn't automatically imply causation, so just regressing a load of explanatory variables won't give you valid results by default. You'll see this in a most empirical econometric papers where most of the paper is given to explaining proof of causation. The actual regressions are only a tiny, tiny part of the paper since the calcs are nowadays pretty much trivial. Criticism of such papers also generally lies with failure of the author to control for correlation as opposed to causation.

Ostrom

Deleted User wrote: »

This thread refers to the use of math in economics - which is tested by econometrics. Econometrics is advanced statistics applied to testing and verifying economic theories.

Again - you seem to be quoting badly done studies. Thats a failure of behalf of sociology to come to terms with statistics rather then a failure of statistics.

Take your marriage example; correlation of variables doesn't automatically imply causation, so just regressing a load of explanatory variables won't give you valid results by default. You'll see this in a most empirical econometric papers where most of the paper is given to explaining proof of causation. The actual regressions are only a tiny, tiny part of the paper since the calcs are nowadays pretty much trivial. Criticism of such papers also generally lies with failure of the author to control for correlation as opposed to causation.

I made no such claims, and I am well aware of the issues involved, there is no need to make such presumptions - incidentally the studies in question did not - nor would any (presumably) reputable social science paper - infer causation from the above. The above points are about interpreting the observed relationships in context.

The point of my post was to discuss one way in which the issue of causation has been dealt with through the use of mixed methods (and if you feel this is inappropriate then you need have done no more than encourage the thread back on topic)

leninbenjamin

nesf wrote: »

The software only runs the regression for you. It can't interpret it for you.

That was entirely my point.

efla

efla wrote: »

The point of my post was to discuss one way in which the issue of causation has been dealt with through the use of mixed methods (and if you feel this is inappropriate then you need have done no more than encourage the thread back on topic)

There are a lot of econometric methods used to identify causation. As Time Magazine mentioned, the field of econometrics has pretty much been focusing on this topic since the 1980s and has made some very good advancements in it.

Simple linear regression is pretty much now a 'tick the box' process when it comes to validating the results. More advanced methods require more advanced tests, but again, there are well defined and understood processes.

Again - bad practice of a subject does not imply that the subject itself is bad. A lot of the output from the social sciences such as psychology and sociology is quite frankly laughable. The people involved clearly have little understanding of the concept or practice of statistics. I'm not being arrogant here, I just get frustrated with people (not you!) coming in and going 'ah sure, statistics is simply running SPSS' which is something equivalent to saying that brain surgery requires nothing more then a knife and knockout gas.

If people took the time to read leading papers and practices in the field of econometrics and took the time to understand the actual nature of statistical tools, there would be a lot less of 'it must be true because I can graph it'.

Ostrom

Deleted User wrote: »

There are a lot of econometric methods used to identify causation. As Time Magazine mentioned, the field of econometrics has pretty much been focusing on this topic since the 1980s and has made some very good advancements in it.

Simple linear regression is pretty much now a 'tick the box' process when it comes to validating the results. More advanced methods require more advanced tests, but again, there are well defined and understood processes.

Again - bad practice of a subject does not imply that the subject itself is bad. A lot of the output from the social sciences such as psychology and sociology is quite frankly laughable. The people involved clearly have little understanding of the concept or practice of statistics. I'm not being arrogant here, I just get frustrated with people (not you!) coming in and going 'ah sure, statistics is simply running SPSS' which is something equivalent to saying that brain surgery requires nothing more then a knife and knockout gas.

If people took the time to read leading papers and practices in the field of econometrics and took the time to understand the actual nature of statistical tools, there would be a lot less of 'it must be true because I can graph it'.

I dont dispute this at all, but econometrics is unfamiliar territory to me so I cannot reasonably contribute. Again, I was not directing the causation comment at economics - I can only contribute from experience

Clearly off-topic, so apologies.

leninbenjamin

Deleted User wrote: »

Again - bad practice of a subject does not imply that the subject itself is bad. A lot of the output from the social sciences such as psychology and sociology is quite frankly laughable. The people involved clearly have little understanding of the concept or practice of statistics. I'm not being arrogant here, I just get frustrated with people (not you!) coming in and going 'ah sure, statistics is simply running SPSS' which is something equivalent to saying that brain surgery requires nothing more then a knife and knockout gas.

It happens everywhere, in both the hard or soft sciences. The cynic in me says much of it is deliberate misrepresentation for financial gain.

leninbenjamin

leninbenjamin wrote: »

It happens everywhere, in both the hard or soft sciences. The cynic in me says much of it is deliberate misrepresentation for financial gain.

It's general ignorance as well, I mentioned in another thread how the people in my LL.M took offence when told they didn't know enough about the subject of statistics to conduct meaningful analysis.

Had they been told they weren't qualified for brain surgery or rocket science, I doubt there would have been the same issue. However, because in general people have little regard for maths or stats, they overestimate their own ability by many orders of magnitude.