http://stickmanscorral.blogspot.com/2010/10/why-we-need-maths-in-economics.html
In case you’re interested: http://www.economicthought.net/2010/10/math-and-the-austrian-school/
“I think it’s important to highlight the difference between the use of econometrics to model economic relationships, and the use of econometrics to derive economic relationships.”
Are you opposed to this (e.g., regression analysis) absolutely or just consider it epistemologically unreliable? (Unreliable vis-à-vis deductive conclusions from self-evident axioms.)
I guess it depends on what is meant by econometrics. If we mean the use of mathematics, it is indeed reliable to derive theory, because calculus is bounded by the same logical constraints as verbal logic. It just a method that allows for less implied dynamism, and I think a method which suffers from the fact that relatively fewer people can actually understand it. So, I see very little advantage to the use of mathematics in deriving theory, apart from the fact that it is true that the use of mathematics allows for a more rigorous application of fixed variables and it may allow for a simpler method by which to derive the importance of relationships (in a limited sense).
If we are talking about gathering statistics and empirical evidence, and then deriving theory from this, yes I am opposed to it. More specifically, I am not opposed to the wish to derive theory from a possible relationship which is thought to exist given a set of data. Rather, I am opposed to empiricism as a method of deriving theory which is held to be absolutely true. A theory can only be absolutely true if it is logically consistent.
Another thought: The vocabulary of the austrian school is very similar to the vocabulary of game theory which in turn is part of mathematics. So applying “informed” game theory should be perfectly consistent with austrian economics and can serve to popularize thoughts of austrian origin.
Since when did math = modelling?
Since when did math = modelling?
Since the day mathematical formulas were used to model economic relationships? We’re talking about the use of math in economics, not the use of math in general (which is still about modelling relationships, in any case).
Also, it’s important to note that there is a substantial body of mathematics concerned solely with the foundations of analysis (of which calculus is a sub-topic) and, particularly, the properties of the functions and spaces which are the proper domain of analysis. Weierstrass famously derived a function which is continuous everywhere but which is differentiable nowhere, meaning, that even though the function is continuous at every point, its rate-of-change cannot be defined at any point. This is has important consequences to the assumptions you make about mathematical variables. Just because you can assign a magnitude to a variable (say, the price of wheat) doesn’t mean that the rate of change of that variable (marginal change in wheat supply or demand) is meaningful in the calculus of real variables. Hence, you have to define it numerically, meaning, you can’t actually get a “price function” out of your mathematics, you just get a numerical relationship between supply, demand and price. I suspect that this is the rule rather than the exception in economics or any social science.
Clayton -
Funny. I thought that math was about solving relationships. You might do both, but… do you realize how mystical it appears to reject the use of math?
Funny. I thought that math was about solving relationships. You might do both, but… do you realize how mystical it appears to reject the use of math?
I’m not sure what exactly you are trying to get accross.
- What do you mean by “solving relationships”? A formula is useful in that it shows you how different variables relate to each other. But, the formula itself is a model of presupposed relationships, otherwise there’s no way the formula could have even come into existence. In other words, a formula — at some point in time — requires there to be an established theoretical relationship between the variables in question. It models this relationship.
- What do you mean when you ask, “do you realize how mystical it appears to reject the use of math?” Nobody in this thread, yet, has absolutely/completely rejected the use of math.
Clayton,
I agree and I guess this is what I mean when I say that mathematics suffers from the disability of properply accounting for a dynamic market. So, there has to be some discretion by part of the economist where it’s proper to use math and when it isn’t. For me, the use of math only makes sense when it simplifies a relationship, or when it allows the economist to better discern a relationship. But, of course, the economist has to be aware of the caveats (which is true with verbal theory, as well, but I think more apparent).
from: What Empiricism Can’t Tell Us and Rationalism Can
Mark R. Crovelli, Mises Daily, 01/26/06
Mathematics introduces a higher level of precision and exactness over literal verbal argumentation. That is why we need it in science in general.
Like when you buy something with cash and have to find the the difference between what you paid and what you owed. Modelling is not a problem. It’s the assumption of values that is the hang-up. Garbage in, garbage out, as they say. It seems like the argument is over how accurate the models are, but AE is still a model, it’s just broader in scope.
bcyclwutztht,
While the topic of econometrics in general deserves worthy revisitation, concerning a priori versus historicism, the use of math in economics is not a problem of methodology per sé. Rather, it is a discussion of precision and utility.
Caley,
Like when you buy something with cash and have to find the the difference between what you paid and what you owed.
Whatever formula you use to derive that is based on a relationship, in this case an accounting identity. The formula models that relationship. It is a bit less obscure when talking about economic modelling (econometrics), as opposed to accounting. In econometrics, the specific purpose is to model.
Modelling is not a problem. It’s the assumption of values that is the hang-up. Garbage in, garbage out, as they say. It seems like the argument is over how accurate the models are, but AE is still a model, it’s just broader in scope.
I’m not sure what your point is. Nobody denies that Austrian economics is a model (better put, Austrian economics is a series of theory that is modeled; for example, the ERE is a model).
I’m coming from the ongoing general debate on the issue that I’ve seen over the years. This is the one issue with Austrians that I haven’t been able to settle. It isn’t good to be talking about rejecting math even if that does have some esoteric meaning.
@JCatalan,
Sorry, I don’t understand what you are saying.
Do you argue that empiricism is a scientifically valid method of economic inquiry—i.e. that empiricism is a method according to which one may obtain scientifically valid economic theories—i.e. theories which describe that which is universally true of particular real world, historical events?
EDIT: Nevermind. See below.
@JCatalan,
On second pass, I think you are not arguing the above—i.e. scientific validity of empiricism. It looks to me like you are saying that it’s ok to use math, as long as one is willing to sacrifice theoretical precision.
But, if one’s economic investigations are non-theoretical in nature, then one is by definition not “doing economics”. That is to say, once one introduces empirics, one is doing economic history. No?
Economics is 80% qualitative 20% quantitative. So i don’t see why the complication with econometrics and stuff like that.
When I did my BS in Economics I found all that stuff meaningless. They fail to predict, asses and improve the economy.
My Ph.D. professor (econometrics specialist) could not predict the real estate market crash while I, a senior college boy DID.
before i head out, i just want to say the blog’s second point about math working to make discussing economics more precise is dead on target and i think the most important contibution math has made to the field.
think of it this way. 70 years ago, you could make a career out of re-interpreting what other economists said. how many articles in that time, for example, have been written on “what keynes really meant”? hundreds? thousands?
these days, thanks to mathematics, there is never any question about what another economist meant because his assumptions are clearly spelled out in the model. they have to be. so we can spend more time thinking about a given economic theory itself and les time trying to figure out what exactly the theory actually is. how is that not an efficiency gain?
as a side note, this is also why i personally think more progress has been made in the field of economics in the past 60 years than was made in the entire 200 years before it. of course, that is a personal impression and i have no way of proving it. anyways, fare thee well!