http://stickmanscorral.blogspot.com/2010/10/why-we-need-maths-in-economics.html
"I'm not a fan of Murray Rothbard." -- David D. Friedman
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 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).
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.
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 -
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).
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.
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
The primary reason we must rely upon the synthetic a priori in the social sciences, so the rationalists contend, is that without some sort of irrefutable axiomatic foundation for social science we have absolutely no way to know whether or not we are falling prey to the post hoc ergo propter hoc fallacy. In other words, there is no way to tell whether or not the "causal-nomological" patterns we empirically observe in the social world are "caused" by the things we think they are, or whether they just coincidentally related and have no necessary connection.
Mathematics introduces a higher level of precision and exactness over literal verbal argumentation. That is why we need it in science in general.
What do you mean by "solving relationships"?
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).