>You could reply that mathematical economics shows that economic intuition is often wrong.
The math happens to match your intuition, many people's intuition is different. Correct math is the same among all people. Intuition varies. Math is the evidence that *your* libertarian intuition is correct and people should believe you instead of the intuition of others.
The problem there is that one can sneakily use math to create evidence of just about whatever you want. As Caplan pointed out, throw in some odd assumptions, for simplification and making the problem tractable of course, and voila it works out the way you want. If it doesn't throw in some different assumptions until it does. Then maybe forget to mention all those assumptions.
Not that everyone doing econ math is doing that, but it is a very easy thing to do, and frankly I think that if your model is halfway tractable you are probably missing out on way too much reality to have a useful model. Useful in the sense that it won't lead you wildly astray when you need it most, that is.
Using math to create "evidence" is harder than just saying "my intuition says so".
At least without the assumptions looking glaringly stupid.
Using maths constrains the space of hypothesis, as it throws out all the things that are inconsistent nonsense. (It still keeps plenty of self consistent nonsense, you need evidence to get rid of that.)
It's harder, but only in that you have to be a bit better at math to do it. There are some amazingly bad assumptions that are just accepted, and many that are just obscured or glossed over. Likewise, while math does narrow the space, often it narrows it to lead to the desired answer, not to lead to reality, the problem being that people mistake "the math works out" with "this matches reality pretty well".
You aren't wrong that applying math does help sort out some "is this even possible?" kind of issues that our intuition might just gloss over, but it doesn't help so much as one might hope, and often clever people will create math models that get the answer they want, intentionally or not.
Marshall was wrong-- math is a good vehicle of inquiry too. What typically happens is this:
1. I have an intuitive idea in economics, e.g., tariffs would increase efficiency as a way to counteract an income tax.
2. I write it up. Most of the time I discover in writing it that hte idea is wrong, and it dies immediately.
3. I do a numerical example. This might well kill it too.
4. I do a formal model. By this point, ordinarily the idea will survive, but in crippled, restrained form. I discover what hidden assumptions were in my mind. These assumptions are often so strong that I kill the idea as being too limited in scope.
5. If the idea survives, though, I translate it back into words in the Intro to the article. People read that part, and skip the proofs. But without the math, I would (a) make overstrong claims, and (b) make false claims. Every good idea can be presented intuitively, in words. But so can lots of bad ideas.
I had a growing feeling in the later years of my work at the subject that a good mathematical theorem dealing with economic hypotheses was very unlikely to be good economics: and I went more and more on the rules---
(1) Use mathematics as a short-hand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life. (5) Burn the mathematics. (6)
If you can't succeed in 4, burn 3. This last I did often.
Agree re intuition v math. How many have looked at Cochrane's recent tome of theory of the price level and worked their way through all the math v just grasping the concept of what John C is trying to address and seeing if it makes intuitive sense?
Yes, to math one will need to be successful in future endeavors, but many advanced programs require math for the sake of math; signaling perhaps of only mathematical competency and have yet to comprehend why the study of topology is required in an advanced economics program.
Models that have real world applicability make sense and even in world of finance CAPM has some applicability if correctly used.
A nice recent personal example: I wrote a substack on the Tariffs Balance Income Taxes example, with a numerical example but no math. My numerical example taught me that I had to restrict the idea to tariffs on labor-intensive goods. I asked for comment. Ivan Werning said it was basically in Mirrlees and Diamond, or, for trade, in a 1986 Dixit and Norman article. I asked Dixit, and he and Werning have been having a big email discussion, because Werning has also written on this. I haven't had time to understand them, but Dixit did convince me my idea was flawed because the only reason a tariff helped in my example was that I had the economy start off with suboptimal income taxes, taxing labor but not capital. Thus, if tariffs were good, that's only because we've set existing taxes wrong, so we might better be direct and fix them and not bother with tariffs.
John Kenneth Galbraith had this to say about economath:
The oldest problem in economic education is how to exclude the incompetent. A certain glib mastery of verbiage—the ability to speak portentously and sententiously about the relation of money supply to the price level—is easy for the unlearned and may even be aided by a mildly enfeebled intellect. The requirement that there be ability to master difficult models, including ones for which mathematical competence is required, is a highly useful screening device.
>You could reply that mathematical economics shows that economic intuition is often wrong.
The math happens to match your intuition, many people's intuition is different. Correct math is the same among all people. Intuition varies. Math is the evidence that *your* libertarian intuition is correct and people should believe you instead of the intuition of others.
Or the other way around.
The problem there is that one can sneakily use math to create evidence of just about whatever you want. As Caplan pointed out, throw in some odd assumptions, for simplification and making the problem tractable of course, and voila it works out the way you want. If it doesn't throw in some different assumptions until it does. Then maybe forget to mention all those assumptions.
Not that everyone doing econ math is doing that, but it is a very easy thing to do, and frankly I think that if your model is halfway tractable you are probably missing out on way too much reality to have a useful model. Useful in the sense that it won't lead you wildly astray when you need it most, that is.
Using math to create "evidence" is harder than just saying "my intuition says so".
At least without the assumptions looking glaringly stupid.
Using maths constrains the space of hypothesis, as it throws out all the things that are inconsistent nonsense. (It still keeps plenty of self consistent nonsense, you need evidence to get rid of that.)
It's harder, but only in that you have to be a bit better at math to do it. There are some amazingly bad assumptions that are just accepted, and many that are just obscured or glossed over. Likewise, while math does narrow the space, often it narrows it to lead to the desired answer, not to lead to reality, the problem being that people mistake "the math works out" with "this matches reality pretty well".
You aren't wrong that applying math does help sort out some "is this even possible?" kind of issues that our intuition might just gloss over, but it doesn't help so much as one might hope, and often clever people will create math models that get the answer they want, intentionally or not.
Marshall was wrong-- math is a good vehicle of inquiry too. What typically happens is this:
1. I have an intuitive idea in economics, e.g., tariffs would increase efficiency as a way to counteract an income tax.
2. I write it up. Most of the time I discover in writing it that hte idea is wrong, and it dies immediately.
3. I do a numerical example. This might well kill it too.
4. I do a formal model. By this point, ordinarily the idea will survive, but in crippled, restrained form. I discover what hidden assumptions were in my mind. These assumptions are often so strong that I kill the idea as being too limited in scope.
5. If the idea survives, though, I translate it back into words in the Intro to the article. People read that part, and skip the proofs. But without the math, I would (a) make overstrong claims, and (b) make false claims. Every good idea can be presented intuitively, in words. But so can lots of bad ideas.
Remember what Alfred Marshall said, https://www.rasmusen.org/zg601/readings/marshall.htm
I had a growing feeling in the later years of my work at the subject that a good mathematical theorem dealing with economic hypotheses was very unlikely to be good economics: and I went more and more on the rules---
(1) Use mathematics as a short-hand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life. (5) Burn the mathematics. (6)
If you can't succeed in 4, burn 3. This last I did often.
Agree re intuition v math. How many have looked at Cochrane's recent tome of theory of the price level and worked their way through all the math v just grasping the concept of what John C is trying to address and seeing if it makes intuitive sense?
Yes, to math one will need to be successful in future endeavors, but many advanced programs require math for the sake of math; signaling perhaps of only mathematical competency and have yet to comprehend why the study of topology is required in an advanced economics program.
Models that have real world applicability make sense and even in world of finance CAPM has some applicability if correctly used.
A nice recent personal example: I wrote a substack on the Tariffs Balance Income Taxes example, with a numerical example but no math. My numerical example taught me that I had to restrict the idea to tariffs on labor-intensive goods. I asked for comment. Ivan Werning said it was basically in Mirrlees and Diamond, or, for trade, in a 1986 Dixit and Norman article. I asked Dixit, and he and Werning have been having a big email discussion, because Werning has also written on this. I haven't had time to understand them, but Dixit did convince me my idea was flawed because the only reason a tariff helped in my example was that I had the economy start off with suboptimal income taxes, taxing labor but not capital. Thus, if tariffs were good, that's only because we've set existing taxes wrong, so we might better be direct and fix them and not bother with tariffs.
The Substack is at https://ericrasmusen.substack.com/p/ready-to-gocan-tariffs-be-justified . I'll be updating it more as I get time to udnerstand Dixit and Werning.
John Kenneth Galbraith had this to say about economath:
The oldest problem in economic education is how to exclude the incompetent. A certain glib mastery of verbiage—the ability to speak portentously and sententiously about the relation of money supply to the price level—is easy for the unlearned and may even be aided by a mildly enfeebled intellect. The requirement that there be ability to master difficult models, including ones for which mathematical competence is required, is a highly useful screening device.
The Substack I'm most proud of is on mathiness in theology. https://ericrasmusen.substack.com/p/abnn-x-therefore-god-exists
Professor presents a model.
Student quibbles about the assumptions.
Professor says, "It's just a model; let's see where these assumptions take us."
Professor presents the full model.
Professor says, "See, the government should ..."
Student has forgotten his quibbles treats the model as reality.