So in your opinion intuition is sufficient. As long as we can tell an intuitive story about something, that is as good as proving it?
I think that “proof” is too high a standard to use in economics. If our knowledge is limited to what we can prove, then we do not know anything. I think that we have frameworks of interpretation which give us insights. This is knowledge, even if it is not as definitive or reliable as knowledge in physics or chemistry.
As an example, take factor-price equalization. The insight is that the easier it is to trade across countries, the more that factor prices will tend to converge. I think that this is an important insight. It is one of what I call the Four Forces driving social and economic trends in recent decades. (The other three are assortative mating, the shift away from manufacturing toward health care and education, and the Internet.)
Paul Samuelson proved a “factor-price equalization theorem” for a special case of two factors, two goods and two countries. However, it is very difficult, if not impossible, to extend that theorem to make it realistic, including the fact that not all industries are subject to diminishing returns. In my view, Samuelson’s theorem per se offers no insight, because it is so narrow in scope. The unprovable broader insight is what is useful.
Incidentally, I also think that factor-price equalization is hard to prove statistically. Too many other things are happening at once to be able to say definitively that factor-price equalization is having an effect, say, on unskilled workers’ wages in the U.S. and China. I believe that it is having an effect, and there are studies that support my view, but it is not provable.
In order to prove something mathematically, you have to make narrow assumptions. In physics or engineering, this often works out well. When you roll a ball down an inclined plane, ignoring friction causes only a small error in the calculation.
In economics, the factors that you leave out in order to build a mathematical model tend to be more important. As a result, the requirement to express ideas in the form of mathematical models is harmful in two ways. We waste time proving false theorems and we miss out on useful insights.
The narrow assumptions lead you to prove something which is false in the real world.. For example, the central insight of the “market for lemons” proof is that a used car market cannot work. However, once we expand the assumptions to allow for warranties, dealer reputations, mechanics’ inspections, and so on, the original theorem does not hold.
Meanwhile, there are insights that are missed because they cannot be represented in an elegant mathematical way. A lot of the insights that I offer in Specialization and Trade fall in that category.
Our goal should be to acquire knowledge. The demand for proof hurts rather than helps with that process.
This is off-topic and probably of little interest to most readers, but I think it’s worth noting that this blog post is a good example of Arnold Kling’s lucid style.
Those simple, clear sentences take a lot of work and practice.
Thanks.
Nope. Noticed here and much appreciated, too.
It’s something!
Took me a decade of real work to unlearn my math background-driven search for closed form solutions for everything. This post defines the role of humans in the machine age. Anything that can be described with an algorithm or “proven” can and will be automated. Humans probably have a handful of decades of competitive advantage vs neural networks in exactly the sort of insights that AK describes.
Similar to human insight, machine-learning is the antithesis of academic “proof”. God complex is a good example of the same cognitive error, like the Unilever example here: http://sloanreview.mit.edu/article/tim-harford-on-trial-error-and-our-god-complex/
Dr. Kling, Given this definition of ‘discipline’, under what condition do you stop believing your intuition? What would you observe that would cause you to drop your belief in price-factor equalization, or, assortative mating?
A good Karl Popper question. I imagine when a preponderance of facts and concatenated logical chains shifts the probabilistic likelihood away from the current intuition
Random nitpick: if you really ignored friction, you would end up calculating how fast a ball would *slide* down an inclined plane, and you would get a much different answer. Static friction is what causes a ball to roll rather than slide in the first place. What you can reasonably ignore in such a calculation is just air friction and rolling resistance.
Intuition is notorious for being wrong. In that, even simple unrealistic models like those of Nick Rowe can reveal flaws and inconsistencies in our intuitions that can force us to revise them. Often is not what we don’t know, but what we know that is wrong that is our greatest obstacle. In this, math should only be a complement, not a substitute, for clear thinking and insights, though sometimes it takes more math before we get by with less and the best insights often require the least.
One legitimate use of math is to demonstrate that a whole model system in internally incoherent, inconsistent with other facts or beliefs, or that purported proponents don’t actually adhere to the implications of the theory when inconvenient to their other preferences or claims.
My question is how does one scrutinize claims of insight, or adjudicate between rival claims.
Indeed, with math type modeling, one can always make the criticism that the assumptions are unrealistic or do not hold, and then show that various claims are not necessarily true in the larger space of possibilities.
I think the ideal answer is a bit of both ways of articulating and communicating logic and insights.
Yes – acquiring knowledge partly needs to know what truths can be proven (not so many outside physical science) and what are unprovable truths. Those insights that can’t be proven true might well be true, or might be sometimes false.
In history, it’s virtually impossible to “prove” that whatever happened actually did happen. But we mostly believe in a lot of history, even that to which we are not eye-witnesses of.
The idea of economics as a discipline, less reliable than natural science yet more insightful than mere uneducated opinions, seems the proper place for economists.