[Oikonomios, an academic macroeconomist, runs up to Epistimia, a theoretical physicist, in the hallway at a university. Shouting from a chorus of voices is heard outside.]
Chorus: Economics isn't scientific!
Oikonomios: Epistimia, help! I can't get away from the complaints that economics isn't scientific!
Chorus: Economics isn't scientific!
Epistimia: Well, they do have a point.
Oikonomios: What?! We respond to evidence; that makes economics a science!
Epistimia: Courts also respond to evidence, but that doesn't make them scientific. That's just being rational.
Oikonomios: We have accumulations of evidence that confirm the applicability of some theories and reject the applicability of others. That should be Popperian enough for an inexact science.
Epistimia: Please don't mansplain science to me. You remember I'm a physicist, right? Science is about much more than positing hypothesis and accepting or rejecting them. That's grade school science class stuff. It's about not fooling yourself. It's about knowing the limitations of your theories and where your assumptions fail. It's about understanding scope. Falsification is a false dichotomy. Popper thought that Einstein's theory of relativity falsified Newtonian gravity, but no physicist would ever think of it as "false". We still teach it ... even in graduate school.
Oikonomios: Sorry. But you do think of general relativity as a better theory, right?
Epistimia: Yes, its scope is much larger than Newtonian gravity, but it isn't consistent with quantum mechanics for example. And it's hard to calculate things with it sometimes. Within its scope, it is a great theory, but then so is Newtonian gravity.
Oikonomios: You mentioned scope twice now ... what do you mean?
Epistimia: Where the theory or model is valid.
Oikonomios: We use data to tell us which models are more applicable.
Epistimia: Ex post or ex ante?
Oikonomios: Ex post ...
Epistimia: [Interrupting] You figure out which model to use ex post?!!!
Oikonomios: [Continuing undeterred]... how could you possibly figure out if a model is applicable before you have any data?
Epistimia: You did build this model, right? It isn't some sort of black box teleported here by aliens or something?
Oikonomios: If you're going to be like that, I think I'd prefer to deal with the chorus ...
Chorus: Economics promotes neoliberalism!
Oikonomios: Maybe not ...
Epistimia: It's just so shocking to me that you'd build a model where you didn't know where it should fail based on the assumptions you made in building it.
Oikonomios: Well that part is really a craft, not a science, especially when the choice of which model has to be made in real time. You could use heuristic decision-making in some cases, but rational choice in others.
Epistimia: But you know which one should work before going in, right?
Oikonomios: Not necessarily ... that's the craft!
Chorus: Economics isn't scientific!
Epistimia: Sure, there's some judgment involved and sometimes you don't know for sure ‒ sometimes you make a discovery. But it shouldn't just be craft. For example, I read all the time about how your rational agent models can't explain individual choices.
Oikonomios: Yes, but rational agents can work fine for some other cases. That's why we sometimes think about behavioral economics.
Epistimia: The scientific thing to say is that rational agents are a possible effective theory when you don't have just one or two agents but rather lots of agents. Physicists treat atoms like tiny hard spheres even though we know that's wrong, but only when we're looking at a large system where there are lots of atoms that are far apart.
Oikonomios: In my class, I once drew a huge tree on the blackboard that showed how most of economics could be derived from principles of rational choice. But go beyond the basics, and add in complications involving information and transactions costs and you very quickly derive competing models.
Chorus: We want one-handed economists!
Oikonomios: I wish they'd be quiet for a minute.
Epistimia: Me too, because I think we're going somewhere here. So you have models that are contradictory when you add different effects, but you should be able to determine that the models either don't have scope in common because they operate at different scales ‒ like general relativity and quantum mechanics ‒ or that one is definitely wrong. When you add transaction costs, there's a certain scale where they don't matter right?
Oikonomios: I have a good story about that. At the end of the first year of graduate school in economics, they make you take long tests on micro- and macroeconomics.
Epistimia: It's the same with physics. Classical mechanics, quantum mechanics, electromagnetism, thermodynamics ...
Oikonomios: Anyway, my micro test lasted five hours, and I still remember a question I missed. It was about those transaction costs: It asked what happened if buyers and sellers had to row from island to island in order to exchange their goods. It turned out that this so-called transaction cost, even though it was tiny, made the market break down ‒ no one bought or sold anything.
Epistimia: Wait, you're saying even a transaction cost that was very small compared to the scale of the transactions qualitatively changed the properties of the system?
Epistimia: Nonperturbative economics, huh? But there are transaction costs in the real world and people buy and sell stuff. What use is this model?
Oikonomios: It's really a toy model. It allows for a quick first pass at some question, or presents the essence of the answer from a more complicated model or class of models. They work as pedagogical devices. They are art as much as science.
Chorus: Economics isn't scientific!
Epistimia: I think I'm back with the chorus on this. How exactly does a toy model where negligible transaction costs stop all economic activity teach anything when it does not describe the real world?
Oikonomios: Sometimes transaction costs are too high and so market activity never gets started.
Epistimia: Yes, but that's not the model you were describing before. That sounds like a model with a scope condition saying transaction costs are small compared to the scale of the goods' value or profits or something. The original sounds like some theory with global scope where any transaction cost greater than zero breaks down the market.
Oikonomios: I'm not sure I understand the difference.
Epistimia: That model in your test question is falsified in Popper's sense. If there are no scales that set the scope, it's like having a building without fire doors. The whole edifice burns down. The fact that there are active markets that have transaction costs burns down the whole islands model. It doesn't burn down a model where transaction costs have a scale.
Now it's true that Newton probably didn't envision his theory of gravity as having a scale where it might fail. Physicists didn't really think that way back then. But now we understand that Newtonian gravity applies when gravitational fields are weak and we can think of the speed of light as fast. Those are its firewalls. The observation of gravity waves doesn't burn down Newtonian gravity. It still applies when it's in scope.
Oikonomios: Does this mean the rational agent model burns down because of the no-trade theorem?
Epistimia: What is that?
Oikonomios: In our rational agent models trading volume is essentially zero. The reason is beautifully set out in Nancy Stokey and Paul Milgrom’s no-trade theorem, which I call the Groucho Marx theorem: don’t belong to any club that will have you as a member. If someone offers to sell you something, he knows something you don’t.
Epistimia: Are you saying there is an economic theorem out there that says no one will trade in the stock market? This is a theorem? What is this, real analysis?
Oikonomios: Actually the paper has three theorems in it. It has deliberately strict assumptions to make a point about information and rational expectations in markets.
Epistimia: Hopefully that point is that information doesn't set the scale of trading volume.
Oikonomios: Actually, it's trying to say that traders don't have rational expectations but instead more limited ... Wait, what?
Epistimia: Well my intuition says that if your agents are just a little bit irrational, then you should just get a little bit of trading volume unless it is highly non-linear. Irrationality sets the scale of trading volume, not information. What happens if you have random agents?
Oikonomios: You mean noise traders?
Epistimia: That sounds kind of derogatory. I'd say their motives are just unknown. Maybe they're selling stock for a loss because they have medical bills to pay.
Oikonomios: Well, we call them noise traders. And Stiglitz and Grossman added them and found that noise traders would mean that volume wouldn't be zero.
Epistimia: So random traders set the scale of the volume in the market?
Oikonomios: I don't think I would put it that way ...
Epistimia: More random traders means more volume?
Oikonomios: Well ... yes.
Epistimia: Then given rational agents on their own don't trade at all and random traders set the scale for market volume, you're really verging on a model where the information content of trades doesn't play a big role in the market but rather just the number of people who participate. The scale you should look at to determine market volume is the number of people who own stock, not the information content of the trades. Of course the scope of that theory would be that the number of rational agents is much smaller than the total number of agents ...
Oikonomios: Interesting. I have not seen economists spend much time thinking about scope and scale. But it's an important topic to think about. I used to nod off when physicists interested in macro went on about scaling. I should have paid more attention.
Epistimia: And stop using falsified models as pedagogical devices.
Oikonomios: I should suggest we take supply and demand out of the curriculum at the next faculty meeting, then. That's probably a good idea. Sadly, though, I bet that we won't.
Epistimia: Really?! That always seemed to me to be one your field's better ideas. It works for Magic, The Gathering cards.
Oikonomios: Well, not in labor markets. The basic supply and demand model suggests even a modest minimum wage should significantly reduce employment, but economists discovered that the evidence did not show this. As this evidence accumulated, monopsony and search models were thought to be more relevant.
Epistimia: So you use those other models to limit the scope of the supply and demand diagram?
Chorus: Economics isn't scientific!
Oikonomios: Well, as you said ... there are no scales in a supply and demand diagram. A single problem burns the whole model down.
Epistimia: But, but ... Magic cards?
Oikonomios: A lot of right wing people use wrong-headed supply and demand arguments to promote policies they want. Like saying a minimum wage costs jobs or immigration lower wages.
Chorus: Economics isn't scientific!
Epistimia: The latter always sounded like a scope problem to me.
Oikonomios: How so?
Epistimia: Well it seems unlikely that adding thousands of people to a city could increase the labor supply without changing the demand.
Oikonomios: Yes, we say that general equilibrium is important in that case. Supply and demand diagrams are partial equilibrium.
Epistimia: That's a scope condition! The supply and demand diagram always moves demand or supply. If both move, you can get anything you want. That's basically an assumption about supply moving faster or changing a lot compared to how fast or how much demand changes. In the case of immigration, you can't increase supply without increasing demand. You can however easily print up a million Magic cards much faster than the nerd demand changes, so supply and demand is in scope there.
Oikonomios: The chorus probably won't be happy with you defending neoclassical economics.
Epistimia: I think they've moved on ...
Chorus: Economics can't forecast!
Oikonomios: Ha! Silly people! Economic models can't predict the future! Think of economists like doctors. We can provide advice on the best course of action when illness strikes. However, we would never dream of condemning doctors because they cannot predict the exact time of our death, still less suggest that this failure indicates they are not doing science.
Epistimia: I'm back with the chorus on this one.
Oikonomios: What?! Physicists can't predict earthquakes, so maybe you're not doing science then.
Epistimia: We have some pretty good theories about nonlinear mechanical failure mechanisms with several different applications that imply that it's really hard to observe the initial crack that leads to a failure in the fault line making them a bit random. However geophysicists can predict where earthquakes are likely to occur. Those doctors can't predict when you'll die of heart attack due to a tiny blood clot, but they know some risk factors. And they do have an idea of how many heart attacks there will be when looking at a large number of people. But really, what is the state of knowledge here? Does economics know that recessions are cascading failures that are triggered by some tiny event?
Oikonomios: There are some network models where that happens. And there are information cascades and the failure for expectations to be consistent ...
Epistimia: But we just said information doesn't set the scale for ... ah, forget it. Sure, if you assume recessions are random events, then you can't predict them. I'm not sure you've made a good case that economists really know what recessions are other than a collection of plausibility arguments. But even if it's true that recessions are random processes, why can't you forecast in the absence of recessions?
Oikonomios: The chorus is talking about the Great Recession.
Chorus: We love Steve Keen's overly complicated models that aren't empirically accurate either!
Oikonomios: Actually I'm not sure what they're talking about.
Epistimia: Neither do I. Keen seems to think economies are like complicated nonlinear electronic oscillator circuits, but you'd never figure out the circuit elements from less than 100 years of macroeconomic data and only a few business cycles. But let's not get distracted ... I'm talking about the failure of DSGE models to forecast even when there's no recession.
Oikonomios: You're just using DSGE as a four-letter word. It is worrying to see the practice of rigorously stating logic in precise mathematical terms described as a flaw instead of a virtue.
Chorus: DSGE stands for Doofuses Study Garbage Economics!
Epistimia: Yeah, um, don't forget I'm a physicist so I'm totally cool with math. And I agree that stating things mathematically is definitely a big step towards testing them. But those "precise and logical" [Epistimia makes air quotes with her hands] DSGE models fail to forecast even a few quarters ahead; they do worse than an AR process.
Oikonomios: They have their issues.
Epistimia: The have 50 parameters!
Oikonomios: That's one of their issues.
Epistimia: You just took a model that says unemployed people are actually on vacation and added that prices don't change very fast!
Oikonomios: I agree that seems too much at odds with reality to be the best starting point. But their purpose is not to forecast. Their purpose is to explore the macro implications of distortions.
Oikonomios: Fitting reality closely should be left to policy models.
Oikonomios: Policy models are for designing ... Why are you just staring at me with your mouth open?
Epistimia: I'm not sure, but I think my brain exploded because the science in my head just came into contact with anti-science.
Oikonomios: Hey, research is hard!
Epistimia: Research is hard, but this isn't. How can you believe a model when it moves to a different location in parameter space ‒ distortions ‒ when it does so terribly when it moves to a different location temporally ‒ forecasting?
Oikonomios: Well, path dependence for one ...
Epistimia: But DSGE models contain only a finite number of lags and the infinite future is cut-off by a discounting factor. They exist in a finite temporal universe. Move forward in time past the discounting time scale or backward before the last lag and that piece of the 50 dimensional parameter-temporal space is independent of the original. There can't be any path dependence except on the scale of the theory. Therefore a model in a different piece of parameter space is not any different than a model in a different piece of temporal space in any way that would make you think that not being able to forecast is bad, but you can still look at distortions.
Oikonomios: Actually, Woodford showed how expectations in the infinite future can have an impact on the present.
Epistimia: Long time horizons compared to what scale?
Oikonomios: What do you mean? He looks at the limit as time goes to infinity.
Epistimia: You can't just take a limit as time goes to infinity.
Oikonomios: Mike Woodford is like our Ed Witten, he probably doesn't make major conceptual errors. I don't see why you can't take a limit as time goes to infinity.
Epistimia: Because time has units. Seconds, years, whatever. Infinity has no units.
Epistimia: So you need to compare the time to something else with the units of time to make a dimensionless parameter you can take to infinity. Like that discount rate. You can look at times further out than the discounting horizon and write ... where's a chalkboard ...
[Epistimia starts looking around.]
Oikonomios: I guess you could compare it to the rate of belief revisions ...
[Epistimia stops looking around.]
Epistimia: That's a start. So time is long compared to the time it takes to make a belief revision.
Oikonomios: Which, if I recall correctly, is then sent to zero.
Epistimia: My brain just exploded again.
Oikonomios: That's perfectly rigorous math.
Epistimia: It's totally fine in high school calculus to take a double limit with two variables that don't represent anything. It wasn't the math ‒ it was the fact that we live in a real universe and those variables represent real things.
Oikonomios: What now?
Epistimia: Zero also doesn't have units, so we can't compare time to the scale of the inverse rate of belief revisions while sending the rate to infinity. There are not four limits where you take one to infinity, the other to infinity, or both to infinity in different orders. There are only two limits that make sense. One: [Epistimia holds up one finger] Revision time is long compared to the time horizon such that you don't revise before you reach the horizon. Two: [Epistimia holds up two fingers] Revision time is short compared to the time horizon, so you revise well before you reach the time horizon.
Oikonomios: There are so four limits! Paul Romer used basically the same limit in his mathiness paper taking the limit as time goes to infinity and the rate of knowledge growth, called beta, goes to zero in different orders to show that the limit did not converge uniformly.
Epistimia: This is sounding more like real analysis than economics again. Uniform convergence. Ha! Is there an economic theorem that says the inflation rate is transcendental? Do you worry about compactness?
Oikonomios: He proved a mathematical proposition about it. There are definitely four limits. T goes to infinity, beta goes to zero, beta then T go to zero and infinity, and T then beta go to infinity and zero. The last two are different so you don't have uniform convergence.
Epistimia: There are two limits! Beta times T is big or beta times T is small! Are you saying proving theorems is doing economics?
Oikonomios: Economic models, and the math involved, are ways of organizing your thinking.
Epistimia: Sounds like your thinking might be pretty cluttered if you need so many models to organize it for so many different situations ...
Oikonomios: We write down mathematical models. That makes us scientific. Our papers look just like physics papers with all those neat LaTeX symbols ...
Epistimia: Math alone isn't really science! You don't collect data and compare the Banach-Tarski paradox to the real world in order to reject the axiom of choice. Where is that chorus?
Chorus: Economics isn't scientific! Economics isn't scientific!
Oikonomios: There are four limits!
Epistimia: There are two limits!
[Epistimia starts running down the hallway towards the shouting chorus.]
Epistimia: Economics isn't scientific!
Chorus: Economics isn't scientific!
* * *
There are several cases above where I copied and pasted from his post with some editing to make it work in a dialogue. However it is also supplemented by a variety of other sources including Ricardo Reis's recent paper, some articles and blog posts from Noah Smith [BloombergView, Noahpinion], Olivier Blanchard's recent blog post [PIIE], a tweet from Paul Romer, an article from Dani Rodrik [Project Syndicate], a blog post from John Cochrane, and a presentation from Michael Woodford. These are listed below:
... and there are a couple references from my blog:
The bit about limits ...
The bit about Magic cards ...
The bit about financial market volume ...
PS I referred to it above pretty consistently as "model scope" or "scope conditions", mostly because Noah Smith called it that and he's a much more widely read blogger than I am so his terminology is more likely to stick. However, in his post he says:
I have not seen economists spend much time thinking about domains of applicability (what physicists usually call "scope conditions"). But it's an important topic to think about.
I'm a physicist, but I do not believe I have ever heard them called scope conditions ("domain of validity" or "scale of the theory", yes, but not "scope conditions"). Maybe it was some other sub-field besides particle physics, or possibly a particular teacher Noah had as an undergraduate physics major. My quick research on the internet makes me think that it's more of a sociology term.