There's a fine line between minimalism and unfurnished. I'm trying to find where that line is. [This is a heavily revised version of an old post.]
Simplicity and minimalism tend to go together, but they are not the same thing.
A simple model is one that is easy to understand. Which is a good enough reason for building a simple model.
A minimalist model is one that deliberately gets rid of everything that is not absolutely essential. The whole point of building a minimalist model is not just to make it easy to understand, but to try to figure out what is and what is not absolutely essential to understanding the phenomenon in question. If you have a successful minimalist model, you should be able to add in the stuff it leaves out and add more details to the story without changing the underlying plot. Everything else is embroidery.
Here is some of the stuff my minimalist model of recessions leaves out:
It is a general equilibrium model, but not a dynamic stochastic general equilibrium model. It leaves out time and uncertainty. It's a one-period model, with certainty.
Because it is a one period model, it leaves out saving and investment, borrowing and lending, and interest rates.
It leaves out production and employment. It is a pure endowment economy. Depending on precisely how you define "GDP", GDP is either fixed exogenously, or else zero.
So if you think time and uncertainty, saving investment and interest rates, fluctuations in output and employment, are essential to understanding recessions, my model says you are wrong. My model says those are optional details, that you can add in if you wish, that do not change the underlying plot of the story. They are just embroidery.
My model is a general equilibrium model of monetary exchange, with one sticky price (the price of money). Those are the things I think are essential.
There are three consumption goods: call them apples, bananas, and mangoes. You need exactly three goods in a minimalist model of recessions. Four is too many, and two is not enough.
All agents have the same preferences U = log(Ca) + log(Cb) + log(Cm)
Half the agents (the alphas) have an endowment of 200 apples and 100 mangoes each. The other half (the betas) have an endowment of 200 bananas and 100 mangoes each.
Let mangoes be the numeraire. Assume the price of apples is always equal to the price of bananas, and call that price P. So 1/P is the price of mangoes in terms of apples or bananas. Assume P is sticky.
Barter equilibrium
In market-clearing competitive equilibrium P=1. Each alpha and beta swap 100 apples for 100 bananas. Each agent consumes 100 of each of the three fruits. That's also the social optimum, for a utilitarian central planner.
If P > 1 there is an excess demand for mangoes and an excess supply of apples and bananas. But this disequilibrium price has zero effect on the allocation of goods. Each alpha and beta still swap 100 apples for 100 bananas. Each agent still consumes 100 of each of the three fruits.
If P < 1 there is an excess supply of mangoes and an excess demand for apples and bananas. But this disequilibrium price has zero effect on the allocation of goods. Each alpha and beta still swap 100 apples for 100 bananas. Each agent still consumes 100 of each of the three fruits.
The reason the sticky price of mangoes in terms of apples or bananas has zero effect on the allocation of goods is because at the market-clearing price P=1 there is no trade in mangoes anyway. The only trade is between apples and bananas, and I have assumed the relative price of apples to bananas is always at the equilibrium relative price, so alphas and betas will always trade the optimal number of apples and bananas.
Monetary equilibrium
Now assume that mangoes are used as the medium of exchange. This means there is a market in which mangoes are traded for apples (the "apple market"), and a market in which mangoes are traded for bananas (the "banana market"), but no market in which apples are traded for bananas directly. The reason is that mangoes are portable, but apples and bananas must be eaten directly off the tree, or they taste bad, and agents are anonymous so can't swap IOUs for apples or bananas. So the only way agents can trade apples and bananas is by using mangoes as the medium of exchange.
If P = 1 the allocation is exactly the same as in barter. The alphas carry mangoes to the betas, buy bananas with mangoes, and eat those bananas on the spot. The betas carry mangoes to the alphas, buy apples with mangoes, and eat those apples on the spot. Each agent consumes 100 of each fruit.
If P > 1 we get a recession. There is an excess supply of apples in the apple market, so the alphas won't be able to sell as many apples as they want. There is an excess supply of bananas in the banana market, so the betas won't be able to sell as many bananas as they want. It is the betas who decide how many apples to buy, and how many apples the alphas can actually sell. It is the alphas who decide how many bananas to buy, and how many bananas the betas can actually sell. Alphas maximises utility taking into account the constraint on how many apples they can actually sell. Betas maximise utility taking into account the constraint on how many bananas they can actually sell.
Let A be the number of apples sold per agent, and let B be the number of bananas sold per agent.
In the banana market, alphas choose B to maximise U = log(200-A) + log(B) + log(100+PA-PB) taking A as given.
In the apple market, betas choose A to maximise U = log(A) + log(200-B) + log(100-PA+PB) taking B as given.
The alpha's first order condition gives us the constrained demand function for bananas:
Bd = 0.5(100/P + A)
The beta's first order condition gives us the constrained demand function for apples:
Ad = 0.5(100/P + B)
[If you are feeling Old Keynesian, you can add the monetary demands for apples and bananas together to get the desired Aggregate Expenditure function: (A+B)d = 0.5(200/P + (A+B)) and interpret (A+B)d as desired Aggregate Expenditure, (A+B) as National Income, and 0.5 as the marginal propensity to consume.]
Solving for the Nash Equilibrium gives us:
A = B = 100/P (for P > 1) [I could re-write it as A = B = M/P where M is the endowment of mangoes.]
This minimalist model of recessions gives us a very simple message: recessions are a reduction in the volume of monetary exchange caused by an excess demand for the medium of exchange. Recessions reduce utility because some mutually advantageous exchanges do not take place.
[For completeness, we can solve the model for P < 1, where there is excess demand for apples and bananas, so it is buyers of apples and bananas who are constrained in how much they can buy. The Nash Equilibrium is A = B = 200 – 100/P ]
Does it really matter that this model leaves a lot of things out?
It would be easy to add output and employment to the model. Replace "apples" with "labour of hairdressers", and "bananas" with "labour of manicurists". People produce services for sale with some of their labour, and consume the rest of their labour as leisure. In a recession output and employment falls, and workers are consuming more leisure than they want to. But it's exactly the same model.
It would be easy to add borrowing and lending to the model, by making it multi-period. We could solve for the rate of interest. But nobody would want to borrow or lend in equilibrium anyway. It's exactly the same model.
We could make mangoes a durable good, that never depreciate, and never get eaten, but you need to carry a stock of mangoes from one period to the next, because you might get hungry at the beginning of the period and want to buy bananas before you have sold any apples. The direct utility from consuming mangoes gets replaced by the indirect utility of being able to buy and consume bananas or apples whenever you feel like it. It's (almost) exactly the same model.
We could have a central bank create paper mangoes, and even pay or charge interest on those holding paper mangoes. Or electronic mango accounts, that could have either a positive or negative balance. It's (almost) exactly the same model.
So what?
Recessions are not about output and employment and saving and investment and borrowing and lending and interest rates and time and uncertainty. The only essential things are a decline in monetary exchange caused by an excess demand for the medium of exchange. Everything else is just embroidery.
Worthwhile Canadian Initiative 
Nick,
I agree that you’ve come up with a model of a kind of recession, but I’m fairly certain that not every recession is caused by excess money demand. A recession can happen if productivity or government spending are hit with a negative shock. Perhaps every nominal recession is caused by excess money demand (relative to what is supplied, so the central bank could all of a sudden reduce the supply of money instead of their simply being a shock to money demand, for instance). Even so, this just seems like a possible narrative for central bank-caused recessions, not necessarily the simplest and best explanation for them. Sometimes, thinking in terms of things like the nominal interest rate is useful because it gives a bit of an explanation of exactly why there might be excess money demand (in this case, money dominates other assets in interest). Then again, maybe this model fulfills its purpose; it defines every demand-caused recession as excess demand for money, but I don’t really know what the use of that is… It’s policy prescription is to increase the money supply in a recession, which we all already knew.
see https://xkcd.com/1318/ (Hover text: Protip: You can win every exchange just by being one level more precise than whoever talked last. Eventually, you’ll defeat all conversational opponents and stand alone.)
More seriously, models with more parameters are more difficult to learn and validate from data and are more subject to over-fitting. When you have noisy, high dimensional data like is usually the case in economics, it is better to use simpler models that generate good but somewhat vague predictions. Otherwise you quickly fall into problems where you need decades of expensively gathered data before you can set the parameters and validate your model or else you end up taking shortcuts, over-fit past seen data and get bad predictions with new or unseen data.
Everybody should read Yudkowsky’s “A Technical Explanation of Technical Explanation”: http://www.yudkowsky.net/rational/technical/
When a recession takes place is an important part of the puzzle. When an excess money demand is created away from the effective demand limit, it has to be very strong to cause a recession. Recessions tend to occur only at the effective demand limit. And my minimalist view of effective demand takes it back to employment and production as conditions to trigger a recession from excess money demand.
You know I like this model as an way of illustrating why particular problems can occur with monetary exchange.
But where we part company (and I know I’m going over old ground here) is over the question of what exactly mangoes in this model represent in the real world. In particular, which monetary assets should we see as being mangoes and which not.
Your model only has one type of mango, so it does not help us decide this question. That’s fine as long as we are only looking at the issue of monetary exchange. But it is not legitimate to conclude that any particular division of real world assets matters.
Consider instead that mangoes here is actually an aggregate of two types of mango: M-mangoes and B-mangoes, and only M-mangoes are accepted in exchange for apples and bananas (or for B-mangoes).
Now, if P>1, it is still true that there is an excess demand for mangoes. But it is less clear that this is specifically an excess demand for M-mangoes. This may just be semantics, but the important point is whether the excess demand can be effectively fixed by taking away people’s B-mangoes and giving them M-mangoes instead, or whether we need to increase the total supply of mangoes. We would need to know more to decide that here.
Point being that this model shows us why the supply of some class of monetary assets may be important in a monetary exchange economy, but it doesn’t tell us which class beyond saying that it must include those particular monetary assets that people directly give up in exchange transactions.
Nick:
This is brilliant.
I also loved this paragraph:
“A minimalist model is one that deliberately gets rid of everything that is not absolutely essential. The whole point of building a minimalist model is not just to make it easy to understand, but to try to figure out what is and what is not absolutely essential to understanding the phenomenon in question. If you have a successful minimalist model, you should be able to add in the stuff it leaves out and add more details to the story without changing the underlying plot. Everything else is embroidery.”
Hear hear!
This “minimalist manifesto” sums up my research philosophy as well. (It’s also rather interesting from a epistemic / philosophy of science point of view, but I digress.)
Your model reminds me of Krugman’s “mini macro” note, which I’ve linked to before:
http://web.mit.edu/krugman/www/MINIMAC.html
I still have to think more about whether there is some important essential difference between your model and Krugman’s, or if they just have different embroidery. His is also a three-good model (leisure/consumption/money), but he doesn’t explicitly model exchange (money is “just another good”). His note is also fairly ad hoc, and doesn’t explicitly deal with all the details the way yours does, so in that sense I think yours is better. I think that someone very hung up on microfoundations would much prefer yours to Krugman’s.
By the way, both your model and Krugman’s boil down to the quantity theory of money with fixed velocity:
Y = V*(M/P)
(with some appropriate redefinitions of course — in your model, “Y” is the value from sale of goods. In Krugman’s model, it’s production. But these are really analogous, as we could make clear by giving all the bananas to agents who only likes apples (and mangoes) and all the apples to agents who only like bananas, so that unsold fruit rots. Then it’s clear that the “exchange” is just analogous to “production”. And V=2 of course.)
Also, Merry Christmas! May all your exchanges be mutually beneficial!
(I assume this is your favorite holiday because it is a societal exercise in barter? Or come to think of it, maybe we just use “good will” as the medium of exchange…)
Excellent blog post. All else is noise.
Nick E: We should probably give this model a name. Are you OK with calling it the “Edmonds-Rowe model”? (“Nick-Nick model” sounds cute, but also a bit silly.)
Thanks all for comments. Back later. Gotta do Christmas stuff.
I think Nick E. is pointing us in the right direction.
This exercise is labeled as a three commodity exchange but it is more correctly considered a four commodity exchange with A-mangoes equal to B-mangoes. By marking the money, we can trace the money movement.
With this additional labeling and assuming P > 1, we can quickly see that each side trading all their A-mangoes and B-mangoes in one single exchange will result in only part of the surplus apples and bananas being traded.
We can also see that the greater the divergence of P from 1, the larger (or smaller) the number of total exchanges of A-mangoes and B-mangoes needed to accomplish complete transfer of surplus apples and bananas. Pricing determines the number of exchanges needed to accomplish the desired re-balancing of the original endowment.
Agree with some comments above.
Add another good, coconuts (bonds).
Coconuts are traded for mangos in another market at the end of the period. Everyone has the same endowment of coconuts. The price of coconuts is flexible.
Now if you are in a recession, you can increase the supply of coconuts. This will lower the price of coconuts (raise the interest rate), and thus lower the value of holding mangoes (money) at the end of the apple and banana markets.
(Increasing the stock of mangoes directly is a helicopter drop. The government buying and selling coconuts to target the price is conventional monetary policy.)
Are you OK with calling it the “Edmonds-Rowe model”?
I wouldn’t object, but I think it overstates my contribution here.
Nick E: you saw what I was looking for, and found it. Edmonds-Rowe it is.
Must make Christmas pudding.
PLUS 16 C and sunny here in Ottawa! Last Winter we were skating on Meech Lake New Year’s eve.
John: a negative productivity shock will cause output and maybe employment to fall. But does it look like a recession, if it not accompanied by an excess supply of goods and labour (in a recession, it is easier than normal to buy goods and labour, but harder than normal to sell goods and labour)? Does an agricultural economy have a “recession” every Winter?
Benoit: I tend to agree. I will check out that Yudkowsky link.
Edward: When I say “effective demand limit”, do you mean what others would call “potential output”, “full employment” “supply constraints”? So in this model that would mean: when 100 apples are traded for 100 bananas?
Nick E: would I be correct in interpreting you as saying that a minimalist model for diagnosing a recession may not be sufficient for telling us what cures would or would not work? If so, Hmmm. Fair point.
jonathan: Thanks!
I really like the Krugman(-Robert Hall?) model too. But I think it helps illustrate the subtle difference between minimalism and simplicity. His model is simpler than mine. But it is not minimalist. His contains employment, output, and money. But it is not at all clear why people use money in his model. If all labour was identical, and if all output was identical, I don’t see why agents in his model would use monetary exchange. Why isn’t it just a collection of separate worker-firms, each consuming his own output? In which case an excess demand for the good he calls “money” would not cause a recession. Robinson Crusoe does not sit idle, just because he wants to buy more gold but nobody will sell him any. The only way to make sense of his model is to assume that each worker has a different type of labour that produces a different type of output, so they all want to trade for money so they can consume a variety of different outputs.
In other words, he (implicitly) has n non-money goods, while I have only 2. Or, if you take my model, and add a very large number of different types of agent (not just 2), you get Paul’s model. But 2 is enough. 3 is 1 too many, for a minimalist. And n is a lot too many.
James: thanks!
Merry Christmas everyone!
Nick,
Carl Eagan used to say,”Extraordinary claims require extraordinary evidence.” You are claiming rather extraordinary things here from a simple “high school” mathematics level model. Now it’s possible that economics has missed something important. But if you wrote your model up, do you think that AER would publish if? If not, why?
Here’s an example: I’m an alpha (goes without saying) and I get my endowment, immediately I eat my 100 mangos, and also eat 100 apples. For the other 100 apples I place a message on my favourite social media site “Eat apples at my place, bring your mangos!”
So Betty Beta shows up with a good set of mangos (background information: the local Chief of Police has been enforcing price controls at a rate of P=2 on the threat of having your mango tree cut down), both Betty and myself are very law abiding (goes without saying, but I’m saying it anyway just to reassure everyone that I’m not about to cheat here). I exchange the Betty’s 100 mangos for my 50 apples which Betty gobbles right off the tree.
“Hey, those apples were excellent, what’s your plan for all the mangos?”
“As it turns out, I just ate 100 mangos this morning, if you know anywhere I can get bananas, I’d really appreciate that.”
“Well then Alpha Man, I have bananas at my place!”
So together we jog on over to Betty’s place, she still has 100 bananas and I buy 50 of them in exchange for 100 mangos at the going rate of P=2. Says Betty: “I’m still hungry for apple, race you back to your place.” No problem, she buys my remaining 50 apples in exchange for 100 mangos and eats them on the spot. “Hey Betty, once again I have my hands on these lovely mangos, but what would really satisfy me is a banana… back to your place?”
Of we go back to Betty’s place, I buy the remaining 50 bananas and she eats the 100 mangos and we are both sated.
“Betty, that was awesome! Meet you up same time next week?”
“Yeah, love to, I hear the Chief of Police’s wife has been studying Keynesian economics, the writing on the palm tree says they are enforcing P=3 next week.“
“Well, we would have to run back and forth three times, I’ll need to invent shoes or something.”
“Oh Silly! Everyone knows you can’t split an apple. We will have to go back and forth FOUR TIMES to get the last item of fruit. That’s double the running we did today.”
A medium of exchange has a habit of circulating, that’s not a mistake, it’s designed to do that. We likes it. Here’s some statistics based on the two-person economy with myself and Betty Beta described above (actual endowment and consumption is same for all cases):
As you can see, the Chief of Police, with his wife reading from the Keynesian textbook can indeed force nominal GDP to go up, but in real terms it is completely meaningless because it is exactly cancelled out by the price inflation which has been imposed on the economy.
Why not use the existing naming convention?
Occam’s razor
Then in a mere two words, everyone will understand exactly what you are attempting. How minimalist!
Avon: it’s a blog post, not an AER submission. Would it be better if the math were more complicated?
Tel: ” I exchange the Betty’s 100 mangos for my 50 apples which Betty gobbles right off the tree.”
Betty will say “no” to that deal. It does not maximise her utility. She will want to buy fewer apples at that price.
“Occam’s Razor”. Hmmm. Fair point.
Nick,
The math might need to be more complicated. I don’t know. What I do know is that your claim is extraordinary. Moreover, this extraordinary claim is completely captured in a simple high school mathematical setting. Now maybe the field has missed some really important low hanging fruit. That’s possible, but I doubt it.
Here’s the rub. Pauli once received a letter from Heisenberg in which he claimed that he had a theory of everything. It could easily be explained. Pauli responded with his own letter. It was a blank page and at the bottom it said “This is to show the world I can paint lime Titian. Only the details are missing.” Heisenberg did not have a tHenry of everything.
Avon: the neat thing about blogs is that you can put something out there, and see how people respond. Anyone can come on here and tell me I’m wrong, and why I’m wrong. I don’t have to be 100% certain I’m right and original. This is certainly not the first very small macro model with simple math. But I am not aware of any as minimalist as this one. And of course, a minimalist model isn’t the best model for all purposes, as Nick E argues above. But I think we can learn from it.
Nick,
It’s not about coming to your blog to say you’re wrong. It’s you who’s saying the world, the field, is wrong. It’s you who’s said that there is a really easy way to see how the field is mistaken about a very important and nontrivial phenomenon. Now maybe you’re right, but you need to convince us. Again maybe there is some really important low hanging fruit, but make no mistake, you are making a extraordinary claim. I would be just as doubtful of someone who said they had created cold fusion and all it takes is some high school math and bathtub of acid and baking soda.
Nick,
Good post but is that model maybe not too basic? If you say a recession is caused by an increase in the demand for MOE do you assume that happens due to a random “shock” that falls outside of the economy? If, however, that change in demand is due to some other economic variables I am not sure if I would still call those “embroidery”. Would you not need to also consider those to really understand why recessions happen?
Nick, she buys just 1 apple for 2 mangos. She eats the apple. So what am I going to do with two mangos?
I still have to buy bananas, and I only have 2 mangos… I’m still going to run to Betty’s place to get the bananas. So you just want to make me run back and forth more times over. Betty and me, we sort this out… everything right above board, don’t you worry 🙂
Here’s the chart of trading with mangos one item at a time at P=2. I allow each party to check two transactions back when deciding whether to keep trading (why two? because both Betty and I have a sense of fair trade and we can see there’s a two-way cycle, neither of us is stupid).
Click to access betty_mangos.pdf
Now I know what you are going to say here: I could squib one transaction early when I’m at (100, 99, 102) and Betty is at (100, 101, 98) and I would be ahead by 0.0042 utility and Betty would be behind by 0.0046 utility, but strangely I don’t do that… so why?
Well, I’m going to want to trade with Betty next week, aren’t I? If she feels she got schlonged (that means she got “beaten badly” like Hillary in the 2008 primaries) then she would be reluctant to talk to me next week. Because of such social leverage you get into a whole reputation thing, iterated Prisoner’s Dilemma, tit for tat. Anyhow, trust me, for the sake of 0.0042 utility, don’t do it.
I know the next thing you are going to say as well… the “agents are anonymous” ruling prevents Betty from holding any social pressure over me, because she will never know who schlonged her. Indeed, I don’t even know if I’m trading with Betty or Bob here. Therefore iterate Prisoner’s Dilemma circumstance no longer applies and thus either party always squibs early without looking even one cycle ahead.
OK, so on those rules Betty bails out with me at (151. 49. 100) and her at (49, 151, 100) both of use at utility 5.8692 thus well below optimum. Is that plausible? What would it translate to in the real world?
Essentially you are saying two things here: [1] fine divisions of currency are not possible to creep past such sticking points and [2] a strong crisis of trust exists such that no parties in the entire system can know each other well enough to overcome a highly localised relative optima (no contracts exist at all, no possible trading arrangements). Sorry, but those are not plausible assumptions for any real world recession. Of course I can still make contracts, and I can remember previous events. Of course reputation still holds. This model simply does not explain observable events.
Avon Barksdale,
I can’t speak for Nick, but here’s my take on this.
I don’t think that models ever actually prove anything about real economies. All they can do is help us understand how certain things might work in theory, which may help us interpret what is actually going on.
If this model demonstrates anything, it is this: That, if bilateral exchanges can only take a limited form (monetary exchange here), then we can get situations in which there are series of bilateral exchanges that taken together are Pareto enhancing, but where the end result cannot be reached by any series of bilateral exchanges that are each individually Pareto enhancing.
This is not a particularly hard point and you don’t need very much maths to show it. But I also don’t think it is hugely revolutionary. I think many economists would agree with this idea without seeing it as disrupting their existing worldview. But I do think this model is a nice neat way of illustrating the point and fluency with the idea is important in deciding whether it matters in real life.
What the model does not do is prove that recessions are caused by an excess demand for the medium of exchange. That’s just Nick’s interpretation and I don’t even agree with it, except perhaps in a somewhat trivial sense. And I don’t think any model is going to resolve that difference either way.
In my view, that’s when economics gets hard – when we’ve finished the maths and have to deploy our judgement.
Avon: see Nick E’s excellent comment (except that bit where he disagrees with my interpretation).
Odie: fair point.
Tel: “Essentially you are saying two things here: [1] fine divisions of currency are not possible to creep past such sticking points and [2] a strong crisis of trust exists such that no parties in the entire system can know each other well enough to overcome a highly localised relative optima (no contracts exist at all, no possible trading arrangements).”
I’m not worried about 1. You can assume all 3 fruits are perfectly divisible if you want. Divisibility only makes a very small difference, if the number of each fruit is large. But 2 is essential. In this model there are only two types of people that need to be involved in exchange, so you could get barter if two people trust each other. In the complex real world there are very many types of people, the Wicksellian circle is very large. Think of n people sitting in a circle, each one wanting to buy the goods owned by the person sitting on his right. All ne people would have to trust each other to do the n person mutually improving barter deal. All it needs is one person to insist on cash on the nail, and it won’t happen. We do see barter increase in recessions (which confirms my perspective on what recessions are), but n-person exchanges are very difficult, if n is large.
Nick E.: Excellent comment. It included copious enlightening material.
I can see that we are in a quest for better models. Toward that end, I propose (in the monetary model) that we treat Mangoes as a necessary but undesirable commodity. The possession of Mangoes would lower utility, so, because Mangoes are required for trade and Mangoes are unavoidable, everyone wants to minimize their holding of Mangoes. Mangoes would carry a negative sign, not a positive sign.
If we made that model change, it seems to me that the first trade would be Pareto neutral to one trader and Pareto enhancing to the other trader. It would work this way:
Trade only occurs because two parties each want to improve their situation or (at least) want to preserve their position. If owners think they have too many apples or bananas, then they have a negative view of holding apples or bananas. Couple that with the requirement of holding Mangoes (also negative), then holding too many apples and too many mangoes causes a negative utility condition. Trading either mangoes or apples or bananas will improve the utility score.
It seems to me that making this model change neither enhances nor disproves Nick’s claim that a mango shortage can cause a recession. The proposed change does make it more believable that people really do want to trade and re-balance their holdings to improve utility.
Nick and Nick E
No, modelling is not the way you put it. You don’t get to take the consequences you like and ignore the rest. That’s how a drunk uses a light post, for support not illumination.
Economics is a science. Understand how to treat it as such. You want to make an extraordinary claim? Fine. But generate real evidence with a real model. But most of all, you have to honest in a scientific way. That’s a actually more than usual honesty. It means bending over backwards to make your result go away. It means not fooling yourself. It means trying as hard as you can to find everything possibly wrong with the idea.
So what do you want to happen Nick? Understanding recessions is a big deal. In physics, understanding the vacuum energy is a big deal – no one knows what it is. Now imagine if I wrote a model down based on high school math a stripped out quantum mechanics and then said that I think this model will help us with this great unsolved problem. Do you think I anyone serious would take me seriously?
Nick
You guys talking about probing things means you don’t understand science. You can’t prove things in science and that goes for economics. You can prove things in math but not science. Regardless of how great a model works, it does not prove the positive.
Economics is a science with ideas proceeding based on evidence, real modelling, and hard work.
Not probing. Proving. Auto correct 😦
“The only essential things are a decline in monetary exchange caused by an excess demand for the medium of exchange.”
Without time and uncertainty, how would this ever occur?
I present a minimal model of a recession here:
http://gene-callahan.blogspot.com/2010/09/what-malthus-and-sismondi-were-thinking.html
That model has no medium of exchange. Does my model prove that money is also not money that is essential? Perhaps recessions are causeless!
I will write a whole post on this later today.
Avon:
I can’t speak for Nick R. but I think his audience is composed of all economic skill levels from none to very skilled. Some of his post seem to be aimed at fellow economics teachers and some post seem to be aimed at the raw beginner.
His technique seems to be to conjure an incomplete(?) model, throw it out for view, and (sometimes) draw conclusions. The resulting chaos can be instructive for those who are truly trying to improve their understanding of economics. I can see that the resulting chaos could be troubling for readers who might be looking for settled economic answers (of which there are few in the science of economics).
I find myself being patient with his technique, in admiration of his provocative skills, and frustrated that he does not conform more to my economic insight. In the end, I learn, and that is the reason that I enjoy and appreciate his posting and efforts.
Sorry, walked away from the computer and forgot where I was in previous post.
Sparks
It’s not about a settled answer. The point is no one really understands the origins of recessions. To say otherwise is just foolishness. Lots of very bright people have thought about this issue and the answer is not some simple high school mathematical set up. It’s much much harder. For most of humanity we had no idea what caused the northern lights. People had all kinds of explanations. But it wasn’t until we developed quantum mechanics and understood the electronic structure of the atom that we could explain the northern lights. Recessions are in the same boat. If we ever get a complete understanding of recessions, it won’t be derived from a high school math exercise.
Nick,
considering the monetary economy, if Xo is the endowment in X then for the alphas isn’t this the correct Lagrangian:
ln(A) + ln(Bo-z) + ln(Mo) + q * { (Mo – M) + PA * (Ao – A) – PB * (Bo – z) }
where z enters in a parametric way for the alphas, q is the Lagrange multiplier and A, M are their choice variables?
Avon Barksdale,
I think what you’re saying about what you can and cannot prove is pretty much the same point I was making. Mathematical economics may include proofs and disproofs, but these are proofs about the mathematical properties of models, not proofs about how real economies work. Likewise in science, we might be able prove that a model makes certain predictions, but we can’t prove that the model is “correct”.
So, as with science, we can only hope to reject those models that fail to map reality. The difficulty in economics is that it is much harder to falsify theories, because there is so much noise and because we cannot conduct controlled experiments. It’s so rare to have a case where observational data allows us to conclusively reject a theory. That’s why so many different theories can survive. And unfortunately, having more complex mathematical models doesn’t seem to make the theories any more falsifiable.
john: I think we are saying the same thing in different notation. In my notation, A is the number of apples alphas actually sell to betas (that betas actually buy from alpahs), and B is the number of bananas betas actually sell to alphas (that alphas actually but from betas). Then we invoke the short side rule A=min{Ad,As} and B=min{Bd,Bs} to see which is a choice variable and which is taken as given by each agent.
And I’m substituting the budget constraint into the utility function to eliminate M.
Except, yours is not right when you say “ln(Mo)”, because it should be lm(M). Probably a typo.
Two questions:
1) Suppose P=2. We end up at the situation where the alphas have 150 apples, 50 bananas, 100 mangoes; the betas have 150 bananas, 50 apples, 100 mangoes. At the given price, the alphas don’t want to buy any more bananas, and the betas don’t want to buy any more apples, so trade stops here. You’re saying at this point, some mutually advantageous exchanges are not taking place, so it’s a recession. Question: how is this different from the 2-good model, with only apples and bananas, but a constraint that apples can only be exchanged for 2 bananas? In your example, there are also mutually advantageous exchanges of bananas for mangoes that aren’t taking place: if the alphas swapped a banana for a mango with the betas, both their utilities increase. In the 2-good case, we end with the alphas having 150 apples and 100 bananas, and the betas having 50 apples and 100 bananas. If they swapped an apple for a banana, both their utilities would increase, but they don’t because of the price constraint. What distinguishes the 3-good model and lets us call it a recession, while the 2-good case isn’t?
2) “The direct utility from consuming mangoes gets replaced by the indirect utility of being able to buy and consume bananas or apples whenever you feel like it. It’s (almost) exactly the same model.” I am not sure that this is almost the same model. In this model, the utility for alphas would be log(Ca)+log(Cb+Cm/P) in the region of interest, where the best thing that the alphas can buy is bananas. Here trade doesn’t get stuck at 150/50/100 — the alphas are indifferent to buying more bananas with their mangoes, while that is utility-enhancing for the betas (since they “value” mangoes at the apples they can buy with them — their utility is log(Ca+Cm/P)+log(Cb)), so trade will continue. It seems to me that for trade to stop, you would require that the marginal utility of a mango is higher than the marginal utility of the optimal consumption basket (of apples and bananas) that can be purchased using the mango, for each type of agent. This could be true during a recession: uncertainty is higher, perhaps people are not sure what their optimal consumption basket actually is, and having money rather than a consumption basket of equal value may have somewhat higher utility via a sort of “option” value. But then the “essential” feature is getting more complicated — we probably also require that the utility from actually buying something is a little bit higher than just having the money in normal times, which could be introduced via discounting.
Just to be clear, in (1) above by “alphas swapped a banana…” I mean the alphas receive one banana from the betas, the betas receive one mango from the alphas.
Gene: in your model there is satiation. Producers would be giving fish away, and nobody would want it, because they are already eating as much fish as they want. The allocation is Pareto Optimal, given the initial mistake of catching too many fish. In my model alphas have too many apples and too few bananas, and betas have too many bananas and not enough apples. It’s not Pareto Optimal, and is a coordination failure, or problem of exchange.
I think my model represents recessions better, and represents Malthus and Mill better.
nive: “Question: how is this different from the 2-good model, with only apples and bananas, but a constraint that apples can only be exchanged for 2 bananas?”
In my model there is an excess supply of both apples and bananas. In your model there is an excess supply of apples and an excess demand for bananas. Recessions look more like my model.
They can all have cash on the nail. Suppose I’m the only guy in the circle who has any cash whatsoever, and I only have one coin. I turn to the guy on my right and buy whatever I can for one coin, the goods move a small step to the left, and the coin moves to the right. But the coin does not get consumed in any way, it can keep moving… that guy buys from his right, the next guy buys from his right and the coin comes around the circle back to me. The medium of exchange circulates, so one coin can zing around the circle pumping an arbitrary volume of goods… and every single person gets cash on the nail, every time. If there’s more goods and less coins then the velocity of the coin must increase, if there’s more coins and less goods then the velocity of the coins decreases.
With the finer divisibility of goods, you can get away with smaller amounts of cash, if you don’t mind buying in small instalments. Admittedly, the shuffling tiny amounts gets unrealistic but who cares because these days it’s all electronic anyway.
I get it, that in your example, it comes to a point where, based on your utility calculation an agent might eat their mangos instead of trading… once all mangos are eaten without barter or IOU notes you hit a local optima that’s far from the global optima, and fine divisibility doesn’t prevent people wanting to eat their mangos (although it does reduce their risk if they speculatively take a punt and circulate the mangos instead of eating them).
I just don’t see how anyone in the real world is going to consume their cash. They might hold their cash, but even then they hold it in a bank account, and the bank can lend it out again.
The sort of sock-stuffing currency crisis you describe here requires a very large number of people to literally physically hold wads of currency in order to pull it out of circulation.
What’s more, they need to stuff their socks very rapidly… during 2006 it was considered a boom year, but by the time we got through 2008 everyone saw it was a tough year indeed and I remember everyone was worried (I can tell you my savings were going DOWN not UP around that time). So you say in just two years some large number of people had pulled significant volumes of physical currency out of circulation, and stacked it somewhere, to impose deflation on everyone else? Who were these people?? Do you really believe that’s what happened?
Nick: that criterion doesn’t seem sufficient to define a recession, though.
Let’s run through the model, this time keeping all relative prices fixed at 1, but changing the utility so that the prices are “wrong”. The scenario with P=2 can be reproduced by assuming that the utility functions change to log(Ca)+log(Cb)+2log(Cm). This creates an excess demand for mangoes and an excess supply of apples and bananas, and the final allocation is 150/50/100, 50/150/100.
Suppose its the price of apples that’s wrong, and the utility function is 2log(Ca)+log(Cb)+log(Cm). The allocations after trading are 150/75/75, 50/125/125, and there is an excess demand for apples, and an excess supply of bananas and mangoes. Is this a recession? Why not?
It’s a far from equilibrium model, and if you are talking about an economy with millions of people, you have to ask how can it get to that far from equilibrium position? You would require widespread and tightly coordinated entrepreneurial failure… but that doesn’t explain anything, you need to answer what caused such a coordinated failure.
To simply say, “Let’s suppose the economy jumps to a far from equilibrium position and let’s suppose it can’t get back,” that just isn’t an explanation of anything. Suppose all the fish turn into sandshoes, those will be tough to eat!
Your model is also pushed away from equilibrium, of course over time “P” would want to come back to a more rational price level, although I accept that this could take some time, and maybe take a long time if government is determined to interfere. Yes, there’s a coordination failure if people have one and only one means of trading with one another (i.e. cannot depend on trust, reputation, IOU notes, or anything else), and also if some external factor is interfering with their one and only means of trading (which could be a sticky price or a sudden preference to eat mangos).
Suppose I said, “Well suddenly everyone in the economy takes on a religious oath that they will not enter a bank branch, must cut up their credit cards, burn their cheque books, and cannot use an ATM either. Ah ha! Now they are all having difficulty trading. How about that?”
It’s a bit of a silly argument… Yes the logic of cause and effect is intact; but why would everyone suddenly do that? What drives this peculiar behaviour?
nive: “there is an excess demand for apples, and an excess supply of bananas and mangoes.”
How many markets are there? How many excess demands/supplies are there for each of the three fruits? (Answers: 2 markets. 1 excess demand/supply for apples, 1 excess demand/supply for bananas, 2 excess demands/supplies for mangoes.
Nick: I think I see. In my example, considering all the goods together, there is excess supply of bananas, since at the given prices, each agent only wishes to consume 75 bananas, but there are 200 bananas in existence. However, in the banana/mango market, there is no excess supply or demand, since considering only those two alone, neither agent wishes to trade at current prices. Is that your point?
Thanks.
nive: I haven’t checked your math, but it sounds like my point.
Nick:
Having recognized that the price (P) of mangoes is a variable, you offer the equation
“U = log(200-A) + log(B) + log(100+PA-PB)”.
It seems to me that if you revalue mangoes in this manner, you should (in a similar manner) revalue every relevant term in the utility equations. I think the equations should read
U = log(P(200-A)) + log(PB) + log(100+PA-PB) [U = log(P(200-A) * PB * (100-PA+PB))]
and
U = log(PA) + log(P(200-B)) + log(100-PA+PB). [U = log(PA * P(200-B) * (100-PA+PB))]
In other words, the decision to revalue mangoes will change the value of the utility equations both before and after any exchanges.
With this change, each trade will constitute equal value for every commodity group and every trade can be sized to be utility enhancing. Trades of a size large enough to cause a lower utility could be prohibited.
Trade could continue until
Ua = Ub = log(P100a) + log(P100b) + log(100m) [Ua = Ub = P100a * P100b * 100m]
which would be the maximum possible utility.
nive: to check your math:
1. Make two guesses: about whether there is excess demand or supply for apples in the apple/mango market; for bananas in the banana/mango market.
2. Given those guesses, remember that buyers will be constrained if there’s excess demand, and sellers will be constrained if there’s excess supply.
3. Have alphas and betas choose the unconstrained thing to maximise utility.
4. Solve for Nash equilibrium.
5. Check to see if your guess was right (do things add up to 200). If not, guess again.