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 
Roger: “It seems to me that if you revalue mangoes in this manner,…”
I am NOT revaluing mangoes.
The utility function is U = log(Ca)+log(Cb)+log(Cm) where Cm is quantity of mangoes eaten (and same for Ca and Cb respectively).
But the budget constraint for alphas tells us that Cm = 100 + PA – PB where A is number of apples sold and B is number of bananas bought. And so I substitute the right hand side of that budget constraint into log(Cm).
This is very standard microtheory (except they can’t sell as many apples as they want).
nive: maybe a better way to check the math would be to make those two guesses, set it up as a Lagrangian, then check your guesses by seeing if the constraint on sales or purchases of apples and bananas is binding or slack in Nash equilibrium.
Hi Nick,
Sorry for answering late. Been wonderfully busy with xmas… happy holidays to you and everyone giving comments… a quick comment before rushing out again.
You asked about effective demand and if it means “when 100 apples are traded for 100 bananas?”
Quick answer… No
First, if the price doubles, a recession can be avoided by doubling the velocity of mangoes. Is velocity then sticky enough to prevent that? Maybe… Mangoes can represent income. In your model, income is capital income that increases its velocity with transactions of mangoes. However, a portion of income is paid as salaries and wages contracted at a certain amount and velocity. The amount and velocity of wages and salaries are sticky if labor is powerless to change contracts that rapidly. If the velocity of growing certain mangoes (paying out wages and salaries) could be doubled as capital income is doubled, then the velocity of the transactions with mangoes has a good chance of being doubled to avoid a recession.
So the velocity of paying wages and salaries can factor into causing or avoiding a recession.
Second, the business cycle is determined by a profit cycle. I do not see a profit factor in your model. The key point in the profit cycle to lead to a recession is the profit equilibrium point (where expected profits are maximized). The profit equilibrium point is where the effective demand limit is. That is where we would find potential output, full employment and all that. We may find that at 100 apples being traded for 100 bananas, there is still increasing profits. So if P>1, a recession can still be avoided if mango velocity can increase, and businesses refuse to contract because profits are still growing. They have incentive to expand production and employment.
We may also find that profit equilibrium is reached when 80 apples are traded for 80 bananas. The effective demand limit would be there and not at 100 apples for 100 bananas.
The effective demand limit is a zero sum game with profits. When one business gains profits, another will lose that amount. Before you reach the effective demand limit, businesses will increase profits together, so that the overall economy is expanding. General business contraction will take place once the zero sum game of profits matures.
Wherever effective demand limit is (profit equilibrium), the economy could stabilize at that point into a steady state. A recession does not necessarily have to happen in theory. However, recessions do get triggered. And that is when we come back to your view of liquidity of mangoes in that sensitive state of the effective demand limit.
The liquidity is influenced by psychology and shocks.
In the last 90’s, the business cycle extended for many years beyond the effective demand limit due to rising labor share keeping wages and salaries in line with capital income. Also the psychology of increasing productivity and potential gave incentive to expand and not contract. Eventually that the recession of that business cycle was triggered due to profits weakening and excess money demand.
So I like your minimalist view. Yet, I also need my minimalist view of effective demand based on labor share and utilization of capital and labor to get a clearer picture of when your view can actually manifest as a one-period model with certainty. You may find that in your model, the recession does not occur at 100 apples for 100 bananas, but at another point. Then you would need a model of effective demand to explain that.
“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.”
I disagree. Recessions can occur in a barter economy without a defined single medium of exchange.
Nick – This post is a neat way of making a point you’ve made before, in fact one of the key points I’ve taken from reading this blog. What you are essentially doing is defining the term “recession” in such a way that it is primarily a monetary phenomenon. You show that excess demand for the medium of exchange can cause the symptoms of a recession. You don’t show that nothing else can cause those symptoms (it’s hard to prove a negative!) but the explanation is good enough, and matches history enough, that everyone should adopt your definition, and use a different word to describe decreases in output or increases in unemployment that are the result of a different fact pattern. It’s a little aggressive to co-opt such a popular word, and that bothers people like Avon.
One thing I don’t see in this simple model is an explanation for how recessions get worse. It doesn’t seem like the excess demand for money is just an exogenous shock that triggers recessions unless or until it is accommodated by the monetary authority. It seems like once the recession begins, there are internal dynamics that deepen the recession, at least in the short-run.
louis: reading through your first paragraph, I find I agree with pretty much all of it. It is indeed hard to prove a negative, but I think the onus is on whoever disagrees to come up with a better minimalist model.
Second paragraph (on recessions getting worse): yep, this model is too minimalist to discuss the propagation mechanism. And that depends so much on the particular monetary policy regime anyway. But this model does say, at least implicitly, that it must be something that makes an initial excess demand for money self-perpetuating. Some sort of snowball feedback effect of the excess demand for money on itself. Something that either increases the demand or reduces the supply of money. And that tells us something. But we can’t really say more than that without talking about a specific monetary policy.
IMHO as an absolute minimal model you need to :
* Include the banking industry (as a cartel) because they make semi-centralized decisions regarding total volume of investment, loans and money creation.
* Model information transfer and uncertainty… as Gene Callahan and nivedita point out above, the primary reason to hold liquid assets is to defer purchasing decisions.
* Allow for additional “sovereign risk” uncertainty imposed by central bank decisions, government policy shifts, weakening the rule of law, etc.
* Abandon the idea of a “sock-stuffing” recession where people are eating their mangos instead of trading, few people hold wads of cash, certainly no one eats currency.
* Discuss concepts of successful investment vs failed investment, entrepreneurial error, when to recognize poor investment decisions, how to gracefully liquidate broken projects, who picks up the cost.
I also recommend Rothbard “The Case Against the Fed” and “America’s Great Depression” for detailed insights and the newer book, “Money, Bank Credit, and Economic Cycles” by Jesús Huerta de Soto.
Nick, my process for coming up with the allocations was essentially trying to see what the successive trades between alphas and betas seem to be converging to, and check it to make sure no further trades will happen 🙂
I think I like my variation together with your model, to illustrate why an excess demand for money is unlike an excess demand for other goods.
Tel, that’s not a minimal model. Nick is not even trying to model why there is excess demand for money, or why prices are sticky.
nive: that should work. We can always just guess the answer, then check to see if it satisfies the first order condition for the agent on the short side of the market.
“I think I like my variation together with your model, to illustrate why an excess demand for money is unlike an excess demand for other goods.”
Yep. I think it’s like a hub-and-spoke airline system. If one of the spokes goes wrong, it’s no big deal. But if the hub goes wrong, the whole system goes down. Though, to really show that, I expect we would need to add carrots to the model, and a third type of agent, with an endowment of carrots and mangoes.
nivedita, if you skip the requirement of needing to know why I can offer an extreme minimal model: “We had a recession, end of story.” Well hey, you wanted minimalist. But let’s go back to the original question here…
Quite so, and being able to give an answer to questions like, “What caused this?” is one of the things I would be looking for when it comes to understanding the phenomenon in question. Actually, it’s the first thing I would be looking for.
Not necessarily every single aspect of what caused this. For example, we know the problems in 2007/2008 had something to do with mortgages and RMBS… I don’t need to know all the names on all those mortgages, nor the addresses of the houses, nor the names of the estate agents… those would be extraneous details. On the other hand, to say we are going to ignore the whole concept of loans and credit and banks entirely would (IMHO) be oversimplification, removing one of the key aspects at the heart of what happened.
Maybe I can ask that question a different way: if the model of a recession depends on “sticky prices” then why can we observe that the prices of certain entities were highly volatile during the crisis? Here’s an example:
Producer Price Index for All Commodities (2005-01-01 => 2011-01-01)
Big swing in commodity prices right through the middle of the recession, with leading ramp up, and then crashing off a cliff. Not even remotely sticky. How does the minimal model demonstrate this?
By the way, if you go looking around you can find other recessions with a similar pattern (not all of them):
Producer Price Index for All Commodities (1918-01-01 => 2011-01-01)
The famous depression of 1920-21, with it’s sharp deflationary shock, supposedly caused by the dreaded gold standard and damnable high interest rates at the Fed. Looks kind of similar to 2008 though when you put the graphs near one another. Suggests to me there might be something happening that cannot be explained by “sticky prices”.
Regarding the definition of a “recession” in this thread, I think it’s important to keep in mind that the way Nick is using the term, a recession is not simply a decrease in aggregate output or utility. That’s easy enough to manage by burning down the apple orchards, and it’s uninteresting.
What Nick is attempting to model is the conditions in which an economy is Pareto-suboptimal, in that there exists a rearrangement of goods such that every agent is better off, yet for some reason those exchanges cannot happen. In the single-period, homogenous-utility fruity model, this is equivalent to asking whether all exchanges that would be made under a barter system will also happen with mangoes as a mandatory MoE.
@Tel 11:23PM:
You’re assuming that this model requires that all prices be sticky. But the obvious retort is, “why didn’t the price of every good have the volatility of commodities prices?” After all, the labour:steel ratio to build a car (for example) didn’t change, and the supply curve of steel didn’t shift dramatically, so why did the same forces that caused the price of steel to shift instead result in a reduction of employment for auto workers?
@Tel 11:29PM:
… or the Fed was also inappropriately tightening the US money supply throughout 2008. This is one of the core insights of the ‘market monetarist’ model and most explicitly championed by Scott Sumner, which argues that despite a constant and then falling Fed Funds rate, the Wicksellian natural rate was falling far more rapidly. The net effect was one of tight money despite the Fed’s internal thoughts on the matter.
You must be referring to that uninteresting recession in Europe, 1939 to 1945 if I remember rightly, someone told them that burning their apple orchards would create economic stimulus (what fools!)
At first glance war cannot be Pareto-optimal, because if all sides stop shooting, then all sides also live longer.
Might be a little more difficult to prove that in detail once you factor in the people at the top of the heap who aren’t directly threatened by the war (gosh, some of them even make a profit, how about that). Very tough to find a situation that is 100% Pareto-suboptimal in any real world scenario (it’s an ill wind that blows nobody good). Anyhow, I’m getting off topic, I get what you mean, but even during downturns like the Great Depression there were people who did well out of it. That may not be a necessary feature for a model, maybe those people were few and perhaps irrelevant, but clearly the Pareto-optimal criteria is not in itself a fundamental constraint on a depression.
It would be nice to have a model that fits observable historic events. The whole idea of “understanding the phenomenon” must surely involve some real-world phenomenon that we are attempting to understand.
At least in the automotive industry there has been a significant shift, we have had Tata Motors harnessing the power of cheap Indian workers; the Chinese are exporting onto the world market with their penchant for mass production; Germany and Japan have driven greater levels of automation and productivity (not to mention imported Turkish workers in Germany, and Brazilians into Japan). That said, none of this happened in the space of a few years, it’s been steadily happening, so it’s a valid question why real economies don’t gradually adjust along with global events and relative prices should do that too. Rapid volatility generally suggests something linked to uncertainty and information propagation.
Mostly I would say that these “sticky prices” are consequences of people digging their heels in and refusing to adjust when they know they should. Eventually it gives way all of a sudden, rather than small steps at a time. The Detroit unions simply wouldn’t believe that their past good times would ever be taken from them. Being militant had served their purposes in the past, so they figured that showing stubbornness was appropriate. Worse than that, many of the Detroit government workers had retired on excellent pensions and were not in a position to renegotiate so stickiness has been baked into the cake for those type of contracts. When the normal avenues of adjustment are blocked up, pressure builds until something abnormal is forced to adjust (often in a dramatic manner).
There are two features in this model that appear to me to be doing the crucial work. One is that P is sticky; the agents are not allowed to bargain to adjust P to the market clearing price of 1. I take it that this is intended to capture the apparent fact that money prices in the real world do tend to be sticky; people expect things to cost today what they cost yesterday, and are particularly sensitive to sharp increases in the price of things they buy or sharp decreases in the price of things they sell (particularly wages).
The other crucial feature is that the agents consume mangoes. But in the real world, money is not a consumable good (at least, fiat money isn’t); its only use is as a medium of exchange. If we adjust your model in this way, making mangoes non-consumable, can’t the agents still execute all desired trades in apples and bananas if P > 1 (i.e., reach the same final state as the case in which P = 1) simply by executing more than one round of exchanges?
Peter: I agree the first feature is important. The second feature was just a quick and dirty way for me to get a one-period model, which makes it simpler. If the velocity of money is fast enough, one dollar circulating quickly enough would be enough money to handle all exchanges. But even though that would be in the collective interest, no individual would have an incentive to spend his money quickly enough, so we get the same result as in my model.
@Nick: “no individual would have an incentive to spend his money quickly enough”
Can you elaborate? Not for the extreme case of only one dollar in the entire economy (or one mango), but for a variant of your model here in which mangoes were not consumed? Are you saying there is some minimum number of mangoes that would have to be present to allow the market to clear? If so, how do we know what that minimum number is?