Thursday, December 8, 2016

Green Stones Don't Reside on Accounts

Ostroy and Starr[1] tell a story of "a pair of Robinson Crusoes":

Two elderly, largely self-sufficient gentlemen live on an island. Having only the most anemic impulses to truck and barter, their sole contact is the irregular exchange of dinners. Since both agree that meal preparation is onerous, they take turns. However, because dinners are exchanged so infrequently and because their memories are not what they used to be, these Robinson Crusoes cannot always agree on who gave the last dinner. On several occasions both have claimed to have provided the last meal. Each gentleman recognizes that this is a self-serving claim since this is what each would like to remember, but neither is sufficiently confident of his recollection to be sure of the truth. These disagreements have produced so much tension and ill-will that dinners are now exchanged even less frequently.
To attenuate this problem, the one who is coming to dinner next picks up a stone and paints it an artificially colored green to distinguish it from other stones and brings it to his host. At the next planning session for a dinner, the most recent host will be reminded by the presence of the green stone that it is his turn to be invited, and he will be expected to bring the stone with him when he arrives. Indeed, without receiving the stone the host may feel justified in turning away his guest as not having the required evidence of an invitation.
This quite rudimentary story reveals an essential feature of monetary exchange. Money is a commonly acknowledged record-keeping device. Here the only information about the past which has to be recorded is who gave the last dinner. Each gentleman "pays" for his dinner by transferring the record of this fact to the other.

That's a nice story which reveals something fundamental about money. The story is so good that I want to write a sequel to it.

Let us assume that in addition to these two gentlemen there is a fully self-sufficient accountant (an oxymoron?), called Monday, on the island. She has a lot of spare time and wants to help the gentlemen. Being elderly, the gentlemen seem to misplace the green stone once in a while, and this has led to a time-consuming search operation on more than one occasion.

Monday suggests that instead of using the green stone as a "counter", the gentlemen could rely on bookkeeping as a record-keeping device. Monday would take care of the bookkeeping. All the gentlemen have to do is to remember to inform Monday about any trades of dinners that take place between them.

Monday finds out that Nick Sr, one of the gentlemen, holds the green stone. She takes this to mean that Abraham, another gentleman, owes a dinner to Nick Sr. Both gentlemen agree on this interpretation, although they are not sure about the total number of meals prepared by each of them over time (what is one dinner between gentlemen!).

Nick Sr gives the stone to Monday, who buries it deep in ground now that it has become redundant as a record-keeping device.

The gentlemen don't know much about accounting. This is how they imagine Monday's ledger looks like:

Abe: 0 stone(s)
Nick Sr: 1 stone

This is how the actual accounts in Monday's ledger look like (being a CPA, she couldn't help using double-entry!):

Abe: -1 dinner
Nick Sr: +1 dinner

End of extended story.

What can we learn from my extension to the original story of Ostroy and Starr?

First, that green stones don't reside on accounts.

Second, that there is no transfer of a green stone, or anything for that matter, from Nick Sr to Abe the next time the latter prepares a meal for the former.

Instead, there is a "transfer" of a meal from Abe to Nick Sr. Monday will record this meal trade in her ledger by debiting Nick Sr's account with 1 dinner and crediting Abe's account with 1 dinner. This will bring balances of both of the accounts to zero. How do the gentlemen then know who is to be invited for a dinner next time? They ask Monday, and by looking at the entries she has made she will find out that it was Abe who prepared the meal last time and is to be invited next time.

Is there a need for Abe and Nick Sr to understand how the accounting works? Does it matter if they continue to think that Monday is transferring stones between the two accounts? I don't think it matters, at least not when the economy is so simple. The only tradable good is a dinner which is assumed to not vary in terms of utility derived from it – if Abe is not as good at cooking as Nick Sr, I'm sure he makes up for it by being an otherwise entertaining host.

We cannot yet talk about a monetary exchange economy in this case. (We need another sequel for that, which in one way or another is forthcoming.) But as Ostroy and Starr write, one could say that the gentlemen "pay" for the dinner by transferring the green stone to the host. So at least in some ways the green stone is comparable to money, or currency more specifically.

With this post I wanted to draw attention to the fact that bookkeeping in a double-entry format might look quite different from record-keeping where "counters" like the green stone are used, even when the object of recording – dinners given and received – is the same.


[1] Ostroy, Joseph M. & Starr, Ross M. 1990. "The transactions role of money," Handbook of Monetary Economics, in: B. M. Friedman & F. H. Hahn (ed.), Handbook of Monetary Economics, edition 1, volume 1, chapter 1, pages 3-62 Elsevier. ("A pair of Robinson Crusoes", p. 8-9) There is a working paper version freely available here.


  1. I feel like the Grinch that is stealing Christmas. Such a nice story and all I can do is to find ....

    Well, first, I notice that the green stone transfer is informational only. No sense of time control is transferred. The holder of the green stone is NOT the one to initiate the next event. You pointed out that the green stone is not representative of money and I would agree because of this lack of time control.

    The second thing I noticed is that Monday was not using the marks themselves to carry information. She was using the SEQUENCE OF ENTRY as the information stream. She effectively was recording the date of the last event.

    Let's look at this from a different way. Monday should have begun the journal with the entry

    Abe: 0 stone(s)
    Nick Sr: 0 stone(s)

    This reflects the fact that there was no record keeping before the first stone was used.

    Then we had a recorded event. A green stone was used for the first time. Following that event we would record

    Abe: 0 stone(s)
    Nick Sr: 1 stone

    At this time, Nick Sr. has the entire stone hoard. FWTW!

    I know you are aware that I write from the mechanical perspective. One of my biggest frustrations is that the initial event is not properly linked. Have I shared my concern with this accounting analogy? More importantly, does it make sense?

    Sorry to be such a Grinch :-(

  2. Nothing to add, except that the accountant, in order to remain credible, has his own interest in making sure that he who owes the next meal 'pays up' and does so without undercutting the last meal he received in quantity or quality.

  3. Roger: I don't understand why you keep on talking about stones when you refer to Monday's bookkeeping?

    We can assume (and here I made a slight change to Ostroy&Starr's original story) that how it all started was that Nick Sr served a dinner to Abe, and Abe acknowledged his debt by painting a stone green and handing it over to Nick Sr and told him the stone is an IOU (a dinner). Alternatively, and what amounts to the same, we can view the stone as an invitation letter to a later dinner served by Abe.

    Monday's records are records of dinners owed and dinners traded. They are not records of stones or "IOU things" held. That's my point.

  4. Oliver: Isn't that up to the gentlemen? They are also the judges of the value of the dinner, and if they don't agree, then they can sue each other -- or fight physically. I don't see what that has to do with the accountant?

    But I can see how we need someone to "police", once there are more than two agents. That's probably where you were going?

  5. Well, not only. Even with only two parties involved, someone has to see to it that the measure of value does not change too much over time. There is some diligence due on behalf of the accountant. In this hypothetical example, the accountant may require the cook to disclose the ingredients, hand in an estimate of the time needed to prepare the meal as well as checking up on the neighbours to see whether either of the two have been known to be irresponsible individuals in the past. So, although Abe and Nick Sr. have been friends for years and are perfectly happy with trading their meals at an exchange rate of 1:1, the accountant could well demand a larger haircut from one of the two leading to the fact that say Nick Sr.'s meals trade at 1:1,2 with Abe's. Or Abe will have to throw in a dessert to keep the books balanced.

  6. Oliver: I see what you mean.

    Why I don't want to agree with you is based on reasoning that goes something like this:

    The accountant (we are both thinking about a bank, right?) has responsibilities like the ones you describe when the accountant is not only an accountant, but is also expected to represent the interests of the agents with credits in its books. This is clearly the case when there are many creditors like this, because then there is no clear link between the creditors and debtors (or debtor). They don't even know each others' identities, so the accountant is necessarily a "middleman".

    In the case of these two gentlemen, the accountant in my view doesn't need to represent the interests of the creditor; the accountant can be quite impartial. She doesn't have the kind of responsibilities she would have if the creditor and debtor weren't aware of each others' indentities, and thus couldn't look after their own interests.

    Do you see what I mean?

  7. Yes, I agree. The example with only 2 people is special in that sense. Although I suppose we could come up with an example of an economy with 2 individuals who don't know each other. Say, 2 merchants who meet at a market place half way between their homes once a year.

  8. Oliver: Would they extend credit to each other if they didn't know each other?

    No, but there could be a third party who is not only an impartial accountant, but who would be willing to bear, or represent those who bear, the credit risk involved. But that makes it an economy of more than two agents, right? (In a way the economy with two gentlemen is a two-agent economy, because the accountant is a self-sufficient, impartial observer-scribe. Do you agree?

  9. I suppose so. That's the way you defined your economy... Where are you going with this?

  10. Antti:

    Is the use of physical money antithetic to your monetary theory?

    I ask because physical money is automatically implied if a scale of value is used.

    I don't think the green stone story is about money, nor is the evolution of green stone to accounting about money. The story is about storage of time related information.

    Could we evolve the green stone story into monetary theory? Maybe by using TWO green stones? Well, if each stone represented one meal, we still would have only an informational recording. Nothing descriptive about the actual meal construction would have been recorded.

    Maybe we can learn from this attempt to make stones represent money. Money needs the ability to communicate quality as well as quantity. Thus we could say that an exchange involving money will always have a value calculated using the formula "Exchange Value = Item Value times number of Items". Item value would be found by referencing a money scale.

    Can we find (here) a bridge from my NGC world into your gift world?

  11. Antti: This extended comment is a supplement to my last comment.

    I got to wondering if the idea of "a money scale" could be foreign to you. I certainly doubt it but decided to elaborate just a little.

    Money can be considered a "digital" scale. Engineers will contrast digital with analog. Think of an analog scale as being continuously dividable. There is no lower limit on the number of lower divisions-they can always be made smaller. (A yardstick is analog. It will be divided into smaller fractions, limited only by your ability to read the marks.)

    Digital is different. A digital scale has a lower limit that defines how small the very smallest measurement can be. Money is a digital system. The cent is the smallest unit, the dollar the largest.

    A digital system can always be represented by other physical units. Hence, we can have a one cent coin. There is no smaller division.

    You probably had that concept before this but wanted to be sure. :-)

  12. Oliver said: "Where are you going with this?"

    I guess I'm just beating around the bush :-)

  13. Testing my patience, eh? ;-)
    My broader point would be that economics must surely be about quality as much as it is about quantity. And, at least in an anonymous exchange, as per your point above, there needs to be some agent / institution that is responsible for quality control.

  14. Quality of what in this case?

    I think you talked about the quality of the dinner earlier, but I'm sure you agree that the quality of the dinner is not something that should concern the accountant (or bank). That is dealed with by private litigation, consumer protection, etc. Right?

    In the story, the gentlemen expect a certain quality from the dinner. The dinner received has a price to both of them, and that price is the dinner they provide on their turn. If one gets something much worse than he gave up earlier, he complains. It's comparable to you going to a restaurant, buying a CHF100 dinner and concluding that the dinner didn't meet expectations people normally have when it comes to dinners in that price category.

    That kind of concerns and disputes fall mostly outside macroeconomics.

    Credit quality is another thing. I would say it's separate from product or service quality. But they might be somehow intertwined in your example? I'd like to hear your thoughts on that.

  15. Maybe I mangled things and those two concepts need to be separated, you're right. But my gut feeling tells me they're deeply intertwined. There is a reason I have an overdraft limit (credit assessment with no further quality control) of 3'000.00 for my checking account but at the same time, by the same bank, am granted a mortgage loan of nearing 300'000.00. The work the bank put into assessing whether the purchase was a deal they'd want be caught ip in if things went south (plus, of course an assessment of the chance if things going south in the first place), was quite considerable. I see a continuum from qualitative to quantitative that should be considered in macro, too. The other social sciences have long accepted qualitative research as giving valuable insights that quantitative research cannot, just as an example.

  16. I don't disagree with you in general. Quality is important, and quantity alone doesn't capture much.

    Now you are talking about credit quality control? Ovedraft/credit card limit at CHF 3,000 requires credit quality assessment. The mortgage usually requires both collateral (real asset quality control?) and credit quality control.

    Perhaps you meant that the bank has to make sure that the one with a liability is not a fraud, but can deliver goods that meet certain standards, and so can get rid of his liability by selling goods (in a legitimate way, satisfying the expectations of the buyer)?

  17. Maybe collateral is a third distinction that needs to be made :-). Thanks for helping me aling...
    I have a particular example in mind of a friend who wanted a mortgage but was only granted a partial mortgage for the part of the refurbishment which the bank considered to be 'usual standard' but not for 'luxury items'. And that was not a question of credit worthiness of the borrower. Also, I know that banks have pretty good tools to assess the value of property. But yes, that is collateral.