I'll begin this post by paraphrasing Nick Rowe (see my first post):
You decide to make a new monetary system from scratch. You give everyone a chequing account on your computer, with an initial balance of 0 skilos. If Andy buys bananas from Betty and pays her 100 skilos, Betty now has a positive balance and Andy now has a negative balance.
Accounting is record-keeping. In Nick's example, what are we keeping records of? That's the question. For the answer we must, logically, look outside the records.
In the economy I described in my first post, there was no money, other than in a unit-of-account sense. Money didn't buy goods and goods didn't buy money, but goods did buy goods. If we now told Betty that she will receive money, 100 skilos, for her bananas, she wouldn't have any idea of what we are talking about. If she nevertheless played along with us, she might ask: receive what, and from whom? What: a credit balance of 100 skilos on her account in a ledger residing on an electronic device. From whom: Not from Andy, because he doesn't have any money, or a credit balance, on his account.
We are obviously not keeping records of people's money holdings.
I notice that Nick doesn't agree:
The central bank creates a box for each person, puts their money in that box, and transfers money between those boxes when it gets their consent to make those transfers.
In both worlds, a rumour spreads that the central bank has actually destroyed all the money, and is simply keeping a record on a ledger about how much money is supposed to be in each person's box. But economists say that rumour has no empirical content; it doesn't matter if it is true or false.
Nick imagines that there exists money holdings – bits of paper in boxes – outside the accounting (ledger). He says it doesn't matter if those money holdings really exist or not. Even if it didn't matter, we must be able to find a simpler, more realistic way than an imaginary box system with green and red bits of paper to explain the records on the ledger. One can easily argue – and Nick fully knows this – that those bits of paper are themselves just a record-keeping device ("counters"), and thus Nick is talking about records of records (which sounds, to quote Depeche Mode, very unnecessary). The question remains: What are we recording? (Besides, Nick's explanation would still make no sense to Betty, because there is no green or red money in existence when Betty and Andy meet; all account balances are zero.)
Nick isn't building a new system from scratch. Instead, he carries a lot of baggage with him from the old system. As I explained in my first post, this is what I want to avoid. On Nick's part this seems to be intentional, though. In the end of the post I quoted from, we can hear him say to New Keynesians: "Don't you try to escape from the old ideas!" (By the way: I'm not a NK economist, nor do I agree with their theory in general. I'm an accountant.)
But let us stay outside the accounting, in the "real world", for now. Betty gave bananas to Andy, but Andy didn't give anything to Betty. For all we know, Andy might have arrived at their meeting empty-handed. Was there an exchange between Andy and Betty? Cambridge Dictionary defines 'exchange': "the act of giving something to someone and them giving you something else". There was no exchange – no quid pro quo – between Andy and Betty. Perhaps we could call it a transaction. Betty transferred, or gave, goods to Andy.
This actually sounds a lot like the world (an "Arrow-Debreu world" with trading?) Ostroy & Starr describe:
Even though each person aims to execute an overall net trade with zero market value, the most efficient way to accomplish this in a sequence of pairwise trades is not to constrain the value of each bilateral commodity transfer to be zero. […] An individual who takes more than he gives at some pairwise meeting is simply executing a part of the overall plan to which the members of the economy have submitted themselves. It is as though the participants are agents in a firm carrying out their assigned tasks in front of each other. The lesson we draw is that in a world of complete information the requirements for enforcing overall budget balance are met, so quid pro quo is an avoidable constraint on the transactions process.
If Betty gave bananas to Andy without receiving anything in return (remember: we are still in the "real world" outside accounting), then we can conclude, following Ostroy's and Starr's wording above, that Andy took more than he gave at this particular pairwise meeting.
This makes it sound like a gift from Betty to Andy. Marcel Mauss has taught us – well, at least those of you who are anthropologists – that there exists no such thing as a pure gift. Keeping that in mind, it would be very unfortunate if no one (but Betty) remembered Betty's gift of bananas the following day; say, Andy suffered from anterograde amnesia – just like the main character in the movie Memento. In the movie, the main character uses Polaroid photos and tattoos to track information he cannot remember. Those photos and tattoos are his record-keeping devices.
Let us for now suppose that Betty gives a gift of bananas to Andy.
Is it a large or a small gift? Betty and Andy agree that the price (nominal value) of those bananas is 100 skilos, so we know something about how they both value the gift.
Now we have a hypothesis: Our new monetary system is about keeping records of gifts given and gifts received by each person. Betty gives a gift and this (transaction) is recorded by making a credit/positive entry – the nominal value of which reflects the value of the gift expressed in terms of the abstract unit-of-account – on her account. Andy receives a gift and this (transaction) is recorded by making a debit/negative entry on his account. Nothing moves from Andy's account to Betty's account, or vice versa. There's only a real-world 'banana flow' from Betty to Andy.
We have found something that takes place outside the accounting, of which it makes sense to keep records. Much remains to be explained, but I will leave it for the coming posts (and the comments section of this post, if you have any questions/critique).
I will end this post by quoting Narayana Kocherlakota. He by no means fully captures the logic of our system, but there is much which resonates with what I've said above (not only the bananas!). He writes (italics in original):
The main result of the paper is that in all of these environments, the set of incentive-feasible allocations generated by adding memory contains the set of incentive-feasible allocations generated by adding money. In this sense, in all of these environments, money is merely a primitive form of memory.
There is a simple reasoning behind the main proposition. John and Mary meet. John has apples and wants bananas. Mary wants apples but doesn't have bananas. In monetary economies, this problem is solved by Mary's giving John money in exchange for apples. John then uses the money to buy bananas from Paul; if John doesn't give the apples to Mary, John doesn't get the money and can't buy the bananas from Paul.
But of course the money itself is intrinsically useless. In terms of the reallocation of intrinsically valuable resources, we can think about the situation as being one in which John is considering making Mary a gift of apples. If he makes the gift, Paul will give him bananas in the future; if he doesn't make the gift, Paul won't give him the bananas. The money that John receives from Mary is merely a way of letting Paul know that John has fulfilled his societal obligations and given Mary her apples.
Thus, if we account for the fact that money itself is useless, monetary allocations are merely large interlocking networks of gifts. The point of this paper is to show that these same reallocations of resources are feasible if agents knew the past history of all actions: Paul could react to different histories of gifts on John's part in the same way that he reacts to John's having different amounts of money. It follows that any function performed by money can be provided by an ability to access the pasts of one's trading partners, their trading partners, and so on.
Part 3: Give and Take
 Keynes touched this problem in the last paragraph of the Preface to his General Theory: "The composition of this book has been for the author a long struggle of escape, and so must the reading of it be for most readers if the author's assault upon them is to be successful,—a struggle of escape from habitual modes of thought and expression. The ideas which are here expressed so laboriously are extremely simple and should be obvious. The difficulty lies, not in the new ideas, but in escaping from the old ones, which ramify, for those brought up as most of us have been, into every corner of our minds."
 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. (p. 10-11) – There is a working paper version freely available here. Another good overview of "mainstream" monetary economics is this paper by Meir Kohn. It is noteworthy that Kohn later gave up the attempt to make sense of money ("theory of exchange") within the general equilibrium framework ("theory of value", or "value paradigm").
 This explains the title of my blog.
 Many of us might be suffering from a mild form of this disease, in the sense that we are unable to let go of our past beliefs about money. Faced with new evidence that contradicts those beliefs, we tend to quickly forget the new evidence. Compare this with what Wikipedia says about anterograde amnesia: "...a partial or complete inability to recall the recent past, while long-term memories from before the event remain intact".
 Kocherlakota, Narayana. 1996/1998. "Money Is Memory". Working paper version (p. 2).