Guest Post: A Double Entry View on the Keen Circuit Model

In there is an iter­a­tion of Steve’s hor­i­zon­tal mon­ey cir­cuit and the tables and equa­tions he uses to build that mod­el. He’s rejigged those mod­els in response to a chal­lenge by Scott Full­wiler to fit the mod­el into dou­ble entry book­keep­ing tables.Now Steve is a great speak­er, a good writer and for­mi­da­ble math­e­mati­cian. But I’m afraid he would get a fail in a book­keep­ing exam. For some­thing to be con­sis­tent with dou­ble entry there has to be at least two entries in the jour­nal and the jour­nal must sum to zero. To abuse Minsky’s words: a dou­ble entry mod­el with a sin­gle entry in it isn’t a dou­ble entry model.So its easy to see why the pre­sen­ta­tion of this par­tic­u­lar mod­el caus­es a few fire­works in schools of thought who are more fas­tid­i­ous in their bookkeeping.My back­ground is in Infor­ma­tion Sys­tem design and archi­tec­ture, with a dose of accoun­tan­cy thrown in for good mea­sure, and I’ve worked in and around the Free Soft­ware move­ment for over twen­ty years. So my nat­ur­al ten­den­cy is to look at ways of re-inte­grat­ing ‘forks’. I believe all the issues com­mon­ly com­plained about in this mod­el can be rec­on­ciled by mak­ing the tables dou­ble entry com­plaint and extend­ing the mod­el slight­ly. I hope this will show to all sides that they are talk­ing about the same thing.And by doing so I am almost cer­tain to upset every­body. Such is life.

First the cur­rent tables. This is a copy of table 14.1 in Debunk­ing Eco­nom­ics (sim­i­lar to table 1 on this post at Steve’s site):

	Assets		Lia­bil­i­ties		Equi­ty
Oper­a­tion	Vault	Loan Ledger	Firms	Work­ers	Safe
Lend Mon­ey	-Lend Mon­ey		+Lend Mon­ey
Record Loans		+Lend Mon­ey
Charge Inter­est		+Charge Inter­est
Pay Inter­est			-Charge Inter­est		+Charge Inter­est
Record Pay­ment		-Charge Inter­est
Deposit Inter­est			+Deposit Inter­est		-Deposit Inter­est
Hire Work­ers			-Wages	+Wages
Bankers Con­sume			+Bankers Con­sump­tion		-Bankers’ Con­sump­tion
Work­ers Con­sume			+Work­ers’ Con­sump­tion	-Work­ers’ Con­sump­tion
Loan Repay­ment	+Loan Repay­ment		-Loan Repay­ment
Record Repay­ment		-Loan Repay­ment

From a dou­ble entry view­point there are a few things that feel uncom­fort­able with this table.

1. the lia­bil­i­ties side is strict­ly the wrong sign. Lia­bil­i­ties are gen­er­al­ly shown neg­a­tive so that when you add them to assets you get zero. You can run them as a pos­i­tive bal­ance but that means the check of sim­ply mak­ing sure the row adds up to zero doesn’t work so well (you have to mul­ti­ply the sum of lia­bil­i­ties by ‑1 first). Also ‘-’ is gen­er­al­ly a cred­it and ‘+’ a deb­it. So in the table you can see that firms appear to pay wages by ‘cred­it­ing’ and work­ers receive wages by ‘deb­it­ing’ which is incon­sis­tent with the way bank accounts are usu­al­ly described.

1. The bank only gets paid when the firm pays the inter­est. Yet in account­ing the bank will ‘recog­nise’ the income (ie cred­it its prof­it and loss account) as soon as it charges inter­est and this will allow it to spend before it gets paid. This isn’t seignior­age as the bank has indeed earned that mon­ey. So the table has a minor tem­po­ral error in it which may or may not be impor­tant.

1. The ini­tial con­di­tions on a bal­ance sheet must be cre­at­ed by a series of jour­nals and must bal­ance to zero. Mon­ey shouldn’t mag­i­cal­ly appear in a Vault.

1. But most impor­tant­ly there are a lot of sin­gle entries in the rows. That makes this table incon­sis­tent with the fun­da­men­tals of dou­ble entry that requires every trans­ac­tion to sum to zero. To be dou­ble entry there must be at least two entries and the jour­nal rows must sum to zero — or it is not a dou­ble entry table. So there is some­thing miss­ing from this mod­el to bal­ance those lines.

Bear in mind that this is a lim­it­ed hor­i­zon­tal cir­cuit mod­el with a lot of heuris­tic assump­tions. It is has sta­t­ic para­me­ters and ignores every­thing oth­er than a sim­ple pri­vate cred­it cir­cuit. So there is no ini­tial cap­i­tal for the bank or equi­ty con­sid­er­a­tions and all the para­me­ters have a fixed val­ue. Those are all delib­er­ate.

It’s job is to show that a pri­vate cred­it cir­cuit with a fixed stock of mon­ey can exist stand­alone which was, pri­or to Steve’s work, thought impos­si­ble.

My job is to rec­on­cile this table so that it works from a dou­ble entry view­point, still have loans cre­at­ing the equiv­a­lent deposits and have them both destroyed and not destroyed at the same time all while sat­is­fy­ing as many view­points as pos­si­ble.

In oth­er words the peren­ni­al accountant’s dilem­ma — how to present a set of accounts.

So let’s have a go at fix­ing this and see how many peo­ple we can upset.

Let’s start with the first line and fix the signs. We’re going to impose a ‘all rows sum to zero’ restric­tion on this table.

	Assets	Lia­bil­i­ties			Equi­ty
Oper­a­tion	Vault	Loan Ledger	Firms	Work­ers	Safe
Lend Mon­ey	+Lend Mon­ey		-Lend Mon­ey

So we have an accu­rate jour­nal on the firm side — cred­it­ing their account with mon­ey is def­i­nite­ly cor­rect. But the bal­anc­ing entry now appears wrong — why would cred­it­ing a Firm account increase a vault asset?

Answer: it wouldn’t. Vault is on the wrong side of the bal­ance sheet. Paper notes in a Vault are a stock of non-cir­cu­lat­ing bank lia­bil­i­ties — as are the elec­tron­ic equiv­a­lent. So let’s move Vault.

	Assets	Lia­bil­i­ties			Equi­ty
Oper­a­tion	Loan Ledger	Vault	Firms	Work­ers	Safe
Lend Mon­ey		+Lend Mon­ey	-Lend Mon­ey

Now it makes sense, the flow is mov­ing the lia­bil­i­ties from the non-cir­cu­lat­ing stock in the Vault to the cir­cu­lat­ing stock at the Firm.

Which then leads onto the next ques­tion. How are there any lia­bil­i­ties in the Vault in the first place?

Well, think­ing in paper for a moment, notes have to be made and there will be a lim­it to how many can be made. And only banks can make these notes, not firms. So what’s the dif­fer­ence?

The banks have a ‘licence to print mon­ey’ that the firms don’t have  (even if its one they gave them­selves — as a tru­ly inde­pen­dent cen­tral or pri­vate bank would do for exam­ple). Tech­ni­cal­ly of course this is a ‘licence to cre­ate mon­ey’ — they are not required to print it. A licence is an ‘intan­gi­ble asset’. The val­ue of the licence to cre­ate mon­ey will vary over time depend­ing upon the terms of the licence, the amount of out­stand­ing loans and var­i­ous oth­er fac­tors. And, like the intrin­sic good­will of the firm or its ‘human resources’, you don’t usu­al­ly see the val­ue on a bank bal­ance sheet.

But in this mod­el we want to know how much ‘poten­tial mon­ey’ is in the sys­tem at any point in time so let’s add in a jour­nal to give the bank the abil­i­ty to cre­ate a fixed amount of mon­ey (remem­ber this mod­el is oper­at­ing under fixed para­me­ter heuris­tic assump­tions). This neat­ly solves the prob­lem of where the ‘ini­tial val­ue’ comes from and makes new mon­ey and old mon­ey the same thing — the val­ue of the licence can vary dynam­i­cal­ly like any oth­er vari­able.

	Assets		Lia­bil­i­ties			Equi­ty
Oper­a­tion	Licence Val­ue	Loan Ledger	Vault	Firms	Work­ers	Safe
Grant Licence	+Grant Val­ue		-Grant Val­ue
Lend Mon­ey			+Lend Mon­ey	-Lend Mon­ey

And then final­ly add in the record­ing of the loan.

	Assets		Lia­bil­i­ties			Equi­ty
Oper­a­tion	Licence Val­ue	Loan Ledger	Vault	Firms	Work­ers	Safe
Grant Licence	+Grant Val­ue		-Grant Val­ue
Lend Mon­ey			+Lend Mon­ey	-Lend Mon­ey
Record Loan	-Lend Mon­ey	+Lend Mon­ey

So now we have an extend­ed bal­ance sheet with the mon­ey cre­ation sys­tem declared explic­it­ly on the face of the bal­ance sheet. A cred­it licence has val­ue and that ini­tial val­ue is added to the bal­ance sheet as a non-cir­cu­lat­ing intan­gi­ble asset and the asso­ci­at­ed non-cir­cu­lat­ing reval­u­a­tion reserve lia­bil­i­ty — which we have called Vault in this mod­el for want of a bet­ter name.

Issu­ing Loans reduces the remain­ing val­ue of the cred­it licence and at the same time the Deposit reduces the remain­ing amount in the Vault. Loans still cre­ate deposits — but by chang­ing non-cir­cu­lat­ing lia­bil­i­ties into cir­cu­lat­ing ones.

So far so good. Let’s add some inter­est.

Inter­est can be seen as an exten­sion to the loan, where the asso­ci­at­ed deposit is imme­di­ate­ly paid over to the Bank. So we can add that in.

	Assets		Lia­bil­i­ties			Equi­ty
Oper­a­tion	Licence Val­ue	Loan Ledger	Vault	Firms	Work­ers	Safe
Charge Inter­est			+Inter­est Charge			-Inter­est Charge
Record Inter­est	-Inter­est Charge	+Inter­est Charge

Gen­er­al­ly there is no sep­a­rate pay­ing of inter­est. As any­body who has a mort­gage knows you just make one repay­ment which cov­ers the prin­ci­pal and accrued inter­est.

But this is real­ly a styl­is­tic point at this stage as the val­ue of the pay­ment is the Loan Repay­ment + Inter­est Charge any­way.

	Assets		Lia­bil­i­ties			Equi­ty
Oper­a­tion	Licence Val­ue	Loan Ledger	Vault	Firms	Work­ers	Safe
Repay Loan and Inter­est			-Loan Repay­ment ?Inter­est Charge	+Loan Repay­ment +Inter­est Charge
Record Loan and Inter­est Repay­ment	+Loan Repay­ment +Inter­est Charge	-Loan Repay­ment ?Inter­est Charge

So the revised Lend­ing table looks like this in total:

	Assets		Lia­bil­i­ties			Equi­ty
Oper­a­tion	Licence Val­ue	Loan Ledger	Vault	Firms	Work­ers	Safe
Grant Licence	+Licence Val­ue		-Licence Val­ue
Lend Mon­ey			+Lend Mon­ey	-Lend Mon­ey
Record Loan	-Lend Mon­ey	+Lend Mon­ey
Charge Inter­est			+Inter­est Charge			-Inter­est Charge
Record Inter­est	-Inter­est Charge	+Inter­est Charge
Repay Loan and Inter­est			-Loan Repay­ment ?Inter­est Charge	+Loan Repay­ment +Inter­est Charge
Record Loan and Inter­est Repay­ment	+Loan Repay­ment +Inter­est Charge	-Loan Repay­ment ?Inter­est Charge

As a check let’s remove the intan­gi­ble asset and asso­ci­at­ed jour­nals from the bal­ance sheet and see what we get:

	Assets	Lia­bil­i­ties	Equi­ty
Oper­a­tion	Loan Ledger	Firms	Safe
Lend Mon­ey	+Lend Mon­ey	-Lend Mon­ey
Repay Loan and Inter­est	-Repay­ment	+Repay­ment
Charge Inter­est	+Inter­est Charged		-Inter­est Charged

Which should look famil­iar to any­body on the MMT side of the debate.

That’s the bank lend­ing items sort­ed. Let’s adding the spend­ing ele­ments and com­plete the cir­cuit. So for the expand­ed bal­ance sheet the final table looks like this:

	Assets		Lia­bil­i­ties			Equi­ty
Oper­a­tion	Licence Val­ue	Loan Ledger	Vault	Firms	Work­ers	Safe
Grant Licence	+Licence Val­ue		-Licence Val­ue
Lend Mon­ey			+Lend Mon­ey	-Lend Mon­ey
Record Loan	-Lend Mon­ey	+Lend Mon­ey
Charge Inter­est			+Inter­est Charge			-Inter­est Charge
Record Inter­est	-Inter­est Charge	+Inter­est Charge
Repay Loan and Inter­est			-Loan Repay­ment ?Inter­est Charge	+Loan Repay­ment +Inter­est Charge
Record Loan and Inter­est Repay­ment	+Loan Repay­ment +Inter­est Charge	-Loan Repay­ment ?Inter­est Charge
Pay Firm Deposit Inter­est				-Firm Inter­est		+Firm Inter­est
Pay Work­er Deposit Inter­est					-Work­er Inter­est	+Work­er Inter­est
Hire Work­ers				+Pay Work­ers	-Pay Work­ers
Work­ers’ Con­sump­tion				-Work­ers’ Con­sump­tion	+Work­ers’ Con­sump­tion
Bankers’ Con­sump­tion				-Bankers’ Con­sump­tion		+Bankers’ Con­sump­tion

Write out the intan­gi­ble assets and you get this:

	Assets	Lia­bil­i­ties		Equi­ty
Oper­a­tion	Loan Ledger	Firms	Work­ers	Safe
Lend Mon­ey	+Lend Mon­ey	-Lend Mon­ey
Charge Inter­est	+Inter­est Charge			-Inter­est Charge
Repay Loan and Inter­est	-Loan Repay­ment ?Inter­est Charge	+Loan Repay­ment +Inter­est Charge
Pay Firm Deposit Inter­est		-Firm Inter­est		+Firm Inter­est
Pay Work­er Deposit Inter­est			-Work­er Inter­est	+Work­er Inter­est
Hire Work­ers		+Pay Work­ers	-Pay Work­ers
Work­ers’ Con­sump­tion		-Work­ers’ Con­sump­tion	+Work­ers’ Con­sump­tion
Bankers’ Con­sump­tion		-Bankers’ Con­sump­tion		+Bankers’ Con­sump­tion

So as you can see the bal­ance sheets that ‘cre­ate’ and ‘destroy’ hor­i­zon­tal mon­ey are con­sis­tent with the one where hor­i­zon­tal mon­ey mere­ly changes state to dor­mant, and the dif­fer­ence is sim­ply to intro­duce an account­ing pol­i­cy requir­ing an intan­gi­ble asset to rep­re­sent poten­tial loan capac­i­ty that cur­rent­ly isn’t in cir­cu­la­tion.

This is a very sim­i­lar to the approach tak­en in account­ing under IFRS 3 when report­ing pur­chased good­will. Pri­or to 2005 pur­chased good­will was writ­ten out of the bal­ance sheet and essen­tial­ly com­bined with the intrin­sic good­will of the pur­chas­ing busi­ness. After 2005 it had to be car­ried explic­it­ly on the face of the bal­ance sheet. To get to the pri­or posi­tion you just take a IFRS 3 com­pli­ant bal­ance sheet and write out the car­ried good­will.

But what ben­e­fit does car­ry­ing the amount of ‘poten­tial loans’ give us in the mod­el? Well it helps to show how ‘hun­gry’ a bank is to lend. A bank with a high val­u­a­tion on its cred­it licence has a lot of capac­i­ty to make loans, where­as one with a low val­u­a­tion hasn’t. It is very like­ly that the first is going to be sell­ing loans as hard as its can where­as the sec­ond is more like­ly to be putting its efforts into lob­by­ing reg­u­la­tors to relax the cap on its lend­ing capac­i­ty.

As I see it, the key point from the expand­ed mod­el is that although it is easy to add cred­it poten­tial to a sys­tem, it is some­what more dif­fi­cult (and may even be impos­si­ble in prac­tice) to get rid of it again as it embeds itself deeply into the dynam­ic struc­ture of the sys­tem.

In addi­tion, by explic­it­ly record­ing the val­ue we can graph it over time and see how close to poten­tial the econ­o­my gets, and as the mod­el evolves we can com­pare dynam­ic caps on the cred­it licence to sta­t­ic caps and see what effect they have. Par­tic­u­lar­ly as our cur­rent cred­it licences in the real world are linked to the amount of ‘reg­u­la­to­ry cap­i­tal’ a bank has and are there­fore dynam­ic in their own right.

So whether you use an expand­ed bal­ance sheet for your hor­i­zon­tal cir­cuit or a col­lapsed one depends on what you’re try­ing to find out with your mod­el.

I’ve cre­at­ed the dou­ble entry mod­el using the QED pro­gram from Steve’s site (which is based on the sim­plest sta­ble mod­el cre­at­ed in Steve’s crash course lec­ture.). QED likes to see things pos­i­tive (or it suf­fers an asser­tion fail­ure), so the lia­bil­i­ty side has all been mul­ti­plied by ‑1 com­pared to the tables above.

The dou­ble entry mod­el con­verges nice­ly and ends up look­ing like this (click for the full size ver­sion):

Where­as the orig­i­nal mod­el end­ed up like this:

As you can see the fig­ures con­verge to the same val­ue — demon­strat­ing that they are the same mod­el at this lev­el of dynamism. The dou­ble entry ver­sion shows the cir­cu­la­tion between the assets and the lia­bil­i­ties hap­pen­ing sep­a­rate­ly (although in step of course) once the cred­it licence has cre­at­ed the ini­tial stock of cred­it mon­ey. And if you add up the pots in each cir­cu­la­tion at any point in time the total stocks should be the same val­ue. The bal­ance sheet now bal­ances as it should.