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

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Neil Wil­son is a UK-based  finance and infor­ma­tion sys­tems pro­fes­sional who blogs at 3Spoken.co.uk, and who is an active par­tic­i­pant in mon­e­tary debates. He has just pub­lished a post where he takes my “God­ley table” mod­el­ing approach and rejigs it to make it con­sis­tent with dou­ble-entry book­keep­ing stan­dards.

I am no accountant–I never stud­ied account­ing at uni­ver­sity (I did an Arts/Law degree as an under­grad­u­ate, major­ing in Eco­nom­ics with minors in Maths & Psy­chol­ogy), and have never had to develop the skills subsequently–so I am happy to take advice from some­one like Neil about how to con­form to proper dou­ble-entry stan­dards.

Neil notes below that a num­ber of mon­e­tary the­ory types rejected my model out of hand because it didn’t con­form to those standards–and they there­fore assumed it had to be intrin­si­cally wrong.

I, on the other hand, devel­oped these mod­els in the first instance as sys­tems of dif­fer­en­tial equations–an area where I do have some training–and was con­fi­dent they were cor­rect.

Neil decided to see whether the basic Cir­cuit model (as out­lined in Debunk­ing Eco­nom­ics II and this down­load­able aca­d­e­mic paper) could be expressed in proper dou­ble-entry-book­keep­ing form. His end con­clu­sion was yes: the model could be rejigged into dou­ble-entry form, and the result­ing sim­u­la­tions were numer­i­cally iden­ti­cal.

In a future post, Neil and I will jointly extend this research–including pub­lish­ing the sys­tem of equa­tions that result. But in the mean­time, I’m very happy to cross-post Neil’s blog entry here.

A Double Entry View on the Keen Circuit Model

Over the last few months I’ve enjoyed Steve Keen’s lec­ture series on You Tube, which are def­i­nitely rec­om­mended for any­body want­ing a solid under­stand­ing of why neo-clas­si­cal macro­eco­nom­ics is com­plete bunkum.

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.

About Steve Keen

I am Professor of Economics and Head of Economics, History and Politics at Kingston University London, and a long time critic of conventional economic thought. As well as attacking mainstream thought in Debunking Economics, I am also developing an alternative dynamic approach to economic modelling. The key issue I am tackling here is the prospect for a debt-deflation on the back of the enormous private debts accumulated globally, and our very low rate of inflation.
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  • glu­bilee

    @Alainton, two more years of delever­ag­ing in u.s. is not “all but over”…if I fol­low Steve’s points, which is a stretch, it’s the rate of delever­ag­ing that is impor­tant and this arti­cle does not address that. Two more years of decel­er­a­tion could be still pretty brutal…and our man­u­fac­tur­ing sec­tor has really roared back, if allour cus­tomers are just start to delever­age, ouch.

  • Ted Stead

    @Tel, seri­ously, that web­site is a joke, surely — “We’ve been max­ing out a new credit card almost every year, even in the good times. If a com­pany were run like this, it would have long been declared bank­rupt.” Some peo­ple prob­a­bly take that kind of non­sense seri­ously…