Monday, 9 January 2012

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.

  2. 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.

  3. 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.

  4. 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.