Negative Money

This post is just for fun – or negative fun – or something.

It follows from a Nick Rowe post with the same title:

I’m going to tell a story that should be similar in concept to Nick’s, but described in quite a different way. I think it should end up in about the same place as a platform for discussing the issues that Nick is interested in. Or maybe not. But anybody who is interested can compare the two.

So, imagine a simple two sector model of the economy – the government and the private sector. There is no central bank and no commercial banking system. Forget about the foreign sector. This is a pure outside money model – no inside money or inside financial system for that matter.

Now consider two different scenarios or ‘worlds’:

a) The positive green money world – the government runs a deficit and funds it by issuing so called positive or green money. The government balance sheet consists of a net liability position composed of green money claims. Green money is a government liability and a private sector asset. The private sector balance sheet in aggregate consists of real assets, green money assets, and equity or net worth on the other side. A constraint is imposed in which individual agents are prohibited from incurring expenses that drive their green money balances negative. This maintains the purity of the green world. There is no red money contamination.

b) The negative red money world – the government runs a cumulative surplus. The government balance sheet consists of assets which are claims on the private sector matched by an equity position on the other side. The asset claims are a form of money called negative red money. Red money is a government asset and a private sector liability. The equity position of government reflects the surplus accumulation from net taxation. The government has in effect acquired assets with the proceeds of surplus taxes. Operationally, it has credited the private sector with negative red money balances as acknowledgement of taxes paid. The private sector balance sheet consists of real assets, red money liabilities, and equity. A constraint is imposed in which individual agents are prohibited from attracting revenues that may drive their red money balances positive. This maintains the purity of the red world. There is no green money contamination.

In the green money world, tighter fiscal policy in the form of lower deficits results in lower green money creation and therefore tighter monetary policy. Fiscal and monetary policy are directly correlated in the green world.

A cumulative balanced budget is the inflection point between the green and red money worlds.

In the red money world, tighter fiscal policy in the form of higher surpluses results in more red money creation. Given the constraint on individual agents that disallows the existence of green balances, higher negative red money balances would seem to allow more room for payees to receive larger money balances per payment, without violating the prohibition against the creation of positive green money balances. This accommodates higher value transactions at lower velocity. That is an easier monetary policy. Thus, fiscal and monetary policy in the red world would seem to have an inverse relationship with respect to policy tightness. The tighter the red money fiscal policy, the easier the monetary policy.

At this point, I depart from Nick Rowe in how payments are described, but the overall result should be the same in effect:

Agents in both worlds make payments using positive money in exchange for goods and services that flow in the opposite direction. This is obvious in the green world. But it is also the case in the red world. An agent who makes a payment from a red money balance will make his red money balance more negative and make the payee’s red balance less negative. That takes a flow of positive money. The restrictions in the red money world that preclude green money balances mean that this positive money flow cannot manifest as a green balance. But it is still a positive money flow. A payer’s drawdown from an opening red balance that makes it more negative is not inconsistent with the interpretation that he is transacting in positive green money. The flow of funds in the red money world is denominated in green money, even though balance sheets never reflect green money balances.

So, depending on the chosen world, stocks of money balances can be green or red. But money flows are always green. And agents pay for goods and services with green money in either the green or red worlds. It’s just that green flows are not allowed to manifest as green balance stocks in the red world.

(Nick characterizes his red money world as follows: “In the red world, if I sell you apples, you agree to take my red money in exchange. Goods and money flow in the same direction around the economy.” That is opposite to what I’ve described, because Nick characterizes payments as a flow of negative money from negative balances that makes them less negative, whereas I characterize them as a flow of positive money from negative balances that makes them more negative. This difference also carries over to the characterization of the velocity equation, below. But apart from that, the models shouldn’t be inconsistent.)

Define the money supply in each of these green and red worlds as the absolute value of money balances. A halving of money supply in the green world is clearly a tightening of monetary policy. And the same holds true for red world. It is the absolute value of the money supply in either world that determines monetary tightness – in the green from the perspective of the constraint on the payer, and in the red from the perspective of the constraint on the payee. Velocity can be determined as the turnover of money stocks in either world.

MV = PY holds in both worlds

P is always positive – real goods and services require positive value in exchange

(Nick goes with negative P in the red world.)

M is the absolute value of money balances in either world, consistent with the transactional flow of green money in exchange for real goods and services in either world.

There is a third world:

c) The green/red mixed world – this is the world in which green and red balances co-exist. Green payers are permitted to go into deficit, incurring red money balances, and red payees are permitted to go into surplus, accumulating green money balances. The government accommodates both red assets and green liabilities on its balance sheet. It’s net balance sheet position in green liabilities and red assets will correspond to its net deficit or surplus position over time. Given the additional flexibility this allows for private sector payment patterns, this relaxation of the green/red world bifurcation might be considered to be a further easing of monetary policy, other things equal.

But how do we determine money supply and velocity in this mixed world?

For example, suppose the government runs a deficit, with green liabilities exceeding red assets.

The aggregate net green position (green less red) is constant – other things equal – unless the government changes its cumulative fiscal position with a net green current fiscal deficit or a net red current fiscal surplus. In other words, the government controls the net position.

But other things equal, the private sector can expand its gross positions with red creating green (e.g. a red payer pays a green payee, which expands both gross positions in their respective directions) and can contract them with green destroying red (e.g. a green payer pays a red payee, which contracts both positions in their respective directions).

What is interesting about this aspect is that it introduces an endogenous money component to what is a pure outside money system. The government controls the aggregate net green/red position as described through its fiscal policy stance. This is an exogenous determination of government relative to the private sector. But individual private sector agents can expand or contract the gross positions that make up that aggregate profile, as just described. That is an endogenous determination of the private sector. So the government controls the net profile; the private sector controls the gross profile within the net constraint.

This is only a skeleton model. There are of course other potential considerations. Does the government constrain red money accumulation through credit limits? Etc.

In any event, in this net green example, it seems natural to attribute the gross green position as “the” relevant money supply at any point in time. It includes the amount of matching green and red gross positions that are in excess of the net green position. That full gross position is of course dynamic as it can be changed momentarily by either endogenous private sector payment patterns or exogenous government sector fiscal effects.

Similarly, the money supply for a net red surplus world in this mixed model context would be the full gross red position.

So velocity can be determined according to that definition of money supply, with all payments being treated as green as described earlier.

Nick Edmonds also posted something in reaction to Nick Rowe’s post:

As I understand it, Nick E constructs a refinement of Nick R’s story, with an emphasis on the question of money velocity. The main differentiating factor seems to be that Rowe constructs a pure outside money model and Edmonds constructs (I think) a pure inside money model. I left a rather lengthy comment at Nick E’s post regarding his model, capturing a number of the same ideas in that context that I’ve included in this post as they relate to Nick R’s model:


I think the green world / red world balance sheet construction above was inspired at least in part by my reading of Godley and Lavoie’s model SIM treatment (at least the green half, which makes the flip bizarro red world version easy).

There is an interesting analogy between the green/red world distinction and something else that Godley and Lavoie touched on. That is the existence of a particular type of distinction in central banking regimes – asset based systems versus overdraft systems. In an asset based system the central bank acquires financial assets such as Treasury bonds in order to provide the reserves to the banking system that ultimately enable commercial banks to pay for the central bank notes that they provide to their customers. In an overdraft system, the central bank lends to the banking system for the same purpose. Apart from all their other differences, the US Fed system is an asset based system (most clearly viewed as such on a pre-2008 footing) and the ECB system is an overdraft system. The non-bank red money world described above is somewhat analogous to an overdraft system in real world central banking. In the model I described above, the red money assets of a government in surplus provide a type of overdraft financing to the private sector in the form of those same private sector red money liabilities.


My own view is that the medium of exchange in all cases in the models I described is green money. Even though green money never exists in stock form in the pure red world, it does exist in flow form according to my description of it. The fact that green balances don’t exist in stock form in the red world is only the consequence of an imposed balance sheet constraint that prevents green flows from manifesting as green stocks.


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Nick Rowe
3 years 1 month ago

JKH: sounds good to me!

Two quibbles:

1. You make no distinction between government green money and government green bonds. A cumulative government deficit is financed by a stock of green “money”. OK. (Not my preferred assumption, but I can run with it.)

2. “Agents in both worlds make payments using positive money in exchange for goods and services that flow in the opposite direction. This is obvious in the green world. But it is also the case in the red world. An agent who makes a payment from a red money balance will make his red money balance more negative and make the payee’s red balance less negative. That takes a flow of positive money.”

I see your logic, but it sounds a bit weird to me. I see negatively charged electrons flowing one way around the circuit in the red world, and you want positively charged current flowing in the opposite direction. The two are logically equivalent, but mine seems more “natural”, because there is a symmetry with the green world. But it shouldn’t make any difference.

(Great to see you joining me on the dark (negative) side!)

3 years 1 month ago

Thanks Nick.

I just used money financed deficits or money financing surpluses as the simplest cases to distinguish between the two types of money.

Regarding the payment orientation – the asymmetry is rude, but I think it works. The easiest way to make the point is an example of a payment that produces an overdrawn deposit account in one bank and a positive balance in another bank. So there is a flow of positive money to be gotten from a red account in that example. It’s just the restriction in the purely red world that prevents that positive money flow from becoming a positive balance there. It works in accounting too. A “credit” to an overdrawn account can result in it still being overdrawn – but it’s the same credit that might cause another account to be positive. So I think it’s the restrictions on the stock balances as opposed to the substance of the flows that can make it appear otherwise. But it can be done either way in the case of a purely negative money world.

Symmetry is a funny thing – depends how you look at it – so it is with monetary realism and monetary unrealism.


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