Sunday, 19 April 2015

A Simple but Helpful Model of the Economy using Stocks and Flows. Part 1; Stocks.

Or: 'Why we need to print money to get out of the economic stagnation'

The part to get out of the way early:

1) I am not an economist or an accountant, so the definitions I use here will probably make some people irritated. But please look beyond this failing as I think that it is worth it.

2) This is all my own work, but, having said that, it is a simple model. I have no doubt that this has been done before. However it is not widely used, as the conclusions reached herein are not widely accepted. 

Also, this is a first draft. I welcome any comments on errors.


This model is intended to be based on accounting identities. In that sense, unless I have made an error in how I set it up, it must, by definition, be correct. I will set up the first part of the model here, and then go through how it can be used to look at the economy.

The idea comes from a system dynamics set-up, in which there are 'Stocks' which are the levels of things (eg. how many fish in a lake) and then 'Flows' which are the changes in these levels (eg. how many fish are caught by fishermen each year). Here I will be modelling at first a closed system (the world) and then later I will look at systems with impacts from external sources (individual countries).

I will begin by defining three assets that will represent in total all assets that can be held.

1) CB Cash:  This is central bank produced money, net of any debt. This is actually only a small proportion of the total cash in bank accounts - the rest is loaned to some other party and thus cancels out for this purpose. Whereas private bank created money is liable for interest, cash from a central bank is assumed to be liable for no interest as it is not a loan. 

2) Equity: This includes everything that isn't debt. So property and shares on companies are the main constituents of this. It also includes paintings and truffles. Holders of equity receive dividends or rent, and for simplicity we will call this 'dividends' from now on. This value of equity is net of debt held by companies and minus the cash held (the cash is counted in the other two parts).

3) Debt: This is government debt, private bank produced debt (total money in bank accounts minus the 'CB Cash' above), corporate debt etc. Holders of debt receive interest - or in some cases, the banks receive interest on their behalf and keep it for themselves. In any case, the borrowers pay interest.

This is the asset side of the balance sheet. One could describe this as all together as Savings. 

I also wish to define a liabilities side of the balance sheet. This has one entry:

Future Liabilities: This is the liability that future people in the country have to the holders of assets above. For example, if someone were born today, with no assets, then they would have to work in return for cash paid out of current cash stocks held by someone now. They would have to pay rent to holders of housing equity. In general, all of the value of current assets must, as an identity, come from work done by people in the future.

Future Liabilities = CB Cash +  Equity + Debt

I would also like to add on extra idea to this:

Reasonably Serviceable Future Liabilities (RSFLs): This is the amount of money that can be reasonably expected to be taken from the work of people in the future. For example, if they create £100 of economic output, it may be reasonable that they pay dividends (to the owners of the company that employs them - this is taken off before they get their salary), rent and interest of £40. I don't know exactly what this figure is, but it is somewhere between 0 and 100% of future economic activity. The 'coefficient of Reasonableness' (coR) will need to be empirically determined. The total amount is a function of future GDP as well as the proportion of assets that are in equity (E) and debt (D) and interest (r) and dividend rates  (d) per year on these.

As an approximation, the amount paid, P, per year, is given as:

P=(r*D +d*E) / GDP                            (1)

The Reasonably Serviceable Future Liabilities (RSFL), if the one year amount is is extrapolated, are then:

RSFL = (Future Liabilities)*coR/P           (2)

One may ask the question, why is there a level that is reasonably serviceable? After all, interest and dividends are only transfers from one person to another. The reason is that the payers of the transfers tend to be those with a high propensity to spend, and the receivers tend on average to have a low propensity to spend. Transfers of this type take demand away from the economy.

The gap between the spending of the two parties is given by the marginal propensity to spend of workers minus the marginal propensity to spend of savers (MPSw - MPSs) - it is assumed here that workers spend more than savers.

The cost to the economy, in terms of lost demand is:

Cost in demand = (r*D +d*E)*(MPSw - MPSs)

So, getting back to the model, we can set up this very simple model as Assets and Liabilities - which obviously must be equal to each other. We will also assume, in this initial example here, that the economy is healthy and that these liabilities are reasonably serviceable. 

Please note that although assets and liabilities may not look equal to each other thanks to the formatting, they are always intended to be.

The future liabilities do not need to be 'Reasonable', however. They can be higher or lower than 'Reasonable'. When they are higher they place a real drag on the future economy, when they are lower they give a boost. This is the conclusion of my previous post, looking at the drag on the economy of too much debt, and the logic here will be explained in a future post, the Part 2 of this model, 'Flows'.

However, with just this extremely basic 'Stocks' framework, we will be able to model many macroeconomic scenarios. 

Private Banks Creating Money

When a private bank makes a loan, it increases the amount of debt in the country. Often, in real terms, value of the future liabilities remains unchanged; it only alters the composition of the assets.  In most cases it replaces equity because, for example, if a company takes out debt and buys back shares then the net equity (equity minus debt minus cash) goes down by the amount of the debt taken out. If a homeowner uses a mortgage then, again, equity minus debt also goes down with the increase.

Here, the value of the Reasonably Serviceable Future Liabilities will change depending on which is cheaper to service - equity or debt.

There are some examples where increase in private bank debt only increase the debt without any compensating reduction in the equity. For example, if someone took out a personal loan to buy this beauty. If the loan is used for consumption then future liabilities will rise with no rise in Reasonably Serviceable Future Liabilities.

Another possibility is that a company takes out debt and, rather than using it for share buybacks or takeovers, actually invests it in improving the productive capacity of their company. In this case, the amount of equity will stay the same and the amount of debt will go up, leading to an increase in future liabilities. But because of the future increase in economic activity the RSFL goes up too.

Central Banks Creating Money through QE

When a central bank undertakes a quantitative easing programme, then what does it actually do? It temporarily replaces some of the debt with some CB cash. This means a temporary reduction in the debt and temporary increase in the cash.

We therefore have the following (theoretical) before and after:

The fact that it doesn't actually do anything on this representation, led Ben Bernanke to make the famous joke that "The problem with QE is that it works in practice, but it doesn't work in theory."

All he was doing was replacing debt securities that were easily changeable into cash, for actual cash.  In the Flows section it will be more clear why quantitative easing only causes a minimal increase in inflation and that is caused only by the rise in asset prices and not by the printing of money.

The reason that it worked in practice was the following...

Asset Prices Rising (/Falling)

By buying bonds, the Federal Reserve reduced the interest rates on bonds which led to a rise both in the value of debt and the value of equity (as the required return from equity went down with the bond yield). Future liabilities will hence go up. But, because these are based on lower yields, the total amount paid by future generations does not go up. Hence the liabilities are higher but they are equally affordable.

Assuming the original liabilities were reasonably serviceable, we now have the following before and temporarily after:

A small proportion of the increase in asset prices was then cashed out and spent within the economy, thus giving a stimulus to demand at a time when it was needed. This is the reason that QE worked in practice but not in theory.

More generally, asset prices and therefore future liabilities can rise (in real terms) for three main reasons:

1) The expected total future economic return is higher than previously thought. Higher economic growth is expected, therefore the reasonably serviceable amount of interest and dividends go up.

2) As in the example above, a lower interest/dividend rate is required. So the same economic growth can be split across more value in future liabilities now.

3) The expected share of the economic return paid in interest and dividends goes up. Although the total economic activity does not go up, the calculation is made that more can be extracted. This has been seen recently where corporate profits as a proportion of GDP have risen.

So, for example, the current equity and debt market rallies are based firmly in reasons 2 and 3. If anything the impact of 1 would have to be assumed to be negative.

Inflation and Deflation

These can be modelled although more needs to be known about the causes to fully understand the impacts. Inflation and deflation, all else being equal, do not affect the future liabilities in real terms. These stay the same. However, they affect the composition of the assets. 

Below I will give an example of how it can be modelled, although different scenarios can be proposed.

Inflation, all things being equal, reduces the value of both cash and of debt. Equity will go up, as the value of debt held by the equity will go down and so net equity will be higher.

If we assume that inflation was caused by increased central bank cash, then cash will go up, debt will go down and equity go up a little bit.

Future liabilities stay the same before and after. But an interesting point is that, assuming that liabilities were reasonable in the 'Before', in the 'After' the Reasonably Serviceable Future Liabilities are higher than the actual Future Liabilities. This is because cash pays no interest and equity share remains the same. Therefore the cost of servicing the liabilities goes down.

Inflation caused by CB cash, before and after:

Inflation caused by greater CB cash therefore reduces the real future cost of servicing the current liabilities.

This reduction in debt share and increase in cash share is great for the future economy for reasons discussed here and here. In summary, one can expect more economic growth in future as less income needs to be paid to the holders of assets, who are less likely to spend. More on this in Part 2.

Inflation due to external causes, which does not increase the cash proportion and reduce the debt proportion, is unambiguously bad, however.

Internal deflation causes the value of cash and debt to go up. In this scenario, since the future liabilities remain the same, the value of equity must therefore go down.

Deflation before and after:

What happens in a crash?

In a market crash, the expected value of all future economic activity goes down. Or possibly the amount of future return required goes hugely up, based, maybe, on a re-evaluation of risk. 

Therefore the Reasonably Serviceable Future Liabilities go down, as do the Future Liabilities. Since the amount of cash remains the same, the equity and debt must fall. Equity takes the main brunt, but there will also be some defaults on debt so we get the following before and after:

This situation is not so bad. The ratio of cash to debt and equity has improved, and the economy has a chance to recover after the revaluation.

However, what if the debt could not be cancelled or if not enough of it was written down? What if the 'After' looked more like this?

In this case scenario, the future liabilities are greater than can be reasonably serviced. I would suggest that this is probably more realistic.

From this, one can see the problem with too much debt after a crash (a crash which often follows from too much debt having been taken out). If the liability was to equity shareholders then the future liability would shrink to the reasonably serviceable liability. But debt is difficult to shrink. Instead of defaulting, society can end up for years paying back more than is reasonable and hampering growth.

I would argue that this situation may be one that we are in at the moment - called a 'Secular Stagnation'.  I will get back to this discussion later in a discussion about the Zero Lower Bound to interest rates and why it is not really a problem.

What happens in a crash in a fixed currency mechanism?

There is an even bigger horror than the above, though. It is called being a Eurozone periphery member in the current crisis.

Here, the crash causes a large reduction in the expected value of the Reasonably Serviceable Future Liabilities. But at the same time the deflation caused (or to be caused) by the attempt to regain competitiveness against Northern Europe in a low inflation environment has led to an increase in the real value of the cash and debt.

This is a representation of Greece's Before and After:

It is a terrible scenario which has led to unemployment and suffering throughout Southern Europe. In effect this shows that, unless the debt is written down, the workers will have to pay a far too large a proportion of their earnings to the creditors. As this takes further demand out of the economy, the situation will worsen. It may have been possible if earnings could grow, but competitiveness has still not been regained and Northern Europe shows no sign of helping in this.

The impossibility of servicing the liabilities, as well as the extreme difficulty of regaining competitiveness are two reasons why I think that Southern Europe should default on debt as soon as possible, before a whole generation of young people suffering from over 50% unemployment atrophies.

The zero-lower-bound problem (or non-problem)

There has been much talk over the last few months about the zero-lower-bound to interest rates. That is that interest rates can not go too far below zero or people could take out cash and store it somewhere where the costs are lower. This puts a limit on stimulus caused by interest rates. In my opinion, this is a ridiculous argument because there is a perfectly reasonable well known for taxing deposits and it is called printing more money. 

I believe that the situation that we are in now looks a little like this:

Here, the Reasonably Serviceable Future Liabilities are lower than the liabilities. Currently debt and equity prices are very high, but a reduction would not help as the dividends and interest would remain the same. 

The problem here is that although the interest rate is officially at zero, no-one can actually borrow at zero so real interest rates for individuals and non-major corporations are high. Corporate profits, due maybe to improved labour saving technology, are also very high. So the amount of income that goes to consumption is too low. This reduces incomes further and the upshot is that even with official interest rates at zero, there is not the incentive to borrow to invest into the economy. It is collectively felt that the return for doing so will not be high enough to cover the real interest paid.

From equations (1) and (2) above, we can see that there are three things that could make the future liabilities reasonably serviceable 

1) Lower interest rates (this suggestion is not helpful here, as we have just discussed)

2) GDP growth

3) Central bank cash to be a larger proportion relative to debt - therefore reducing interest payments

And so actually the zero lower bound is not, in practice, a problem. Possibility 1 may be out of the question, but if one were to 

a) print money and invest it in future GDP growth, either through education, research or capital investment, and 

b) print money and monetise government debt 

then you would be fulfilling options 2 and 3. With the lack of demand at the moment it would probably not be too inflationary - but even if it were, it might not be a bad thing.

The taboo around printing money needs to be overcome. I hope this model helps to demonstrate how the composition of assets is important and hopefully will make a positive contribution to the debate.

My next post, as previously mentioned, will be about 'Flows'; how money moving about can create or take away demand. I haven't written it yet, but I imagine that the conclusion there will also be to print more money. That tends to be my solution to the Secular Stagnation we appear to be in.

Comments would be greatly appreciated here, by the way.


  1. Ari, are you familiar with:

    1. Thanks Anonymous, I will read that. It looks excellent from my brief skimming.

      I am aware of Godley through Steve Keen's work (and of course his prescient anti Euro article in LRB) and I would say that my knowledge of the Godley tables, as well as the work of Michael Pettis is behind this work.

      On reading the textbook, I am not sure if it will turn out that this is a subset of his work. As said, I am not claiming originality here. It would make sense to me that it has been done before, as it is very simple.

      I do think that it is extremely important though that people are aware of the situation and it doesn't seem to be addressed in normal monetary policy.

    2. Ari, I agree with you. It seems to me that you have entered the world of post-Keynesian economics, regarded by mainstream economists as heterodox, a fancy word for heretic. But probably, you already knew that? Another book tip:


    3. Thanks Anton, really appreciate it. I'm buying it now.

    4. And I think that you are right about the heteredox route I am on. But it is a shame that one seems to have to choose a side, rather than being able to take all of the good things about both approaches.

      I read economists whom I respect a lot, and whom I agree with 80% of the time, who just won't look at the issue of debt even though it is staring them so clearly in the face. And I think that it is a shame that a divide has opened up rather than everyone working together to find the best approach.

  2. Could you explain the concept of CB cash a little more thoroughly? I'm having a bit of trouble understanding just exactly what it is. Does it correspond with a specific M-number in the American economy?

    To me, it seems the goal of any economy—using the 'stocks' model here as our conceptual framework—should be a constantly increasing amount of equity and having that equity distributed as widely as possible. Also, keeping equity out of mortgage and preventing its transformation back into debt would seem to be another worthy goal. However, if equity dominated our asset side of the balance sheet—there were no significant debts—it would seem like economic activity itself would decrease or cease.

    Debt—in our framework—is an engine for activity and activity seems to generate the goods and property that we consider equitable.

    1. The CB cash is the monetary base, so maybe this figure here:

      You can see it went up a lot due to QE, and because interest is repaid to the government it does count as a reduction in debt and increase in cash. In theory this is temporary but reversing it is tricky. The problem is that political it is still seen as debt so the federal government can not run the deficits it needs to run for the economy to have enough demand.

      I don't believe that debt needs to be the engine for activity - I think that equity does an equally good job. But I agree that for a variety of reasons, including tax benefits, debt has become the driver. This is no longer healthy because of the spiral of higher debt leading to higher asset prices which then leads to the creation of more debt.


Sorry, I have had to moderate comments because of an annoying pest spammer who keeps posting American football matches links.