Wednesday, 22 April 2015

Rising inequality explained (not using r-g)

Using a stocks model to demonstrate how inequality and secular stagnation are the same thing, and how both are caused by high private sector debt

In my last post, I set out a 'stocks' model of the economy. The 'flows' part will follow, but in the mean time I wanted to use the model to show the reason, in my opinion, for the build up of inequality. This is actually the same as secular stagnation and I hope to show how these are the same thing. It is an inequality between those with savings and workers.

Please look at my earlier post here before starting, showing the empirical cost of private sector (and to a lesser extent government) debt. It is very high; each 10% of GDP increase in private sector debt is associated with a reduction in GDP growth by 0.15% per year every year going forwards. Considering we currently have over 200% of GDP in private sector debt in the UK, one can see that this is a potentially a large problem. This model provides a framework explaining why.

Going back to my previous post. I define the model (and it is really very simple) as this:

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 in 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 was 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) 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)

I will now take the concept of Reasonably Serviced Liabilities further. I will define it as the liabilities which can be serviced by the people of the country without an increase in debt whilst still allowing growth.

I will also define here that the 'savers' are the people holding the equities, the debt and having money in the bank. And the 'workers' are the people who have the liability to pay them in the future.

Now, using this model we will go through what I see as the main problem with the economy at the moment.

Let's start the clock 30 years ago, when Marty McFly was about to get in his time machine. I choose this particular year arbitrarily but it was a time before the recent explosion of debt. In the city, men with bowler hats could still be found, and finance was just taking off. Although hover boards and self lacing shoes have still not become ubiquitous, the economy has changed greatly since then.

Here is a representation of an economy at the start of the series. At this time, imagine that on my model we are in an equilibrium. By equilibrium, I mean that the servicing of the debt and equity by the workers of the country was not causing an increase in debt. Or put another way, net savings were not increasing. 

As an aside, please note that in a closed economic system if anyone wants to save more money then, if GDP is not to shrink, either the central bank must produce more cash or someone must go into debt. The other option is that GDP shrinks, forcing lower savings on to everyone else to make up for the higher savings of the extra saver. For an economy to be in what I call equilibrium, then, there should be no net savings.

Now, imagine in 1985 that this equilibrium was broken by some people borrowing to buy new cars and houses. What would happen. According to my empirical evidence, for 90% of that money debt would replace equity (it is not spent in the economy) and 10% would Be spent in consumption and just cause an increase in debt. Debt would go up, and the total future liabilities would thus have risen by the amount of debt that did not replace equity.

However, the RSFL would not have gone up. It would be the same; as there is nothing that would improve future growth in what has happened.

The system is now out of equilibrium. And unfortunately in this system, unlike normal macroeconomic models, there is positive feedback rather than a stabiliser that returns the model to equilibrium.

What does this mean? The savers have now saved more and are now receiving more in dividends and interest from the workers. The holders of equity and debt, the savers, tend to be the richer members of society, the payers of the interest and dividends tend to be poorer members of society. The savers tend to spend a lower proportion of their income on consumption, the workers a higher proportion.

So in the next year, the demand for consumption in the economy has gone down by the change in interest and dividends paid multiplied by the differences in the two marginal propensities to spend. More simply put, there is less demand.

Also simply put, the (on average) richer have put some more savings away, the (on average) poorer have gone more into debt.

The next year, 1986, may see more people borrowing money that then flows through to consumption. But now, more borrowing is needed in order to replace the demand lost by the extra debt servicing costs. After this year the gap between liabilities and RSFL has risen.

Next year, the larger gap means that more needs to be borrowed. Standard macroeconomic policy will say to reduce interest rates to make up for lost demand. This does increase GDP, but does so with more borrowing.

This continues for 30 years. The gap between what can be reasonably serviced and the actual liabilities grows each year. Whenever growth slows, interest rates are lowered.

On top of this, the rise in debt has led to a worldwide rise in house prices. The unaffordability caused by this has dragged up rents. Thus now even equity can take more than can be reasonably serviced. Recently, corporate profits have also been rising as a share of GDP, having a similar effect. Both of these increase the savings rate. And as we have seen, an increase in the savings rate by definition means an increase in the debt rate.

Now, it is important at this stage to show the difference between debt and equity. Whilst it is possible for equity to take from people more than what is reasonably serviceable, it is a lot harder. Equity is a share of profits and if profits go down then so does the amount going to equity holders. Debt, however, while possible to write down is a lot more difficult. Debt will only be written down when it is impossible to pay. Equity will be written down when ability to pay goes down.

So when there is a market crash, the following happens (assuming RSFL was the same as future liabilities at the beginning):

The expected value of all future economic activity goes down and so the RSFL goes down. The equity shrinks a lot. The debt, though, does not go down much.

This is why debt is so much more dangerous than equity after a crash. It does not shrink as much and it makes unreasonable demands on the workers of the future.

On top of this, too much debt is often the cause of the crash in the first place; a self-perpetuating asset price rise spiral which feeds off debt and causes more debt.

Where we are now

The upshot is that after 25 years of rising debt followed by a major crash, our situation looks like this. 

2015 figuratively

The savings have been going up and up. The rich have been getting richer and richer. Every year, the transfer of more and more expenditure to the savers - funded by the taking out of more debt - has caused a huge build up in savings.

But the ability to pay has shrunk. Because the amount that is reasonably serviceable is so much smaller than the actual liabilities. Workers are paying so much of their economic output in dividends, rents and interest that there is not enough left to spend in the economy.

What does this mean for interest rates? They are at zero officially but in real terms for borrowers they are still much too high. The cost of servicing current liabilities means that, if nothing changes, demand will be weak for a very long time and we are condemned to slow growth going forwards.

Government bonds give negative real and sometimes even negative nominal yields. Why? Because there is very little growth expected in the future. Bond and equity prices are going up because, realising that there is no economic growth to look forwards to, savers are eager to get whatever they can. The risk premium has gone down. The smaller and smaller pot of future earnings is being divided between a larger value of total assets.

Even with official interest rates at zero, there is still no investment. Why? Because there is the collective feeling that the return for doing so will not be high enough to cover the real interest paid. Economic growth in the future will not justify the outlay now.

In one way, the rise in asset prices has made the savers (typically the richer) richer. But in another way, they do not have a claim on any more of the future work, except where, for example the rise in property prices actually drags up rents to make them less affordable. But the claim that has already been amassed on future workers are much too high already. 

This is secular stagnation. 

We are now at a stage, due to savings increasing year on year, that the rich are richer than ever in living memory. This is how I would explain the rise in inequality, and it is not because  r > g, it is because (r*D + d* E) > the amount that is reasonably serviceable.

The solution

We are in a spiral of weak demand, increased savings and then even weaker demand. This spiral needs to be broken out of.

What is the solution? This is from my previous post:

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.

So actually to reduce inequality, you don't necessarily have to tax the highly mobile rich that are so difficult to pin down. What you need to do is change the distribution of liabilities from:

2015 figuratively

to the far more healthy:

Using just methods a) and b) above one could affect a large change. One could also add pure stimulus spending in the form of helicopter drops to this, if there were not enough investment opportunities.

Although no-one would actually have less money in nominal terms, the servicing costs of the liabilities would be so much lower that the workers would have much more money in real terms, and the savers would have a far smaller claim over the work of others in the future. Effectively the problem would have been solved by two methods: 1) inflation would erode some of the savers' savings and 2) economic growth would increase the workers' earnings.


  1. this is excellent.
    I agree we need productive deficit spending financed interest free by the CB.
    BUt having read this article and
    I wonder what other policy proposals would you look at to address demand leakages created by interest claims on the productive economy.

    I´ve come across a group called ,mathematical perfected economy founded by mike montagne.
    They advocate a system which would introduce a public agency to monetize people´s promissory notes interest free. Consequently there would be no interest claims on the productive economy, This would lower the cost of everything,as people would only have to pay back principal.It would also address the demand leakages you have cited, as income could be spent on consumption,not interest payments.They also explain that this would eliminate both inflation and deflation.
    I would be interested to hear if you corroborate their math, and what your view on their proposals and views and positions on inflation and deflation.And whether you think it has any limitations or is more sustainable than the status quo
    they have a fb group,and some websites (check out the mathematics page)


    1. Thanks Jake,

      I've been to the facebook page, and it is difficult for me to find the actual idea that you are discussing. Reading posts by Adriano Lorenzo, I do find the language quite inflammatory, as well as his attack on Steve Keen completely unjustified. He may well be unrepresentative. But overall I am not sure he understands the mechanism by which money is created.

      In any case, I do not wish to criticise others - I only do so in reference to his attack on Steve Keen, who, in my opinion, perfectly understands these matters.

      In terms of the idea, it is effectively a writing off of all debt. If no interest is payable ever then there is no need to ever repay the principal. I would need to be convinced here that this transfer of wealth from savers to borrowers is justified. It appears to be pretty extreme to me.

      Anyway, I haven't read the full idea so maybe should not be commenting on it. The principle of reducing debt money relative to base money (in a way that does not involve more saving) is one that definitely needs to be included in the solution to this problem.

  2. Thanks for having a look

    try using this,it hashes it out.:


    But the crux of their idea is this:Their Fundamental ideas is to provide the public with a "Common Monetary Infrastructure" which allows people
    to monetise their promissory notes (normally written up for bank mortgages) into fungible exchangeable currency.
    This public entity will allow people to issue their own credit interest free. All self issued currency(principal) would be paid back or retired from circulation back to the CMI, at an agreed upon rate(the rate of consumption and depreciation of the property). The "CMI" would publish the funds so that the "obligor" could pay someone for his property. But Then the "obligor" would retire down the principal so that they would be extinguished. The rate of payment would be the same as the rate of consumption, so typically a $100,000 property would be consumed over 100 years, and the obligor would only have to pay $83.33 a month.

    The 'borrower' is obligated to retire the principle on a scheduled basis at a agreed upon rate,the rate of consumption/depreciation.So they would have to repay the principle over a period of time in monthly segments

    The only debt that will be written off is the interest part of the debt, whereas the 'borrower' is still liable to repay the principle. However many over indebted people having already repaid the principle many times over,so some people's mortages could end up being written off.

    'It addresses the issue of demand deficiency created through interest claims.Which you point out here are cumulative "But now, more borrowing is needed in order to replace the demand lost by the extra debt servicing costs. After this year the gap between liabilities and RSFL has risen"

    In regards to you point about savers; in the sense that banks generate deposits in exchange for people's promissory notes and then charge interest on it,no real savers miss out.(correct me if I am wrong)

    so these ideas would directly address demand deficiency created by interest claims and hoarding, by removing interest costs from the credit creation process .As opposed to just compensating by using CB created money and government spending to fill the demand gap.

    maybe the maths aspect would be of interest


    1. Hi Jake,

      I have great misgivings about this idea - which I may not have fully understood. I am not even sure where to begin.

      Although I agree that interest is a large cost to society, there is only one thing worse than having too much interest and that is having no interest at all.

      One problem is that a zero interest rate encourages speculation. It also means that there is no limit to the amount of money that can be created for free. I don't see how this can be avoided. This means that we will get a huge inflationary spiral of asset prices and huge increase in money supply leading to hyper inflation in goods. When giving out money effectively for free this can not be avoided. The presence of interest prevents this.

      People who borrowed early would get huge windfall gains as everyone started following suit and paying more and more for their property as it would be so cheap.

      Interest rates are required to prevent a build up of credit. But also, we need to find another way of putting money into the economy to replace credit. The MPE credit is one way of doing this but it is uncontrolled and will lead to misallocation of resources.

      Unless I have completely misunderstood it it appears to be a completely impractical solution. Much better to get the economy back to one where debt is a much smaller share of GDP, bankers and rent seekers get a smaller share of the pie and house prices etc are more affordable. To do this we need considerably larger government deficits and actually higher interest rates. And in my opinion, these government deficits should be partially monetised to increase the amount of sovereign money vs debt money.


  3. that is an interesting criticism of the mpe model.My intial response would be to advocate a land value tax, to prevent prevent property price inflation and land speculation.Although that georgist approach is not part of the mpe program.

    I believe the mpe proponents would argue that true cause of inflation is the increasing costs of debt servicing incurred by interest charges,forcing everybody to push up prices to meet those costs.They also have this interesting ratio rule,I have just come across a more succinct explanation here .The group’s critique of how interest servicing takes up more and more of circulation flows is exactly the same as yours.

    But more generally,It strikes me that the optimum system would have no “unearned income” or “rents” in it. Even Keynes sought to eliminate these rents,in his piece euthanasia of the rentier:
    “Now, though this state of affairs would be quite compatible with some measure of individualism, yet it would mean the euthanasia of the rentier, and, consequently, the euthanasia of the cumulative oppressive power of the capitalist to exploit the scarcity-value of capital. Interest today rewards no genuine sacrifice, any more than does the rent of land. The owner of capital can obtain interest because capital is scarce, just as the owner of land can obtain rent because land is scarce. But whilst there may be intrinsic reasons for the scarcity of land, there are no intrinsic reasons for the scarcity of capital.”
    Would you consider interest unearnt rent ?

    I agree with overt monetary(Central bank) financing of government deficits. But It strikes me that no public debt issuance would be better than higher interest rates. High interest rates are just a public subsidy to financial institutions, by providing them with a safe income yielding asset to park their funds.Why not simply prevent asset price inflation (affordable house prices) through a land value tax,and completely do away with speculative investments.By steering credit towards socially useful and productive investments to the real economy through,high capital gains taxes on financial assets and securitiesand/or capital controls.We need to direct credit to tangible capital formation which increases economic output.


  4. * I meant credit guidance not capital controls.

  5. Great post today. An interesting read for any person who would agree with your views. Long may these posts continue.


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