Tuesday 22 December 2015

How high could a UK Universal Basic Income be?

Tom Streithorst, in Coppola Comment, discusses the rationale for a Universal Basic Income (UBI). He states that:
It may seem impractical, even utopian: but I am convinced the BIG [UBI]will be instituted within the next few decades because it solves modern capitalism’s most fundamental problem, lack of demand.
It is a view that that I have a lot of sympathy with. There is clearly not enough demand in the economy and this is one way of fixing this. Also, as Streithorst points out, and I discuss here, technology may be improving productivity, but it is up to us to make sure that this translates into improved quality of life for everyone rather than a bounty for the owners of technology and serfdom for the remainder. UBI is one way of distributing the wealth of society more evenly.

When a £72 a week basic income was included in the Green party election manifesto, at a cost of £280bn per year, Natalie Bennett, the Green party leader, was ridiculed for not having details of funding. However, I believe that it is possible and here I propose to work out an approximate level of basic income that would be feasible given that the government is trying to hit a nominal GDP target.

The basis of these calculations is the DBCF model I develop here. This model looks at demand and how targeting of cash flows can influence this demand and hence NGDP. The analysis from the paper is that the UK economy has a structural savings rate of around 3%. This is to say that for every £100 spent on GDP additive goods and services in year 1, only £97 is spent in year 2. The remainder of the demand is made up for  in government deficits and private sector debt.

We currently have a chronic shortage of demand and the UBI can fill this gap. For this reason, and because it has a high multiplier, it is valid expenditure. It can be funded either with a helicopter drop or with government debt; the important point is that a NGDP level is targeted and that it is done responsibly so there is no loss of confidence in the government.

I attach a spreadsheet here with the calculations so any assumptions made can be changed by the reader.

The assumptions are as follows (the reasons for these can largely be found in my paper here):

  1. The structural savings rate in the economy is 3%.
  2. NGDP growth target is 5%.
  3. The multipliers of both UBI spending on NGDP and current government deficit spending on GDP are both 1.
  4. Recipients will be all people 15 years and older.
  5. Current government deficit is 4%.
  6. All UBI is taxed at marginal rates of income tax.
  7. The average marginal rate of income tax is 30%.
  8. The UBI replaces 80% of current pension spending.
  9. The UBI replaces 50% of current welfare spending.
Given all of these assumptions, a viable level for the Universal Basic Income is shown to be approximately:

Note that this level is around the level of the basic state pension, so pensioners would not lose out. This could replace tax credits and also a fair amount of welfare spending (I have put 50% into the calculation above). 

Obviously it would be recommended that this is slowly built up to; the assumptions, especially around multipliers, may be incorrect. But it gives an approximate idea - and I think that this is important.

Tuesday 15 December 2015

Working Paper: The Relationship Between High Debt Levels and Economic Stagnation, Explained by a Simple Cash Flow Model of the Economy

UPDATE: Download latest, Feb 2016 version here. This version contains the derivation.

My working paper, in which I bring together the ideas from this blog in the past year, has now been finished. It is available here (this link may stop working - probably safest to use the above one):

The Relationship Between High Debt Levels and Economic Stagnation, Explained by a Simple Cash Flow Model of the Economy

Empirical data is presented suggesting that high private and, to a lesser extent, public debt levels place a strong drag upon economic growth. A simple, demand based, cash flow (DBCF) model of the economy is developed, separating out flows by marginal propensity to spend. This approach is both logically sound and empirically consistent with the data. It supports a prognosis for the economy and estimate of future NGDP growth. Importantly, it is a model that is flexible enough to incorporate high debt scenarios, and is able to explain the secular stagnation currently experienced by Western economies and Japan. A simulation is also provided to show the danger to stability of allowing private sector debt to fill lost demand. The conclusion is that the zero lower bound has been reached because there is too much private sector debt for the economy to sustain. Demand is perpetually too low because of structural excess saving. The proposed solution is to rebalance the economy using large, preferably monetised, government deficits.

Monday 31 August 2015

Why Shares are too Expensive. And, while we're at it, is the idea that shares always out-perform partly just a historical anomaly?

To start, a disclaimer... this is not a suggestion to trade, merely an observation on the economy and what it should mean for share prices. There is a reasonable chance that I am wrong; I invite you to look at the arguments and decide. And even were I correct that prices are too high, it does not mean that they will come down. In fact they can get a lot higher because, to paraphrase the great economist Hyman Minsky, whenever the market is too high, people are prone to get a little over-excited.

People have been arguing for a while now that shares are too expensive against their historical valuations. Various metrics are used to define this. For example, the CAPE Shiller ratio looks at the price of shares against 10 year trailing earnings. Historically US shares have traded at a median of 16 times earnings. In the past valuations have reverted to a multiple 16, but it is difficult to time this; in the dot com boom it reached almost 45. At the moment the multiple is roughly 25. This suggests that the market would need to drop by almost 40% in order to be fairly valued.

Nonsense, the bulls say. This model is irrelevant. Have you not seen what has happened to government bond yields? A thirty year US treasury now only pays you around 3% per year. The short term bonds pay almost zero. Stocks are cheap because there is nowhere else to get a good return. Central bank action will always support asset prices and they'll just keep printing more money. Even a mediocre return is better than nothing, and stock prices reflect this.

I believe that shares are substantially overpriced based on any normal return expectation. There is an idea that shares always perform well in the long term; this may be true in the very long term but a period of very high growth followed by a series of one-off changes have led to large rises in share values over the past 80 years and these are unrepeatable. I will discuss all this in the rest of the post.

First, the share valuation model. For those unfamiliar with corporate finance models, a share can be valued by taking the sum of all of its future dividends and discounting them to the present. This means that if you will expect to receive £100 in dividends next year, you will value it slightly less than if you had £100 now.

There are two components of this discount. The first is for the interest you could receive if you invested in a risk-free (in most cases) government bond. This means that you need to receive at least the rate of interest you could have got for no risk. The second component of this discount rate is called a 'risk premium'. It is the extra return that you need to receive for taking risk with your money. If one only receives the same as the government interest rate, why would anyone make risky investments? In the recent past the risk premium for U.S. stocks could be reasonably said to be around 4%. So people invest in stocks with the expectation of receiving the risk free interest rate plus a risk premium.

As I show here, in relation to the UK, the total amount of debt has skyrocketed over the past 45 years.  This means that the total gross wealth in financial assets (not including property) has gone up from around 4x GDP to around 13x GDP in the UK (these are approximations). Similar trends are observed internationally. There are therefore a lot more savings than there were before. A savings glut, in fact (which is the same as a debt glut but viewed from the other side). For this reason, I would argue that the risk premium should reasonably be a lot lower than it has been in the past - maybe 2%. This would mean that share prices should be a lot higher than they would be with a 4% risk premium. I am taking this into account and I say that, even despite this, equities are now too expensive.

From here on, I will be looking at the US stock market, specifically the S&P 500 index; the most traded share index in the world.

Since 1945 share prices have been in one long bull market. They have been going up almost relentlessly. This leads to the idea that shares always out-perform bonds or cash in the long term. As I say, this may be true, but in the time period we have seen a number of important changes that have led to one-off increases in share prices.

  1. The reduction in government bond yields - 25 years ago a 30 year government bond paid 8%. Now it is closer to 3%. 
  2. The reduction of risk premium required - in 1990 I calculate the implied risk premium using my dividend valuation model to have been around 2%. Now I calculate it to be 0%
  3. Corporate profits as a share of GDP are at a high since 1945. In fact, the share has more than doubled since 1990. This would mean, all things being equal, a doubling in the fair value of shares.
These three effects would account for approximately a 20 fold increase in the value of shares since 1990. In fact the rise has been only around 6 fold.  As of 1990, the  S&P 500 was trading at around 350; at the time of writing (Aug 15) it is around the 2000 level.

Had these three one-time changes to risk preference and corporate rent-seeking ability not occurred then the stock market would actually have gone down considerably since 1990. 

Since 1990, owning the shares in the S&P 500 would not have been better than owning a portfolio of 30 year bonds. This is despite the doubling of corporate profit share to GDP and reduction in risk premium. This really highlights how poor equities’ performance has been since 1990 (relative to bonds) - and how the great fall in bond yields has managed to disguise this. Perhaps this has convinced investors that equities have a natural right to perform well in the long term.

The reason for this relative under-performance of the S&P 500 has been the performance of nominal GDP.

If the proportion of corporate profit to GDP remains the same, then corporate profit can only grow with nominal GDP. This is an extremely important point that many analysts appear to miss when making earnings growth projections.

Between 1945 and 1990 nominal GDP growth averaged around 8% per year. This means that total profits could be expected to grow by around 8% per year. In this period, there would be every reason to think that shares would keep increasing in value. However, between 1990 and today, GDP growth is closer to 4.6% PA. And in the current period of secular stagnation we may only be able to expect around 3.5%. In fact since 2008, we have averaged 2.7%.

Taken in conjunction, the change in the expected nominal GDP growth from 8% to 4.6%, along with points 1-3 above can account for the change in value of the S&P 500 since 1990.

Since 1-3 are one-off events, I would argue that there has actually been no evidence since 1990 that stocks are better than bonds in the long term, despite the apparent 6 fold increase in price.

So going forward, will shares outperform? I use the discounted dividend model above with the following parameters:

o Nominal GDP growth prediction of 3.5% per year
o Disruption rate set at 2%
o Dividend growth, g = Nominal GDP minus disruption
o Discount rate, r, of the US treasury 30 year yield (approx. 3%) plus 2% risk premium, giving r = 5%

By ‘disruption’ I mean that if one held a portfolio of all the stocks in the S&P 500, each year, 2% of profits will go to new companies that we did not already own shares in. In other words, if one bought the whole S&P 500 index today and held the shares for 30 years, one would only have shares in 55% of the S&P index at that future time. The index rebalances for new participants, but there is friction as it does so.  We assume that corporate profit share does not increase from this post-war high level, and that risk premiums and risk free rates do not decrease further from these all-time lows.

How realistic is this pricing model? Looking at the actual  performance of dividends against nominal GDP we can find the following. Given a) the increase in nominal GDP between 1990 and today and b) the share of corporate profit rising from 4.2% to 10.1% of GDP in the same time period, then we would expect dividends to rise by around 8.5% per year. In fact they rose by about 6.5% per year which accounts for the 2%  'disruption' discussed above. This means that a nominal GDP model for modelling dividend returns is not unreasonable empirically (as well as it being an economic identity).

So this pricing methodology has held well in the past. Now, it is dependent on the assumptions put in of course. All of these assumptions can be changed and all affect prices considerably. Maybe nominal GDP will be higher than 3.5%, maybe lower. Maybe corporate profit share will go up, maybe down. This is why evaluation of fair value is so difficult.

However, using what I consider to be the reasonable assumptions above, the only way that I can get that shares are fairly priced is by assuming almost a zero risk premium. This is absurd and can not continue indefinitely. 

With a risk premium of just 2%, I get that fair value is 40% lower than the current price. Or the S&P at around 1200. This actually broadly agrees with CAPE Shiller.

This is not to say that prices will definitely go down. They could just stay roughly where they are for many years before fair value catches up. But the market tends not to work like that and this is why I believe that, despite central bank intervention to support share prices, we will still see a large correction.

According to this model, calculated using a 2% risk premium, share prices have been overpriced since 1990 (with the exception of a short period in 2008-09).  The worst period was at the height of the 2000 dot com bubble where they were 300% overvalued. Stocks have kept going up despite this over-pricing, because of falling bond yields.  If bond yields stop falling then we may have reached the point where gravity takes its toll.  With so many central banks at the lower bound it is arguable that they cannot repeat their asset inflation success of the last 30 years.

My conclusion is that risk free bonds are a better investment than shares at this time in the long term. For those that worry about a large printing of money to stave off disaster, and the subsequent inflationary impacts, I would suggest that inflation linked bonds may be suitable, certainly on a risk-return basis. But as mentioned before, I am not giving investment advice and caution strongly against listening to me about anything.

I believe that low interest rates have driven shares to irrationally high levels and that ultimately they should either fall by a lot, or have a long time waiting for fundamental value to catch up with the current price. We will see if I am correct.

Saturday 11 July 2015

A Union of Deflation and Unemployment

On Twitter recently, someone posted that anyone who doesn't understand the importance of the difference between a sovereign money supply and a non-sovereign money supply does not understand economics. I wholeheartedly agree with this. And the majority of comments I see on articles about the Greek situation confirms that most people don't understand economics.

I don't even know where to begin with criticisms of the idea of a shared currency without shared government. There are three main problems:

Problem 1: It is very easy to get into debt: 

A country in the Euro has no control of its monetary policy. Therefore when Greece had negative real interest rates during the boom time, there was nothing it could do to prevent people borrowing money. When added to a government also borrowing to appease special interests, this can be disastrous. But Spain had this problem even whilst running government budget surpluses. 

A country in the Euro has very little control over fiscal policy due to the rules determining how much governments can borrow and save. So even if a government wanted to combat loose monetary policy with correctly tight fiscal policy, it couldn't. There was literally nothing within the rules that Spain could have done to prevent the situation it is in now, with around 25% unemployment. 

The powers that be were very worried about government money creation as they did not want to debase the Euro. But they didn't bother worrying about private bank money creation. So when Ireland's banks built up huge books of loans, greatly increasing the money supply, nothing was done to stop them. Until it was too late. And the ECB forced Ireland's taxpayers to pay for it rather than the banks' bondholders. 

To add to this, one country in the Euro made it a policy to run huge trade surpluses by reducing worker incomes to subsidise exporters. As this was the largest economy in the Eurozone, these had a large impact on the rest of the countries in the union, notably the less competitive ones. The excess savings flowed into the poorer countries and, as Michael Pettis wonderfully explains, there was little they could do other than take on debt. 

So overall, it was pretty easy to get into debt.

Problem 2: Once in debt is impossible to get out of debt: 

There are three main ways a government has historically gotten out of debt. The first is economic growth; a growing economy means that debt to GDP ratios go down as GDP rises. The second is inflation; if a government's debt gets too large it can always resort to the printing press to help it out. The third is outright default.

Debt, when taken, is not allowed to be defaulted upon as this is against the EU rules. A limited one was allowed for Greece but this was when the holders were largely Greek banks and pension funds that the government had to recapitalise anyway so it didn't help much. Recently it has been made very clear that Greece will not be allowed to default on its government debt; although this may be relaxed a little on Sunday, they have had to go through a Great Depression magnitude loss of output to reach this and it will probably be not a large reduction.

Inflation is also verbotten. Inflation in Weimar Germany is cited as the reason why Germans are so anti-inflation. Whilst that episode was horrible for people with money; it was more the collapse of the economy caused by payment of reparations that caused the damage than the inflation. In fact, the wiping out of all internal debt helped Germany recover more quickly afterwards. It seems to have been forgotten that it was the depression caused by the deflation (due to the attempt to keep to the gold standard) in the early 1930s that actually brought Hitler to power. The important lesson from the inter-war period about money supply was that deflation is bad, but people seem to remember only that inflation was bad.

In any case, for whatever reason, the German government has shown by its actions that it would watch the Eurozone starve before abandoning a low inflation target. The inflation route has therefore been eliminated.

Then there is the growth route. Unfortunately that is out of the question too. 

Problem 3: After both of these are realised, economic growth becomes very difficult:

As I discuss here in order to have economic growth, the economy needs fresh sources of money. Since 1945, typically in the West this has been provided by credit growth, both by the government sector and the private sector. Another method could be printing new money.

As I also discuss in the above post, private sector debt is extremely inefficient in that for every 100 EUR of private sector debt taken out, only 13 EUR gets added to the demand in the economy. 

Governments, chastened by the experience of Greece and knowing that they are effectively borrowing in a foreign currency, can not borrow much more. A sovereign nation would have no problem issuing 150 or 200% debt to GDP. The central bank would support them and they would know that real interest rates could not get too high. Not so a borrower of a foreign currency. As soon as there is a fear that debts can not be paid, the interest rates can skyrocket and the economy can be destroyed. Greece only had around 100% government debt to GDP in 2007 but the internal devaluation and higher interest rates made it unpayable.

So no sane government will now borrow much money. In any case, they are bound to the (what would in a sovereign currency be a ridiculously low) upper limit of 3% of GDP. Greece is bound to run a primary surplus - they are taking money out of the economy every year.

The private sector is already over-leveraged. Even in the UK and US it is difficult to encourage much borrowing, despite interest rates being at the zero lower bound. The situation is accentuated in Europe because deflation will increase the values of the loans each year and real interest rates, especially in the periphery, are very high. So the private sector will not borrow.

There is therefore very little new money added to the economy from credit and the result is low growth. 

The necessity of running a current account surplus

There is one other source of new money each year, and this is the only one available to Greece now. It is foreign trade. Countries must run a trade surplus if they are to get any growth. 

This, in fact, seems to be the German idea of a perfectly functioning Euro. One where everyone runs a trade surplus. It is certainly the only Euro that is viable without debt disasters.

This comes with a couple of catches.

The first catch is that the only way to do this, since tariffs are not possible, is by reducing internal demand. This means effective internal devaluation and reduction of wages. This is a very slow and extraordinarily painful process if done in a world of low inflation. As I show here, the stickiness of prices means that as demand is reduced, prices and wages are very slow to react. Unemployment comes first and takes most of the impact. If average Eurozone inflation is 0.5% then a 2% adjustment per year means 1.5% deflation is required. The effect on the economy of this is huge. 

The second is that Germany already has a huge trade surplus (a structural change enacted during the boom times when it was much easier) and shows no signs of giving up on it. This means that the Euro is already too high for the rest of the Eurozone and the German exports are cheap relative to the rest of the Eurozone. Therefore the level of internal devaluation required is even higher than would be required anyway.

The third catch is that the rest of the world will have to be happy running a deficit to cope with the huge surpluses of the whole Eurozone. As it is a parasitic policy, bringing debt in the countries it sucks demand out of, they may object to this and retaliate. 

The downward spiral

The fourth, and quite important, catch here is that the more that each country does this, the more that the other countries in the Eurozone (and indeed the rest of the world) will react by doing the same. As one country reduces domestic demand so that they buy fewer imports, another country must have fewer exports. That country then needs to reduce internal demand to reduce its imports. This then affects the first country that then needs to further reduce internal demand.

This leads to a spiral of internal devaluations and unemployment that could last for many years.

The Conclusion

I think I show three things here:
  1. The only policy a country can follow if it wants to avoid debt crisis is to run a current account surplus.
  2. This leads to a policy of internal devaluation and deflation.
  3. This creates a positive feedback mechanism which leads to a spiral of deflation and unemployment.
This is true certainly as long as Germany insists on low inflation and trade surpluses but possibly anyway, just by the nature of the riskiness of sovereign borrowing.

I would like to hereby offer my humble advice to the leaders in Europe; now is the time to give up on this unworkable idea before it becomes even more of a disaster.

Friday 26 June 2015

The government must run deficits, even in good times.

It is my view that it is very important to keep things simple and this is what I will aim to do here. I will get down to the simplest identity and build from there using empirical data. I will draw conclusions which  logically follow from the data and base assumptions. But despite the elementary nature of the idea, I still think that what it will show is very informative and the conclusion it leads to is one that the current government in the UK would be appalled to consider.

Although the conclusion will be surprising to some people, I believe that every step of the logic shown here is undeniably true. I would be very interested if someone can show me a faulty link in the chain.

The starting point is the basic identity here:

If GDP in one year is given by £A, then the total amount of money spent on domestic goods and services is £A. 
If nominal GDP the next year grows by proportion n, then GDP in year two is given by £A*(1+n) and the total amount of money spent in year two is also £A*(1+n). 
What it means is that, if, for example, growth is 2% and inflation is 2%, then a total of 4% more money MUST be spent in year two than was spent in year one. 

The question I will mainly be answering in the rest of this post is 'where does this money come from?'. I will not just try to answer this question in the abstract but to quantify the effect of different sources of money.

When money is spent in an economy then it contributes to nominal GDP. Nominal GDP growth is the increase in A above. The economy can be simplified to how much money was spent and how much of that leads to real growth and how much to inflation. I will try to show, using empirical data, the source of funding for our economic growth and how this leads to the conclusion that we have a big problem now.

I am trying to keep things simple so I will avoid using any long equations, but to see this idea broken down into greater detail, it can be seen in the model I develop here and give an example of here (where I explain that the next crash we will have could well be a painful one).

I am not too concerned with the supply side during this discussion; it is a different issue. For example, better infrastructure and training will increase future real growth by improving productivity. There are two sides to an economy and both are important. However all of this is irrelevant for this analysis because it is just looking at the importance of demand. Deficiencies in supply will be shown in inflation figures.

The supply side can expand supply to fill a certain amount of the demand as demand grows. This is dependent upon the spare capacity in the economy. If many people are out of work, then it would be easier to fulfill an increase in demand than if there is full employment. This will show in the numbers. The higher the level of GDP, the higher proportion of the extra spending that will lead to inflation.

In any case, a change in total spending can be defined as the total increase/decrease in GDP plus total increase/decrease in inflation. This is an identity. The next question is, how much does it contribute to real growth and how much to inflation?

A constant quantity of money

Imagine if the money supply stayed constant. Imagine an economy of one million people where there were a total of 100 million coins and no more could ever be made or borrowed.

Also, imagine that there is economic growth in this economy. One year 1 billion units of clogs are made (this economy uses clogs for shoes and fuel, builds shelter from clogs, eats chocolate clogs and is, apart from clogs, a nudist colony so clogs are all it needs). The price of 10 pairs of clogs is 1 coin and everyone spends all their money once so there are an average of 1,000 pairs of clogs per person. But next year, the same amount of work produces 1.1 billion pairs of clogs. What would happen?

There are no more coins. Assuming that people spend 100% of their income from the previous year, the obvious answer would be that the price of clogs goes down and now one coin can buy 11 pairs of clogs.

So the natural state of the economy in growth is deflation.

What's wrong with deflation?

Austrian school economists would point to this and say, what's wrong with deflation? Who says prices have to keep rising? Theoretically nothing says this, but there is a problem.

Although some economists claim that people delay purchases in times of deflation because it will be cheaper to buy things in the future, the most obvious reason that deflation is a problem is the stickiness of prices and wages. Simply put, this means that even when the economy is bad, people are very averse to taking cuts in wages and therefore producers are unable to reduce prices.

If people are buying less and no-one will take a cut in wages then the result is unemployment.

I don't like stating things that I can't back up with data so I will show you some data. This takes 24 OECD countries with credible central banks over the period of 1996 to 2013. I am plotting inflation (y-axis) against real GDP growth (x-axis).

What is shown in this data is that, below 1% GDP growth, average inflation stays reasonably constant at around 1% regardless of the state of the economy. In this data when growth is below 1% then there is very little correlation between growth and inflation. Very approximately speaking, with this data, a 1% reduction in growth is associated with a 0.08% fall in inflation.

The assumption here is that when growth is low, then the economy has capacity to produce more. More money spent does not lead to rises in prices because production can easily be raised. Conversely when money is taken out of the economy, wages and prices are not cut, leading to unemployment.

Above 1% growth, however, we see a different story. Now the economy is running closer to capacity. Here, empirically we see that a 1% increase in real GDP is associated with a 0.36% increase in inflation

This graph shows price stickiness in action. More data is required to confirm this, but, if supported by other studies, it is very important.

Why do central banks target 2% inflation?

The above graph demonstrates exactly why a 2% inflation target for the central bank is a minimum reasonable target. The reason is that it is extremely important to be on a part of the curve where a reduction in spending is not all taken out of real GDP. 

The graph above approximately suggests that 1% is on average the minimum inflation level; in periods of negative growth in the period of study, inflation is still around 1%. In order to be safely above this point, central banks aim for 2% inflation. Unfortunately they can't reach this level at the moment; this is because of the lack of demand explained later.

When inflation is above 2%, real growth averages 2.8%. When it is below 1%, real growth averages 0.9%

Why not target higher? Looking at the graph, it seems that there is a reasonable chance that a higher inflation target would lead to more growth. There is another reason as well; in my opinion a higher inflation target, maybe 3%, is needed to reduce inequality between savers and workers, as I discuss here.

The economic theory says that a lower target is to keep 'economic stability', but often economic arguments end up protecting people who are already wealthy, and this is a further example.

The other risk of a higher inflation target is that in order to achieve that target under the current system, more debt is needed to be taken; this means that historically high growth periods can lead to later crashes when debts can not be repaid. However, this need not be the case if the inflation target is hit without unsustainable debt. More on this later.

Conclusion 1: Inflation targeting should target a minimum of 2% because of the stickiness of inflation at 1%. Personally, I believe an even higher inflation target of maybe 3% would help rebalance the economy, as discussed here.

So, where does the money come from?

At the beginning, I pointed out that in order to have GDP growth, more money must be spent each year. Now, it is possible that there is a natural spending rate of over 100% of GDP. This would mean that for every £1 received in year one, maybe £1.05 is spent in year two. This is possible because the money can be spent by one person and then spent again within the same year. The 'velocity' of money goes up.

However, whilst this is possible I aim to show that this does not happen in our economy. In fact, I will show that the savings rate is greater than zero, meaning that actually less money is spent in the next year than is received as income in the previous year. I would speculate that if there were no debt in society, and if wages as a share of GDP were a lot higher, then we may indeed have a coefficient of spending greater than 1. However, this is not the economy that we live in, so the only option is to provide more money.

Since seigniorage (new banknotes made by the central bank) is relatively tiny, we need to look elsewhere. There are three main sources of new money:

  1. Private banks. Every time a bank makes a loan, it is creating new money. As this excellent report by the Bank of England explains, banks pretty much produce money from nowhere. They create a credit and a debit. One side of it may be the mortgage on a house and the other side is cash in someone's bank account. This extra money is mostly just adding to people's bank accounts, but partially spent in the economy. 
  2. Corporate debt. Every time a company issues a bond, it is effectively printing new money. This is because it creates the bond and then people with savings in cash use it to buy the bonds. As far as the savers are concerned they have got a (slightly less safe) equivalent of cash. But now the company also has the actual cash to spend, so there is an increase of money type instruments in the system. 
  3. Government debt. This is the same as the corporate debt described above, but is even closer to cash because it is backed by the sovereign.
If these parties did not choose to add new money to the system, then, under the current system, there is no new money added to the money supply. This means that, without existing savers spending more money than that being saved by new savers or an increase in the velocity of wages, there will be no increase in nominal GDP.

Note that all three of these methods above mean increasing debt levels. In the economy as it is, there is no way of sustainably increasing nominal GDP without an increase in debt.

This is quite an important point, no? And yet, if the savings rate is not negative, it must be true as a) more money must be spent each year for GDP to rise and b) there is no other significant source of new money.

However, it is a point that is largely ignored in discussion over monetary and fiscal policy.

Conclusion 2: In the current system, the only way to increase the money supply is using new debt.


As I discuss here, there is nothing good for society about people saving money. If people could save something useful, like the environment, then they would be doing a social good. But saving numbers on a computer screen does nothing.

Going back to our clog economy, it assumes that 100 million coins are spent per year. If people continue to spend the equivalent of all of their income, then this will continue and every year 100 million coins will be spent. Some people can save in this system, but others will spend their existing savings and the two will cancel.

But what if people decided to save 10% of their income and no existing savings were spent? In this case, only 90 million coins would be spent the next year. This is deflationary, as I discuss in more detail here. And as we have seen above, deflationary actions end up with unemployment due to stickiness of wages.

In the Western economies, I believe that there is too small a share going to the workers in the form of wages. And after this, too much of that income is then spent on rental or interest on houses. These are both, I believe, largely due to the high private debt economy that has built up over the past 40 years. More on this is here.

Because workers spend most of their income, and the savers (eg pension funds and wealthier people) spend a far smaller proportion, this leads to an economy that saves too much. This means that there is now even more money that needs to be replaced each year. Servaas Storm and C. W. M. Naastepad (pg 130) find the discrepancy between savings rates on profits and on wages to be 0.41 for OECD countries and Onaran And Galanis find the gap to be 0.44 for the Euro Area 12 countries, so this has been empirically shown to be the case.

In addition to this, foreign savings need to be taken into account. This comes in the form of a current account balance. A surplus means that domestic savings are going abroad. In the UK and US there is typically a deficit, meaning that foreigners are putting their savings in the UK and US. This increase in saving in local currency takes money out of the economy. As I discuss here, there is not a one for one relationship between a current account deficit and loss of domestic demand; some of the saving is just a transfer of savings from domestic to foreign savers. In any case, wherever the saving comes from, it reduces demand in the economy.

So structural excess saving makes the problem even worse.

Conclusion 3: If people are not (net) spending (on domestic goods and services) all of their income from time period 1  in time period 2, then the spending in time period 2 will be lower than that in time period 1. This spending will have to be replaced with new money to keep GDP up at the level from time period 1.
How to keep GDP up without new money?

There are ways to keep GDP up without providing new money. They all involve getting people to spend more of existing money. These include:
  • Looking at government spending and focusing it on spending where the highest multiplier on GDP is. For example, spending on foreign weapons systems do not increase domestic GDP but paying higher unemployment benefits mean almost guaranteed spending in the economy.
  • Getting people to spend existing savings. This can be done using certain government policy. For example, in the UK recently the government announced that pensioners can take out their full private pension on retirement instead of being forced to buy annuities. This would bring forward spending (just in time for the election in this case).
  • The wealth effect of increasing stock markets means that people with investments spend a bit more even if they did not earn it as income. This has been one effect of the recent QE programmes which, contrary to public belief, did not print new money. They replaced one form of money (government bonds) with another (cash), but in doing so increased asset prices and reduced longer term interest rates.
It all comes down to direction of money in the economy to those who will spend it and in the short term there are stimulus measures that can be used. The recent stock market and bond rally is in example of a one-off stimulus measure which has helped to increase spending in the economy by making people wealthier. However, most of these measures have a one-off impact.

If spending needs to be increased then new money will need to be produced.

What is the best way to get new money into the economy?

Since the economy needs new money to grow, and since relying on debt to do this is not optimal for various reasons discussed below, it would seem that the obvious thing to do would be for the government to provide new money. That is to say that if the nominal GDP growth target is 5% per year then 5% of GDP in new cash should be created by the government and spent in the economy in a way that has a multiplier of 1 on spending.

This would create a stable economy that does not rely on debt to grow.

However, this is not the way the economy runs. So working with what we have, there are two main sources of new money. Either private sector debt or government debt.

The predictability of nominal GDP growth

The economy is not as complex as some people would have you believe. If you can predict how much will be spent then you can predict the GDP. This is not straightforward because some parts of predicting spending are difficult; for example, a prediction about consumer confidence next year would be made incorrect in the case of a crash. However, I will separate GDP into four components:

  1. New money coming in as increase/decrease in debt levels.
  2. Confidence of consumers; this affects the propensity to spend.
  3. Wealth effect on existing savings; if share prices have gone up people are richer and spend more.
  4. The structural effect on the economy of previous debt levels; increased debt levels exert a drag on the economy.
A note on point 4. As discussed above, I believe that debt weighs on the potential growth of an economy because of the redistribution of income from those more likely to spend to those more likely to save. The more debt, the higher the structural savings in an economy will be. For this reason I include total debt in the regression.

Using OECD data from 24 countries from 1996 to 2013, I am able to run a regression to see the effect of all of the components. I use the following to represent each of the four components:

  1. For new money coming into the economy I look at the change in private sector debt levels. Government debt is more tricky to put into a regression as it is counter-cyclical and so it is difficult to separate the impact of increased spending from the reason why it is increased - for this reason I use only private sector debt for this component.
  2. For confidence I use the change of change of debt as a proxy. Typically an increase in confidence causes a reduction in the increase of debt because more money is spent in the economy. Lower confidence forces people to take out more new debt than the previous year.
  3. For the wealth effect I take the return from the S&P 500 index the year before the year in question. This could also be a predictor of consumer confidence so serves two purposes.
  4. For the structural effect of debt,  I look at the total level of government and private sector debt.
Amazingly, using ONLY debt related data and the stock market index return the year before, I can create a proxy that is 71% correlated to the actual nominal GDP growth in a country in a year during this time period. This is without knowing anything else about the country or the time.

A scatter plot of the proxy against the actual growth in nominal GDP is shown below:

A robust regression gives the following equation to predict nominal GDP growth:

NGDP growth estimate = 

7.00% + 0.13*IncrPSD - 0.017*TotDebt +0.06*S&PRet - 0.09*ChgofChgDebt

Where IncrPSD is the increase in private sector debt in the year divided by GDP, TotDebt is the total private and public sector debt level divided by GDP, S&PRet is the return of the S&P 500 index from the year before and ChgofChgDebt in the change in IncrPSD from the previous year.

For the technically minded, the p-values for all of these are zero to at least thirteen decimal places. This means that the results are very statistically significant.

It is important to bear in mind here that government deficit is not included. Since this was an average of 3.9% throughout the period, we can assume that growth would have been considerably lower had the government been running balanced budgets. 

Note that all of these factors primarily relate to the demand side of the economy. One predicts how much money will be spent by looking at how much is received and what the propensities to spend of the receivers are.

Conclusion 4: Nominal GDP can be predicted using only a prediction of cash flow. It is not necessary to look at the supply side of the system.
Conclusion 5: New private sector debt has a multiplier of 0.13 on nominal GDP. This makes it an inefficient way of stimulating spending vs government spending. 
Conclusion 6: Existing debt exerts a drag on the economy equivalent to 1.7% of the level of debt. This is an average of all different interest rates and marginal propensities to spend, but as an example it could correspond to an interest rate of 4% and a difference between the marginal propensities to spend between payer and receiver of 42.5% (4%*42.5% = 1.7%).

Putting some numbers in for government and private sector debt

I am going to make my first assumption here that is not backed up with any data. It is about the multiplier of government spending. Because this is a subject of intense economic debate, I am going to assume that it is close to what I believe to be a reasonable consensus. It is very dependent upon what the money is spent on. In any case, I believe that studies put the multiplier on real GDP to be approximately 0.8. For this reason, using the inflation assumption discussed below, I am going to assume that the multiplier on nominal GDP is 1. This would correspond to a (reasonably conservative) estimate of the fiscal multiplier as 0.72 on GDP, with a multiplier of 0.28 on inflation.

So we have a multiplier on private sector debt of 0.13 and a multiplier on government debt of 1.

We have average nominal GDP growth throughout the period of 4.0%, average government borrowing of 3.9% and average change in private sector debt of 11% of GDP.

Putting this all together, it means that if we take out the contributions of government and private sector debt, we get a nominal GDP growth of -1.3% per year (4% -3.9%*1 - 11%*0.13).

This, I believe, is the savings rate of the economy. For every £100 spent in year 1, only £98.70 is spent in year two, with £1.30 being saved.
Conclusion 7: The average net savings rate from income over the time period of 1996-2013 was 1.3%. This sending was replaced in the economy by spending of borrowed money.

This is a broad approach. Looking at the US and UK separately gives:

UK had average nominal growth of 4.2%, average govt deficit of 4.8% and average private sector debt increase of 12.2%, giving:
Estimate of UK Net Saving per Annum = 1*4.8% + 0.13*12.2% - 4.2%  = 2.2%

US had average nominal growth of 4.8%, average govt deficit of 5.9% and average private sector debt increase of 10.5%, giving:
Estimate of US Net Saving per Annum =  1*5.9% + 0.13*10.5% - 4.8%  = 2.5%
The savings rates of the US and UK are higher than average, probably partly due to the effect of the persistent current account deficits.

Conclusion 8: The savings rates mean that we need to create new spending of this amount on top of the amount required for inflation and real growth. Giving an example of 5% nominal GDP growth, we need to find an extra 7.2% spending in the UK. If we are to avoid increasing private sector debt, and assuming government multiplier of 1, it means a government deficit of 7.2% per year on average.

Growth vs Inflation

The equation can be plotted against real GDP growth and inflation separately to give an idea of the breakdown between real growth and inflation contained in this nominal GDP growth. The plots below show the two separated.

Conclusion 9: On average, when more money is spent in an economy, 72% goes towards growth, 28% goes towards inflation. This obviously will change depending on how close the economy is to full capacity, but it is a useful rule of thumb.
Also notable on the graph is that 0% predicted nominal growth gives inflation of approximately 0.9% and growth of approximately -0.9%. Price stickiness in action.

It actually is not too far away from the rule of John Taylor, which implies that a 1.5% rise in interest rates (which causes a certain amount of a reduction in spending) should lead to a 3% fall in growth and a 1% fall in inflation. So his rule suggests that as a rule of thumb, 75% of money spent is growth increasing and 25% of money spent  is inflationary.

This yields the surprising conclusion that I am in agreement with John Taylor.

Where are we now?

Since the second world war, the economy has been growing using a combination of government debt and private debt. When more stimulus was needed, interest rates were reduced and more debt taken out. This private debt has got larger and larger until the crash of 2008. 

Since 2008 it has not been possible to encourage substantially more private debt. Interest rates have finally hit bottom but due to poor growth prospects, high house prices, and high real interest rates charged by banks, even at zero base rates it has been very difficult to stimulate more growth. The UK government has tried its best with schemes such as Funding for Lending and Help to Buy, but it has faced strong headwinds.

It is now difficult to get more private debt even if it were desirable. And for this reason we are in a secular stagnation in the West. The previous ways of funding economic growth are no longer there and we are still paying for the old ways.

Not all money is created equal

Supposing the government created £10 billion of new money, would it cause growth and inflation?

The question is where it is spent. If it were spent on increasing welfare payments to those with incomes below the poverty line, the chances are it would be spent in the economy so quickly that it would actually be spent again before the year is out. This gives it a multiplier greater than one on nominal GDP.

If, on the other hand, they just put it in my bank account as a gift, and even supposing I went on a Brewster's Millions style spending spree, it would make virtually no difference to the economy.

My point here, is that when creating money we really want it to be used in the most efficient way possible to boost growth. When private banks create money it is not very efficient as very little is spent in the economy.

We should concentrate on producing money that gives the maximum economic impact, whilst removing money that has less economic impact. This means increasing government debt (or even better, allowing monetarisation) and reducing private debt.

Do we want a high private debt society or a low private debt society?

In some ways, this is a value judgement. Do we want a society where house prices are so high that very few people starting work today in London will ever be able to afford one? Do we want a society where workers are rewarded less and rentiers rewarded more? Do we want an economy with high levels of instability, prone to pro-cyclical booms and busts?

In some ways though, it is just a matter of common sense. In order to get the spending required to increase GDP, we need to make a decision whether to increase private or public sector debt. Since the drag on the economy by both is comparable, the only question is which provides more of a stimulus.

Spending by the government is probably about 8 times more efficient at stimulating the economy and therefore, if we have decided we want debt then we have to choose government debt over private debt.

The other important consideration is that when a private sector debt crisis occurs, usually the government needs to take some of the loss onto its books anyway. So even using the narrow criteria of trying to keep government debt down, choosing the private sector debt route may end up with a worse outcome.

Can we struggle along as it is?

The answer here is yes, just about. But it is with low growth and greater risk of financial crisis. Taking a government multiplier of 1 we get a trend growth, using the equation above of:

NGDP trend estimate = 

3.1% + 1*AveIncrGov+ 0.13*AveIncrPSD - 0.017*TotDebt 

Where AveIncrGov is the average annual increase in government debt levels and AveIncrPSD is the average annual increase in private debt levels (both are divided by GDP total at the start of the year) .

A sustainable debt ratio is one where the economy can grow and debt to GDP ratio does not rise from year to year. As an example, supposing we had a government debt of 100% of GDP and nominal GDP growth of 5%, we could increase government debt by 5% per year without increasing the ratio of government debt to GDP.

If we assume, as we had in 2013 in the UK on OECD figures, 214% of GDP private sector debt and 93% government debt and decide that these are the levels we wish to keep, then there is actually a solution that can make these levels sustainable: it targets 10% nominal GDP growth and has government deficits of 9.3% of GDP per year.

I would not advise such a drastic course of action, however. There may be unforseen consequences; inflation would be above target and credibility of the central bank may be put in doubt.

Going back to reality for now, with the UK government running deficits similar to where we are at the moment, we have a shortfall in spending. Nominal GDP growth of around 4% can be achieved but the cost would be an increase in private sector debt of around 10% per year.

The government is actually planning to reduce the deficit to zero in the next five years. It will be a good test of the equations above. I don't think it will be good for much else.

But even if the government is sensible and keeps deficits where we are now, the system is inherently unstable and will eventually collapse.

An equilibrium

An example of a sustainable economy is one where we have very high government debt but very low private debt. It works as follows:

Imagine we were happy as a society with 150% government debt levels. By increasing government debt to reach that point, we would give stimulus to the economy. When the economy heats up, instead of reducing government spending we could raise interest rates and therefore not increase total level of private debt whilst the economy is growing (reducing the ratio of private debt to GDP).

At 150% government debt to GDP, with private sector debt down to 150% of GDP too, assuming that the government took most of the responsibility for spending new money, both private and public sector debt would be going down relative to GDP every year.

As a worked example, with 150% government debt and 150% private sector debt, a 5% nominal GDP growth target could be hit with a 7% increase in government debt and a 0% increase in private debt. This reduces both government debt to GDP and private debt to GDP ratios.

The resulting economy is one built on stable foundations, not speculation caused by increases in private debt. Rentier capitalism is reduced due to the relative reduction in debt levels and inequality will be reduced. And the debt levels are sustainable.

Conclusion 10: The only 'sustainable' level of government debt is a high one. This is because it allows a higher government deficit without increasing the ratio of debt to GDP.

Risks of running high government debt

There have been a lot of scare stories about how too high levels of government debt will 'scare bond markets' and risk bankrupting the country. This may be true for a country that has borrowed in another currency (see Greece), but for the issuer of a sovereign currency this is ridiculous. The reason is simply that if there is any perceived credit risk on the government debt, the central bank can buy unlimited quantities of it, in what are termed 'outright monetary transactions' (the promise by the ECB to use these saved Spain and Italy from default in 2012).

To put it simply, it is impossible for a sovereign state to default unless it chooses to. For an example of high government debt with very low interest rates one only needs to look to Japan. With a couple of exceptions of default by choice (eg Russia 1998) every single sovereign debt crisis ever has been because the state can not issue the currency in which the money is owed. The central bank needs to agree to stand behind the currency and this risk disappears. A credible central bank should maintain an inflation target and as long as it does this, there is no risk to the debt.

The other risk is that nominal economic growth powers away and real interest rates rise. As Marlo would say, it sounds like one of them good problems. Although the government would have more interest to pay, the economy would be in healthy shape and able to take it. Also, in this circumstance, it is much better that the government owes a smaller amount of money then the situation where private debt is much higher given above.

In any case, the cost to productivity of the paying of interest is already, to a large extent, included in this calculation. The coefficient for existing debt is -1.7%. As previously stated, this could correspond to a 4% average interest payment, with a 42.5% difference in marginal propensity to consume between payer and receiver. If interest rates were higher then either the sustainable rate of debt would be a little higher, or the government could divert some of the other (non-interest payments) part of the budget to people with a higher propensity to consume.

The two routes to 150% government debt to GDP ratio

We are in a situation now where we have two broad choices ahead of us (or somewhere in between of course). Let me pave out the two roads we can take.

1) Increase government debt by an average of, say 9% of GDP per year, going down to 7% of GDP per year as private sector debt to GDP reduces. This will enable interest rates to rise and private sector debt to reduce. It will enable a nominal GDP growth of 5% per year. It will lead to a sustainable growth not relying on private debt bubbles. It will put us, in ten years time, with a government debt to GDP ratio of below 150%, a strong, vibrant economy and much lower private debt to GDP levels.
 2) Keep a balanced government budget and encourage private sector debt. Imagine that we can encourage 20% of GDP per year of private debt. This will lead to sluggish average nominal GDP growth of maybe 1-2% in the good times.  It will lead to a large build up of private debt to GDP. Inequality will increase, house prices will continue rising. In maybe ten years time, when we have 300% private debt to GDP and government debt of around 80% of GDP we will have a crash. The government will need to bail out the banks and pick up the pieces of the economy. Most of the real growth will be wiped out. In the few years after this next crash government debt will still rise to 150% of GDP. A GDP that is significantly lower, a society that is more divided along lines of wealth and an economy burdened with huge levels of private and public debt.

Overall Conclusion

New money needs to be created to keep up nominal GDP growth. Since we have tried the private sector debt route to growth and since it has a) failed to keep the economy stable, b) led to a rentier economy and c) can't even give us growth any more, we need to find a new way of creating the new money.

Here, in my opinion, there are only two choices.

1) Allow central banks to create new money, corresponding to 5-7% of GDP per year which it gives to the government.

2) Allow governments to run larger deficits.

Trying to keep government debt low is unsustainable, destroys growth prospects and creates private debt crises.

Counterintuitively, the only 'sustainable' level of government debt is a high level.

Tuesday 16 June 2015

Why was r greater than g? Will it continue? And how to reverse it.

First to own up that I have not read Thomas Piketty's 'Capital in the Twenty-First Century' , in which the idea of return on capital, r, being greater than economic growth, g, is used to explain rising inequality. So this is not a review of the book. I have, however, recently read a very interesting critique of the book by Yanis Varoufakis and also Brad DeLong's discussion which I quote below:
Looking simply at my own family history, my Grandfather Bill reached not just the 1% or the 0.1% but the 0.01% back in the late 1960s in the days before the rise in inequality by selling his construction company to a conglomerate back in 1968...
Today, you need roughly 3.5 times the wealth now in the U.S. and 8 times the wealth worldwide to achieve the same percentile rank in the distribution (see Atkinson, Piketty and Saez (2011), Piketty (2014), Saez and Zucman (2014)). I find it simply impossible to conceptualize such an extreme concentration as in any way a return to a factor of production obtained as the product of "hours spent studying" times "brainpower", even when you also multiply by a factor "luck" and a factor "winner-take-all-economy".
So what, then, is going on and driving the sharp rise in inequality, if not some interaction between our education policy on the one hand and the continued progress of technology on the other? Thomas Piketty (2014) has a guess. Piketty guesses that the real explanation is that 1914-1980 is the anomaly. Without great political disturbances, wealth accumulates, concentrates, and dominates. The inequality trends we have seen over the past generation are simply a return to the normal pattern of income distribution in an industrialized market economy in which productivity growth is not unusually fast and political, depression, and military shocks not unusually large and prevalent.
In a previous post, I seek to explain this rising inequality as an inequality between savers and workers; the rising share of GDP going to capital instead of labour. And that the reason for this is predominantly the rise in endogenous money - more commonly referred to as debt. The servicing costs of this debt (and the corresponding high house rental prices) are too high as a proportion of GDP hence more return to savers and less to workers. I wish to discuss this further here.

What particularly strikes me is the unsatisfactory nature of r>g as an explanation for inequality for two reasons. 

First, there needs to be a mechanism that explains how r is greater than g. Saying that it is a natural process that returns the income distribution to 'normal' is not good enough as an explanation for me. Why is there this 'normal pattern'? 

Second, there needs to be an understanding of whether this will continue. Piketty appears to suggest that this will keep going unless higher taxes are enforced upon the rich. I believe that this ignores the true cause of the inequality of capital.

Why was r > g?

To answer the first question, we need to examine what it means for r to be greater than g. I will look here only at financial assets, rather than real assets. This means all cash, stocks, bonds, property and assets with financial value but that do not produce anything real. If in year t we have GDP of Pt and total wealth in financial assets of Wt, then in year t+1 we will have total GDP of Pt+1 = (1+gt)*Pt and total wealth of Wt+1 = (1+rt)*Wt.

If r>g then it means that Wt+1/Wt Pt+1/Pt. In other words, wealth grows faster than GDP. This is actually not a natural state of affairs - it is an anomaly that needs to be explained.

Wealth can be described as a claim on future work. If I have money, it is given value because I can use it to pay for goods and services in the future provided by work done by future workers. Every unit of wealth receives some return, call it a dividend, d, per year. The total value of d*W must be some proportion (χ, where 0 < χ < 1) of GDP. So, in a given year, d*W  = χ*P.

Therefore, if wealth goes up relative to GDP then one of two things must be true. Either expected future d has gone down or expected future χ has gone up. Either the expected future return goes down or the expected return to savers increases versus the return to workers.

This means that r > g is not an explanation in itself. A consistent r > g means that either that expected future dividends have gone down or that the capital share of GDP has increased relative to the worker share. Or indeed both. 

As luck would have it, I have looked at both of these in previous posts. Starting with worker share of GDP. In my post on debt causing the economic stagnation, I show this graph of worker share of GDP in the US:

This shows how since 1970 the share of GDP going to those actually doing the work has reduced. On top of this, as I discuss in the post, property rentals as a proportion of income have risen so workers have even less disposable income than this shows. Therefore the share of GDP going to capital has greatly increased. I argue that the reduced worker share is due to a combination of both recently improved rent seeking on the part of corporations as well as the cost of servicing all of the corporate debt that has built up since the 1970s often not used for productive purposes.

However, this is itself only would explain maybe a 30-40% increase in wealth relative to GDP. There is another large reason for the increase in wealth. I present the following graph in my post on why interest rates can't rise much from here:

It charts the total value of financial assets (bonds, shares and cash) in the UK, not including housing. It shows how total wealth has risen from approximately 4 times GDP in 1979 to closer to 13 times GDP in 2014. 

This, on its own, is enough to explain DeLong's question as to why one needs 3.5 times as much wealth now to be in the top 0.01% as one did in the late 1960s. The majority of the economy consists of workers, whose increases in pay are proportional to GDP. If the richest people today have the same proportion of wealth as the rich in 1979 then they will have over three times as much wealth relative to the workers.

How has wealth gone up so much? Almost all of the increase in wealth is in the form of endogenous money - either cash created by private banks (about 97% of all cash is created by private banks) or bonds created by companies and the government. Without this there is almost no increase in gross wealth to GDP (maybe the 30-40% assumed by the increase in capital share above). But every time a bank creates a mortgage for someone to buy a house, the seller receives money and so there is an increase in savings. Every time the government issues debt to fund spending, there now exists all previous savings plus some more government bonds so there is an increase in savings. Every time a company issues debt, they increase the amount of money-like assets in the system.

So here we have the reasons why r has been greater than g. It is partly because of the increased share of GDP going to capital. But it is mainly because of the increase in wealth caused by the explosion of private sector and (to a lesser extent) government debt. 

Incidentally this is why interest rates can not rise much from here; the wealth is higher so the d must be lower.

Will it continue?

For r to continue to be greater than g, we need the wealth to GDP ratio to keep rising. As discussed, if there is no fall in GDP, then this can happen for two different reasons. The first is the increase in endogenous money. We can not rule this out, but since 2008 it has been harder and harder to encourage more private sector debt to be taken out. Even with interest rates at zero, growth prospects are deemed so poor and property prices so high, that private sector debt has, in the West, actually reduced. Although it is not impossible to increase private sector debt, and the UK government is trying its best, the higher the level, the higher it becomes to force it higher.

The other way would be for capital to continue to extract more from labour. This can be done either with better technology where robots replace humans, or through reduction of wages in the economy (as has happened in the UK) due to increase of labour supply. However, this is also self-defeating as the reduction in wages then leads to a reduction in demand for goods produced. The equilibrium level where demand = supply will be at a lower level of GDP than we currently have. The sensible move then would be more redistribution from robot owners to other citizens, as I discuss here

For these reasons inequality may well be close to a peak. The easy rise in inequality, caused by explosion of debt, has ended. Wealth to GDP is no longer rising.

Inequality may well rise again but it will be due to a fall in the denominator. It would be accompanied by a horribly shrinking economy, not by economic growth as before; due to a reduction in the equilibrium in a way similar to that I discuss here

The problem, as I discuss in many places (eg. here) is that we have a structural lack of demand in the economy caused by debt leading to over-saving. This may well lead to the crash that causes inequality on an even larger scale.

How to reverse inequality and prevent the crash - no, not higher taxation

Here, most people look at higher taxes as the answer. Whilst I agree that higher taxes are good (up to a limit) for reducing inequality and increasing growth, the problem is that capital is very mobile and pinning down taxable profits is very difficult. Also, taxes can alter incentives in the wrong way as it is more common to tax work than capital. In fact, although phasing out the tax relief given to interest payments would be a good start, higher taxes are not necessary to redistribute wealth.

In order to reduce inequality we need to increase the share of income going to poor rather than rich. One way of doing this is for the central bank to print money and give it to the government for government spending. As government spending disproportionately goes to the poorer in society this will increase income at the bottom end.

The increase in demand caused by this money will help return the economy towards the trend growth line that it was on until 2008 when the flow of money (previously supplied by private sector debt) in the economy was cut off. This will therefore increase GDP meaning each member of the economy gets more in absolute terms. 

Those worried that this will cause inflation need not be, if the rise in central bank money is undertaken responsibly (as discussed here). They were not worried about inflation when private sector debt increased the money supply on a scale far greater than this. It is a fallacy to think that government money is so much more inflationary when we have low demand in the economy. It will first create growth with only small inflation, then, only when supply can not take the increase in demand, higher inflation.

This procedure will also eventually lead to a reduction in the wealth to GDP ratio by removal of private debt from the economy. It would work as follows.

As central bank money in the economy increases, and moderate inflation returns, the central bank can raise interest rates thus reducing the amount of private sector debt. This means that the real cost of servicing the debt will reduce therefore allowing more of GDP to go to the workers. The multiplier of government expenditure on GDP is much higher than private sector debt; a 1% increase in central bank money could probably take 5% of debt money out of the system.

Similarly house prices relative to GDP should decline as interest rates go up, debt is reduced, and GDP rises. Since much of the rise in house prices was caused by increase in debt used to buy them; it follows that a reduction in private sector debt should lead to a relative reduction in house prices. More affordable house prices should mean working people more able to buy their houses and therefore lower rentals. Higher rentals, caused by those unable to afford the down-payment on their own house, redistribute money to the rich from young workers. A reduction of house prices, again, reduces the amount of income relative to GDP flowing to the owners of capital.

In general, to reduce the inequality, one must look at ways to reduce wealth to GDP by both reducing gross assets and increasing GDP. For example, a change in patent law to reduce rent seeking from patents would probably help to reduce profit margins of corporate incumbents. 

The minimum wage probably still has a fair way to go up while still improving economic growth. This is because almost all money going to those on the minimum wage will be spent in the economy, increasing demand. It also shifts more of the share of GDP from capital to labour. The minimum wage should be set to gradually rise in real terms every year until the point that it causes detriment to economic growth.

Other methods to redistribute in the UK would include building more houses to reduce rental costs. Another would be removal of the tax exemption of debt on buy-to let houses, which would encourage repayment of debt and also reduce house prices relative to GDP (although the economy would suffer without a replacement of the demand with government money). Removal of the corporate tax exemption of debt would be very good but practically would result in corporations switching jurisdiction. 

But by far the most growth increasing and inequality reducing measure a government can do is to allow the central bank to print and give it money in a controlled, inflation targeting manner. It increases income to the poorer, reduces asset prices and increases GDP in a low demand economy.

As I discuss here, it is not only desirable but necessary as the economy is in a very unstable state. Without it, I fear at best long-term stagnation and at worst economic misery.