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Rational Exuberance - The Equitile Blog

30th November 2019

Posted by: George Cooper

The Magical Mathematics of Mr Piketty Part 1

I have been asked to re-post four articles origionally written in April/May 2014 about the ideas of Thomas Piketty in his book Capital in the Twenty First Century: The Magical Mathematics of Mr Piketty Part 1 and Part 2, Credit in the Twenty First Century and The Horrible History of Mr Piketty

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The Magical Mathematics of Mr Piketty Part 1

To my mind the best quote from Thomas Piketty’s new book Capital in the Twenty-First Century is: “To put it bluntly, the discipline of economics has yet to get over its childish passion for mathematics…” p32

I could not agree more. But this does not mean we should dispense with mathematics entirely. Some problems in economics are easily formulated in mathematics, for those the equations can be a useful tool to test the validity of the underlying logic. This is true for the ideas in Piketty’s own book.

There are only three important mathematical relationships in Piketty’s book but I am having trouble reconciling them, especially in the low growth world that Piketty wants to analyse.

The three relationships are:

  1. Piketty’s inequality page 25:

“This fundamental inequality, which I will write as r > g (where r stands for the average annual rate of return on capital, including profits, dividends, interest, rents, and other income from capital, expressed as a percentage of its total value, and g stands for the rate of growth of the economy, that is the annual increase in income or output), will play a crucial role in this book. In a sense, it sums up the overall logic of my conclusions.”

r > g

  1. Piketty’s first fundamental law of capitalism page 52:

“I can now present the first fundamental law of capitalism, which links the capital stock to the flow of income from capital. The capital/income ratio β is related in a simple way to the share of income from capital in national income, denoted α. The formula is

α = r × β

Where r is the rate of return on capital.

For example, if β=600% and r = 5%, then α = r × β = 30%.

In other words, if national wealth represents the equivalent of six years of national income, and the rate of return on capital is 5 percent per year, then capital’s share in national income is 30 percent.”

  1. Piketty’s second fundamental law of capitalism page 166:

“In the long run, the capital/income ratio β is related in a simple and transparent way to the savings rate s and the growth rate g according to the following formula:

β = s / g

For example, if s = 12% and g = 2%, then β = s/g = 600%.

In other words, if a country saves 12 percent of its national income every year, and the rate of growth of its national income is 2 percent per year, then in the long run the capital/income ratio will be equal to 600 percent: the country will have accumulated capital worth six years of national income.”

In summary the three key relationships in Piketty’s mathematical framework are:

The inequality r > g

The first fundamental law of capitalism: α = r × β

The second fundamental law of capitalism: β = s/g

Of these Piketty’s inequality has captured most attention. Piketty is at pains to emphasise that, r, the return on capital is always greater than, g, the growth rate of the economy. He also maintains that r is more or less a constant at around 4 to 5% and he expects growth to head lower toward around 1 to 1.5%.

We can explore what happens to these relationships as the rate of economic growth falls toward zero.

To keep the examples simple I will assume a constant return on capital of 5% and a constant savings ratio of 10%. This leaves the growth rate, g, as the only free variable in the system.

The following table shows the key variables under different growth scenarios.

 

Growth rate g 4% 2% 1% 0.50% 0.25% 0.125%
Savings Rate s 10% 10% 10% 10% 10% 10%
Return on Capital r 5% 5% 5% 5% 5% 5%
Capital/Income ratio s/g             2.5                5              10              20              40              80
Share of national income going to owners of capital r x(s/g) 12.5% 25.0% 50.0% 100.0% 200.0% 400.0%
Share of national income going to workers 1-r x(s/g) 87.5% 75.0% 50.0% 0.0% -100.0% -300.0%

 

As growth falls capital values rise pushing up the share of national income accruing to the owners of capital – one of Piketty’s key concerns. However as growth falls toward zero it becomes apparent that all is not well in this model. The capital/income ratio eventually rises to a point where more than 100% of the national income goes to the owners of capital - clearly an impossible scenario.

The problem arises because Piketty’s second ‘fundamental’ law of capitalism β=s/g contains a singularity , a divide by zero, which sends the value of capital toward infinity as the economy stagnates. When coupled with Piketty’s assertion that the return on capital remains above g, at around 4 to 5%, this sends the income from capital to infinity – another impossibility

Piketty’s equations simply cannot hold true in the low growth environment which he is trying to analyse.

The question is how to fix them. The most logical approach is to accept that the yields on assets fluctuate to reflect the growth rate of the economy. If growth is cut in half then asset prices will double but their yields will also be cut in half, a condition met when r = g.

If the scenarios are re-run with r = g we get the following results shown in the table below.

If we accept that the real return on assets floats with growth, r = g not, as Piketty claims, r > g, then there is no conflict with either of Piketty’s two fundamental laws of capitalism.

 

I expect the r = g assumption will make more intuitive sense to investors who have seen the real yields on, for example, inflation protected bonds collapse as growth has fallen. It also helps explain why pension funds are struggling to meet their funding targets and why the UK government has recently relaxed the requirement for pensioners to buy annuities – because annuity yields have fallen in line with economic growth.

However the r = g assumption causes a significant issue for Piketty’s case for a wealth tax. If r = g prevails in a low growth world then Piketty’s 2% wealth tax could push the return on capital into negative territory potentially crushing entrepreneurial activity.

In conclusion – Piketty’s own fundamental laws of capitalism appear at odds with the inequality on which much of his book is based. This is especially true in the low growth world he is concerned about.

 

 

Growth rate g 4% 2% 1% 0.50% 0.25% 0.125%
Savings Rate s 10% 10% 10% 10% 10% 10%
Return on Capital r=g 4% 2% 1% 1% 0.25% 0.125%
Capital/Income ratio s/g             2.5                5              10              20              40              80
Share of national income going to owners of capital r x(s/g) 10.0% 10.0% 10.0% 10.0% 10.0% 10.0%
Share of national income going to workers 1-r x(s/g) 90.0% 90.0% 90.0% 90.0% 90.0% 90.0%
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30th November 2019

Posted by: George Cooper

The Magical Mathematics of Mr Piketty Part 2

I have been asked to re-post four articles origionally written in April/May 2014 about the ideas of Thomas Piketty in his book Capital in the Twenty First Century: The Magical Mathematics of Mr Piketty Part 1 and Part 2, Credit in the Twenty First Century and The Horrible History of Mr Piketty

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The Magical Mathematics of Mr Piketty Part 2

The philosopher Friedrich Nietzsche wrote: “There is no more dangerous error than confounding consequence with cause: I call it the intrinsic depravity of reason.” In economics the problem of confusing cause and effect is rife and frequently leads to disastrous policy mistakes.

The more I think about the logical framework of Thomas Piketty’s Capital In The Twenty-First Century, the more I become concerned that Mr Piketty has fallen into Nietzsche’s trap. I fear that Piketty has got his causes and effects the wrong way round.

To explain where I think the problem lies, I am going to use a simple thought experiment:  

***

Consider an isolated island kingdom. Half of the island is covered in productive farmland and half is covered in unproductive land which is too rocky to farm. The island is a perfect feudal society. The King owns all of the land and therefore all of the capital of the island. All of the island’s inhabitants work for the King.

Fortunately the island’s farmland is fertile enough to produce more food than is needed to pay the wages of the farmworkers who tend the crops. As a result, in each year, the King enjoys a surplus value of food which he uses to pay the wages of additional workers. The King employs these additional workers to clear the rocky-land thereby turning it into new productive farmland.

It so happens that each acre of farmland requires exactly 9 people to farm it, yet in each year it produces enough food to pay the wages of exactly 10 workers. It also happens that it takes exactly 20 years of labour to turn each acre of rocky land into productive new farmland.

The upshot of these convenient numbers is, for each twenty acres of land owned by the King he is able to employ enough workers to convert exactly one additional acre of land into new productive farmland each year. As a result the King’s farmland, and therefore the island’s economy, grows at a steady rate of 1/20, or 5%, per year.

It also so happens that the King’s hobby is accountancy – stay with me! The King likes to idle away his time tallying his earnings and wealth. For convenience he chooses to do this by accounting for everything in units of ‘years of labour’.

The King notes that, each year, each of his acres of farmland produces enough food to purchase 10 years of labour. He also notes that, in order to receive this 10 years of labour, he must spend 9 years of labour to pay the wages of the farm workers. He therefore considers that each acre of land generates a profit to himself of 1 year of labour.

He also notes that it takes 20 years of labour to turn an acre of rocky-land into productive farmland and therefore considers that each new acre of land costs 20 years of labour. Once cleared of rocks the new farmland is no more nor less productive than the old farmland. He therefore considers old and new farmland to be of equal value and accounts for each of his acres as being worth 20 years of labour.

As each acre of land produces a surplus value of 1 year of labour and is valued as being worth 20 years of labour the King considers that he receive a return on his farmland of 1/20 or 5% per year.

The King notes that the yield he receives on his farmland, r, and the rate of growth of his acreage, g, are both equal, r = g, at 5%.

The King is so intrigued by the coincidence between the 5% return on his farmland and the 5% rate of growth of his acreage that he commissions two of his most venerated priests to investigate the phenomenon. The two priests, Karl and Adam, set about their task of investigating the r = g conundrum.

After years of research the two priests are summoned to present their findings to the King’s court.

Karl presents his report first. His is an enormous work running to hundreds of pages and is packed with charts and tables.
Karl begins speaking: “My lord, I have researched the r = g conundrum and I can conclude that it is just an incredible coincidence, there’s no natural force behind this incredible coincidence of pushing the growth rate of the economy toward the rate of return on capital.”

The King is clearly disappointed by this finding but Karl continued: “Nevertheless, my studies have lead me to discover new and important laws and relationships governing the workings of our island’s economy. I have studied all the records of this land, through all of its known history, and I can tell you that the return on farmland has always been 5% per year. So reliable has been this rate of return I am forced to conclude that a 5% return on capital must now be considered to be something close to a universal constant of economics.
Furthermore, I have discovered the ratio of the value of the capital of the economy relative to the value of its annual production is governed by a new fundamental law of capitalism. This law states that the ratio of capital to income is the same as the ratio of the savings rate to the growth rate of the economy.”

The King looked rather more pleased with these exciting new findings but his enthusiasm was soon dashed by the terrible news that Karl delivered next: “Unfortunately, my Lord, these new findings lead me to conclude that the island is about to suffer a terrible famine.”

At this point Karl pauses for dramatic effect and to give time for the assembled audience of high priests to nod and mutter their approval. One of the high priests becomes too excited to contain himself. He leaps to his feet and declares: “If you think you have found an obvious hole, logical or empirical, in Karl then you’re very probably wrong.”

Karl continues: “I have been up to the north of the Island to survey the rocky-lands that are yet to be cleared. The news is very dire. I can report that this land is much rockier than any we have cleared so far. I estimate that the cost of clearing this land will be not 20 years of labour per acre but 40 years of labour.”

Again he pauses for effect as the priests gasp at this terrible news.

Karl continues:” Once we are forced to start clearing the very-rocky land I am afraid to say the whole island will be plunged into a dreadful famine.”

At this point the King, who is becoming increasingly bemused, interjects with a question. The King asks: “You are saying that today we are able to feed ourselves quite amply and also able to clear the less rocky land but that in the future, when we start clearing the rockier land, there will suddenly be famine. How can this be so? Will the island not still have the same farmland that it had before?”

Karl responds: “Let me explain. It is my new laws of capitalism which show the inevitability of this famine. Clearing the rockier land will take not 20 but 40 years of labour. As a result the price of purchasing each new acre of land will double. Once this happens we will be forced to revalue the rest of Your Majesty’s capital. The value of your capital will double, to reflect the new higher cost of purchasing new land.
It is this higher valuation of capital that will cause the dreadful famine. Due to my newly discovered law, showing that the return on capital is always 5%, your income will double so that you will now receive not 1 but 2 years of surplus value per acre. This doubling of income being necessary to keep the yield of your land at 2/40 or 5%.

As a consequence there will be just 8 years of labour available to pay for the 9 farmworkers required to tend each acre of land. Incomes will fall sharply and sadly people will starve.”

At this point the King, loses his temper and turns to the second priest demanding: “Adam, is this true? Are the farmers facing famine?”

Adam, who was becoming increasingly agitated during Karl’s presentation, hands the King his own report – a single sheet of paper marked with just one expression “r ≡ g”.

Adam begins speaking: “My Lord, I fear that my most esteemed colleague, Karl, is talking poppycock. There will be no famine. The problem is, he has got his cause and effect the wrong way round.”

The priests in the gallery, who sense their beautiful crisis slipping away, start hissing and catcalling.

Adam continues: “The relationship between growth and the return on land is not a coincidence. The two are tied together by nothing more nor less than your own accounts, My Lord.
Each acre of land produces 1 year of surplus value and each acre of land is valued at the price, in years of labour, of clearing a new acre of land. It follows that yield of your land is simply 1 divided by years of labour needed to clear new land. However that same calculation also gives you the fraction of each new acre that can be cleared with the surplus generated from each existing acre. You are choosing to calculate the yield on your existing land from the cost of purchasing new land and so the two numbers, r and g, are the same.
Let me explain with some examples.

If it takes 10 years of labour to clear an acre of land, each acre will be worth 10 and will have a yield of 1/10. And each year of labour will pay for 1/10th of a new acre of land. The yield and the rate of growth will be 10% in both cases.

If it takes 20 years of labour to clear an acre of land, each acre will be worth 20 and will have a yield of 1/20. And each year of labour will pay for 1/20th of a new acre of land. The yield and the rate of growth will be 5% in both cases.

If it takes 40 years of labour to clear an acre of land, each acre will be worth 40 and will have a yield of 1/40. And each year of labour will pay for 1/40th of a new acre of land. The yield and the rate of growth will be 2.5% in both cases.

In all cases r will be equal to g simply because, My Lord, you are choosing to value your existing capital at the same price as the cost of acquiring new capital.

I have heard rumours that, in distant lands, this practice is referred to as the no-arbitrage condition or the law of one price and is considered by some to be a fundamental law of capitalism.”

The King pauses for a moment before asking: “And what of the famine and my surging income and asset prices?”

Adam replies: “The price of your land will double, when accounted for in years of labour, but each acre will still produce the same 1 year of surplus value, so the yield on your land will be halved. Your incomings and outgoings will remain unchanged and your workers will be paid just as before. However the rate at which you accumulate new land will be halved.

There will be no famine.”

***

I may be missing something obvious in how I am thinking about Piketty’s thesis. He is arguing we face a low growth future. To my mind, this means that we are faced with a situation where it becomes more expensive to purchase additional economic activity. That is to say the return on new investment must be lower. Yet at the same time he is also saying that the return on the existing stock of investment will remain high even in this new low growth world. I am struggling to understand how the markets will not arbitrage away the different returns available on new and existing capital.

The question I am asking myself is: Does Piketty’s thesis require the impossible situation of having two different prices for interchangeable, fungible, assets?

Clearly the story above is not a model of a modern developed economy. Nevertheless it is a useful aid to assist thinking about the relationships between: return on capital, economic growth, savings rates and capital valuations. Hopefully it helps to demonstrate that it is unreasonable to consider these variables as being independent of one another.

Piketty is of the view that r, the return on capital, and, g, the rate of economic growth are quite independent of one another – to quote: “There’s no pilot in the plane, there’s no natural force that will make this incredible coincidence of pushing the growth rate toward the rate of return happen, and so we need to find another plan in case this does not happen.”

Reasonable people can take a different view on this. Piketty warns of a future low growth world with much higher levels of capital and as a consequence capital’s share of income rising significantly: “experience suggests that the predictable rise in the capital/income ratio will not necessarily lead to a significant drop in the return on capital… With a capital/income ratio of seven to eight years and a rate of return on capital of 4-5 percent, capital’s share of global income could amount to 30 or 40 percent, a level close to that observed in the eighteenth and nineteenth centuries, and it might rise even higher.”

My questioning of Piketty’s thesis is not an attempt to defend the status quo. I have myself written on the flaws in economic theory and offered suggestions on how we may go about reforming the science of economics. Both our economic policies and our economic theories have failed us terribly in recent years. The science of economics needs a radical overhaul, but leaping from one flawed theory to another, without thoroughly testing its logic, is not the way to proceed. 

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30th November 2019

Posted by: George Cooper

The Horrible History of Mr Piketty

I have been asked to re-post four articles origionally written in April/May 2014 about the ideas of Thomas Piketty in his book Capital in the Twenty First Century: The Magical Mathematics of Mr Piketty Part 1 and Part 2, Credit in the Twenty First Century and The Horrible History of Mr Piketty

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The Horrible History of Mr Piketty

This weekend’s Eurovision Song contest saw Austria romp to victory with 290 points, leaving France languishing in last place with only 2 points. Naturally this got me thinking about how the economic ideas of these two great nations stack up against one another. More specifically how Thomas Piketty’s theory of capital accumulation compares with Joseph Schumpeter’s creative-destruction of capital.

***

Whenever it comes to a clash of ideas between the Austrian and orthodox schools of economics you can be sure that methodological differences will figure somewhere in the discussion, so let’s get that out of the way first.

The world is too complicated to understand in the raw so we use simplifying models make sense of what we see. Invariably our simplifying models don’t describe the world perfectly, leaving us with an annoying gap between reality and model – the error term. If the gap is small enough we ignore it, if it is large we are forced to construct secondary models to explain it. Put differently, we construct primary models to explain how the world works and secondary models to rationalize why the primary models don’t work – the former provide the explanations and the latter the excuses.

If we have a good understanding of the system, the primary models will do the heavy lifting leaving little need for the supporting excuses. If we have a poor understanding of the system the gap between model and reality will be large and we will find ourselves defending our models with all sorts of complex excuses.

The orthodox and Austrian schools of economics have developed two very different approaches to modelling economic systems. Orthodox economics insists that the primary model be framed in mathematical language, just like the grownup sciences. These mathematical models tend to describe the economy, with a few equations, as something akin to a mechanistic clockwork system. However, when it comes to providing the secondary excuses, explaining why real economies deviate from the mathematics, orthodox economics is forced to fall back on looser narrative models. By contrast the Austrian school argues that the narrative models usually dominate the clockwork mathematics. So the Austrians prefer to cut out the middle man and go directly to the narrative approach. Put differently, Austrians prefer to be roughly right rather than precisely wrong.

I have sympathy with the honesty and pragmatism of the Austrian school. On the other hand the orthodox school’s approach at least makes it explicit where the model ends and the excuses begin: the former is the maths and the latter the story. The downside of this mixed approach is the necessity to consider the integrity of the mathematical model and the plausibility of its supporting narrative.

The description of capitalism presented in Thomas Piketty’s new book is a good example of the mixed mathematical/narrative genre. The primary model is presented via three mathematical relationships: r > g; β=s/g; α= β×r. These describe a mechanistic process of capital accumulation and the division of national income between workers and the owners of capital. The secondary model is a narrative of capital destruction, centered on World War I:

“In both Britain and France, the total value of national capital fluctuated between six and seven years of national income throughout the eighteenth and nineteenth centuries, up to 1914. Then, after World War I, the capital/income ratio suddenly plummeted, and it continued to fall during the Depression and World War II…

The capital/income ratio fell by nearly two-thirds between 1914 and 1945 and then more than doubled in the period 1945-2012…

Broadly speaking it was the wars of the twentieth century that wiped away the past to create the illusion that capitalism had been structurally transformed.” p117/118

So far, most of the focus of attention has been on Piketty’s mathematical model with little attention given to his supporting narrative.

In the following I am going to play devil’s advocate, providing an alternative story of both the process of European capital destruction and its recent rebound. This alternate story has a distinctly Austrian tone, emphasizing first Schumpeter’s creative-destruction of capital and later the use of monetary policy to manipulate asset prices.

Before I start I should emphasize, this alternative narrative agrees with Piketty’s core message: inequality is problematically high. However, it leads to a different explanation for this problem and therefor points toward different remedial policies.

Piketty presents the following chart to show the precipitous decline in the value of European capital due to World War I. (Figure I.2.)

Capital Fig 1.2

Later in the book Piketty provides a richer data set showing the composition of the different components of capital which make up the data in Figure I.2. These are figures 3.1, 3.2 and 4.1 showing the value of agricultural land, housing, other domestic capital and net foreign capital for Britain, France and Germany respectively.

The charts of the composition of capital in Britain and France are especially informative. These show that the movements in the value of capital, from 1700 to the present day, have been dominated by two processes. The first was the near total destruction of the value of European agricultural land, the dominant form of capital in 1700. The second is the more recent rise in the value of housing over the last three or four decades.

Capital Fig 3.1

Capital Fig 3.2

If we choose to focus on the changes in the value of Agricultural land and Housing, individually, it becomes more difficult to associate their changing values with the two World Wars. The decline of agricultural land values began in Europe long before WWI while the surge in the value of housing really only took-off at the start of the 1980’s.

It is worth also looking at Piketty’s first chart, Figure I.1, showing the share of total income going to the top 10% of wage earners in America.

Capital Fig 1.1

This chart is interesting because it shows a clear change in behavior at the start of the 1980’s. Although not in Piketty’s data set another pair of charts showing a similar change in behavior around the start of the 1980’s is the total debt to GDP ratio for the US and the fraction of national income taken by corporate profits.

US Debt-GDP

US Profit-GDP

An alternative story, describing the trends in these charts, could be constructed from a pair of emerging market shocks rather than a pair of World Wars.

Emerging Market Shock #1 - North American Agriculture

Throughout the 19th century European agriculture came under increasing competitive pressure from the emerging economies of North America. This pressure was stepped up around the middle of the 19th century with the abolition of the Corn Laws in England and later the end of the American Civil War in 1865. At around this time there was a major expansion of the railway system within North America and a dramatic improvement in the speed and reliability of sea freight, with the development of steam ships. Both the railways and the steam ships connected North American grain producers directly into the newly liberalized European export markets. This drove down grain prices and therefore European agricultural land values. Then in the 1880’s the invention of refrigerated shipping opened up the European markets to competition from foreign producers of meat and dairy produce.

As a result, European landowners were progressively priced out of the newly globalized food market. Farm rents and therefore land values fell, while on the other side of the coin, labor prices remained high due to increased demand for labor through emigration to North America and migration to industrial work.

These developments are well illustrated by the following passages:

“Free-trade policies, which had been fully introduced in the 1850’s and 1860’s had left British agriculture highly vulnerable to foreign competition, which proved to be the main factor in producing a long period of agricultural depression during the last quarter of the nineteenth century, as cheap cereals began to flow in from Canada, the USA, Australia and Argentina, while the invention of refrigerated shipping in the 1880’s brought livestock farmers too within the range of foreign competition. Agricultural prices, rents, and land values all fell sharply, undermining the economic basis of landed power…

…Following the repeal of the Corn Laws in 1846, the living conditions of the labouring classes in England, roughly 70 percent of the whole population at that time, at last began to improve slowly at first but later at a quickening pace… The lowest paid of all the working classes throughout this period were the agricultural labourers… an index of their money wage levels in England and Wales moved from 72 in 1850 to 110 in 1901, a rise of 53 percent. In real terms, moreover, their wage rise had been even larger, because this increase in money wages had taken place against a background of generally falling prices…” Agriculture and Politics in England 1815-1939 J.R. Wordie

“The effects of depression on the three economic groups involved in farming were unequal…landlords fared worst with a decline of about 30 percent in their income from the land between 1880 and 1900…the group who fared best, mainly because of the huge decrease in their numbers from over 1.4 million in 1861 to around a million in 1911 , were farmworkers, whose average incomes rose by over 50 percent… by the 1890’s neither tenants nor landlords had sufficient capital left to adapt to new conditions…in East Anglia, Essex, Wiltshire, Oxfordshire, Berkshire or Kent rental values declined by over 36 percent between 1873 and 1911.” Agriculture in Depression 1870-1940, Richard Perren

Clearly the downward pressures on agricultural land, the main component of European capital, was in place long before World War I. Indeed the social disruption caused by the declining wealth of the landed aristocracy, coupled with the emergence of organised labor in the industrializing cities, makes it possible to paint a picture which reverses Piketty’s direction of causality between capital destruction and World War I. It could be argued that World War I was more a symptom of the social upheaval caused by the destruction of European agricultural capital rather than its cause. By 1914 the ruling elite had neither the wealth nor the incentive to preserve the status quo and avoid war.

The rise of North American agriculture could be considered as a land shock – suddenly the world had a dramatic increase in agricultural land and therefore a relative shortage of labor. The effect of this was to drive down the price of what the rich had – land – and drive up the price of what the poor had – labor – causing society to become more egalitarian.

Emerging Market Shock #2 - Chinese Manufacturing

The second emerging market shock began in the 1980’s and continues today with the rapid industrialization of the emerging market economies of Asia, Latin America and Eastern Europe but most especially China. Competitive pressures from cheap labor in these emerging economies held back wage growth in developed economies, especially in the Anglo Saxon economies which were most ideologically wedded free market competition.

In addition, the surge in low priced exports to the developed economies drove down inflation. The central banks of the developed economies responded to the lower inflationary pressures and weaker wage growth by attempting to artificially stimulate their domestic economic activity with lower interest rates. This policy, inadvertent or not, then lead directly to the asset price inflation which is behind the rise in the price of European housing and which is largely responsible for the increase in what Piketty classifies as European capital.

For global corporations this was the perfect scenario, they were able to maximize profits by borrowing money where it was cheapest – in effect from their domestic central banks – and combine those cheap funds with the cheap emerging market labor. Meanwhile their domestic customers were kept buoyant with a binge of debt fueled spending. Taken together, these factors conspired to drive up the profit to GDP ratio. At least some of what Piketty calls the super-managers managed to persuade their shareholders that this surging profitably was due to their own acumen rather than the twin tailwinds provided by central banks and cheap labor.

The rise of Chinese manufacturing could be considered as a labor shock – suddenly the world had a dramatic increase in labor and therefore a relative shortage of capital. The effect of this was to drive down the price of what the poor had – labor – and drive up the price of what the rich had – capital – causing society to become less egalitarian (at least when considered from the perspective of the Western worker).

This alternative narrative in no way diminishes the inequality problem that Piketty is highlighting but it does throw up an important challenge to his primary mathematical model. The destruction of European agricultural capital in the 19th century was not due to an exogenous World War but to an endogenous process of innovation. European agricultural capital was wiped out by connecting American farmers and cowboys to their European customers with the innovation of steam trains, steam ships and refrigeration.

Capitalism may be better viewed as an innovative, Darwinian, competitive struggle rather than a clockwork process of never ending accumulation. Winners – Apple’s iPhone – often create capital by destroying the capital of the losers – Nokia. This endogenous capital destruction is missing from Piketty’s mathematics but is well captured by Schumpeter’s creative-destruction.

Schumpeter’s model of creative destruction does not lend itself to simple mathematical modelling, none the less it has history on its side. The Austrian narrative approach to understanding economies may be imprecise but, at least until the mathematics catches up with reality, it should not be dismissed.

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30th November 2019

Posted by: George Cooper

Credit in the Twenty First Century

I have been asked to re-post four articles origionally written in April/May 2014 about the ideas of Thomas Piketty in his book Capital in the Twenty First Century: The Magical Mathematics of Mr Piketty Part 1 and Part 2, Credit in the Twenty First Century and The Horrible History of Mr Piketty

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Credit in the Twenty First Century

 

The economist Thomas Piketty has a new theory of capitalism and he is using it to argue for a radical overhaul of the global tax system – he wants an annual wealth tax, imposed on all our assets, including our houses, at a top rate of 2 percent per year. So far, he has convinced a lot of leading economists and he is doing his best to persuade policymakers also.  The Nobel prize-winner Paul Krugman says: ‘if you think you’ve found an obvious hole, empirical or logical, in Piketty, you’re very probably wrong.’ – I suspect there is such a hole and it’s a big one.

Make no mistake, the ideas in Mr Piketty’s new book Capital in the Twenty-First Century are important. If his new theory of capitalism is correct we risk a future of Dickensian income inequality – it would be disastrous to ignore him. On the other hand, if his theory is incorrect his tax policies could crush economic growth – it would be disastrous to follow him. Either way, it is worth understanding his ideas and probing for their weaknesses.

Piketty’s new theory all turns on a simple inequality, his now famous, r > g. This means the return on capital, r, is always greater than the growth rate of the economy, g. To understand why this is so important we have to delve into the theory and data in Piketty’s book.

Piketty is known for his studies of income inequality. His most famous chart shows, since the 1980’s, the top 10% of wage earners in the United States have been taking home a steadily larger and larger slice of the economic pie. Currently they are taking almost half of all earnings, a figure not seen since prior to World War II (Fig I.1 p24).

Capital Fig 1.1

Income inequality is only a small part of Piketty’s new book. He now has a new concern – wealth inequality. To Piketty, wealth inequality is an even bigger problem than income inequality because wealth is less evenly spread and is growing much faster than wages, a trend he expects to continue. (Fig I.2, P26).

Capital Fig 1.2

To understand why Piketty is so worried about the consequences of wealth inequality it is necessary to understand his new theory of capitalism. Fortunately it’s very simple.

Piketty explains that the equilibrium ratio of national assets to national income, β, is determined by the economy’s annual savings rate, s, and its annual growth rate, g, according to the formula:β =s/g . So, if an economy saves 10% of its income and grows at 2% it will eventually accumulate assets worth five years of annual income, β = 10%/2% = 5.

Piketty also notes that the share of the national income going to the owners of the economy’s capital is simply the value of the capital, β, multiplied by the average return on capital, r. Therefore, if an economy has 5 years of capital, yielding 5%, the owners of that capital will enjoy 5x5% or 25% of the annual income of the economy, leaving the other 75% for the workers.

Piketty expects that economic growth will decline, due to lower birth rates and less technological progress. Anticipating lower demographic growth is uncontroversial, forecasting falling productivity growth is a bit more speculative. To illustrate his argument, I will consider what happens as economic growth declines from 2% to just 1%.

According to Piketty’s model this prospective halving of economic growth will cause a doubling of the value of the capital of the economy. Assuming the savings rate stays constant, at say 10%, the capital stock will go from being worth 5 to 10 years of income.

So far there is nothing new or controversial in Piketty’s ideas.

The novelty in Piketty’s thinking is that, he believes, the return on capital, r, is something akin to a universal economic constant. Piketty thinks capital always earns an average real yield of 4-5%, which is itself always higher than the economic growth rate, which rarely gets above 2%, hence r > g. For simplicity I will assume a return on capital of 5%.

We can now see the source of Piketty’s concern. As growth falls from 2% to 1% the value of the capital in the economy will rise from being worth 5 to 10 years of annual income. As that capital earns a fixed 5% yield, the returns enjoyed by the owners of the capital will increase from 25% to 50% of the annual income. Consequently the share of income available for wages will fall from 75% to 50% percent.

Put bluntly, as growth halves, the rich owners of capital can expect their earnings to double while the workers can expect their wages to be cut by one third. This is why Piketty anticipates a Dickensian level of inequality in a future low-growth economy.

This logic leads directly to Piketty’s call for a 2% annual tax on the value of capital. By imposing this tax, as growth falls and capital values rise, the revenue from the 2% wealth tax will automatically rise, providing greater revenues to subsidise the falling wages of the workers.

Before leaping Krugman-like onto Piketty’s bandwagon we should pause for thought.

Until just a few weeks ago conventional wisdom said that we should expect the returns on capital to move up and down with economic growth – high growth means high yields and low growth means low yields. Indeed, the working assumption of many in the financial markets was that the average real return on the whole stock of capital was equal to the real rate of economic growth: r = g , rather than Piketty’s r > g.

The distinction between r > g and r = g is important. If the return on capital moves up and down with economic growth then, as growth halves, the value of capital will double. But this doubling of capital will be exactly offset by a halving of its yield, leaving the returns on capital unchanged. In other words, if r = g, changing rates of economic growth will do nothing to shift the relative balance between the incomes of workers and the owners of capital. Piketty is admirably forthright on the importance of his r > g assertion: ‘This fundamental inequality, which I will write as r > g … sums up the overall logic of my conclusions.’ P25

This brings me to a curious aspect of Piketty’s 600+ page book which is generously peppered with charts and tables. Over the last three or four decades we have had a series of excellent empirical tests of Piketty’s inequality. Economic growth in Japan slumped dramatically at the end of the 1980’s, followed more recently by similar slumps in Europe and North America. Over this period the keeping of records of both growth and yields has been comprehensive – yet we find none of this, very relevant, data in Piketty’s book.

Unfortunately for Piketty’s thesis, we have found, reliably and repeatedly, that when economic growth falls asset yields also move down – often dramatically. The data of recent decades overwhelmingly refutes Piketty’s claim that the return on capital is independent of and substantially higher than the underlying economic growth rate. The data is far more supportive of the conventional wisdom, r = g and not of Piketty’s new claim r > g. The perilous funding position of many pension funds and the recent decision to remove the requirement for pensioners to buy annuities are both direct consequence of investors being unable to invest at the returns Piketty claims are available.

Piketty provides some very curious data to support his r > g claim, the most interesting of which is a chart showing economic growth rates and returns on capital from the birth of Christ to almost 100 years from now. So far this part of Piketty’s data has attracted little attention, but it is by far the most important data in his book.

(Fig 10.9, P354).

Capital Fig 10.9

As discussed, the brief period for which we do have reliable data refutes Piketty’s r > g inequality and we can say nothing with certainty about the future. Therefore the empirical support for Piketty’s thesis rests, oddly, on his estimates of economic growth and capital returns in antiquity.

We can be surprisingly precise in our estimates of economic growth in antiquity – there wasn't any, or at least very little. We know this because archaeological evidence tells us that population growth rates were very limited and technological progress almost absent in this time. Living standards in the year 1,000 were not markedly better than those when Christ was alive. For this to be the case the average annual economic growth in the first millennium must have been very close to zero, as Piketty’s data suggests. 

On the face of it, it is more difficult to say anything reliable about the returns on capital in this time, but with a little imagination we may be able to learn something interesting.

Consider an isolated island kingdom in the year zero. It is a perfect feudal society where the King owns everything and his subjects work for him. Half of the island is covered in productive farmland, the other half of the land is too rocky to farm. The King employs all of the workers in the economy. Most workers are employed to farm the productive land, while a few are employed to clear rocks from the unproductive land. Over many generations the kingdom is handed down from father to son. Each new King continues investing in the expansion of the island’s productive land. By the year 1,000 the whole of the island’s land has been converted into productive farmland.

Over the millennium, the island’s economy would have doubled in real terms, as the farmland expanded – a cumulative growth of 100%. The King in the year 1,000 would own an economy twice as large as that of his ancestor the first King. The cumulative return on the first King’s original capital would have been 100% in line with the 100% growth of the economy. This requires that real economic growth and real capital returns must be identical, r = g.

This helps explain a potential problem with Piketty’s logic. If the total stock of capital represents ownership of the entire economy: how can the entire capital stock grow at a rate that differs, in any way, from the growth of the whole economy? Indeed, it could be argued, that the whole capital stock and the whole economy are one in the same thing. If this logic proves valid – and it should be tested – conventional wisdom is correct: average real returns on capital and average real economic growth rates are synonymous. If so, then perhaps we can add a third fundamental law of capitalism to Piketty’s collection: r ≡ g. In which case there are very big empirical and logical holes Piketty’s theory.

If r = g is found to be valid, how can we explain the gap between r and g shown in Piketty’s chart in ancient times? It may be that these yields represent not a return on capital but rather a return on credit. Let me explain:

During the millennium-long island dynasty, it would be quite possible for the islanders to borrow and lend between themselves, perhaps at quite high interest rates. The interest rates, on these loans, would represent only the charges on the debts and credits between citizens. Since every credit was exactly offset by its matching debit these transactions would, by construction, net to exactly zero and would not therefore represent any ownership of the island’s capital. However, the interest rates charged on these loans would represent a mechanism for transferring income between citizens. If the interest rates charged were sufficiently high and the stock of credit sufficiently large this could represent a powerful wealth polarizing force acting between the citizens of the island. The King may own all of the capital of the island but still, through the mechanism of credit, the wealth of individual citizens could become quite polarized relative to one another. I do not know for certain, but I suspect, the interest rates recorded in antiquity, and shown in Piketty’s chart, are more representative of returns on credit rather than the average real returns available on whole stock of the economy’s capital in those times.

Piketty has done the world a service in placing income inequality at the centre of the economic debate, where it should be. He has also got people thinking about whether or not capitalism suffers a tendency toward wealth polarization – it must do, otherwise progressive taxation would have long since depleted the fortunes of the rich. But the validity of his new theory is doubtful. If his r > g relationship proves incorrect and real yields on capital do in fact move with underlying economic growth then, in a low growth environment, the imposition of a 2% wealth tax could push real yields on capital negative potentially bringing entrepreneurial activity to a shuddering halt. What’s more we should consider the pro-cyclical nature of such a taxation: in a recession when profits collapse the owners of capital could be forced to sell assets, into a falling market, in order to fund taxes levied on historic elevated valuations. For this reason alone taxation based on tangible income received rather than based on ephemeral market valuations is to be preferred.

Progressives may wish to consider another aspect of Piketty’s argument. Piketty’s thesis says inequality is caused by slowing growth. Therefore, Piketty’s story says that even if inequality is addressed growth will not return – demographic factors are fixed and innovation he sees as exogenous. This offers little in the way of incentives for the tough political decisions necessary to achieve reform. There are other, more persuasive, more optimistic, arguments that put the causality the other way round – excessive inequality causes slow growth. These arguments offer more powerful incentives for constructive reform.

Conclusion

I suspect Piketty’s thesis r > g will not prove robust to either empirical or theoretical scrutiny. His proposed wealth tax looks to be neither desirable, necessary nor attainable. His focus on capital rather than credit as the principal wealth polarizing mechanism is, I believe, a misdirection which risks diverting attention away from credit, banking, financial market and monetary reform. For these reasons I worry that Piketty’s thesis may ultimately prove to be something of a Trojan horse for genuine reformers.

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