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# Why Wealth-to-GDP Must Mean-Revert –

Reversion to the mean is the iron rule of the financial markets.

John C. Bogle

## Issues to be addressed in this research paper

A few weeks ago,  a gentleman, who had just subscribed to ARP+, gave us his reasons why he had signed up.  Most importantly, he said, he wanted to read our thoughts on wealth-to-GDP, and why it is due to mean-revert.  That was a first for me, so I got intrigued and contacted him.  Cutting a long story short, you are now holding the gist of that dialogue in your hands.  It is indeed a fascinating topic and, if the underlying theory is anywhere near correct, we could be in for some rather tricky times in financial markets.

Before I begin in earnest, allow me to share a definition with you:

“Gross national income (GNI) is defined as gross domestic product (GDP), plus net receipts from abroad of compensation of employees, property income and net taxes less subsidies on production.” (source: OECD).

As you can guess from that quote, GNI and GDP are highly correlated, and that correlation is critical, when I argue that wealth-to-GDP must mean-revert.  GNI, and therefore also GDP, ultimately ends up in one of two pockets – either the pockets of labour or those of capital owners.  Total wealth in society is the combined wealth of those two groups of economic agents.  Growth in wealth in any given year is only a fraction of GNI/GDP that same year, whereas total wealth in society exceeds GDP in any given year.  The Americans provide much more detailed data on this topic than we do here in Europe; hence, in the following, I will use US data to make my case.  I should point out, though, that the underlying logic is exactly the same, whatever country or region you look at.

One more point before I move on.  According to OECD Data, total wealth is defined as the total value of household assets (financial as well as non-financial) minus the total value of outstanding liabilities of households.  On top of that, the wealth of non-profit organisations is added.  As the same methodology is applied all over the OECD, wealth data is comparable across the OECD but not necessarily across the world.

## The main components of wealth

As of the latest count, total US household wealth amounts to $143.3Tn. That is made up of$162.5Tn of assets and $19.2Tn of liabilities. The parts that make up most of that wealth are equity in property (20.6% of total household wealth), pension entitlements (20.5%), corporate equities held directly (17.0%), equity in non-corporate businesses, typically family-owned businesses (11.8%) and mutual funds (6.5%) (Exhibit 1). The three asset classes that make up most of that wealth are equities, bonds and property. As you can see in Exhibit 2 below, equity holdings account for the lion’s share of financial assets in US households. The numbers clearly support the perception that Americans are, first and foremost, equity investors. In fact, more household capital is tucked away in equities than in bonds and bank deposits combined. This dynamic is supportive of economic growth in bull market times; however, given the substantial sell-off in US equities this year, the negative impact on GDP growth should be measurable. In fact, some impact has already been noticed. US GDP declined in the first two quarters of this year, -1.6% in Q1 and -0.6% in Q2. Although the National Bureau of Economic Research (NBER) chose not to declare a recession (in the US, only the NBER holds the power to decide whether it is a recession or not), by European standards, a shallow recession clearly hit the US economy in the first half of 2022. The US approach is very different from most of the rest of the world, where two consecutive quarters with negative GDP growth automatically make it a recession. The drop in US equities in the first half of this year had a meaningful impact on household wealth. As you can see in Exhibit 3 below, US household wealth dropped marginally in Q1 and by about$6Tn in Q2.  As you can also see, the drop in equity valuations explains almost all of the loss in wealth.

The composition of total wealth varies from country to country.  For example, in the Germanic part of Europe, the appetite for income-generating investment vehicles (mostly bonds) is much bigger than it is in the US.  Therefore, fluctuations in equity markets will not have nearly the same impact on wealth there as it will in the US.  That also means that a big selloff in equity markets in (for example) Germany won’t affect German consumer spending as much as a big selloff in US equity markets will affect American consumer spending.  That said, the underlying logic is exactly the same everywhere.

We publish investment strategies and opportunities in our research papers. This research paper is available to professional investors as part of ARP+ subscription.

## Recent trends in labour’s share

Wealth-to-GDP has followed the same trajectory as capital owners’ share of GNI, which happens to be the inverse of labour’s share of GNI.  Labour’s share started to decline in the 1980s (Exhibit 4) and, consequently, wealth-to-GDP began to rise (Exhibit 5).  Effectively, capital owners began to take as bigger slice of the pie.

As you can see in Exhibit 4, the phenomenon is not unique to the US.  In many other OECD countries has labour’s share been under pressure over the last 30-40 years.  As you can also see, in no country is it a straight line, but labour’s share has been trending down in most countries.  Although there are exceptions to that rule (e.g. Sweden and the UK), as you can see in Exhibit 6, on an aggregate basis, the trend is clear, whether we look at advanced economies (AEs), emerging market economies or developing economies (jointly EMDEs).  Labour’s share has fallen all over the world and, when that happens, wealth-to-GDP is on the rise.

Although there are countries that deviate from that trend (e.g. Sweden and the UK), as you can see in Exhibit 6, on an aggregate basis, the trend is clear, whether we look at advanced economies (AEs), emerging market economies or developing economies (jointly EMDEs).  Labour’s share has fallen in most countries and, when that happens, wealth-to-GDP goes up.

I should add that, in most research conducted on this topic, the ratio of total payrolls-to-sales is used as a proxy for labour’s share of national income, and it is indeed a good proxy.

## Why wealth-to-GDP must mean-revert

Back in February 2021, I wrote the first paper on this topic (you can find it here).  In it, I made the following observations:

“In economic growth theory, the capital-to-output ratio is long-term stable. In the US, it has traded in a range of 3.1-3.8 times [over the last two centuries], depending on which types of capital you include in the numerator. For example, earlier growth models did not include human capital, but they do now, leading to a larger numerator and thus a higher capital-to-output ratio more recently.”

Now, almost two years later, two questions are still hanging in the air.  What is the wealth-to-GDP ratio now and why must it mean-revert?  Why can’t wealth-to-GDP just keep growing?  The simple question first.  As you can see in Exhibit 5, US wealth-to-GDP has corrected somewhat since 2021, where it peaked at 6.2 times but is still elevated at 5.6 times. Although other countries do not provide the same underlying data, which would allow you to calculate the precise ratio, I can comfortably say that it is elevated everywhere but not as dramatically as in the US.  Years of asset price inflation explain why.

To answer the second question, I need to go into the economic theory behind it all.  The key parameter is the elasticity of substitution between capital and labour – a measure that drives labour’s share of national income.  When capital is highly substitutable for labour, i.e. when the elasticity of substitution is higher than one, a decline in the relative cost of capital drives firms to substitute capital for labour to such a high degree that, despite the lower cost of capital, labour’s share of national income declines very quickly.  When the elasticity is between zero and one, labour’s share still declines but more slowly when the cost of capital drops.

In theory, the elasticity of substitution could be zero.  In that case, labour’s share of national income would be unaffected by the cost of capital.  In practice, the elasticity of substitution is never zero but almost always less than one.  The reason I can’t  give you an exact number is that is very much depends on the assumptions behind the study in question.  What doesn’t vary from study to study is the trendline, though.  All research into this topic suggests that the elasticity of substitution has been on the rise in recent years.

This finding is consistent with the discovery that labour’s share of national income has been falling in recent years.  The higher the elasticity of substitution,  the more likely companies are to switch from one to the other, assuming the relative costs change.  As interest rates have come down, the cost of capital has declined meaningfully.  The combination of rising elasticity of substitution and lower capital costs has led to a drop in labour’s share of national income.  (See the list of supporting literature at the end, if you want to dig deeper on this topic.)

Now, the macroeconomic argument in favour of mean reversion is that the cost of capital cannot fall forever.  At some point, interest rates will rise.  Thus, the cost of capital will also rise.  Evidence from 2022 is pretty powerful in this respect.

I introduced the microeconomic argument in favour of mean reversion in the 2021 paper.  As I said, you can prove mathematically that the ratio of capital-to-output is always in the range of 3-4 times, regardless of how developed the economy in question is, as long as it is an open market economy.  Therefore, you cannot apply the logic to China.

Capital-to-output is another term for wealth-to-GDP; i.e. you can prove that the economy is only in balance when wealth is 3-4 times that of GDP.  Any ratio outside of that range will lead to mean reversion.  Some ARP+ subscribers have argued that the introduction of advanced robotics and AI is going to drive wealth-to-GDP much higher, but the follow-on from the above is that the capital-to-output ratio should be unaffected by the invention of new technologies.  Consequently, so should wealth-to-GDP.   Therefore, we know that the steep rise in wealth-to-GDP over the last 25 years (see Exhibit 5 again) is unsustainable and can only be justified if the underlying theory can be proven wrong, and nobody has been able to do so yet.

Summing it all up, there are effectively two reasons why wealth-to-GDP must mean-revert in the years to come:

1. So long as the elasticity of substitution between capital and labour is positive (and it has always been), when the rise in interest rate reaches a certain point, it will no longer make sense for companies to substitute capital for labour.  At that point, labour’s share of national income will begin to rise again.

2. Irrespective of what happens to interest rates, the economy is only in balance when wealth-to-GDP is in the range of 3-4 times.  In the US, it is currently almost 6 times.

Before I close for Christmas, one final observation.  In the studies I have read in preparation for this paper, many reasons have been given for why labour’s share has actually fallen in recent years.  In no particular order, the following five reasons stand out:

1. lower costs on capital-heavy equipment, particularly IT equipment, after digitisation was first introduced in the 1990s;

2. more international trade and outsourcing;

3. reduced unionisation, i.e. lower bargaining power;

4. changing social norms, for example more spare time demanded by workers; and

5. the rise of superstar firms.

Although all of these factors have most likely played some role, the rise of superstar firms has, in academic circles, probably become the generally accepted primary cause.  The logic is fairly simple.  If a change in the economic environment provides the most productive firms (the so-called superstar firms) with an advantage, product market concentration will rise and the labour share will fall, as the share of value-added generated by the most productive firms in each sector grows (source: Quarterly Journal of Economics).

Going forward, one could argue (as some of our subscribers have done) that reason #1 above will, in the years to come, play a major role and effectively drive wealth-to-GDP to new all-time highs.  Think advanced robotics, AI, IoT, etc.  Although the economic theory behind all of this says nothing about timing, nor does it say anything about how much out-of-balance wealth-to-GDP can be before it must mean-revert, it is pretty obvious that the overall economy is not in balance at present.

The gap between rich and poor continues to get bigger and bigger.  After a bonanza year in financial markets in 2021, the wealthiest 1% of all Americans ended up with 32.3% of national wealth, equal to $46Tn in net worth – a rise of no less than$12Tn during the pandemic.  Meanwhile, working class families are increasingly struggling to make both ends meet.  Children go hungry to school, and families are evicted from their home, as there is not enough money to pay the bills.

Whether you believe in the underlying economic theory or not, governments should remind themselves that the French revolution in 1789 happened for a reason.  There is a limit as to how much misery people are prepared to accept, and the sharply rising gap between rich and poor should be addressed, before the mob takes it into its own hands.

Have a most enjoyable festive season!

Niels C. Jensen

21 December 2022