Since it bottomed on March 18 the JSE had been roaring upwards like most other global share markets as investors shrugged off all the gloom and doom of the Covid-19 pessimists and gleefully pointed out that the pandemic was less a catastrophe that might forever change the world and more a golden opportunity to scoop up gilt-edged assets at bargain-basement prices.
Now it is back to normal with a sideways trend projected for the JSE All Share Index for the foreseeable future. And if you find that disappointing, be grateful because the outlook for the South African economy, within whose constraints JSE companies have to operate, if far from healthy. Indeed, the leaders in the JSE Top 40 Index predominantly source their profits abroad and, without them, our marketplace would be a very lackluster place. Consider my first graph into which I have drawn two parallel trend lines dating back to the start of 2019 which, interestingly almost perfectly contain ShareFinder’s projection for the overall index through to the middle of next year:
Bar the two banks, all the top ten weighted shares in the Top40 draw most of their profits from abroad. They are Naspers with a 17.44% weighting, BHP with 11.05%, Richemont with 9.37%, Standard Bank with 4%, FirstRand with 3.51%, MTN with 3.12%, Prosus with 2.96%, Sasol with 2.69%, BAT with 2.62% and Mondi with 2.38%.
Care to total those percentages and you will see that they represent nearly two-thirds of the index (59.14%) while just the top three represent nearly 40 percent of the index. So, bearing those weightings in mind, it is really interesting to look at the performance of the JSE Top40 Index since the JSE peaked in November 2017, after one of the longest bull runs in its history. Here, considering my next graph, you can see that I am able to draw in the same parallel trend lines onto the Top40 Index, making clear that it was in a decline throughout that period. However, ShareFinder predicts that an upward break-out is now likely and that for the next 12 months it will remain well above the upper trend line.
The obvious conclusion to make from this is that listed companies which draw their profits from abroad are likely to outperform the locals in the foreseeable future. But before you opt to move too rashly, and bearing in mind that since we began measuring the accuracy of these forecasts in January 2002 their average accuracy rate has been 85.83 percent, let us consider what ShareFinder says about the New York Stock Exchange.
Countless studies have shown New York, as depicted in my graph below, by the most representative of its indices, the S&P500 Index, is the main driver of all the world’s major exchanges. Thus, the prediction traced out by my red trend line that Wall Street is already in a decline that is likely to continue until at least the first week of November, should suggest that long-term investors exercise caution about investing on any of the world’s exchanges for the next few months:
Here, it is probably appropriate to add that ShareFinder predicted a major crash in 2020 which was what prompted me to write the book ‘The Crash of 2020’, which has been serialized within this publication and which, I hope, warned the most of you to at least exercise caution late last year and, hopefully, create cash within your portfolios in order to take advantage of it.
I am not, however, seeking to criticise the cautious folk who did not listen. After all, before resorting to our normal route of publishing direct to everyone on the ShareFinder International database, I offered the manuscript of “The Crash” to every major book publisher on a “no royalty” basis because I believed it urgent that as many South Africans as possible be warned in advance. To my deep regret, all of them, as well as all of the financial journals, completely ignored the book.
Throughout history, of course, people have preferred to kill the messenger rather than accept unpalatable news, so I really should not bear those editors any malice. After all, innumerable studies have shown that those who resisted the temptation to regularly buy and sell win hands down in the long run because it is nearly impossible to successfully time the market every time while those who try to do so usually end up benefitting the tax man and their stockbrokers more than they do themselves. Of course, these studies have largely represented unit trust investments which have generally performed badly for investors in South Africa, but that is another story!
That view is surely borne out by the 67-year history of the S&P500 Index. You just need to look at the graph to see that the passive investor who invested one dollar on February 5 1953, where our database begins, and never once traded it, would have seen his one dollar grow to $13 750.68:
I would, however, beg to differ in part with this ‘buy and hold’ viewpoint because, in theory anyway, the incredible predictive accuracy of the ShareFinder computer programme is a clear game-changer. Nevertheless, I have to admit that although I designed the programme and have used it consistently to guide my own investments for over 30 years, I have NEVER been able to consistently buy at the bottom nor consistently sell at the top. I have, however, usually managed to average my way in at the bottom while capital gains taxation has prevented me from selling out completely whenever I have seen markets peaking.
But let us take the theoretical position of an investor who saw that the JSE was bottoming all the way back in February 1988 following the great 1987 market crash. It happened on February 29 when the JSE Overall Index stood at 151.80 and thereafter it rose with leaps and bounds until it peaked at 6177.67 on January 26 2018….the most impressive market climb in the world!
Since then, under pressure from recent recessionary conditions, it fell fairly steadily until the world was hit by the pandemic when it went into a seeming death spiral. Then it turned again and recovered to a peak value of 5562.71 on June 23.
My graph below indicates that any investor lucky enough to have bought the index at its precise bottom in 1988 and held it unchanged until the January 2018 peak, as highlighted by my green trend line would have, every year since, enjoyed a compound annual average gain of 13 percent while, if he had continued holding until this week his annual average gain would have been 11.7 percent as represented by my red line.
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If you care to work that out for yourself, you will see that had our investor put in R1 000 back in 1988 his investment would have been worth R40 696.11 at the 2018 peak and R36 644.91 last week. You can compare this type of investment to a tracker unit trust which seeks to replicate the index….a far better performance in a much shorter period that Wall Street managed!
But remember, that was the share market average and, of course, quality really does makes a difference when you choose your investments which is why I set about building the ShareFinder system in the first place. By sorting out the companies that had paid constant or rising dividends for a minimum of ten years and applying a few other tests relating to tradability, return on capital and so forth, I derived a “Quality List” and within the ShareFinder system we have tracked the value of a portfolio of such shares since that Blue Chip Index bottomed on November 6 1987 at an index value of 4597. The index subsequently peaked on January 26 2018 at a value of 920 390 which represents a compound annual average gain of 17.9 percent while, had our investor continued holding such an investment it would have given him a compound annual average gain to date of 17.5 percent with an index value on June 23 of 769 874.
The difference in capital gain between the two approaches is dramatic. If you care to work that out, you might see for yourself that by applying the quality test, you could massively enhance your investment. In monetary terms, R1 000 invested back in 1987 would by this method have grown to R200 215.36 which clearly illustrates that by matching superior quality to the power of compound you can dramatically improve your results. That sum is a massive five times the gain that would have been achieved by someone who simply followed the JSE Overall Index itself…or bought a tracker fund!.
Furthermore, it really is possible, by using the tools that the ShareFinder system provides, to improve upon those averages without having to incur massive capital gains penalties. To justify this claim I have to use the real live example of my own portfolio and here I should add that my stockbroker recently commented to me that, “You NEVER sell.” It was fair comment since I am absolutely not prepared to pay our outrageous levels of capital gains tax and furthermore, after paying the also outrageous obligatory 20 percent dividend tax, I these days draw down all dividend income. Thus, the only way I am able to create cash within my own portfolio ahead of an impending crash is to sell off loss-makers to balance selling a portion of my gainers in order to create a capital gains neutral position and simultaneously allow me to periodically re-balance my portfolio.
I trust readers will thus forgive me for, in the interests of modesty, removing the right-hand scale of my personal portfolio performance graph depicted on the next page. What is important for readers is, after all the percentage movement of the portfolio rather than its actual value. Reading off the best case green trend line shows that during the lifetime of this portfolio it had grown at an annual average rate of 22.8 percent until it peaked in January 2018 while at this week’s value it had achieved a compound annual average growth rate of 17.1 percent as denoted by the red trend line. So, in contrast with the Blue-Chip Index, I have achieved a 41 percent better return.
How is this possible? Well, you need to recognise that, once again, the Blue Chip Index is an average of the performance of, at the current count, 43 different shares which, while offering one a very comfortable investment spread, also offers a spread of share price average growth rates. By contrast, my personal portfolio consists of, the best-performing half; a very diverse 21 shares which, with few exceptions, are all enjoying much higher than average share price growth rates than our Blue Chip Index.
Inevitably then many readers will ask why, if it is possible to use the superior selection tools offered by the ShareFinder system to choose the shares in my portfolio, I still have underperformers to sell off whenever I need to create cash ahead of an anticipated crash? And the answer to that is, of course, that yesterdays’ long-term top performers do not always remain top performers. Take the example of former super Blue Chip Sasol which I bought back in March 2003 at the then price of R85.68 and continued buying periodically up until February 2006 so that my average cost was R261.
When Sasol dropped its dividend in 2008, the shares crashed but soon began recovering with good fundamentals until mid-2014 when problems with their Lake Charles project began to surface. They were already on my radar to sell by then, because their fundaments had begun to deteriorate but, at R636 a share, the capital gains implications for a share that had cost me on average R261 were too great to contemplate. But when they began to fall like a stone this year, it was clear that bad was turning to worse and I cut my losses, in the process providing myself with a very useful lump sum with which to re-enter the market at the end of March.
Over the years I have learned that with some inevitability that yesterday’s winners do not necessarily remain tomorrow’s gainers. But the major single enemy of the long-term investor is capital gains taxation which hinders rational portfolio management. Ironically it makes so little for the tax man that I frequently wonder why this tax is maintained, particularly when it so severely deters South Africa’s desperate need to attract long term investment
Below I have reproduced the Sasol graph since then. The green line describes its ultra Blue Chip era when it was gaining at compound 23.2 percent annually from 1999 to 2014, followed by a sideways trend until mid 2019 and then the death spiral to R20.77 and equally dramatic recovery to R183.88 which I was fortunate to catch and which has, ironically, left me with more Sasol shares than I previously owned and a likely even bigger capital gains problem as they recover further in the future to, if technical analysis is correct, around R350.
As a footnote, however I should add that, happily the proceeds of the Sasol sale allowed me to also buy a good spread of other better quality shares so my entire portfolio became much more robust in the process.
Furthermore, as my last graph illustrates, ShareFinder has again advanced the date of its predicted next Dow Jones down-wave. The program now says the decline began on June 9 and is likely to last until October 23 in its first of several down phases which will all subsequently end around January 22.
Sadly then, all the doom and gloom is far from over and, for South Africa with nowhere else to turn for more cash to keep on running a spendthrift state, the International Monetary Fund is about to put us into the monetary world’s equivalent of Business Rescue. That is not necessarily a bad thing though. They can hardly do worse than the Command Council which is promising us more of their tried and failed Soviet era command economics in which apparatchiks with no business experience whatsoever believe they can tell our corporates how to do things!
China, the last of the big global economic growth engines still growing in a worldwide sea of stagnation, is beginning to suffer the consequences of its recent private debt binge. Since 2008, it has poured $18-trillion into new private loans and the consequences have begun to show.
In 2011, China’s GDP growth rate was 15.4 percent. Now the official rate is 6 percent but many analysts think it is actually closer to 4 percent or less. This is the weakest growth rate since the first quarter of 1992 amid persistent trade tensions with the US, weakening global demand and alarming off-balance-sheet borrowings by local governments. GDP Annual Growth Rate in China averaged 9.39 percent from 1989 until 2019, reaching an all time high of 15.40 percent in the first quarter of 1993.
In its rush to grow, China has simply built far too many buildings, produced far too much steel and other commodities and made far too many bad loans. Its overcapacity is so pronounced that it will take years for demand to catch up with this oversupply. And the knock-on effect is devastating many global economies. The latest victim is South Africa’s Saldanha steel works which is costing some 900 workers their jobs and, as the principal local industry, will have massive impact upon the local economy. Despite this China continues producing 40 percent more steel than the world needs.
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Furthermore, China is compounding the problem by continuing to over-lend and overproduce though with diminishing returns. China is now the world’s largest creditor with overseas lending now standing ostensibly at $5-trillion: twice as large as both the World Bank and the International Monetary Fund combined. China’s non-government loans have grown almost a trillion dollars recently.
In 2015, China’s stock market collapsed costing investors 45 percent of their savings. Now its economy is decelerating and its soaring private debt ratio has reached 300 percent of GDP signaling the inevitability of a further economic slow-down.
The Chinese are taking a problem whose size and scope is unprecedented and making it all that much bigger. So here it is worth turning to China’s Asian neighbor Japan, where a not too dissimilar process led to very high GDP growth in the 1980s. Fueled primarily by runaway lending, Japan suffered a stock market crash in 1990, then a real estate collapse in 1991, and finally a bank rescue in 1998. And Japan has posted 22 years of near-zero growth since that rescue.
Even if it can avoid catastrophic collapse, China’s economic trajectory is to continue slowing, resulting in downward long-term pressure on commodity prices. Deflation will inevitably spill over to countries that are economically intertwined with it in the Asia Pacific region, such as South Korea, Australia, Thailand, Vietnam, Singapore, and Japan. Africa and South America which will also be profoundly impacted because both the latter continents are disproportionately dependent on commodity exports to China. In 2018 South Africa shipped exports worth $8.7 billion to China representing 9.2 percent of total exports; by far the greatest single destination. Next was Germany with 7.5 percent, the United States with 6.8 percent and Britain with 5.1 percent.
At best the world economic outlook is for a future of economic stagnation and steadily rising inflation which will impoverish everyone. At worst, a catastrophic economic crisis is inevitable, precipitated by a black swan event…something we can’t anticipate but can at least prepare for.
Nobody can pick the date of the probable collapse, so (at the time of publication) I have opted for October 2020….because the most devastating share market corrections in the past have happened in October. But there is no other argument to justify it. Neither can anyone pick the year with any certainty except to note that unless we take drastic steps to correct our towering global debt imbalance, collapse must come sooner or later and sooner seems more likely than later….meanwhile my uncannily accurate ShareFinder software has picked October 7 2020 (Actually it began on February 17) as the likely start date and lasting until the following April for the next bear market.
ShareFinder employs artificial intelligence to extrapolate future investment market events and we have audited its forecasts for the past 17 years during which the average accuracy rate has been 85.31 percent. So there is a high probability of a market correction around that date. The only thing we cannot be certain of is the magnitude of the correction.
ShareFinder similarly projects that Hong Kong will go down on October 13, London on the 14th and, as the contagion spreads, Wall Street is likely to follow in June 2021 through to the end of May 2022. (ShareFinder now sees it currently under way and likely to end around January 22)
Since the impetus that will be driving future monetary events must be hyperinflation because that is the only way indebted governments will be able to engineer their way out from under their towering debt loads, it’s a reasonable conclusion that inflation rather than protracted economic stagnation will be the consequence as central banks move to counter the immediate results of global market collapses that threaten the onset of their greatest fear, an economic recession that will make the Great Depression of 1929 look like a Sunday School picnic.
It is anyone’s guess what rate inflation could climb to in the initial aftermath of a full-blown monetary crisis but it reached 18.41 percent at the peak of South Africa’s 1986 monetary crisis following the Rubicon speech. Note the following graph of the past 35 years of South African inflation history.
For convenience let us assume that it only goes to 14.4 percent because that is the rate that would halve South Africa’s total debt in five years and, although there would be an inevitable knock-on in the shape of a raised prime rate with ripples through to mortgage and hire purchase rates which would represent a massive hidden tax upon the public, there would be no impact upon the interest payment amounts governments have to make on their existing debts since these are almost entirely built in at a fixed rate at the time the loans are issued.
Since the share market inevitably moves to reflect major changes in money market rates, such a move in the sovereign bond rate would likely precipitate around a 50 percent share market decline. So if you knew a crash was coming in a year’s time it would be logical to prepare for it by selling off what shares you could without invoking too much Capital Gains Tax pain in order to create cash with which to buy them back at half price once the market had settled the following year.
Of course, if you knew that the coming bear market would be as severe as a 50 percent decline, it would usually pay you to sell off most of your share portfolio, but there is no way of knowing for sure. Furthermore, for share market investors who have held top quality Blue Chips for very lengthy periods, the Capital Gains Tax impact of selling them would be so severe that it would be foolhardy to sell on the uncertain probability of a forecast share market decline. To understand this view, consider the table below which lists all the significant bull and bear phases of the JSE since October 1987:
Reading from the deduced averages the calculations imply that the average decline has been 23.51 percent with the most severe resulting in a loss of 46.4 percent and the least 9.77 percent. The average decline lasted 23.11 weeks preceded by an average market gain of 75.32 percent in an average of 75.21 weeks. However, if you study the table it is clear that there is no clear correlation between the length of the run-up period, the extent of the gain and the subsequent extent and duration of the decline.
What is clear, however, is that the majority of bear phases were insufficient to have warranted selling off portfolios had one been able to anticipate the timing of such declines with any accuracy. At best then, I have long come to the conclusion that the best strategy to adopt when one senses that a bear market is probable is to clean out the underperforming and loss-making holdings in your portfolio; to spring clean rather than dispose of the entire portfolio.
Of course, an entirely different approach would be recommended were capital gains taxation not applicable. Modern computerised share market analysis systems like the ShareFinder programme have demonstrably reached such a degree of forecast accuracy that in the absence of such taxation it would be a normal and healthy strategy to sell out completely whenever the bear was stalking the marketplace. But we currently have to live with CGT.
More fortunate in such cases are people who have invested via unit trusts for although these generally offer lower capital growth rates over time they do partially compensate by offering the facility to move from an equity portfolio to a money market portfolio without incurring capital gains tax provided investors remain within the same family of funds. If you are invested in this latter category, however, do make sure that you move to a money market fund and not one that takes its value from the bond market because rising bond yields result in capital losses for investors. And of course the same argument applies to direct investment in bonds and preference shares which are similarly adversely affected in times of rising interest rates.
The time to buy this category of interest-yielding investments is always when interest rates are peaking. That way you lock into a contractually-fixed interest rate yield and will continue to enjoy the benefit of that rate for as long as you hold the bond. Thus, for example, were you to buy a bond at a crisis peak yield rate of 20 percent at the time of purchase and subsequently rates were to begin falling such that the quoted yield of the bond you were holding fell to 10 percent, other investors would be prepared to pay you twice what you originally paid to buy the bonds. And should rates subsequently fall to five percent, your capital value would double again.
As a rule, when interest rates peak, share markets bottom. In the graph composite below I have illustrated how, as Wall Street’s S&P500 Index (blue) has climbed to its highest ever peak, the 30-year US long bond average (red) has fallen to its lowest ever yield of 1.91 percent:
Between December 24 2018 and November 2019, the S&P500 rose 27 percent while 30-year US long bonds fell from a peak yield of 3.43 percent to 1.91 representing a gain of 80 percent.
So, it was clear that in this instance you would have made nearly three times as much if you could have correctly timed the bond market than you would have made investing in one of the most rapid share price gains in modern history.
But they do not always move in tandem. From December 2005 when the JSE All Share Index (blue) rose from a value of 158 009 to 329 077 in May 2008 representing a gain of 108 percent, South African long bonds (red) were weakening from a yield of 7.405 to a yield of 11.175. Then, at a time when shares were crashing down to an index low of 178 144 representing a 45.8 percent loss the E170 long bond gained from its weakest level of 11.175 percent yield to a high of 7.79 percent representing a gain of 43.5 percent in capital terms as the graph below illustrates:
So, there can be no hard and fast rules about the relationship between the two types of securities and investors would thus need to be alert to the changes happening around them. At the time of writing, long bonds had been gaining in value since they peaked at a yield of 9.9 percent in December 2015 reaching a yield low of 8.09 percent in early September 2019 before reversing upwards to 8.565 percent on ratings agency fears in November 2019.
Of course, long-term investors in share market Blue Chip shares have long realized that, if they are prepared to sit things out, the market always recovers and continues its upward trajectory. So, if you have the tenacity to simply sit tight, you should see your losses restored with time. The graph below illustrates how the JSE All Share Index has climbed relentlessly at a compound annual average rate of 12.5 percent, though four major market declines occurred during that time.
Next month I will offer an argument as to why governments should scrap Capital Gains Taxation which has proved to be one of the leading reasons why global economies have stagnated since the tax was introduced. Should the South African Government recognize the need to remove this highly controversial form of taxation amid a process of reconstructing the economy it will of course change share investor strategy significantly to justify a reversion to allow for timing the market employing the ever-increasingly accurate technical analysis tools like those offered by the ShareFinder computer system. It would also allow speculators to re-enter the property market in the manner I described in chapter one. But that is a discussion for another era.
For those fearful of a pending major market correction but unwilling to pay the Capital Gains Tax consequence of selling their portfolio now, the only remaining option is simply to sit tight. In this latter case, however, do take the opportunity to review your portfolio to ensure that it consists ONLY of ultra-Blue Chips.
The simplest test to determine whether the shares you hold are Blue Chips is to examine their long-term dividend growth records. Companies that have delivered constantly-rising dividends for a minimum of ten years are the ones most likely to survive an economic catastrophe for the simple reason that the management teams that have achieved such statistics either possess superior products or superior management ability…and it will require both to survive a monetary crisis.
The table on the right lists, in descending order of quality, the companies that have passed the many Blue-Chip tests within my ShareFinder analysis system. If your holdings are not included in this list, I would recommend you get rid of them.
Finally, let me direct you to a graph of how these Blue Chip shares have performed in the long term; through four bear markets which, you will notice if you study the graph below, have with time become all but un-noticeable within the relentless up-surge in value of these well-managed companies.
They have doubled in value every 3.7 years, growing at a compound annual average rate of 19.7 percent a year since April 1986, making it clear that these represent the nearest thing to your best bet to survive the coming economic storm. Such companies have won their spurs as blue chips because they possess a culture of management excellence that have allowed them to dominate the production niche that they occupy and it is this factor that can be expected to endow them with the ability to ride out whatever economic and political storms the future might throw at them.
I said “the nearest thing to your best bet to survive the coming storm” because of course there is one investment that is better placed to protect your wealth and that is gold, which as I have illustrated throughout this book, has held its value over very extended periods of time. My last graph illustrates how Kruger Rands have maintained their value, rising in value at a compound annual average rate of 10.8 percent, rising in value from R753 in April 1986 to their most recent peak value of R25 100 on August 15 2019:
Clearly in this latter comparison you would have been better off with the Blue Chips with their 19.7 percent compound annual average growth rate coupled with a 3 percent average dividend which would have assured you of a healthy and growing income throughout. Gold coin would, after all, not have given you any dividend or interest income, but you would with gold be assured of a ready market at all times, portability and universal acceptance anywhere on planet earth.
What shape will the global economy take after the lock downs are fully relieved? Will households and firms be allowed to act more freely in their own interest and in that of the greater society?
But how fast will the global economy grow when something like normality resumes? A persistently mere one or two percent extra output a year is what we would call secular stagnation. There are those who argue that we have entered an extended period of economic stagnation. Some also argue that demand will have difficulty in keeping up with the modest extra supplies of goods, services and labour; that monetary policy has shot its bolt because interest rates cannot go much below zero.
If there is to be economic stagnation, it will be for a want of willingness to supply, not from any permanent lack of demand. Stimulating demand is the easy part.
We should dismiss such under consumption theories. Monetary stimulus comes not only from lower interest rates but also in the form of increases in the supply of money itself, as is now being demonstrated by the central banks in the developed world creating extra money at a rate never attempted before. This policy is having a demonstrably helpful (in the form of extra spending) impact on asset prices. If there is to be economic stagnation, it will be for a want of willingness to supply, not from any permanent lack of demand. Stimulating demand is the easy part.
The current very low interest rates, both short and long, in the developed world, mean that the return on savings or investing them in real assets is expected to remain low for an extended period of time. The expected returns on capital formation by firms and governments must accordingly be equally low. Slow growth in output and low returns on investing in additional output go together.
But does this relative abundance of savings and lack of demand for them represent a permanent state of economic affairs? Is the monetisation of debt not a large part of the explanation for low interest rates? More fundamentally, is improved technology now something of the past rather than the future? Are higher taxes and more interfering regulations going to stultify the inventors, innovators and the entrepreneurs, who are the true source of economic progress, in their quest to get more out of less?
Robotics and artificial intelligence (AI) still promise to eliminate the drudgery and danger in work. Given enough time, all work may be done by robots, built supervised and repaired by other robots.
Progress in science and its application in production and distribution is surely not stagnant. Perhaps growth itself has become less capital intensive: we are getting more out of the machines than we used to, so reducing the real amount that has to be invested. Robotics and artificial intelligence (AI) still promise to eliminate the drudgery and danger in work. Given enough time, all work may be done by robots, built supervised and repaired by other robots. In this way, they will provide their human owners at some future point in time with an abundance of goods and services that would make work, incentives to work, inequality and so economic growth itself superfluous. The economic problem of scarcity will then have been solved.
Realising eventual abundance means doing everything now to encourage the demand for and supply of capital, and innovation in the application of savings to capital formation. This would include encouragement to take risk in science and knowledge and in its application by enterprises of all kinds. Incentives that reveal inequalities of economic outcomes are still necessary to the economic purpose. Low interest rates, for now, are also part of the encouragement needed. Higher real interest rates would then be welcome, indicating that the demand for capital for productive purposes had increased and that growth was picking up.
The current low global cost of capital moreover encourages a flow of capital to those parts of the world where interest rates are much higher. That is because savings and capital are still scarce and well rewarded in these countries, and potential supplies of labour are relatively abundant. Accordingly, these are countries where the standard of living and production per person employed compares poorly with the developed world. As is the case in South Africa where secular stagnation, alas, has become a predicted reality.
The global abundance of capital is our opportunity to attract capital our way to improve the output of workers and their incomes. If only we could play by the well-recognised rules that encourage capital inflows. Adopting those rules with enthusiasm will avoid post Covid-19 stagnation.
Predictions are difficult, especially those about the future. That old proverb (often attributed to Yogi Berra) is right but you can’t live without making certain presumptions. You presume your car will start, your refrigerator will stay cold, the lights will turn on when you flip the switch.
In fact, you could argue this “predictability” separates advanced economies from primitive ones. Most of us don’t have to worry about being attacked in our sleep or having food tomorrow. That security frees us to do other things.
Right now, some basic assumptions are no longer safe. The economy will keep suffering until they are reliable again, or we replace them with new assumptions. We can’t travel or even go to a restaurant or visit friends without wondering about our health. Where does that leave us?
Today I’ll defy the proverb, consider what we know and don’t know, and try to tell you where I think we’re going. In the long run (after The Great Reset in the late 2020s), I still foresee a wonderful new world. But we have to get there first.
Economists use the word “recovery” to define a rebound from the previous time period. So if there was a 30% drop, a 10% increase would, for an economist, be a “recovery.” But in the real world, it still means you are 20% below where you started. Recovery doesn’t necessarily mean recovered. Even optimistic projections say we won’t see anything like 2019 GDP until late 2021. Many suggest it will be even longer.
Even then, the changes we will have to put into our operating business models, not to mention the massive amounts of capital that it will take to start new businesses or resupply old ones, will make the “recovered” economy look significantly different than that of 2019.
And just for the record, because I am not optimistic about the speed of economic recovery does not mean that I am necessarily bearish on the stock market. When the Federal Reserve pumps $5 trillion (or whatever) into the system it is going to find a home. While I think earnings will take a severe hit in 2021, the market could hold simply due to massive Fed support.
There have been numerous times when the economy and the stock market were out of sync. Don’t equate the two. The stock market doesn’t necessarily tell us anything about the economy, or vice versa.
Last week the Federal Reserve sent Congress its latest “Monetary Policy Report.” These are usually rather vague, dry documents on everything the Fed is doing right and what could possibly go wrong. This one is more interesting than usual because so many things have gone wrong and may get even worse. Not that the Fed has good answers, of course.
Anyway, my friend Mish Shedlock blogged about the report and particularly the six downside risks it identifies. Kudos to the Fed for actually giving a fairly transparent, coherent, and reasonable list of risks. Here they are.
I could write an entire letter on any one of these risks, but let’s start at the beginning: “The future progression of the pandemic remains highly uncertain.”
Here’s what we know. Many of the first countries the virus struck—China, South Korea, Japan, New Zealand, Italy, Spain—brought it under control with aggressive lockdowns, testing, contact tracing, social distancing, and isolation of confirmed cases. Yet little outbreaks keep popping up. Life is still far from normal in those places. Read this Financial Times account of conditions in South Korea to see what I mean.
Here in the US, the national numbers are much improved since March and early April. That’s not the case everywhere, though. Look deeper and you’ll see the New York/New Jersey crisis is easing but cases are rising elsewhere. Testing numbers are up but that’s not the full explanation. Hospitalizations are also up in some states, as is the testing “positivity rate.” Those indicate actual virus spread. This was expected as more people circulate in public but could get out of hand if not handled well.
Former Food and Drug Administration head Dr. Scott Gottlieb said the states hardest hit by the latest coronavirus surge are “on the cusp of losing control.” Ten states, most of them concentrated in the South and West, have recently seen new record-high, seven-day averages of new coronavirus cases. Those states are Alabama, Arizona, California, Florida, Nevada, North Carolina, Oklahoma, Oregon, South Carolina, and Texas. Gottlieb is a serious medical professional and not prone to wild statements. We should pay attention.
To be clear, I believe the initial closures were necessary, given what we knew at the time. They successfully flattened the curve. But they were a brute force strategy with very harmful economic side effects and needed to end quickly. Scientists have learned a lot in the last three months. We can now attack the problem more precisely.
But even then, we are not going back to normal until late this year, at best. More likely it will be 2021 before a vaccine can be successfully developed, tested, produced, and widely distributed. That means many more months with masks, social distancing, reduced travel, and no large gatherings, at least like we knew in the past. It also assumes no more large-scale outbreaks. So the best-case scenario is still disastrous for big parts of the economy.
There was much celebration as retail sales showed a rather robust rise. Talk of a V-shaped recovery was in the air. Except that we have only roughly recovered to ~2015 in terms of GDP. The comments and table below come from Danielle DiMartino of Quill Intelligence (daily must-reading for me).
First, the good news. E-commerce and food are the big winners. Sales in the three months ended May are running well above their prior 12-month average while employment was relatively steady. This should open up short-run opportunities for job growth in these two areas. Anecdotes back this as we’ve seen job hiring announcements in these spaces.
Building materials and recreation, which includes sporting goods, hobby, book and music stores, also have moderately positive sales-to-employment capacity rates. Both sectors focus on DIY, at-home activities—endeavors rendered more attractive to millions of people working from home.
Unfortunately, losers outnumber winners. Clothing, gasoline, electronics, food service & drinking places and autos highlight the sectors at risk for future job cuts should the current sales levels be sustained in coming months. These five red categories represent 11.1 million payroll jobs, more than twice the 5.3 million of the four groups that are in the green.
It is certainly easy to see the restaurant businesses and their brethren are seeing extremely bad data. How soon before we go back to a movie theater? When we can watch from home, generally for less cost, even with a few friends for the human experience? How many other businesses have similar dynamics?
It is going to take several years for the employment situation to sort itself out. If your job is gone, what do you do now?
We can see that in continuing claims for jobless benefits. While off the highs, they have so far been stubbornly flat in June (H/T MishTalk).
Continuing claims are clearly at an all-time high. Only once before, in the middle of the Great Recession, did continuing claims even rise above 5 million.
The economy is currently being sustained by federal government largess. Those 20 million continuing benefit claimants are all getting at least $600 a week. Ironically, we have set the philosophical stage for Guaranteed Basic Income, at a much higher level than Andrew Yang’s $1,000 a month proposal. Furthermore, many businesses are staying alive only through the Paycheck Protection Program’s forgivable loans.
Let’s jump to an insight from David Rosenberg’s (Rosenberg Research) morning report.
There is nothing in the data, as of yet, to show that personal incomes are rising on their own—the story remains one of cash-flow support from Uncle Sam’s generosity and the ability (and willingness) of millions of Americans to skip their loan payments. Spending premised on such weak underpinnings does not constitute an official recovery. Not to mention the reality of historical data showing that recessions end when jobless claims get closer to 500K, not 1.5 million, which is where we are right now.
This isn’t something governors can easily reverse. They can let businesses open, but they can’t make consumers come back and spend freely. People have to feel safe; the economy can’t “recover” if even a small number don’t. As I’ve said, recovering even 90% of the previous consumer spending isn’t enough. We need it all, or close to all. We will get there, but it is going to take time.
That brings us to the Fed’s second risk: collapsed demand could bankrupt many businesses. In fact, collapsed demand already bankrupted some businesses. More will surely follow. Nowhere is this more evident than restaurants.
I have a soft spot for independent restaurant owners. I enjoy great meals and appreciate the hard work that goes into them. Those who can actually do it consistently and profitably? They are among humanity’s best. They feed both our bodies and our souls. The tsunami that just hit them is indescribably painful. It hurts me to think of the places I’ve enjoyed wonderful evenings with friends, in dozens of different countries, that are now probably gone forever.
One recent survey of San Francisco restaurant owners found 60% lose money by staying open. They are low-margin even in normal times. Now capacity restrictions, combined with a general desire to stay home, make their prospects bleak indeed. Many won’t survive. The may hang on awhile, helped by PPP and other programs, but their challenge is deeper.
Nor is it just restaurants. The same or similar problems apply to bars, hotels, casinos, nightclubs, theaters, music venues—basically anywhere people gather in crowds. The crowds make them profitable. These businesses often can’t survive at 50% or even 80% capacity. They need to be full and now they can’t be. Can they change their model? Of course. But that will mean fewer employees and lower profits.
Which brings us to the real problem: These businesses employ millions of workers directly, and millions more depend on them indirectly. Many who lost their jobs in the last three months won’t get them back.
Here’s where it gets tough. I talk often about capitalism’s “creative destruction.” We go through times when the world changes. Businesses and workers must adapt. We don’t yet know how this will all develop, but COVID-19 seems likely to permanently change some industries. That could make many of these “temporary” job losses permanent.
Economists call this a “reallocation shock.” Affected workers have no good choices. They can either change careers, which might require expensive and time-consuming education, or move someplace that has jobs matching their skills. Neither is easy. It is similar to the way outsourcing and technology eliminated US manufacturing jobs in recent decades. This time, service industry workers are the unlucky ones, except the shock is happening much faster.
This has important social and political consequences but let’s stick with the economic ones. They are also bad.
From a US perspective, this crisis began as a “supply shock” back in January/February, when China’s shutdowns threatened global supply chains. Now we have a demand shock, too. The millions who are staying home demand different goods, and their net spending is less. Others who have lost jobs or taken pay cuts or who are just concerned about the future are also spending less. That’s probably wise individually, but in a consumer-led economy it is devastating in the aggregate.
University of Texas economist James Galbraith explained it well in a recent Project Syndicate note. As he says, consumer incentives are to save, not spend.
Faced with radical uncertainty, US consumers will save more and spend less. Even if the government replaces their lost incomes for a time, people know that stimulus is short term. What they do not know is when the next job offer—or layoff—will come along.
Moreover, people do distinguish between needs and wants. Americans need to eat, but they mostly don’t need to eat out. They don’t need to travel. Restaurant owners and airlines therefore have two problems: They can’t cover costs while their capacity is limited for public-health reasons, and demand would be down even if the coronavirus disappeared. This explains why many businesses are not reopening even though they legally can. Others are reopening, but fear they cannot hold out for long. And the many millions of workers in America’s vast services sector are realizing that their jobs are simply not essential.
Meanwhile, US household debts—rent, mortgage, and utility arrears, as well as interest on education and car loans—have continued to mount. True, stimulus checks have helped:
Defaults have so far been modest, and many landlords have been accommodating. But as people face long periods with lower incomes, they will continue to hoard funds to ensure that they can repay their fixed debts. As if all this were not enough, falling sales- and income-tax revenues are prompting US state and local governments to cut spending, compounding the loss of jobs and incomes.
These household debt problems eventually become government debt problems. I have argued for years we are on an unsustainable fiscal path. This year it suddenly got much worse.
State and local governments were already a problem, too. Many were over their heads in pension debt and now the crisis is decimating their tax revenue. This, too, may turn into federal debt.
The demand shock is aggravating a sharp decline in freight volumes, which was already in progress before the pandemic. Here’s the latest Cass Freight Index, which I’ve referenced before.
Cass said in its commentary it doesn’t expect freight will return to 2019 levels until 2021 at the earliest. Note this isn’t just international freight. It is about goods and materials being shipped within the US.
Add all this up and we are already in a deep recession and, barring some miraculous COVID-19 cure, not going to recover this year. That will have serious effects that are more than economic. More on that later.
US federal debt is over $26 trillion and rising rapidly. There will likely be at least a $1 trillion additional stimulus package before July 31 that extends the additional unemployment benefits for some period. There is some debate on the amount. I expect a further multi-trillion stimulus/infrastructure bill before the election.
This table from the Economic Policy Institute shows hourly wages of all workers, by wage percentile, for 2000–2018 (in 2018 dollars).
Current federal unemployment benefits of $600 per week, assuming a 40-hour week, equal $15 an hour (plus the state portion, which varies). That means the bottom 30% of US workers are better off keeping unemployment as long as they can. Especially the bottom 20%. Even the 40th percentile might be better off taking the unemployment benefit as they have no cost of getting to and from work.
I have no idea what the next level of benefits will be or how long they will last. But as I said earlier, we are moving toward a Guaranteed Basic Income which, added to other entitlement spending, would push us closer to $2 trillion-plus annual deficits.
The world will not come to an end with a $30 trillion US debt. How far will future US Congresses push that number? Explaining to the average politician that debt is a drag on future growth is futile. Spending money today helps them get re-elected tomorrow. They will worry about the future later. Or at least most of them. Sigh.
This, along with Federal Reserve policy, is going to push us to a very uncomfortable place towards the end of this decade. Stay tuned…
For now, what can we do? Our immediate problem stems from two sources.
One simple thing we can all do will help attack both problems: Wear a mask in public. We can live with the virus risk, but not when a noticeable part of the population acts in ways others perceive as reckless. Walking around in public without a mask is like wearing an “I want a deeper recession” sign.
Note, it doesn’t matter whether you believe the mask really helps, or the virus is really dangerous. Perception is what counts. As long as substantial numbers believe normal life is too risky, the economy can’t recover. It is really that simple.
I’ll go further. Near-universal mask usage would help the economy more than another multi-trillion-dollar stimulus package would—a lot more, and faster, too. And without adding a penny to the national debt. You can see that in other countries.
My local gym has opened, sort of. You have to wear a mask, bring your own face towel, and half the air conditioning is down, so it’s kind of like working out in a sauna. But then again, a little sweat never hurt anyone.
I spend a lot of time considering how to find a semblance of certainty for investors in these times. There are opportunities. Progress has not stopped. It just looks different, especially in a world where everything is being re-priced. But for now, it’s time to hit the send button. Have a great week!
Your dealing with uncertainty analyst.
In arriving at our funding priorities—including criminal justice reform, farm animal welfare, pandemic preparedness, health-related science, and artificial intelligence safety—Open Philanthropy has pondered profound questions. How much should we care about people who will live far in the future? Or about chickens today? What events could extinguish civilization? Could artificial intelligence (AI) surpass human intelligence?
One strand of analysis that has caught our attention is about the pattern of growth of human society over many millennia, as measured by number of people or value of economic production. Perhaps the mathematical shape of the past tells us about the shape of the future.
It’s extraordinary that the larger the human economy has become—the more people and the more goods and services they produce—the faster it has grown on average. Now, especially if you’re reading quickly, you might think you know what I mean. And you might be wrong, because I’m not referring to exponential growth. That happens when, for example, the number of people carrying a virus doubles every week. Then the growth rate (100% increase per week) holds fixed. The human economy has grown super-exponentially. The bigger it has gotten, the faster it has doubled, on average. The global economy churned out $74 trillion in goods and services in 2019, twice as much as in 2000. Such a quick doubling was unthinkable in the Middle Ages and ancient times. Perhaps our earliest doublings took millennia.
If global economic growth keeps accelerating, the future will differ from the present to a mind-boggling degree. The question is whether there might be some plausibility in such a prospect. That is what motivated my exploration of the mathematical patterns in the human past and how they could carry forward. Having now laboured long on the task, I doubt I’ve gained much perspicacity. I did come to appreciate that any system whose rate of growth rises with its size is inherently unstable. The human future might be one of explosion, perhaps an economic upwelling that eclipses the industrial revolution as thoroughly as it eclipsed the agricultural revolution. Or the future could be one of implosion, in which environmental thresholds are crossed or the creative process that drives growth runs amok, as in an AI dystopia. More likely, these impulses will mix.
I now understand more fully a view that shapes the work of Open Philanthropy. The range of possible futures is wide. So, it is our task as citizens and funders, at this moment of potential leverage, to lower the odds of bad paths and raise the odds of good ones.
Humans are better than viruses at multiplying. If a coronavirus particle sustains an advantageous mutation (lowering the virulence of the virus, one hopes), it cannot transmit that innovation to particles around the world. But humans have language, which is the medium of culture. When someone hits upon a new idea in science or political philosophy (lowering the virulence of humans, one hopes) that intellectual mutation can disseminate quickly. And some new ideas, such as the printing press and the World Wide Web, let other ideas spread even faster. Through most of human history, new insights about how to grow wheat or raise sheep ultimately translated into population increases. The material standard of living did not improve much and may even have declined. In the last century or so, the pattern has flipped. In most of the world, women are having fewer children while material standards of living are higher for many, enough that human economic activity, in aggregate, has continued to multiply. When the global economy is larger, it has more capacity to innovate, and potentially to double even faster.
To the extent that superexponential growth is a good model for history, it comes with a strange corollary when projected into the future: the human system will go infinite in finite time. Cyberneticist Heinz Von Foerster and colleagues highlighted this implication in 1960. They graphed world population since the birth of Jesus, fit a line to the data, projected it, and foretold an Armageddon of infinite population in 2026. They evidently did so tongue in cheek, for they dated the end times to Friday the 13th of November. As we close in on 2026, the impossible prophecy is not looking more plausible. In fact, the world population growth rate peaked at 2.1%/year in 1968 and has since fallen by half.
That a grand projection went off track so fast should instil humility in anyone trying to predict the human trajectory. And it’s fine to laugh at the absurdity of an infinite doomsday. Nevertheless, those responses seem incomplete. What should we make of the fact that good models of the past project an impossible future? While growth in the number of people has slowed in the last half century, growth in the scale of our activity, as proxied by gross world product (GWP), has not slackened as much. Historically poor countries such as China are catching up with wealthier ones, adding to the global totals. Of course, there is only so much catching up to do. And economically important ideas may be getting harder to find. For instance, keeping up with Moore’s law of computer chip improvement is getting more expensive. But history records other slowdowns, each of which ended with a burst of innovation such as the European Enlightenment. Is this time different? It’s possible, to be sure. But it’s impossible to be sure.
Since 1960, when Von Foerster and colleagues published, other analysts have worked the same vein—now including me. I was influenced by writings of Michael Kremer in 1993 and Robin Hanson in 2000. Building on work by demographer Ronald Lee, Kremer brought ideas about “endogenous technology” (explained below) to population data like that of Von Foerster and his co-authors. Except Kremer’s population numbers went back not 2,000 years, but a million years. Hanson was the first to look at economic output, rather than population, over such a stretch, relying mainly on numbers from Brad De Long.
You might wonder how anyone knows how many people lived in 5000 BCE and how much “gross product” they produced. Scholars have formed rough ideas from the available evidence. Ancient China and Rome conducted censuses, for example. McEvedy and Jones, whose historical population figures are widely used, put it this way:
There is something more to statements about the size of classical and early medieval populations than simple speculation… We wouldn’t attempt to disguise the hypothetical nature of our treatment of the earlier periods. But we haven’t just pulled numbers out of the sky. Well, not often.
Meanwhile, until 1800 most people lived barely above subsistence; before then the story of GWP growth was mostly the story of population growth, which simplifies the task of estimating GWP through most of history.
I focused on GWP from 10,000 BCE to 2019. I chose GWP over population because I think economic product is a better indicator of capacity for innovation, which seems central to economic history. And I prefer to start in 10,000 BCE rather than 1 million or 2 million years ago because the numbers become especially conjectural that far back. In addition, it seems problematic to start before the evolution of language 40,000–50,000 years ago. Arguably, it was then that the development of human society took on its modern character. Before, hominids had developed technologies such as hand axes, intellectual mutations that may have spread no faster than the descendants of those who wrought them. After, innovations could diffuse through human language, a novel medium of arbitrary expressiveness—one built on a verbal “alphabet” whose letters could be strung together in limitless, meaningful ways. Human language is the first new, arbitrarily expressive medium on Earth since DNA.
Here is the data series I studied the most:
The series looks like a hockey stick. It starts at $1.6 billion in 10,000 BCE, in inflation-adjusted dollars of 1990: that is 4 million people times $400 per person per year, Angus Maddison’s quantification of subsistence living.
For clarity, here is the same graph but with $1 billion, $10 billion, $100 billion, etc., equally spaced. When the vertical axis is scaled this way, exponentially growing quantities—ones with fixed doubling times—follow straight lines. So, to show how poorly human history corresponds to exponential growth, I’ve also drawn a best-fit line:
Finally, just as in that 1960 paper, I’ve done something similar to the horizontal axis, so that 10,000, 1,000, 100, and 10 years before 2047 are equally spaced. (Below, I’ll explain how I chose 2047.) The horizontal stretching and compression change the contour of the data once again. And it bends the line that represented exponential growth. But I’ve fit another line under the new scaling:
The new “power law” line follows the data points remarkably well when plotted this way. The most profound developments since language—the agricultural and industrial revolutions—shrink to gentle ripples on a rather steady, long-term climb.
This graph raises two important questions. First, did those economic revolutions constitute major breaks with the past, which is how we usually think of them, or were they mere statistical noise within the longer-term pattern? And where does that straight line take us if we follow it forward?
I’ll tackle the second question here and return to the other later. I’ve already extended the line on the graph to 10 years before 2047, i.e., 2037, at which time it has GWP reaching a stupendous $500 trillion. That is ten times the level of 2007. If like Harold with his purple crayon you extend the line across your computer screen, off the edge, and into the ether, you will come to 1 year before 2047, then 0.1 before, then 0.01…. Meanwhile GWP will grow horrifically: to $30.7 quadrillion at the start of 2046, to $1.9 quintillion 11 months later, and so on. Striving to reach 2047, you will drive GWP to infinity. That was Von Foerster’s point back in 1960: explosion is an inevitable implication of the straight-line model of history in that last graph.
Yet the line fits so well. To grapple with this paradox, I took two main analytical approaches. I gained insight from each. But in the end the paradox essentially remained, and I think now that it is best interpreted in a non-mathematical way. I will discuss these ideas in turn.
An old BBC documentary called the Midas Formula tells how three economists in the early 1970s developed the E = mc2 of finance. It is a way to estimate the value of options such as the right to buy a stock at a set price by a set date. Fischer Black and Myron Scholes first arrived, tentatively, at the formula, then consulted Robert Merton. The BBC documented the work of Black, Scholes, and Merton not only because they discovered an important formula, but also because they co-founded the hedge fund Long-Term Capital Management to apply some of their ideas, and the fund imploded spectacularly in 1998.
In thinking about the evolution of GWP over thousands of years, I experienced something like Merton experienced, except for the bits about winning a Nobel and almost bringing down the global financial system. I realized I needed a certain kind of math, then discovered that it exists and is called the Itô calculus.
The calculus of Isaac Newton and Gottfried Leibniz excels at describing smooth arcs, such as the path of Halley’s Comet. Like the rocket in the BBC documentary, the comet’s mathematical situation is always changing. As it boomerangs across the solar system, it experiences a smoothly varying pull from the sun, strongest at the perihelion, weakest when the comet is out beyond Neptune. If at some moment the comet is hurtling by the sun at 50 kilometers per second, then a second later, or a nanosecond later, it won’t be, not exactly. And the rate at which the comet’s speed is changing is itself always changing.
One way to approximate the comet’s path is to program a computer. We could feed in a starting position and velocity, code formulas for where the object will be a nanosecond later given its velocity now, update its velocity at the new location to account for the sun’s pull, and repeat. This method is widely used. The miracle in calculus lies in passing to the limit, treating paths through time and space as accumulations of infinitely many, infinitely small steps, which no computer could simulate because no computer is infinitely fast. Yet passing to the infinite limit often simplifies the math. For example, plotting the smooth lines and curves in the graphs above required no heavy-duty number crunching even though the contours represent growth processes in which the absolute increment, additional dollars of GWP, is always changing.
But classical calculus ignores randomness. It is great for modeling the fall of apples; not so much for the price of Apple. And not so much for rockets buffeted by turbulence, nor for the human trajectory, which has sustained shocks such as the fall or Rome, the Black Death, industrial take-off, world wars, depressions, and financial crises. It was Kyosi Itô who in the mid-20th century, more than anyone else, found a way to infuse randomness into the calculus of Newton and Leibniz. It is called the stochastic calculus, or the Itô calculus. Think of an apple falling toward the surface of a planet whose gravity is perpetually, randomly fluctuating, jiggling the apple’s acceleration as it descends. Or think of a trillion molecules of dry ice vapour released to scatter and careen across a stage. Each drop of an apple or release of a molecule would initiate a unique course through space and time. We cannot predict the exact paths but we can estimate the distribution of possibilities. The apple, for example, might more likely land in the first second than in the 100th.
I devised a stochastic model for the evolution of GWP. I borrowed ideas from John Cox, who as a young Ph.D. followed in the footsteps of Black, Scholes, and Merton. The stochastic approach intrigued me because it can express the randomness of human history, including the way that unexpected events send ripples into the future. Also, for technical reasons, stochastic models are better for data series with unevenly spaced data points. (In my GWP data, the first two numbers are 5,000 years apart, for 10,000 and 5,000 BCE, while the last two are nine apart, for 2010 and 2019.) Finally, I hoped that a stochastic model would soften the paradox of infinity: perhaps after fitting to the data, it would imply that infinite GWP in finite time was possible but not inevitable.
The equation for this “Bernoulli diffusion” model (as I call it) generalizes that implied by the straight “power law” line in the third graph above, the one we followed toward infinity in 2047. It preserves the possibility that growth can rise more than proportionally with the level of GWP, so that doublings will tend to come faster and faster. Here, I’ll skip the equations and stick to graphs.
The first graph shows twenty “rollouts” of the model after it has been calibrated to match the GWP history. All twenty paths start where the real data series starts, at $1.6 billion in 10,000 BCE. The real GWP series is in red. Arguably the rollouts meet the Goldilocks test: they resemble the original data series, but not so perfectly as to look contrived. Each represents an alternative history of humanity. Like the real series, the rollouts experience random ups and downs, woven into an overall tendency to rise at a gathering pace. I think of the downs as statistical Black Deaths. The randomness suffices to greatly affect the timing of economic takeoff: one rollout explodes by 3000 BCE while others do not do so even by 5000 CE. In the path that explodes early, I imagine, the wheel was invented a thousand years sooner, and the breakthroughs snowballed from there.
The second graph introduces a few changes. Instead of 20 rollouts, I run 10,000. Since that is too many to plot and perceive, I show percentiles. The black curve in the middle shows the median simulated GWP at each moment—the 50th percentile. Boundaries between grey bands mark the 5th, 10th, 15th, etc., percentiles. I also run 10,000 rollouts from the end of the data series, $73.6 trillion in 2019, and depict them in the same way. And to take account of the uncertainty in the fitting of my model to the data, each path is generated under a slightly different version of the model. So, this graph contains two kinds of randomness: the randomness of history itself, and the imprecision in our measurement of it.
The actual GWP series, still in red, meanders mainly between the 40th and 60th percentiles. This good fit is the stochastic analog to the good fit of the power law line in the third graph in the earlier triplet. As a result, this model is the best statistical representation I have seen of world economic history, as proxied by GWP. That and a dollar will buy you an apple.
Through the Itô calculus, I quantified the probability and timing of escalation to infinity. The probability that a path like those in the first of the two graphs just above will not eventually explode is a mere 1 in 100 million. The median year of explosion is 1527. Applying the same calculations starting from 2019—that is, incorporating the knowledge that GWP reached $73.6 trillion last year—the probability of no eventual explosion falls to 1 in 1069, which is a number-of-atoms-in-the-universe sort of figure. (OK, there may be more like 1086 atoms in the universe. But who’s counting?) The estimate of the median explosion year sharpens to 2047 (95% confidence range is ±16 years), which is why I used that year in the third graph of the post. In the mathematical world of the best-fit model, explosion is all but inevitable by the end of the century.
Incorporating randomness into the modelling does not after all soften the paradox of infinity. An even better mathematical description of the past still predicts an impossible future.
I will put that conundrum back on hold for the moment and address the other question inspired by the power law’s excellent fit to GWP history. Should the agricultural and industrial revolutions be viewed as ruptures in the flow of history or as routine, modest deviations around a longer-term trend? To assess whether GWP was surprisingly high in 1820, by which time the industrial revolution had built a head of steam, I fitted the model just to the data before 1820, i.e., through 1700. Then I generated many paths wiggling forward from 1700 to 1820. The 1820 GWP value of $741 billion places it in the 95th percentile of these simulated paths: the model is “surprised,” going by previous history, at how big GWP was in 1820. I repeat the whole exercise for other time points, back to 1600 and forward to 2019. This graph contains the results:
The model is also surprised by the next data point, for 1870, despite “knowing” about the fast GWP growth before 1820. And it is surprised again in 1913. Now, if my stochastic model for GWP is correct, then the 14 dots in this graph should be distributed roughly evenly across the 0–100% range, with no correlation from one dot to the next. That’s not what we see. The three dots in a row above the 90th percentile strongly suggest that the economic growth of the 19th century broke with the past. The same goes for the four low values since 1990: recent global growth has been slower and steadier than the model predicts from previous history.
In sum, my stochastic model succeeds in expressing some of the randomness of history, along with the long-term propensity for growth to accelerate. But it is not accurate or flexible enough to fully accommodate events as large and sudden as the industrial revolution. Nevertheless, I think it is a virtue, and perhaps an inspiration for further work, that this rigorous model can quantify its own shortcomings.
To this point I have represented economic growth as univariate. A single quantity, GWP, determines the rate of its own growth, if with randomness folded in. I have radically caricatured human history—the billions of people who have lived, and how they have made their livings. That is how models work, simplifying matters in order to foreground aspects few enough for the mind to embrace.
A longstanding tradition in the study of economic growth is to move one notch in the direction of complexity, from one variable to several. Economic activity is cast as combining “factors of production.” Thus we have inherited from classical economists such as Adam Smith and David Ricardo the triumvirate of land, labour, and capital. Modern factor lists may include other ingredients, such as “human capital,” the investment in skills and education that can raise the value of one’s labour. A stimulus to one of these factors can boost economic output, which can be reinvested in some or all of the factors: more office buildings, more college degrees, more kids even. In this way, factors can propel their own growth and each other’s, in a richer version of the univariate feedback loop contemplated above. And just as in the univariate model that fits GWP history so well, the percentage growth rate of the economy can increase with output.
I studied multivariate models to though I left for another day the technically daunting step of injecting them with randomness. I learned a few things.
First, the single-variable “power law” model—that straight line in my third graph up top—is, mathematically, a special case of standard models in economics, models that won at least one Nobel (for Robert Solow) and are taught to students every day somewhere on this Earth. In this sense, fitting the power law model to the GWP data and projecting forward is not as naive as it might appear.
To appreciate the concern about naiveté, think of the IHME model of the spread of coronavirus in the United States. It received much attention—including criticism that it is an atheoretical “curve-fitting” exercise. The IHME model worked by synthesizing a hump-shaped contour from the experiences of Wuhan and Italy, fitting the early section of the contour to U.S. data, then projecting forward. It did not try to mathematically reconstruct what underlay the U.S. data, the speed at which the virus hopped from person to person, community to community. If “the IHME projections are based not on transmission dynamics but on a statistical model with no epidemiologic basis,” the analogous charge cannot so easily be brought against the power law model for GWP. It is in a certain way rooted in established economics.
The second thing I learned constitutes a caveat that I just glossed over. By the mid-20th century, it became clear to economists that reinvestment alone had not generated the economic growth of the industrial era. Yes, there were more workers and factories, but from a fixed amount of labour and capital, industrial countries extracted more value in 1950 than in 1870. As Paul Romer put it in 1990,
The raw materials that we use have not changed, but…the instructions that we follow for combining raw materials have become vastly more sophisticated. One hundred years ago, all we could do to get visual stimulation from iron oxide was to use it as a pigment. Now we put it on plastic tape and use it to make videocassette recordings.
So, in the 1950s economists inserted another input into their models: technology. As meant here, technology is knowledge rather than the physical manifestations thereof, the know-how to make a smartphone, not the phone itself.
The ethereal character of technology makes it alchemical too. One person’s use of a drill or farm plot tends to exclude others’ use of the same, while one person’s use of an idea does not. So a single discovery can raise the productivity of the entire global economy. I love Thomas Jefferson’s explanation:
Its peculiar character … is that no one possesses the less, because every other possesses the whole of it. He who receives an idea from me, receives instruction himself without lessening mine; as he who lights his taper at mine, receives light without darkening me. That ideas should freely spread from one to another over the globe, for the moral and mutual instruction of man, and improvement of his condition, seems to have been peculiarly and benevolently designed by nature, when she made them, like ﬁre, expansible over all space, without lessening their density at any point.
That ideas can spread like flames from candle to candle seems to lie at the heart of the long-term speed-up of growth.
And the tendency to speed up, expressed in a short equation, is also what generates the strange, superexponential implication that economic output could spiral to infinity in decades. Yet that implication is not conventional within economics, unsurprisingly. Since the 1950s, macroeconomic modeling has emphasized the achievement of “steady state,” meaning a constant economic growth rate such as 3% per year. Granted, even such exponential growth seems implausible if we look far enough ahead, just as the coronavirus case count couldn’t keep doubling forever. But, in their favour, models predicting steady growth cohered with the relatively stability of per-person economic growth over the previous century in industrial countries (contrasting with the acceleration we see over longer stretches). And under exponential growth the economy merely keeps expanding; it does not reach infinity in finite time. “It is one thing to say that a quantity will eventually exceed any bound,” Solow jabbed in 1994. “It is quite another to say that it will exceed any stated bound before Christmas.”
The power law model that fits history so well, yet explodes before Christmas, is mathematical kin with Solow’s influential models. So how did he avoid the explosive tendencies? To understand, step over to my whiteboard, where I’ll diagram a typical version of Solow’s model. The economy is conceived as a giant factory with four inputs: labor, capital, human capital, and technology. It produces output, much of which is immediately eaten, drunk, watched, or otherwise consumed: Some of the output is not consumed, and is instead invested in factors—here, the capital of businesses, and the human capital that is skills in our brains:
A final dynamic is depreciation: factories wear out, skills fade. And the more there are, the more wear out each year. So, I’ve drawn little purple loops to the left of these factors with minus signs inside them. Fortunately, the reinvestment flowing in through the orange arrows can compensate for depreciation by effecting repairs and refreshing skills. Labor and technology can also depreciate, since workers age and die and innovations are occasionally lost too. But Solow put the sources of their replenishment outside his model. From the standpoint of the Solow model, they grow for opaque reasons. So, they receive no orange arrows. And to convey their unexplained tendency to grow, I’ve drawn plus signs in their purple feedback loops:
In the language of economics, Solow made technology and labour exogenous. This choice had two virtues and a drawback. I’ll explain them with reference to technology, the more fateful factor.
One virtue was humility: it left for future research the mystery of what sets the pace of technological advance. The other virtue was that defaulting to the simple assumption that technology—the efficiency of turning inputs into output—improved at a constant rate such as 1% per year led to the comfortable prediction that a market economy would converge to a “steady state” of constant growth. It was as if economic output were a ship and technological advance its anchor; and as if the anchor were not heavy enough to moor the ship, but its abrasion against the ocean floor limited the ship’s speed. In effect, Solow built the desired outcome of constant growth into his model.
In general, the drawback of casting technology as exogenous is that it leaves a story of long-term economic development incomplete. It does not explain or examine where technical advance comes from, nor its mathematical character, despite its centrality to history. On its face, taking the rate of technological advance as fixed implies, implausibly, that a society’s wealth has zero effect on its rate of technical advance. There is no orange arrow from Production to Technology. Yet in general, when societies become richer, they do invest more in research and development and other kinds of innovation. It was this observation that motivated Romer, among others, to reconfigure economic models to make technological advance endogenous (which eventually earned a Nobel too). Just as people can invest earnings into capital, people can invest in technology, not to mention labour (in the number, longevity, and health of workers). Making this link in the model merely requires writing the same equations for technology and labour as for capital. It is like drawing the sixth branch of a snowflake just like the other five. It looks like this:
I discovered that when you do this—when you allow technology and all the other factors to affect economic output and be affected by it—the modelled system is unstable. (I was hardly the first to discover this.) As time passes, the amount of each factor either explodes to infinity in finite time or decays to zero in infinite time. And under broadly plausible (albeit rigid) assumptions about the rates at which that Production diamond transforms inputs into output and reinvestment, explosion is the norm.
It can even happen when ideas are getting harder to find. For example, even though it is getting expensive to squeeze more speed out of silicon chips, the global capacity to invest in the pursuit has never been greater. Here’s a demonstration of how endogenous technology creates explosive potential. Imagine an economy that begins with 1 unit each of labour, capital, human capital, and technology. Define the “units” how you please. A unit of capital, for example, could be a hand axe or a million factories. Suppose the economy then produces 1 unit of output per year. I’ve diagrammed that starting point by writing a 1 next to each factor as well as to the right of the Production diamond. To simplify, I’ve removed the purple depreciation loops:
Now suppose that over a generation, enough output is reinvested in each factor other than technology that the stock of each increases to 2 units. Technology doesn’t change. Doubling the number of factories, workers, and diplomas they collectively hold is like duplicating the global economy: with all the inputs doubled, output should double too:
Now suppose that in addition over this same generation, the world invests enough in R&D to double technology. Now the world economy extracts twice the economic value from given inputs—which themselves have doubled. So, output instead quadruples in the first generation:
What happens when the process repeats? Since output starts at 4 per year, instead of 1 as in the previous generation, total reinvestment into each input also quadruples. So where each factor stock climbed by 1 unit in the first generation, now each climbs by 4, from 2 to 6. In other words, each input triples by the end of this generation. And just as doubling each input, including technology, multiplied output by 2×2 = 4, the new cycle multiplies output by 3×3 = 9, raising it from 4 to 36:
The growth rate accelerates. The doubling time drops. And it drops ever more in succeeding generations.
Again, it is technology that drives this acceleration. If technology were stagnant, or if, as in Solow’s model, its growth rate was locked down, the system could not spiral upward so.
In the paper, I carry out a more intense version of this exercise, with 100 million steps, each representing 10 minutes. I imagine the economy to start in the Stone Age, so I endow it with a lot of labor (people) but primitive technology and little capital or human capital. I start population at 1 (which could represent 1 million) and the other factors lower. This graph shows how factor stocks and economic output (GWP) evolve over time:
Apparently my simulated economy could not support all the people I gave it at the start, at least given the fraction of its income I allowed it to invest in creating and sustaining life. So population falls at first, until after about 500 years the economy settles into something close to stasis. But it is not quite stasis, for eventually the economy starts to grow perceptibly, and within a few centuries its scale ascends to infinity. The sharp acceleration resembles history.
It turns out that a superexponential growth process not only fits the past well. It is rooted in conventional economic theory, once that theory is naturally generalized to allow for investment in technology.
How then are we to make sense of the fact that good models of the past predict an impossible future?
One explanation is simply that history need not repeat itself. The best model for the past may not be the best for the future. Perhaps technology can only progress so far.
It has been half a century since men first stepped on the moon and the 747 entered commercial service; contrast that with the previous half century of progress in aeronautics. As we saw, the world economy has grown more slowly and steadily in the last 50 years than the univariate model predicts. But it is hard to know whether any slowdown is permanent or merely a century-scale pause.
A deeper take is that infinities are a sign not that a model is flatly wrong but that it loses accuracy outside a certain realm of possible states of the world. Beyond that realm, some factor once neglected no longer can be. Einstein used the fact that the speed of light is the same in all inertial reference frames to crack open classical physics. It turned out that when such great speeds were involved, the old equations become wrong. As Anders Johansen and Didier Sornette have written,
Singularities are always mathematical idealisations of natural phenomena: they are not present in reality but foreshadow an important transition or change of regime. In the present context, they must be interpreted as a kind of ‘critical point’ signaling a fundamental and abrupt change of regime similar to what occurs in phase transitions.
What might be that factor once neglected that no longer can be? One candidate is a certain unrealism in calculus-based economic models. Calculus is great for predicting the path of comets, along which the sun’s pull really does change in each picosecond. All the models we’ve looked at here treat innovation analogously, as something that happens in infinitely many steps, each of infinitely small size, each diffused around the globe at infinite speed. But real innovations take time to adopt, and time lags forestall infinities. If you keep hand-cranking the model on my white board, you won’t get to infinity by Christmas. You will just get really big numbers. That is because the simulation will take a finite number of chunky steps, not an infinite number of infinitely small steps.
The upshot of recognizing the unrealism of calculus, however, seems only to be that while GWP won’t go to infinity, it could still get stupendously big. How might that happen? We have in hand machines whose fundamental operations proceed a million times faster than those of any brain. And researchers are getting better at making such machines work like brains. Artificial intelligence might open major new production possibilities. More radically, if AI is doing the economic accounting a century from now, it may include the welfare of artificial minds in GWP. Their number would presumably dwarf the human population. As absurd as that may sound, a rise of AI could be seen as the next unfolding of possibilities that began with the evolution of talkative, toolmaking apes.
A more profound neglected factor is the flow of energy (more precisely, negative entropy) from the sun and the earth’s interior. As economists Nicholas Georgescu-Roegen and Herman Daly have emphasized, depictions of the economic process like my whiteboard diagrams obscure the role of energy and natural resources in converting capital and labor into output. For this reason, at the end of my paper, I add natural resources to the model, rather as the classical economists included land.
Since sunlight is constantly replenishing the biosphere, I have natural resources appreciate rather depreciate. And to capture how economic activity can deplete natural resources, I cast the “reinvestment” in resources as negative.16 This is conceptually awkward, but I don’t see a better way within this modeling structure.
I indicate these dynamics with a positive sign in the purple loop for natural resources and a minus sign on its orange reinvestment arrow:
In the simulation, the stock of resources is taken as initially plentiful, so it too starts at 1 rather than a lower value. The slow, solar-powered increase in this economic input (in green) hastens the explosion by about 1000 years. But because the growing economy depletes natural resources more rapidly, the take-off initiates a plunge in natural resources, which eventually brings GWP down with it. In a flash, explosion turns into implosion.
The scenario is, one hopes, unrealistic. Its realism will depend on whether the human enterprise ultimately undermines itself by depleting a natural endowment such as safe water supplies or the greenhouse gas absorptive capacity of the atmosphere; or whether we skirt such limits by, for example, switching to climate-safe energy sources and using them to clean the water and store the carbon.
…which points up another “neglected factor”: how people respond to changing circumstances by changing their behavior. While the model allows the amount of labor, capital, etc., to gyrate, it locks down the numbers that shape that evolution, such as the rate at which economic output translates into environmental harm. This is another reason to interpret the model’s behavior directionally, as suggesting a tendency to diverge, not as literally pointing toward utopia or dystopia.
Still, this run suffices to demonstrate that an accelerating-growth model can capture the explosiveness of long-term GWP history without predicting a permanently spiralling ascent. Thus the presence of infinities in the model neglecting natural resource degradation does not justify dismissing superexponential models as a group. This too I learned through multivariate modelling.
I do not know whether most of the history of technological advance on Earth lies behind us or ahead of us. I do know that it is far easier to imagine what has happened than what hasn’t. I think it would be a mistake to laugh off or dismiss the predictions of infinity emerging from good models of the past. Better to take them as stimulants to our imaginations. I believe the predictions of infinity tell us two key things. First, if the patterns of history continue, then some sort of economic explosion will take place again, the most plausible channel being AI. It wouldn’t reach infinity, but it could be big. Second, and more generally, I take the propensity for explosion as a sign of instability in the human trajectory. Gross world product, as a rough proxy for the scale of the human enterprise, might someday spike or plunge or follow complicated paths in between. The projections of explosion should be taken as indicators of the long-run tendency of the human system to diverge. They are hinting that realistic models of long-term development are unstable, and stable models of long-term development unrealistic. The credible range of future paths is indeed wide.