The Stock Market is Exponentially Accelerating too

Many still have significant doubts about my article on how economic growth is growing at an accelerating pace.  To this, I offer the basic evidence that the world economy comfortably grows at more than 4% per year, and this rate was unheard of in any part of human history prior to the second half of the 20th century, because if such growth existed from, say, the Roman Era, then the compounding over 2000 years would make everyone alive today a billionaire.

Another place in which to judge the rate of exponential growth is the stock market.  Below is a chart of the S&P500 index from 1950 to today.  I have added the red trendline to show how the market is moving in quite a predictable, exponential trajectory.  The economic malaise of the 1970s, the bubble of the late 1990s, and the bust of 2001-02 all negated each other to invariably move back to the trendline.

If we see the same image on a logarithmic scale, the exponential trend (which now is a straight line) is clear, and timing the long-term future milestones of the market are semi-predictable.

This also shows that current levels are certainly not overvalued, and are in fact almost exactly where the trendline would expect them to be.

And for those who insist that the Nasdaq should be shown instead, I would point out that a) the Nasdaq has been around for a shorter time, and b) the Nasdaq is less a representation of the broader market than the S&P500, as it is technology-heavy.  Nonetheless, a logarithmic Nasdaq chart also shows a similar trendline, and the late 1990s boom and bust revert back to the trendline.

Part of the reason we don't see an increase in the rate of increase in this logarithmic chart (which would make even this line curve upwards gently) is because some of the surplus growth is occuring in overseas markets.  A composite chart of the full world's stock markets over the last 55 years would be interesting.  If I find a good one, I will add it. 

Comments

[jeffolie]

You are clearly guilty of "curve fitting" in graph I. Had you ended the data set at 2000, the trend as predicted would have been broken severely.

You are guilty of selective data in GraphII by starting in 1975. Had you done a regression analysis starting in 1950 ending in 1968, the next 12 years would not be consistent with the prior 18. The 1950 graph would be a consistent uptrend and the1968-80 line would be perpendicular.

You are guilty of eliminating the NASDAQ. It hit a high of 5000 and now is more than 50% below that. It fell from 5000 to 1000. That would totally destroy your "The Stock Market is Exponential and Accelerating too".

Curve fitting + selective data + ignoring data = bad analysis + wrong conclusion

[jeffolie]

The 1950 graph would be a consistent uptrend and the1968-80 line would be perpendicular.

this should have read horizontal

The 1950 graph would be a consistent uptrend and the1968-80 line would be horizontal.

[GK]

Jeffolie,

Check again. The Nasdaq also follows a steady trendline, and the boom-bust were merely bigger deviations from the trendline than with the S&P500.

[jeffolie]

You have not adjusted for inflation.

[jeffolie]

See an inflation djia adjust trend at:

http://home.earthlink.net/~intelligentbear/com-dj-infl.htm

[GK]

But excluding dividends is not accurate either. 41% of the total gain of the stock market is from dividends.

[GK]

Stock market real returns are about the same as real GDP growth, plus dividends (about 1.5% a year).

Real GDP = 3.5% a year.

Thus, total return = 3.5% + 1.5% = 5% per year ahead of inflation. Taxes take a big bite, which is why IRAs and 401Ks are more suitable for stocks.

But, as we know, real GDP for the aggregate world is rising at an accelerating rate..

[jeffolie]

You have not responded to my charting objections.

Here is another problem with your graphs. You use a log scale on one axis and not the other. This skews the curve.

Use a log-log graph.

Here is another problem. Stocks used in the indexes are the weighted stocks by capitalization. Their is a survivorship bias. As stocks loose capitalization, they are replaced. This results in an upward bias.

Regarding dividends and the taxation. Most stocks are not in IRAs and are taxed on dividends. As stock indexes change taxation occurs to change the stocks.

The "accelerating" has disappeared from 2 of the 3 charts. And on a log-log chart the 4% slope would drasticly be reduced.

[jeffolie]

When you adjust dividends for taxation, keep in mind that the marginal rates change often. Today's marginal tax rates are some of the lowest in the history of the income tax.

[GK]

I have extended the trendline to the full length of the charts. They don't go further back in time than that.

Why would you want the x-axis to be log? It is a measure of years (just 35 in the Nasdaq case). Plus, that option does not exist in Yahoo anyway.

As far as surviorship bias, the accurate measure would then be total capitalization of the entire US stock market (currently $13 trillion). If we chart that, we would see an accelerating trend.

[jeffolie]

GDP as announced by the government is a joke of manipulated numbers. The data set are hedonics, false by ommision, using false CPI adjustments.

"....the BLS has been gaming the CPI numbers for some time (hedonics, substitution, excluding “volatile” food, energy, food, non-rental housing, etc.). This allows the Feds to spend less on those programs in real terms as inflation slowly erodes the purchasing power of dollars paid out to entitlement program receipients."

All these problems of GDP , CPI and charts apply to your thread of accelerating economic growth.

[GK]

All that balances out, so the GDP trend is accurate.

Unless you are suggesting that the world is not experiencing any increases in wealth at all. Check out the Human Development Index post in the January archives. Human development is rising, and rising fastest in economies that also report high GDP growth.

The rate of electricity consumption, internet diffusion, etc. also corelate closely to GDP growth. It is impossible that all of these measures are rigged.

[jeffolie]

Since you are not using a log-log chart, then do not use a log on only one axis. Do not use a log scale at all. Why, because the trendline is skewed left giving a false regression analysis.

A lot of stocks in the broader market go to zero or is delisted and shows up again in the pink sheets. By looking at the indexes, you get a false and upward view of the broader market.

[jeffolie]

Wrong. GDP must be adjusted accurately for CPI and does not "balance out". Using real GDP is required for any significant period of time:

Whereas nominal GDP refers to the total amount of money spent on GDP, real GDP adjusts this value for the effects of inflation in order to estimate the actual quantity of goods and services making up GDP. The former is sometimes called "money GDP," while the latter is termed "constant-price" or "inflation-corrected" GDP -- or "GDP in base-year prices" (where the base year is the reference year of the index used). See real vs. nominal in economics.

The Human Development Index is not an economic number and is false. Just look at the false positive index shown for Japan. Japan is a dying nation with shrinking and aging population:

JAPAN'S DEPRESSION MENTAL, ECONOMIC = DYING COUNTRY
Japan Turning into a "Society without Children"

TOKYO, December 3, 2004 (LifeSiteNews.com) - A record number of Japanese women are unmarried and childless, leading the country perilously close to a childless society. The country has actually coined a new term to describe the phenomenon - 'shoshika,' which means "a society without children," according to a BBC report.

The population, if current trends continue, will be reduced by 20 percent by mid-century, with nearly 50 percent of those being elderly -- an "impossible" situation for maintaining the health and pension systems.

Women in the country are reticent to marry, blaming employer and social expectations, such as long working hours for men, coupled with the expectation that women stay at home after having children.

According to the figures, deaths are likely to outnumber births by about 10,000 this year, the first decline since 1899. Japan's population reached 127,687,000 in October 2004. The health ministry said births were set to fall by 44,000 to 1,067,000 this year, with deaths going up 48,000 to 1,077,000.

The declining population fuels fears for the pension system as a smaller workforce supports a mass of pensioners. Young Japanese feel children are a burden to their careers and lifestyles.

Germany and Italy are among other nations whose population have started to decline. The Cabinet Office of Japan predicted that the population will halve to 60 million people by 2100.

[GK]

So is poverty across the world, as an aggregate, dropping or rising, in your view?

Has US prosperity, on aggregate, dropped or risen, in the last 20 years?

[jeffolie]

I do not have an opinion on world wide poverty because there are no good sources for such a vast data set. Some places have gotten better and some worse.

Overall the poverty rate in the US has remained range bound between 12-14%. These numbers are probably understated by the illegals not reported.

Overall real wages have remained flat for the last 20 years:

http://globaleconomicanalysis.blogspot.com/2005/03/real-inflation-adjusted-wage-growth.html

Housing affordability is a total diaster.

The amount of debt carried on the family basis is huge. The twin national deficits are huge. Overall we are living way beyond our means on borrowed money.

Technology has been a gain in the last 20 years.

Overall prosperity appears to me to be flat to slightly down over the last 20 years in the US. I am not optimistic that the next 20 years will be much different or better; perhaps, it will be worse.

[GK]

I strongly disagree, as there are many pieces of evidence that poverty has dropped a lot on a WW basis. Even if you don't buy into the Human Development Index, things like growth in electricity consumption, literacy, telephone and PC density, drops in infant mortality and life expectancy, etc. indicate a rise in living standards. It is impossible for all these to be rigged, and improper to not count them.

Even in the US, the percentage of people with a college degree has risen. The price of a car, as a percentage of income, has fallen. Life expectancy has risen. The Internet has improved productivity greatly, and opened up many new means of entrepreneurship.

Twin deficits don't worry me at all, as subjective measures of savings are not counted in current metrics (see the "Economy is stonger than we think" article, and the BW article linked there.)

The housing bust will hurt a people, but it will be a medium-sized recession, not a depression. The housing bust will make affordability for first time buyers improve, so while owners lose out, young people who were priced out would then be able to get in.

[jeffolie]

Vehicle affordability as defined by the government is a lie. The government does not count mandatory options and upgrades:

Uncle Sam's "Optional Extras"
Where all that inflation in car prices has come from.
by Eric Peters (2004-02-23)

In 1980, the base price of a brand-new Toyota Corolla was $5458. Today, a new Corolla starts at $13,570 - more than double the 1980 cost.

Why the massive uptick?

Inflation is a factor, but only part of the reason. Even adjusted for inflation, the price of cars has gone up markedly. For example, the MSRP "sticker price" of a brand-new 1984 Chevy Impala sedan (a popular family-type car) was about $8600. That works out to about $16,000 in today's dollars. But the MSRP of the '04 Impala is $21,485 - a difference of $5485.

So who is making you fork over the extra five grand?

The answer is, the government - in the form of regulatory costs that are passed on to consumers and mandated "options" such as airbags, 5-mph bumpers and CFC-free air conditioners that have added thousand of dollars to the price of today's new cars and trucks - both in terms of initial cost to buy, as well as over-the-road costs to maintain, repair and even insure.

RE COLLEGE GRADUATES

Quanitity does not means quality. We have dumbed down our education system to the point of functional illiteracy.

December 26, 2005
College Illiteracy
Arnold Kling

The Washington Post reports

Literacy experts and educators say they are stunned by the results of a recent adult literacy assessment, which shows that the reading proficiency of college graduates has declined in the past decade, with no obvious explanation.

"It's appalling -- it's really astounding," said Michael Gorman, president of the American Library Association and a librarian at California State University at Fresno. "Only 31 percent of college graduates can read a complex book and extrapolate from it. That's not saying much for the remainder."

INTERNET ENTREPRENEURSHIP = PORN

The biggest growing segment of businesses on the internet is porn.

Internet porn is more insidious than other types of porn because it’s cheap—plenty of images are free—it’s anonymous and it’s easily accessible. The Sunday Paper clicked through several dozen explicit porn sites without ever using a credit card, for example, just continuously clicking on icons that read “I’m over 18”—something that an 8 year-old could just as easily have done.

Dr. David Greenfield, a clinical psychologist and founder of the Center for Internet Studies, conducted one of the largest surveys on the topic to date: a study of 18,000 Internet users who logged onto the ABC News Web site. He found that 5.7 percent of his sample met the criteria for compulsive Internet use. Of those participants, 75 percent said they had gained "feelings of intimacy" for someone they'd met online; 62 percent said they regularly logged on to pornography sites, spending an average of four hours a week viewing the material; 37.5 percent of that group masturbated while online. And that was in 1998.

(For his part, Abel says that spending four to six hours a night on porn sites is par for the course for people he counsels.)

In 2003, Nielsen/NetRatings estimated that 34 million Americans visited porn sites in just one month—about one in four Internet users in the United States. Neilsen also reported that the average user views 121 pages of porn, going back six times and spending an hour and seven minutes every month looking at adult-related material.

Of course, porn sites are in business for the same reason that everyone else is in business—to make money. The National Research Council, which advises Congress on technology, issued a report in 2002 that predicted the online porn industry would grow to become between a $5 billion and $7 billion business before 2007. They underestimated. According to an InformationWeek magazine article in June, current estimates of the revenues generated by online porn range from $8 billion to $12 billion. Abel says a user with a problem may spend as much as $400 to $600 per week on porn sites.

LEVEL OF DEBT

The new Fed chairman is very worried, I am very worried and you should be very worried.

HOUSING BUST

Japan has been deflation for 15 years and going for more since its housing bust.

The GSEs will go bust and be delisted. They are in violation of the NYSE and FASB rules:

WASHINGTON, Feb 10 (Reuters) - A report on Fannie Mae's multibillion-dollar accounting problems, due from the investigator hired by the mortgage finance giant, could be released as early as Feb. 23, sources said on Friday.

Accounting problems at Fannie Mae (FNM.N: Quote, Profile, Research) are expected to result in a profit restatement of as much as $11 billion. The company is still under investigation by its regulator and other federal agencies.

The U.S. House Financial Services Committee plans to hold an oversight hearing to review the report due from former New Hampshire Sen. Warren Rudman, the panel has told Fannie Mae.

The company, a government-sponsored housing enterprise, has not filed financial results for 2004 or 2005.

WORLD WIDE PROSPERITY

Japan is dying. Russia is dying with a lifespan of only 58 now. Africa is dying. Backward, 14th century Islam is the fastest growing religion in the world with 1.6 billion adherents. South America is turning toward communism which depresses freedom and prosperity.

[Fewlesh]

Jeffolie,

love the doom and gloom baby! I'm going to do a little point by point analysis.

After all this death from Japan, they sure as hell make great cars though.

Car price -- agree with you there. Bought a honda accord for 20k. It was much cheaper before. I did get a bunch for my 20k though:
airbags, super low emissions, same horsepower, more reliability?. If I had the choice, I wish I could have bought it for 10k though. There are no good cars for 10k anymore.
check -- agree with you.

College Grads -- I went to a UC school. 50% of the majors were psychology. WTF. I agree with you there. These mooching childen are going to a party school to spend their parents money so they can be part of the Bachelor's Club. But there were a bunch of us studying our asses off in new tech -- biotech, nanotech, computer. So I give you a half check on this one.

Internet -- Well, you did miss google, yahoo, microsoft, oracle, sap, redhat. Tech has been kicking some butt. We've had exponential gains in processing speed, performance, network capacity. Google may get strong AI, software greatly increases productivity of office works, etc.We have gotten VERY cheap communication technologies: cell phones, etc. no check there.

Levels of debt: it's freaking scary. Hold the gold baby. big check.

housing bust: see above, check again.

world wide prosperity:
China and India industializing -- millions are being lifted out of abject agririan poverty. The middle east is cashing in BIG time. They are living like the kings they are! Advanced Western countries properity is going to drop, unless they produce (unlikely). But the rest of the world is going to party like it is 1999, after they dump US dollar hegemony, and the mooching economies of the EU and UK. half check.

[penty]

use of a log scale on one axis and not another is perfectly acceptable.

[Jim Gaser]

The thing missing here is the corrections for devaluation of the currency. Look at a 100 year CPI style graph of the value of a "dollar". It is a fairly straight line, then gets a "hockey stick" acceleration in 1971 when Nixon permanently took us off the gold standard. Inflation isn't the same as growth, prosperity, or wealth. All your calculations, to be fair, should be made in "inflation adjusted dollars". Inflation is the most cruel tax, because people don't understand it. Not only do we get whacked on dollars, and anything denominated in dollars, we also get killed with capital gains tax on gains that don't actually exist in buying power terms.

[Jeremy]

This Jeffolie guy is obviously a complete idiot. The stock market DOES follow an exponential trend, as do many other things in nature where population statistics are important.

The equation for an exponential function is:
y = A exp(B*x)

To linearize this equation, you take the log of both sides:

ln y = ln A + Bx

Thus, if you want to fit a linear trend to an exponential equation, you must make a graph where the y axis is logarithmic, and the x axis is linear. All of this is not only perfectly valid, it is also the preferred method for viewing exponential data trends, as smaller variations are easily hidden when doing an exponential fit on linear-linear axes.

The one problem I have with the data you presented is that you don't go back far enough in time. If you use the Dow Jones index and follow the market back to just after the 1929 crash, the extrapolation changes, and you'll see that the market is currently overvalued by about half of what it was when the tech stock crash occurred.

[csl]

Jeffolie doesn't likely to be a idiot but a stubborn nerd instead...

[purity mbogo]

judging the rate of exponential growth using the stock market may not be very accurate to arrive at 4% world economic growth rate.......because of high rate of corruption in developing countries

[W]

Inflation adjusted GDP per capita is linear. Otherwise, awesome post.

https://fred.stlouisfed.org/series/A939RX0Q048SBEA

[Kartik Gada]

Inflation adjusted GDP per capita is linear.

False. It is exponential. You have to check the centuries-long trend.

[Geoman]

here we are in 2019 - and the exponential growth noted continues unabated.

[John Smith]

Very good post and I commend the OP for his/her efforts and I commend the objectors for their views. Sam Pittsburgh