Personal vs Macro Dimensionless Ratios

2017 March 3
by Daniel Lakeland

Here's a different version of a graph I posted yesterday:


This graph is (GDP/capita) * (Wages As Percentage Of GDP/100) / (GDP/capita * Stock Market Capitalization as Percentage of GDP/100) = Wages as Percent / Stock Market Cap as Percent.

Note also that the per capita cancels on the top and the bottom.

It looks like GDP cancels but note that this is problematic. Conceptually the dimensions of this number are actually 1/[Time] since GDP is not a dollar measure but an INCOME measure, so when they calculate "Stock Market Cap as Percent" they're really calculating "Stock Market Cap as Percent of the GDP Income Rate times 1 year". Whereas wages as a percentage of GDP are in fact in units of Dollars/Time. The overall dimensions are 1/[Time] with units of 1/Year.

So, this graph shows you how if you saved *all* your wages for a year, how big a fraction of the stock market could you buy relative to "the share that everyone would have if the stock market were equally divided among all people".

In 1975 you could buy a little more than "your equal share" (I won't call it "fair" it's just equal). These days you can buy a little less than 30% of an equal share.

Here's another relevant question. How much would an epsilon share of the stock market buy you in consumer goods if you sold it?

This is (stock market capitalization as a fraction of GDP * GDP/capita) / CPI * epsilon where epsilon is a sufficiently small dimensionless number that the results are in dollar amounts you might carry in your wallet.

In 1988 your per capita share of the stock market would buy you consumer goods equivalent to $25 today (3 chicken sandwiches?), whereas by 2000 it would buy you what $80 would buy you today (a sushi dinner for 3?), and it's been on a wild ride ever since. On the other hand, if you look at growth rates prior to 1990, you can see that the extension of those growth rates would put the stock market at the bottom of the 2008 crash about at the "right" level. Hmm... Certainly we do things more efficiently now that we have computers, so I could see an increased growth rate being reasonable, but pretty obviously given the periodic oscillations, there's way too much optimism.


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