The Bubble People

Financial Times did one of their paid-advertising posts on my Facebook feed the other day, with this article: America’s Middle-class Meltdown.

I wish I could preserve for posterity the article, and especially the conversation that follows, because when future historians scratch their heads and wonder how a national superpower like the United States suddenly flipped over and sank to the bottom of an ocean of red ink with no warning and no corrective actions taken, they could read this article, and all would become clear.

Here’s the graphic the article was built around:


The graph doesn’t make much sense, and the longer you stare at it, the less sense it makes.

The article is a long one that attempts to tease meaning out of this chart. But the chart has a glaring flaw. Does anyone else see it?

It’s right up at the top: “in 2014 dollars.”

Of course, in 1971, people weren’t earning or spending 2014 dollars, they were using 1971 dollars, which — due to inflation eroding the value of the dollar over the intervening four decades — were worth a lot more in terms of what you could buy. When people publish these “adjusted for inflation” numbers, they use the official “inflation rate” figures published by the Department of Labor Statistics to determine how much value the dollar lost over the course of four decades, and cite an income people would have been making in 1971, had they been using the less-valuable 2014 dollars.

This calculation is critically dependent on the inflation rates used. Let me demonstrate just how critical this is.

Inflation, like compound interest, is exponential in nature. You take your original value, multiply by one plus the interest or inflation rate, and repeat forty times to get from 1971 to 2011 (forty years). It looks like this:

(1 + \frac{rate_{nom}}{100})^{40} = p_{nom}^{40}

The “nom” subscript stands for “nominal,” meaning “named” or “official.” So if you have a nominal 3% inflation rate, it looks like:

(1 + \frac{3}{100})^{40} = 1.03^{40} = 3.26\%

That means overall prices will more than triple over the course of forty years. We all know how this works: we’ve been living with it our entire lives.

Now, let’s say that this official inflation number is too low by a tenth of a percent: that the actual inflation rate is 3.1%, while the official value is 3.0%. Since inflation figures are generally only cited to one decimal place, a consistent rounding error could make the number wrong by this amount.

It’s convenient in what follows to consider the fractional error:

f = \frac{p_{act}}{p_{nom}}

If we look at the actual inflation, we get:

(p_{act})^{40} = (\frac{p_{act}}{p_{nom}} \cdot p_{nom})^{40} = (f \cdot p_{nom})^{40} = f^{40} \cdot p_{nom}^{40}

In our example,

f^{40} = (\frac{1.031}{1.030})^{40} = (1.00097)^{40} = 1.0396 = (1 + \frac{3.96}{100}) = 3.96\%

It’s a little shocking, when you turn this into wages. If the economists consistently rounded down when reporting the general inflation rate, your inflation-adjusted salary in 2011 should be four percent higher than they say it should be, based on your 1971 salary. That’s more than most of us have seen in a cost-of-living adjustment in years.

Just for fun, let’s see what would happen if the economists were off by a full percentage point.

f^{40} = (\frac{1.04}{1.03})^{40} = (1.00971)^{40} = 1.472 = (1 + \frac{47.2}{100}) = 47.2\%

An error of a single percentage point on a three percent nominal inflation rate means that their comparison would be off by 47%. It means that a 1971 salary was worth half-again as much as the official inflation-adjusted numbers indicate. Which means that the peak of the blue curve above, sitting at around $50k, would need to be stretched to the right to $75k.

And that, my friends, tells an entirely different story about the economy.

So just how accurate are these nominal inflation values?

One thing we always had to do in my physics studies years ago was to come at a problem from multiple directions, calculate results with different simplifying assumptions, and see if the numbers all kind of fell in the same ballpark. If something was way out of whack, we’d have to go back and try to figure out the mistake. I still do this kind of thing every few months with software development issues, especially when making performance measurements.

So I started with annual nominal inflation rates published at the US Inflation Calculator. These are Consumer Price Index values from the Bureau of Labor Statistics, and are presumably the same numbers Financial Times used. I made a little spreadsheet, plugged in the numbers, and computed cumulative inflation rates from 1960 to 2015, then checked it against their inflation calculator on the website, and my spreadsheet matched their calculator. So I got that much right.

I then took the period from 1960 to 2006 (I’ll tell you why in a moment), and computed an “averaged” inflation rate over those 46 years: meaning, I computed the inflation rate that, if it were exactly the same, year after year, would result in the same endpoint of 6.814, which is the overall inflation in prices between 1960 and 2006, according to the government economists. For the geeks out there, this is:

p_{avg} = e^{\frac{ln 6.814}{46}} = 1.0426 = (1 + \frac{4.26}{100}) = 4.26\%

So the government says that from 1960 to 2006, there was an “average” inflation rate of 4.26%, resulting in a nearly seven-fold increase in prices.

Now the problem is that in 2006, I sold my father’s house to pay for his nursing care, after restoring the original wood floors and generally bringing it back to its original 1960 condition, and it struck me that the house sold for almost exactly ten times what he’d paid for it (new) in 1960. This intrigued me, so I went back and did a little research, and found that prices across the board — cars, food, dinner out, children’s clothing — were all about ten times higher in 2006, compared to 1960. Even gasoline was about ten times higher: $0.35/gallon compared to the (wildly-fluctuating) $3.50/gallon in the mid-2000’s.

There’s more than a bit of a difference between a seven-fold increase, and a ten-fold increase. In a physics or engineering problem, this is a clear sign of a severe mistake in the calculations, somewhere. (Except in astrophysics, of course. Sorry, it’s an inside joke.)

If I compute an average inflation rate for the observed ten-fold increase, I get:

p_{avg} = e^{\frac{ln 10}{46}} = 1.0513 = (1 + \frac{5.13}{100}) = 5.13\%

This seems to indicate that the economists working for the Bureau of Labor Statistics were off by, on average, about a full percentage point for the forty-six years from 1960 to 2006. Over this period, their error fraction would be:

f^{40} = (\frac{1.0513}{1.0426})^{46} = 1.465 = (1 + \frac{46.5.4}{100}) = 46.5\%

So that means if this Financial Times chart had “inflation-adjusted” a 1960 salary into 2006 dollars, the adjustment would make the 1960 salaries too low. You’d have to boost them by almost half again to correctly compare with 2006 salaries.

I haven’t done the research on 1971 prices compared to 2015 prices, but I see no reason to think economists have gotten any better at their jobs in the last nine years. So I went ahead and drew this (I don’t have FT’s actual numbers, so I had to eyeball it from their chart — it should be pretty close):

The yellow line just follows the red bars, from the FT article.

The blue line is from the FT article.

The orange line is what happens when you correct the blue line for presumably underreported inflation rates. [For you wonks, I simply multiplied the x-axis values of the blue curve by the error factor of 1.465, and divided the y-axis values by 1.465 to normalize the area under the curve.]

I also found their cutoff at $200k on current data (red bars and yellow line) extremely peculiar. According to most sources I’ve seen (e.g. CNNMoney), the top 2% of income starts at around $300k. But their 2015 data (the red bars) stops at $200k and only totals to about 92.5% of the population, leaving that last 7.5% or so unaccounted for — they lump it all into the $200k+ category — which explains the huge spike at the end of the chart.

This is especially peculiar because the blue line — their inflation-adjusted 1971 data — covers 99% of the population, leaving a 1% spike at the end. I have no idea why they cut off current incomes at $200k, leaving 7.5% of the population unaccounted for, instead of running it out to $300k, which would have covered 98% of the population.

So I went ahead and fudged in 5.5%, spread out in a tail between $200k and $300k, which then leaves 2% making above $300k. There could be a 5.5% spike right at $242k for some bizarre reason, but I doubt it.

As I said, this now tells a very different story.

Most of this article was econobabble that tries to explain away something that pops right out at you: the blue line says that (apart from about 1% of the population that has fallen into serious poverty) everyone is doing better in 2014 than they were doing in 1971. Yes, there are a lot fewer people making between $10k and $75k, but this is because there are so many more people making more than $85k.


The orange curve — if correct — shows that no one, on the whole, has benefitted in the 2014 economy, except maybe the folks up in the top percent or two. This looks a lot more like what most of us have experienced: hiring freezes, capital budget trimming, layoffs of skilled workers, people picking up what low-paid work they can just to keep body and soul together, combined with relentless rise in the price of consumer goods, even as the official “inflation rate” remains negligible.

The blue curve does not match reality. The orange curve does.

All I had to do to correct this was to look at actual price increases over the period from 1960 to 2006, determine that the Bureau of Labor Statistics apparently underreports inflation by about one percent on a consistent basis, and then apply that one percent correction to the article data.

This is more than just a little disturbing. If the Bureau of Labor Statistics is systematically low-balling the inflation figures, it has profound repercussions throughout every measure of the US economy. Among other things, it means that the US economy isn’t growing as fast as reported, and may not be growing at all.

If you look into the methodology the Bureau of Labor Statistics uses, and read some of the critiques, there is clearly game-playing going on. Which makes sense: governments don’t like to see high inflation numbers, and it is pretty easy for them to lean on people to figure out ways to misreport the numbers, year after year.

Let me give just one amusing example. Hedonics. It works like this (and I choose exaggerated examples, for effect, but I believe this is essentially accurate):

Let’s say you want to compute inflation between 1927 and 2015, based on car prices. So you look up the cost of a new Ford Model T in 1927 ($360), and the cost of a popular low-end car in 2014, say a Ford Fiesta ($14,500).

“But wait!” cries the professor of Hedonics. “That’s not a fair comparison. The Fiesta is a much better car. It has windshield wipers! And a radio! And electric locks! And the paint lasts longer!”

So they start discounting the “improvements” to the Fiesta, using estimates of the desirability of those features in an open market (how much you’d pay for those windshield wipers if they weren’t included), and end up with an imaginary car that is equivalent to a Model T, and would sell for $5000. So the Hedonics-adjusted inflation is based on the change from $360 to $5000, not $360 to $14,500. That additional $9500 is paid for actual value, and doesn’t count as inflation.

The obvious fallacy, here, is that you cannot buy the Model T equivalent car for $5000, or for any price, because it doesn’t exist. If you want a new, low-end car, you have to pay $14,500, and you get the “improvements” whether you want them or not.

Another Hedonics trick is to make substitutions of “equivalent value.” If you can’t afford beef because the price of beef is going through the roof, you can just switch to mayonnaise and Soylent Green, which is (according to someone) nutritionally equivalent, and costs exactly what beef used to cost. So, you see, there is really no inflation at all.

The key is to understand that all of these various “fine tuning” methods somehow always lower the consumer price index. They never raise it. Especially compared to the commonsense meaning of inflation, which has to do with how far your paycheck will stretch in buying the necessities that are actually available for purchase.

Over time, this game-playing means that both government and private enterprises are flying blind, and are merely telling themselves comforting bedtime stories about the economy, believing their own propaganda.

Which brings me back to the Financial Times article. I don’t read Financial Times, and after this exposure, never will: it appears to be the Fox News of the financial industry.

But the comments on this article were priceless. I have decided to call the Financial Times readers The Bubble People: they live in little bubbles of illusion that float free of the Earth and all its troubles and cares, and the messy reality of it all. I imagine they have personal assistants who actually pay the bills.

For instance, The Bubble People here complain quite a bit about how “ungrateful” Liberals are, since the graph (the original FT chart) clearly shows that things are much better for the common people: see how many fewer are making less than $50k, and how many more are making over $100k/year, compared to what people were making in 1971? People should be grateful they aren’t living in that icky lower-income bulge any more, and have been pushed into making more money. But no, they aren’t grateful, they just complain — that’s just what those Ungrateful Liberals do.

The Bubble People also gush about how cars and computers (and yachts?) are ever-so-much better these days, and how they think Hedonics makes perfect sense. It’s a better car, dammit, of course it should cost more. Has nothing to do with inflation. Nothing at all.

The real irony, however, is that these are the people who don’t trust the government. You see them telling each other that corporations produce all the good things in life, and the government just gets in their way and screws things up. Yet it never seems to occur to even one of them to question the inflation figures that come directly from the government they so completely distrust. Maybe they’re just ignorant: perhaps they don’t realize that “inflation-adjusted wages” are adjusted based on inflation rates that are generated and published by the government.

More likely, of course, is that they think with their appetites, rather than their minds. When a chart tells them something they want to believe (like things are getting better for those “common people” who make less than $200k, or Liberals are all stupid whiners), then the chart must reflect reality.

I don’t know if the Bureau of Labor Statistics is underreporting inflation rates. Maybe Mr. Alan Smith of Financial Times made some other error in posting that blue curve, and simply needs a dope slap. My little mathematical exercise above is nothing more than suggestive. But were I in charge of the Bureau of Labor Statistics, I would be asking some deadly serious questions, with a number of economists’ jobs on the line.

Because this isn’t just an academic matter. If the CPI is chronically understated by one percent, then no one — not one, single working economist or financial expert in the country — has any idea what the economy is actually doing. If the orange curve above is anything like correct, it tells a story of economic pain on a vast scale. Pain becomes anger, and widespread anger is dangerous. People who become convinced that a game is rigged — whether rightly or wrongly — tend to kick the board over and start throwing rocks. Ask the ghost of Marie Antoinette: I used to think the “let them eat cake” story was apocryphal, but after reading the comments of The Bubble People in the Financial Times, I’m no longer sure.

N.B. Some minor corrections have been made to the calculations since the original version.

This entry was posted in General.

Leave a Reply

Please log in using one of these methods to post your comment: Logo

You are commenting using your account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s