The Visual Misrepresentation of Quantitative Information: Wages and Debt

Regular readers will know that I have a bit of a Thing about bad graphs used in the media and on blogs. When people use stupid presentation tricks to exaggerate features of data to make their argument look stronger, it bugs me. But what really irks me is when people use stupid presentation tricks to trample their own arguments.

Today’s exhibit for the prosecution is this graph by Mike Konczal via Kevin Drum comparing median wages to household debt over the last thirty years:


The blue line is debt, the reddish one income (adjusted for inflation, I believe). Both data sets are normalized so that the 1980 value is 1.00. You can’t tell that easily, because for no good reason, Konczal has chosen to bury his point by plotting them on separate vertical scales– the red line uses the numbers on the right side of the graph, while the blue line uses those on the left.

“I don’t know,” you say. “If they weren’t on different scales, you wouldn’t be able to see the variation in the wages line.”

Yes, I know. And that’s the whole point of the graph.

This is intended to show that consumer debt absolutely exploded relative to income in the last ten years. But the point it partially obscured by the fact that the lines are on two different scales. Visually, it looks like income started higher than debt, and grew by about 50% (from roughly 4 on the left-hand scale to roughly 6). Debt clearly grew faster, but it looks like the two passed each other at around 2002.

In fact, the red line uses the right-hand scale, where zero is somewhere way off the bottom of the plot. The actual growth in income was about 20%. There was maybe a brief period in the early 80’s when income exceeded debt on this scale, but the growth was nowhere near comparable. Here’s a really crude mock-up of what it would look if the two were plotted on the same scale:


The green line is roughly what the red line would be if it were on the same scale as the blue line. I haven’t attempted to reproduce all the little wiggles, because they don’t matter on this scale. From 1980-2007, income increased 20%, and debt increased 1000%.

And there’s no reason why they can’t be plotted on the same scale– they’re both dimensionless quantities, having been normalized to 1980 values. In fact, putting them on the same scale makes the important point clearer than having them on different scales.

Now, this is being a little unfair, as the normalization hides the relative sizes of the initial numbers. One would hope that income exceeded debt for much of this period, and if it did, then starting both at 1 would confuse the issue in a different way. A more accurate presentation might use absolute numbers adjusted for inflation, or represent both as a fraction of inflation-adjusted income, or something like that.

And, to be fair, both Drum and Konczal talk about these as if the really important thing is the tiny change in the average slope of the red line around 2000, where it goes from infinitesimally upward to essentially flat. You might miss that change on the current scale, and you’d definitely miss it on my preferred graph. Then again, the divergence between the two curves at that time would probably be even more dramatic if they were plotted in a sensible way.

The simple, general lesson to draw from this is: Think carefully before using a two-axis plot. Make sure you’re not trampling your own point with a lousy presentation format.

8 Replies to “The Visual Misrepresentation of Quantitative Information: Wages and Debt”

  1. Actually, you have to drill back to original blog post to even understand the graph–income is annual median household income, and the “borrowing” is the annual change in total outstanding household debt, in billions of dollars. They’re completely different sets of numbers, so it doesn’t really matter if they’re on the same scale or not. It would be better if the debt number was also median per household, then the two lines would be directly comparable.

  2. I think that your green line in the final figure overestimates the slope of the income ratio. It should be even flatter!

  3. @2: You may be thinking of the oft-quoted stat that per worker incomes have been flat (in real terms) since 1973. The labor participation rates of women continued to increase in the 1980s and 1990s. Since that curve is a household income measure, it makes sense that household income would increase as number of workers per household increased. The curve flattens out after 2000, reflecting saturation of that mechanism for boosting household income.

  4. All of what you said, plus why does the axis say “Income ratio”? Ratio of income to what? Is it trying to acknowledge, however clumsily, that it’s been normalized to 1? If so, it really isn’t doing a good job.

    I’d also like to point out that “debt” and “borrowing” are very different things, but seem to be used interchangeably on the other y-axis.

    In short: BAD GRAPH.

  5. To elaborate on what Moopheus said @1:

    The income graph is what you think it is. Start with inflation corrected median HOUSEHOLD income (which would only be two incomes if there are two adults in the household) and normalize to the income in 1980.

    The red graph is f(year)/f(1980).

    The blue debt graph is g'(year)/g'(1980).

    Rather than start with inflation corrected data for the debt PER HOUSEHOLD, he started with the DERIVATIVE of TOTAL borrowing in the household credit market. Part of this is due to population growth and a big part is due to inflation, but the important detail is that it is a derivative! Household debt is rising a lot (about 200 to 300 billion dollars per year) when the blue curve is flat.

    It is a borrowing ratio, not a debt ratio.

    And inflation plays an important role. That derivative of 1200 billion per year in 2008 is actually 460 billion in 1980 dollars, and the derivative was almost 200 billion per year in 1980. I think his “debt” ratio only goes up to 3 (still big) if corrected for inflation.

  6. In fairness to Mike, his post says, “I’m on a time crunch, so I’m sorry that’s a terribly messy graph….” He was just trying to quickly put something together that shows both (a) flattening income and (b) skyrocketing year-over-year growth in debt starting in the late 90s. He’s a pretty sharp guy who would do it better if he had more time.

  7. Of course, I have no such excuse for reposting his messy graph. In my case, it was just pure laziness.

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