## A graph at war with its caption. Also, how to visualize the same numbers without giving the display a misleading causal feel?

Kaiser Fung discusses the following graph that is captioned, “A study of 54 nations–ranked below–found that those with more progressive tax rates had happier citizens, on average.”

As Kaiser writes, “from a purely graphical perspective, the chart is well executed . . . they have 54 points, and the chart still doesn’t look too crammed . . .” But he also points out that the graph’s implicit claims (that tax rates can explain happiness or cause more happiness) are not supported.

Kaiser and I are not being picky-picky-picky here. Taken literally, the graph title says nothing about causation, but I think the phrasing implies it. Also, from a purely descriptive perspective, the graph is somewhat at war with its caption. The caption announces a relationship, but in the graph, the x and y variables have only a very weak correlation. The caption says that happiness and progressive tax rates go together, but the graph uses the U.S. as a baseline, and when you move from the U.S. point on the graph to the right-hand side (more progressive taxes), you see a lot more points below the line than above the line. Thus the visual impression of the graph is that more progressive taxes will lead to lower happiness—the opposite of the message from the caption.

What can be done here?

I don’t exactly think the graph is “bad data,” and, although the graph says little directly about causation, the data have some relevance to our understanding of policy debates over taxes. If nothing else, we learn that tax progressivity and average happiness some variation among countries. I think a start would be to reframe and put happiness on the x-axis and the tax system on the y-axis, which would allow us to see that, at any happiness level, there is a range of tax systems. with none of the very happiest countries having flat taxes.

Better still might be to make a line plot with three columns: First, a list of country names, in decreasing order from richest to poorest (using, for example, per-capita GDP (yes, I know, such data aren’t perfect!)), then a column showing tax progressivity (if that’s the measure they want to use), then a column showing average happiness.

The advantage of this pair of dotplots is that you get to see the spread in each of these variables with respect to a natural measure (how rich the country is), and there’s no implicit causal story getting in the way.

1. JVM says:

Also tax progressivity is a terrible measure of equality or “national progressiveness” or whatever this is supposed to be measuring. There’s no way Canada is on net less progressive than the United States, and Denmark being virtually tied with the US on this measure pretty much invalidates it.

Why not use net tax transfer? Or gini index?

• Andreas Baumann says:

I was about to make this point exactly. See how far Sweden is from Denmark & Norway – that, to me, indicates that there is something rotten in this instrument.

• Patrick says:

Also, they seem to be doing a simple max(tax rate) – min(tax rate) which doesn’t really inform as much as you’d expect. Along with that statistic we would also want to know the relative size of the populations in each bucket.

2. jonathan says:

That chart stood out to me when published so I spent a few minutes typing Oishi Schimmack (until I got it right) and found the original. The chart to me doesn’t accurately label the data source: it implies a measure of total progressivity but it’s actually more a basic arithmetical difference between highest and lowest rates, with some adjustment I didn’t get into involving effective rates and then some other adjustments based on earnings levels and government spending. I’m not sure all of those make logical sense but whatever. They didn’t have decent data for about half the countries and the line drawn is one of those regression lines which slopes upward but which essentially runs through a scattered pile of data points. But my point for the graph was that isn’t the measure of progressivity most used because it doesn’t directly address major sources of taxation in many countries, notably VAT. The chart says “tax burdens” but that is not true.

3. Nameless says:

One more problem is that the graph does not control for other things that might affect happiness, like, for example, per capita GDP.

If you take the graph and only keep the points corresponding to developed countries, you’ll notice two things: (1) developed countries are generally quite happy (the only one that ranks below 6 on the vertical scale is Portugal), there’s a definite trend towards _lower_ happiness at higher progressivity.

4. Rahul says:

http://www.bloomberg.com/news/2013-05-01/six-ways-to-separate-lies-from-statistics.html

Six Ways to Separate Lies From Statistics
By Betsey Stevenson & Justin Wolfers May 2, 2013

The discovery of a spreadsheet error in an influential study by Harvard University economists Carmen Reinhart and Kenneth Rogoff inevitably raises a troubling question: To what extent can we trust what any researcher claims to be true?

5. I would love to know how they compute the tax rate. I can’t imagine that if you take the full tax burden (payroll and income, not to mention sales) that Canada is less progressive than the US. It sure wasn’t back when I was a kid (and lived in Canada).

• Nameless says:

They are not using the absolute value of the tax burden, they are using its progressivity. The article mentions a few different data sources, but, as far as I can tell, all data in the chart comes straight from here

http://www.worldwide-tax.com/index.asp#partthree

without any modifications or checks.

The web site reports income tax range of 28-49% in Norway, 15-29% in Canada, 15-35% in the U.S. and 0-57% in Sweden. Sure enough, in the chart, we see Canada at 14%, U.S. at 20%, Norway at 21% and Sweden at 57%.

I don’t have the slightest idea how the web site came up with 15-35% in the U.S., since the lowest tax bracket was lowered to 10% in 2001 but the highest tax bracket was only lowered from 39.6% to 35% in 2003.

Some variation seems to come from varying definitions of “low tax bracket”. In all four countries, the first \$100 earned is tax-free, but this fact may be described as “personal exemption” or as “0% tax bracket”. Saying that the lowest tax bracket is 28% in Norway but 0% in Sweden is, at the minimum, misleading, and most likely also factually incorrect (as far as I can tell, there are no fundamental differences between their tax systems that would allow you to make this statement.)