Friday, July 13, 2007

Another Simple Chart

A couple of weeks ago I posted a chart showing, for the G7 economies, GDP per capita plotted against government's share of GDP. It took a bit of flak, with correspondents pointing out that if you x'd out the US, all you had was a flat(ish) line. In short, the chart did not illustrate the OECD's inverse relationship between GDP and "tax pressure" at all.

You could see what they meant. Previous (unblogged) versions of the same chart had worked better, but on reflection, this latest one was a tad creaky. Stung into action, I've taken a further look at the OECD's published data, and come up with the revised chart above.

First, cards on the table, let's all recognise that a chart of this kind is never going to "prove" an association. As BOM commenters have said, there are a lot of differences between economies besides simply the share of GDP spent by the government.

No, to reach proper conclusions you clearly have to take all that into account systematically, just as the OECD's own work has done. And those of you who've waded through the definitive OECD paper (The Sources of Economic Growth in OECD Countries) may recall their summary table:

(click image to enlarge)

As you can see, they conclude that, in the long-run, a 1 percentage point increase in the tax burden reduces overall output per working age person by 0.6-0.7%. A very clear conclusion that captures what has now become pretty well the consensus among mainstream researchers.

But there's a problem. And the problem is that the conclusion is buried deep within a 249 page econometric study. The kind of thing normal people take one look at and immediately slip into deep deep unconsciousness.

Now, wouldn't it be great if we just had a simple picture. Something that would illustrate the conclusion without needing to wade through all that stuff.

And that's precisely what I'm after. A simple chart to illustrate the OECD's conclusion: to wit, for economies like ours, on average, taking one thing with another, more tax means less per capita income.

So I've had another shot.

What I've now done is to plot the same data, but for all the rich OECD economies, which I've defined as those having per capita GDP at or above the OECD average. These are the 18 economies most like us, and not for example, still in catch-up transition from the old Soviet empire. From that group, I've also excluded Luxembourg as being a small weird outlier (much of its wealth reflecting its controversial status as the EU's onshore tax haven/laundry), and Norway as floating on oil. Which leaves 16 countries, including the UK.

The result is shown above, with a simple regression line through the points.

Now OK, the regression fit is not going to get Tyler a Nobel Prize (R2=.26). And OK, there's still a bit of a L shape in the plotted data.

But at least the line does slope the right way, and the slope coefficient at -0.77 is remarkably close to the OECD's -0.6 to -0.7 (especially taking account of the linear scaling on my simple regression). Thus in its highly simplified broadbrush way, the chart does capture the study's conclusion.

There are two questions in my mind.

First, does this chart work better than the last one? While not perfect, I think it does.

And second, is it bad to use a picture like this? Is it wrong to gloss over the raft of underlying complexity? Is it corrupt to use a seductively simple picture to persuade people who will never themselves delve into those 250 dense pages of stuff?

Personally, I don't think so. I reckon much of modern life depends on such simplifications to communicate complex ideas. And surely it can't be that misleading when we've got the boys and girls from Paris behind us.

Or am I just a really really bad person?

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