## More on why you’re better off in a high tax state

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I put up a blog yesterday under the title â€šÃ„Ã²Why you’re better off under a high tax state’. I was pretty happy that the data I presented showed in the way I presented it the story I wanted to tell. My right wing critics weren’t happy with that, of course, and did, as usual, play the man not the arguments.

But one commentator — who has for reasons he has explained to me  wished to remain anonymous — decided something much more constructive could be done with the data. That was possible — because as is my usual practice I don’t simply make assertions — I publish my data too

He took it, reworked it and from thereon I’ll pretty much use his own words to describe what he did and found:

First of all, as far as I can tell, the regression coefficients Gary has referred to do not reflect a particularly robust test of the correlation we're talking about.  I'm afraid the reason for this is that the way the trend lines in your graphs appear to have been produced is not the best way of using these data.  I think what they effectively demonstrate is the extent to which a country's rank in the tax-rate league table is correlated with its per capita GDP.  As we see, there is a correlation, but what they don't reflect, however, is the correlation between a country's actual rate of tax and per capita GDP.  The size of the difference in tax rate between a country and the one ranked immediately below it is not factored in.  Fortunately, given the distribution of the data and the number of countries involved, this doesn't appear to have a huge impact on the correlation demonstrated, but in order to conduct a robust analysis it is inappropriate to reduce the data in this way.

That's the bad news.  The good news is that, when you do a more powerful test, a stronger correlation is demonstrated, at least for the dataset which includes only the larger countries.

Please find attached some graphs I have produced from the data.  I believe these more clearly demonstrate the correlations you've described.

[The first graph uses the first data set — of all countries]

[The second data set is of the top 85 countries by population]

In addition to the data cleaning you've done (i.e. excluding the smallest half of the countries), I've produced a third graph considering only (larger) countries with a per capita GDP above the mean.

The (slightly less) strong correlation shown among this group appears to suggests that tax as a proportion of GDP remains relevant even as a country becomes more prosperous.

It should be noted that, whichever (sub)set of data is used, the correlation is highly statistically significant.  For the stats geeks like me:
All data: R^2 = 0.14; p<0.0001
Countries above median population: R^2 = 0.44; p<0.0001
Countries above median population; above average GDP: R^2 = 0.32; p<0.0073

As Gary suggests, the R^2 values indicate that other factors are at play: given the complexity of an entire country it would be absurd to expect there not to be.  However, the p-values are an estimate of the probability of the observed correlation being down to chance.  Values under 0.05 are regarded for most purposes as statistically significant; <0.001 as highly significant.  It certainly looks like something is going on.

All in all I think it's a worthwhile and interesting question to be looked at, and certainly merits further attention.  In the light of the Wilkinson and Pickett analysis we should perhaps be questioning the importance of GDP growth as a policy goal for its own sake in a developed country, but as those on the right in favour of regressive taxation are so keen to argue that low taxation promotes GDP growth, evidence that the opposite is true is yet another weapon against them.

My considerable thanks to my commentator.

As I said when doing the original data — the connections seem obvious. This analysis shows they are in a more formal presentation.

I await the nitpicking.

But I think the challenge implicit in my commentator’s last paragraph is interesting.