How big is too big?

When it comes to the government, anyhow, the answer seems to be that most of the developed world is experiencing economic sclerosis as a result of having a bloated government.

While I generally agree with the conclusions (and am not that surprised to see that the data show government size to be hampering economic growth), it is worth looking at some of the implications of the econometrics in more detail:

• The authors find that a 1% increase in government spending leads to a .13% reduction in economic growth. However, when they include spending squared, they find that there is at most a weakly significant effect. There are good reasons to believe that the relationship between government size and growth is nonlinear, and I'm guessing they just didn't find the right non-linearity. Nonetheless, the nonlinearity they are finding would seem to imply that reductions in government size would be less effective in stimulating growth in countries with big governments than in countries with small governments. This is not good news for those of us who are in favour of small government, as cuts in government spending will have their smallest effect in the economies that need the cuts the most! The authors only briefly mention this point in a footnote.
  
• It is very easy to look at the regression results and calculate things like "the optimal size of government is 0," or "the most inefficient size of government is 76% of GDP," or "maximal government is just as efficient as 52% of GDP," or other such interesting claims. However, all of these claims would be made out of sample, and are thus invalid. The results hold for government sizes between (roughly) 18% and 67% of GDP, but not outside those bounds. This may be a no-brainer for people with economic training, but I don't think bad statistics are generally generated for economists' consumption.
  
• One of the results that struck me as odd was where the authors examined the components of government revenue and their effect on growth. They argue that direct taxes have little effect on growth, while indirect taxes and social contributions have a negative effect. I'm not sure why this might be the case, and I sincerely doubt that the prevalence of loopholes in income tax code or the relative difficulty in evading indirect taxes relative to direct taxes holds the answer. I think the answer lies in misinterpreting the regression coefficients. Say you can raise revenue in one of 4 ways: direct taxes, indirect taxes, social contributions, and "other" (e.g. inflation, revenue from sales, plundering neighbouring states, etc) If the government wants to raise one dollar, it has to do it one of those 4 ways. This means that, for each country, the percentage of income coming from each of these 4 sources sums to 100%. This is important, because that means in order to run a regression you must omit one of the variables (in this case it is "other"), but this necessarily implies that the coefficients of the 3 reported revenue sources are to be interpreted relative to the missing variable, not on their own. So direct taxes are no worse than "other," and are not as bad as indirect taxes or social contributions, but we can't say they have no effect. In other words, you need to treat it like a dummy variable!
• On the same issue, the problem may also lie in the fact that the authors don't appear to control for government size in those regressions (note: they might in fact control for it, I just don't see it). It seems plausible that governments would increasingly rely upon revenues from indirect taxes and social contributions as they grow larger. In other words, governments can only tax income up to a certain point, and if they want more income, they need to tax something else. This would imply that the result is not in fact causation, but rather correlation. Basically, increased government size leads to using indirect taxes and contributions more as well as reduced growth. This makes it look like indirect taxes and social contributions slow growth down if you don't control for it.
  

HT: Thoughts on Freedom