Let us continue the discourse from where we stopped last week.

The second problem with SoG is that its GEI sub-component has a strong negative correlation with the other three sub-components: government consumption, transfers, and tax rates. Also, if we look at the relationships of the SoG sub-components with independent variables – such as GDP, GDP growth, health, education, and safety – we find that the correlations for GEI are positive, whereas those for the other components are negative. Creating a composite indicator out of sub-components that correlate negatively with one another and that have opposite relationships to independent variables is a statistically dubious procedure.

Again, resorting to analogy, suppose we want to devise a composite indicator of heating efficiency for residential buildings? We know that the size of a building’s windows and the thickness of its walls are relevant variables: but, how do we combine them? Simply averaging the thickness of the walls of each building and the area of its windows would not give us a reasonable composite indicator, since the two variables have opposite effects on heating efficiency. A house with small windows and thick walls could have the same score as one with large windows and thin walls, even though the former would be far more efficient than the latter. Instead, either we should treat windows and walls as separate variables in a multivariate analysis. Or, if it is important to have a single compound indicator, we should reverse the sign on window area before combining it with wall thickness.

My guess is that the people at Fraser who created the economic freedom index never thought about this problem. More likely, they used ideological rather than statistical criteria in formulating the SoG indicator. They probably assumed, a priori, that higher taxes, more government consumption, more transfers and more government investment all make us less-free and, accordingly, assumed that an average of the four would make a good measure of the size of government for their economic freedom index. The result is statistical mush.

None of this means that the size of government is unimportant. It suggests, instead, that Fraser’s SoG indicator is not a statistically sound measure of the size of government. We can check that by comparing SoG with a simpler measure based on the ratio of total government expenditures to GDP, which we will abbreviate as SGOV. The required data are available for all countries in our sample, from the IMF’s World Economic Outlook database. For easier comparison with SoG and with other components of the EFI, I express SGOV on a scale of 0 to 10, with 10 indicating the smallest government. (Specifically, if G is the ratio of government expenditure to GDP as expressed by the IMF on a scale of 0 to 100, then SGOV = (100-G)/10).

The SGOV indicator turns out to have much more explanatory power than Fraser’s SoG. The correlation of SGOV with the log of GDP per capita is -0.48, compared with -0.25 for SoG. Both correlations suggest that higher levels of GDP are associated with larger government sectors and both coefficients are statistically significant, but the association is stronger for SGOV, derived from the simple ratio of government expenditure to GDP, than for Fraser’s original SoG indicator.

Turning to the personal freedom index, the simple correlation of SGOV with PFI is -0.39, compared to -0.16 for SoG. Both indicators suggest that personal freedom increases as the size of government increases, but the coefficient for SGOV is larger, and it is statistically significant, whereas that for SoG is not. Here are scatter plots for the two measures of the size of government versus the personal freedom index:

As in earlier cases, we should not rely solely on the simple correlation, which is attributable in part to the fact that both the size of government and personal freedom correlate strongly with GDP per capita. We can get a more accurate picture by using a multiple regression to control for GDP. A regression of PFI on SGOV and the log of GDP per capita shows a correlation of 0.53, with all coefficients significant at the 0.01 level. The slope estimate indicates that on average, a one point decrease in SGOV is (that is, a one-point movement towards larger government) is, on average, associated with a quarter-point increase in personal freedom.

As a further test of the relative statistical power of the two indicators, I ran a multiple regression of PFI on both SGOV and SoG, plus the log of GDP per capita. When both measures of the size of government were included, the relation of SGOV to PFI was positive and statistically significant but SoG had no statistically significant relation to PFI.

Finally, I got similar results when I used the EHS measure of prosperity as the independent variable. The correlation coefficient for EHS and SoG is -0.18, indicating a tendency for larger government sectors to be associated with greater prosperity, but the absolute value of the coefficient is too small to be statistically significant. The correlation of EHS with SGOV is -0.48. In this case, the value of the coefficient is statistically significant and the negative sign again indicates a tendency for countries with larger governments to have higher scores for education, health, and personal safety. Here are the scatter-plots:

As before, we can refine the results from the simple correlations, using a multiple regression controlling for GDP per capita. Doing so shows that SGOV, the ratio of government to GDP, has a negative and statistically significant association with EHS, showing that larger government is associated with higher levels of education, health, and personal safety. However, SoG, Fraser’s size-of-government measure, has no statistically significant association with EHS.

Investigations lead to two substantive conclusions

First, the data appear to support notion that economic freedom makes a positive contribution to personal freedom and prosperity. That holds true whether we measure prosperity in a narrowly economic sense, as GDP per capita, or in a broader sense, using non-economic indicators of education, health and personal safety. Second, the data do not support the notion that a larger government is necessarily detrimental to either freedom or prosperity. On the contrary, countries with larger government sectors tend to have more personal freedom and higher indicators of education, health and personal safety.

These findings suggest that libertarians need to do some further thinking about Our Enemy, the State, as Albert Jay Nock expressed it in the title of his classic books.

On a purely technical level, the analysis also suggests that the authors of the Fraser Institute’s economic freedom index need to rethink their size-of-government indicator, which appears to me to have serious methodological flaws that undermine its statistical value. A simpler indicator, based on the ratio of government expenditures to GDP, has significantly greater explanatory power in a variety of circumstances.

More broadly, we need think in a more nuanced way about the potential threat that government poses to freedom and prosperity. Size of government alone is an inadequate measure of the threat. The results we have reported do not just hold for a few outliers like France and Sweden that are relatively free and prosperous, despite having large governments. Rather, an association of freedom and prosperity with large governments is a general tendency that holds across countries at all levels of income and in all parts of the world.

For further discussions, business advisory services and training, send me a message via WhatsApp or SMS.

•Lawrence Nwaodu is a small business expert and enterprise consultant, trained in the United Kingdom and the Netherlands, with an MBA in Entrepreneurship from The Management School, University of Liverpool, United Kingdom, and MSc in Finance and Financial Management Services from Rotterdam School of Management, Erasmus University Netherlands. Mr. Nwaodu is the Lead Consultant at IDEAS Exchange Consulting, Lagos. He can be reached via nwaodu.lawrence@hotmail.co.uk (07066375847).

Update news