Fun with Statistics

I gathered statistics on different countries so I could look at the correlations between different things.

Executive Summary

I attempted to investigate whether nine different national indices of freedom correlated positively with various national statistics that are somewhat reflective of protections for life, liberty, and the pursuit of happiness. I found that countries scoring high on most of the indices of freedom do have better statistics in these three areas. The indices of property rights, freedom from corruption and business freedom correlated most positively. The indices of limited government, gun rights, and freedom from taxes correlated weakly and in some cases negatively. I attempted a weighting of the various freedom indices to take all my analysis into account, and determined that I would rather move to Finland than North Korea.

Background

I have had some discussions on-line about libertarianism. Libertarians are very sure that logic and reason are on their side and that life will be better if government just gets out of the way and lets private enterprise take care of everything. I'm not very ideological about who provides services in society as long as it works well. I do have concerns about any system that places far more value on one aspect of society (in this case, freedom) than on all the other things we value. Other one-directional systems have not worked very well in practice, however nice they might sound on paper.

Unfortunately, the libertarians I have asked can't point to a country where their system has been tested out in real life. I can't look at the most libertarian country and poke around at what life is like there and decide if it's a good place to live, because no one can identify such a country. I don't believe in selecting a political system based on its theory - I live in Canada, which has been described as a country that "works in practice, but not in theory." I want to know how it will work, because otherwise it's like buying a pig in a poke.

What Did I Do?

There are some websites that attach numbers to freedom indices for different countries, so I can look at various kinds of freedom: business freedoms, freedom of speech, tax freedom, property rights, etc. I thought if I could match those various rating numbers against other national statistics, such as life expectancy or average income, I might be able to pick out some trends.

In general, I'll break my discussion of results into three categories: life, liberty, and the pursuit of happiness. Under life, for example, I could look for a correlation between life expectancy in a country and its freedom of speech index. If I saw a statistically valid correlation with a positive slope, that would tell me that the average country with more freedom of speech has longer average life expectancy. There are a couple of general caveats:

If there is a positive, statistically valid correlation, however, I can say that if you move from your country to one with a higher score on the freedom of speech index, you will most likely be moving to a country with longer average life expectancy.

The Freedom Indices

I went looking for a source of numerical values for several freedom indices for many countries that I could easily download into Excel. I also wanted the source to be an organization that appeared to be libertarian in nature. I wanted to investigate their claims, so I thought it would be good to use a source in which they would have confidence. I think I found such a source at FreeExistence.org, on this page: http://www.freeexistence.org/freedom.shtml. FreeExistence.org provides number ratings between 0 and 100 for the following nine indices:

Of these, the one that made me really curious was the Index of Limited Government. The creator of the FreeExistence website had no information on where that index came from, and there is no email address on the site for posing questions. If you read further, you'll see that this index gives very different results from most of the other ones, so it became important to figure out what it was based on. I recently downloaded country-by-country data on government spending as a percentage of GDP and compared it against this Index of Limited Government. Plotting them against each other, I got a curve so nearly perfect that it is clear to me that's what this index is. The formula is:

Freedom Index = 99.645 + 0.0237 x (Govt Spending %) - 0.0303 x (Govt Spending %)2

The R squared value of this correlation is 0.9998. That qualifies as a slam dunk in my books. This makes it possible to plot the other statistics I was interested in against the government spending percentage itself, rather than against the Index of Limited Government. I think that makes it more meaningful. I will add notes [in square brackets] to that effect in each of the discussions below.

The Rest of the Data

For the other statistics I was interested in, I mostly downloaded data from Wikipedia. These are not necessarily the highest quality sources of data, but this is just a curiosity project, not an academic study. If someone wants to do a more rigorous analysis, that would be good. If someone has already done a better analysis of this sort, I would be interested in seeing how their results differ from mine.

The Results: Life

In the life category, I looked at infant mortality, life expectancy, murder rates, and suicide rates. I consider lower infant mortality, longer life expectancy, lower murder rates, and lower suicide rates to be the desirable direction.

This is what I found for correlations between the freedom indices and infant mortality. These are in descending order of the strength of the correlation. On average, a country scoring 10 points higher on the index of:

This is what I found for correlations between the freedom indices and life expectancy. These are in descending order of the strength of the correlation. On average, in a country scoring 10 points higher on the index of:

This is what I found for correlations between the freedom indices and murder rates. These are in descending order of the strength of the correlation. On average, a country scoring 10 points higher on the index of:

This is what I found for correlations between the freedom indices and suicide rates. These are in descending order of the strength of the correlation. On average, a country scoring 10 points higher on the index of:

For most of the freedom indices, if you move to a country with a higher freedom index, you will be moving to a country with lower infant mortality, longer life expectancy, lower murder rates, and higher suicide rates. The one exception is the index of limited government. If you move to a country with a higher score on the limited government index [i.e., where government spending is a lower percentage of GDP], you will on average be moving to a place with higher infant mortality, lower life expectancy, higher murder rates, and lower suicide rates.

The Results: Liberty

In the liberty category, I mainly looked at cross-tabulations between the nine freedom indices. In addition, I looked at incarceration rates.

The cross-tabulations between the freedom indices showed that most of them are positively correlated with each other, some of them very strongly. A few pairs of indices have no statistically significant correlation, and one pair, limited government and freedom of expression, are negatively correlated. The following table shows the relationships between the nine indices. In this chart, a cell indicates the average number of points the index at the left will change if the index at the top increases by 10. For example, if one country's freedom from corruption is 10 points higher than another country's, the first country's property rights index will on average be 9.6 points higher. If a country's limited government index is 10 points higher, its freedom of expression index will on average be 1.8 points lower.

Business
Inflation
Property
Taxes
Corruption
Ltd Govt
Expression
Drugs
Guns
Business
8.9
7.8
6.3
7.3
3.1
2.7
4.8
3.4
Inflation
7.1
5.4
7.4
4.8
4.6
1.2
2.7
2.9
Property
8.0
7.0
3.3
9.6
1.2
4.4
7.1
1.9
Taxes
6.2
9.0
3.1
2.3
6.1
   
2.7
Corruption
6.1
5.0
7.7
1.9
 
2.6
5.0
 
Ltd Govt
4.1
7.6
0.2
8.2
 
-2.1
   
Expression
3.2
1.8
5.0
 
3.7
-1.8
9.6
4.1
Drugs
1.3
0.9
1.9
 
1.7
 
2.2
1.0
Guns
1.5
1.7
0.9
1.3
   
1.6
1.7

The table is arranged so that the indices with the strongest correlations to the other eight are generally found towards the top left and the ones that correlate the most weakly are generally to the bottom right. If the number in the table is black, the correlation is statistically significant with at least 99% confidence. If the number is green, the correlation is statistically significant with at least 95% confidence. If the number is purple, the correlation is statistically significant with at least 90% confidence. Red is used to show a negative correlation - in both cases these are statistically significant with confidence of at least 99%. If the cell is empty, there is no statistically significant correlation. Cells on the diagonal are blanked out, because an index's correlation with itself is trivial. [I didn't look at the relationship between government spending as a percentage of GDP and these other indices, because I was primarily interested in how they relate to each other.]

This is what I found for correlations between the freedom indices and incarceration rates. On average, a country scoring 10 points higher on the index of business freedom has 7.7 more prisoners per 100,000 people, with 95% confidence that this is a statistically valid correlation. None of the other freedom indices had statistically valid correlations with incarceration rates [including government spending].

It appears that incarceration rate is not very indicative of the influence of these indices of freedom on "liberty" since it has only a weak correlation with just one of the indices. The correlations between the indices seem more useful. Based on the table above, the business freedom index seems to be the best "bellwether" indicating whether a country is likely to score well on the indices of the other freedoms. Gun rights seems to be the least predictive, having weak or no correlation with half of the other indices.

The Results: The Pursuit of Happiness

I wasn't sure how best to define the pursuit of happiness. There is a Global Barometer of Happiness, based on interviews of nearly 53,000 people in 58 countries by Leger Marketing. As mentioned below, I found only weak correlations with two of the indices of freedom and no statistically significant correlation with any of the others. Moreover, happiness is not the same as the pursuit of happiness. I'm not sure quite what is required to pursue happiness, but I looked at some things that might influence people's ability to go after the things they want: average income (based on purchasing power parity), income inequality (the Gini coefficient), and the Human Development Index, which is a composite of life expectancy, literacy, education and standards of living.

This is what I found for correlations between the freedom indices and the Global Barometer of Happiness. These are in descending order of the strength of the correlation. On average, a country scoring 10 points higher on the index of:

This is what I found for correlations between the freedom indices and per capita income (based on purchasing power parity). These are in descending order of the strength of the correlation. On average, in a country scoring 10 points higher on the index of:

This is what I found for correlations between the freedom indices and income inequality (based on the Gini coefficient). A higher Gini coefficient would indicate that the wealthy have incomes farther above the average income than in other countries. A lower Gini coefficient would indicate that the poor are not as far below the average income as in other countries. Thus, it is less a measure of the overall ability to pursue happiness within a society as it is a measure of who can pursue happiness within the society more easily. The relationships below are in descending order of the strength of the correlation. On average, a country scoring 10 points higher on the index of:

This is what I found for correlations between the freedom indices and the Human Development Index. These are in descending order of the strength of the correlation. On average, a country scoring 10 points higher on the index of:

For most of the freedom indices, they have little or no statistically valid correlation to the Barometer of Happiness, but they do have correlations with the other three values under pursuit of happiness. If you move to a country with a higher freedom index, you will be moving to a country with higher average income and a higher score on the Human Development Index. The exception to this is limited government. If you move to a country with a higher score on the limited government index [i.e., where government spending is a lower percentage of GDP], you will on average move to a country with lower average income and a lower Human Development score. The Gini index is positively correlated with some indices (limited government and tax freedom) and negatively correlated with others (freedom from corruption, property rights, and business freedom).

Conclusions

Most of the indices of freedom correlate positively with a society's ability to foster life, liberty, and the pursuit of happiness, based on the national statistics I examined. The exceptions are: the index of limited government, which appears to be correlated with decreasing ability to protect both life and the pursuit of happiness; and freedom from taxes and gun rights, which are both apparently correlated with a decreasing ability to protect the pursuit of happiness. Shuffling all these correlations together is a fairly arbitrary process, very dependent on your personal values. I have made an attempt, combining the strength (r value) of the correlations in each category and then weighting each of the three categories equally. In order from most to least positively correlated with these three categories, the nine indices fall in the following order:

If I weight the nine indices according to this pattern and rank countries according to a composite index of freedom, the top 10 countries in the dataset are as follows: Finland, New Zealand, Denmark, Netherlands, Canada, Australia, Sweden, Germany, Iceland, and Ireland. The next 10 are mainly in Western Europe, with the exception of Hong Kong, Singapore, and Barbados. The United States places 21st. The bottom countries include quite a few for which the indices are not available due to lack of data. The bottom five are: North Korea, Somalia, Sudan, Afghanistan, and Iraq. If we exclude countries for which various indices are missing, the bottom five are: Burma, Eritrea, Libya, Turkmenistan, and Democratic Republic of Congo.

A Few Notes on the Statistical Analysis

I am not a professional statistician, though I use statistics in my work. I did this analysis in Excel, because (as my friends will attest) I use Excel for all kinds of things from tracking my investments to timing the cooking of a ham. I would be interested in seeing this analysis done more rigorously by someone who really knows what they're doing.

To obtain my correlations, I plotted the indices of freedom against the other statistics in Excel and let Excel's built-in regression system find the best linear equation and calculate the r-squared value. In many cases, a different shape of curve might have offered a higher r-squared value than a straight line, but I wanted to keep things simple so I didn't pursue that. To test the statistical validity of an r value, I used a table from the appendix of Statistical Methods, Seventh Edition, 1980, by George Snedecor & William Cochrane. The table was originally from Statistical Methods for Research Workers, 1925, by R.A. Fisher. 1925! We stand on the shoulders of giants.

If I wanted to push this analysis further, Snedecor & Cochrane describe how to estimate the expected distribution of the y-variable for a given value of x in a correlation like this. That would enable me to, for example, estimate the variance for the life expectancy in countries with a freedom of expression index value of 60. In theory, then, if you lived in a country whose freedom of expression index was 50, you could estimate the odds that average life expectancy would increase if you moved to one with an index of 60. It seemed like too much work, so I didn't go there.

The major thing missing from this analysis is time series data. I can talk about how countries compare with each other, but I can't talk about how a given country changes with time. In five years, presumably many of the freedom indices and many of the other statistics will change. At that point, just as an example, I could plot change in life expectancy versus change in the index of freedom of expression. That would permit a discussion of what societal changes tend to go together and which ones go in opposite directions.


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Last Updated: 11 January 2012
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