Per-Capita GDP = cf + d

where c is a proportionality constant (measured in dollars), f is the “freedom fraction,” the fraction of the population with freedom scores that exceed a specified threshold, and d is another constant representing baseline GDP in the absence of any “freedom fraction” at all, expected to be close to zero. Unfortunately, we do not know that threshold a priori, so we will try a number of thresholds to find best fit to the data.
Using the Excel worksheetfunction NORMDIST calculates the integral of a normal distribution below a threshold expressed in standard deviations. The “freedom fraction” would therefore be the remainder of the curve, the region above the threshold, or the quantity returned by the NORMDIST calculation subtracted from one. The equation looks like this:
freedom fraction = 1-NORMDIST(threshold, median population score, SD of population, TRUE)

since we have normalized the national scores already, threshold and median scores are expressed in units of standard deviation (SD), and the standard deviation is by definition one, since the scores are normalized. The TRUE argument ensures that the function returns the integral, not the center of mass, and is just an artifact of Excel.
Plotting “freedom fractions” vs. per-capita GDP with a range of thresholds generates the following series of graphs:
Plotting per-capita GDP versus freedom fraction appears to linearize the scatterplot quite nicely, particularly for threshold values in the range of 1.0, giving an R2 vale of .54. While the data is still clearly scattered, the fact that it has been linearized suggests that our proposed equation, GDP = cf + d is a reasonably good mathematical approximation of a curve that would describe the pattern of the points in the original scatterplot. Using the linear equation of the trendline generated by Excel, we can extract our two constants c and d for the original equation, which now reads:
Per-Capita GDP = $42751*f + $2201.3

Finally, if we plot our newly created model equation against the normalized scatterplot, or the original scatterplot if the SD units are converted back to the original scoring system, we obtain the following graph:
which, given a few outliers and some spread in the data due to the fact that we are dealing with relatively complex systems, appears to describe the data rather nicely.
Results and Discussion
The fit of the data to the model tends to support the contention that societal wealth is a function of the degree of embrace of a libertarian economic ethic by a society, at least to a rough first approximation. It is entirely possible that a more sophisticated model which attributes differential contributions of various slices of the “freedom curve” within a population might give a better fit, for example, by steepening the slope of the middle part of the curve and creating a sharper transition between the flat upper and lower regions with the sloping central region, but in any case, in the absence of better, more direct measurements, such an attempt would be even more speculative than this exercise.
There are several important implications if this model is correct. The first, and arguably most important, is that societal wealth is not a function of governing economic policy per se. Rather, it appears that both economic policy and societal wealth are functions of the beliefs and attitudes of the population which makes up the body of the society, as these were the explicit assumptions made in the generation of the model. The distinction is important. It implies that top-down policymaking by governing bodies is far less important to improving the economic lot of a society than the actual embrace of libertarian principles by said society at large. Just as “societal wealth” is a measurement of aggregated individual human action, it appears that individual human belief and action at the lowest levels, not the highest, are responsible both for setting the prevailing ethic of the marketplace, and the resulting potential for expanding the productive capabilities and motivations experienced by individual economic actors. In short, human action looks to be the relevant factor here, not government policy.
Another surprising set of implications, at least to this author when he decided to take up the subject, is that increasing wealth through embrace of economic liberty is bounded, as the flat, upper region of the curve implies, and that a fair number of real human societies actually appear to have reached the cusp of this plateau, as clearly visible by the data points at the far right of the curve. The threshold which was found to best fit the available data corresponds to a freedom score of only 70.5, which is to say, that individuals whose attitudes reflect this degree of economic freedom or better are part of the “freedom fraction” and contribute to per-capita GDP improvement at the higher level, while those below this threshold correspond to the baseline. This score corresponds approximately to the scores received by Spain, Sweden, Germany, Cyprus, and Norway, not despotic regimes by any means, but certainly not freewheeling capitalist societies either. The rightward skew of the national score histogram, which we noted earlier, coupled with this low threshold results in a few top scoring societies nearly “saturating” the effect of liberty on per-capita GDP, implying, for example, that over 99% of members of the top-scoring society, Hong Kong, would be above this threshold, though their failure to achieve the per-capita GDP predicted by their score would tend to suggest that there is a disparity between government policy and real public attitudes, assuming the model is correct.
Is this the case? It is certainly a testable hypothesis. If the model is correct, it implies that the standard for maximization of human productivity is actually not all that high, at least with regard to economic liberty, as a few nations have actually come very near to achieving it. Though it might be more satisfying to libertarians if the upper end of the curve were boundless, continuing on into infinity, this is probably not reasonable. If not bounded by restrictions on liberty, it stands to reason that a man’s productivity is bounded by something, whether present-day technology, or the near satisfaction of desires at the cost of an additional increment of his time and effort, or simple, overwhelming complexity as the division of labor lengthens indefinitely. It is certainly a hopeful finding that it is within human capacity to achieve the minimal libertarian ethic that allows maximization of human potential, at least in one regard.
This model produces a variety of testable hypotheses, as well as suggests further studies. It would be very interesting to determine the actual individual “freedom score” distributions of national populations to test the several assumptions of this study and further validate or refute the model. Perhaps this could be done through polling with a well designed questionnaire. It would also be interesting to combine this model with others, particularly doing a multivariate analysis to determine if the deterministic effects seen in this study can account for the “deviations” seen in another, particularly La Griffe’s IQ study, or vice versa. It could be that only a few determinants can effectively predict the observed economic distributions, if the relatively good fit found here and in his study are any indication.
Conclusion
A theoretical, mathematical model relating per-capita GDP to economic liberty which appears to have predictive value and real world implications is generated by relating the fraction of a population sympathetic to economic liberty, described by a simple normal distribution, with a proportionality constant. The success of this model suggests that increases in GDP are bounded in the limit of near universal individual acceptance of a certain minimal threshold of economic liberty, that the attitudes of individual economic actors towards economic liberty are more important than governing policy, and that several real-world societies actually approach the maximization of productive potential with respect to this variable. This simple approach appears to be a useful model for further investigations.
----Update!----
In case you are interested....
(click on the graph to enlarge)
Scott,

ReplyDeleteGreat to see the application of solid,public data to back theory. Always needed for solid argumentation. Great work.

Scott Smith

Scottroyalsmith@gmail.com

Thanks a lot!

ReplyDelete