Benford’s Law

Benford’s Law is an interesting statistical nuance which is important to understand when dealing with statistics in general and with economic statistics such as GDP growth rates.  It is not related to the law of diminishing marginal returns directly but unwittingly gives it a statistical basis.  In summary, Benford’s Law states that:

“in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way.”

Benford’s Law appears to flay in the face of logic.  Why don’t the leading digits (1-9) simply occur 10% of the time, as logic may suggest?  The reason is that, as something grows exponentially, the numerical data sets produced tend to take longer to double from 1 to 2, or from 1,000,000 to 2,000,000, than they do to double from say 2,000,000 to 4,000,0000, etc.  The tendency is so strong and widespread that apart from economic phenomena, it applies to the measurement of natural phenomenon such as earthquakes, infectious diseases, and even pulsars!

The Distribution of Benford’s Law
Can Bedford’s Law Explain Higher GDP Growth Rates for Developing Countries?

GDP Rates, an example of Benford’s Law in action.  We start with a hypothesis:

“As a predominantly Engineered (Socialist) economy becomes less Engineered and more Organic (Capitalist), it experiences exponentially increasing rates of economic growth.  Conversely as a predominantly Organic economy becomes more Engineered, it experiences exponentially decreasing rates of economic growth.”

We will define economic growth as an increase in capital goods within an economy.  For lack of a better measure, we have looked at year over year GDP growth in the East and the West.

For the sake of simplicity, we further postulate that the Eastern economies (China, Japan, etc.) more closely resemble “Engineered” or state controlled economies and that Western Economies (US, France, etc.) more closely resemble “Organic” or Capitalist economies.  These may not be perfect definitions on a country by country basis but the general distinction between East and West will give us a good starting point in trying to confirm or deny our hypothesis on a country by country basis.  Naturally, the US and China, the world’s largest trade relationship, should be our first case study.

What complicates matters is that there does not exist, to our knowledge, a perfectly Organic nor a perfectly Engineered economy on the planet that would be available for study.  Rather, we will encounter a jumbled mix of qualities within a country that will make it seem at once Organic and Engineered.  What we are looking for, then, is evidence that and economy is becoming generally more Organic or generally less Engineered and vice versa.

If our hypothesis is correct, we would expect to see an Eastern economy, which is moving from a state of being Engineered to a state of being allowed to grow Organically, grow its GDP at a faster rate year over year than an economy that is moving from a state of Organic growth to a state of being Engineered.  We expect that Organic growth not only creates wealth faster but does a better job of maintaining the capital that has been previously accumulated.  On the other hand, any attempt to Engineer an economy has the consequence of destroying capital and reducing wealth on a net basis.

What does this have to do with our hypothesis?  We are still wondering ourselves, but we think it has something to do with how the GDP growth percentage increase is measured.  For a rapidly increasing GDP number, as we would expect to see in a developing economy moving from an Engineered state to an Organic state, the percentage increases would appear greater for data points between 1,000,000 and 2,000,000, for example.  Since Bedford’s Law says that roughly 30% of the readings will start with one, as a smaller economy doubles in size, its rates of GDP growth expressed as a percentage will be higher than those of an economy moving from, say, 2,000,000 to 3,000,000.  This rate of exponential growth would decrease and perhaps turn negative in an economy moving from an Organic state to an Engineered state.

To sum it up, the higher GDP growth percentage of an economy becoming less Engineered is because the Engineered economy is starting the GDP growth race from a very low GDP number.  Logic and Benford’s Law dictate that it will outpace growth rates of the already high GDP Organic economies.

As an economy, once you’ve gone Organic, there is no turning back.  The longer you stay Organic, the more dangerous becomes any attempt to Engineer it.  Legislation such as the Dodd-Frank Financial Reform and Health Care Reform are large scale attempts to further Engineer the US’s Organic economy.  Is it any wonder, then, that its growth rates should lag those of the East?

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