Gross Domestic Product per Capita

One of the primary indicators of the health and well being of a society, used by many, is the Gross Domestic Product, (GDP.) The GDP is important, but doubling the population, (everything else remaining the same, such as GDP per capita,) doubles the GDP, but no one is better off.

A far better indicator of the health and well being of a society is the GDP per capita, since it is a metric of the standard of living of the society. An increase in the GDP per capita raises the standard of living, and a decrease, lowers it.

Note that both the population and GDP can not be zero, (or negative-but the GDP per capita can be negative.) Further, the GDP will fluctuate, as the society confronts complex, and unanticipated, situations.

Therefore, it would be expected that the GDP of a society will have the characteristics of geometric Brownian motion fractals over time.

There are a few initial observations of the GDP being a geometric Brownian Motion fractal:

• The GDP per capita can be calculated by dividing the GDP by the population to get the average, (or more correctly, the mean,) GDP per capita, (usually, this is the limit of available data.)
• It is not the average, (or mean,) GDP per capita that is of interest in the growth, (or lack thereof,) of the GDP-it is the median. The median is the important parameter.
• Over time, the GDP per capita will evolve into a Log Normal Distribution, noting that the mode, median, and, mean, of the distribution are all related by two variables: the location parameter; and the scale parameter. (Taking the logarithm of the ordinate of a log normal distribution results in a Normal Distribution.)

Additionally, it is important to note that there are three methods of calculating GDP: the Production approach; the Income approach; and the Expenditure approach, and all, in principle, give the same result.

It is the objective here to study the World GDP per capita since the end of the stone age, (about -5000 CE,) and the US GDP from its beginning, 1792.

Simulation of Gross Domestic Product

As a starting point, a simulation of a society with populations that vary over four orders of magnitude, with parametrics that are similar to the last two centuries of the US GDP can be found at, tsinvestsim-lognormal. Note that the simulated GDP grew at as a near perfect exponential. This is due to near perfect governance. It is the function of governance to create a stable economic environment of positive growth per capita, (e.g., consistent positive movement of the median GDP per capita.) Metrics on the stability of governance, relative to consistent economic growth, is one of the subjects of this study.

Note that issues of governance effects everyone, (at least to some degree,) in the society, as the median GDP fluctuates, and this is different than the fluctuations in individual wealth as individuals take risks in an attempt to better their economic position-and since geometric Brownian Motion fractals are high entropy, the gain in individual wealth is subject to the Kelly Criterion, which will be another subject of this study.

Also, note that the growth in individual wealth is subject to both risks, governance and the mediation of the gambling skill of individuals, and these affect the distribution of the GDP per capita-which offers an analytic methodology, (if both risks are assumed to be IID-at least in the sense of the inefficiencies compared to a perfectly efficient system.)

World Historical Economics

The World Historical Economics analysis was based on data from 1,000,000BCE through 2,000CE, but most of the analysis commences at the late stone age, (about -5000 CE,) with particular attention to the modern economy, (since about the sixteenth century, CE,) and its relation to the contemporary economy.

US Historical Economics

The US Historical Economics analysis was based on data from 1790 through 2000, but contains additional analysis since WWII and an analysis of the 1964 through 1974 productivity and standard of living "bubble."

The US GDP Historical Economic Business Cycle geometric Brownian motion analysis was based on data from 1790 through 2010-it is a study of "Bubbles," in the US GDP.

The US Historical Federal Debt argues that federal debt can not have geometric Brownian motion characteristics, but has arithmetic Brownian motion characteristics, instead. The analysis was based on data from 1792 through 2010.

The US Historical Energy Consumption analyzes US energy usage from 1635 to 2000, and the effect energy costs on the US GDP per capita, i.e., the US standard of living.

Archive

The data presented here can be reconstructed, in its entirety, from the historical.economics.tar.gz tape archive file, which contains all data and references, thereto. The source code to all programs used in the analysis is available from the NtropiX site, tsinvest.tar.gz, and, the NdustrixX site, fractal.tar.gz, tape archive files. All use the "standard" Unix development systems of rcs(1) and make(1) to facilitate replication.

It should be noted that many of the data set sizes are pitifully small-some as few as two hundred data points, (a standard error of about 7% of the standard deviation,) and conclusions can only be regarded as circumstantial.

License

The information contained herein is private and confidential and dissemination is strictly forbidden, except under the provisions of contractual license.

THE AUTHOR PROVIDES NO WARRANTIES WHATSOEVER, EXPRESSED OR IMPLIED, INCLUDING WARRANTIES OF MERCHANTABILITY, TITLE, OR FITNESS FOR ANY PARTICULAR PURPOSE. THE AUTHOR DOES NOT WARRANT THAT USE OF THIS INFORMATION DOES NOT INFRINGE THE INTELLECTUAL PROPERTY RIGHTS OF ANY THIRD PARTY IN ANY COUNTRY.

So there.

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