User:Gabrielcwong
Using the historical/prehistorical estimates table, one can determine the following % growth rates:
Time Period | Average (mean) GDP growth rate per time period | Median | Compounded | Continuous Compounding
1,000,000 BCE to 2012 | 44% | 22% | 26% | 19%
1 CE to 2012 | 23% | 22% | 21% | 27%
1920 CE to 2012 | 27% | 25% | 23% | 21%
Comparing these three figures, one can deduce that the long-run GWP growth rate (non-compounded/compounded/continuous) is roughly 22%, excluding the outlier growth rates in pre-historical times, and taking into account time periods of historical events that caused a roughly 200% rate of growth or higher (see 1800-1850 Industrial Revolution, 1900s World War 1, etc.). This growth rate is real GWP (PPP), which does not account for inflation (historically, without central banks to control inflation, different countries would have varying and extreme inflation rates).
Using the Golden Ratio of Interest (GRI) rule (citation pending), we can deduce that the long-run average inflation rate is either 14% or 35% (22%/1.618 or 22%*1.618). The long-run inflation under GRI would likely be 35%, with inflation being larger than real interest given the lack of inflation control. Then, using the Fisher equation, one can deduce historical long-run nominal GDP growth rate of 1.22*1.35=1.64 or 64%. Alternatively, natural inflation of 14% implies nominal interest of 39%.
Modern GRI would likely use real interest as larger than natural inflation, given inflation-targeting at 2%. However, this does not imply a fixed real interest rate of 3.2%, because GRI is not commutative. The real interest rate fluctuates, and GRI can be used to determine "natural" inflation, which is not the same as realized inflation or targeted inflation, nor is it necessarily independent of targeted inflation. Given that central banks would like to control inflation regardless of real interest rates (e.g. if real interest is 8%, we do not want 5% or 13% inflation), this does not contradict the GRI.
In a negative real interest rate environment such as in 2014 with the ECB, the negative value for the golden ratio can be used. A real rate of -0.2% and golden ratio of -0.618 implies an inflation rate of 0% and nominal rate of roughly 0%. This is close to the actual figure, not accounting for artificial adjustments to the rate because of monetary policy (see Fisher hypothesis) where inflation is targeted at 2%.
To summarize, GRI can be used to determine inflation. Specifically, GRI provides four values (*1.618, /1.618, *-.618, /-.618) to determine natural inflation given a real rate of interest. Real interest is generally independent of monetary policy under the Fisher hypothesis, and GRI implies a one-to-one mapping of real interest to natural rate of inflation, while the Fisher hypothesis implies a one-to-one mapping of inflation to nominal interest. The natural inflation rate can also generally be considered to be independent of monetary policy, regardless of inflation-targeting, and generally long-run focused, so as not to disrupt the Phillips curve.
Considering 2006-2014 world GDP annual growth rates (roughly 3-5%, except 2009) and worldwide inflation targets at 2%, the GRI value of 3.2% is actually incredibly accurate, with disparities only existing because of nations without central banks where there is hyperinflation.