Estimating natural rate of unemployment and potential output
I think the difference you are looking for...
The efficient level of output is how much output a competitive market would produce. In this situation, we would expect that there would be no unemployment and the inflation rate would correspond exactly to changes in the money supply as only real variables would matter.
Potential output is the maximum output that could be produced if there was imperfect competition, meaning that there was some unemployment which arises because of the inefficiencies that arise from monopolies.
For the second part of the question, I am going to attempt to calculate the natural rate of unemployment and the potential GDP.
Natural rate of unemployment
For a better understanding of the natural rate of unemployment, see
here. In essence, it is the non-cyclical unemployment which exists. To “detrend” the business cycle component, we could assume that the natural rate of unemployment was the average of the previous 5 years of unemployment. Using U.S data, let’s try and compute the natural rate of unemployment.
Monthly data for the US unemployment rate can be found here:
Collecting data from 1962 to 2016, the first thing that had to be done was to take the average unemployment rate for each year (all the data used in this post can be found in the excel spreadsheet at the bottom of the post). Once the average for each year was calculated, the natural rate of unemployment was calculated for each year. We had to remove the first 4 years since the natural rate of unemployment was assumed to be the average of the previous 5 years. This leaves us with 50 years of data from 1966 to 2016. The graph of our data should look as follows:
These calculations were performed using excel. However, to understand how we arrived at these figures we can calculate the natural rate of unemployment for the year 1966. The data needed for this calculation is:
Thus the natural level of output for 1966 is: 5.57 + 5.64 + 5.15 + 4.50 = 4.93.
For comparison sake, we can look at our data next to natural unemployment data calculated by the federal reserve bank of St. Louis here: https://fred.stlouisfed.org/series/NROU
Their methodology employed would be much more sophisticated than ours. However, our data follows a similar trend up until 2000. Given the simplistic nature of our analysis, this is seems to be a reasonable result.
The next step is to calculate the potential GDP (or natural level of output) and GDP gap. The data collected for GDP was sourced here: https://www.bea.gov/national/xls/gdplev.xls
Here is a post which outlines how to calculate the potential GDP.
In the post
here, you can see how to calculate the potential GDP. Using the data from 1966 again, we can calculate the potential GDP as:
Potential GDP = (1 - 0.0493)÷(1 - 0.0379) * 815 = 1148.65
We can use this data to calculate the GDP gap as:
GDP Gap = 1148.65 - 815 = 333.65
We can graph the following calculations as follows: