The FRB, the BEA, and the BLS lie on inflation. Update

Two years ago we posted on the federal funds rate and demonstrated that the Federal Reserve has been retaining an extremely simplistic approach when formulating its monetary policy. Figure 1 depicts the cumulative values of effective rate, R, and the rate of consumer price inflation, CPI, multiplied by 1.4. In the long run, these two curves evolve along the same trend and intercept every fifteen to twenty years. In December 2013, the cumulative R was approximately 20 points higher that the cumulative 1.4CPI. With the currently low rate of inflation in consumer prices, it will take another few years for the headline CPI to intercept the cumulative R curve. This means that R will be very low in the years to come, likely through 2020.  
We presumed that the main idea to keep R above the rate consumer price inflation is that a higher funds rate should suppress price inflation due to the effect expensive money. On the other hand, the FRB has likely to retain the interest rate at the long term level of price inflation in order to create neutral conditions for money supply. This would be a wise prerequisite for a central bank.  Then why the FRB needs that factor of 1.4? Actually it does not and the answer comes from the historical GDP data.  The problem of the multiplier is in wrong estimates of inflation since 1950. Essentially, the FRB, the BEA, and the BLS all lie.
Figure 2 depicts the evolution of real GDP per capita in the US since 1970. As we have already mentioned in our posts, there are two trends in the historical GDP data – before and after 1950. Before 1940, the (red) regression line with a slope of ~$61 per year in Figure 2 provides a good approximation of the actual curve. After 1950, the actual curve evolves along a straight line with a slope of $387 per year, i.e. the slope rises by a factor of 6.34 after 1950. Real GDP is defined as the ratio of nominal GDP and the GDP deflator. Both values are measured and estimated (also using a subjective hedonic factor) by the BEA and BLS. Therefore, the estimates of real GDP per capita heavily depend on the definition of price inflation. 
Let’s suppose that the real GDP curve evolves along the old trend after 1940, as shown in Figure 2. Then the level of real GDP per capita in 2008 would have been $10,774 instead of $31,178 as estimated by. This means that the GDP deflator was underestimated by a factor of 2.89 (=31178/10774).  The reported increase in the level of consumer prices since 1960 was of 7.27, i.e. CPI(2008)/CPI(1960) =7.27.  Then we expect that the actual price increase (i.e. reported plus underestimated) would have been 7.27+2.89=10.16, and the rate of CPI inflation was underestimated by 10.16/7.27=1.4 times.
This is exactly the factor of the federal funds rate above the rate of price inflation.  Hence, the FRB retains the interest rate at the level of actual inflation and thus does not influence inflation. The BEA, BLS and FRB lie (intentionally or not) about the rate of inflation and the growth in real GDP. The current level of GDP per capita in the US should be around $11,000 not $31,000.  

Figure 1. Cumulative values of the monthly estimates of R and the CPI multiplied by a factor of 1.4.
Figure 2. Historical estimates of real GDP per capita.

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