How CPI drives the federal funds rate

The interest rate defined by the Federal Reserve is an instrument to control inflation. Ignoring the heaps of quasi-economic lie around the effect of the monetary policy we just present some observations.  Figure 1 depicts the effective rate, R, and the consumer price inflation. The former has to control the latter. One can see that the rate lags behind the CPI since 1980, i.e. inflation grows at its own rate and R has to follow up. The idea of R is that a higher rate should suppress inflation due to the effect expensive money. The reaction of inflation is also expected not momentarily but with some time lag.
The cumulative influence of the interest rate should produce a desired effect in the long run and inflation should go in the direction towards bearable values. Figure 2 displays the cumulative effect, i.e. the cumulative values of the monthly estimates of R and CPI multiplied by 1.4. This is an intriguing plot. In the long run, the R curve fluctuates around the CPI one and returns to it every 15 to 20 years. It seems that the sign of deviation of R from the 1.4CPI curve does not affect the behavior of the CPI. Therefore, the influence of monetary policy is under strong doubt. The Feds have tried all means to return the CPI to R without any success and have to return R to the CPI.  

Figure 1. The federal funds rate, R, and the rate of consumer price inflation, CPI, between 1956 and 2012.

Figure 2. Cumulative values of the monthly estimates of R and CPI multiplied by a factor of 1.4.

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