Introduction
The 73 years from 1951 to 2024 are divided into three types of inflationary behavior:2
An inflation change is significant if it is more than or equal to 4.0% with no intervening counter-trend change that is more than 1.5%. Previously, we defined the partitioning of inflation into the pattern in Table 1.
Table 1. Timeline of Inflation Data for 1951-2024 (Previously Table 2.2)
Previously,1 a data set was found for which one of the variables (the Fed Funds Rate) had no meaningful change while a significant increase occurred in CPI Inflation. A strong correlation was measured between the two variables even though there was no meaningful change in one of them. The correlation was determined by “noise,” i.e., small fluctuations in the unchanged value of one variable. We will examine this in detail.
Data
The data is from previously prepared tables.3 There are 49 monthly timeline alignments. Some notable trends include the following:
The specific data for more detailed examination is for the Fed Funds Rate (FFR) and CPI Inflation from June 2009 to July 2011.1
Analysis – Example of Noise Overwhelming Calculated Correlation
From September 2009 to October 2011, CPI inflation increased from -1.6% to +3.7%, a rise of 5.3%, or by a different calculation, from -2.3% to +5.6%, a rise of 5.7%.3 During these 26 months, the Fed made no change in interest rates. The Fed Funds Rate remained at 0-0.25% the entire time.4 However, there were minor variations within the range. The monthly values ranged from 0.07% to 0.20%. The monthly changes ranged from -0.02% to +0.04%. In Figure 1, the change for each month is the three-month-moving average, and the range is -0.02% to +0.03%.
Figure 1. Fed Funds Rate and Inflation for September 2009-October 2011
Despite the Fed Funds Rate remaining unchanged during the 26 months, there is a strong negative correlation between changes in the FFR and the CPI, as shown in Figure 2.
Figure 2. Monthly Changes in Fed Funds Rate (x) vs. CPI Inflation (y) for September 2009-October 2011
Let us disaggregate the correlation. See Figure 3.
Figure 3. Disaggregation of Fed Funds Rate and Inflation for September 2009-October 2011
Separating the two periods (B and D) where the deviations occurred from the average for FFR over the 26 months defines five periods, A through E. The first period with minor FFR deviations, B, also has a series of CPI readings with negligible change. The second period, D, covers a time when significant changes occurred in CPI.Table 2 shows the disaggregated correlations.
Table 2. Disaggregated Correlations between FFR and CPI Monthly Changes (Three-Month MA) for September 2009-October 2011
This data shows one reason correlation does not necessarily represent cause and effect. Here, we see that correlation varies widely across subsets of the total data set. The strongest correlation occurs in period A. CPI showed a meaningful decline in that interval, but the FFR data only showed noise.Interval D shows a moderate correlation for meaningful changes in CPI, but only noise in the FFR data. And, of course, Figure 2 shows a strong association between FFR and CPI for the entire 26 months when FFR is unchanged except for noise fluctuations the entire time: R = –78% and R2 = 61%.
Effective Noise Limitation
The observations of the spurious results obtained with monthly changes in variables such as FFR and CPI make it imperative to find a way to remove or minimize the effects of data noise from the calculations. Previously (formerly Figure 12), data was smoothed using three-month moving averages for each month. This is shown in Figure 4.
Figure 4. Fed Funds and CPI Monthly Changes (Three-Month Moving Averages) for 1954-2024
But is this the correct smoothing factor?
Figure 5. Data Smoothing Fed Funds Rate Monthly Changes for January 1979-December 1982
In Figure 5, the un-smoothed data has significant noise differences from the three smoothed data options. This suggests that smoothing the data is the correct decision. However, would smoothing more than a three-month moving average lose useful information?The method used to define the inflation surges utilized the monthly year-over-year changes in CPI with three-month moving average data. That result (previously Figure 32) is in Figure 6.
Figure 6. 12-Month CPI Inflation Every Month (Three-Month MA) for 1951-2024
Figure 6 shows some fluctuation, but it mainly does not occur during significant moves in CPI. This indicates that using monthly year-over-year changes to study correlations might reduce the noise problem experienced using the monthly changes themselves.
Conclusion
Next week, we will look more closely at the process of using monthly year-over-year changes to evaluate associations between changes in the Fed Funds Rate and CPI inflation.
Footnotes
More By This Author:Fed Funds Rate and Inflation. Part 2Fed Funds Rate and Inflation. Part 1Where Does US Money Come From And Where Does It Go?
