EFFICACY OF THE FEDERAL FUNDS INTEREST RATE
Introduction
The federal funds interest rate is used by the Federal Reserve to attempt to either stimulate the economy or to curb inflation. Generally it is believed that higher interest rates cut inflation but dampen the economy, while lower interest rates do the opposite. The Federal Open Market Committee (FOMC) meets eight times a year to set a target rate, and although the open market determines the effective federal funds interest rate, that effective rate does not vary greatly from the target rate. To quote the Federal Reserve Board itself, “The effective federal funds rate is essentially determined by the market but is influenced by the Federal Reserve through open market operations to reach the federal funds rate target.”[1]
The purpose of this study is to determine if the last 60 years of empirical data support the idea that the effective federal funds interest rate affects the economy in the way it is supposed to. Scatterplots and linear regression are the tools used. Scatterplots give an immediate visual impression of any relationship between two variables and are particularly useful for spotting strong relationships that may be non-linear. Linear regression analysis gives a quantitative measure of how two variables are linearly related, but fails to bring out those that are non-linear.
One fact to keep in mind is that any relationship may be two-way. We know beforehand the economic conditions affect the effective federal funds rate because the FOMC uses that information to decide on the target rate. The question that I am trying to answer in this paper is whether the relationship also goes the other way, and if so, in the manner intended. I used the Origin 2015 software for the calculations
Annual Data
Annual GDP growth rate figures back to 1955 are readily available on the Bureau of Economic Analysis (BEA) website[2]. The website of reference 1 gives effective federal funds interest rates daily, weekly, bi-weekly, monthly, or annually over the same period. Using those annual numbers for the period 1955-2014, I obtain the following scatterplot and linear regression information.
Figure 1
The slope of the regression line is not significantly different from zero, meaning either that the two variables are not really affecting one another, or perhaps that the federal funds rate is accomplishing its thermostat function of keeping GDP growth on an even keel. The coefficient of determination (COD) is only about 0.03%; this number tells how much of the variation in either variable can be attributed to variation in the other. So even if the federal funds interest rate is working as intended on GDP growth, its effect is very small. A low COD value is also shown by the large scatter of empirical points around the regression line.
For inflation I used the annual inflation rate figures from the data tables on the Bureau of Labor Statistics website[3]. Theses tables give inflation rate calculated from the Consumer Price Index for All Urban Consumers (CPI-U): U.S. city average, all items.
The scatterplot is shown in Figure 2, and in this case the slope is significantly different from zero, positive, and the COD is 56.6% (note the much smaller scatter of points from the regression line). The positive slope probably means that we are seeing the effect of inflation on the effective federal funds rate rather than vice-versa. If the federal funds rate works as intended, higher interest rates should bring lower inflation rates.
Figure 2
Thus, neither GDP growth nor inflation shows the desired dependence on the federal funds interest rate. But perhaps annual figures represent too broad a brush to paint the picture we are interested in seeing. All Figure 2 really says is that years with high inflation tend to also have high average effective federal funds rates, not too surprising a result. Let us turn to shorter time intervals.
Quarterly Data
Reference 2 allows the user to view quarterly GDP growth rates. The Federal Reserve site does not have quarterly interest rate values but does have monthly effective federal fund rates over the whole 60 year period. I averaged over the three months of a quarter to get average effective federal funds rates to use with the quarterly GDP growth rates. Then I applied one more device to restrict any causation to one direction only: I paired quarterly GDP growth rates for any quarter with average effective federal funds interest rates in the previous quarter. It is clear that the growth rate in any quarter cannot directly affect the interest rate in a previous quarter, but the latter can affect the former since causation works forward, not backward, in time. With that method I arrived at the scatterplot below.
Figure 3
In this case the slope is negative and significantly different from zero as is appropriate if the federal funds rate is working on the economy as desired: decreases in the interest rate in a quarter are generally followed by better GDP growth in the next quarter. However the COD is only 2%, meaning most (98%) of the changes in quarterly GDP growth must be due to factors other than the federal funds rate.
The inflation rates from reference 3 are not given quarterly either, but there are monthly CPI values. I calculated quarterly inflation rates by finding the percent difference between the ending monthly CPI values in each quarter. That is, I found the inflation rate for any quarter by looking at the difference between month 3 of that quarter and month 3 of the previous quarter. Once again, I paired each inflation value with the average effective federal funds rate from the previous quarter to restrict causation to federal funds rate on inflation.
Figure 4
The slope is positive and significantly greater than zero. The positive slope is in the wrong direction from the way the federal funds rate is supposed to work. We would like an increase in the interest rate in one quarter to be followed by lower inflation in the next, which implies a negative slope for this graph. Furthermore, this linear regression has a COD of 27%. This looks very much like the federal funds interest rate has been doing the opposite of what was intended, with higher interest rates accounting for 27% of the increase in inflation.
Monthly Data
Since we have monthly values for the effective federal funds interest rate and also monthly values for the CPI over the whole 60 year period, we could look at linear regression of monthly inflation rate versus federal funds rate, again pairing federal funds rates with inflation rates one month later. Actually, the regression analysis of quarterly values, given above, is much like looking at inflation 3 months later, so we wouldn’t expect any big changes. Nevertheless it is relatively easy to come up with the monthly inflation analysis below.
Figure 5
Once again the slope is positive and statistically significant and the COD=22%. This result seems to confirm what we learn from the quarterly data.
Conclusions
The empirical data support the hypothesis that lower federal funds interest rates help GDP growth and higher rates impede that growth. However the effect is small, with variations in the federal funds rate accounting for no more than 2% of the variations in GDP growth rates.
The empirical data do not support the hypothesis that higher federal funds interest rates reduce inflation. In fact the data are more consistent with the hypothesis that higher rates exacerbate inflation, possibly accounting for as much as 27% of the variation in quarterly inflation rates.
I should add that the belief that higher interest rates curb inflation is not exclusively a conservative one: it seems that everyone believes it. I certainly believed it until I looked at the numbers. It’s just that I believe the dictum from Richard Feynman more: “It does not make any difference how beautiful your guess is. It does not make any difference how smart you are, who made the guess, or what his name is – if it disagrees with experiment it is wrong. That is all there is to it.”[4] Change the word “experiment” (economists don’t do experiments) to “empirical data” and you have the theme of this whole website.
Gary Waldman
September 2015, revised March 2019
[1] www.federalreserve.gov/releases/h15/data.htm
[2] www.bea.gov. Go to the interactive tables. In Table 1.1.1 modify to get the information desired.
[3] www.bls.gov/cpi/cpid1508.pdf - Table 24
[4] Quoted in C. Tavris & E. Aronson – Mistakes were Made (But Not by Me) – Mariner Books, Houghton Mifflin Harcourt Publishing Co., New York, NY (2007), p. 103
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