Federal Reserve Interest Rates, 1954-Present

Synopsis

Why Interest Rates Matter:

Interest rates are at the center of all financial transactions.

They impact the economy by influencing:

  • Stock and Bond Interest Rates
  • Consumer and Business Spending
  • Inflation
  • Recessions
  • Unemployment

The Federal Reserve’s Role:

The Federal Reserve adjusts the federal funds rate, or the interest rate at which banks borrow money. The fed funds rate is generally referred to as an indication to the rise or fall of other interest rates. The Federal Reserve’s goal is to watch for indicators of inflation in order to adjust the fed funds rate to control prices.

In summary, the higher the interest rate, the more expensive it is to borrow money, and the more expensive it is to borrow money, the less money people spend.

The Phillips Curve, seen below, indicates that over time there is a supposed inverse relationship between unemployment rates and the inflation rate. As the relationship between the Federal Funds Rate and unemployment and inflation rates are analyzed, we will attempt to see if the Short Run Phillips Curve (SRPC) is representative of the data collected over the 62-year period.

Source: Investopedia- Interest Rates Affecting Markets

Packages Required

The following packages were used:

  • ReadXL: Used to load in the Dataset which was downloaded as a CSV file
  • Knitr: Used to enhance table display
  • Plyr: Used to rename variables
  • Tidyr: Used to organize dataset
  • GGPlot2: Used to visualize variables into graphs
  • Dplyr: Used to summarize data
  • Tibble: Used to create tibbles containing specific variables and/or time frames
  • DT: Used to create Datatables
  • GGAlt: Used for emphasize data trends through encircling
  • GGCorrPlot: Used for correlogram creation
library(readxl)
library(knitr) 
library(plyr) 
library(tidyr) 
library(ggplot2) 
library(dplyr)
library(tibble)
library(DT) 
library(ggalt)
library(ggcorrplot)

Data Preparation

Data Source: The dataset is composed of statistics provided by the Federal Reserve Bank of St. Louis’ Economic Data Portal, the US Bureau of Economic Analysis, and the US Bureau of Labor Statistics.

The dataset contains 904 observations and 10 variables.

  • Kaggle provided the dataset in the form of an excel file.
#Read Data via Excel File
read_excel("FinalProjectData.xlsx")

#Load and Save Data as a .RMD file
load(file="Final.Data.RData")
save(Full.Data, file="Final.Data.RData")

#Create Dataframe
d<- read_excel("FinalProjectData.xlsx")

#Exploring the Dataset:

#Find Total Number of Observations
nrow(d)

#Find Variable Names
names(d)

#Summarize Dataset Characteristics
summary(d)

What the Dataset Measures: The data analyzes changes in the following variables every month from July of 1954 through March of 2017:

  • Federal Funds Target Rate (including upper and lower target rates), FFTR
  • Effective Federal Funds Rate, FFR or Interest Rate
  • Percentage Change in Real GDP, GDP
  • Unemployment Rate, UR
  • Inflation Rate, IR

Analytic Tools and Processes

Using descriptive, exploratory, causal, and predictive analysis, I’d like to determine the extent to which changes in Federal Fund Rates directly correlate with changes in unemployment, GDP, and inflation. Given the patterns provided in the data, I’d like to notice any seasonality associated with the data points, while accounting for important historical changes within the US economy and the Federal Reserve.

Data Cleansing

#Renaming Variables . . .
d <- plyr::rename(d, c("Effective Federal Funds Rate"="FFR",
            "Federal Funds Target Rate"="FFTR",
            "Federal Funds Upper Target" = "FFUT", 
            "Federal Funds Lower Target"="FFLT", 
            "Real GDP (Percent Change)" = "GDP",
            "Unemployment Rate" ="UR",
            "Inflation Rate"= "IR")) 

#Simplifying Date . . . 
dd <-unite(d, Date, Year, Month, Day, sep="-")
#Organize Date by Year
years <- d %>%
  group_by(Year) %>%
  summarise_all(funs(mean),na.rm=TRUE)

#Eliminate Month and Day Variables from Yearly Data
y <- years[, -c(2:3)]

A few of the time periods I would like to consider in my analysis:

  • The Dot-Com Bubble (DC), 1995 - 2001
DC <- d %>%
unite(Date, Year, Month, Day, sep="-") %>%
filter(Date>="1995-1-1") %>%
filter(Date<"2002-1-1") 
datatable(DC)
  • The “Great Recession” (GR), December 2007 - June 2009
GR <- d %>%
unite(Date, Year, Month, Day, sep="-") %>%
filter(Date>"2007-12-1")%>%
filter(Date<"2009-6-1")
datatable(GR)
  • The Dodd-Frank Wall Street Reform and Consumer Protection Act (DF), Passed: July 2010
DF <- d %>%
unite(Date, Year, Month, Day, sep="-") %>% filter(Date>="2010-1-1") %>%
filter(Date<="2011-1-1")
datatable(DF)

Exploratory Data Analysis

The data were compiled with the intention of addressing the following questions:

  • How does economic growth, unemployment, and inflation impact the Federal Reserve’s interest rates decisions?
  • How has the interest rate policy changed over time?
  • Can you predict the Federal Reserve’s next decision?

Other implications for the information drawn from this data could include the observation of cyclical patterns for unemployment levels and inflation, further emphasizing the impact the Federal Reserve has on day-to-day life.

Interest Rates and Unemployment: * The correlation matrix below highlights the weak relationship between the Federal Funds Rate and Unemployment, regardless of the day of the month or the month in which the data was collected. While the relationship between these two variables is weak, the Federal Funds Rate stimulates a variety of economic factors, including inflation and GDP that ultimately determine the state of the job market, and subsequently, employment.

corr <- round(cor(years),2)
ggcorrplot(corr,
           type="lower",
           lab=TRUE,
           lab_size=5,
           colors=c("seagreen", "lightblue", "blue", "white", "darkblue"),
           title="Fed Funds Rates and Unemployement Rates",
  ggtheme=theme_bw)

  • The Federal Reserve sets target interest rates, or the rates at which banks borrow money from each other, after reviewing current economic data. The Fed gives banks high incentive to meet the target rates by setting the effective interest rate in the loans they provide.

  • The mean target rate over the 62-year period was approximately 5.7%, however, it reached a high of 11% in periods of low economic growth.

qplot(d$FFTR, geom="histogram",
binwidth = .5,
main="Frequency of Effective Federal Funds Target Rates",
xlab="Federal Funds Rate",
ylab="Frequency",
fill=I("blue"),
col=I("darkblue"),
alpha=I(.3))+
  theme_minimal()

  • Although it would be ideal for the Federal Reserve to predict upcoming economic activity, and adjust interest rates accordingly, it is impossible to do so. As a result, the Fed seems to adjust rates in response to changes in consumer habits, which change based on how much money consumers have and how favorable the economy is at any given time.

  • Over the 62-year period, the mean Interest Rate was 4.9% and the median Interest Rate was 4.7%.

qplot(d$FFR, geom="histogram",
binwidth = .5,
main="Frequency of Effective Federal Funds Rates",
xlab="Federal Funds Rate",
ylab="Frequency",
fill=I("darkblue"),
col=I("blue"),
alpha=I(.3)) +
  scale_x_continuous(NULL, limits=c(.1,20))+
  theme_minimal()

  • GDP represents the total dollar value of all goods and services produced over a time period. Annual changes in GDP could reflect adjustments in consumer spending and changes in the state of the economy overall. During the 62-year period, the mean and median annual change in GDP was 3.1% However, in certain years GDP decreased as much as 10%, and increased as much as 16%.
qplot(d$GDP, geom="histogram",
binwidth = .5,
main="Frequency of Change in GDP",
xlab="Change in Gross Domestic Product (GDP)",
ylab="Frequency",
fill=I("darkblue"),
col=I("blue"),
alpha=I(.3))+
  theme_minimal()

  • Inflation is generally regarded as the increase of prices of goods and the decrease in the purchasing power of money. In terms of this analysis, inflation is seen as a response variable to the interest rates set by the Fed.

  • Over the 62-year period, the mean inflation rate was 3.7% and the median, the more appropriate measure for this skewed data, is 2.8%. Inflation rises from a mere 0.6% to 13.6% and tends to decrease over the long-run as unemployment rates increase. The relationship between inflation and interest rates is generally regarded as inverse. When consumers spend more, inflation increases, however, when interest rates rise, consumers spend less and save money for higher returns.

  • Unemployment rates rise when the economy is slow and as a result, spending power for consumers decrease, and the Fed and banks attempt to find ways to get consumers to borrow and spend more money.

  • During the 62-year period, unemployment rates ranged from 3.4% to 10.8%, with the average being 5.9%. The current average US unemployment rate for 2017 is 4.3%. A low unemployment rate is plausible considering how low interest rates have been since the Great Recession.

qplot(d$UR, geom="histogram",
binwidth = .5,
main="Frequency of Unemployment Rates",
xlab="Unemployment Rate",
ylab="Frequency",
fill=I("blue"),
col=I("darkblue"),
alpha=I(.3))+
  theme_minimal()

  • Further analyzing the relationship between the Effective Federal Funds Rate and the Inflation Rate over the 62-year period, there appears to be a positive, linear relationship between the variables. This is because as the cost of borrowing money increases, so do prices for goods and services. However, when the rising prices for goods and services begin to hinder consumer spending, the Fed is likely to step in and lower the Target Federal Funds Rate.
ggplot(dd, aes(FFR, IR))+
  geom_point(color="seagreen")+
  ggtitle("The Federal Reserve's Impact on Inflation",
          subtitle= "The Effective Federal Funds Rate and Inflation Rate 1956-2016")+
    labs(y="Inflation Rate", x="Effective Federal Funds Rate") +
  geom_abline(col="lightgreen", lwd=2)+
  theme_minimal()

  • The relationship between Inflation and the Effective Federal Funds Rate over time shows how closely the two rates mimic each other. Generally speaking, the Effective Federal Funds Rate would spike, and Inflation Rates would shadow shortly after.
y %>%
  ggplot(aes(x=Year)) +
  geom_line(aes(y=IR, size=0),   color="darkgreen", show.legend=FALSE)+
  geom_line(aes(y=FFR, size=0), color="darkblue", show.legend=FALSE) +
  geom_ribbon(aes(ymin=IR ,  ymax=FFR),fill="lightgreen", alpha= .5) +
  scale_x_continuous(NULL, limits=c(1955,2016), breaks =seq(1956,2016, by=5)) +
  ggtitle("The Federal Reserve's Impact on Inflation Rates",
          subtitle= "The Effective Federal Funds Rate and the Inflation Rate from 1956-2016")+
  theme_minimal()+
  theme(panel.grid.minor = element_blank())

  • To further analyze the cyclical nature of unemployment rates, three periods are highlighted in the analysis. The first of which, The Dot Com Bubble, shows a downward trend in unemployment. This is likely due to an increase in technology jobs during the period.
ggplot(y, aes(Year, UR, size='qsec'))+
  geom_line(color="seagreen",  show.legend=FALSE) +
  geom_hline(aes(yintercept = 4.6), linetype= "dashed")+ annotate("text", x=1996.5, y=4.5, label= "Average Unemployment Rate: 4.6%", size=3)+
  scale_x_continuous(NULL,breaks=seq(1995,2000, by=1), limits = c(1995,2000))+
   scale_y_continuous(NULL, limits=c(2,6))+
  theme_minimal()

  • Unemployment during the Great Recession followed a much different pattern than that of the Dot Com Bubble. The average unemployment rate during the Great Recession was 6.9%, however, it reached a maximum of 10%.
ggplot(y, aes(Year, UR, size='qsec'))+
  geom_line(color="seagreen", show.legend=FALSE) +
  geom_hline(aes(yintercept = 6.9), linetype= "dashed")+ annotate("text", x=2006.5, y=7.5, label= "Average Unemployment Rate: 6.9%", size=3)+
  scale_x_continuous(NULL, limits=c(2005,2010))+
   scale_y_continuous(NULL,breaks=seq(0,10, by=1, limits=c(3,10)))+
  labs(title="Unemployment Rates during Great Recession",
       subtitle="Great Recession begins December 2007 and ends July 2009",
       x="Year",
       y="Unemployment Rate")+
  theme_minimal()

  • The Dodd-Frank Act was passed in response to the Great Recession, in an attempt to stabilize the economy. As a result, unemployment rates decreased. However, it took several years before the impact of the Act was evident.
ggplot(y, aes(Year, UR, size='qsec'))+
  geom_line(color="seagreen", show.legend=FALSE) +
  geom_hline(aes(yintercept = 9.6), linetype= "dashed")+ annotate("text", x=2010, y=10.5, label= "Average Unemployment Rate: 9.6%", size=3)+
  scale_x_continuous(NULL, limits=c(2009,2012))+
   scale_y_continuous(NULL,breaks=seq(6,12, by=1, limits=c(7,11)))+
  labs(title="Unemployment Rates during Dodd Frank Reform",
       subtitle="Dodd-Frank Act Passed in July 2010",
       x="Year",
       y="Unemployment Rate")+
  theme_minimal()

  • The Great Recession is the period that best mimics the effects of the Phillips Curve in regard to the correlation between Unemployment Rates and Inflation. The average Effective Fed Funds Rate was 2.35%, though it rose over 5% throughout the period.
ggplot(GR, aes(UR, IR, size='qsec'))+
  geom_line(color="seagreen", show.legend=FALSE) +
  labs(title="Inflation and Unemployment Rates During Great Recession",
       subtitle="Data from 2007-2009",
       y="Inflation Rate",
       x="Unemployment Rate")+
  theme_minimal()

  • The relationships between unemployment rates and inflation during the three periods are highlight below. Of the three periods, The Dot Com Bubble demonstrates the strongest linear relationship between the two variables, however, the results of the comparison demonstrate that the two factors may be driven by outside factors, and not by each other. Instead, this proposes that unemployment and inflation are responses to other changes in the economy, such as changes in interest rates.
ggplot(NULL,aes(UR, IR))+
  geom_point(data=DF, color='lightblue', size=2) +
  geom_point(data=GR, color='blue',size=2) +
  geom_point(data=DC, color='seagreen3', size=2) +
  geom_encircle(aes(x=UR, y=IR),
                data=DC,
                color="red",
                size=2,
                expand=0.03)+
  annotate("text", x=6.75, y=3, label= "Dot Com Bubble", size=3)+
   annotate("text", x=8, y=2, label= "Great Recession", size=3)+
   annotate("text", x=8.5, y=.75, label= "Dodd Frank Act", size=3)+
  theme_minimal()+
  labs(subtitle="Unemployment Vs. Inflation",
       y="Inflation Rate",
       x="Unemployment Rate",
       title="The Fed's Impact on Employement")

  • As indicated earlier, the interest rates you and I encounter are not directly set by the Fed, instead, target interest rates are set, and banks follow suit with setting borrowing guidelines for consumers. The relationship between the Target Federal Funds Rate and the Effective Federal Funds Rate over time is shown below. The darker bars indicate lower target rates, which generally correspond to lower effective interest rates.
ggplot(y, aes(x=Year, y=FFR))+
  geom_bar(stat='identity', aes(fill=FFTR),width=.5)+
  labs(subtitle="Effective Fed Funds Rate from 1955-2017",
       title="Fed Funds and Fed Funds Target Rates")+
  theme_minimal()

  • Now that we have established the relationship between interest rates and inflation, it is natural to wonder how economic value (GDP), is impacted. The data below indicate there is a balance that exists between interest rates, subsequent inflation, and the change in value of the economy. The highest GDP change values correspond to mid-range interest and inflation rates.
ggplot(years, aes(x=IR, y=FFR))+
  geom_point(aes(col=GDP))+
  labs(subtitle="Inflation and the Effective Federal Funds Rate from 1955-2017",
       y="Effective Federal Funds Rate",
       x="Inflation Rate",
       title="The Fed's Impact on Inflation Rates")+
  geom_smooth(method="lm")+
  theme_minimal()

  • The concentration of high GDP volatility near mid-to-low range interest rates further demonstrates a necessary balance between moderate interest rates and GDP change. Gradual economic growth seems to favor mid-range interest rates.
ggplot(dd %>%group_by(FFR)%>%
  summarise('Mean GDP'=mean(GDP)),
aes(FFR, 'Mean GDP')) +
  geom_bar(stat="identity", fill=hcl(195,100,65))+
  theme_minimal()+
  labs(title="GDP Change based on Fed Funds Rate",
       x="Effective Federal Funds Rate",
       subtitle="Data from 1955-2016")

Summary

The Problem: Many factors in the economy depend on interest rates, which are determined by target rates set by the Federal Reserve. It may seem ironic that the central government has so much control over the ever-changing cost of necessities and commodities; including but not limited to, the housing marketing, student loan rates, and gas prices. However, upon analyzing the impact the Federal Reserve’s Target and Effective Rates have on economic inflation, unemployment rates, and change in GDP, it becomes clear that the impact of the federal reserve exists to minimize the negative aspects of our economy, such as high inflation and unemployment.

The Data and Methodology: Over the course of the 62-year time period covered in the data, three specific periods of versatile economic activity were highlighted: The Dot Com Bubble, the Great Recession, and the passing of the Dodd-Frank Act. The data were analyzed over these periods to determine the effectiveness of the Federal Reserve during times of uncertainty in the economy, due to factors that are relatively out of the government’s control.

The data were observed for variable frequency and averages, correlation between variables, and dramatic changes in variable value over time.

Take-Aways:

Although it is not possible for the Federal Reserve to predict economic activity, it can manage drastic changes by setting target rates in response to on-going fluctuations in GDP, inflation, and unemployment. Inflation and unemployment generally follow the Phillips Curve, and inflation decreases as unemployment increases as indicated by the Short Run Phillips Curve. GDP changes in response to inflation and unemployment, which are impacted directly by the effective federal funds rate, set by banks and other lending institutions.

In conclusion, economic volatility is unpredictable. The Federal Reserve raises and lowers interest rates mainly with the focus on correcting consumer spending by changing the cost of borrowing money. There is no concrete solution or method of finding balance in the economy. Rather, the Fed makes slight frequent adjustments to target rates to address negative economic activity. In periods of uncertainty, it appears that no action is sometimes the best action. In recent years, the Fed has developed a stigma for maintaining low interest rates as a result of the Great Recession, however, closer analysis of recent patterns of economic activity show that unemployment and inflation rates have not warranted a drastic raise in interest rates.

Limitations of the Analysis:

The biggest limitation of the analysis comes in the form of missing values, and lack of certainty in some of the variables. While GDP, Inflation, and Unemployment have strong relationships with interest rates, the economy ultimately operates on many factors that exist outside of this analysis.