Loading packages, defining colors and using data

We first clear the workspace using rm(list = ls())and then include all packages we need. If a package is missing in your R distribution (which is quite likely initially), just use install.packages("package_name") with the respective package name to install it on your system. If you execute the code in the file install_packages.R, then all necessary packages will be installed into your R distribution. If the variable export_graphs is set to TRUE, then the graphs will be exported as pdf-files. In addition, we define a set of colors here to make graphs look more beautiful. Furthermore, we define some axis breaks for graphs to look nicer.

# Clear the workspace and load libraries
rm(list = ls())
library(zoo)
library(xts)
library(dynlm)
library(reshape2)
library(base)
library(ggplot2)
library(grid)
library(scales)
library(stringr)
library(tidyverse)
library(fredr)
library(mFilter)
library(formattable)

# should graphs be exported to pdf
export_pdf <- FALSE

# define some colors
mygreen <- "#00BA38"
myblue  <- "#619CFF"
myred   <- "#F8766D"

# define plotting breaks
xbreaks <- c(seq(from = as.Date("1970-01-01"), to = as.Date("2020-01-01"),by = "10 years"))

Quarterly data from the FRED database

Like in the previous document, we again load multiple series from the FRED database at once. This time, we want to compare data from the US with data from Germany.

# Load function to get FRED data
source("chap06_func_get_fred_data.R")

# US recession dates
selection <- data.frame(series = "DEURECDP", names = "RECESSION")

# real time series
selection <- rbind(selection, c("GDPC1", "GDP_US"))
selection <- rbind(selection, c("NAEXKP01DEQ661S", "GDP_DE"))

# additional series
selection <- rbind(selection, c("CE16OV", "EMPL_US"))
selection <- rbind(selection, c("LFEMTTTTDEQ647S", "EMPL_DE"))
selection <- rbind(selection, c("UNRATE", "UNEMP_US"))
selection <- rbind(selection, c("LRUNTTTTDEQ156S", "UNEMP_DE"))
selection <- rbind(selection, c("CPALTT01DEQ659N", "INFL_DE"))
selection <- rbind(selection, c("TB3MS", "NOMRATE_US"))
selection <- rbind(selection, c("IRLTLT01DEQ156N", "NOMRATE_DE"))

# pull all data series from FRED
fred <- get_fred_data(selection$series, selection$names, "1970-01-01", "2022-09-30", "q")
## [1] "Loading series GDPC1"
## [1] "Loading series NAEXKP01DEQ661S"
## [1] "Loading series CE16OV"
## [1] "Loading series LFEMTTTTDEQ647S"
## [1] "Loading series UNRATE"
## [1] "Loading series LRUNTTTTDEQ156S"
## [1] "Loading series CPALTT01DEQ659N"
## [1] "Loading series TB3MS"
## [1] "Loading series IRLTLT01DEQ156N"


Note that the annualized inflation rate for the US (meaning price changes relative to the same quarter in the last year) need to be calculated by hand from the GDP quarterly deflator series. For Germany, this series exists.

# calculate inflation for US
deflator <- fredr(series_id = "GDPDEF",
                  observation_start = as.Date("1969-01-01"),
                  observation_end = as.Date("2022-09-30")
)

fred$INFL_US <- diff(deflator$value, lag = 4)/deflator$value[1:(length(deflator$value)-4)]*100

Create different cyclical plots

We first want to create different cyclical plots. Therefore, we calculate US recession dates. Furthermore, we convert real GDP per capita in the US and in Germany into log values and apply the HP filter to these series in order to decompose them into trend an cycle.

# calculate regression beginnings and ends
fred$REC_DATES <- 0
fred$REC_DATES[2:length(fred$REC_DATES)] <- diff(fred$RECESSION)

# date at beginning and end of recessions
rstart <- fred$date[fred$REC_DATES == 1]
rend   <- fred$date[fred$REC_DATES == -1]
rec_df <- data.frame(rstart, rend)

# calculate log gdp for US
fred$log_gdp_US = log(fred$GDP_US)

gdp_ts <- xts(x = fred$log_gdp_US, order.by = as.Date(fred$date))
res_hpf <- hpfilter(gdp_ts, freq=1600, type="lambda")
fred$c_hpf_US <- res_hpf$cycle

# calculate log gdp for Germany
fred$log_gdp_DE = log(fred$GDP_DE)

gdp_ts <- xts(x = fred$log_gdp_DE, order.by = as.Date(fred$date))
res_hpf <- hpfilter(gdp_ts, freq=1600, type="lambda")
fred$c_hpf_DE <- res_hpf$cycle

Cycle after HP-filtering

This plot shows the cycle of GDP both in the US and in Germany. The gray shaded areas denote officially dates US recessions.

# set minimum and maximum
ymin <- -0.1
ymax <-  0.05
dy   <- (abs(ymin)+abs(ymax))/2

# plot cycle
myplot <- ggplot(data = fred) + 
  geom_rect(data=rec_df, aes(xmin=rstart, xmax=rend, ymin=ymin-0.05*dy, ymax=ymax+0.05*dy), fill='gray', alpha=0.5) + 
  geom_hline(yintercept=0, color="gray", linewidth=0.5) +
  geom_line(aes(x=date, y=c_hpf_US, color="US"), linewidth=0.5) +
  geom_line(aes(x=date, y=c_hpf_DE, color="DE"), linewidth=0.5) +
  scale_x_date(breaks = xbreaks, date_labels = "%Y", expand=c(0, 0)) +
  scale_y_continuous(breaks=seq(ymin, ymax, 0.025), expand=c(0, 0)) +  
  labs(x = "Year t",
       y = "Log of real GDP (cyclical component)") +
  scale_color_manual(breaks = c("US", "DE"),
                     labels = c("US", "Germany"),
                     values = c("darkblue", myred), name='') +
  theme_bw() +
  theme(legend.position="bottom")

# print the plot
print(myplot)

Employment

Here, we plot growth rates of employment both for the US and for Germany.

# calculate employment changes for US
fred$D_EMPL_US <- NA
fred$D_EMPL_US[1:(length(fred$EMPL_US)-1)] <- diff(fred$EMPL_US)/fred$EMPL_US[1:(length(fred$EMPL_US)-1)]*100

# calculate employment changes for Germany
fred$D_EMPL_DE <- NA
fred$D_EMPL_DE[1:(length(fred$EMPL_DE)-1)] <- diff(fred$EMPL_DE)/fred$EMPL_DE[1:(length(fred$EMPL_DE)-1)]*100

# set minimum and maximum
ymin <- -14
ymax <- 8
dy   <- (abs(ymin)+abs(ymax))/2

# plot cycle
myplot <- ggplot(data = fred) + 
  geom_rect(data=rec_df, aes(xmin=rstart, xmax=rend, ymin=ymin-0.05*dy, ymax=ymax+0.05*dy), fill='gray', alpha=0.5) + 
  geom_hline(yintercept=0, color="gray", linewidth=0.5) +
  geom_line(aes(x=date, y=D_EMPL_US, color="US"), linewidth=0.5) +
  geom_line(aes(x=date, y=D_EMPL_DE, color="DE"), linewidth=0.5) +
  scale_x_date(breaks = xbreaks, date_labels = "%Y", expand=c(0, 0)) +
  scale_y_continuous(breaks=seq(ymin, ymax, 2), expand=c(0, 0)) +  
  labs(x = "Year t",
       y = "Employment Change (in %)") +
  scale_color_manual(breaks = c("US", "DE"),
                     labels = c("US", "Germany"),
                     values = c("darkblue", myred), name='') +
  theme_bw() +
  theme(legend.position="bottom")

# print the plot
print(myplot)

Unemployment

This graph shows unemployment rates for both the US and Germany.

# set minimum and maximum
ymin <- 0
ymax <- 15
dy   <- (abs(ymin)+abs(ymax))/2

# plot cycle
myplot <- ggplot(data = fred) + 
  geom_rect(data=rec_df, aes(xmin=rstart, xmax=rend, ymin=ymin-0.05*dy, ymax=ymax+0.05*dy), fill='gray', alpha=0.5) + 
  geom_hline(yintercept=0, color="gray", linewidth=0.5) +
  geom_line(aes(x=date, y=UNEMP_US, color="US"), linewidth=0.5) +
  geom_line(aes(x=date, y=UNEMP_DE, color="DE"), linewidth=0.5) +
  scale_x_date(breaks = xbreaks, date_labels = "%Y", expand=c(0, 0)) +
  scale_y_continuous(breaks=seq(ymin, ymax, 2.5), expand=c(0, 0)) +  
  labs(x = "Year t",
       y = "Unemployment Rate (quarterly, in %)") +
  scale_color_manual(breaks = c("US", "DE"),
                     labels = c("US", "Germany"),
                     values = c("darkblue", myred), name='') +
  theme_bw() +
  theme(legend.position="bottom")

# print the plot
print(myplot)

Inflation

Here we see the inflation rates in the two countries.

# set minimum and maximum
ymin <- -2
ymax <- 12
dy   <- (abs(ymin)+abs(ymax))/2

# plot cycle
myplot <- ggplot(data = fred) + 
  geom_rect(data=rec_df, aes(xmin=rstart, xmax=rend, ymin=ymin-0.05*dy, ymax=ymax+0.05*dy), fill='gray', alpha=0.5) + 
  geom_hline(yintercept=0, color="gray", linewidth=0.5) +
  geom_line(aes(x=date, y=INFL_US, color="US"), linewidth=0.5) +
  geom_line(aes(x=date, y=INFL_DE, color="DE"), linewidth=0.5) +
  scale_x_date(breaks = xbreaks, date_labels = "%Y", expand=c(0, 0)) +
  scale_y_continuous(breaks=seq(ymin, ymax, 2), expand=c(0, 0)) +  
  labs(x = "Year t",
       y = "Inflation Relative to Previous Year (in %)") +
  scale_color_manual(breaks = c("US", "DE"),
                     labels = c("US", "Germany"),
                     values = c("darkblue", myred), name='') +
  theme_bw() +
  theme(legend.position="bottom")

# print the plot
print(myplot)

Nominal interest rate on 3-month interbank market

And finally nominal interest rates on the 3-month interbank market.

# set minimum and maximum
ymin <- 0
ymax <- 16
dy   <- (abs(ymin)+abs(ymax))/2

# plot cycle
myplot <- ggplot(data = fred) + 
  geom_rect(data=rec_df, aes(xmin=rstart, xmax=rend, ymin=ymin-0.05*dy, ymax=ymax+0.05*dy), fill='gray', alpha=0.5) + 
  geom_hline(yintercept=0, color="gray", linewidth=0.5) +
  geom_line(aes(x=date, y=NOMRATE_US, color="US"), linewidth=0.5) +
  geom_line(aes(x=date, y=NOMRATE_DE, color="DE"), linewidth=0.5) +
  scale_x_date(breaks = xbreaks, date_labels = "%Y", expand=c(0, 0)) +
  scale_y_continuous(breaks=seq(ymin, ymax, 2), expand=c(0, 0)) +  
  labs(x = "Year t",
       y = "3-month nominal rate (in %)") +
  scale_color_manual(breaks = c("US", "DE"),
                     labels = c("US", "Germany"),
                     values = c("darkblue", myred), name='') +
  theme_bw() +
  theme(legend.position="bottom")

# print the plot
print(myplot)