~/data/gfd/

Info

source	dataset	Title	Download	Compile
eurostat	phillips	Phillips curves	NA	2023-04-10
eurostat	tipsna62	Employees, domestic concept - annual data	2023-04-01	2023-03-26
fred	phillips	Phillips curves	2023-03-23	2023-04-10
gfd	phillips	Phillips curves	NA	2021-08-22
ilo	phillips	Phillips curves	NA	2023-04-10
oecd	phillips	Phillips curves	NA	2023-04-10
wdi	phillips	Phillips curves	NA	2022-11-18

LAST_DOWNLOAD

dataset	LAST_DOWNLOAD
cpi	2021-01-09
unr	2021-03-16

Germany

Without 1922, 1923

data_DEU <- cpi %>%
  bind_rows(unr) %>%
  filter(iso3c %in% c("DEU"),
         month(date) == 12,
         variable %in% c("CPM", "UNM")) %>%
  select(variable, date, value) %>%
  spread(variable, value) %>%
  na.omit %>%
  mutate(UNM = UNM / 100,
         CPM = log(CPM),
         CPM = (CPM - lag(CPM, 1))) %>%
  filter(date != as.Date("1923-12-31"),
         date != as.Date("1922-12-31"))

data_DEU %>%
  gather(variable, value, -date) %>%
  left_join(variable, by = "variable") %>%
  ggplot(.) + 
  geom_line(aes(x = date, y = value, color = Variable, linetype = Variable)) + 
  theme_minimal() + xlab("") + ylab("Unemployment, Inflation") +
  scale_x_date(breaks = seq(1700, 2020, 20) %>% paste0("-01-01") %>% as.Date,
               labels = date_format("%Y")) +
  scale_y_continuous(breaks = 0.01*seq(-50, 100, 5),
                     labels = percent_format(accuracy = 1, prefix = "")) +
  scale_color_manual(values = viridis(5)[1:4]) +
  theme(legend.position = c(0.7, 0.80),
        legend.title = element_blank())

Germany (post 1960)

data_DEU %>%
  filter(date >= as.Date("1954-01-01")) %>%
  gather(variable, value, -date) %>%
  left_join(variable, by = "variable") %>%
  ggplot(.) + 
  geom_line(aes(x = date, y = value, color = Variable, linetype = Variable)) + 
  theme_minimal() + xlab("") + ylab("Unemployment, Inflation") +
  scale_x_date(breaks = seq(1700, 2020, 5) %>% paste0("-01-01") %>% as.Date,
               labels = date_format("%y")) +
  scale_y_continuous(breaks = 0.01*seq(-50, 100, 1),
                     labels = percent_format(accuracy = 1, prefix = "")) +
  scale_color_manual(values = viridis(5)[1:4]) +
  theme(legend.position = c(0.2, 0.9),
        legend.title = element_blank())

if (knitr::is_html_output()) type <- "html" else type <- "latex"
DEU_post_1971 <- data_DEU %>%
  filter(date >= as.Date("1971-01-01")) %>%
  lm(CPM ~ UNM, data = .)

DEU_pre_1971 <- data_DEU %>%
  filter(date <= as.Date("1971-01-01")) %>%
  lm(CPM ~ UNM, data = .)

DEU_pre_1914 <- data_DEU %>%
  filter(date <= as.Date("1914-01-01")) %>%
  lm(CPM ~ UNM, data = .)

stargazer(DEU_post_1971, DEU_pre_1971, DEU_pre_1914,
          header = F,
          df = F,
          title = "\\textsc{Phillips Curve}",
          column.labels = c("Post 1971", "Pre 1971", "Pre 1920"),
          dep.var.labels = "Inflation",
          covariate.labels = "Unemployment",
          intercept.bottom = F,
          omit.stat = c("f", "ser", "rsq"),
          omit = "Constant",
          style = "qje",
          notes = "Data",
          notes.append = F,
          notes.align = "l",
          notes.label = "Note:",
          type = type)

**Phillips Curve**

	Inflation
	Post 1971	Pre 1971	Pre 1920
	(1)	(2)	(3)

Unemployment	-0.345^***	-0.433^*	-0.587
	(0.106)	(0.218)	(0.429)

N	45	73	26
Adjusted R²	0.178	0.039	0.034

Note:	Data

Switzerland

Scatter

1980-2005

bind_rows(unr, cpi) %>%
  filter(iso3c == "CHE",
         variable %in% c("UNM", "CPM")) %>%
  select(variable, date, value) %>%
  spread(variable, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(year = year(date) + 1,
         inflation = 100*(CPM/lag(CPM, 1)-1)) %>%
  filter(year >= 1980,
         year <= 2005) %>%
  ggplot(.) + theme_minimal() + 
  geom_point(aes(x = UNM/100, y = inflation/100)) +
  xlab("Unemployment Rate") + ylab("Inflation") +
  scale_x_continuous(breaks = 0.01*seq(-10, 30, 1),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_y_continuous(breaks = 0.01*seq(-20, 20, 1),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_color_viridis_d(option="C", name = "Period", begin = 0.15, end = 0.85)+
  stat_smooth(aes(x = UNM/100, y = inflation/100), linetype=2, method="lm") + 
  theme(legend.title = element_blank(),
        legend.position = c(0.2, 0.9))

1970-2020

bind_rows(unr, cpi) %>%
  filter(iso3c == "CHE",
         variable %in% c("UNM", "CPM")) %>%
  select(variable, date, value) %>%
  spread(variable, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(year = year(date) + 1,
         inflation = 100*(CPM/lag(CPM, 1)-1)) %>%
  filter(year >= 1970,
         year <= 2020) %>%
  ggplot(.) + theme_minimal() + 
  geom_point(aes(x = UNM/100, y = inflation/100)) +
  xlab("Unemployment Rate") + ylab("Inflation") +
  scale_x_continuous(breaks = 0.01*seq(-10, 30, 1),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_y_continuous(breaks = 0.01*seq(-20, 40, 2),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_color_viridis_d(option="C", name = "Period", begin = 0.15, end = 0.85)+
  stat_smooth(aes(x = UNM/100, y = inflation/100), linetype=2, method="lm") + 
  theme(legend.title = element_blank(),
        legend.position = c(0.2, 0.9))

Time Series

1970-2020

bind_rows(unr, cpi) %>%
  filter(iso3c == "CHE",
         variable %in% c("UNM", "CPM")) %>%
  select(variable, date, value) %>%
  spread(variable, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(year = year(date) + 1,
         CPM = 100*(CPM/lag(CPM, 1)-1)) %>%
  filter(year >= 1970,
         year <= 2005) %>%
  gather(variable, value, -date, -year) %>%
  mutate(Variable = ifelse(variable == "UNM", "Unemployment Rate", 
                                 "CPI Inflation")) %>%
  ggplot(.) + geom_line(aes(x = date, y = value/100, linetype = Variable)) +
  theme_minimal() + ylab("") + xlab("") +
  scale_x_date(breaks = as.Date(paste0(seq(1960, 2020, 10), "-01-01")),
               labels = date_format("%Y")) + 
  scale_y_continuous(breaks = 0.01*seq(-50, 50, 2),
                     labels = scales::percent_format(accuracy = 1)) +
  theme(legend.position = c(0.8, 0.8),
        legend.title = element_blank())

1980-2020

bind_rows(unr, cpi) %>%
  filter(iso3c == "CHE",
         variable %in% c("UNM", "CPM")) %>%
  select(variable, date, value) %>%
  spread(variable, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(year = year(date) + 1,
         CPM = 100*(CPM/lag(CPM, 1)-1)) %>%
  filter(year >= 1980) %>%
  gather(variable, value, -date, -year) %>%
  mutate(Variable = ifelse(variable == "UNM", "Unemployment Rate", 
                                 "CPI Inflation")) %>%
  ggplot(.) + geom_line(aes(x = date, y = value/100, linetype = Variable)) +
  theme_minimal() + ylab("") + xlab("") +
  scale_x_date(breaks = as.Date(paste0(seq(1960, 2020, 10), "-01-01")),
               labels = date_format("%Y")) + 
  scale_y_continuous(breaks = 0.01*seq(-50, 50, 2),
                     labels = scales::percent_format(accuracy = 1)) +
  theme(legend.position = c(0.8, 0.8),
        legend.title = element_blank())

Japan

Scatter

1980-2005

bind_rows(unr, cpi) %>%
  filter(iso3c == "JPN",
         variable %in% c("UNM", "CPM")) %>%
  select(variable, date, value) %>%
  spread(variable, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(year = year(date) + 1,
         inflation = 100*(CPM/lag(CPM, 1)-1)) %>%
  filter(year >= 1980,
         year <= 2005) %>%
  ggplot(.) + theme_minimal() + 
  geom_point(aes(x = UNM/100, y = inflation/100)) +
  xlab("Unemployment Rate") + ylab("Inflation") +
  scale_x_continuous(breaks = 0.01*seq(-10, 30, 1),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_y_continuous(breaks = 0.01*seq(-20, 20, 1),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_color_viridis_d(option="C", name = "Period", begin = 0.15, end = 0.85)+
  stat_smooth(aes(x = UNM/100, y = inflation/100), linetype=2, method="lm") + 
  theme(legend.title = element_blank(),
        legend.position = c(0.2, 0.9))

1970-2020

bind_rows(unr, cpi) %>%
  filter(iso3c == "JPN",
         variable %in% c("UNM", "CPM")) %>%
  select(variable, date, value) %>%
  spread(variable, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(year = year(date) + 1,
         inflation = 100*(CPM/lag(CPM, 1)-1)) %>%
  filter(year >= 1970,
         year <= 2020) %>%
  ggplot(.) + theme_minimal() + 
  geom_point(aes(x = UNM/100, y = inflation/100)) +
  xlab("Unemployment Rate") + ylab("Inflation") +
  scale_x_continuous(breaks = 0.01*seq(-10, 30, 1),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_y_continuous(breaks = 0.01*seq(-20, 40, 2),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_color_viridis_d(option="C", name = "Period", begin = 0.15, end = 0.85)+
  stat_smooth(aes(x = UNM/100, y = inflation/100), linetype=2, method="lm") + 
  theme(legend.title = element_blank(),
        legend.position = c(0.2, 0.9))

Time Series

1970-2020

bind_rows(unr, cpi) %>%
  filter(iso3c == "JPN",
         variable %in% c("UNM", "CPM")) %>%
  select(variable, date, value) %>%
  spread(variable, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(year = year(date) + 1,
         CPM = 100*(CPM/lag(CPM, 1)-1)) %>%
  filter(year >= 1970,
         year <= 2005) %>%
  gather(variable, value, -date, -year) %>%
  mutate(Variable = ifelse(variable == "UNM", "Unemployment Rate", 
                                 "CPI Inflation")) %>%
  ggplot(.) + geom_line(aes(x = date, y = value/100, linetype = Variable)) +
  theme_minimal() + ylab("") + xlab("") +
  scale_x_date(breaks = as.Date(paste0(seq(1960, 2020, 10), "-01-01")),
               labels = date_format("%Y")) + 
  scale_y_continuous(breaks = 0.01*seq(-50, 50, 2),
                     labels = scales::percent_format(accuracy = 1)) +
  theme(legend.position = c(0.8, 0.8),
        legend.title = element_blank())

1980-2020

bind_rows(unr, cpi) %>%
  filter(iso3c == "JPN",
         variable %in% c("UNM", "CPM")) %>%
  select(variable, date, value) %>%
  spread(variable, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(year = year(date) + 1,
         CPM = 100*(CPM/lag(CPM, 1)-1)) %>%
  filter(year >= 1980) %>%
  gather(variable, value, -date, -year) %>%
  mutate(Variable = ifelse(variable == "UNM", "Unemployment Rate", 
                                 "CPI Inflation")) %>%
  ggplot(.) + geom_line(aes(x = date, y = value/100, linetype = Variable)) +
  theme_minimal() + ylab("") + xlab("") +
  scale_x_date(breaks = as.Date(paste0(seq(1960, 2020, 10), "-01-01")),
               labels = date_format("%Y")) + 
  scale_y_continuous(breaks = 0.01*seq(-50, 50, 2),
                     labels = scales::percent_format(accuracy = 1)) +
  theme(legend.position = c(0.8, 0.8),
        legend.title = element_blank())

U.K.

Scatter

1867-1914

bind_rows(unr, cpi) %>%
  filter(Ticker %in% c("UNGBRM", "CPGBRM")) %>%
  select(Ticker, date, value) %>%
  spread(Ticker, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(year = year(date) + 1,
         inflation = 100*(CPGBRM/lag(CPGBRM, 1)-1)) %>%
  filter(year >= 1867,
         year <= 1914) %>%
  ggplot(.) + theme_minimal() + 
  geom_point(aes(x = UNGBRM/100, y = inflation/100)) +
  xlab("Unemployment Rate") + ylab("Inflation") +
  scale_x_continuous(breaks = 0.01*seq(-10, 30, 2),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_y_continuous(breaks = 0.01*seq(-20, 20, 1),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_color_viridis_d(option="C", name = "Period", begin = 0.15, end = 0.85)+
  stat_smooth(aes(x = UNGBRM/100, y = inflation/100), linetype=2, method="lm") + 
  theme(legend.title = element_blank(),
        legend.position = c(0.2, 0.9))

1914-1945

bind_rows(unr, cpi) %>%
  filter(Ticker %in% c("UNGBRM", "CPGBRM")) %>%
  select(Ticker, date, value) %>%
  spread(Ticker, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(year = year(date) + 1,
         inflation = 100*(CPGBRM/lag(CPGBRM, 1)-1)) %>%
  filter(year >= 1914,
         year <= 1945) %>%
  ggplot(.) + theme_minimal() + 
  geom_point(aes(x = UNGBRM/100, y = inflation/100)) +
  xlab("Unemployment Rate") + ylab("Inflation") +
  scale_x_continuous(breaks = 0.01*seq(-10, 30, 2),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_y_continuous(breaks = 0.01*seq(-30, 40, 5),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_color_viridis_d(option="C", name = "Period", begin = 0.15, end = 0.85)+
  stat_smooth(aes(x = UNGBRM/100, y = inflation/100), linetype=2, method="lm") + 
  theme(legend.title = element_blank(),
        legend.position = c(0.2, 0.9))

1970-2000

bind_rows(unr, cpi) %>%
  filter(Ticker %in% c("UNGBRM", "CPGBRM")) %>%
  select(Ticker, date, value) %>%
  spread(Ticker, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(year = year(date) + 1,
         inflation = 100*(CPGBRM/lag(CPGBRM, 1)-1)) %>%
  filter(year >= 1970,
         year <= 2000) %>%
  ggplot(.) + theme_minimal() + 
  geom_point(aes(x = UNGBRM/100, y = inflation/100)) +
  xlab("Unemployment Rate") + ylab("Inflation") +
  scale_x_continuous(breaks = 0.01*seq(-10, 30, 1),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_y_continuous(breaks = 0.01*seq(-30, 40, 1),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_color_viridis_d(option="C", name = "Period", begin = 0.15, end = 0.85)+
  stat_smooth(aes(x = UNGBRM/100, y = inflation/100), linetype=2, method="lm") + 
  theme(legend.title = element_blank(),
        legend.position = c(0.2, 0.9))

2000-2020

bind_rows(unr, cpi) %>%
  filter(Ticker %in% c("UNGBRM", "CPGBRM")) %>%
  select(Ticker, date, value) %>%
  spread(Ticker, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(year = year(date) + 1,
         inflation = 100*(CPGBRM/lag(CPGBRM, 1)-1)) %>%
  filter(year >= 2000) %>%
  ggplot(.) + theme_minimal() + 
  geom_point(aes(x = UNGBRM/100, y = inflation/100)) +
  xlab("Unemployment Rate") + ylab("Inflation") +
  scale_x_continuous(breaks = 0.01*seq(-10, 30, 1),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_y_continuous(breaks = 0.01*seq(-30, 40, 1),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_color_viridis_d(option="C", name = "Period", begin = 0.15, end = 0.85)+
  stat_smooth(aes(x = UNGBRM/100, y = inflation/100), linetype=2, method="lm") + 
  theme(legend.title = element_blank(),
        legend.position = c(0.2, 0.9))

1947-2020

bind_rows(unr, cpi) %>%
  filter(Ticker %in% c("UNGBRM", "CPGBRM")) %>%
  select(Ticker, date, value) %>%
  spread(Ticker, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(year = year(date) + 1,
         inflation = 100*(CPGBRM/lag(CPGBRM, 1)-1)) %>%
  filter(year >= 1867) %>%
  mutate(period = case_when(date <= as.Date("1914-01-01") ~ "1867-1914 (Gold Standard)",
                            date <= as.Date("1967-08-15") ~ "1914-1967 (Intra Year)",
                            T ~ "1967-2020 (Flexible Exchange Rates)")) %>%
  ggplot(.) + theme_minimal() + 
  geom_point(aes(x = UNGBRM/100, y = inflation/100, color = period)) + 
  xlab("Unemployment Rate") + ylab("Inflation") +
  scale_x_continuous(breaks = 0.01*seq(-10, 10, 1),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_y_continuous(breaks = 0.01*seq(-20, 40, 5),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_color_viridis_d(option="C", name = "Period", begin = 0.15, end = 0.85)+
  stat_smooth(aes(x = UNGBRM/100, y = inflation/100, color = period), linetype=2, method="lm") + 
  theme(legend.title = element_blank(),
        legend.position = c(0.2, 0.9))

Time Series

1800-1900

cpi %>%
  filter(iso3c == "GBR") %>%
  select(date, variable = Ticker, value) %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(value = log(value) - lag(log(value), 1)) %>%
  bind_rows(unr %>%
              filter(iso3c == "GBR") %>%
              select(date, variable = Ticker, value) %>%
              filter(month(date) == 12, day(date) == 31) %>%
              mutate(value = value / 100)) %>%
  mutate(variable_label = ifelse(variable == "UNGBRM", "Unemployment Rate", 
                                 "CPI Inflation")) %>%
  ggplot(aes(x = date, y = value, linetype = variable_label), data = .) + geom_line() + theme_minimal() + 
  scale_x_date(breaks = as.Date(paste0(seq(1800, 2025, 10), "-01-01")),
               labels = date_format("%Y"),
               limits = as.Date(paste0(c(1800, 1900), "-01-01"))) + 
  scale_y_continuous(breaks = 0.01*seq(-50, 50, 5),
                     labels = scales::percent_format(accuracy = 1)) +
  theme(legend.position = c(0.5, 0.15),
        legend.title = element_blank()) + 
  ylab("") + xlab("")

1900-1970

cpi %>%
  filter(iso3c == "GBR") %>%
  select(date, variable = Ticker, value) %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(value = log(value) - lag(log(value), 1)) %>%
  bind_rows(unr %>%
              filter(iso3c == "GBR") %>%
              select(date, variable = Ticker, value) %>%
              filter(month(date) == 12, day(date) == 31) %>%
              mutate(value = value / 100)) %>%
  mutate(variable_label = ifelse(variable == "UNGBRM", "Unemployment Rate", 
                                 "CPI Inflation")) %>%
  ggplot(aes(x = date, y = value, linetype = variable_label), data = .) + geom_line() + theme_minimal() + 
  scale_x_date(breaks = as.Date(paste0(seq(1900, 1970, 10), "-01-01")),
               labels = date_format("%Y"),
               limits = as.Date(paste0(c(1900, 1970), "-01-01"))) + 
  scale_y_continuous(breaks = 0.01*seq(-50, 50, 5),
                     labels = scales::percent_format(accuracy = 1)) +
  theme(legend.position = c(0.5, 0.15),
        legend.title = element_blank()) + 
  ylab("") + xlab("")

1960-2020

bind_rows(unr, cpi) %>%
  filter(Ticker %in% c("UNGBRM", "CPGBRM")) %>%
  select(Ticker, date, value) %>%
  spread(Ticker, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(year = year(date) + 1,
         CPGBRM = 100*(CPGBRM/lag(CPGBRM, 1)-1)) %>%
  gather(variable, value, -date, -year) %>%
  mutate(Variable = ifelse(variable == "UNGBRM", "Unemployment Rate", 
                                 "CPI Inflation")) %>%
  filter(year >= 1960) %>%
  ggplot(aes(x = date, y = value/100, linetype = Variable), data = .) + geom_line() + theme_minimal() + 
  scale_x_date(breaks = as.Date(paste0(seq(1960, 2020, 10), "-01-01")),
               labels = date_format("%Y"),
               limits = as.Date(paste0(c(1960, 2020), "-01-01"))) + 
  scale_y_continuous(breaks = 0.01*seq(-50, 50, 5),
                     labels = scales::percent_format(accuracy = 1)) +
  theme(legend.position = c(0.8, 0.8),
        legend.title = element_blank()) + 
  ylab("") + xlab("")

U.S.

Rolling Regressions

Non-accelerationist PC

data_US_price <- bind_rows(unr, cpi) %>%
  filter(Ticker %in% c("UNUSAM", "CPUSAM")) %>%
  mutate(year = year(date) + 1,
         value = value / 100) %>%
  filter(month(date) == 12) %>%
  mutate(date = date + 1) %>%
  select(Ticker, date, value) %>%
  spread(Ticker, value) %>%
  mutate(CPUSAM_log = log(CPUSAM),
         inflation = CPUSAM_log - lag(CPUSAM_log),
         inflation_lag = lag(inflation, 1)) %>%
  select(date, UNUSAM, inflation, inflation_lag) %>%
  na.omit

rolling_lm <- rollify(.f = function(inflation, UNUSAM){
  lm(inflation ~ UNUSAM)
  }, window = 20, unlist = FALSE)

data_US_price %>%
  mutate(roll_lm = rolling_lm(inflation, UNUSAM)) %>%
  filter(!is.na(roll_lm)) %>%
  mutate(tidied = purrr::map(roll_lm, broom::tidy, conf.int = TRUE)) %>%
  unnest(tidied) %>%
  select(date, term, estimate, std.error, statistic, p.value, conf.low, conf.high) %>%
  filter(term != "(Intercept)") %>%
  ggplot(data = ., aes(x = date, y = estimate)) +
  geom_ribbon(aes(ymin = conf.low, ymax = conf.high), alpha = 0.25)+
  geom_line(color = "black") + 
  geom_hline(yintercept = 0, linetype = "dashed", color = "red") +
  scale_x_date(breaks = seq(1760, 2025, 20) %>% paste0("-01-01") %>% as.Date,
               labels = date_format("%Y")) +
  scale_y_continuous(breaks = seq(-10, 10, 1)) +
  theme_minimal() + labs(x = "", y = "Slope of the Phillips Curve")

Figure 1: Slope of the U.S. Phillips Curve

Accelerationist PC

rolling_lm <- rollify(.f = function(inflation, UNUSAM, inflation_lag){
  lm(inflation ~ UNUSAM + inflation_lag)
  }, window = 10, unlist = FALSE)

data_US_price %>%
  mutate(roll_lm = rolling_lm(inflation, UNUSAM, inflation_lag)) %>%
  filter(!is.na(roll_lm)) %>%
  mutate(tidied = purrr::map(roll_lm, broom::tidy, conf.int = TRUE)) %>%
  unnest(tidied) %>%
  select(date, term, estimate, std.error, statistic, p.value, conf.low, conf.high) %>%
  filter(term != "(Intercept)") %>%
  mutate(termf = case_when(term == "inflation_lag" ~ "Persistence of Inflation",
                           term == "UNUSAM" ~ "Slope of the Phillips Curve")) %>%
  ggplot(data = ., aes(x = date, y = estimate)) +
  geom_ribbon(aes(ymin = conf.low, ymax = conf.high), alpha = 0.25)+
  geom_line(color = "black") + 
  facet_wrap(~termf, nrow = 2) +
  geom_hline(yintercept = 0, linetype = "dashed", color = "red") +
  scale_x_date(breaks = seq(1760, 2025, 20) %>% paste0("-01-01") %>% as.Date,
               labels = date_format("%Y")) +
  scale_y_continuous(breaks = seq(-10, 10, 1)) +
  theme_minimal() + labs(x = "", y = "")

Figure 2: Slope of the U.S. Phillips Curve

1890-1945

bind_rows(unr, cpi) %>%
  filter(Ticker %in% c("UNUSAM", "CPUSAM")) %>%
  select(Ticker, date, value) %>%
  spread(Ticker, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(year = year(date) + 1,
         inflation = 100*(CPUSAM/lag(CPUSAM, 1)-1)) %>%
  filter(year <= 1945) %>%
  mutate(period = case_when(date <= as.Date("1971-08-15") ~ "1947-1971 (Bretton Woods)",
                            TRUE ~ "1971-2020 (Flexible Exchange Rates)")) %>%
  ggplot(.) + theme_minimal() + 
  geom_point(aes(x = UNUSAM/100, y = inflation/100)) + 
  xlab("Unemployment Rate") + ylab("Inflation") +
  scale_x_continuous(breaks = 0.01*seq(-10, 10, 1),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_y_continuous(breaks = 0.01*seq(-20, 20, 1),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_color_viridis_d(option="C", name = "Period", begin = 0.15, end = 0.85)+
  stat_smooth(aes(x = UNUSAM/100, y = inflation/100, color = period), linetype=2, method="lm") + 
  theme(legend.title = element_blank(),
        legend.position = c(0.2, 0.9))

1890-2020

Ci

bind_rows(unr, cpi) %>%
  filter(Ticker %in% c("UNUSAM", "CPUSAM")) %>%
  select(Ticker, date, value) %>%
  spread(Ticker, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(year = year(date) + 1,
         inflation = 100*(CPUSAM/lag(CPUSAM, 1)-1)) %>%
  mutate(period = case_when(date <= as.Date("1945-12-01") ~ "1890-1945 (Gold Standard)",
                            date <= as.Date("1971-08-15") ~ "1945-1971 (Bretton Woods)",
                            TRUE ~ "1971-2020 (Flexible Exchange Rates)")) %>%
  ggplot(.) + theme_minimal() + 
  geom_point(aes(x = UNUSAM/100, y = inflation/100, color = period)) + 
  xlab("Unemployment Rate") + ylab("Inflation") +
  scale_x_continuous(breaks = 0.01*seq(-10, 30, 2),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_y_continuous(breaks = 0.01*seq(-20, 20, 2),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_color_viridis_d(option="C", name = "Period", begin = 0.15, end = 0.85)+
  stat_smooth(aes(x = UNUSAM/100, y = inflation/100, color = period), linetype=2, method="lm") + 
  theme(legend.title = element_blank(),
        legend.position = c(0.7, 0.9))

Fill = NA

bind_rows(unr, cpi) %>%
  filter(Ticker %in% c("UNUSAM", "CPUSAM")) %>%
  select(Ticker, date, value) %>%
  spread(Ticker, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(year = year(date) + 1,
         inflation = 100*(CPUSAM/lag(CPUSAM, 1)-1)) %>%
  mutate(period = case_when(date <= as.Date("1945-12-01") ~ "1890-1945 (Gold Standard)",
                            date <= as.Date("1971-08-15") ~ "1945-1971 (Bretton Woods)",
                            TRUE ~ "1971-2020 (Flexible Exchange Rates)")) %>%
  ggplot(.) + theme_minimal() + 
  geom_point(aes(x = UNUSAM/100, y = inflation/100, color = period)) + 
  xlab("Unemployment Rate") + ylab("Inflation") +
  scale_x_continuous(breaks = 0.01*seq(-10, 30, 2),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_y_continuous(breaks = 0.01*seq(-20, 20, 2),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_color_viridis_d(option="C", name = "Period", begin = 0.15, end = 0.85)+
  stat_smooth(aes(x = UNUSAM/100, y = inflation/100, color = period), linetype=2, method="lm", fill = NA) + 
  theme(legend.title = element_blank(),
        legend.position = c(0.7, 0.9))

1947-2020

bind_rows(unr, cpi) %>%
  filter(Ticker %in% c("UNUSAM", "CPUSAM")) %>%
  select(Ticker, date, value) %>%
  spread(Ticker, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(year = year(date) + 1,
         inflation = 100*(CPUSAM/lag(CPUSAM, 1)-1)) %>%
  filter(year >= 1947) %>%
  mutate(period = case_when(date <= as.Date("1971-08-15") ~ "1947-1971 (Bretton Woods)",
                            TRUE ~ "1971-2020 (Flexible Exchange Rates)")) %>%
  ggplot(.) + theme_minimal() + 
  geom_point(aes(x = UNUSAM/100, y = inflation/100, color = period)) + 
  xlab("Unemployment Rate") + ylab("Inflation") +
  scale_x_continuous(breaks = 0.01*seq(-10, 10, 1),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_y_continuous(breaks = 0.01*seq(-20, 20, 1),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_color_viridis_d(option="C", name = "Period", begin = 0.15, end = 0.85)+
  stat_smooth(aes(x = UNUSAM/100, y = inflation/100, color = period), linetype=2, method="lm") + 
  theme(legend.title = element_blank(),
        legend.position = c(0.2, 0.9))

1960-2019

bind_rows(unr, cpi) %>%
  filter(Ticker %in% c("UNUSAM", "CPUSAM")) %>%
  select(Ticker, date, value) %>%
  spread(Ticker, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(year = year(date) + 1,
         UNUSAM = UNUSAM/100,
         inflation = log(CPUSAM) - lag(log(CPUSAM), 1)) %>%
  filter(year <= 1940) %>%
  mutate(period = case_when(year <= 1933 ~ "1890-1933 ($20 Gold Standard)",
                            TRUE ~ "1933-1941 ($35 Gold Standard)")) %>%
  ggplot(.) + theme_minimal() + 
  geom_point(aes(x = UNUSAM, y = inflation, color = period)) +
  geom_text_repel(aes(x = UNUSAM, y = inflation, label = year, color = period)) +
  xlab("Unemployment Gap") + ylab("Inflation") +
  scale_x_continuous(breaks = 0.01*seq(-10, 40, 2),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_y_continuous(breaks = 0.01*seq(-20, 20, 2),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_color_viridis_d(option="C", name = "Period", begin = 0.15, end = 0.85) +
  stat_smooth(aes(x = UNUSAM, y = inflation), linetype = 2, method = "lm", color = viridis(3)[2]) + 
  theme(legend.title = element_blank(),
        legend.position = c(0.75, 0.9))

Figure 3: U.S. Phillips curve (1960-2019)

1890-2019

bind_rows(unr, cpi) %>%
  filter(Ticker %in% c("UNUSAM", "CPUSAM")) %>%
  select(Ticker, date, value) %>%
  spread(Ticker, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(year = year(date) + 1,
         UNUSAM = UNUSAM/100,
         inflation = log(CPUSAM) - lag(log(CPUSAM), 1)) %>%
  ggplot(.) + theme_minimal() + 
  geom_point(aes(x = UNUSAM, y = inflation)) +
  geom_text(aes(x = UNUSAM + 0.009, y = inflation, label = date %>% year)) +
  xlab("Unemployment Rate") + ylab("Inflation") +
  scale_x_continuous(breaks = 0.01*seq(0, 30, 5),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_y_continuous(breaks = 0.01*seq(-20, 20, 5),
                     labels = scales::percent_format(accuracy = 1)) +
  stat_smooth(aes(x = UNUSAM, y = inflation), linetype = 2, method = "lm")

Figure 4: U.S. Phillips Curve (1890-2019): Unemployment and Price Inflation.

US 1955-1968 Price Phillips Curve

unr %>%
  filter(Ticker == "UNUSAM") %>%
  rename(unr = value) %>%
  select(date, unr) %>%
  left_join(cpi %>%
              filter(Ticker == "CPUSAM") %>%
              rename(cpi = value) %>%
              select(date, cpi), 
            by = "date") %>%
  filter(date <= as.Date("1968-01-01"),
         date >= as.Date("1955-01-01")) %>%
  # Make Annual
  filter(month(date) == 12 & day(date) == 31) %>%
  mutate(cpi_d1ln = log(cpi) - lag(log(cpi), 1),
         unr = unr / 100) %>%
  ggplot(.) + theme_minimal() + 
  geom_point(aes(x = unr, y = cpi_d1ln)) +
  geom_text(aes(x = unr + 0.002, y = cpi_d1ln, label = date %>% year)) +
  xlab("Unemployment Rate") + ylab("Price Inflation") +
  scale_x_continuous(breaks = 0.01*seq(0, 40, 0.5),
                     labels = scales::percent_format(accuracy = 0.5)) +
  scale_y_continuous(breaks = 0.01*seq(-20, 20, 0.5),
                     labels = scales::percent_format(accuracy = 0.5)) +
  stat_smooth(aes(x = unr, y = cpi_d1ln), linetype = 2, method = "lm")

Figure 5: U.S. Price Phillips Curve (1955-1968).

1891-1945

bind_rows(unr, cpi) %>%
  filter(Ticker %in% c("UNUSAM", "CPUSAM")) %>%
  select(-variable, -iso3c) %>%
  spread(Ticker, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  filter(date <= as.Date("1946-01-01")) %>%
  mutate(CPUSAM_log = log(CPUSAM),
         price_inflation = CPUSAM_log - dplyr::lag(CPUSAM_log),
         UNUSAM = UNUSAM/100) %>%
  select(date, UNUSAM, price_inflation) %>%
  gather(variable, value, -date) %>%
  mutate(variable_desc = case_when(variable == "UNUSAM" ~ "Unemployment Rate",
                                   variable == "price_inflation" ~ "Inflation (Price)")) %>%
  ggplot(.) +
  geom_line(aes(x = date, y = value, color = variable_desc)) + 
  ylab("Unemployment Rate, Inflation") + xlab("") +
  scale_color_manual(values = c(viridis(4)[1], viridis(4)[2])) +
  scale_linetype_manual(values = c("solid", "solid")) +
  scale_x_date(breaks = as.Date(paste0(seq(1850, 2020, 5), "-01-01")),
               labels = date_format("%Y")) +
  scale_y_continuous(breaks = 0.01*seq(-50, 50, 2),
                     labels = scales::percent_format(accuracy = 1))  +
  theme_minimal() +
  theme(legend.position = c(0.2, 0.90),
        legend.title = element_blank(),
        legend.key.size = unit(0.9, 'lines')) + 
  geom_vline(xintercept = as.Date("1933-01-01"), linetype = "dotted", color = "black") +
  geom_rect(data = data_frame(start = as.Date("1933-01-01"), 
                              end = as.Date("1939-08-15")),
            aes(xmin = start, xmax = end, ymin = -Inf, ymax = +Inf),
            fill = viridis(4)[4], alpha = 0.1) + 
  geom_rect(data = data_frame(start = as.Date("1890-01-01"), 
                              end = as.Date("1933-01-01")),
            aes(xmin = start, xmax = end, ymin = -Inf, ymax = +Inf),
            fill = viridis(4)[3], alpha = 0.1) +
  geom_text(data = data_frame(start = c(1910, 1908, 1932, 1928) %>% paste0("-01-01") %>% as.Date, 
                              percent = c(0.26, -0.135, -0.135, 0.26),
                              name = c("Gold Standard", "Phillips curve Period", "Missing Deflation", "$ deval (Roosevelt)"),
                              color_new = c("black", "black", "black", grey(0.3))),
            aes(x = start, y = percent, label = name),
            size = 3, vjust = 0, hjust = 0, nudge_x = 50, color = c(grey(0.3), grey(0.3), grey(0.3), "black"))

1890-1960

bind_rows(unr, cpi) %>%
  filter(Ticker %in% c("UNUSAM", "CPUSAM")) %>%
  select(Ticker, date, value) %>%
  spread(Ticker, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(date = date + 1,
         UNUSAM = UNUSAM/100,
         inflation = log(CPUSAM) - lag(log(CPUSAM), 1)) %>%
  filter(date <= as.Date("1960-01-01")) %>%
  ggplot(.) + theme_minimal() + 
  geom_point(aes(x = UNUSAM, y = inflation)) +
  geom_text_repel(aes(x = UNUSAM, y = inflation, label = format(date, format = "%y"))) +
  xlab("Unemployment Rate") + ylab("Inflation") +
  scale_x_continuous(breaks = 0.01*seq(0, 30, 2),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_y_continuous(breaks = 0.01*seq(-20, 20, 5),
                     labels = scales::percent_format(accuracy = 1)) +
  stat_smooth(aes(x = UNUSAM, y = inflation), linetype = 2, method = "lm", color = viridis(3)[2])

Price 1890-1933

No label

unr %>%
  filter(Ticker == "UNUSAM") %>%
  rename(unr = value) %>%
  select(date, unr) %>%
  left_join(cpi %>%
              filter(Ticker == "CPUSAM") %>%
              rename(cpi = value) %>%
              select(date, cpi), 
            by = "date") %>%
  filter(date <= as.Date("1933-01-01"),
         date >= as.Date("1890-01-01")) %>%
  # Make Annual
  filter(month(date) == 12 & day(date) == 31) %>%
  mutate(cpi_d1ln = log(cpi) - lag(log(cpi), 1),
         unr = unr / 100) %>%
  ggplot(.) + theme_minimal() + 
  geom_point(aes(x = unr, y = cpi_d1ln)) +
  geom_text_repel(aes(x = unr, y = cpi_d1ln, label = date %>% year)) +
  xlab("Unemployment Rate") + ylab("Price Inflation") +
  scale_x_continuous(breaks = 0.01*seq(0, 40, 2),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_y_continuous(breaks = 0.01*seq(-20, 20, 2),
                     labels = scales::percent_format(accuracy = 1)) +
  stat_smooth(aes(x = unr, y = cpi_d1ln), linetype = 2, method = "lm", color = viridis(3)[2])

Label

cpi %>%
  bind_rows(unr) %>%
  filter(Ticker %in% c("UNUSAM", "CPUSAM")) %>%
  select(Ticker, date, value) %>%
  spread(Ticker, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(year = year(date) + 1,
         UNUSAM = UNUSAM/100,
         inflation = log(CPUSAM) - lag(log(CPUSAM), 1)) %>%
  filter(year <= 1933) %>%
  ggplot(.) + theme_minimal() + 
  geom_point(aes(x = UNUSAM, y = inflation)) +
  geom_text(aes(x = UNUSAM + 0.009, y = inflation, label = year)) +
  xlab("Unemployment Rate") + ylab("Inflation") +
  scale_x_continuous(breaks = 0.01*seq(0, 30, 5),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_y_continuous(breaks = 0.01*seq(-20, 20, 5),
                     labels = scales::percent_format(accuracy = 1)) +
  stat_smooth(aes(x = UNUSAM, y = inflation), linetype = 2, method = "lm")

US 1890-1933 Price Phillips Curve

unr %>%
  filter(Ticker == "UNUSAM") %>%
  rename(unr = value) %>%
  select(date, unr) %>%
  left_join(cpi %>%
              filter(Ticker == "CPUSAM") %>%
              rename(cpi = value) %>%
              select(date, cpi), 
            by = "date") %>%
  filter(date <= as.Date("1933-01-01"),
         date >= as.Date("1890-01-01")) %>%
  # Make Annual
  filter(month(date) == 12 & day(date) == 31) %>%
  mutate(cpi_d1ln = log(cpi) - lag(log(cpi), 1),
         unr = unr / 100) %>%
  ggplot(.) + theme_minimal() + 
  geom_point(aes(x = unr, y = cpi_d1ln)) +
  geom_text(aes(x = unr + 0.01, y = cpi_d1ln, label = date %>% year)) +
  xlab("Unemployment Rate") + ylab("Price Inflation") +
  scale_x_continuous(breaks = 0.01*seq(0, 40, 2),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_y_continuous(breaks = 0.01*seq(-20, 20, 2),
                     labels = scales::percent_format(accuracy = 1)) +
  stat_smooth(aes(x = unr, y = cpi_d1ln), linetype = 2, method = "lm")

Figure 6: U.S. Price Phillips Curve (1890-1933).

1890-1941 Scatter

cpi %>%
  bind_rows(unr) %>%
  filter(Ticker %in% c("UNUSAM", "CPUSAM")) %>%
  select(Ticker, date, value) %>%
  spread(Ticker, value) %>%
  na.omit %>%
  filter(month(date) == 12, day(date) == 31) %>%
  mutate(year = year(date) + 1,
         UNUSAM = UNUSAM/100,
         inflation = log(CPUSAM) - lag(log(CPUSAM), 1)) %>%
  filter(year <= 1940) %>%
  mutate(period = case_when(year <= 1933 ~ "1890-1933 ($20 Gold Standard)",
                            TRUE ~ "1933-1941 ($35 Gold Standard)")) %>%
  ggplot(.) + theme_minimal() + 
  geom_point(aes(x = UNUSAM, y = inflation, color = period)) +
  geom_text(aes(x = UNUSAM + 0.009, y = inflation, label = year, color = period)) +
  xlab("Unemployment Gap") + ylab("Inflation") +
  scale_x_continuous(breaks = 0.01*seq(-10, 40, 2),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_y_continuous(breaks = 0.01*seq(-20, 20, 2),
                     labels = scales::percent_format(accuracy = 1)) +
  scale_color_viridis_d(option="C", name = "Period", begin = 0.15, end = 0.85) +
  stat_smooth(aes(x = UNUSAM, y = inflation), linetype = 2, method = "lm") + 
  theme(legend.title = element_blank(),
        legend.position = c(0.75, 0.9))

Figure 7: (ref:us-PC-1890-1941-colors)

Phillips curves

Data - GFD

François Geerolf

Info

Related

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Germany

Without 1922, 1923

Germany (post 1960)

Switzerland

Scatter

1980-2005

1970-2020

Time Series

1970-2020

1980-2020

Japan

Scatter

1980-2005

1970-2020

Time Series

1970-2020

1980-2020

U.K.

Scatter

1867-1914

1914-1945

1970-2000

2000-2020

1947-2020

Time Series

1800-1900

1900-1970

1960-2020

U.S.

Rolling Regressions

Non-accelerationist PC

Accelerationist PC

1890-1945

1890-2020

Ci

Fill = NA

1947-2020

1960-2019

1890-2019

US 1955-1968 Price Phillips Curve

1891-1945

1890-1960

Price 1890-1933

No label

Label

US 1890-1933 Price Phillips Curve

1890-1941 Scatter