Inflation adjustment

Adjusting for inflation is a simple way of taking into account that 5$ in 1950 would get you much more than 5$ would today. This compensation is usually done by a consumer price index, which is standardized to a specific year (in the video below we show examples with 2010 and 2015 as reference years).

Let Y_t denote the raw time series and Y_t^\star the inflation adjusted. Let \text{CPI}_t denote a relevant consumer price index defined to be 100 in the reference year t^\star. Then Y_t^\star = Y_t \cdot \frac{100}{\text{CPI}_t}. More generally, we can choose the reference year t^\star and write this as Y_t^\star = Y_t \cdot \frac{\text{CPI}_{t^\star}}{\text{CPI}_t}.

The inflation adjusted series is then measured in the unit “year t^\star-money”.

# --- Inflation adjusted GDP per capita by country ---
scandinaviaUSA %>%
  autoplot(GDP/Population *100 / CPI) +
  labs(title= "GDP per capita = GDP / Population", y = "$US")

# --- CPI FOR NORWAY (data from Statistics Norway)---
CPI <- read.csv("data/CPI_norway.csv", sep = ";") %>% as_tibble() %>%
  select(1:2) %>%
  rename(Year = X,CPI = Y.avg2) %>%
  mutate(Year = as.numeric(Year), CPI = as.numeric(CPI))%>%
  filter(Year < 2022) %>%
  as_tsibble(index = Year)

# --- CPI figure ---
CPI %>%
  autoplot(CPI, color = "blue", lwd = 1.2) +
  labs(title= "Consumer Price Index", y = "NOK",
       subtitle = "Data source: Statistics Norway")+
  geom_hline(yintercept = 100, lty = 2) + geom_vline(xintercept = 2015, lty = 2)+
  scale_x_continuous(breaks = seq(1925,2025,10))+
  scale_y_continuous(breaks = seq(0,120,10))

# --- BIG MAC price index ---
bigMac <- read_csv("https://raw.githubusercontent.com/TheEconomist/big-mac-data/master/output-data/big-mac-raw-index.csv")
norBigMac <- bigMac %>%
  filter(name %in% c("Norway")) %>%
  mutate(Year = lubridate::year(date)) %>%
  as_tsibble(index = "date")%>%
  filter(Year <2022) %>%
  left_join(CPI, by = "Year")

# --- BIG MAC price index figure ---
norBigMac %>%
  autoplot(local_price) +
  labs(title= "Big Mac price in Norway", y = "NOK",
       subtitle = "Data source: The Economist") +
  geom_smooth(method = "lm", se=FALSE)

#--- Inflation adjusted BIG MAC price index figure ---
norBigMac %>%
  mutate(cpiAdjusted =local_price / CPI * 100)  %>%
  as_tsibble(index = date) %>%
  autoplot(cpiAdjusted)+
  labs(title= "Inflation adjusted Big Mac price in Norway", y = "NOK (2015)",
       subtitle = "Data sources: The Economist (big mac index), Statistics Norway (CPI)") +
  geom_smooth(method = "lm", se=FALSE)