Do prices feel like they are rising more than the CPI says?

      Do prices feel like they are rising more than the CPI (Consumer Price Index) says? Yes.

      For 2025 the overall CPI increased by a pretty moderate 2.7% (CPI-U for all urban consumers, December to December). The CPI measures the price change of a basket of goods over eight major categories: food & beverages, housing, apparel, transportation, medical care, recreation, education & communication, and other, over a large number of metropolitan statitical areas (MSA). Each month Bureau of Labor Statistics data collectors collect about 94,000 prices. For some items, prices are adjusted to remove the effect of a change of quality (for example today's Toyota Corolla is a much different car than ten years ago). There are separate indices for over 200 items countrywide, and separate indices for the eight major categories by MSA.

      Of course what matters is price changes on the items YOU buy, and especially the items you buy frequently like food. Each individual item has its own reasons for its price changes - egg prices are affected by bird flu, coffee prices are affected by weather and geopolitical conditions in other countries, etc. These factors are beyond our control.

      I was interested in comparing food price changes for common frequently purchased items. This is based on CPIs for countrywide data in categories like eggs. Of course I am not measuring YOUR specific egg purchase (such as store brand, organic, medium size, white, 12 count, at CTown in Intercourse, Pennsylvania).

      I began with 11 years of December values of ten separate food categories and also the overall CPI-U, seasonally adjusted. The values I used are as follows (although I understand values change as there are changes to seasonal adjustment factors, weightings, etc.)

      For comparison purposes I set all eleven indices to a 100 index value at 2015, and I plotted them on a line graph. Each year's value is now relative to 2015.

      On a ten-year basis, ground beef, eggs, and lettuce are running higher than the overall CPI. Those three food indices have experienced a lot of volatility. The pandemic year 2022 was the year of the largest increase for many foods. Interestingly, apple prices have gone down!

      Another way to look at this is to look at bar graphs with percentage changes. Here are graphs with percentage changes 2015 to 2025, 2024 to 2025, and 2021 to 2022:

      For 2025 compared with 2015, I was not aware how much the prices had risen for ground beef, lettuce, and eggs.

      For 2025 compared to 2024, the increase in prices for ground beef, eggs, and coffee have been much larger than the 2.7% overall increase in the CPI. This is probably no surprise if you are the household member doing the grocery shopping.

      For 2022 versus 2021, the increase in all foods except ground beef exceeded the overall CPI. We probably remember this during the Covid pandemic years.

      In the insurance world, the goods and services that insurance pays for have also increased by more than the overall CPI. For example, medical care costs, auto maintenance & repair costs, and building construction & repair costs have consistently outpaced the overall CPI. So don't be surprised to see health insurance, auto insurance, and home insurance prices to continue to increase.

      Here is the R code:

library(readxl)
library(dplyr)
library(tidyr)
library(ggplot2)

df <- read_excel("C:/Users/Jerry/Desktop/R_files/CPI_10_years.xlsx")
print(df, n = Inf, width = Inf)

# 1. Convert data to 'long' format for easier plotting
df_long <- df %>%
  pivot_longer(cols = -Year, names_to = "Category", values_to = "Index")

# 2. Re-base every category so 2015 = 100
df_normalized <- df_long %>%
  group_by(Category) %>%
  mutate(Index_100 = (Index / Index[Year == 2015]) * 100) %>%
  ungroup()

# 3. Plot line graph "Race to the Top"
ggplot(df_normalized, aes(x = Year, y = Index_100, color = Category)) +
  geom_line(aes(size = Category == "Overall CPI"), show.legend = FALSE) +
  # Use subset to only label the last point (2025)
  geom_text(data = subset(df_normalized, Year == 2025), 
            aes(label = Category), 
            hjust = -0.1,  # Push text to the right of the point
            size = 4, fontface="bold",
            show.legend = FALSE) +
  # Fix X-Axis: No decimals, every year labeled
  scale_x_continuous(breaks = seq(2015, 2025, 1), limits = c(2015, 2027)) +
  # Highlight the Overall CPI in black/thicker line
  scale_size_manual(values = c("TRUE" = 2.0, "FALSE" = 0.8)) +
  scale_color_manual(values = c("Overall CPI" = "black", 
                                "Eggs" = "red", 
                                "Ground Beef" = "darkred",
                                "Apples" = "forestgreen",
                                "Milk" = "blue",
                                "Bread" = "orange",
                                "Coffee" = "brown",
                                "Lettuce" = "lightgreen",
                                "Soup" = "#008080",
                                "Breakfast Cereal" = "purple",
                                "Other Fresh Veg" = "gray")) +
  theme_minimal() +
  theme(
    legend.position = "none",        # Remove legend
    plot.title = element_text(face = "bold", size = 16), 
    axis.title = element_text(face = "bold"), 
    axis.text = element_text(face = "bold"),
    plot.margin = margin(r = 100),   # Add space on the right for labels
    panel.grid.minor = element_blank()
  ) +
  coord_cartesian(clip = 'off') +    # Prevent labels from being cut off
  labs(title = "Cumulative Food Price Changes (2015 = 100)",
       subtitle = "Food categories vs. Overall CPI Baseline",
       y = "Index (2015 = 100)",
       x = "Year")

#4 Plot bar graph with % changes
# filter data for start and end years 

plot_cpi_change <- function(data, start_yr, end_yr) {
  
  # 1. Prepare dynamic column names for the mutation step
  start_col <- paste0("Yr", start_yr)
  end_col <- paste0("Yr", end_yr)
  
  # 2. Data Processing
  df_bar <- data %>% 
    filter(Year %in% c(start_yr, end_yr)) %>%
    pivot_longer(cols = -Year, names_to = "Category", values_to = "Index") %>% 
    pivot_wider(names_from = Year, names_prefix = "Yr", values_from = Index) %>%
    # Use .data[[]] to dynamically reference the columns created by pivot_wider
    mutate(Pct_Change = ((.data[[end_col]] - .data[[start_col]]) / .data[[start_col]]) * 100) %>%
    mutate(Category = reorder(Category, -Pct_Change))
  
  # 3. Visualization
  ggplot(df_bar, aes(x = Category, y = Pct_Change, fill = Category)) +
    geom_bar(stat = "identity", color = "black", size = 0.5) +
    # Logic for text placement based on positive/negative change
    geom_text(aes(label = paste0(round(Pct_Change, 1), "%"),
                  vjust = ifelse(Pct_Change >= 0, -0.5, 1.5)), 
              fontface = "bold", size = 4.5) +
    scale_fill_manual(values = c("Overall CPI" = "black", "Soup" = "#008080", "Eggs" = "red", 
                                 "Ground Beef" = "darkred", "Apples" = "forestgreen", "Milk" = "blue", 
                                 "Bread" = "orange", "Coffee" = "brown", "Lettuce" = "lightgreen", 
                                 "Breakfast Cereal" = "purple", "Other Fresh Veg" = "gray")) +
    theme_minimal() + 
    theme(legend.position = "none", 
          plot.title = element_text(face = "bold", size = 18, hjust = 0.5), 
          axis.title = element_text(face = "bold", size = 14), 
          axis.text.x = element_text(face = "bold", size = 11, angle = 45, hjust = 1), 
          axis.text.y = element_text(face = "bold", size = 11), 
          panel.grid.major.x = element_blank()) +
    coord_cartesian(clip = 'off') +
    labs(title = paste("CPI FOOD PRICE CHANGES (", start_yr, "TO", end_yr, ")"), 
         y = "PERCENT CHANGE (%)", x = "CATEGORY")
}

plot_cpi_change(df, 2015, 2025)
plot_cpi_change(df, 2024, 2025)
plot_cpi_change(df, 2021, 2022)

End

Ten Lords-a-Leaping

Just what is a lord-a-leaping? Well, what is a lord? A lord is a title of nobility, usually inherited, that exists in the UK and other countries. And those lords like to leap, especially during the twelve days of Christmas.

The song the Twelve Days of Christmas is a well-known Christmas song, whose earliest known publication was in London in 1780. There are various versions of the lyrics, various melodies, and meanings of the gifts. As usual, this is all nicely summarized in Wikipedia https://en.wikipedia.org/wiki/The_Twelve_Days_of_Christmas_(song) .

PNC Bank, one of the largest banks in the US, has been calculating the prices of the twelve gifts given by my true love since 1984, and has trademarked its PNC Christmas Price Index ® . Two senior executives at PNC calculate the prices, and many of the details are available at https://www.pnc.com/en/about-pnc/topics/pnc-christmas-price-index.html#about , especially in their FAQ. In particular, they note that the price of services has generally increased while the price of goods has slowed. The price index is a humorous proxy for the general cost of inflation.

On day one there was 1 gift (the partridge). On day two there were 3 gifts (2 doves + 1 partridge). On day three there were 6 gifts (3 hens + 2 doves + 1 partridge). On day twelve there were 78 gifts, and 78 is the sum of the first 12 natural numbers, whose general formula Σn = n(n+1)/2 was known by Gauss in the 1700’s.

The cumulative number of gifts is 1 + 3 + 6 + … + 78, whose sum is 364. (One fewer than the number of days in a year. Coincidence?) Each of these numbers is called a Triangular number T_i , and the general formula of their sum is Σ T_i = n(n+1)(n+2)/6.

The PNC Christmas Price Index ®, or the Total Cost of Christmas reflects the total cost of the 78 gifts: one set of each of the gifts. For 2023 that cost is $46,729.86, versus $45,523.33 in 2022, a change of + 2.7%. The prior year’s change was 10.5%. The largest individual item in the index is not the five gold rings as I had thought ($1,245), but rather those leaping lords ($14,539, up 4.0%), followed by the swimming swans ($13,125 and unchanged for many years).

PNC also calculates the True Cost of Christmas, which is the cost of 364 gifts. For 2023 that cost is $201,972.66, a change of 2.5% over a year ago.

And PNC calculates a core index excluding the swans, which some time ago had been the most volatile item, and also an e-commerce index buying all items online.

The overall Bureau of Labor Statistics CPI for All Urban Consumers (CPI-U) increased 3.2% for twelve months ending October 2023. October is the closest month for CPI-U to the PNC data. CPI-U of course is based on a broad market basket of goods including food, energy, medical care, housing, transportation, etc., which are not the gifts given in the song, but CPI-U is a common measure of inflation. The PNC index is based on a very specific twelve items and is heavily weighted toward the lords and the swans.

The PNC website contains detailed information on its calculations, but it does not contain historical information on CPI-U. I used twelve-month October historical CPI-U percent changes from https://www.bls.gov/regions/mid-atlantic/data/consumerpriceindexhistorical_us_table.htm . Then I graphed the percentage changes of the PNC Christmas Price Index® , the PNC True Cost of Christmas index, and the CPI.

With such a small number of items, the two PNC indices fluctuate drastically. 2014 reflects a one-time increase in the cost of the swans. 2020 was the unusual year during the pandemic when some of the gifts (including the lords!) were unavailable and so the cost that year was zero. The two PNC indices were fairly close to CPI-U for five years starting in 2015 and again for 2022 and 2023. Maybe these PNC indices are pretty good.

PNC uses the Philadelphia Ballet to calculate the cost of the lords-a-leaping.

Here is the R code I used:

library(readxl)
library(ggplot2)
df1 <- read_excel("C:/Users/Jerry/Desktop/R_files/xmas.xlsx", sheet = 1)
df2 <- read_excel("C:/Users/Jerry/Desktop/R_files/xmas.xlsx", sheet = 2)
cpi <- round(df2$Percent_change,3)
df1 <- df1[c(3:13)]
year <- as.numeric(colnames(df1)[2:11])
total_cost_dollars <- colSums(df1)
total_cost_index <- vector()
true_cost_dollars <- vector()
true_cost_index <- vector()
for(i in 1:length(total_cost_dollars)){
true_cost_dollars[i] <- 12*df1[1,i] + 11*df1[2,i] + 10*df1[3,i] + 9*df1[4,i] + 8*df1[5,i] +
7*df1[6,i] + 6*df1[7,i] + 5*df1[8,i] + 4*df1[9,i] + 3*df1[10,i] + 2*df1[11,i] + 1*df1[12,i]
}
true_cost_dollars <- unlist(true_cost_dollars)
for(i in 1:length(total_cost_dollars) - 1){
total_cost_index[i] <- round(100*(total_cost_dollars[i+1]/total_cost_dollars[i] - 1),1)
true_cost_index[i] <- round(100*(true_cost_dollars[i+1]/true_cost_dollars[i] - 1),1)
}
df <- data.frame(cbind(year, total_cost_index, true_cost_index, cpi))

colors <- c("total_cost_index" = "red", "true_cost_index" = "navy", "cpi" = "grey")
ggplot(df, aes(x=year)) +
geom_line(aes(y=total_cost_index, color="total_cost_index")) +
geom_line(aes(y=true_cost_index, color="true_cost_index"))
geom_line(aes(y=cpi, color="cpi")) +
labs(title = "12 Days of Christmas", x = "Year", y = "Percent change", color = "Legend") +
scale_color_manual(values = colors) +
# scale_y_continuous(labels = scales::percent_format(scale = 1, prefix = "", suffix = "%")) +
theme(
legend.position="right",
plot.title = element_text(size=15, face="bold"),
axis.title = element_text(size=15, face="bold"),
axis.text = element_text(size=15, face="bold"),
legend.title = element_text(size=15, face="bold"),
legend.text = element_text(size=15, face="bold"))