Chicago Fed National Activity Index: Diffusion Index (CFNAIDIFF) Comparison

• Class: ECON 6635-01

• School: Pompea College of Business

• University: University of New Haven

• Author: Sajan Punthalamalayil Ninan

Introduction

Understanding the dynamics of the U.S. economy requires both national and localized perspectives. This study constructs a diffusion index using data on employment, industrial production, and consumer sentiment. By capturing the proportion of improving economic indicators, the diffusion index provides insights into trends in economic activity. It is then compared with the Chicago Fed National Activity Diffusion Index (CFNAIDIFF) to identify patterns of growth and contraction over time. This comparison highlights alignments and deviations, offering a comprehensive view of economic performance and its underlying drivers. The analysis serves as a tool to assess broader economic trends and localized conditions.

Data selection and Diffusion Index Construction.

The diffusion index reflects economic expansion and contraction based on pulling data for three selected variables. Here selected variables are Employment, industrial production, and housing starts.

suppressWarnings({
  suppressPackageStartupMessages({
    library(tidyverse)
    library(quantmod)
    library(tsbox)
    library(zoo)
  })
})

options(digits = 3, scipen = 99999)
graphics.off()

# Load economic variables
getSymbols(c("PAYEMS", "INDPRO", "HOUST"),
           src = "FRED", return.class = 'xts', 
           from = "2010-01-01", to = Sys.Date())

## [1] "PAYEMS" "INDPRO" "HOUST"

Comparison of Custom Diffusion Index and CFNAIDIFF

• Correlation Coefficient:

  • The correlation between your custom Diffusion Index and the Chicago Fed National Activity Diffusion Index (CFNAIDIFF) indicates the extent to which the two series move together.

  • A strong positive correlation (close to 1) would imply that your index is effectively capturing the same economic dynamics as CFNAIDIFF.

  • For example, if the correlation is 0.8 or higher, it suggests that your index is a good proxy for CFNAIDIFF, reflecting similar economic trends over the analyzed period.

# Data preprocessing
employment <- PAYEMS
industrial_production <- INDPRO
housing  <- HOUST

employment_ss <- employment["2010-01-31/2024-09-01"] |> ts_ts()
industrial_ss <- industrial_production["2010-01-31/2024-09-01"] |> ts_ts()
housing_ss <- housing["2010-01-31/2024-09-01"] |> ts_ts()

mydata <- cbind.data.frame(employment_ss, industrial_ss, housing_ss)

mydf <- mydata %>%
  mutate(
    emp_diff = tsibble::difference(employment_ss, differences = 1),
    ind_diff = tsibble::difference(industrial_ss, differences = 1),
    house_diff = tsibble::difference(housing_ss, differences = 1)
  ) %>%
  dplyr::select(emp_diff, ind_diff, house_diff) %>%
  na.omit()

Visual Observations (First Plot):

• General Alignment: At times, the custom Diffusion Index and CFNAIDIFF exhibit closely aligned trends, indicating that your index effectively captures critical aspects of economic activity, especially during periods of growth or contraction.

• Divergence Periods: At times, the indices diverge (e.g., the blue line rises or falls significantly compared to the orange line). These differences may stem from variations in the variables used in your index compared to those in CFNAIDIFF, such as:

  • CFNAIDIFF uses a broader range of variables beyond employment, industrial production, and consumer sentiment.

  • Your index may have specific sensitivities, such as being more influenced by employment or housing data.

• Post-September Observations:

  • Since CFNAIDIFF data ends in September 2024, your custom index provides valuable insights into recent economic activity.

  • If your index shows a decline after September, it could indicate a weakening economy, while stability or growth would suggest resilience.

# Construct diffusion index
mydf_mat <- apply(mydf, 2, sign)
pos <- apply(mydf_mat, 1, function(row) sum(row > 0))
neg <- apply(mydf_mat, 1, function(row) sum(row < 0))
tot <- pos + neg
index <- (pos / tot - neg / tot) * 100
ma_index <- rollmean(index, 7, align = "right", na.pad = TRUE)

Date <- seq.Date(from = as.Date("2010-05-01"), length.out = length(index), by = "month")
diffusion_df <- cbind.data.frame(Date, index, ma_index)

ggplot(diffusion_df, aes(x = Date, y = index)) +
  # Line for the diffusion index
  geom_line(color = "pink", size = 0.8) +
  # Smoothed trend line with transparency
  geom_smooth(color = "orange", fill = "blue", alpha = 0.3, size = 1.2) +
  # Adding labels to key points
  geom_text(data = diffusion_df[c(1, nrow(diffusion_df)), ],
            aes(label = paste0(round(index, 2), "%")), 
            vjust = -1, size = 3.5, fontface = "bold", color = "yellow") +
  # Adding a horizontal reference line
  geom_hline(yintercept = 0, linetype = "dashed", color = "black", size = 0.8) +
  # Vertical line for a key event (e.g., COVID-19)
  geom_vline(xintercept = as.Date("2020-03-01"), linetype = "dotted", color = "green", size = 1) +
  annotate("text", x = as.Date("2020-03-01"), y = -90, 
           label = "COVID-19", color = "green", size = 4, hjust = 0, angle = 90) +
  # Title, subtitle, and axis labels
  labs(
    title = "U.S. Economic Diffusion Index Over Time",
    subtitle = "Analyzing economic trends",
    x = "Year",
    y = "Diffusion Index (%)"
  ) +
  # Adjust y-axis limits to zoom out
  scale_y_continuous(limits = c(-120, 120)) +
  # Enhance visual appearance with themes
  theme_minimal(base_size = 14) +
  theme(
    plot.title = element_text(size = 20, face = "bold", hjust = 0.5, color = "brown"),
    plot.subtitle = element_text(size = 14, face = "italic", hjust = 0.5, color = "darkblue"),
    axis.title.x = element_text(size = 14, face = "bold", color = "black"),
    axis.title.y = element_text(size = 14, face = "bold", color = "black"),
    axis.text = element_text(size = 12, color = "black"),
    panel.grid.major = element_line(color = "gray", size = 0.5),
    panel.grid.minor = element_blank(),
    legend.position = "none",
    plot.background = element_rect(fill = "white", color = "white")
  )

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

## Warning: The `size` argument of `element_line()` is deprecated as of ggplot2 3.4.0.
## ℹ Please use the `linewidth` argument instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'

Long-Term Trend in Diffusion Index

• Visual Observations (Second Plot):

  • Overall Trend: There is a slight long-term decline in the custom Diffusion Index (indicated by the red smoothed line), suggesting a gradual weakening in economic activity over the last decade. This could reflect structural challenges in the economy, such as slowing growth in key sectors.

  • COVID-19 Impact: The sharp drop in the index around March 2020 corresponds to the onset of the COVID-19 pandemic. This emphasizes the index’s sensitivity to major economic disruptions.

  • Recovery and Plateau: Post-2020, the index appears to recover but stabilizes at a lower level compared to the pre-pandemic period. This could indicate a slower recovery or a new “normal” for the economy.

• Short-Term Observations:

  • The index shows periodic fluctuations, which could reflect the cyclical nature of the economy. For example, regular peaks and troughs might align with business cycles or seasonal patterns in employment and industrial production.

  • The shaded light blue area (confidence band for the trend line) suggests some variability but also provides a clear central trajectory for the economy’s performance.

# Load CFNAIDIFF
getSymbols("CFNAIDIFF", src = "FRED", return.class = 'xts', from = "2010-01-01")

## [1] "CFNAIDIFF"

cfnaidiff_ss <- CFNAIDIFF["2010-05-01/2024-09-01"] |> ts_ts()
min_length <- min(length(ma_index), length(cfnaidiff_ss))
ma_index <- ma_index[1:min_length]
cfnaidiff_ss <- cfnaidiff_ss[1:min_length]
Date <- Date[1:min_length]

# Prepare the comparison data frame
compare_df <- cbind.data.frame(Date, diffusion_index = ma_index, CFNAIDIFF = cfnaidiff_ss)

correlation <- cor(compare_df$diffusion_index, compare_df$CFNAIDIFF, use = "complete.obs")

# Enhanced comparison plot with interactivity
plotly::ggplotly(
  ggplot() +
    geom_line(data = compare_df, aes(x = Date, y = diffusion_index, color = "Diffusion Index"), size = 1.2) +
    geom_line(data = compare_df, aes(x = Date, y = CFNAIDIFF * 100, color = "CFNAIDIFF"), size = 1.2, linetype = "dashed") +
    scale_color_manual(
      values = c("Diffusion Index" = "violet", "CFNAIDIFF" = "red")
    ) +
    labs(
      title = "Comparison of Diffusion Index and CFNAIDIFF",
      x = "Year",
      y = "Index Value",
      color = "Legend"
    ) +
    theme_minimal(base_size = 8) +
    theme(
      plot.title = element_text(size = 10, face = "bold", hjust = 0.5),
      legend.position = "bottom"
    )
)

Key Economic Insights

• Strengths of the Custom Diffusion Index:

  • It effectively captures major economic events, such as the COVID-19 recession.

  • The index tracks the CFNAIDIFF well in many periods, making it a credible proxy for broader economic trends.

• Weaknesses or Limitations:

  • Differences during divergence periods suggest that the inclusion of additional variables could improve alignment with CFNAIDIFF.

  • Sensitivity to short-term data fluctuations may require smoothing or additional preprocessing for clearer interpretation.

Recent Economic Conditions (Post-September 2024)

• If your custom index is trending downward after September 2024:

  • This may indicate a softening in economic activity, potentially due to weaker industrial production, employment, or consumer sentiment.

  • Such trends could reflect challenges like rising interest rates, inflationary pressures, or other macroeconomic headwinds.

• If the index is stable or rising:

  • This suggests resilience in the economy, with positive contributions from the included variables.

Conclusion

The Diffusion Index reveals significant economic fluctuations, recently driven by declines in employment, industrial production, and consumer sentiment. In contrast, the CFNAIDIFF exhibits steadier national activity with lower volatility. A weak correlation of 0.157 underscores their differing focuses: the Diffusion Index is more responsive to localized economic shifts, while CFNAIDIFF reflects broader national trends. This divergence suggests that the Diffusion Index signals regional or sectoral weaknesses, whereas CFNAIDIFF indicates a stable national economy with no widespread contraction. Together, these indexes provide complementary insights, highlighting localized vulnerabilities against a backdrop of steady national economic conditions.