Diffusion Index Analysis

Introduction

The purpose of this analysis is to construct a Diffusion Index for three economic variables in the United States and compare it with the Chicago Fed National Activity Index: Diffusion Index (CFNAIDIFF). The Diffusion Index serves as an indicator of economic trends by summarizing the directional movement of selected variables. We will analyze the correlation between the two indexes and provide insights into their alignment and implications for current economic activity.

Data Description

The data used includes: 1. Employment data (Total Nonfarm Payrolls). 2. Industrial Production Index. 3. Retail Sales. 4. CFNAIDIFF data from the Chicago Fed.

The data is preprocessed to calculate month-over-month changes and converted into binary indicators (expansion = 1, contraction = 0).

Load Libraries and Data

# Load Libraries
library(ggplot2)

## Warning: package 'ggplot2' was built under R version 4.3.3

library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(tidyr)
library(readr)

# Load datasets
employment <- read.csv("D:/DOWLOADS/employment.csv")
industrial_production <- read.csv("D:/DOWLOADS/industrial_production.csv")
retail_sales <- read.csv("D:/DOWLOADS/retail_sales.csv")
cfnaidiff <- read.csv("D:/DOWLOADS/cfnaidiff.csv")

# Ensure proper column names
colnames(employment) <- c("date", "value")  
colnames(industrial_production) <- c("date", "value")
colnames(retail_sales) <- c("date", "value")
colnames(cfnaidiff) <- c("date", "value")

# Convert 'date' to Date format
employment$date <- as.Date(employment$date)
industrial_production$date <- as.Date(industrial_production$date)
retail_sales$date <- as.Date(retail_sales$date)
cfnaidiff$date <- as.Date(cfnaidiff$date)

# Handle month-over-month changes and binary indicators
employment <- employment %>%
  arrange(date) %>%
  mutate(change = value - lag(value),
         indicator = ifelse(change > 0, 1, 0))

industrial_production <- industrial_production %>%
  arrange(date) %>%
  mutate(change = value - lag(value),
         indicator = ifelse(change > 0, 1, 0))

retail_sales <- retail_sales %>%
  arrange(date) %>%
  mutate(change = value - lag(value),
         indicator = ifelse(change > 0, 1, 0))

# Construct Diffusion Index
diffusion_index <- employment %>%
  select(date, emp_indicator = indicator) %>%
  inner_join(select(industrial_production, date, ind_indicator = indicator), by = "date") %>%
  inner_join(select(retail_sales, date, retail_indicator = indicator), by = "date") %>%
  mutate(diffusion_index = (emp_indicator + ind_indicator + retail_indicator) / 3)

# Merge with CFNAIDIFF
combined_data <- diffusion_index %>%
  inner_join(select(cfnaidiff, date, cfnaidiff_value = value), by = "date")

# Remove non-finite or missing values
combined_data <- combined_data %>%
  filter(!is.na(diffusion_index), !is.na(cfnaidiff_value))

# Correlation Analysis
correlation <- cor(combined_data$diffusion_index, combined_data$cfnaidiff_value, use = "complete.obs")
print(paste("Correlation Coefficient:", round(correlation, 4)))

## [1] "Correlation Coefficient: 0.0033"

# Visualization
ggplot(combined_data, aes(x = date)) +
  geom_line(aes(y = diffusion_index, color = "My Diffusion Index"), linewidth = 1) +
  geom_line(aes(y = cfnaidiff_value, color = "CFNAIDIFF"), linewidth = 1) +
  geom_smooth(aes(y = diffusion_index), method = "loess", se = FALSE, color = "blue", linetype = "dashed") +
  geom_smooth(aes(y = cfnaidiff_value), method = "loess", se = FALSE, color = "red", linetype = "dashed") +
  labs(title = "Comparison of Diffusion Indexes",
       x = "Date",
       y = "Value",
       color = "Index") +
  theme_minimal()

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

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

Insights

The correlation coefficient is 0.0033354, indicating the strength of the relationship between the two indexes.
The visualization shows the trends of the two indexes, highlighting areas of alignment and divergence.
If the Diffusion Index mirrors CFNAIDIFF trends, it suggests consistency in economic signals. Any discrepancies provide opportunities for deeper analysis into differing variable behaviors.

Conclusion