Inflation Analysis
Our current economic climate is unique with the rise of the coronavirus. In the economy, we are seeing unique factors such as a high inflation rate paired with a low unemployment rate. Historically, stagflation or recession-inflation occurs which is a situation where the inflation rate is high and unemployment remains high as well. We are particularly interested to see how these changes in the unemployment rate are potentially impacting the increase in the inflation rate. By using Python, we will analyze the impact of unemployment on inflation, but also other factors that could potentially impact inflation.
For more information on the research on inflation, I have written a paper on the current state and impacts on inflation for the year 2022:
Resources
- Analysis Software:
Jupyter Lab 3.4.4 - Programming Languages:
Python 3.10 - Data Source: www.stlouisfed.org
Federal Reserve Data
Our data is from the Federal Reserve Bank of St. Louis. The Federal Bank is central to the nation's economy and provides economic resources and data for US economic statistical analysis. We also used Yahoo Finance which is a data source to access stock market data.
For our X variables, we chose to look at the monthly unemployment rate (UNRATE), Federal Funds Effective Rate (DFF), and the S&P 500 Index (SPY).
The unemployment rate represents the number of unemployed as a percentage of the labor force. Labor force data are restricted to people 16 years of age and older, who currently reside in 1 of the 50 states or the District of Columbia, who do not reside in institutions (e.g., penal and mental facilities, homes for the aged), and who are not on active duty in the Armed Forces.
The federal funds rate is the interest rate at which depository institutions trade federal funds (balances held at Federal Reserve Banks) with each other overnight. When a depository institution has surplus balances in its reserve account, it lends to other banks in need of larger balances. In simpler terms, a bank with excess cash, which is often referred to as liquidity, will lend to another bank that needs to quickly raise liquidity.
The Standard and Poor's 500, or simply the S&P 500, is a stock market index tracking the stock performance of 500 large companies listed on stock exchanges in the United States. It is one of the most commonly followed equity indices.
For our Y variable, we chose to look at the Inflation Rate (INFRATE). We can calculate the inflation rate using the Consumer Price Index. The Consumer Price Index for All Urban Consumers: All Items (CPIAUCSL) is a price index of a basket of goods and services paid by urban consumers. Percent changes in the price index measure the inflation rate between any two time periods. The most common inflation metric is the percent change from one year ago. It can also represent the buying habits of urban consumers. This particular index includes roughly 88 percent of the total population, accounting for wage earners, clerical workers, technical workers, self-employed, short-term workers, unemployed, retirees, and those not in the labor force.
The CPIs are based on prices for food, clothing, shelter, and fuels; transportation fares; service fees (e.g., water and sewer service); and sales taxes. Prices are collected monthly from about 4,000 housing units and approximately 26,000 retail establishments across 87 urban areas. To calculate the index, price changes are averaged with weights representing their importance in the spending of the particular group. The index measures price changes (as a percent change) from a predetermined reference date. In addition to the original unadjusted index distributed, the Bureau of Labor Statistics also releases a seasonally adjusted index. The unadjusted series reflects all factors that may influence a change in prices. However, it can be very useful to look at the seasonally adjusted CPI, which removes the effects of seasonal changes, such as weather, school year, production cycles, and holidays.
Data Process
Given the large time frame of data, we parsed the unemployment and inflation into four time periods of relatively equal lengths.
| Time Periods | Years |
|---|---|
| Period 1 | 1948 - 1966 |
| Period 2 | 1967 - 1984 |
| Period 3 | 1985 - 2002 |
| Period 4 | 2003 - 2022 |
| Overall | 1948 - 2022 |
We then calculated the Inflation Rate by subtracting the past-date CPI from the current-date CPI and dividing the answer by the past-date CPI. From there, we multiplied the results by 100.
$$ Inflation = \frac{(CPI_{x+1} - CPI_x)}{CPI_x} * 100 $$Ordinary Least Squares Assumptions:
- Standard Errors assume that the covariance matrix of the errors is correctly specified.
- The condition number is large, 1.22e+03. This might indicate that there are strong multicollinearity or other numerical problems.
- The linear regression model is "linear in parameters."
- There is a random sampling of observations.
- There is homoscedasticity and no autocorrelation.
Unemployment Analysis
Python Code:
start_date = "01/01/1948"
end_date = "12/31/2022"
df = dataframe[(dataframe['DATE'] > start_date) & (dataframe['DATE'] < end_date)]
x_axis = df['DATE'].values
y_axis1 = df['INFRATE'].values
y_axis2 = df['UNRATE'].values
# Create the plot.
plt.plot(x_axis, y_axis1, label = "Inflation")
plt.plot(x_axis, y_axis2, label = "Unemployement")
uni_mod = smf.ols(formula="INFRATE ~ UNRATE", data = df)
uni_result = uni_mod.fit()
We will use the same structure of Python code to display the graph and the linear regression from the different periods.
Period 1 (1948 - 1966) results:
OLS Regression Results
==============================================================================
Dep. Variable: INFRATE R-squared: 0.017
Model: OLS Adj. R-squared: 0.011
Method: Least Squares F-statistic: 2.582
Date: Mon, 17 Oct 2022 Prob (F-statistic): 0.110
Time: 22:20:53 Log-Likelihood: -225.96
No. Observations: 150 AIC: 455.9
Df Residuals: 148 BIC: 461.9
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 2.2862 0.483 4.729 0.000 1.331 3.241
UNRATE -0.1472 0.092 -1.607 0.110 -0.328 0.034
==============================================================================
Omnibus: 0.263 Durbin-Watson: 0.067
Prob(Omnibus): 0.877 Jarque-Bera (JB): 0.376
Skew: 0.091 Prob(JB): 0.829
Kurtosis: 2.835 Cond. No. 29.4
==============================================================================
In Period 1, the intercept of the regression is 2.2862 and the R-squared is 0.017. The R-squared is the proportion of the variation in the dependent variable that is predictable from the independent variable. Due to the R-squared being small, it is not the total determinant of inflation. This means that around 1.7% of the variability observed in the target variable is explained by this regression model. Additionally, unemployment is not statistically significant and as unemployment increases by 1%, the inflation rate decreases by 0.1472 percentage points.
Period 2 (1967 - 1984) results:
OLS Regression Results
==============================================================================
Dep. Variable: INFRATE R-squared: 0.025
Model: OLS Adj. R-squared: 0.020
Method: Least Squares F-statistic: 5.374
Date: Mon, 17 Oct 2022 Prob (F-statistic): 0.0214
Time: 22:28:00 Log-Likelihood: -549.38
No. Observations: 215 AIC: 1103.
Df Residuals: 213 BIC: 1109.
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 5.0465 0.761 6.634 0.000 3.547 6.546
UNRATE 0.2652 0.114 2.318 0.021 0.040 0.491
==============================================================================
Omnibus: 17.328 Durbin-Watson: 0.018
Prob(Omnibus): 0.000 Jarque-Bera (JB): 18.012
Skew: 0.666 Prob(JB): 0.000123
Kurtosis: 2.515 Cond. No. 24.2
==============================================================================
In Period 2, the intercept of the regression is 5.0465 and the R-squared is 0.025. The R-squared is the proportion of the variation in the dependent variable that is predictable from the independent variable. This means that 2.5% of the variability observed in the target variable is explained by this regression model. Additionally, unemployment is statistically significant and as unemployment increases by 1%, inflation increases by 0.2652 percentage points.
Period 3 (1985 - 2002) results:
OLS Regression Results
==============================================================================
Dep. Variable: INFRATE R-squared: 0.010
Model: OLS Adj. R-squared: 0.005
Method: Least Squares F-statistic: 2.062
Date: Mon, 17 Oct 2022 Prob (F-statistic): 0.152
Time: 22:32:49 Log-Likelihood: -331.00
No. Observations: 215 AIC: 666.0
Df Residuals: 213 BIC: 672.7
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 2.4887 0.431 5.768 0.000 1.638 3.339
UNRATE 0.1064 0.074 1.436 0.152 -0.040 0.253
==============================================================================
Omnibus: 9.557 Durbin-Watson: 0.059
Prob(Omnibus): 0.008 Jarque-Bera (JB): 10.056
Skew: 0.529 Prob(JB): 0.00655
Kurtosis: 2.942 Cond. No. 33.4
==============================================================================
In Period 3, the intercept of the regression is 2.4887 and the R-squared is 0.010. The R-squared is the proportion of the variation in the dependent variable that is predictable from the independent variable. Due to the R-squared being small, it is not the total determinant of inflation. This means that around 1% of the variability observed in the target variable is explained by this regression model. Additionally, unemployment is not statistically significant and as unemployment increases by 1%, the inflation rate increases by 0.1064 percentage points.
Period 4 (2003 - 2022) results:
OLS Regression Results
==============================================================================
Dep. Variable: INFRATE R-squared: 0.147
Model: OLS Adj. R-squared: 0.144
Method: Least Squares F-statistic: 40.45
Date: Mon, 17 Oct 2022 Prob (F-statistic): 1.05e-09
Time: 22:40:33 Log-Likelihood: -458.12
No. Observations: 236 AIC: 920.2
Df Residuals: 234 BIC: 927.2
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 4.5071 0.346 13.018 0.000 3.825 5.189
UNRATE -0.3454 0.054 -6.360 0.000 -0.452 -0.238
==============================================================================
Omnibus: 41.668 Durbin-Watson: 0.084
Prob(Omnibus): 0.000 Jarque-Bera (JB): 61.971
Skew: 1.038 Prob(JB): 3.49e-14
Kurtosis: 4.412 Cond. No. 20.5
==============================================================================
In Period 4, the intercept of the regression is 4.5071 and the R-squared is 0.147. The R-squared is the proportion of the variation in the dependent variable that is predictable from the independent variable. This means that 14.7% of the variability observed in the target variable is explained by this regression model. Additionally, unemployment is statistically significant and as unemployment increases by 1%, inflation decreases by 0.3454 percentage points.
Overall (1948 - 2022) results:
OLS Regression Results
==============================================================================
Dep. Variable: INFRATE R-squared: 0.011
Model: OLS Adj. R-squared: 0.009
Method: Least Squares F-statistic: 8.767
Date: Mon, 17 Oct 2022 Prob (F-statistic): 0.00316
Time: 22:44:03 Log-Likelihood: -2008.1
No. Observations: 819 AIC: 4020.
Df Residuals: 817 BIC: 4030.
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 2.5340 0.363 6.971 0.000 1.821 3.248
UNRATE 0.1759 0.059 2.961 0.003 0.059 0.293
==============================================================================
Omnibus: 214.844 Durbin-Watson: 0.020
Prob(Omnibus): 0.000 Jarque-Bera (JB): 469.262
Skew: 1.439 Prob(JB): 1.26e-102
Kurtosis: 5.340 Cond. No. 23.2
==============================================================================
Overall, the intercept of the regression is 2.5340 and the R-squared is 0.011. The R-squared is the proportion of the variation in the dependent variable that is predictable from the independent variable. In this case, unemployment does have an impact on inflation, but due to the R-squared being small, it is not the total determinant of inflation. This means that 1.1% of the variability observed in the target variable is explained by this regression model. Additionally, unemployment is statistically significant and as unemployment increases by 1%, inflation increases by 0.1759 percentage points.
Other Variables
In our next analysis, we will only look at the years 1993 - 2022 since the data available for SPY is between this time period.
Python Code:
uni_mod = smf.ols(formula="INFRATE ~ UNRATE + DFF + SPY", data = other_df)
uni_result = uni_mod.fit()
Output:
OLS Regression Results
==============================================================================
Dep. Variable: INFRATE R-squared: 0.234
Model: OLS Adj. R-squared: 0.228
Method: Least Squares F-statistic: 35.86
Date: Mon, 17 Oct 2022 Prob (F-statistic): 3.03e-20
Time: 23:10:04 Log-Likelihood: -610.30
No. Observations: 356 AIC: 1229.
Df Residuals: 352 BIC: 1244.
Df Model: 3
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 1.2686 0.517 2.456 0.015 0.253 2.285
UNRATE -0.0650 0.056 -1.151 0.250 -0.176 0.046
DFF 0.2578 0.050 5.178 0.000 0.160 0.356
SPY 0.0070 0.001 7.090 0.000 0.005 0.009
==============================================================================
Omnibus: 36.171 Durbin-Watson: 0.091
Prob(Omnibus): 0.000 Jarque-Bera (JB): 50.053
Skew: 0.710 Prob(JB): 1.35e-11
Kurtosis: 4.165 Cond. No. 1.22e+03
==============================================================================
From this analysis, we can see that the intercept of the regression is 1.2686 and the R-squared is 0.234. This means that 23.4% of the variability observed in the target variable is explained by this regression model. From our independent variables, we can see that the unemployment rate is not statistically significant while the federal funds rate and S&P 500 are statistically significant. Thus, as the federal funds rate increases by 1%, inflation increases by 0.2578 percentage points. This makes sense because the Federal Reserve increases the rate to combat inflation. High fed funds rate is correlated to high inflation etc. Additionally, as the price of the S&P 500 Index increase by 1 percentage point, inflation increases by 0.007 percentage points. It shows that there is some impact from the S&P 500, but it isn't large.
Possible Explanations
Why are we seeing low unemployment with high inflation?
- Job Availability
- Anyone who wants a job can get one, as there is a large group of people that simply do not want to work.
- Global Pandemic
- Despite an initial short increase in job loss, many companies have now transitioned to a work-from-home model, limiting job cuts.