businessanalyticsproject_relationship between inflation, unemployment & fed rate

INFLATION, UNEMPLOYMENT & THE FEDERAL FUNDS RATE-WHAT ARE THE KEY ELEMENTS?

INFLATION, UNEMPLOYMENT, & THE FEDERAL FUNDS RATE

WHAT ARE THE KEY ELEMENTS?

By: Jonel Jakupi, Marcus Jones, and Paul Torres

December 6, 2015


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Table of Contents

Abstract………………………………………………………………………………………..3

Statement of the Problem…………………………………………………………………..5

Background Information…….………………………………………………………….......6

Methodology…………………………………………………………………………………11

Statistical Analysis…………………………………………………………………………12

Conclusion…………………………………………………………………………………..18

References…………………………………………………………………………………..20

Appendix…………………………………………………………………………….………21


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Abstract

Economists have long studied the relationship between unemployment and inflation.

A.W. Phillips was the first economist to find a correlation between the two. He studied

wage inflation and unemployment rates in the United Kingdom from 1861 to 1957 and

found a consistent inverse relationship between the two (Fitgerald, Holtemeyer, &

Nicolini, 2013). Hence, when unemployment was high, wages increased slowly, and

while unemployment was low, wages grew rapidly. Data in the US during the 1960s

showed correlations similar to the research conducted by Phillips in the UK.

However, research over the past 40 years has found that the Phillips curve is not as

stable in the United States anymore. The statistical analysis of current employment and

future inflation has produced various results that depended on the time it was analyzed.

For this reason, economists have considered other variables in their research that could

affect inflation. The study found that the national data varies primarily due to the

monetary policy used by the Federal Reserve. Therefore, we decided to test the

correlation between the Fed funds rate and the inflation rate as well. This study is

intended to test the correlation of the unemployment rate, the Fed fund rate, and the

inflation rate over the past ten years, from 2005 to 2015.

We tested to see if there was a significant correlation between these three variables; we

used a simple correlation and regression analysis. We compared the results of the

other studies that we had researched and include those findings in this paper as

described in detail in the background section.


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The results of the correlation and regression analysis for the unemployment rate versus

the inflation rate and the Fed rate versus the inflation rate show a moderate correlation

in both cases, which is consistent with the studies of the national data over the past 40

years. As expected, unemployment’s correlation with inflation is negative, while the Fed

rate’s correlation is positive.

We found a strong negative correlation between the unemployment rates and the Fed

rates, which is a good indicator of the Federal Government changing interest rates in

the opposite direction of the unemployment rates to control inflation.


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Statement of the Problem

The common theory among economists is that when unemployment is low, interest

rates should be high and vice versa. According to the U.S. Department of Labor, the

current unemployment rate is at 5.1% and current inflation is at 0% for September 2015.

During this time, the Federal funds rate is at .14%. The unemployment rate of 5.1% is

considered to be close to full employment. According to economic theory, inflation

should be rearing its ugly head and we have yet to see any signs of this being the case.

These three statistics appear to be working in unison with each other which is opposite

to the theory.

The study will attempt to support this theory or reject it based on analyzing various

statistics related to inflation, unemployment, and the federal funds rate. The U.S. labor

market has experienced several varying levels of unemployment over the past ten years

with little to no inflation within the market. The federal funds rate has remained

relatively flat over this same period. This study will attempt to decipher the key statistical

elements as well as determine if there is a relationship between inflation, the federal

funds rate and unemployment. The results of this analysis will help us better

understand where inflation and interest rates are headed.


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Background Information

History of the Problem

Economic theory has shown that there is an inverse relationship between the

unemployment rate, the federal funds rate, and the inflation rate. This theory has not

held up over the past several years as we have seen little to no inflation, while the

unemployment rate is currently at 5.1%. Another key indicator is the federal funds rate,

which saw a high of 5.02% in 2007 but has remained relatively flat since 2008 as shown

in Table 1. We will analyze data over the past ten years to determine if a relationship

exists between these three key economic indicators as the theory indicates. Since 2005,

we have experienced the monthly unemployment rates as high as 10% and as low as

4.4%. During this same time, inflation and the federal funds rate have remained

relatively flat.

While unemployment has reached, what some consider full employment, inflation has

been held relatively low. The U.S. monetary policy could be the cause for this.

According to Athanasios Orphanides in an article titled Fear of liftoff: uncertainty, rules,

and discretion in monetary policy normalization, “the Federal Reserve’s muddled

mandate to attain simultaneous the incompatible goals of maximum employment and

price stability invites short term oriented discretionary policymaking inconsistent with the

systematic approach needed for monetary policy to contribute best to the economy over

time”.


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This report will study these three essential elements that make up today’s economy.

The relationship of unemployment, inflation, and the federal fund rate will be examined

in an attempt to determine if a relationship exists among the three.

Secondary Research

Economists around the world have long studied the relationship between unemployment

and inflation; A.W. Phillips became famous for exploring this relationship. The study

conducted by Phillips found that the unemployment rate and the inflation rate have an

inverse relationship with each other. Hence, when unemployment is high, inflation

tends to be low. Although he was not the first economist to study this relationship

between unemployment and inflation, A. W. Phillips was the first to develop a curve,

which was named after him: The Phillips curve. Phillips studied the wage rates, inflation

rates, and unemployment rates, in the United Kingdom from 1861 through 1957 and

found that an inverse relationship between unemployment and inflation was consistent.

In other words, Phillips found that when unemployment was high, wages increased

slowly, and when unemployment was low, wages increased rapidly (Fitgerald,

Holtemeyer, & Nicolini, 2013). Other economists have used this curve for their studies

and have found similar trade-offs. Although, they primarily tested price inflation, rather

than wages, against unemployment.

Figure 1 shows the Phillips curve depicting data in the United States from 1961 to 1969.

This data suggests that the US had a similar tradeoff to the research Phillips conducted

in the UK. The close relationship between the curve and the data have encouraged

many economists to use the Phillips curve for policy options. However, research over


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the past 40 years in the United States have found that the Phillips curve is not as stable

as it was in the past (Fitgerald, Holtemeyer, & Nicolini, 2013). The statistical analysis of

current employment and future inflation has produced various results depending on the

time it was analyzed.

For this reason, the Federal Reserve Bank of Minneapolis conducted a research study

to examine the Phillips curve in the United States. Their main purpose was to

investigate the stability of the Phillips curve using national and regional data. The

research found that national data varies primarily due to the monetary policy employed

by the Federal Reserve. The Central Bank has been able to control inflation by

changing interest rates, regardless of the unemployment level. The bank’s primary

function is to maintain price stability despite changes in the economy, including

unemployment. The Federal Reserve has been successful in keeping inflation at 1.9%

per year. Therefore, we are using a third variable, the federal funds rate, to study the

correlation between inflation and monetary policy.

In contrast, the study found that the Phillips curve is very stable at the regional level.

The US economy is made of several regions and only one central bank. The central

bank does not interfere with regional activity. All regions have their own disturbances,

which effect inflation and unemployment. The central bank does not intervene on a

regional level, but on a national level, which is composed of the average data coming

from all regions. Hence, in the absence of the Fed trying to regulate regional inflation,

the study finds that estimates are stable for regional data. The results show that a 1%

point reduction in the unemployment rate translates to a 0.3% point increase in the

inflation rate for the following year (Fitgerald, Holtemeyer, & Nicolini, 2013).


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Another study made by Cornell University researched the connection between inflation

and unemployment in the United States. They acknowledged the inverse correlation

between inflation and unemployment in the 1960s, shown in the Phillips curve in Figure

1. They explained the downward sloping line on the premise of excess demand. When

demand exceeds economic capacity, the unemployment rate will tend to fall, and vice

versa. Similarly, demand in excess of supply will tend to push up both wages and

prices. During times when an increase in prices will reduce real wages, the demand for

labor will increase; therefore, reducing unemployment (Cashell, 2004).

Other economists’ have contested this view. They argued that fiscal policy could be

manipulated temporarily to realize a wanted combination of unemployment and inflation.

They argued that when prices increase and workers are suffering a reduction in real

wages, the trade-off will work until the workers realize that they have lost their buying

power. Eventually, they will adjust their wage demands to reflect the higher prices. In

the long run, the unemployment rate will be represented by the supply and demand for

labor. This level is believed to be the “natural rate” of unemployment, which is the rate

of unemployment consistent with a stable rate of inflation. In other words, it is the level

of unemployment when the people have caught onto the rise in prices (inflation).

Economists believe that the natural rate of unemployment is somewhere between 5 and

6% (Cashell, 2004).

In contrast, in the1990’s the unemployment rate was well below 5% for some time.

According to the natural rate theory, when unemployment falls below the natural rate,

inflation should accelerate. However, inflation fell thus suggesting that other factors,

such as oil prices, interest rates, and imports, all affected inflation.


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Since 2007, the Fed has handled monetary policy with a hands-on approach in an

attempt to foster an economic recovery. Past recessions have seen the Fed ease up on

economic policy after seven months to three years of the recession being over. The last

recession lasted from December 2007 through June of 2009, and the Fed has yet to

allow the market to dictate what the inflation rate truly is. This over coddling approach

has its downsides and only time will tell if the current monetary policy will have a bubble

effect on inflation when the Fed eases its policies (Orphanides, 2015).

According to an article published by Cornell University titled, Inflation and

Unemployment: What is the connection?, Brian W. Cashell (2004) stated that inflation

tends to be slow to respond to those changes in policy which affect it. Many economists

view the natural rate of unemployment as a way of measuring the tightness in the labor

market, which looks to have a future impact on the rate of inflation. The U.S. labor

market is approaching full employment, if it has not done so already, which is an

indication that the economy is heating up. It is believed that when full employment is

considered the price of goods and services will increase because the labor rate to

produce those goods and services will also increase. This short term effect is what

causes inflation, but we have yet to see those results. In an article published in the

Wall Street Journal titled, Fed’s rate Dilemma: Job Gains vs. Low Inflation, Jon

Hilsenrath stated that the stronger job market gives officials reason to consider raising

short-term interest rates to prevent the economy from overheating, but little wage

growth and inflation suggest such overheating isn’t near and give them cause to wait.

The four literary sources cited, Fear of liftoff: uncertainty, rules, and discretion in

monetary policy normalization, Inflation and Unemployment: What is the connection?,


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Is There a Stable Phillips Curve After All?, and Fed’s rate Dilemma: Job Gains vs. Low

Inflation, all have research and varying hypothesis as to what causes inflation. This

study will focus on the changes in the unemployment rate, the changes in the federal

funds rate and the changes in the inflation rates and will test to see if a relationship

exists among the three.

Methodology

We collected data on inflation, unemployment, and the Fed interest rates for ten years,

from 2005 to 2015. We used the convenience method of data collection, which is a

non-random sampling method; we chose this method because the data was readily

available. We collected the data from the Bureau of Labor Statistics and Board of

Governors of the Federal Reserve System, www.federalreserve.gov and www.dol.gov,

which are both reliable sources of the data used in this study. Both of our data sources

use a finite sampling distribution. We used a parametric statistical test since the data

being used was both continuous and ratio data.

We are using a simple linear correlation and regression analysis to measure the

relationship between these three variables, which, as described above, are the inflation

rate, the unemployment rate, and the Fed funds rates. We decided to use a linear

correlation, rather than a multiple regression test, to be able to better understand the

correlation between the variables from one to the other. We used Minitab and Excel

software to perform all calculations, and the results are included in the Appendix

section. The results of the tests will show if the correlation between the variables is

significant. The hypothesis testing being conducted is non-directional for test number

http://www.federalreserve.gov/

http://www.dol.gov/


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two and directional for the other two tests. We performed all three tests to measure the

correlations as described below:

Test the correlation between the unemployment rates and the inflation rates. The

independent variable (x) is the unemployment rate, and the dependent variable (y) is

the inflation rate.

Test the correlation between the unemployment rates and the federal funds rates.

The independent variable (x) is the unemployment rate and the dependent variable

(y) is the federal funds rate.

Test correlation between the federal funds rate and the inflation rates. The

independent variable (x) is the federal funds rate and the dependent variable (y) is

the inflation rate.

Statistical Analysis

Test 1: Correlation Between the Unemployment Rate Average and the Inflation

Rate Average

Step 1: Analyze scatter diagram

After reviewing the scatter plot of inflation versus unemployment, we find that there is a negative linear correlation.

Step 2: Calculate correlation coefficient

r² = .3679; r = -0.6065; 1-r² = .6321

r² is the amount of variation explained by inflation (y). The fact that it is lower


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than .50 means that there is more error than we can explain. We aspire to be > .500. The r value (-0.6065) indicates that there is a relatively moderate correlation between unemployment and inflation.

Step 3: Create regression equation

ŷ= a + b(x)

ŷ= 5.002 + (-.3915)(x); Where y is the inflation rate and x is the unemployment

rate

Inflation rate = 5.002 + (-.3915)(Unemployment rate)

The slope of the line is -.3915, which means that for every unit decrease in

unemployment (x), inflation (y) is a predicted to decrease by -.3915. The slope is

smaller than one which mean that unemployment (x) is growing faster than

inflation (y).

Step 4: Calculate the standard error of the estimate

s = 1.0620

The s value indicates the error between the true y value and the predicted y

value. Since s = 1.0620, this indicates that the observations are close to the fitted

line.


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Step 5: Test the hypothesis for a significant correlation.

The hypotheses for Test 1 are as follows: Ho: β ≥ 0; Ha: β < 0. Using a 95%

confidence interval (α = .05). The data indicated a calculated t-score of -2.16 we

determine the critical value to be -1.86. The decision rule is to reject Ho if the

-2.16 < -1.86. The decision for Test 1 is to reject the Ho. Therefore, there is a

significant linear correlation between unemployment and inflation.

Test 2: Correlation Between the Federal Fund Rate Average and the

Unemployment Rate


After reviewing the scatter plot of the federal fund rate versus the unemployment

rate, we find that there is a negative linear correlation.

Step 2: Calculate correlation coefficient

r² = .6972; r = -0.835; 1-r² = .3028

r² is the amount of variation that is explained by Fed rate (y). The fact that it is

lower than .50 means that there is more error than we can explain. We aspire to

be > .500. The r value (-0.835) indicates that there is a relatively strong

correlation between unemployment and Fed rate.



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ŷ= a + b(x)

ŷ = 7.7636 + (-.8878)(x); where y is the federal fund rate and x is the

unemployment rate.

Federal fund rate = 7.7636 + (-.8878)(Unemployment)

The slope of the line is -.8878, which means that for every unit decrease in

unemployment (x), Fed rate (y) is a predicted to decrease by -.8878. The slope is

smaller than one which mean that the unemployment (x) is growing faster than

the Fed rate (y).


s = 1.2111


value. Since s = 1.2111, this shows that the observations are close to the fitted

line.

Step 5: Test the hypothesis for a significant correlation.

The hypotheses for Test 2 are as follows: Ho: β = 0; Ha: β ≠ 0. Using a 95%

confidence interval (α = .05). The data indicated a calculated t-score of -4.29 we

determine the critical value to be +/-2.306. The decision rule is to reject Ho if the

-4.29 < -2.306 or -4.29 > 2.306. The decision for Test 2 is to reject the Ho.

Therefore, there is a significant linear correlation between the unemployment rate

and the federal funds rate.


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Test 3 Correlation Between the Federal Funds Rate Average and the Inflation Rate

Average


After reviewing the scatter plot of the federal funds rate versus the inflation rate, we find

that there is a positive linear correlation.

Step 2: Calculate the correlation coefficient

r² = .3090; r = 0.556; 1-r² = .6910

r² is the amount of variation that explained by inflation (y). The fact that is lower

than .50 means that there is more error than we can explain. We aspire to be >

.500. The r value (0.556) indicates that there is a relatively moderate correlation

between Fed rate and inflation.


ŷ = a + b(x)

ŷ = 1.7431 +.3374(x); where y is the inflation rate and x is the federal funds rate

Inflation rate = 1.7431 + .3374(Fed rate)

The slope of the line is .3374, which means that for every unit increase in the Fed

rate (x), inflation (y) is a predicted to increases by .3374. The slope is smaller

than one which mean that Fed rate (x) is growing faster than inflation (y).



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s = 1.110


value. Since s = 1.110, this indicates that the observations are close to the fitted

line.

Step 5: Test the hypothesis for a significant correlation

The hypotheses for Test 1 are as follows: Ho: β ≤ 0; Ha: β > 0. Using a 95%

confidence interval (α = .05). The data indicated a calculated t-score of 1.89 we

determine the critical value to be 1.86. The decision rule is to reject Ho if the 1.89

> 1.86. The decision for Test 3 is to reject the Ho. Therefore, there is a significant

linear correlation between the Fed rate and inflation.

In all three test, we reject Ho, which indicates a significant linear correlation between the

unemployment rate average, inflation, and the Fed rate.


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Conclusion

In this study, we were initially interested in the correlation between unemployment and

inflation. Economists have examined this relationship for many years, and William

Phillips found a correlation between the two. Phillips studied these two variables in the

United Kingdom from 1861 to 1957 and found a consistent inverse relationship between

the two. Studies in the US during the 1960’s show a similar correlation. However,

research over the past 40 years in the United States has shown that this correlation is

not as stable anymore. The research, which we analyzed in this study, found that

national inflation data is linked to the monetary policy used by the Federal Reserve.

Hence, we decided to test the correlation of the Fed rates to inflation as well. We

examined the correlation of unemployment, Fed interest rates, and inflation over the last

ten years, from 2005 to 2015.

The results of the correlation and regression analysis for unemployment versus inflation

shows a moderate negative relation of the two variables while the analysis of the Fed

rate versus the inflation rate shows a moderate positive correlation. We were

anticipating such a result, as they are consistent with the studies of the national data

over the past 40 years. We found a strong negative correlation between the

unemployment rates and the Fed rates, which indicates the Federal Government

modifies the Fed rates in the opposite direction of unemployment rates to keep inflation

under control.


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One of the limits of this study was the exclusion of a multiple linear regression test

which would have helped us identify the explained variation. Given the time, a future

study of this topic would undoubtedly include a multiple regression analysis.


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References

Fitgerald, T., Holtemeyer, B., & Nicolini, J.B. (2013). Is there a Stable Phillips Curve After All? Region (10453369), 27(4), 4-11.

Cashell, B.W. (2004). Inflation and unemployment: What is the connection? Washington, DC: Congressional Research Service.

Orphanides, A. (2015, Fall). Fear of liftoff: uncertainty, rules, and discretion in monetary policy normalization. Federal Reserve Bank of St. Louis Review, 97(3), 173+.

Hilsenrath, J. (2015, February 7). Fed’s Rate Dilemma: Job Gains vs. Low Inflation. Wall Street Journal (Online). p. 1.

U.S. Bureau of Labor Statistics. (2015, October 2). Retrieved October 17, 2015, from http://www.bls.gov/

Economic Research and Data. (2015, October 2). Retrieved October 17 2015, from http://www.federalreserve.gov/

http://www.bls.gov/

http://www.federalreserve.gov/


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Appendix

Year Unemployment Average Inflation Average FED Rate

2005 5.1 3.4 3.22

2006 4.6 3.2 4.97

2007 4.6 2.8 5.02

2008 5.8 3.8 1.92

2009 9.3 -0.4 0.16

2010 9.6 1.6 0.18

2011 8.9 3.2 0.1

2012 8.1 2.1 0.14

2013 7.4 1.5 0.11

2014 6.2 1.6 0.09

Table 1: Raw data


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-2.0

0.0

2.0

4.0

6.0

8.0

10.0

12.0

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

Unemployment VS Inflation VS FED Rate

Unemployment Average Inflation Average FED Rate

-2.0

0.0

2.0

4.0

6.0

8.0

10.0

12.0

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

Unemployment VS Inflation

Unemployment Average Inflation Average


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0.0

2.0

4.0

6.0

8.0

10.0

12.0

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

Unemployment VS FED Rate

Unemployment Average FED Rate

-1

0

1

2

3

4

5

6

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

Inflation VS FED Rate

Inflation Average FED Rate


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Unemployment vs Inflation

Regression Statistics Values

Multiple R 0.606561462

R Square 0.367916807

Adjusted R Square 0.288906408

Standard Error 1.062051062

Observations 10

ANOVA

df SS MS F Significance F

Regression 1 5.252380335 5.252380335 4.656561806 0.06299451

Residual 8 9.023619665 1.127952458

Total 9 14.276

Coefficients Standard Error t Stat P-value

Intercept 5.001709345 1.305222024 3.832075505 0.005003147

Unemployment Average-0.391472038 0.181412856 -2.157906811 0.062994512


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Unemployment vs Fed Rate

Regression Statistics


R Square 0.69715278



Observations 10

ANOVA


Regression 1 27.0154301 27.0154301 18.4159598 0.002646416

Residual 8 11.7356599 1.466957487

Total 9 38.75109


Intercept 7.763620889 1.488496301 5.215747519 0.00080676

Unemployment Average -0.887827528 0.206886155 -4.291382038 0.00264642


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Fed rate vs Inflation

Regression Statistics


R Square 0.309081241



Observations 10

ANOVA


Regression 1 4.41244379 4.41244379 3.578785336 0.095166606

Residual 8 9.86355621 1.232944526

Total 9 14.276


Intercept 1.743131638 0.451477897 3.860945682 0.004802487

FED Rate 0.337440831 0.178373284 1.891767781 0.095166606

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