Dividend Policy and Dividend Decision Theories.pptx
United States Unemployment Rate Predictor Model
1. 1
Predictor Model for the United
States Unemployment Rate
Veshal Arul Prakash | Sloane Castleman | Nathan Hwang
STA375H
May 7, 2018
2. 2
SUMMARY
One of many factors that determine the overall quality of life in the United States is the
unemployment rate. The unemployment rate is an important metric to consider because
unemployment can significantly transform the lifestyle of a household. Our goal for this project
was to identify the best predictor model for unemployment rate. The United States government or
an individual could use this simple predictor model to determine a forecasted unemployment rate
one year into the future. With the ability to predict the unemployment rate one year in advance,
the United States government could better prepare for and pass fiscal policies necessary to control
the economy, and thus, unemployment too. Individuals could use it to plan their personal financials
and lives. We collected data on the United States unemployment rate and other prospective
explanatory variables from 1990 to 2016. Through our research and data analysis using individual
regressions between each variable and the unemployment rate, we realized that the following
individual explanatory variables are statistically significant according to the p-value: Federal
Funds Interest Rate, Net Income from Abroad, GDP Growth, GDP Per Capita Growth, Exports of
Goods and Services, General Government Final Consumption Expenditure, and General
Government Debt. To find the best predictor model leveraging backwards regression, we ran
approximately seventy different models by using various combinations of at least four of the seven
explanatory variables. Thus, the best predictor model for the United States unemployment rate is
𝑌𝑈𝑅 = −0.2239 − 0.3006𝑋 𝐹𝐹𝐼𝑅 − 2.0133𝑋 𝑁𝐼𝐴 + 0.5168𝑋 𝐸𝐺𝑆 + 1.6161𝑋 𝐺𝐹𝐶𝐸. Lastly, we
confirmed that our model satisfied the regression assumptions. While we acknowledge that our
model has limitations, it can decently approximate the unemployment rate a year from the present.
INTRODUCTION
Our initial idea for this project was to seek a prediction for the overall quality of life in the
United States based on macroeconomic metrics and indicators. In further honing our idea, we
decided to use the unemployment rate as our measure that was representative of the overall quality
of life for people in the United States. Having experienced the financial crisis of 2008, our group
has seen the effects of unemployment through close friends and family. The high rates of
unemployment at the time introduced new difficulties for many families in the United States. Our
group experienced first-hand how such an event had a significant impact on not only our overall
quality of life but also how we go about our day-to-day lives. Our group believed that exploring
this important macroeconomic indicator could produce thought-provoking results and prove useful
in predicting future economic events.
As defined by “Focus Economics”, “unemployment rate” is the percent of unemployed
workers in the total labor force. The unemployment rate “provides insights into the economy’s
spare capacity and unused resources”, as it is “cyclical” and maintains an inverse relationship with
3. 3
the growth of the economy. Although there is no absolute measure for overall quality of life, we
felt that unemployment rate was the most comprehensive as a lower unemployment rate indicates
security, prosperity, and happiness for society.
The unemployment rate is a closely watched economic indicator that directly affects
people’s quality of life – a high unemployment rate is a universal sign of financial distress and a
struggling economy. With that said, we understand that the other end of the extreme with 0%
unemployment rate is also not good for the economy, as the natural unemployment rate is between
4.5% and 5%. We believe the unemployment rate is an indicator that most strongly and directly
impacts the people in the country’s financial security. Unemployment also has other qualitative
adverse effects on an individual besides an absence of steady income. Consequently, a lack of
income is closely associated with poor mental health, higher crime and suicide rates, and higher
rates of drug abuse and alcoholism.
We sought to determine a relationship, if any, between various macroeconomic indicators
and the unemployment rate of the United States from 1990 to 2016, attempting to find a predictor
model for the unemployment rate based on the metrics from the previous year. We felt that
identifying statistically significant relationships between the economic metrics from the previous
year and the unemployment rate of the current year could, in theory, be useful in preparing fiscal
policy. Understanding what affects the unemployment rate in the short term (one year) can help
predict the unemployment rate, allow the government to keep a strong pulse on the economic state
of the country, and enable the government and individuals to better prepare for circumstances
driven by the unemployment rate, especially when it is high.
We chose to analyze eleven economic metrics of the United States to determine which ones
might predict the unemployment rate most accurately. The selected explanatory variables are
among the most widely used metrics to understand the state of the economy and government
spending, which is the cornerstone of our logical reasoning for selecting them. Therefore, we
hypothesized that these metrics would be the best measures of the future (short-term) economic
state, including the unemployment rate. The eleven explanatory variables we looked at are the
following:
• Inflation measured by the Consumer Price Index → CPI
• Federal Funds Rate → FFIR
• Net Income from Abroad (% of GDP) → NIA
• GDP Growth (Annual %) → GDP Growth
• GDP Per Capita Growth (Annual %) → GDP Per Capita Growth
• Trade (% of GDP) → Trade
• Imports of Goods and Services (Annual % Growth) → IGS
• Exports of Goods and Services (% of GDP) → EGS
4. 4
• Household Final Consumption Expenditure, etc. (% of GDP) → HFCE
• General Government Final Consumption Expenditure (% of GDP) → GFCE
• Central Government Debt, total (% of GDP) → CGD
Initially, based on prior knowledge and exploring the topic through news articles, we
believed that the Consumer Price Index (CPI) and Federal Funds Interest Rate would be the best
predictors of the unemployment rate. Our reasoning behind the CPI and interest rates is that, when
inflation is growing, that is a sign of growth in economic activity and rapid economic development.
High levels of economic activity and economic development typically creates more jobs, which
then decreases the unemployment rate. The Federal Reserve uses interest rate hikes throughout the
year to slow down economic activity and limit inflation, so we believe that if the interest rate
increased in the past year, unemployment will also increase due to subdued economic activity.
This hypothesis was rigorously tested, and our findings can be found in detail in the analysis and
results section. In addition, the paper will cover which explanatory variables are the most
statistically significant regarding impacting the unemployment rate, and how those factors would
play a role in the predictor model.
DATA COLLECTION
Our data sets were extracted from the World Bank online database. The original
spreadsheet displayed every country in the world along with numerous economic metrics such as
GDP, net savings, imports & exports, etc. We filtered the dataset spreadsheet to remain with just
the United States data for the above-mentioned eleven explanatory variables and the
unemployment rate. We evaluated the data with a time frame ranging from the beginning of 1990
to the beginning of 2016 for several reasons.
5. 5
Rationale
Technical
1. 1990 was the first year with reliable data available for all the explanatory variables.
On the other hand, 2016 was the final year with reliable data available for all the
explanatory variables.
2. 1990 – 2016 provides 27 years of data, which we believe was sufficient to build a
valid predictor model for unemployment rate. This accounted for potential financial
or world crises that are associated with the macroeconomic ebbs and flows. The
longer period allowed us to identify outliers in our data that may skew the
relationships present in the dataset.
Contextual
1. The early 1990’s marked the conclusion of the United States-Soviet Union Cold
War. The reason why this is significant is because both countries invested large
amounts of capital to compete against each other which impacted various sectors of
the economy.
2. The early 1990’s marked the rise of the Internet Age, and ever since, the lifestyle of
Americans has significantly transformed. The way people find information and
communicate information drastically changed. The landscape of the economy and
available professional opportunities replaced parts of what existed before.
By examining the data and running histograms and boxplots on each of our explanatory
variables, we found that 2009 was a significant year with outliers in some of the explanatory
variables due to the financial crisis beginning in 2008. 2009 was the only year in which the CPI
was negative. Percent GDP growth was -.0277 in 2009, and the next closest case has GDP growth
at -.0029 in 2008. Percent GDP per capita growth was -.036 in 2009, and the next closest -.012 in
2008. Lastly, the percent growth of imported goods and services was -.137 in 2009 and the next
closest was -.028 in 2001. We believe these outliers will not skew our data dramatically. First,
these outliers only represent a year’s worth of data in a data set comprised of 27 data points.
Second, only a few explanatory variables have outliers. Finally, these outliers in 2009 helps build
a more complete and accurate story about their effect on the unemployment rate. In 2009, the
unemployment rate in the United States was relatively high.
Before running regressions and analyzing the data, we lagged several of the explanatory
variables by one year: CPI, interest rate, net income from abroad, trade, exports of goods and
services, household final consumption expenditure, general government final consumption
expenditure, and central government debt. However, GDP growth, GDP per capita growth, and
imports of goods and services were not lagged because these variables already accounted for the
change in the metric from the past year. We chose to lag the data by one year because we wanted
to get a predictor model of the unemployment rate in a given year based on the metrics from the
previous year. The goal was to create a short-term, more immediate predictor model for
unemployment rate. Also, considering that the average length of the United States business cycle
6. 6
after World War II is 56 months, which is almost five years, a one-year lag seemed reasonable to
assume that relationships would exist between the explanatory variables and the unemployment
rate.
ANALYSIS AND RESULTS
Elimination of Statistically Insignificant Explanatory Variables
After introducing a lag into the data set to help with creating a predictor function, our initial
goal with a multivariable regression was to discover a model with as few explanatory variables as
possible, where all the explanatory variables are significant. There are different methods –
backward regression, forward regression, stepwise regression, and best subsets regression. With
eleven initially selected prospective variables, a backward regression was the most practical
option. The backward regression process starts with several variables and helps eliminate variables
until all remaining variables are significant. The p-value was used to determine whether each
explanatory variable was statistically significant in predicting the unemployment rate a year from
now.
We ran single-variable linear regressions for each of the eleven initial prospective
explanatory variables. Of those eleven prospective explanatory variables, any that had a p-value
greater than 0.05 was eliminated from further continuing in the process for discovering the
predictor model due to statistical insignificance. Any of the prospective explanatory variables with
a p-value less than 0.05 were confirmed as statistically significant explanatory variables.
As displayed in the table below, only seven of the eleven prospective explanatory variables
were statistically significant. Federal funds interest rate, net income from abroad, GDP growth,
GDP per capita growth, exports of goods and services, general government final consumption
expenditure, and central government debt are considered statistically significant because the p-
value was less than 0.05. In contrast, the consumer price index to track inflation, trade, imports of
goods and services, and household final consumption expenditure are considered statistically
insignificant because the p-value is greater than 0.05.
7. 7
Variable Y-Intercept Coefficients Std.
Error
t-value p-value Statistically
Significant?
Consumer Price
Index
0.062568 -0.329428 0.24668
9
-1.335 0.194 No
Federal Funds
Interest Rate
0.065775 -0.374297 0.09868
0
-3.793 0.000841 Yes
Net Income from
Abroad (% of
GDP)
0.03727 2.28428 0.53561 4.265 0.00025 Yes
GDP Growth
(Annual %)
0.065154 -0.444310 0.16053
8
-2.768 0.0105 Yes
GDP Per Capita
Growth (Annual
%)
0.060641 -0.444886 0.16967
6
-2.622 0.0147 Yes
Trade (% of GDP) 0.02543 0.11649 0.08016 1.453 0.159 No
Imports of Goods
and Services
(Annual %
Growth)
0.058746 -0.081839 0.04783
0
-1.711 0.0995 No
Exports of Goods
and Services (% of
GDP)
0.01004 0.40441 0.18631 2.171 0.0397 Yes
Household Final
Consumption
Expenditure (% of
GDP)
-0.1755 0.3450 0.1772 1.947 0.0628 No
General
Government Final
Consumption
Expenditure (% of
GDP)
-0.17491 1.50739 0.20038 7.523 7.08e-08 Yes
Central
Government Debt
(% of GDP)
0.03299 0.03555 0.01092 3.256 0.00324 Yes
Explanation of the Independent Variables
Our group was surprised by some of the results we returned from running regressions on
each variable individually against the unemployment rate. To justify and seek an explanation for
our results, we have provided qualitative or potential regression factors that could have affected
our results:
8. 8
Consumer Price Index: The consumer price index is the weighted average of prices of a basket
of consumer goods and services. Based on our regression of just the CPI lagged by a year against
the unemployment rate, we found the previous year’s CPI to be statistically insignificant with a
high p-value. This was our most surprising result, as we had believed that the CPI would be a
strong predictor of unemployment rate. We believe that this could be statistically insignificant in
our case because our data is less than thirty years and thus may not completely reflect the different
cyclical fluctuations in the economy. Another reason our data disconfirmed CPI could be the
amount that we chose to lag is because the Federal Reserve typically raises interest rates to control
growing inflation. Lagging inflation by one year may not capture the effect of inflation on
unemployment because this effect is less immediate than some of the other explanatory variables
and could require more time for fiscal policy to play out in the actual economy.
Federal Funds Interest Rate: The Federal Funds Interest Rate is the interest rate at which
depository institutions trade federal funds. The Federal Reserve, by increasing or decreasing this
rate, controls the national interest rates because, historically, private banks match this rate. In
accordance with our initial hypothesis, the Federal funds rate lagged by a year has a significant
explanatory relationship with the unemployment rate. However, we found that an increase in the
interest rate in one year led to a decrease in the unemployment rate in the next. We found this to
make sense because the Fed raises interest rates when the economy is booming and on the rise.
The manifestation of increased interest rates probably takes more than a year and does not slow
down the economy within the year. Instead, the interest rates being raised indicates an active
economy and continued falling of the unemployment rate until investment spending responds to
increased interest rates.
Net Income from Abroad: The Net Income from Abroad is the difference between the total values
of the primary incomes receivable from, and payable to, non-residents. We found that when the
percent of net income from abroad in the GDP increased, the unemployment rate increased. In
other words, as foreign buyers contribute more to US GDP, that signals more economic inactivity
from US citizens. As citizen’s purchasing slows, that indicates economic slump which is then
reflected in a hike in the unemployment rate.
GDP Growth: The GDP Growth is the change in the market value of all the goods and services
produced in a country in a select period. Our results state that as GDP growth increases in one
year, the unemployment rate decreases in the next. This outcome logically follows economic
theory: as the economy grows more, unemployment drops.
GDP Per Capita Growth: The GDP Per Capita Growth represents the GDP changes divided by
the population. These results are nearly the exact same as GDP growth with small fluctuations
based on change in population.
Trade: Trade is the international exchange of goods, services, and capital. We found no
statistically significant predictor relationship between trade and unemployment rate. We believe
that trade is necessary regardless of the state of economy and a steadier metric than the others
because it includes both imports and exports. Thus, changes in trade are not necessarily predictors
9. 9
of changes in unemployment rate because changes in trade are more arbitrary rather than indicative
of economic fluctuation.
Change in Imports of Goods and Services: The Imports of Goods and Services represents the
goods and services that are sourced into the United States from another country. This also did not
have a statistically significant relationship with the unemployment rate. This could be because this
metric was represented by the annual percent growth of imports rather than the percent of GDP.
Exports of Goods and Services: The Exports of Goods and Services represent the amount of
goods produced in one country and shipped to another country for possible future sales. Unlike the
imports, the exports of goods and services reflected is a significant predictor of the unemployment
rate. As more goods are exported, companies require an increase in labor, so the unemployment
rate decreases. An increase in exports of goods and services often goes hand in hand with a weaker
dollar, which could be an underlying variable that strengthens the relationship between exports
and unemployment.
Household Final Consumption Expenditure: The Household Final Consumption Expenditure
is the market value of all goods and services purchased by households. We thought that this
variable would be a more specific metric of household spending and use of disposable income. We
found, however, that this did not have a statistically significant relationship with the
unemployment rate and thus increased household consumption does not predict unemployment
rate. In this case, decreased unemployment could possibly be a predictor of a future increase in
household consumption.
General Government Final Consumption Expenditure: The General Government Final
Consumption Expenditure represents the total transaction amount of government expenditure on
goods and services that are used for direct satisfaction of individual needs. Our results show that
an increase in government consumption expenditure strongly predicts an increase in
unemployment. So, as the government injects more money into the economy on consumption
expenditures, which is an instrument the government uses in fiscal policy, employment decreases.
We believe this is because government spending can cause crowding out, which discourages
private investment and then winds up adversely affecting employment.
General Government Debt: The General Government Debt represents the amount the central
government borrows to finance all its planned expenditure. We found that as government debt as
a percent of GDP increases, unemployment also increases. This aligns with the government final
consumption expenditure, as increased government spending, in consumption and investment,
could increase debt.
Discovery of Strongest Predictor Model
After identifying the seven statistically significant explanatory variables for unemployment
rate, the next step was to discover the best predictor model for the unemployment rate. Initially,
all the seven statistically significant explanatory variables were combined into one function. This,
however, yielded in only two of the seven – Federal Funds Rate and General Government Final
10. 10
Consumption Expenditure – to be statistically significant according to the p-value. Having said
that, the p-value for the overall model suggested that the model is statistically significant.
Furthermore, the R-squared value shows that a large percentage of the unemployment rate can be
explained by combining these factors. The results for this model can be seen below:
Although this model is overall statistically significant, there was still an interest in finding
a stronger model that is more representative of predicting the unemployment rate, especially using
fewer variables. At first, each of the seven variables were removed one-at-a-time, and the results
were observed. Then, two of the seven variables were removed in all possible combinations to
observe the results. Next, three of the seven variables were removed in every possible combination
to view the results. Thus, approximately 70 more models with unique combinations of explanatory
variables were tested. No more than three explanatory variables were removed at a time to test the
models because we believed that at least half of the seven individual statistically significant
explanatory variables should be represented in the model.
Another filtration process followed with searching for the models with the maximum
number of statistically significant explanatory variables. This narrowed down the list of possible
models from approximately 70 to under 10, as a handful of the models had the same number of
statistically significant explanatory variables. The overall p-values of the remaining models were
then compared against one another to identify the model with the lowest overall p-value, which
should therefore be the best predictor model for unemployment rate. The results for the best model
can be viewed below:
11. 11
Multivariable Predictor Model for Unemployment Rate:
As seen above, the overall p-value for this predictor model is 2.155e-09, which confirms
that the model is extremely statistically significant, further proving that the model should be able
to predict the unemployment rate. Even though the “net income abroad” explanatory variable
marginally missed out on statistical significance, it is important to note that none of the 70 or so
tested models had all the explanatory variables to be statistically significant. Across all the models,
there was a maximum of three explanatory variables per model that were statistically significant.
As mentioned earlier, we decided to not compromise on our belief that at least half of the seven
individual statistically significant explanatory variables should be represented in the data, so we
chose to continue with the best model available to predict the unemployment rate. Despite the
limitation present in our forecasting model, this model should be a strong predictor of
unemployment rate due to the high overall statistical significance displayed in the extremely low
p-value and high R squared.
Testing the Regression Assumptions
To verify the validity of our regression, we tested our results to check whether they satisfied
the linear regression assumptions. We first tested linearity, which confirms that the relationship
between the dependent and independent variables is linear, and that the data points are randomly
distributed around the regression line. We plotted the residuals of the regression against the
unemployment rate and found consistent linearity around the regression line as shown by the graph
below. To test that the error terms are normally distributed, we created a histogram of the residuals.
While the residuals did not have a perfectly normal curve, the residuals have a somewhat normal
distribution centered at around 0 with an outlier at -.02 as seen in the graph below to the right. We
𝑌𝑈𝑅 = −0.2239 − 0.3006𝑋 𝐹𝐹𝐼𝑅 − 2.0133𝑋 𝑁𝐼𝐴 + 0.5168𝑋 𝐸𝐺𝑆 + 1.6161𝑋 𝐺𝐹𝐶𝐸
12. 12
also created a QQ plot for the residuals vs. the normal distribution and compared these to a line
corresponding to percentiles of normal distribution. Though the data around the most extreme ends
of the plot is a little off, it stayed on the line for the most part. Finally, we plotted the residuals
against time to test if the residuals are independent of each other. We found that the residuals were
slightly correlated, where negative values briefly followed negative values from 2000 to 2005. We
then calculated the correlations between all the variables and found that the interest rate was the
variable that correlated with the rest. This is not surprising because the interest rate is a main driver
in executing fiscal policy and a large factor in the economy. Ultimately, we decided to keep it in
our regression despite some multicollinearity. In conclusion, none of our results when testing the
regression assumptions are perfect. However, the implication of working with real world data is
typically imperfect results, which is what we expected when running our analysis. We believe our
data meets the standards of the regression assumptions necessary to confirm the validity of our
regression models.
13. 13
CONCLUSION
For this report, we sought to find which macroeconomic factors would best predict the
unemployment rate of the next year. Our initial hypothesis was that the Federal Funds interest rate
and inflation as measured by the Consumer Price Index would hold the strongest predictive
relationship. To do this, we used data from 1990 to 2016 and conducted backward regression by
running individual regressions to eliminate some of our eleven initial explanatory variables. We
narrowed these variables down to seven and then tested approximately 70 different combinations
of the seven variables to identify the model with the greatest statistical significance based on the
lowest p-value. We used backwards regression to avoid including an insignificant explanatory
variable or omitting a significant explanatory variable. Through this, we found that the Federal
Funds interest rate, net income from abroad, exports of goods and services, and government
consumption expenditures together are the most significant predictors. We then tested our model
against the regression assumptions to confirm its validity. Our regression satisfied all the
assumptions well except for the independence of the explanatory variables. We found that they
were correlated across time, but, upon further inspection, the Federal fund interest rate was the
underlying variable that was correlated with the rest. We decided not to exclude the interest rate
after this because it is a significant variable in predicting the unemployment rate and an established
driver of the economy.
Our results are important because the ability to predict the unemployment rate in the short
term can affect many individuals lives. The unemployment rate is a widely followed metric of the
economy and directly affects the individuals in the country. Unemployment can be harmful for
families and the overall economic health of the country. The ability for both individuals and the
government to predict and appropriately prepare for heightened unemployment can be helpful to
maintain the financial security and stability for many individuals. Also, the government can shape
fiscal policies and other legislative and executive matters to mitigate against harmful
unemployment rates.
14. 14
Works Cited
Amadeo, K. (2018, March 26). Why Zero Unemployment Isn't as Good as It Sounds. Retrieved
May 7, 2018, from https://www.thebalance.com/natural-rate-of-unemployment-
definition-and-trends-3305950
Bachman, D. (2014, December 12). Business cycle length and the probability of a recession.
Retrieved May 7, 2018, from https://www2.deloitte.com/insights/us/en/economy/behind-
the-numbers/business-cycle-length.html
Belle, D., & Bullock, H. (n.d.). The Psychological Consequences of Unemployment. Retrieved
May 7, 2018, from
https://www.spssi.org/index.cfm?fuseaction=page.viewpage&pageid=1457
Effective Federal Funds Rate. (2018, May 01). Retrieved from
https://fred.stlouisfed.org/series/FEDFUNDS
FocusEconomics. (n.d.). What is the unemployment rate?
Retrieved from https://www.focus-economics.com/economicindicator/unemployment-
rate
Fouladi, M. (2010). The Impact of Government Expenditure on GDP, Employment and Private
Investment a CGE Model Approach. Iranian Economic Review,15(27). Retrieved May 7,
2018, from ftp://ftp.repec.org/opt/ReDIF/RePEc/eut/journl/20103-4.pdf.
Simpson, C. S. (2017, May 05). The Cost of Unemployment to the Economy. Retrieved from
https://www.investopedia.com/financial-edge/0811/the-cost-of-unemployment-to-the-
economy.aspx
World Bank Group - International Development, Poverty, & Sustainability. (n.d.). Retrieved
from http://www.worldbank.org/