TSA Median Incomes p.1
Running head: Time & Money
Time & Money: An analysis of United States median incomes
Tim Callahan
PRD 590 Time Series Analysis Robert Morris University
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TSA Median Incomes p.2
As we go through life gaining knowledge, experiencing new things and maturing it is common for to
build a lifestyle based on social economic status and means. The lifestyle is usually supported financially
by income generated from one’s occupation or family contributions. Median family income and
employment rates play a major factor on the quality of life that can be sustained. People debating making
a location change and students who are approaching graduation should take median family incomes
associated with geographical locations into consideration prior to relocating. A collection of data
applicable to median incomes in the Midwestern region and unemployment rates will be analyzed. This
research has been conducted with the intention of answering the following research question. While
holding all other variables constant, how will median incomes in the Midwestern region correlate with
unemployment rates over a 15 year period (1998-2012)? It is hypothesized that median incomes and
unemployment rates will have an inverse relationship; as the unemployment rate goes down the median
income will go up or vice versa. The hypothesis is logically deduced under the general assumption that as
more people work, household incomes will increase due to a steadier cash-flow compared to if the same
people were neither working nor generating income.
Operational Definitions:
Median Household Income- The gross amount of money generated (earned) by each household.
o Used interchangeably as: median income, median family income and median household income.
Midwestern Region – A collection of the follow 12 states: Illinois, Indiana, Iowa, Kansas,
Michigan, Iowa, Kansas, Michigan, Minnesota, Missouri, Nebraska, North Dakota, Ohio, South
Dakota & Wisconsin.
Unemployment – The absence of a job that is taxed by the U.S. government.
Unemployment rate – a calculation of individuals who are seeking unemployment but are unable
to successfully secure a job. This computation is reached from dividing the amount of people in a
particular state who are unemployed (by force) divided by the state population.
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TSA Median Incomes p.3
Assumptions:
It is believed that the data used is accurate.
The assumption that past trends can be used to project future occurrences under similar
circumstances has been made.
Literature Review:
According to Perry, there are two main factors that are driving down the median incomes. The
amount of retirees and one earner household has been influential factors as shown below in figure 1.1.
Data also shows that as households with two earners decrease, households with one income increase.
Perry research was primarily about the effects of individuals who are not in the workforce on the median
incomes. In regards to unemployment rates, the computation usually takes individuals who are seeking
employment into account. Retirees in many cases generate passive income through 401k, pension and
other investment vehicles. The past research provides a point of reference. The strongest difference is the
intention of the current analysis to determine how median incomes and employments rate correlate
overtime versus the effects of the non-working population on family incomes. Perry’s research provides
an inverse perspective considering that retirees are not considered voluntarily unemployed instead
unemployed by choice and are not calculated within the state unemployment rates. According to Robert
Pear of the NY Times, as of 2012 median incomes have not returned to where they were prior to the
recession of 2007. Our research questions are similar; the main difference is the time series lengths.
Figure 1.1 Figure 1.2
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TSA Median Incomes p.4
Analysis:
Various steps were taken to progressively analyze the statistical outputs of the median family
incomes and unemployment rates for the 12 states located in the Midwestern region over a 15 year time
period. The following have been taken into consideration: sample randomness, trend identification,
seasonality, lag effects and mean smoothing. The focus of this research is the median incomes of the
Midwestern region between 1998 and 2012.The variable median incomes (MI) has been measured over a
sequential time period; there is a linear relationship present between time and the MI variable. Figure 1.3
provides a visual scatterplot output specifying the median incomes identified by the shape legend on the
left. The X axis (horizontal) scales the time analyzed (1995-2012) and the Y axis (vertical) specifies the
median income associated with the time component. Figure 1.3 shows the moving average (2) trend line
have fluctuated in a manner that seems to be random, it is difficult to determine if there is a clear increase
or decrease, further analysis and re-plotting (shown) below will make it easier to draw general
conclusions.
Figure 1.3
Oct-95 Jul-98 Apr-01 Jan-04 Oct-06 Jul-09 Apr-12 Dec-140
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
Median Income '98-'12IllinoisIndianaIowaKansasMichiganMinnesotaMissouriNebraskaNorth DakotaOhioSouth DakotaMoving average (South Dakota)Wisconsin
Time
Med
ian
Inco
me
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TSA Median Incomes p.5
The unemployment rates graphically represented in figure 2.1 show irregular fluctuations. Seasonality
has been strategically suppressed by using the mean for each year. Since suppression has been employed,
seasonal and cyclical effects were considered in addition to underlying trends and the possibility of
measuring the effect of a variable that is displayed through a time lag. There is a repeated pattern over
several years which make the data set cyclical. Figure 2.2 shows the median income which display a
“shark tooth” effect meaning that they is cyclical effect. The mean smoothing process decreased the
cyclical effects and provides a trend line. The trend line (linear) is going up which represents an increase.
There may be a time lag present, due to the use of this research; the possibility is not further explored.
Time lags would become more applicable when projection models are formulated. The trend line is going
down which represents overall decrease, the past cyclical effects supports a loose projection that an
increase will occur in the near future but the trend line will continue to go down over time.
Figure 2.1 Figure 2.2
Oct-95 Jul-09 Mar-230
2
4
6
8
10
12
Series2Linear (Series2)
Time
Unem
ploy
men
t Rat
e
1 4 7 10 1346,000
48,000
50,000
52,000
54,000
56,000
58,000
Series1Linear (Series1)
Time
Median INC
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TSA Median Incomes p.6
Figure 2.3 below quantifies the median income decreases over the 15 year time series.
Figure 2.4 provides a numerical output of the $3000 variation in the means of incomes ($51k-$54k) and
the difference of the lowest median income of approximately 42K and the highest of 67K yearly median
incomes.
Figure 2.3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 1546,000
48,000
50,000
52,000
54,000
56,000
58,000
54,669
56,544 57,346
55,575 54,561
53,309 54,037
54,813
53,200 52,282
51,027 51,479 Series1Linear (Series1)
Time
Median INC
Figure 2.4 (Descriptive Statistics)
N Minimum Maximum Mean Std. Deviation
y98 12 42630.00 67420.00 54669.1667 6602.98643
y01 12 46421.00 68323.00 55574.5833 5450.81461
y02 12 46202.00 69714.00 54561.4167 5751.54337
y03 12 49340.00 65946.00 54982.3333 4257.96360
y05 12 49430.00 63765.00 53378.9167 4164.01256
y06 12 46745.00 64013.00 54036.6667 4371.81862
y07 12 50945.00 64293.00 54813.0833 3630.87524
y08 12 49096.00 58573.00 53199.6667 2896.17382
y12 12 44375.11 61794.92 51478.7927 4493.38074
y11 12 45373.86 59027.79 51029.8126 4758.71179
Valid N (listwise) 12
Figure: 2.5 below confirm that the unemployment rate in the Midwest is on an upward trend regardless of
what may appear to be a decrease during the last year of observation.
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TSA Median Incomes p.7
Figure 2.5
Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 Jan-120
2
4
6
8
10
12
3.7 3.6 3.74.5
5.5 5.9 5.7 5.4 4.9 5.16
9.6 9.48.3
7.4
Midwest Unemployment Rates'98-'12
Series1 Linear (Series1)
Data Collection &Manipulation Methods Employed:
Data was extrapolated from the United States Bureau of Labor Statistics and census data.
Both of the data source are provided through the United States Government and believed to be true and
accurate. Midwestern region unemployment data was taken from the original set at organized
chronologically from 1998-2012. The data consisted of 12 data points for each year; 180 entries. The 12
point data was averaged to create a statistical mean for each 12 month period. The means for each 12
month period was used to compile the unemployment rate data set. Averages were used considering the
research does not intend nor need to identify seasonality to provide support or denial of the hypothesis..
Data from the census bureau was used to compile the median incomes for each state within the Midwest
region during the years of 1998-2012. The data was re-organized to match the time restraints of the study.
The overall change in buying power and currency strength (dollar inflation) was taken into consideration
during government data collection. This study used “2013” dollars which modified the amounts of past
years to replicate the currency strength and buying power as of 2013.
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TSA Median Incomes p.8
Conclusion:
The original hypothesis prior to analysis predicted that there would be inverse relationships between
median incomes and unemployment rates over time. As unemployment rates go up, median household
incomes will go down. The data confirms that the hypothesis is acceptable and true. The variable have a
negative correlation, this does not infer causation in any form. As represented in figure 2.6 below, when
unemployment rates increase, median family incomes show a downward trend. Pear’s past research has
also been confirmed; since median incomes have not returned to the point they were prior to the recession.
Also, there are many news reports that state the unemployment rate is going down, the reports have truth
when analyzed from a short term perspective. The 15 year time series show that unemployment is on an
upward trend. Hopefully this research will be furthered by another member in the data analysis
community. It would be interesting to see if median incomes are a function of job availability, low wage
job offerings or people’s willingness to work jobs that pay less in comparison to what they were will to do
prior to the recession.
Figure 2.6 Unemployment & Median Income combined
Jan-98
Jan-99
Jan-00
Jan-01
Jan-02
Jan-03
Jan-04
Jan-05
Jan-06
Jan-07
Jan-08
Jan-09
Jan-10
Jan-11
Jan-12
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
0
2
4
6
8
10
12
3.7 3.6 3.74.5
5.55.9 5.7 5.4
4.9 5.16
9.6 9.4
8.37.4
Midwest INF AVGLinear (Midwest INF AVG) Unemployment rate Linear ( Unemployment rate )
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TSA Median Incomes p.9
References:
Pear, Robert. Median income rises but is still 6% below level at start of recession in ’07. Retrieved on November 13, 2014 from http://www.nytimes.com/2013/08/22/us/politics/us-median-income-rises-but-is-still-6-below-its-2007-peak.html
Perry, Mark . Has changing household composition retirement caused decline median household income? Retrieved on November 15, 2014 from, http://www.aei.org/publication/changing-household-composition-retirement-caused-decline-median-household-income/ .
Data Sources:
Midwest Unemployment Rate Data:
http://data.bls.gov/timeseries/LASRD920000000000006?data_tool=XGtable
Median Income Data:
http://www.census.gov/hhes/www/income/data/statemedian/
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