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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