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7/31/2019 The Highest US Unemployment Rates: Obama years compared with historic highs in Unemployment levels
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The Highest US Unemployment RatesThe Obama years and Historical Data (1941-2011)
From want a job to dont want a store!
A brief look at the US economy from 1941-2012.
Courtesy: Great Depression Pictures
http://techbuddha.files.wordpress.com/2009/09/nobody_knows_you.jpg
Protests on June 27, 2012 against the opening of a new Walmart store in Los
Angeles. No Store = No Jobs = Poverty ??? What happened in the USA?
http://i.huffpost.com/gen/668692/thumbs/s-LA-WALMART-PROTEST-
large300.jpg
http://techbuddha.files.wordpress.com/2009/09/nobody_knows_you.jpghttp://techbuddha.files.wordpress.com/2009/09/nobody_knows_you.jpghttp://i.huffpost.com/gen/668692/thumbs/s-LA-WALMART-PROTEST-large300.jpghttp://i.huffpost.com/gen/668692/thumbs/s-LA-WALMART-PROTEST-large300.jpghttp://i.huffpost.com/gen/668692/thumbs/s-LA-WALMART-PROTEST-large300.jpghttp://i.huffpost.com/gen/668692/thumbs/s-LA-WALMART-PROTEST-large300.jpghttp://i.huffpost.com/gen/668692/thumbs/s-LA-WALMART-PROTEST-large300.jpghttp://techbuddha.files.wordpress.com/2009/09/nobody_knows_you.jpg7/31/2019 The Highest US Unemployment Rates: Obama years compared with historic highs in Unemployment levels
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Table of Contents
No. Topic Page No.
1. Summary 32. List of Figures and Brief Captions 4
3. Introduction 6
4. The BIG Picture 8
5. Brief Discussion 17
6. Summary and Conclusions 23
7. Appendix I: Reinterpretation of the data using the Work
Function and review of Historical data for Presidential terms
25
8. Appendix II: Effect of time on unemployment stats 44
9. Appendix III: Legendres linear regression and Millikans
method of determining the Planck constant h
47
Everyone is forced to act helplessly according to the qualities they have
acquired from the modes of material nature; therefore no one can refrain
from doing something, not even for a moment. From the Bhagavad Gita,
chapter 3, verse 5.
The universal law, y = hx + c, relating the labor force x and the number of
unemployed y, also implies the existence of a critical labor force x = x0 below
which the number of unemployed y will go to zero, y = h (x - x0), where the criticallabor force x0 = - c/h can be deduced from the empirical observations on the
economy. Our observations suggest a single universal h = 0.0946 for the US
economy, based on three very unique values (x, y) pairs observed over the past 70+
years. It is also possible to reduce unemployment level to zero (with x < x0).
http://books.google.com/books?id=dSA3hsIq5dsC&pg=PA151&lpg=PA151&dq=
na+hi+kascit+ksanam+api&source=bl&ots=nY3FJfKF6m&sig=OJUaurIscnjtxkbp
3OAttE7HhsY&hl=en&sa=X&ei=mT0AUIyuGqfk6QHM0bSFBw&ved=0CEcQ6
AEwAzgK#v=onepage&q=na%20hi%20kascit%20ksanam%20api&f=false
http://www.thebhagavadgita.com/bg_3.html
http://www.ahwan.org/article65.htm
http://www.bhagavad-gita.us/categories/The-Gita%3A-Chapter-3/
http://books.google.com/books?id=dSA3hsIq5dsC&pg=PA151&lpg=PA151&dq=na+hi+kascit+ksanam+api&source=bl&ots=nY3FJfKF6m&sig=OJUaurIscnjtxkbp3OAttE7HhsY&hl=en&sa=X&ei=mT0AUIyuGqfk6QHM0bSFBw&ved=0CEcQ6AEwAzgK#v=onepage&q=na%20hi%20kascit%20ksanam%20api&f=falsehttp://books.google.com/books?id=dSA3hsIq5dsC&pg=PA151&lpg=PA151&dq=na+hi+kascit+ksanam+api&source=bl&ots=nY3FJfKF6m&sig=OJUaurIscnjtxkbp3OAttE7HhsY&hl=en&sa=X&ei=mT0AUIyuGqfk6QHM0bSFBw&ved=0CEcQ6AEwAzgK#v=onepage&q=na%20hi%20kascit%20ksanam%20api&f=falsehttp://books.google.com/books?id=dSA3hsIq5dsC&pg=PA151&lpg=PA151&dq=na+hi+kascit+ksanam+api&source=bl&ots=nY3FJfKF6m&sig=OJUaurIscnjtxkbp3OAttE7HhsY&hl=en&sa=X&ei=mT0AUIyuGqfk6QHM0bSFBw&ved=0CEcQ6AEwAzgK#v=onepage&q=na%20hi%20kascit%20ksanam%20api&f=falsehttp://books.google.com/books?id=dSA3hsIq5dsC&pg=PA151&lpg=PA151&dq=na+hi+kascit+ksanam+api&source=bl&ots=nY3FJfKF6m&sig=OJUaurIscnjtxkbp3OAttE7HhsY&hl=en&sa=X&ei=mT0AUIyuGqfk6QHM0bSFBw&ved=0CEcQ6AEwAzgK#v=onepage&q=na%20hi%20kascit%20ksanam%20api&f=falsehttp://books.google.com/books?id=dSA3hsIq5dsC&pg=PA151&lpg=PA151&dq=na+hi+kascit+ksanam+api&source=bl&ots=nY3FJfKF6m&sig=OJUaurIscnjtxkbp3OAttE7HhsY&hl=en&sa=X&ei=mT0AUIyuGqfk6QHM0bSFBw&ved=0CEcQ6AEwAzgK#v=onepage&q=na%20hi%20kascit%20ksanam%20api&f=falsehttp://www.thebhagavadgita.com/bg_3.htmlhttp://www.thebhagavadgita.com/bg_3.htmlhttp://www.ahwan.org/article65.htmhttp://www.ahwan.org/article65.htmhttp://www.bhagavad-gita.us/categories/The-Gita%3A-Chapter-3/http://www.bhagavad-gita.us/categories/The-Gita%3A-Chapter-3/http://www.bhagavad-gita.us/categories/The-Gita%3A-Chapter-3/http://www.ahwan.org/article65.htmhttp://www.thebhagavadgita.com/bg_3.htmlhttp://books.google.com/books?id=dSA3hsIq5dsC&pg=PA151&lpg=PA151&dq=na+hi+kascit+ksanam+api&source=bl&ots=nY3FJfKF6m&sig=OJUaurIscnjtxkbp3OAttE7HhsY&hl=en&sa=X&ei=mT0AUIyuGqfk6QHM0bSFBw&ved=0CEcQ6AEwAzgK#v=onepage&q=na%20hi%20kascit%20ksanam%20api&f=falsehttp://books.google.com/books?id=dSA3hsIq5dsC&pg=PA151&lpg=PA151&dq=na+hi+kascit+ksanam+api&source=bl&ots=nY3FJfKF6m&sig=OJUaurIscnjtxkbp3OAttE7HhsY&hl=en&sa=X&ei=mT0AUIyuGqfk6QHM0bSFBw&ved=0CEcQ6AEwAzgK#v=onepage&q=na%20hi%20kascit%20ksanam%20api&f=falsehttp://books.google.com/books?id=dSA3hsIq5dsC&pg=PA151&lpg=PA151&dq=na+hi+kascit+ksanam+api&source=bl&ots=nY3FJfKF6m&sig=OJUaurIscnjtxkbp3OAttE7HhsY&hl=en&sa=X&ei=mT0AUIyuGqfk6QHM0bSFBw&ved=0CEcQ6AEwAzgK#v=onepage&q=na%20hi%20kascit%20ksanam%20api&f=falsehttp://books.google.com/books?id=dSA3hsIq5dsC&pg=PA151&lpg=PA151&dq=na+hi+kascit+ksanam+api&source=bl&ots=nY3FJfKF6m&sig=OJUaurIscnjtxkbp3OAttE7HhsY&hl=en&sa=X&ei=mT0AUIyuGqfk6QHM0bSFBw&ved=0CEcQ6AEwAzgK#v=onepage&q=na%20hi%20kascit%20ksanam%20api&f=false7/31/2019 The Highest US Unemployment Rates: Obama years compared with historic highs in Unemployment levels
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1. Summary
A quick review of the significance of the three periods with the highest recorded
unemployment levels in the last 70+ years, from 1941-2011, is presented here to
gain additional insights into the current jobs crisis facing the US economy in the
Obama years. This is best understood by reviewing the data compiled below.
The highest US unemployment levels on record
Year Labor force, x
(millions)
Unemployed, y
(millions)
1941 55.91 5.56
1982 110.204 10.6782010 153.889 14.825
Data Source:http://www.bls.gov/cps/cpsa2011.pdf
A careful analysis of the above data provides further evidence for the universal law
y = hx + c relating labor force x and unemployment level y. It also suggests a
sound empirical approach to determining the numerical values of h and c by
considering the highly unique data points for the three periods with the highest
unemployment levels. The universal value of h = 0.0946 is thus deduced as a
fundamental characteristic of the US economy, a unique property akin to otherfundamental constants observed in the hard sciences, like physics. The intercept
c in this law is exactly analogous to Einsteins work function in the photoelectric
law. Improvements or deteriorations in the economy can be interpreted as evidence
for changes in the intercept c, which can be viewed as the work function for the
economy.
P. S. This document will be further revised and updated to improve any
faults in the current presentation and is being posted here, in preliminary
form, because of the obvious and urgent attention this problem needs.
http://www.bls.gov/cps/cpsa2011.pdfhttp://www.bls.gov/cps/cpsa2011.pdfhttp://www.bls.gov/cps/cpsa2011.pdfhttp://www.bls.gov/cps/cpsa2011.pdf7/31/2019 The Highest US Unemployment Rates: Obama years compared with historic highs in Unemployment levels
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2. List of Figures and brief captions
Figure 1: The US unemployment data for the years 1941-1960.
Figure 2: The US unemployment data for the years 1941-1995.
Figure 3: The unemployment data for the period 1941-2011.
Figure 4: The highest unemployment levels on record in the data compiled by the
Bureau of Labor Statistics (see http://www.bls.gov/cps/cpsaat01.pdf) for 1941 and
the years 1982 and 1983 and the Obama years (2009-2011).
Figure 5: The unemployment rate, defined as the ratio y/x (converted to a percent)
for the years 1941-2011 plotted as a function of the labor force, x.
Figure 6: The unemployment rate, y/x converted to a percent, for 1941-2011, is
plotted here as a function of the unemployment level y.
Figure 7: Series of parallels with the general equation y = hx + c = 0.0946x + c
superimposed on to the US unemployment data in Figure 3.
Figure 8: The unemployment diagram for the period 1990-2008, which covers the
two Bush presidencies and the Clinton presidency.
Figure 9: The unemployment data for the period 1990-2008.
Figure 10: Reinterpretation of the unemployment data for the period 1990-2011
using the idea of the economic work function and a single universal constant h =
0.0946.
Figure 11: Reinterpretation of the unemployment data for the period 1970-1983
which covers theNixon, Ford, Carter, and Reagan years, using the idea of the
economic work function and a single universal constant h = 0.0946.
Figure 12: The unemployment diagram for theKennedy-Johnson era and the first
two years of theNixon presidency (1960-1970).
Figure 13a: The complex zigzag path taken by the economy, in the unemployment
diagram for the period 1941-1952 which includes the terms ofPresidents FDR
(last term) and Truman, beginning 1945.
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Figure 13b: The unemployment diagram for the period 1941-1952 which includes
the terms ofPresidents FDR (last term) and Truman, beginning 1945.
Figure 14: The unemployment diagram for the period 1953-1960 which includes
President Eisenhowers two terms.
Figure 15: TheKennedy-Johnson era,which followed Eisenhowers terms, has
already been considered (in Figure 12).
Figure 16: The unemployment diagram for 1975-1983, covering the Presidential
terms ofFord (1975 only), Carter, and Reagans first three years.
Figure 17: The unemployment diagram for the period 1980-1988 which covers
PresidentReagans two terms.
Figure 18: The unemployment diagram for the period 1988-2000 which covers the
terms ofBush I (1988-1992), Clintons two terms and the first year ofBush II
presidency.
Figure 19a: The reduction in the economic work function between 1961 and 1966
(the Kennedy-Johnson years, see also Figure 12) is illustrated here.
Figure 19b: The unemployment diagram for the years 1992-2002 which covers the
Clinton years.
Figure 20: The unemployment data for 1941-952 along with the data for 1958
(Eisenhower era) is plotted here.
Figure 21: The labor force has increased steadily over the last 70+ years due to
the overall increase in the population.
Figure 22: The unemployed y, has been going up and down over the years with
changes in economic conditions.
Figure 23: The unemployment rate, y/x, expressed as a percent, for 1941-2011.
Figure 24: The unemployment rate y/x, for the years 1941-2011 (expressed here as
a fraction), versus labor force x. This is the same as the graph in Figure 5, along
with three members of the family of hyperbolas y/x = h + (c/x) = 0.0946 + (c/x)
superimposed on to the data (see Appendix III).
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3. Introduction
The unemployment rate is defined as the ratio y/x where the numerator y is the
number of unemployed workers and the denominator x is the total labor force.Although large volumes of tables of x and y, which include the monthly, quarterly,
and annual values of these two variables, are available, attention has always been
focused on the behavior of the ratio y/x instead of an analysis of the nature of the
underlying x-y relationship.
In a companion article, which discusses the US unemployment data during the
Obama years, seehttp://www.scribd.com/doc/99647215/The-US-Unemployment-
Rate-What-happened-in-the-Obama-years, I have shown that (based on a careful
study of the unemployment data compiled by the US Department of Labor, Bureauof Labor Statistics BLS, seehttp://www.bls.gov/cps/cpsa2011.pdf)
1. The labor force x, which was growing slowly during the 2008 Presidentialcampaign, from Jan 2008 to Oct 2008, suddenly began shrinking and the
number of unemployed y suddenly increasing rapidly in Nov 2008 and Dec
2008, even before President Obama was sworn in office.
2. During Obamas first full year in office, the labor force continued to shrinkand the number of unemployed jumped by 5.341 million (from 8.924 million
in 2008 to 14.265 in 2009). The US economy had literally made a U-turn, as
shown dramatically on the x-y graph (number unemployed y versus labor
force x) and was heading in the WRONG direction.
3. The number of unemployed reached a peak value of 15.421 million inOctober 2009 and has since been coming down slowly, with a simultaneous
increase in the labor force. The number unemployed was 12.75 million in
June 2012. While this recent trend (from second quarter 2009 to second
quarter 2012) is definitely favorable, the absolute number of unemployed isstill too high compared to the 8 million levels during 2005-2008.
4. A simple linear law y = hx + c seems to relate the general trends revealed inthe x-y graphs of labor force versus the number of unemployed. Of great
fundamental interest is the fact that the US economy seems to be operating
on essentially parallel tracks, moving up and down parallel lines when the
http://www.scribd.com/doc/99647215/The-US-Unemployment-Rate-What-happened-in-the-Obama-yearshttp://www.scribd.com/doc/99647215/The-US-Unemployment-Rate-What-happened-in-the-Obama-yearshttp://www.scribd.com/doc/99647215/The-US-Unemployment-Rate-What-happened-in-the-Obama-yearshttp://www.scribd.com/doc/99647215/The-US-Unemployment-Rate-What-happened-in-the-Obama-yearshttp://www.bls.gov/cps/cpsa2011.pdfhttp://www.bls.gov/cps/cpsa2011.pdfhttp://www.bls.gov/cps/cpsa2011.pdfhttp://www.bls.gov/cps/cpsa2011.pdfhttp://www.scribd.com/doc/99647215/The-US-Unemployment-Rate-What-happened-in-the-Obama-yearshttp://www.scribd.com/doc/99647215/The-US-Unemployment-Rate-What-happened-in-the-Obama-years7/31/2019 The Highest US Unemployment Rates: Obama years compared with historic highs in Unemployment levels
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number of unemployed was going up and then coming down, with increase
and decrease in the labor force.
Table 1: The highest US unemployment levels on record
Extracted from Bureau of Labor Statistics
Year Labor force, x
(millions)
Unemployed, y
(millions)
1941 55.91 5.56
1942 56.41 2.66
1943 55.54 1.07
1982 110.204 10.678
1983 111.55 10.717
2009154.142 14.265
2010 153.889 14.825
2011 153.616 13.747
Data Source:http://www.bls.gov/cps/cpsa2011.pdf
It should be remembered that the labor force decreased for a while, during the
Obama years, since discouraged workers (who had stopped looking for work) were
no longer counted as a part of the labor force x. They, however, still contribute to
the high unemployment rate, y/x, since they move from unemployed column in
the BLS tables to the not in the labor force column. Instead of contributing to a
higher numerator y (when they are looking for work), they were contributing to the
lower denominator x (when not looking for work and so not in the labor force).
A review of the historical data for US unemployment (1941-2011) is presented in
this article since it reveals some unique insights into the unprecedented and
historically record levels of unemployment that we are currently experiencing
since President Obama took office. This is best illustrated by considering the data
compiled in Table 1, which includes the three highest unemployment levels on
record since 1941. The three years, 1941, 1983, and 2010 represent a significant
jump in the number of unemployed for that era and the size of the labor force,
see also the graphs presented in Figures 1 to 3. Each of these years, with the then
highest recorded unemployment levels, represents a unique era in US history.
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Imperial Japan attacked Pearl Harbor on December 7, 1941, a date which will
forever live in infamy, as proclaimed by then President FDR. In 1983, Reagan
was facing re-election, having been elected President following the disastrous
Iranian hostage crisis of 1979-1980, which consumed the final year of the doomed
Carter Presidency. And, 2010, the era that we are now witnessing, follows the neartotal economic collapse and the financial crisis of 2008 which propelled Obama
into office. Yet, there is a remarkable relationship between the unemployment
levels for these three years as will become clear from a review of Figures 1 to 3.
4. The Big Picture
The high unemployment level for 1941 is quite clearly an outlier on the x-ygraph in Figure 1. For the labor force level x in 1941, the number of unemployed y
was very high, compared to all the subsequent years. The labor force first increased
and then decreased, between 1941 and 1943, but the unemployment levels dropped
for three consequent years to reach the lowest level of 0.67 million in 1944. After
this, both the labor force x and the number of unemployed y were rising until they
reached the highest level (for this era) in 1958.
The relationship between labor force x and the number unemployed y appears to be
a simple linear relation of the type y = hx + c = h(xx0) where x0 = -c/h may be
thought of as the cut-off labor force level at which the number of unemployed
will go to zero. The graph prepared in Figure 1 begs the conclusion that if the labor
force is less than some critical level (x < x0), there will be ZERO unemployed. One
could extrapolate, after imposing a straight line on to this graph, to deduce the
numerical value for this cut-off labor force x = x0.
This leads us to the next question. How do we fix the numerical values of the
constants h and c in y = hx + c? One could, using linear regression analysis to
deduce the numerical values. Or, to keep things simple, one could just take the line
joining (x, y) pairs for 1944 and 1958, the two extreme points in the data set, as a
good description of the general trend for this era. Or, one can envision a number of
nearly parallel lines, defined by the slope of the line joining the (x, y) pairs for
1942 and 1958, sweeping through this data set. The (x, y) pairs for 1942, 1949, and
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1958 seem to fall on single straight line. Many cut-off values are therefore
suggested, depending on the (x, y) pair that is chosen to fix the numerical value of
h. However, all these arguments overlook the significance of this outlier, the
highest unemployment level observed in 1941.
Figure 1: The US unemployment data for the years 1941-1960.
Is this high unemployment level to be simply ignored as a mathematical
nuisance, since it is not amenable to any kind of elegant statistical analysis? So,
before we hasten to determine the numerical values of h and c, let us consider the
data for the next time period, 1961-1995 and merge it with the 1941-1960 dataset.
The overall trend in Figure 2 is exactly similar to the trend in Figure 1. As the
labor force x increases, the number of unemployed y also seems to increase. The
(x, y) pairs for the years 1982 and 1983 now appear as outliers in this graph. We
can connect the (x, y) pairs for 1941 and 1982 or 1941 and 1983 with a straight
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0
Labor force, x millions
Unem
lo
ed,
millions
1941
1942
1944
1958
1949
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line. The slope h = 0.0927 for the line joining the 1941 and 1983 data and h =
0.0943 for the line joining the 1941 and 1982 data. The average of these two slopes
is h = 0.09345. This is illustrated by the blue line joining these highest
unemployment levels. This straight line, to which we are naturally led by the
unemployment data, clearly seems to have some fundamental significance.Indeed, it is possible now to again imagine a series of parallel lines joining the
various (x, y) pairs on this graph all having the slope h = 0.0935. One need not do
any actual number crunching to accept that the argument that the numerical value
of the slopes h determined by considering many (x, y) pairs in the data set will
agree with the slope h = 0.0935 deduced from the highest unemployment levels.
Figure 2: The US unemployment data for the years 1941-1995.
In other words, it appears that we have discovered a universal law, and also a
method of fixing the numerical value of the constants h and c in this universal law,
by considering all of the US unemployment data. Whenever the labor force goes
0
2
4
6
8
10
12
0 20 40 60 80 100 120 140
Labor force, x millions
Unemplo
yed,y[millions]
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up by a fixed amount x, the number unemployed seems to increase by the same
fixed amount y= hx. Let us now consider the next time period as well which
lends additional support to these findings.
Figure 3: The unemployment data for the period 1941-2011 reveals three
outliers. These are periods of very high unemployment: 1941, 1982 and 1983
and the most recent period 2009-2011.
An interesting pattern is again revealed by this simple graphical representation of
the data. It appears that the (x, y) pairs corresponding to the three highest levels of
unemployment lie on a single straight line. The slope h = 0.0946 for the linejoining 1941 to 2010 is virtually identical to the slope h = 0.0943 for the line
joining 1941 and 1982. Many other slopes between these three data points with the
highest unemployment levels can be determined to find some kind of an average
slope (at least 11 different slopes were determined). However, the virtual identity
of the slopes of the lines joining 1941 to 1982 and 1941 to 2010 is the slope that
0
2
4
6
8
10
12
14
16
0 25 50 75 100 125 150 175 200
Labor force, x [millions]
Unem
loe
d,
millions
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recommends itself as the fundamental characteristic of the US economy for the last
70+ years. We will take h = 0.0946, the slope of the linejoining the two extreme
points 1941 and 2010 as the defining slope. This is illustrated in Figure 4.
Figure 4: The highest unemployment levels on record in the data compiled by the
Bureau of Labor Statistics (seehttp://www.bls.gov/cps/cpsaat01.pdf) for 1941 and
the years 1982 and 1983 and the Obama years (2009-2011) is plotted here. The
three highest unemployed levels data fall on a PERFECT straight line with the
equation y = hx + c = 0.0946x + 0.2731. This specific equation was determined by
connecting the 1941 and 2010 data points. The above straight line is a precisecomputer generated straight line based on the mathematical equation here. From
the average slope of h = 0.0935 deduced from 1941, 1982, and 1983, we arrive
at h = 0.0946 for the line joining 1941, 1982, and 2010.
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
0 20 40 60 80 100 120 140 160 180 200
Labor force, x millions
Unemployed
,y[millions]
1941, 1982: h = y/x = 5.118/54.294 = 0.0943
1982, 2010: h = y/x = 4.147/43.685 = 0.0949
1941, 2010: h = y/x = 9.265/97.979 = 0.0946
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Clearly, what appears to be a mind bogglingly high level of the unemployment,
more than 15 million at its peak in October 2009 (with an average household size
of just 3 to 4, this means between 45 to 60 million of the current population was
affected), is simply a reflection of the expansion of the labor force. When things
turn sour in the economy, more will be unemployed in an economy with ahigher labor force than in an economy with a lower labor force. This is the
simple and dispassionate explanation for what seems to be unacceptably high
unemployment levels (and, likewise, budget deficits and national debt levels) that
we are witnessing in the Obama years. The law relating the highest unemployment
levels, and by extension, ALL unemployment data is the simple law y = hx + c,
where h and c are determined by considering at least three such highest
unemployment levels!
This is really what the graph in Figure 4 is telling us. The US economy in 1941
(that was before I was born and many who are reading article this were born), the
US economy in 1982 and 1983 (that I have lived through, the Reagan years that I
can vividly recall) and the US economy in 2009-2011, that we are all living
through now, the Obama years, have something in common that has escaped the
attention of economists, academic scholars, and our business and political leaders.
The significance of the apparently often puzzling and the erratic variations in the
unemployment rates, see Figures 5 and 6, can now be understood, as follows.
Let y = hx, where h is a constant. This is the simplest type of x-y relationship with
c = 0. The x-y graph passes through the origin (0, 0). The number of unemployed y
goes to zero when the labor force x goes to zero. There is no cut-off! This means
the unemployment rate y/x = h = the unknown constant. If the labor force x
increases or decreases, the number of unemployed y will also increase or decrease,
correspondingly. Hence, the changes in the unemployment rate y/x are entirely due
to the changes in this unknown constant h.
Now, compare this with the slightly modified relation y = hx + c, a universal law,
which has been deduced here from the empirical observations on the US economy.
Now, the unemployment rate y/x = h + (c/x) = h {1 + [c /(yc)}. Because of the
nonzero intercept c, the unemployment rate will be affected by both the changes in
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the unknown constant h and also by the size of the labor force x. Depending on the
numerical values of h and c, which may be positive or negative, the unemployment
rate can go up or down even if the slope h is PERFECTLY constant and does
not change with the size of the labor force x.
Figure 5: The unemployment rate, defined as the ratio y/x (converted to a percent)
for the years 1941-2011 plotted as a function of the labor force, x. The three
periods with the highest unemployment rates observed (in 1941, 1982 and 1983,
and 2009-2011) again separate themselves in this graphical representation of the
data. Why did the ratio y/x = h go up and down with increasing labor force x? Or,
why is it nearly constant at the highest rates although labor force had increased?
If we take y = 0.0946x +0.2731, as the law relating the highest unemploymentrates, then the unemployment rate y/x = 0.0946 + (0.2731/x) 0.0946 (about 0.1
or 10%) since the intercept c = 0.2731 is quite small compared to the labor force
levels which varied from about 55 million to 155 million.
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0 25 50 75 100 125 150 175
Labor force, x [millions]
Unem
lo
mentrate,
100(/x)
1941 1982-83 2009-11
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It is interesting, in particular, to see the data separating itself into three periods in
Figure 6: the 1941 era with unemployment rates below the peak value, the 1982-83
era, again with unemployment rates below the peak but with higher unemployed,
and the current era. This is still evolving, with very few data points.
Figure 6: The unemployment rate, y/x converted to a percent, for 1941-2011, is
plotted here as a function of the unemployment level y. The three periods with the
highest unemployment rates observed (in 1941, 1982 and 1983, and 2009-2011)
again separate themselves in this graphical representation. We also see the
unfortunate reversal from 2000 to 2012 (highlighted by the red dashed line).
Two important observations can be made from the plot in Figure 6. First, the
absolute unemployment level y was very nearly the same in 1941 and in 2000. But,
the unemployment rate was at its peak in 1941 and very low in 2000. This is
entirely due to the differences in the labor force x. This emphasizes the importance
of systematically accounting for the size of the labor force in all unemployment
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0 2 4 6 8 10 12 14 16
Unem lo ed, millions
Unemploymentrate,
100(y/x)
2000
1941 1982-83 2009-11
2008
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studies. Second, this also suggests the very real possibility that we might witness a
similar drop in the unemployment rates in the years ahead, with increasing labor
force x but lower unemployment levels y than the current high levels. The x-y
graph, on the other hand, see Figure 7 for example, accounts for the complex
interaction between the effects of the labor force size x, the unemployment level y,and the unemployment rate y/x via the simple linear law y = hx + c.
Figure 7: Series of parallels with the general equation y = hx + c = 0.0946x + c
superimposed on to the US unemployment data in Figure 3. The intercept c varies
from c = 0.2731 for the highest unemployment levels (Line A) and decreases as the
unemployment levels decreases. The parallels with c = - 0.938 (Line B), c = -4.496(Line C), c =-7.791(Line D) are added and cover the entire range of data. The
corresponding value of the cut-off labor force x0 are 9.924 million (Line B), 47.54
million (Line C) and 82.39 million (Line D).
-10
-5
0
5
10
15
20
0 25 50 75 100 125 150 175 200
Labor force x millions
Unemployed,y[mi
llions]
A
D
C
B
x0 = 82.39
2008 Start of
Obama years
2011
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The lowest parallel D is chosen so that it passes through the data for 2000 (final
year of Clintons two terms) with the lowestunemployment level of 5.692 million
(labor force 142.583 million). Since 2000, the unemployment levels first increased
(work function increased to value on Line C) and then decreased (during the Bush
II term) before the dramatic increase that began in the Obama years (startingNovember 2008). Parallel B passes through the 1975 data (Fords term) andalso
the current (2011) data.Parallel C passes through 1944 data (FDRs last term). It
is of interest to see that the financial meltdown of 2008 took the unemployment
levels to well below what they were in 1944 (after accounting for the increased
labor force) when the economy was on the upswing in the final year of FDRs term
after the record high unemployment in 1941.
5. Brief Discussion
The x-y graphs, or the unemployment diagrams, for different Presidential terms are
presented in Appendix I. In each case, we find that the economy has taken many
complex turns (or what may be called a random walk, or a drunkards walk) to
get from point A to point B at the start and end of each term, see for example
Figure 8 for the George W Bush years (W-like pattern, with unemployment levels
going up and then down) or Figure 13 for the FDR-Truman years (a complex
zigzag, the slopes h for individual segments vary from h = -5.8 for 1941-42 to h =
0.02 for 1946-47 to h = 6.46 for 1950-51).
Instead of these complex zigzags, we can just as easily envision a series of
parallels with a slope h = 0.0946 and the general equation y = hx + c = h(xx0) =
0.0946x + c, with various values of the economic work function c or the cut-off
labor force x0 = - c/h, see Figure 7. As the work function c decreases (more
negative), the cut-off labor force x = x0 increases. There is no unemployment when
the labor force x is less than this cut-off value x0. When the labor force x > x0, the
number unemployed always increases by the same fixed amount y = hx when
the labor force increases by x. Also, the constant h = 0.0946 for the US economy
for the reasons just discussed.
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This, in brief, is the new philosophy, see also the detailed numerical calculations
presented later in Figure 19 of Appendix I. The change in the work function is
proportional to the span of the bracket (in blue) added on the labor force axis.
The reduction in unemployment levels is due to this change.
What we are witnessing here in the unemployment data may indeed like other
universal laws of nature, which can often be expressed in simple mathematical
formulations. Some well-known examples that, I am sure, most of us have studied
at some point in our high school and college years, are:
1. Hubbles law V = H0D relating distance D of a galaxy and its recessionalvelocity V. This is a linear law describing the expansion of the universe. Theslope of the line, H0, is called the Hubble constant. The intercept c = 0, see
further discussion of this point in the bibliography cited.
2.Newtons law of viscosity for a fluid, = (d/dt). This law relates the shearstress and the shearing rate (d/dt). The viscosity is the slope of the
straight line. Again, we have a zero intercept. The viscosity of water, air,
motor oils, blood, and many other fluids is determined using this law. The
thicker a fluid, the higher its viscosity.
3.Newtons force law, F = ma, relating force F and acceleration a is anotherexample of a linear law with zero intercept. In this case, the slope of the
straight line is the mass m of the body on which the force acts to produce the
acceleration, a.
4. Ohms law, V = RI, relating voltage V and current I flowing through asimple electrical circuit (zero intercept).
5. Hookes law relating stress and strain , a linear law, with zero intercept, = E with the slope E being the Youngs modulus, or simply the elastic
modulus.
6. Charles law relating volume V and temperature T of an ideal gas. This is alinear law with a finite positive intercept on the volume-axis. V = a + bT.
7. Pascals law relating pressure p and depth d below the free surface of water,again with a finite positive intercept, p = p0+ gd, where is the density of
water (or any other liquid) and g is the gravitational acceleration.
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8. Einsteins photoelectric law (linear law relating maximum kinetic energy Kof an electron to the energy of a photon, negative intercept on K-axis).
Also, since we are dealing with a simple linear law, with a nonzero intercept, this
also suggests at least three possibilities, depending on the numerical values of theconstants h and c (positive or negative).
1. Case I: Positive h, negative c. Both the absolute number of unemployed
y and the unemployment rate y/x increase as the labor force x increases.
2. Case II: Positive h, positive c. The absolute number of unemployed y
increases but the unemployment rate y/x decreases as the labor force x
increases.
3. Case II: Negative h, positive c. The unemployment level y and theunemployment rate y/x decreases (or increases) as the labor force x
increases (or decreases). This is quite commonly observed during
periods of decreasing unemployment levels.
All three cases are, indeed, observed if we study unemployment data, for short
periods of time, at the county level, the state level or the national level. For
example, I remember reading an article in The Wall Street Journal, in the early
2000s (the Bush years) entitled, If the unemployment rate is going down, why are
so many people unemployed? Or, something very close to this (unfortunately,
have not been able to find the exact citation).
The author of this nice investigative article was discussing the devastating effect of
the high unemployment levels in various counties in Ohio, around the Cleveland
area that I am intimately familiar with. The author was obviously unaware that the
unemployment data for Ohio, in that time period, followed a linear law, Case II
above, with a positive slope h and a positive intercept c. This is the reason why the
unemployment rate y/x was going down but the number of unemployed y was
going up. This can be understood using a simple example.
Let y = hx + c = 0.5x + 2. Hence, as the labor force x increases, the number of
unemployed y increases. The unemployment rate y/x = h + (c/x) = 0.5 + (2/x).
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Hence, as the labor force x increase the number of unemployed y increases but the
unemployment rate y/x goes down and y/x = h = 0.5 when x becomes infinite.
Table A: Operating Equations for the Unemployment Law in different eras
Years President Equation Comments
1941-43 FDR y = -1.08x +66.5 Case III, Decreasing unemployment
1944-46 FDR/Truman y = 0.554x -29.58 Case I, Rising unemployment
1949-52 Truman y = - 2.06x +129.8 Case III, Decreasing unemployment
1953-60 Eisenhower y =0.301x17.4 Case I, Rising unemployment
1961-66 Kennedy/
Johnson
y = -0.352x + 29.56 Case III, Decreasing unemployment
1968-74 Nixon y = 0.177x -11.12 Case I, Rising unemployment
1974-76 Ford y = 0.535x -44 Case I, Rising unemployment
1976-79 Carter y = -0.144x +21.27 Case III, decreasing unemployment
1980-82 Reagan y =0.932x - 92 Case I, Rising unemployment
1983-88 Reagan y = -0.397x + 54.99 Case III, decreasing unemployment
1990-92 Bush I y = 1.133x135.5 Case I, Rising unemployment
1992-95 Clinton y = -0.526x + 77 Case III, decreasing unemployment
1996-99 Clinton y = -0.25x + 40.72 Case III, decreasing unemployment
2000-02 Bush II y = 1.18x -162.28 Case I, Rising unemployment
2003-06 Bush II y = -0.361x + 61.59 Case III, decreasing unemployment2007-08 Bush II y = 1.59x236.4 Case I, Rising unemployment
2008-09 Obama y = -37.1x + 5731.4 INVERSE Case III, Rising
Unemployment
2010-11 Obama y = 2.51x371.5 INVERSE Case I, Decreasing
unemployment
Notice the rather unusual numerical values of the constants h and c for Obama.
Also, the only example of what might be called INVERSE Case I (positive but
decreasing employment, most recent trend) and INVERSE Case III (negative slope
but rising unemployment, unlike any other earlier period). All these operating
equations can be reinterpreted using the economic work function introduced here.
The x-y graphs are presented in Appendix I for different Presidential terms.
******************************************************************
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Table B: Operating Equations for the Unemployment Law in different eras
Years President Slope h Intercept, c Cut-off Laborforce, x0
(millions)
Constants h, c for Periods of Decreasing Unemployment levels
2008-09 Obama -37.1 5731.4 154.49
1949-52 Truman -2.06 129.8 63.01
1941-43 FDR -1.08 66.5 61.57
1992-95 Clinton -0.526 77 146.39
1983-88 Reagan -0.397 54.99 138.55
2003-06 Bush II -0.361 61.59 170.611961-66 Kennedy/Johnson -0.352 29.56 83.98
1996-99 Clinton -0.25 40.72 162.88
1976-79 Carter -0.144 21.27 147.71
Constants h, c for Periods of Increasing Unemployment levels
1968-74 Nixon 0.177 -11.12 62.82
1953-60 Eisenhower 0.301 -17.4 57.81
1974-76 Ford 0.535 -44 82.24
1944-46 FDR/Truman 0.554 -29.58 53.39
1980-82 Reagan 0.932 -92 98.71
1990-92 Bush I 1.133 -135.5 119.592000-02 Bush II 1.18 -162.28 137.53
2007-08 Bush II 1.59 -236.4 148.68
2010-11 Obama 2.51 -371.5 148.01
The values of the constants h and c in Tables A and B above are determined by
considering the individual x-y diagrams for the periods indicated. These do not
take into account the idea of a single universal h = 0.0964 proposed here by
considering the data for the years with the highest levels of unemployment. In
Table B, the data is sorted by increasing values of the slope h.
******************************************************************
In the companion article, it was shown that during the second Clinton term, the
unemployment levels decreased with increasing labor force (Case III above), see
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Figure 3 in that article. We also see evidence for Case III if we consider the
improvement in the economy, between 1941-1944, and again between 1958-1970.
The unemployment levels were decreasing with an increase in the labor force,
during these local subperiods. These points are discussed further in Appendix I
where some additional graphs are being presented.
Nonetheless, local observations of both Case II and Case III can be reinterpreted
in terms of a changing intercept c with the economy fundamentally exhibiting only
the linear law of Case I, as evidenced by its behavior in the periods of the highest
unemployment levels. This line of reasoning can be restated as follows.
a) There is a single value of h that is a characteristic of the US economy that ismanifested by considering special points in the economy, such as the threeeras with the highest unemployment levels. (Likewise, we can deduce the
value of h for any other economy, if we make empirical observations similar
to what has been possible with the US economy, for say, Canada, UK,
Germany, Japan, Singapore, Australia, Norway and Sweden, and Denmark,
the BRIC countries, Brazil, Russia, India and China).
b) The nonzero intercept c suggested by this observation of a universal h is tobe treated like the work function in Einsteins photoelectric law K = E W
= hfW. This point is discussed more completely in the Appendix here.
The reader is also referred to the articles on Google and Research in Motion
(RIM), Limited, and Kia Motor Company, where the analogy with Einsteins
photoelectric law is used to explain financial data. The intercept c in the
universal law, y = hx + c, governing the unemployment problem is exactly
like the work function W. It is the changes in the work function for the
economy, i.e., the intercept c, which can go from a negative value (for low
unemployment levels) to a high value (for high unemployment levels and
period of the peak unemployment), determine the unemployment level.
When the economy improves, or worsens, a fixed change in the labor force
x always yields the same change in the unemployment level y = hx,
where the universal constant h is deduced as discussed here.
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6. Summary and Conclusions
1. A review of the unemployment statistics for the past 70+ years (1941-2012)is presented here to gain some insights into the current unprecedented andhistorically high unemployment (15.421 million at its peak in October
2009). This review indicates that there were three periods of very high
unemployment: 1941, 1982 and 1983, and the current period 2009-2011.
2. The labor force x and the number of unemployed y can be shown to berelated by the simple linear law y = hx + c, where the constants h and c are
to be deduced from the empirical observations on the economy.
3. It is shown that the historically high unemployment data (labor force andunemployment levels) fall on a PERFECT straight line with a slope h =0.0946. It is suggested that h is a universal constant, a unique property of the
US economy, akin to other natural constants in the hard sciences, such as
physics. The constant c in this law can therefore be compared to the work
function W in Einstein's photoelectric law. The changes in c, the economic
work function, determine the absolute levels of unemployment, with the
increase and decrease in the unemployment level, at any labor force, always
proceeding at the fixed rate h. If labor force increases or decreases by a fixed
amount, the economy will respond with the same fixed increase or decrease
in the unemployment levels, if the economic work function remains
constant. The situation is exactly analogous to Millikans photoelectricity
experiments, with different metals, to test Einstein's law.
4. The highest unemployment levels observed in 1941 (5.6 million), 1983 (10.7million) and 2010 (14.8 million) can be seen to be roughly proportional to
the increase in the size of the labor force from 1941 (56 million) to 1983
(112 million) to 2010 (154 million), or about 10% for each 50 million labor
force. This is consistent with h = 0.0946 and the fact that the intercept c 0
for the line joining the highest unemployment data.
5. A review of the unemployment data from 1941-2011 also leads to somegeneral observations. Although this does have some obvious political
overtones, the observations are firmly rooted in the mathematical facts of the
x-y unemployment diagrams presented in Appendix I).
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a) The sizeable shrinking of the labor force (due to discouraged workersleaving the work force) during the Obama years appears to be
unprecedented. Most presidential terms, with increasing or decreasing
unemployment levels, have generally been accompanied with an
increasing labor force.b) Unemployment levels have generally increased under most
Republican presidents (with Reagans second term, actually starting
1983, being an exception; with Bush II it is a mixed record as revealed
by the W-pattern on the x-y graph) and decreased under most
Democratic presidents (with FDR-Truman being an exception). The
current unprecedented high level of unemployment thus seems to be
exceptional for a Democratic President.
c) Unemployment levels also went up immediately after Reagan tookoffice and reached record high levels before the steady decline beganafter 1983. This process seems to have begun with Obama since early
2010. But the jump 2009 was unprecedented and so the recovery
can also be expected to take an extended period. Can the Presidents
policies make a difference? YES. (This is the only person opinion
being expressed here!)
6. A fuller understanding of the meaning of the economic work functionproposed here as a fundamental characteristic of the economic system (akin
to the work function in physics which also alludes to a rather complex
phenomenon) will help device policies that will keep unemployment levels
low. At least two periods of record high unemployment levels revealed in
this analysis were followed by a healthy recovery. Hence, we can expect the
coming years to witness a return to the much lower unemployment levels
that have been a hallmark of the US economy.
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7. Appendix IReinterpretation of the Unemployment data
in terms of the Economic Work FunctionIf we accept the idea of a universal constant h = 0.0946, in the unemployment law
y = hx + c, it is possible to reinterpret all the US unemployment data as merely a
reflection of the changes in the work function.
When light shines on the surface of a metal, such as lithium or sodium in
Millikans Nobel Prize winning experiments, it is being bombarded with a stream
of photons with an energy E = hf where h is the universal constant, called the
Planck constant and f is the frequency of light. According to Einstein, the photonproduces an electron with the maximum kinetic energy K = EW where W is the
work function, a unique characteristic of each metal. Here W represents the work
that must be done to eject the electron from within the metal. This means the K-f
relation is a linear, K = hfW = h(ff0). The graph of K versus f will have a
slope equal to the Planck constant h and will make finite positive intercept f = f0 =
W/h on the frequency axis. When f < f0, K = 0, i.e., no electrons are produced. All
of the energy E is absorbed fully by the metal.
Since the cut-off frequency, or what is the same the work function W, depends on
the metal on which the light shines, the data on the photoelectric effect (if we plot
say the K-f data for experiments with Li, Na, K, Cu, and Zn) will be represented by
a series of parallel lines with a slope h, the Planck constant, and an intercept W (on
K-axis) or f0, on the f-axis.
The same ideas can now be extended to the unemployment data which seems to
obey the law y = hx + c = h(xx0). Mathematically speaking, this is exactly
analogous Einsteins photoelectric law. When the labor force is less than a criticallevel, x < x0, the cut-off level, which is akin to the cut-off frequency f0 in physics,
there is no unemployment and the number of no unemployed workers y = 0. As the
labor force increases above this level, the number of unemployed workers
increases. However, the rate of increase is always constant and is given by the
fixed slope h which was deduced, as shown by consider the three rather unique
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points of highest unemployment levels observed in the last 70+ years. Thus, h =
0.0946 is similar to the other universal constants observed in nature and is a
fundamental property of the US economy. At this point, this is merely a bold
suggestion and it is obvious that further studies will be required to confirm the
universality of h by studies on the economy at different levels and in differentcountries (akin to Millikans photoelectricity experiments with different metals).
With this background, let us how we can reinterpret data, such as the data
presented in the first article on the Obama years using the idea of the economics
work function (seehttp://www.scribd.com/doc/99647215/The-US-Unemployment-
Rate-What-happened-in-the-Obama-years).
We start with the x-y unemployment diagram in Figure 8, which represents the
data for the years 1990-2008, which covers the Presidencies of the Senior Bush(George H W Bush), Clinton, and the Junior Bush (George W Bush). The data also
interestingly reveals a W-like pattern.
The labor force was increasing and the unemployment level was also increasing
(although the economy was not in any real crisis mode, as in the Obama years).
This is revealed by the first three points (1990-1992) which seem to fall on a
straight line with a positive slope. Nonetheless, it was sufficient to get Bill Clinton
elected President, with the slogan, Its the economy, Stupid, a hallmark of the
1992 Presidential campaign. The unemployment levels started falling promptly in
the Clinton years, with a concurrent expansion of the labor force. The general trend
is indicated by the straight line with a negative slope h = -0.25 joining the (x, y)
pairs for 1996 and 1999. There is nothing special about this line, other than the fact
it seemed like the correct one to pick, before I was able to deduce the universal
value of h = 0.0946 by considering historical data (after publishing the analysis for
the Obama years on July 10, 2012). One could just as easily have used a lower
slope h = -0.181 (1991 and 1999) or a higher slope h = -0.31 (1993 and 1999). If
Legendre could say that his least squares line is just one of many lines that couldbe superimposed to reveal a linear trend, then the choice of the line with h = -0.25
picked earlier is also just one of many lines that describes this data.
The reversal in the slope began in 2000, just as the first term of the George W
Bush was beginning after a historic election that decided by the courts. The
http://www.scribd.com/doc/99647215/The-US-Unemployment-Rate-What-happened-in-the-Obama-yearshttp://www.scribd.com/doc/99647215/The-US-Unemployment-Rate-What-happened-in-the-Obama-yearshttp://www.scribd.com/doc/99647215/The-US-Unemployment-Rate-What-happened-in-the-Obama-yearshttp://www.scribd.com/doc/99647215/The-US-Unemployment-Rate-What-happened-in-the-Obama-yearshttp://www.scribd.com/doc/99647215/The-US-Unemployment-Rate-What-happened-in-the-Obama-yearshttp://www.scribd.com/doc/99647215/The-US-Unemployment-Rate-What-happened-in-the-Obama-years7/31/2019 The Highest US Unemployment Rates: Obama years compared with historic highs in Unemployment levels
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Figure 9: The unemployment data for the period 1990-2008, with the straight line
y = hx + c = - 0.25x + 40.722 (Case III), see also Figure 3 in the companion
article discussing the Obama years. The W-pattern is much less prominent here
based of the difference in the scales used for the graph. The same data can,
however, be interpreted in terms of the changing economic work function if we
accept the notion of a single universal h = 0.0946 for US economy, deduced as
discussed in this article. This is illustrated in Figure 7 and again in Figure 10.
To show how the data can be reinterpreted, we expand the scale of the graph once
again to include the highest unemployment level recorded in 2010. Now, draw a
straight line y = hx + c through the 2010 (x, y) pair with the slope h = 0.0946, the
universal constant for the US economy. The equation of this line, as shown earlieris y = hx + c = 0.0946x + 0.267. Notice that the intercept c is positive and the
graph therefore does not cut the labor force axis. Instead it cuts the unemployed y-
axis at y = 0.267. The intercept c 0 and this defining line can be taken virtually as
a straight line passing through the origin (0, 0).
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
100 110 120 130 140 150 160 170 180
Unemployed,y[milli
ons]
Labor force x millions
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Now, since h is fixed, we can now construct a series of parallel lines (the dashed
lines in Figure 10) through any point we choose. The intercept c = yhx can be
deduced since h and the values of x and y are now known. Thus, we can construct
a family of parallels sweeping through the data, with the economic work function c
having different values on each line.
Figure 10: Reinterpretation of the unemployment data for the period 1990-2011
using the idea of the economic work function and a single universal constant h =
0.0946, deduced from the data for the years with the three highest unemployment
levels recorded over the last 70+ years.
Notice how the data for the Clinton years, which seemed to fall unmistakably on
a straight line with a negative slope, now appear to be merely cascading down the
parallels with decreasing values of the work functions. The rising unemployment
levels, which began during the second term of the Bush II presidency and
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
0.0 50.0 100.0 150.0 200.0 250.0
Unemployed,y[millions]
Labor force x millions
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deteriorated greatly in the Obama years can be seen to represent an increase in the
work function, a reversal of the trend during the Clinton years. An exactly similar
reinterpretation of the data is presented in Figures 8 for the period 1970-1983
which includes the years 1982 and 1983 when the unemployment levels were at
record high levels for that era. Again, the two straight line segments, labeled A andB with falling (negative slope, A) and rising (positive slope, B) unemployment
levels, with an increasing labor force, can interpreted in terms of the changing
economic work function.
Figure 11: Reinterpretation of the unemployment data for the period 1970-1983which covers the Nixon, Ford, Carter, and Reagan years, using the idea of the
economic work function and a single universal constant h = 0.0946, deduced as
discussed here. The line segments A with the negative slope is for period 1975-
1978 and covers the Carter presidency (doomed as a result of the Iranian hostage
crisis). This was followed by increasing unemployment levels during the first
-4.0
-2.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0 20 40 60 80 100 120 140 160
Unem
ployed,y[millions]
Labor force x millions
A B
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Reagan term, line segment B, leading to the highest recorded levels for that era in
1982-1983. The labor force was increasing during these years of reversals in the
slope, which can be interpreted as the back and forth changes in the economic
work function.
Figure 12: The unemployment diagram for the Kennedy-Johnson era and the first
two years of the Nixon presidency (1960-1970). The straight line with the negative
slope, with the equation y = -0.352x + 29.563, joins the (x, y) pairs for 1961 and
1966. The expansion of the labor force was accompanied with a decrease in the
unemployment levels. This trend was reversed in 1969 and 1970 when theunemployment levels started rising again, with the labor force continuing to
increase. The same data can be reinterpreted using the idea of a work function by
referring to Figure 2. The high unemployment level of 1941 looms in the
background in this plot.
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
48 52 56 60 64 68 72 76 80 84
Unemployed,y[
millions]
Labor force x millions
1941
1970
1969
1966
1961
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The following x-y unemployment diagrams are included here for completeness
for different Presidential terms revealing significant patterns. Table A and B
summarize the operating equations.
Figure 13a: The complex zigzag path taken by the economy, in the unemployment
diagram for the period 1941-1952 which includes the terms ofPresidents FDR
(last term) and Truman, beginning 1945. The slopes of the individual line
segments go from high negative to high positive values: h =y/x - 5.8 for 1941-42
(decreasing unemployed y, increasing labor force x) to h = 6.46 for 1950-51
(decreasing unemployed and decreasing labor force) with h = 0.02 for 1946-47.
The accompanying graph in Figure 13b suggests a less perplexing view based on
the universal law y = hx +c.
0.0
1.0
2.0
3.0
4.0
5.0
6.0
52 54 56 58 60 62 64
Labor force x millions
Unemployed
,y[millions]
1941
1952
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Figure 13b: The unemployment diagram for the period 1941-1952 which includes
the terms ofPresidents FDR (last term) and Truman, beginning 1945. The
unemployment level came down rapidly from its high of 5.56 million (which was
used to deduce the constant slope h = 0.0946 for the US economy) to about 1million in 1942. It then started increasing starting 1944 and reached a high of 3.63
million before falling again to about 2 million by 1951-52. The straight line joining
the 1944 and 1946 data has the equation y = 0.554x29.6 and is shown above.
The many zigzag turns taken by the economy to get to the lower unemployment
level in 1952 from the then highest level in 1941 can just also easily be understood
by envisioning a series of parallels with a slope h = 0.0946 and equation y = hx +
c = 0.0946x + c, with various values of the economic work function c. The
reduction in unemployment levels can thus be attributed to the reduction in theeconomic work function, as follows. The defining equation y = hx + c = h(x - x0).
Hence, the line through 1941point with slope h = 0.0946 has the equation y =
0.0946x + 0.271 = 0.0946 (x + 2.86). The parallel line through the 1952 point has
the equation y = 0.0946x3.995 = 0.0946 (x42.23). The change in the
numerical value c, or equivalently the numerical value of x0 (the cut-off labor force
0.0
1.0
2.0
3.0
4.0
5.0
6.0
52 54 56 58 60 62 64
Labor force x millions
Unemployed,y[millions]
1941
1945
1943
1949
1952
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when unemployment y = 0) is the change in the economic work function. As the
cut-off value x0 increases more of the labor force will be employed before
unemployment levels increase at the fixed rate y = hx = 0.0946x when x > x0;
see Figure 19 for a more detailed numerical calculation.
Figure 14: The unemployment diagram for the period 1953-1960 which includes
PresidentEisenhowerstwo terms. The straight line y = 0.305x17.395 joins the
(x, y) pairs for 1953 and 1960. The overall trend was one of increasing
unemployment levels with an increasing labor force. The four data points that lie
above the line could be taken as suggestive of changes in the economic workfunction which led to the higher unemployment levels during those years.
0.0
1.0
2.0
3.0
4.0
5.0
6.0
60 62 64 66 68 70 72 74 76
Labor force x millions
Unemployed,y[
millions]
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Figure 15: The Kennedy-Johnson era, which followed Eisenhowers terms, has
already been considered (in Figure 12). This diagram is for the period 1968-1974
which covers President Nixons terms. The straight line y = 0.177x 11.122 joins
the (x, y) pairs for 1968 and 1974. As with Eisenhower, the overall trend is again
one of increasing unemployment levels with an increasing labor force. The data
points that lie above and below the line again suggest changes in the work function
which lead to the higher (or lower) unemployment levels during those years.
0.0
1.0
2.0
3.0
4.0
5.0
6.0
78 80 82 84 86 88 90 92 94
U
nemployed,y[millions]
Labor force x millions
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Figure 16: The unemployment diagram for 1975-1983, covering the Presidential
terms of Ford (1975 only), Carter, and Reagans first three years. The labor force
was increasing and the unemployment levels were going down in the Ford-Carter
years. This trend reversed itself and unemployment levels started rising by 1980
reaching their highest recorded for the era by 1982 and 1983 (two years that
contribute to the determination of the universal constant h = 0.0946 for the US
economy). As seen earlier, in the latter part of the Reagan years, the
unemployment levels again started going down, with an increasing labor force.
0.0
2.0
4.0
6.0
8.0
10.0
12.0
90 95 100 105 110 115
Labor force x millions
Unemployed,y[millio
ns]
1975
1979
1983
1982
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Figure 17: The unemployment diagram for the period 1980-1988 which coversPresident Reagans two terms. The initial trend was one of increasing
unemployment levels with an increasing labor force. This was followed by a
sustained period of decreasing unemployment levels, again with increasing labor
force. The straight line y = 0.932x92 joins the (x, y) pairs for 1980 and 1982
whereas the downward sloping line y = - 0.347x + 48.91 joins the data points for
1982 and 1988.
The Bush I, Clinton, Bush II and Obama years have been discussed using similar
graph in the companion article to highlight the dominant trend during their terms.From Figure 18 presented earlier in the main text, under discussion of the work
function, this era witnessed the lowest unemployment levels recorded in US
history, just before George W Bush (Bush II) took office, see also Figure 9
presented earlier in the text and Figure 18 that follows next.
0.0
2.0
4.0
6.0
8.0
10.0
12.0
105 110 115 120 125
Labor force x millions
Unemployed,y[millions]
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Figure 18: The unemployment diagram for the period 1988-2000 which covers the
terms of Bush I (1988-1992), Clintons two terms and the first year of the Bush II
presidency. The unemployment level dropped every year from 1992 to 2000 falling
from a high of 9.613 million in 1992 (final year of Bush I presidency) to its
historically lowest level of 5.692 million in 2000 (final year of Clinton presidency).
The declining trend is indicated by the downward sloping line with a negative
slope. The best-fit line (linear regression) for the period 1992-2000 has the
equation y = -0.268x + 43.34 = -0.268(x 161.76) with the linear regression
coefficient r2
= 0.923. (The above is just a trend line, see also Figure 19.)
4.0
5.0
6.0
7.0
8.0
9.0
10.0
120 125 130 135 140 145
1992
2000
Labor force x millions
U
nemployed,y[millio
ns]
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Figure 19a: The reduction in the economic work function between 1961 and 1966
(the Kennedy-Johnson years, see also Figure 12) is illustrated here. (Please also
see explanation offered in the next figure caption.)The equation of the line joining
1961 and 1966 is y = -0.352x + 29.56. The labor force changed by x = 5.221 and
the unemployed changed by y = - 1.839; unemployed decreases with increasing
labor force. The parallels with the slope h = 0.0946 are:
Line through 1961: y = 0.0946x1.96 = 0.0946 (x20.72), see x-axis intercept.
Line through 1966: y = 0.0946x4.29 = 0.0946 (x45.38), see x-axis intercept.
The change in the work function c is proportional to the difference in the x 0 values
(span of the bracket on x-axis) given by the parallels: (45.38 20.72) = 24.66.
From 1961-1966, y = 1.839.Move along the top parallel for 1961 with slope h =
0.0946, with constant c, to produce the change y. The labor force has decreased.
Thus, let a = y/0.0946 = 19.44. This equals the x1 needed to reduce unemployed
0.0
2.0
4.0
6.0
8.0
10.0
0 20 40 60 80 100 120 140
Labor force x millions
Unemployed,y[millio
ns]
a
b
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andkeep labor force unchanged. Now add b = y/0.352 = 5.221, the numerical
value of the change x2 (change in labor force). This also equals the move along
the blue operating line with slope h = -0.352, intersecting the parallels. Hence,
thesum (a + b) = x1+ x2 = 19.44 + 5.22 = 24.66. This is exactly the change in
the work function or the difference in x0 values (span of the bracket) given by theparallels: (45.38 20.72) = 24.66 = (19.44 + 5.22). Thus, labor force matches
and unemployed match the observed valuedue to reduced work function!
Figure 19b: The unemployment diagram for the years 1992-2002 which covers the
Clinton years. The unemployment levels were decreasing year after year, starting
1992, and reached the lowest recorded level in US history, 5.692 million in 2000.
Linear regression yields the best-fit line, y = -0.268x + 43.34 = -0.268(x161.76)
The negative slope h = - 0.268 is due to the decreasing unemployed y with
increasing labor force x. This will be referred to as the operating line since this
is what we obviously perceive given the (x, y) data. The two parallels A and B, with
the slope h = 0.0946, can be superimposed with c = -2.51 and c = - 7.796. Start
with the 1992 data point. The number unemployed will decrease if the labor force
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0 20 40 60 80 100 120 140 160 180
Labor force x millions
Un
employed,y[million
s]
A B
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decreases along parallel A (c = - 2.51, x0 = -c/h = 26.5, see intercept on x-axis).
Move down to the horizontal red line, which is the reduced unemployment level in
2000. This is reduction of unemployment at constant work function. But actually,
the labor force increased. So, now we move along the red horizontal to the labor
force observed. The change in the work function can be seen to correspond to theincreased labor force. As in Figure 19a, we first bring labor force level to the
vertical from the 1992 data point and then proceed to the parallel B to match
increased labor force. At the vertical from the 1992 point, there is zero change in
labor force. This means work function must be reduced from the 1992 value to
produce both reduced unemployment and also an increase labor force. Or,
equivalently, the cut-off labor force x0, below which there is no unemployed, must
increase to reduce the unemployment levels.
Perhaps, the following observations from the FDR-Truman era provide some more
insights into the how changes in the work function increase/decrease the
unemployment levels.
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Figure 20: The unemployment data for 1941-952 along with the data for 1958
(Eisenhower era) is plotted here. The line y = 0.173x7.1 = 0.173 (x41.02)
joins the (x, y) pairs for 1942 and 1958 with the 1949 data lying practically on this
line. The dashed line through the 1942 data has the universal slope h = 0.0946 andhas the equation y = 0.0946 (x28.29). The cut-off labor force equals 28.29
million below which y = 0. If the work function is constant, and the labor force
increases, the unemployed will increase following this line. Notice that the data for
1950 falls almost on this line. It also appears that other data points here can be
joined by parallel lines with different values for work function c, or the cut-off
labor force x0. Now, the task is to a) understand what specific factors control
this economic work function and b) to promote policies that lead to low
unemployment.
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0 20 40 60 80
Labor force x millions
1942
Unemployed,y[millions]
1949
1958
1941
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8. Appendix II
Effect of time on unemployment stats
For completeness, let us consider now the direct effects of time, the ravages of
that all-powerful time, if any, on the unemployment statistics, by plotting the three
key parameters, the labor force x, the number of unemployed y, and the
unemployment rate, y/x, as a function of time, expressed in calendar years.
Figure 21: The labor force has increased steadily over the last 70+ years due to
the overall increase in the population. However, there are two notable exceptions.The labor force decreased during WWII (the FDR-Truman years), decreasing from
56.41 million in 1942 to 53.86 million in 1945. This is the small dip seen in the
initial years of the graph. More significant is the decrease in the labor force in the
Obama years, between 2009 and 2011. The labor force was 154.286 million in
2008 and decreased to 154.142 million in 2009 and was down to 153.616 million
0
20
40
60
80
100
120
140
160
180
1930 1940 1950 1960 1970 1980 1990 2000 2010 2020
Time, t [years]
Labo
rforce,x[millions]
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in 2011. This is largely due to the fact that discouraged workers, the long-term
unemployed, decided to leave the labor force.
Figure 22: The unemployed y, has been going up and down over the years with
changes in economic conditions. The three highest unemployment levels ever
recorded again clearly separate out in this plot. The data again falls on a NEAR
PERFECT straight line. The equation y = at + b = 0.134 t255.1, where t is time
in calendar years, describes this trend in the highest recorded unemployment
levels. The equation is determined by considering the 1941 and 2010 data.
Interpolating to 1983 gives 11.2 million unemployed, which is slightly higher than
the observed 10.72 million.
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
1930 1940 1950 1960 1970 1980 1990 2000 2010 2020
Time, t [years]
Unemployed,y[millions]
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Figure 23: The unemployment rate, y/x, expressed as a percent, for 1941-2011.
This has been going up and down with the highest recorded rates again separating
out on this graph. This rate is roughly constant and is essentially independent oftime. This suggests that the huge technological changes that we have witnessed
since WWII have played little or no effect as far as the high unemployment rates
are concerned.
Thus, it appears that we can draw the following conclusions based on these
empirical facts. When things get sour in the economy, at least in the US economy,
the unemployment rate seems to climb to a maximum of about 10%. It was 9.94%in 1941, reached 9.69% in 1982 (and 9.61% in 1983). The current highs were
9.25% in 2009 and 9.63% in 2010. This suggests that the fundamental idea of a
work function c (or the cut-off labor level x0 = - c/h) is worthy of further study.
0.0
2.0
4.0
6.0
8.0
10.0
12.0
1930 1940 1950 1960 1970 1980 1990 2000 2010 2020
Time, t [years]
Unemploymentrate(percent),
100(y/x)
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What are the socio-political and economic factors, including technological factors
that affect this economic work function? Can it be readily controlled via sound
economic policies? Is population the over-riding factor? Does employability, via
right educational and experiential skills, affect the economics work function? If so,
what policies can be adopted to affect the longer term societal objective of havinga vibrant economy with the lowest levels of unemployment?
9. Appendix III
Legendres Linear Regression and Millikans determination of the Planck
constant h from Einsteins Photoelectric Law
Although a simple linear law y = hx + c recommends itself, with the huge scatter
that we see in the unemployment data, one is forced to wonder what justification
there is, if any, for the choice of the numerical values of h and c. For example, in
the companion article on the state of the US unemployment levels during the
Obama years, the constants h and c were fixed using certain unique points in the
data being examined. However, such an analysis is of limited value unless we can
develop some kind of a theoretical justification for the choice of h and c.
The obvious solution to this dilemma is statistical analysis, such as the linear
regression analysis. This was developed by the French mathematician Legendre, in
a famous 1805 paper. It is also worth recalling here what Legendre himself says, in
this paper, when he introduces this new method, also called the method of least
squares. Legendre presented his ideas in a really short paper, with a worked out
example. Within ten years, the method came to be widely accepted and used in all
statistical analysis. Legendres exact words are, Of all the principles which can beproposed for that purpose, I think there is none more general, more exact, and
more easy of application, that of which we made use in the preceding researches,
and which consists of rendering the sum of squares of the errors a minimum.
http://www.stat.ucla.edu/history/legendre.pdfEnglish translation of the original
paper. (see also Stigler, Stephen M. (1986). The History of Statistics: The
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Measurement of Uncertainty Before 1900. Cambridge, MA: Belknap Press of
Harvard University Press.ISBN0-674-40340-1.)
When we see data points that seem to fall approximately, but NOT exactly, on a
straight line, any line is as good as any other. We only need two very good datapoints that we fully trust in order to determine the slope h and the intercept c. This
is what Legendre is pointing out here. So, how do we choice a best-fit line?
Legendre recommends his method of least squares.
Imagine a line that we think is the best-fit line through the data points. The
equation of this line is yb = hxb + c. Some of the (x, y) pairs will lie above this line
and some lie below this line. We can determine the deviation (yyb) of each point
in our data set from the best-fit line. The sum of all such deviations from thebest-fit line will be zero. This does not tell us much. However, the square of the
deviation (yyb)2will always be positive and the sum of all the squares (y yb)
2
will also be positive. Using elegant mathematical arguments, Legendre provides us
with a mathematical formula for the slope h which minimizes the sum of these
squares. Hence, the name least squares method.
However, there is nothing unique or sacrosanct about the best-fit line, or linear
regression analysis, as Legendre himself points out. It is just a simple and elegant
way of fitting a straight line when we are confronted with a huge scatter but with
an underlying linear trend (with either positive or negative slope).
Now, let us compare this with what Millikan does in his Nobel Prize winning
experiments (reported in 1916) on the photoelectric effect to deduce the value of
the universal constant h, one of the fundamental constants of nature. Millikan
published two papers on this subject, both in 1916, describing his direct
determination of the Planck constant h, from the slope of the K-f graph predicted
by Einsteins photoelectric law K = EW = hfW. Without getting into details
(this is discussed more completely in the article on Google Inc.), Einsteins theory
states that the Planck constant h is the slope of the graph of the maximum kinetic
energy of the electron K and the frequency of light f, with an intercept W which is
a property of the metal on which light is shining.
http://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/International_Standard_Book_Numberhttp://en.wikipedia.org/wiki/Special:BookSources/0-674-40340-1http://en.wikipedia.org/wiki/Special:BookSources/0-674-40340-1http://en.wikipedia.org/wiki/Special:BookSources/0-674-40340-1http://en.wikipedia.org/wiki/Special:BookSources/0-674-40340-1http://en.wikipedia.org/wiki/International_Standard_Book_Number7/31/2019 The Highest US Unemployment Rates: Obama years compared with historic highs in Unemployment levels
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Only two points on the K-f graph are required to fix the slope h. And, this is
exactly what Millikan does in his first paper of 1916. He published his results on
the experiments with lithium where he had determined the value of K accurately
using light of two different frequencies. Only two (K, f) values are presented,
promising more in the future, with the first direct determination of the numericalvalue of the universal constant h.
Only two points were needed to fix the Planck constant h because a simple theory
had been proposed to explain this complex problem of photoelectricity that was
puzzling physicists of the late 19th
and early 20th
centuries.
It is of interest to note here what Millikan does in his second paper. Here publishes
his results with lithium (K-f graph with five light frequencies) and sodium (K-fgraph with six light frequencies). One can determine at least 10 different slopes
and determine the average value of h for lithium. Or, better yet, use Legendres
least squares method and fix the slope h. Likewise, one can determine 15 slopes for
the sodium experiments and determine an average.
Millikan, however, does NOT go through all these exhaustive slope determinations
to arrive at the numerical value of one of the most fundamental constants of nature.
He determines an average value of the Planck constant h for considering only a
few slopesI suspect the slopes corresponding to what he believes are his best
measurements, considering the accuracy with which the frequency f of light is
determined (the color light used determines the frequency f).
The same approach has been taken here to determine the numerical value of h in
the universal law y = hx + c which applies to the unemployment problem of
interest to us. The observations with the highest unemp