The Highest US Unemployment Rates: Obama years compared with historic highs in Unemployment levels

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.jpg


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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=false


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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.pdf


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2. List of Figures and brief captions

Figure 1: The US unemployment data for the years 1941-1960.


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.


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-years


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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.


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.


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


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


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-years


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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]



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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.


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]



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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]


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]


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


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



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


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]



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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


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




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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


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


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


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


1942


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]



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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
http://www.stat.ucla.edu/history/legendre.pdfhttp://www.stat.ucla.edu/history/legendre.pdf


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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_Number


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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

Documents

The Highest US Unemployment Rates: Obama years compared with historic highs in Unemployment levels