The US National Debt Growth Rate: The Clinton-Bush-Obama Transition
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Page 1 of 32
The US National Debt Growth Rate
The Clinton-Bush-Obama Transitions A Glimpse of the Economic Work Function
http://25.media.tumblr.com/tumblr_m9kqzq6NNw1qedj2ho1_400.jpg
http://i.dailymail.co.uk/i/pix/2012/09/06/article-2198703-14BE41B1000005DC-
131_634x425.jpg In an amazing display of patriotism, the Republicans claim to have “built” the
entire $16T national debt during their recently concluded nominating convention! (DNC joke!)
The national debt was $71.060 million on Jan 1, 1790 and $75.463 million
on Jan 1, 1791. It crossed the $100 million mark in 1815-1816. It was
NOT allowed to double to $200 million or quadruple to $400 million.
Instead, it was gradually paid off and the national debt was down to
$33,733.05 on Jan 1, 1835 and briefly $0 around Jan 8, 1835. Yes, zero!
The debt crossed the $100 billion mark in 1942-43 (WWII). It doubled by
1944 and quadrupled, crossing $400 billion mark, in 1971-1972.
The USA entered the era of the trillion dollar national debt in 1981, when
Reagan was President (ten-fold increase in just 40 years!)
The national debt quadrupled, from $1T in 1981 to $4T in 1992, when the
senior George Bush was President.
It has now quadrupled a second time, crossing the $16T mark on August 31,
2012 under President Obama.
The first quadrupling (in the trillion dollar era) was accomplished in just
under three Presidential terms. The second quadrupling has taken 4.9 terms
(two Clinton, two Bush, and the partial Obama term).
Page 2 of 32
§ 1. Summary
The rate of growth of the national debt D as a function of time t, given by the slope
h = dD/dt of the D-t graph is just as important as the absolute debt level D.
Unfortunately, very little attention seems to have been devoted (at least in popular
discussions of this topic) to the precise determination of the debt growth rate,
dD/dt, and its fundamental implications.
For example, the national debt has increased by $5.363 trillion in a period of just
1319 days, less than one Presidential term (1461 days), under President Obama. It
has just crossed the $16 T mark (T = trillion) on August 31, 2012. The debt
increased by only $4.899 T during the two full terms of the Bush presidency.
The reason for the rapid rise in the debt in the Obama years is shown here to be
due to the higher rate of growth of the debt, dD/dt, towards the end of the Bush
presidency ($4585 million per day) which matches very closely with the calculated
initial debt growth rate for the Obama term ($4698 million per day). This explains
why the debt has increased so rapidly under Obama. (It has actually slowed down
to a lower rate of about $3550 million per day since Dec 31, 2010!)
The debt growth rate accelerated significantly during the Bush presidency, from an
initial rate of $1096 million per day, to a final rate of $4585 million per day. The
deviation from the initial lower rate coincides with the start of the Iraq war and the
final rapid increase in the rate coincides with the initial steps taken to arrest the
total financial meltdown of 2008.
Going a step further, it is shown here that the initial debt growth rate, during the
Clinton presidency, was about $906 million per day, which is remarkably close to
the initial growth rate for the Bush presidency. In fact, a lower initial rate of $940
million per day can be deduced for the Bush presidency (by including more data
points), making the initial rates virtually identical for the Clinton and the
Bush presidencies. In other words, the D-t graph appears to be a set of parallels
with intervening periods of a deceleration (slowing down, Clinton and Obama
terms), or an acceleration (Bush), of the debt growth.
Page 3 of 32
With the recent slowing the debt growth rate, the economy may actually be headed
towards a new parallel to the initial Clinton and Bush growth lines, which should
be established in the coming quarters.
These empirical observations (mostly) and conjectures (a few) also lead us to the
far-reaching idea of an “economic work function”, akin to the work function
conceived by Einstein to explain the photoelectric effect.
Related articles by the author available at this website
1. http://www.scribd.com/doc/104833993/Are-You-Better-Off-Than-You-Were-
Four-Years-Ago Published Sep 4, 2012. Briefly highlights the slowing down
the debt growth rate as we cross the $16 T mark. The national debt could have
been as high as $19.5T on August 30, 2012 if the high rate at the end of the
Bush presidency had continued.
2. http://www.scribd.com/doc/104803209/The-Rate-of-Growth-of-the-National-
Debt-The-Obama-versus-the-Bush-years Published Sep 3, 2012. The
importance of the debt growth rate h = dD/dt, as opposed to the debt level D, is
emphasized. The significance of the debt growth rate does not seem to have
been recognized, at least in the popular discussion.
3. http://www.scribd.com/doc/104677653/The-US-National-Debt-Brief-History-
Good-News-The-Rate-of-Growth-of-the-Debt-is-Slowing-Down , Published
Sep 1, 2012. Brief summary of the historical debt data starting with President
George Washington with attention being drawn to the recent slowing down of
the debt growth rate. The importance of the debt growth rate, as opposed to debt
levels, does not seem to have been recognized, at least in the popular
discussion.
4. http://www.scribd.com/doc/104659108/The-US-National-Debt-and-the-Long-
Term, first published on June 17, 2011, and republished Sep 1, 2012.
5. http://www.scribd.com/doc/104659448/The-US-National-Debt-Retirement-
Program, first published on June 23, 2011, before the debt default crisis which
led to lowering of the US rating, republished Sep 1, 2012.
6. http://www.scribd.com/doc/104662291/A-Radical-Proposal-to-Permanently-
Reduce-the-Unemployment-Rate, first published on October 13, 2011,
republished Sep 1, 2012.
7. http://www.scribd.com/doc/104661297/Is-Taxing-the-Rich-an-Option-for-
Budget-Deficit-Reduction, first published on July 3, 2011, republished Sep 1,
2012.
Page 4 of 32
Table of Contents
§ No. Topic Page No.
1 Summary 1
2 Introduction 5
3 Debt growth rate and speed of a moving vehicle 6
4 Bush presidency: Initial and final debt growth rates 7
5 Clinton presidency: Initial and final debt growth rates 10
6 Brief Discussion: Economic Work Function 14
7 Appendix I: Growth of the national debt during Clinton era 17
8 Appendix II: Annual Debt data from Carter to Obama 18
9 Appendix III : Bibliography of Related Articles 22
http://www.usdebtclock.org/
Page 5 of 32
§ 2. Introduction
The national debt has grown by more than $5 trillion since President Obama took
office on Jan 20, 2009, see Table 1, and has crossed the $16 trillion mark on Friday
August 31, 2012, over the Labor Day weekend. Indeed, the debt added during the
Obama years (∆D, the “delta” D, in the last column of Table 1) already exceeds
the total debt added during the two full terms of President George W Bush. Why
has the debt grown so rapidly in the Obama years?
Table 1: The US National Debt from Clinton to Obama
President Start Date Time t
(Days in office)
Debt, D
$, trillions
Debt added,
∆D
Bill Clinton 1/20/1993 2922 4.188 1.540
George W Bush 1/20/2001 2922 5.728 4.899
Barrack Obama 1/20/2009 1318 15.99 5.360
Source: Treasury Direct, Bureau of Public Debt. For President Obama, the debt
added is as of August 30, 2012. Click on hyperlink above to get the debt values for
the desired date ranges. Values analyzed here and in the earlier articles are the
quarterly figures obtained from this website.
As discussed in a recent article, Ref. [2] above (click here), the rate of growth of
the national debt, measured by the slope h = dD/dt, of the graph of debt D versus
time t, is just as important as the debt level, D. Here the time t is measured in days.
The debt growth rate is measured in dollars per day (trillions, billions, or more
conveniently, millions). Just as the speed of a moving vehicle determines how fast
it will arrive at a new location, the debt growth rate determines how quickly the
debt will reach a new level. The debt growth rates determined from the current
analysis, for these three presidencies (to date) is summarized in Table 2.
The widespread prevalence of a ticking “national debt clock” (in several countries)
implies that one is able to program a computer to display how the debt grows as a
function of time (presumably at some fixed growth rate).
Page 6 of 32
§ 3. Debt growth rate and the speed of a moving vehicle
The debt level D is just like the position x of a moving vehicle, such as a car,
moving unimpeded on an open highway. The rate of growth of the debt h = dD/dt,
is like the instantaneous speed of the vehicle. The instantaneous speed is not the
same as the average speed. The instantaneous speed is the speed at which one is
traveling when stopped, for example, by a cop, for a speeding violation. The
average speed is the total trip distance divided by the total time for the trip.
Table 2: US National Debt Growth Rate: Clinton to Obama
President Time period Debt growth rate dD/dt
Bill Clinton Jan 20, 1993 to June 30, 1994 $906 million per day
Bill Clinton Sep 30, 1999-Dec 31, 2000 - $310 million per day
Bill Clinton Jan 20, 1993-Jan20, 2001 $527 million per day
George Bush June 29, 2001-June 30 2002 $1096 million per day
George Bush June 30, 2008-Dec 31, 2008 $4585 million per day
George Bush Jan 20, 2001-Jan 20, 2009 $1677 million per day
Barrack Obama Jan 20, 2009-June 30, 2010 $4698 million per day
Barrack Obama Dec 31, 2010 to August 30, 2012 $3350 million per day
Note: The calculations and graph that support the above are described in the text
below. The high debt growth rate towards the end of the Bush presidency matches
the high growth rate at the beginning of the Obama term. The debt growth rate has
slowed down to a lower level since then and is now about $3350 million per day.
The Clinton era also experienced a brief period (Sep 30, 1999 to Dec 31, 2000) of
NEGATIVE debt growth (negative $310 million per day).
The future position of a vehicle depends not only on its current location but also on
the speed (or velocity, v) with which the vehicle is moving. The speed v = ∆x/∆t,
or more correctly the instantaneous speed, is the rate of change of distance with
time. If the vehicle is moving at 30 mph it will cover twice the distance as a
vehicle moving at 15 mph, in the same time interval ∆t. If it is moving at 60 mph,
Page 7 of 32
it will cover two times the distance covered when it is traveling at 30 mph, and
four times the distance when it was traveling at 15 mph. Likewise, the future debt
level D depends on the instantaneous rate at which the debt is growing at any point
in time, i.e., on the numerical value of h = dD/dt.
§ 4. Bush presidency: Initial and final debt growth rate
As shown in Ref. [2], where a comparison of the debt growth rate during the
Obama and Bush years is presented, the debt growth rate dD/dt was quite low at
the start of the Bush presidency: dD/dt = $1096 million per day, see Figure 3 on
page 8 here. However, by the end of the Bush presidency, this rate had increased to
$4585 million per day, see Figure 2 on page 7 here. These two graphs are
reproduced, for convenience, as Figures 1 and 2 in the current article.
The initial growth rate for the Bush presidency was determined by considering the
data from Jan 20, 2001 to Dec 31, 2003. Notice that the debt dropped slightly
between March 31, 2001 and June 30, 2001, before resuming its upward trend. All
the other data points, through Sep 30, 2002, lie almost perfectly on a straight line.
The slope of this straight line h = 0.001096 trillion per day ($1096 million per day)
was determined using classical linear regression analysis.
Subsequently, deviations from this initial growth line, labeled A, began and greatly
accelerated after the start of the Iraq war. The data for June 30, 2003 marks the
beginning of an acceleration in the growth rate (see Figure 1 of current article)
which culminates in the highest growth rate of h = 0.004585 trillion per day ($4585
million per day) observed towards the end of the Bush presidency, see Figure 2 of
the current article. This higher growth rate also matches with the initial growth rate
for the Obama years (see also Ref. [3]), which was determined exactly as just
described, for the Bush presidency.
This also explains why the debt has grown so rapidly during the Obama years and
why ∆D (“delta” debt) for the Obama term to date exceeds the ∆D for the two full
Bush terms. The growth rate of the debt had accelerated significantly, by more
than four times, from $1096 million per year to $4585 million per year, akin to
increasing the speed of a car from 15 mph to 60 mph. This higher growth rate
Page 8 of 32
continued into the beginning of the Obama term and has actually fallen since then,
to about $ 3350 million per year, see more detailed discussion here and here.
Figure 1: The initial rate of growth of the debt during the Bush presidency, Jan
20, 2001 to Dec 31, 2003. The straight line D = 0.001096t + 5.544 is the best-fit
line based on five quarterly data points obtained from the Bureau of Public Debt,
for the period June 29, 2001 to June 28, 2002.
If the high growth rate had continued during the Obama term, the debt today would
be more than $17 trillion, or even higher, about $19.5 trillion if one uses a higher
rate of h = 0.00656 ($6560 million per day) the rate between June 30, 2008 and
Dec 31, 2008 (click here for the graphical presentation of this point, Ref. [1]).
It should be noted that initial growth rate was determined by considering the
evolution of the debt over six quarters. This certainly does not make this rate an
“instantaneous” rate in the sense that the term “instantaneous” is used in physics,
or in vehicle speed determinations (to ascertain a speeding violation). Nonetheless,
the nice linearity observed here, over several quarters, permits the use of such a
5.00
5.50
6.00
6.50
7.00
0 200 400 600 800 1000 1200
Time t [Days in office]
US
Nati
on
al
De
bt,
D [
$, tr
illi
on
s]
D = 0.001096 t + 5.544 r
2 = 0.9912
Initial growth rate for Bush
A
6/30/2003
12/31/2002
Page 9 of 32
designation for the initial rate of growth of the debt. Perhaps we should call it the
“local” rate as opposed to the “overall” rate for the entire duration of the
presidency, or a presidential term (16 quarters).
Figure 2: The growth in the national debt during the transition between the Bush
second term and the Obama term. There is a near perfect match in the growth
rate h = dD/dt, as revealed by the slope of the dashed straight line which connects
the data points during this transition.
We will now discuss the debt growth characteristics during the two Clinton terms
which brought us into the 21st century. As we know, the country enjoyed a period
of relative prosperity during the Clinton years, with budget surpluses (see here in
Clinton’s own words, speaking to the Arkansas delegation during the Democratic
8.00
8.50
9.00
9.50
10.00
10.50
11.00
11.50
12.00
12.50
13.00
2000 2200 2400 2600 2800 3000 3200 3400
Time t [Days in office]
US
Nati
on
al
De
bt,
D [
$, tr
illi
on
s]
D = 0.004585 t – 2.613 Final growth rate, Bush
3/31/2008
12/31/2008
B
Page 10 of 32
National Convention, on Tuesday night, Sep 4, 2012). As we will see shortly, the
budget surplus reveals itself as an actual decrease in the national debt, or a negative
debt growth rate.
§ 5. Clinton presidency: The initial and final growth rates
The national debt at the start of the Clinton presidency was $4.188 trillion and
increased to $5.738 trillion for an average growth rate of $1.54T/2922 days =
$0.000527 trillion per day, or $527 million per day. This overall average growth
rate can be compared with the overall average growth rate for the Bush presidency
which also lasted for the same duration, $4.899T/2922days = $0.001677 trillion
per day ($1677 million per day). The average debt growth rate for the Bush years
was thus more than three times the Clinton average. The instantaneous rates,
determined by considering shorter time periods were even higher.
Figure 3: The initial debt growth rate for the Clinton presidency determined using
a linear regression analysis (data for Jan 20, 1993 through June 30, 1994).
4.00
4.20
4.40
4.60
4.80
5.00
5.20
5.40
0 200 400 600 800 1000 1200
Time t [Days in office]
US
Nati
on
al
De
bt,
D [
$, tr
illi
on
s]
6/30/1994
1/20/1993
9/29/1995
D = 0.000906 t + 4.187 r
2 = 0.9958
Initial growth rate for Clinton
Page 11 of 32
For the Clinton presidency, the initial debt growth rate was determined as
described earlier for the Obama and Bush presidencies by considering the data for
the period Jan 20, 1993 to June 30, 1994, see Figure 3. A remarkably linear trend is
observed with the best-fit line having a slope h = dD/dt = 0.000906 trillion per day,
or $906 million per day. The overall evolution of the debt during the two Clinton
terms is illustrated graphically in Figure 4.
Figure 4: Overall evolution of the debt during the two Clinton terms. The blue
diamonds represent the Clinton data. The red squares represent the initial data for
the Bush presidency and yields the initial debt growth rate for the Bush presidency.
Notice that the initial growth rates were roughly the same for both the Clinton
and the Bush presidencies with the data falling on roughly parallel lines.
It is important to note that the data begins to deviate significantly from this initial
growth line after Sep 29, 1995. There was a significant slowing down in the debt
growth rate. We also observe a small peak (maximum point) on the graph and
an actual decrease in the debt (negative slope) due to the budget surpluses that
were enjoyed during these years. This is highlighted separately in Figure 5.
4.00
4.50
5.00
5.50
6.00
6.50
7.00
0 1000 2000 3000 4000 5000
Time t [Days in office]
US
Nati
on
al
De
bt,
D [
$,
trilli
on
s]
D = 0.00091 t + 4.187 r2 = 0.9958
Initial growth rate for Clinton
D = 0.00094 t + 5.71 Initial growth rate, Bush
Page 12 of 32
The dashed red line with the negative slope is the overall change between Sep 30,
1999 and Dec 31, 2000. The red square represents the final data point, the national
debt on the last day of the Clinton presidency. The debt increased slightly between
Election Day 2000 and Inauguration Day, Jan 20, 2001.
Figure 5: The debt growth rate slowed down during the Clinton years, starting
with the third quarter of 1995 (Sep 29, 1995). A small peak was observed on the D-
t graph followed by a brief period where the debt D was actually decreasing with
time t, yielding a negative slope dD/dt, which is highlighted here using an
expanded scale. The red dashed line with the negative slope illustrates the overall
change from Sep 30, 1999 to Dec 31, 2000. There was a small increase in the debt
between Election Day 2000 and Inauguration Day 2001 (red square).
Finally, a composite plot of the debt growth for the Clinton-Bush-Obama years is
presented in Figure 6. The initial growth rate established during the Clinton first
term is indicated by the straight line labeled A. It is of interest to note that, because
of the significant slowing down of the debt growth rate during the Clinton
5.64
5.66
5.68
5.70
5.72
5.74
5.76
5.78
5.80
2400 2500 2600 2700 2800 2900 3000
Jan 20, 2001
12/31/2000
9/30/1999
Time t [Days in office]
US
Nati
on
al
De
bt,
D [
$, tr
illi
on
s]
Negative Debt Growth Rate, Clinton
D = -0.00031t + 6.5662
Page 13 of 32
presidency, much of the data for the Bush years falls below the extrapolation based
on this initial debt growth rate for the Clinton era. The crossover occurred between
September and December 2007. On Sep 28, 2007, the debt D had just crossed the
$9T mark and was equal to $9.008 trillion. The projection based on Line A is
slightly higher, being $9.047 trillion. On Dec 31, 2007, the debt D was $9.229T
and the projected value was slightly lower, being $9.132 T.
Figure 6: Composite plot illustrating the growth of the debt during the Clinton-
Bush-Obama years. Extrapolating from the initial growth line A, established
during the Clinton presidency shows that the national debt, on August 31, 2012
(day 7164 since Clinton took office), would be $10.677 T instead of $16.106T.
In other words, the “prosperity” of the Clinton era, and the reduction in the growth
of the debt during the two Clinton terms seems to have been sufficient to “cushion”
even the multi-trillion dollars spent on the Bush wars, see also Figures 7 and 8 in
Appendix II. (It remains to be seen if democracy will take root in Iraq and in the
larger Middle East!).
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
18.00
0 1000 2000 3000 4000 5000 6000 7000 8000
Time t [Days in office]
US
Nati
on
al
De
bt,
D [
$, tr
illi
on
s]
D = 0.00091 t + 4.187 r2 = 0.9958
Initial growth rate for Clinton
Clinton Bush Obama
A
Page 14 of 32
The debt growth rate accelerated significantly and started rising above the Clinton
Base Line A, only after the total financial meltdown experienced in 2008. As
discussed earlier, the debt growth rare dD/dt increased to $4585 million per day
(slope of the line joining March 31, 2008 and Dec 31, 2008 data points) as the
Bush presidency came to an end. An even higher growth rate dD/dt = $6560
million per day is deduced if we consider the June 30, 2008 and Dec 31, 2008. The
lasting effects of this huge acceleration in the debt growth rate in 2008 are still
being felt, although the debt growth rate has indeed slowed down to about $3550
million per day, since March 2011.
§ 6. Brief Discussion: The Economic Work Function
Quite interestingly, with the start of the Bush presidency, the debt started
increasing once again (see red squares in Figure 4) at roughly the same rate as the
initial rate observed for the Clinton presidency. As noted earlier (see also Figure 1
of current article), the initial debt growth rate for the Bush era was calculated at
$1096 million per day, using classical linear regression analysis. Five out of seven
data points from Jan 20, 2001 to June 28 2002 were used to develop this regression
equation. (The data for Jan 20, 2001 and March 31, 2001 were excluded since the
debt decreased slightly at first before moving along the line labeled A in Figure 1).
Instead, if we use the data points for March 30, 2001 and March 31, 2003, we
deduce a slightly lower slope h = 0.00094 trillion per day ($940 million per day)
which matches almost exactly the initial Clinton slope of $906 million per day.
This seems like a remarkable coincidence.
This observation leads us to the speculation that the national debt data, like other
financial data for corporations such as Microsoft (click here and here) and the new
General Motors (click here and here), may also essentially be “jumping” from one
parallel to another with an extended transition period, as observed during the
Clinton presidency. This, therefore, lends support to the far reaching idea of an
“economic work function” governing the functioning of the economy as a whole,
as well as individual corporations. The economic work function suggested here is
akin to the work function W introduced by Einstein when he formulated his
Page 15 of 32
famous photoelectric law, in 1905. Further discussion of this point may be found in
the articles discussing the financial performance of Microsoft, Google, the new
General Motors and Kia Motor Company.
Einstein’s photoelectric law is a simple linear law K = E – W = hf – W = h(f – f0)
which is exactly similar to the linear law y = hx + c = h(x – x0) relating revenues x
and profit y for a company and now the national debt D and time t. As discussed in
several articles cited, this linear profits-revenues law is a consequence of the
classical “breakeven” analysis for the profitability of a company. The nonzero
intercept c, often observed in the analysis of financial data, and now the national
debt data as well, is analogous to Einstein’s work function W from physics.
Very briefly, when light shines on the surface of a metal, electrons are ejected
which can be collected and made to flow in an external circuit. Modern photocells,
used in a variety of applications, work on this principle. The photons that strike the
metal surface have the energy E = hf where h is a universal constant called the
Planck constant and f is the frequency (of light, which also have a wave
characteristic). Some of this energy E must be given up to do the work needed to
overcome the forces that bind the electron to the metal. Einstein calls this the work
function W, which is a characteristic property of the metal. Hence, the maximum
(kinetic) energy of the electron K = E – W. The graph of K versus f is thus a
series of parallels with an intercept c = - W, the negative of the work function.
As the frequency f increases above the cut-off value of f0, the kinetic energy of the
electron K also increases, following the linear K-f law. However, if there is a
fundamental change in the characteristic of the metal upon which the photons
strike, the work function W changes and the photoelectric data (K, f values) shifts
to a parallel line with the same slope h but with a different intercept c = - W, which
may be higher or lower depending on the nature of the metal with which the
photons are interacting.
We see exactly the same kind of movement along parallels when we study the
financial data for “good” companies like Microsoft and Google which have set the
modern standard of excellence for financial performance. Interestingly, the new
GM also reveals the same behavior. The financial world is governed by the
Page 16 of 32
universal law P = R – C where profits P is exactly analogous to the energy K of the
electron, the revenues R is exactly analogous to the energy of the photon E and the
costs C are exactly similar to the “work” that must be done to produce the electron.
Not all of the revenues R will appear as profits P. Some of the revenue must be
given up, in the form of costs C, just as the energy W must be given up in the
photon-electron interaction problem. More generally, the nonzero intercept c can
be thought of as a “generalized work function” whenever we observe a simple
linear law when analyzing the behavior of a complex system.
And so, it appears that we may be witnessing, or getting at least a glimpse, of
exactly a similar type of behavior with the national debt data.
A more complete study of ALL of the national debt will, no doubt, reveal further
insights into this suggestion. More importantly, future observations will be even
more meaningful. We already know that the debt growth rate has slowed down
significantly during the Obama term to date. Perhaps, the data is moving towards a
new parallel, with a lower (or more negative) value of the intercept in the simple
law, D = ht + c, relating debt D and time t.
In summary, the reader is urged to consider the graph in Figure 4, which shows
the initial slope is, quite amazingly, almost exactly the same for both Clinton
and Bush. It is this striking feature of the D-t graph that has prompted the
discussion here about the “economic work function”, i.e., the name that can be
given to the nonzero intercept in all linear laws, y = hx + c. This nonzero intercept
can be thought of as the analog of the work function in Einstein's photoelectric law.
Also, important are the findings as presented in Figures 6, 7 and 8, with the last
two being relegated to Appendix II. Going beyond partisan rhetoric, these graphs
show that the huge acceleration of the debt growth rate, as the Bush presidency
came to an end, has now been stopped. However, like a relay runner, President
Obama was also stuck with the high debt growth rate handed to him, which is
clearly primarily the result of the financial meltdown. The analysis in Figure 6 to 8
implies that the effect of the financial meltdown was even more important than the
effect of the Bush wars: the Iraq war, the Afghan war, and the war on terrorism.
Page 17 of 32
§ 7. Appendix I US National Debt during the Clinton terms
Date Time t (days in office) Debt, D $, trillions
1/20/1993 1 4.188
3/31/1993 71 4.226
6/30/1993 162 4.352
9/30/1993 254 4.411
12/31/1993 346 4.536
3/31/1994 436 4.576
6/30/1994 527 4.646
9/30/1994 619 4.693
12/31/1994 711 4.800
3/31/1995 801 4.864
6/30/1995 892 4.951
9/29/1995 983 4.974
12/29/1995 1074 4.989
3/29/1996 1165 5.118
6/28/1996 1256 5.161
9/30/1996 1350 5.225
12/30/1996 1441 5.271
3/31/1997 1532 5.381
6/30/1997 1623 5.376
9/30/1997 1715 5.413
12/30/1997 1806 5.502
3/31/1998 1897 5.542
6/30/1998 1988 5.548
9/30/1998 2080 5.526
12/31/1998 2172 5.614
3/31/1999 2262 5.652
6/30/1999 2353 5.639
9/30/1999 2445 5.656
12/31/1999 2537 5.776
3/31/2000 2628 5.773
6/30/2000 2719 5.686
9/29/2000 2810 5.674
12/31/2000 2903 5.662
1/20/2001 2923 5.728
Source: Bureau of Public Debt. A similar tabulation of the debt data for the Bush
and the Obama years is provided in Refs. [1-3] cited earlier.
Page 18 of 32
§ 8. Appendix II
Annual National Debt from Carter to Obama
President Year Debt, D
$, trillions
President Year Debt, D
$, trillions
Clinton 1993 4.411
Ford 1976 0.620 1994 4.693
Carter 1977 0.699 1995 4.974
1978 0.772 1996 5.225
1979 0.827 1997 5.413
1980 0.908 1998 5.526
Reagan 1981 0.998 1999 5.656
1982 1.142 2000 5.674
1983 1.377 Bush-II 2001 5.807
1984 1.572 2002 6.228
1985 1.823 2003 6.783
1986 2.125 2004 7.379
1987 2.350 2005 7.933
1988 2.602 2006 8.507
Bush-I 1989 2.857 2007 9.008
1990 3.233 2008 10.025
1991 3.665 Obama 2009 11.910
1992 4.065 2010 13.561
2011 14.790
8/31/2012 16.016
Source: Bureau of Public Debt. Daily debt values (from which the quarterly data
were deduced) are only available through 1993. Annual data are available from
1790 to present. The above debt figures are for fiscal year ending Sep 30 of each
year. Hence, Ford was still President in 1976, on the date corresponding to the
debt figure here. The $1 T mark was crossed in 1981, when Reagan was President.
The debt figure crossed the $4T mark in 1992 (President Bush-I), the $9T mark in
2007 and $10T mark in 2008 (President Bush-II). It has now crossed the $16T
mark under President Obama, on August 31, 2012.
Page 19 of 32
Figure 7: Growth of the national debt from 1976 to 2001. Values plotted here are
for the fiscal year ending Sep 30 of each year.
The main purpose here is to discuss briefly the debt growth rate in the era since
1981 when the national debt crossed the $1T mark (one trillion) during the first
year of the Reagan presidency. As we see here, the debt was actually increasing at
an accelerating rate (curve with increasing slope) between 1976 and 1986 after
which the debt started increasing at a fixed rate (constant positive slope). The
equation for the best-fit line (deduced using linear regression analysis), considering
ALL the data from 1985 to 1995, is D = 0.327t – 646.9, with a very high linear
regression coefficient r2 = 0.9932. The debt growth rate then slowed down starting
1997, during the second term of the Clinton presidency.
The rate of growth of the debt, given by the slope of the best-fit line, h = dD/dt =
0.327 trillion per year, or $0.000895 trillion per day, or $895 million per day, is in
agreement with the value of $906 million per day deduced as the initial growth rate
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
1976 1980 1984 1988 1992 1996 2000 2004
Time t [in Calendar years]
US
Nati
on
al
De
bt,
D [
$, tr
illi
on
s]
Cale
nd
ar
years
]
Quadrupling of debt $1T to $4T
Reagan-Bush I
Approx. 50% increase in Debt
$4T to ≈ $6T Clinton
D = 0.327t – 646.9 r2 = 0.9932
A
Page 20 of 32
for the Clinton presidency, which started in 1993, overlapping the period 1985 to
1995 used to arrive at the slope here.
Figure 8: The growth of the national debt from Sep 30, 1976 to August 31, 2012.
The debt figures are for fiscal year ending Sep 30, except the 2012 value.
As noted earlier, the national debt quadrupled, from $1T to $4T, in the Reagan and
Bush I presidencies (3 terms). It has quadrupled again and crossed the $16T mark.
This, however, occurred, over 4.9 presidential terms (Clinton 2, Bush-II 2, and
Obama 1319 days out of 1461 for first term). The effect of the slowing down in the
debt growth rate during the Clinton terms is also obvious in the plot prepared in
Figure 7. The debt values are lower than predicted by the extrapolation of the line
A, the slope of which matches the initial growth rate for the Clinton presidency
(deduced using quarterly figures). The debt starts deviating and increasing rapidly
above this Line A only after 2008, which coincides again with the near total
financial meltdown experienced that year. The red line B, with the steeper slope
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
18.00
20.00
1976 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016 2020
Time t [in Calendar years]
US
Nati
on
al
De
bt,
D [
$, tr
illi
on
s]
Cale
nd
ar
years
]
D = 0.327t – 646.9 r2 = 0.9932
D = 1.51t – 3021.7 r2 = 0.9921
A
B
Page 21 of 32
now describes the data. The equation of the line joining the 2007 and 2011 data is
D = 1.4455t – 2892. The slope h = dD/dt equals $1.44T per year or $0.004058
trillion per day, or $4058 million per day, is again seen to be in agreement with the
high rate of h = dD/dt = $4585 million per day deduced as the final rate for the
Bush-II presidency. The best-fit line through these five points has the equation D =
1.51 t – 3021.7 with a linear regression coefficient r2 = 0.9921. The slope h = D/dt
= $1.51T per year is again in agreement with the slope $1.4455T per year deduced
using only two data points.
Figure 9: The quadrupling US march to its first trillion in national debt. The debt
crossed the $100 billion mark, as the US entered WWII (1941-1942). It doubled to
$200 billion by 1944 and quadrupled to $400 billion by 1971-1972. This
quadrupling took about 30 years (8 Presidential terms). It crossed the $1T mark in
1981 when Reagan was President and quadrupled to $4T by 1992 when the senior
George Bush was President (3 Presidential terms). It has quadrupled again to
$16T in Obama’s first term (4.9 Presidential terms).
0
200
400
600
800
1000
1200
1400
1600
1936 1944 1952 1960 1968 1976 1984 1992
US
Nati
on
al
De
bt,
D [
$,
bil
lio
ns
]
Cale
nd
ar
years
]
Time t [in Calendar years]
Page 22 of 32
Figure 10: Between 1946 and 1948, after the end of WWII, the US actually started
paying off its debt. The debt also went down between 1950 and 1951 and 1955 and
1956. This negative slope on the D-t graph was seen again during the Clinton era;
see historical tables on budget deficits and surpluses going back to 1789 (George
Washington was sworn in as the first President, there was no White House then);
see http://www.gpo.gov/fdsys/pkg/BUDGET-1996-TAB/pdf/BUDGET-1996-
TAB.pdf . (Between 1920 to 1930 the US enjoyed a period of uninterrupted budget
surpluses, see Figure 11.)
250
255
260
265
270
275
280
285
290
1944 1948 1952 1956 1960 1964
Time t [in Calendar years]
US
Nati
on
al
De
bt,
D [
$,
bil
lio
ns
]
Cale
nd
ar
years
]
Page 23 of 32
Figure 11: The US national debt from 1900-1940, just before the entry into WWII.
In the 1920s, as we see here, the US enjoyed a period of uninterrupted budget
surpluses with government receipts exceeding outlays each year, resulting in a
reduction in the debt and the negative slope of the D-t graph. Notice also the
remarkably linearity of the graph. The debt then started rising again, following
again a remarkably linear trend. The general equation describing these trends is D
= ht + c, where the slope h and the intercept c can be fixed by considering the end
points for the time period of interest. Alternatively, one could perform a linear
regression analysis, if more accurate quantitative estimates are of interest. The
equation D = -0.977t + 1901.3, for the downward trend, is deduced by simply
joining the two ends points 1920 and 1930. The upward trend is described by D =
2.907t – 5597.5 = 2.907 (t – 1925.2). The slope, or the rate of increase or decrease
dD/dt is in billions per year; see historical tables on budget deficits and surpluses
http://www.gpo.gov/fdsys/pkg/BUDGET-1996-TAB/pdf/BUDGET-1996-TAB.pdf .
0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
45.00
50.00
1896 1904 1912 1920 1928 1936 1944 1952
Time t [in Calendar years]
US
Nati
on
al
De
bt,
D [
$,
bil
lio
ns
]
Cale
nd
ar
years
] D = -0.977t + 1901.3
D = 2.907t - 5597
Page 24 of 32
We can learn from the historical trends described here in Figures 6 to 11 (see also
Ref.[4] listed in the beginning of this article) and not get paralyzed by the
mindboggling trillions that are now being repeatedly thrown at us. Billions were
mindboggling numbers too, in an earlier era. The debt will eventually be paid off,
as the US has done repeatedly in its history.
The national debt has always increased when the US was faced with a crisis. In
most cases, based on history, it appears that the rise in the debt can always be
associated with wars the US got engaged in: first the Revolutionary war debt, then
war of 1812, then the Civil war, then the WWII, the Cold war, the Vietnam war,
and more recently the war on terrorism and the Iraq and Afghan wars. The only
exception to this war-debt rise scenario is the rapid rise in the debt that we observe
following the financial meltdown in 2008, towards the end of the Bush presidency.
Even the Bush wars, thanks to the reduction in the debt growth rate of the Clinton
era, did not lead to the acceleration we see following the self-inflicted wounds of
the financial sector in 2008. The debt levels were lower than the extrapolated
values (based on the initial Clinton debt growth line, see Figure 6) up until the
financial crisis of 2008.
JOBS, Jobs, Plenty of jobs, is what we need today to regain our lost prosperity.
I sincerely hope everyone will reflect on this before heading for the polls on, or
before (in some cases, absentee ballots, I mean), November 6, 2012.
Page 25 of 32
§ 9. Appendix III: Bibliography
Related Internet articles posted at this website
Since the Facebook IPO on May 18, 2012
The first article listed below discusses a little known mathematical property of a
straight line. Figures 1 to 3 in this article provide the philosophical basis for
considering the significance of a nonzero intercept c as it applies to many problems
in the real world. We make observations (x and y values of interest to us) to deduce
y/x, usually called “rates”, “ratios”, or percentages.
1. http://www.scribd.com/doc/102000311/A-Little-Known-Mathematical-
Property-of-a-Straight-Line-Strange-but-true-there-is-one Published August 4,
2012.
Financial data (Profits-Revenues) analysis and Generalization of Planck’s law
beyond physics.
2. http://www.scribd.com/doc/95906902/Simple-Mathematical-Laws-Govern-
Corporate-Financial-Behavior-A-Brief-Compilation-of-Profits-Revenues-
Data Current article with all others above cited for completeness, Published
June 4, 2012 with several revisions incorporating more examples.
3. http://www.scribd.com/doc/94647467/Three-Types-of-Companies-From-
Quantum-Physics-to-Economics Basic discussion of three types of
companies, Published May 24, 2012. Examples of Google, Facebook,
ExxonMobil, Best Buy, Ford, Universal Insurance Holdings
4. http://www.scribd.com/doc/96228131/The-Perfect-Apple-How-it-can-be-
destroyed Detailed discussion of Apple Inc. data. Published June 7, 2012.
5. http://www.scribd.com/doc/95140101/Ford-Motor-Company-Data-Reveals-
Mount-Profit Ford Motor Company graph illustrating pronounced maximum
point, Published May 29, 2012.
Page 26 of 32
6. http://www.scribd.com/doc/95329905/Planck-s-Blackbody-Radiation-Law-
Rederived-for-more-General-Case Generalization of Planck’s law,
Published May 30, 2012.
7. http://www.scribd.com/doc/94325593/The-Future-of-Facebook-I Facebook
and Google data are compared here. Published May 21, 2012.
8. http://www.scribd.com/doc/94103265/The-FaceBook-Future Published May
19, 2012 (the day after IPO launch on Friday May 18, 2012).
9. http://www.scribd.com/doc/95728457/What-is-Entropy Discussion of the
meaning of entropy (using example given by Boltzmann in 1877, later also
used by Planck to develop quantum physics in 1900). The example here shows
the concepts of entropy S and energy U (and the derivative T = dU/dS) can be
extended beyond physics with energy = money, or any property of interest.
Published June 3, 2012.
10. The Future of Southwest Airlines, Completed June 14, 2012 (to be
published). http://www.scribd.com/doc/102835946/The-Future-for-Southwest-
Airlines-The-Unknown-Story-of-Rising-Costs-and-the-Maximum-Point-on-
Profits-Revenues-Curve Published August 14, 2012.
11. The Air Tran Story: An Important Link to the Future of Southwest Airlines,
Completed June 27, 2012 (to be published).
http://www.scribd.com/doc/102832984/The-Air-Tran-Story-The-Merger-and-
Maximum-Point-on-Profits-Revenues-Graph Published August 14, 2012.
12. Annie’s Inc. A Single-Product Company Analyzed using a New
Methodology, http://www.scribd.com/doc/98652561/Annie-s-Inc-A-Single-
Product-Company-Analyzed-Using-a-New-Methodology Published June 29,
2012
13. Google Inc. A Lovable One-Trick Pony Another Single-product Company
Analyzed using the New Methodology.
http://www.scribd.com/doc/98825141/Google-A-Lovable-One-Trick-Pony-
Another-Single-Product-Company-Analyzed-Using-the-New-Methodology,
Published July 1, 2012.
Page 27 of 32
14. GT Advanced Technologies, Inc. Analysis of Recent Financial Data,
Completed on July 4, 2012. (To be published).
15. Disappearing Brands: Research in Motion Limited. An Interesting type of
Maximum Point on the Profits-Revenues Graph
http://www.scribd.com/doc/99181402/Research-in-Motion-RIM-Limited-Will-
Disappear-in-2013 Published July 5, 2012.
16. Kia Motor Company: A Disappearing Brand
http://www.scribd.com/doc/99333764/Kia-Motor-Company-A-Disppearing-
Brand, Published July 6, 2012.
17. The Perfect Apple-II: Taking A Second Bite: A Simple Methodology for
Revenues Predictions (Completed July 8, 2012, To be Published)
http://www.scribd.com/doc/101503988/The-Perfect-Apple-II, Published
July 30, 2012.
18. http://www.scribd.com/doc/101062823/A-Fresh-Look-at-Microsoft-After-its-
Historic-Quarterly-Loss Microsoft after the quarterly loss, Published July 25,
2012.
19. http://www.scribd.com/doc/101518117/A-Second-Look-at-Microsoft-After-the-
Historic-Quarterly-Loss , Published July 30, 2012.
20. http://www.scribd.com/doc/103265909/A-Brief-Analysis-of-Groupon-s-Profits-
Revenues-Data Published August 19, 2012.
21. http://www.scribd.com/doc/103027366/Groupon-Analysis-of-Profits-
Revenues-Data-and-its-Business-Model Published August 16, 2012. More
detailed analysis including discussion of the idea of a work function.
22. http://www.scribd.com/doc/103369016/Analysis-of-Zynga-s-Profits-Revenues-
Data-Maximum-point-on-the-profits-revenues-curve Published August 20,
2012.
General Motors Financial Data
23. http://www.scribd.com/doc/103600274/The-New-GM-A-Brief-Analysis-of-the-
Profits-Revenues-Data-through-1Q2011, Published May 9, 2011 and again on
August 22, 2012, Discussion of the new GM data from 1Q2010 to 1Q2011.
24. http://www.scribd.com/doc/103607023/Why-Can-t-General-Motors-be-more-
like-Microsoft-The-new-GM-may-just-be Published August 22, 2012.
Page 28 of 32
25. http://www.scribd.com/doc/103938349/GM-Before-the-Bankruptcy-Maximum-
Point-on-Profits-Revenue-Graph GM Before the Bankruptcy: Maximum
point on the profits-revenues graph, Published August 25, 2012.
******************************************************************
The Unemployment Problem: Evidence for a Universal value of h in the
unemployment law.
26. http://www.scribd.com/doc/100984613/Further-Empirical-Evidence-for-the-
Universal-Constant-h-and-the-Economic-Work-Function-Analysis-of-
Historical-Unemployment-data-for-Japan-1953-2011 Single universal value of
h for US, Canada and Japan in the unemployment law y = hx + c, Published
July 24, 2012.
27. http://www.scribd.com/doc/100939758/An-Economy-Under-Stress-
Preliminary-Analysis-of-Historical-Unemployment-Data-for-Japan, Published
July 24, 2012.
28. http://www.scribd.com/doc/100910302/Further-Evidence-for-a-Universal-
Constant-h-and-the-Economic-Work-Function-Analysis-of-US-1941-2011-and-
Canadian-1976-2011-Unemployment-Data Published July 24, 2012.
29. http://www.scribd.com/doc/100720086/A-Second-Look-at-Australian-2012-
Unemployment-Data, Published July 22, 2012.
30. http://www.scribd.com/doc/100500017/A-First-Look-at-Australian-
Unemployment-Statistics-A-New-Methodology-for-Analyzing-Unemployment-
Data , Published July 19, 2012.
31. http://www.scribd.com/doc/99857981/The-Highest-US-Unemployment-Rates-
Obama-years-compared-with-historic-highs-in-Unemployment-levels ,
Published July 12, 2012.
32. http://www.scribd.com/doc/99647215/The-US-Unemployment-Rate-What-
happened-in-the-Obama-years , Published July 10, 2012.
****************************************************************
Traffic-fatality and Teen pregnancy problem
33. http://www.scribd.com/doc/101982715/Does-Speed-Kill-Forgotten-US-
Highway-Deaths-in-1950s-and-1960s Published August 4, 2012.
34. http://www.scribd.com/doc/101983375/Effect-of-Speed-Limits-on-Fatalities-
Texas-Proofing-of-Vehciles Published August 4, 2012.
Page 29 of 32
35. http://www.scribd.com/doc/101828233/The-US-Teenage-Pregnancy-Rates-1
Published August 2, 2012.
36. http://www.scribd.com/doc/102384514/A-Second-Look-at-the-US-Teenage-
Pregnancy-Rates-Evidence-for-a-Predominant-Natural-Law Published August
8, 2012.
Government and National Debt
37. http://www.scribd.com/doc/104663110/The-United-States-Postal-Service-A-
Test-Case-to-Understand-the-US-Government-Inefficiencies-and-Budget-Cuts-
Ahead United States Postal Service: A Test case for government inefficiencies,
Published Sep 2, 2012.
38. http://www.scribd.com/doc/104833993/Are-You-Better-Off-Than-You-Were-
Four-Years-Ago Published Sep 4, 2012. Briefly highlights the slowing down
the debt growth rate as we cross the $16 T mark. The national debt could have
been as high as $19.5T on August 30, 2012 if the high rate at the end of the
Bush presidency had continued.
39. http://www.scribd.com/doc/104803209/The-Rate-of-Growth-of-the-National-
Debt-The-Obama-versus-the-Bush-years Published Sep 3, 2012. The
importance of the debt growth rate h = dD/dt, as opposed to the debt level D, is
emphasized. The significance of the debt growth rate does not seem to have
been recognized, at least in the popular discussion.
40. http://www.scribd.com/doc/104677653/The-US-National-Debt-Brief-History-
Good-News-The-Rate-of-Growth-of-the-Debt-is-Slowing-Down , Published
Sep 1, 2012. Brief summary of the historical debt data starting with President
George Washington with attention being drawn to the recent slowing down of
the debt growth rate. The importance of the debt growth rate, as opposed to debt
levels, does not seem to have been recognized, at least in the popular
discussion.
41. http://www.scribd.com/doc/104659108/The-US-National-Debt-and-the-Long-
Term, first published on June 17, 2011, and republished Sep 1, 2012.
42. http://www.scribd.com/doc/104659448/The-US-National-Debt-Retirement-
Program, first published on June 23, 2011, before the debt default crisis which
led to lowering of the US rating, republished Sep 1, 2012.
Page 30 of 32
43. http://www.scribd.com/doc/104662291/A-Radical-Proposal-to-Permanently-
Reduce-the-Unemployment-Rate, first published on October 13, 2011,
republished Sep 1, 2012.
44. http://www.scribd.com/doc/104661297/Is-Taxing-the-Rich-an-Option-for-
Budget-Deficit-Reduction, first published on July 3, 2011, republished Sep 1,
2012.
Page 31 of 32
About the author
V. Laxmanan, Sc. D.
Email: [email protected]
The author obtained his Bachelor’s degree (B. E.) in Mechanical Engineering from
the University of Poona and his Master’s degree (M. E.), also in Mechanical
Engineering, from the Indian Institute of Science, Bangalore, followed by a
Master’s (S. M.) and Doctoral (Sc. D.) degrees in Materials Engineering from the
Massachusetts Institute of Technology, Cambridge, MA, USA. He then spent his
entire professional career at leading US research institutions (MIT, Allied
Chemical Corporate R & D, now part of Honeywell, NASA, Case Western Reserve
University (CWRU), and General Motors Research and Development Center in
Warren, MI). He holds four patents in materials processing, has co-authored two
books and published several scientific papers in leading peer-reviewed
international journals. His expertise includes developing simple mathematical
models to explain the behavior of complex systems.
While at NASA and CWRU, he was responsible for developing material processing
experiments to be performed aboard the space shuttle and developed a simple
mathematical model to explain the growth Christmas-tree, or snowflake, like
structures (called dendrites) widely observed in many types of liquid-to-solid phase
transformations (e.g., freezing of all commercial metals and alloys, freezing of
water, and, yes, production of snowflakes!). This led to a simple model to explain
the growth of dendritic structures in both the ground-based experiments and in the
space shuttle experiments.
More recently, he has been interested in the analysis of the large volumes of data
from financial and economic systems and has developed what may be called the
Quantum Business Model (QBM). This extends (to financial and economic
systems) the mathematical arguments used by Max Planck to develop quantum
physics using the analogy Energy = Money, i.e., energy in physics is like money in
economics. Einstein applied Planck’s ideas to describe the photoelectric effect (by
treating light as being composed of particles called photons, each with the fixed
quantum of energy conceived by Planck). The mathematical law deduced by
Page 32 of 32
Planck, referred to here as the generalized power-exponential law, might actually
have many applications far beyond blackbody radiation studies where it was first
conceived.
Einstein’s photoelectric law is a simple linear law, as we see here, and was
deduced from Planck’s non-linear law for describing blackbody radiation. It
appears that financial and economic systems can be modeled using a similar
approach. Finance, business, economics and management sciences now essentially
seem to operate like astronomy and physics before the advent of Kepler and
Newton.
Cover page of AirTran 2000 Annual