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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).

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§ 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.

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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.

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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/

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§ 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).

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§ 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,

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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

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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

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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

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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

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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

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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

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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

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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

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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: vlaxmanan@hotmail.com

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