Income Taxes II

 

Georgia Tech Fight Song 

I'm a Ramblin' Wreck from Georgia Tech
And a hell of an engineer 

What does an engineer think of the income tax code? 

Engineers, such as me, think Talking Barbie is correct. Math is hard.  Engineers try to come up with “Rules of Thumb” to use that are close to being correct.  Mathematicians would say is not possible to state Pi exactly because it is an irrational number. Engineers might say “Let’s just get close enough”.  If engineers said that Pi was 3, then this would result in 4.5% error in computations, which is not close enough.  If engineers said that Pi was 22/7, then the error in computations would be only 0.4%, which is probably close enough.  Similarly, non-linear equations, especially non-linear equations of an exponential since the exponential itself is another irrational number, are approximated by engineers as a series of linear equations, also known as straight lines. 

The mean income by quintile (i.e. 20% ranges) is reported annually by the US Census, which also reports the mean income of the top 5 percent. Assuming that the mean income of a quintile is the income of the midpoint of that quintile, or in plain English, if between 20% and 40% of the incomes had a mean income of $12,196 in 2019 dollars, the income at 30%, the midpoint of that quintile, is assumed to be $12,196.  With this assumption, the reported incomes by quintile can be shown to follow an exponential association with a fit of 95.3%.  The transient income, the only coefficient needed for this equation, is $53,450.26 .  This exponential association can be approximated by a series of 6 simple linear equations, with a correlation of 99.88%, as shown in the following figure.

An equitable distribution of income taxes should follow this same distribution of income.  The taxes should thus be 

Taxes = Income * Maximum Tax * Distribution of income

If the distribution of income is approximated by six linear equations, which are the equivalent to tax brackets, and the transient income which is defined by the income distribution is $53,450, then if the median rate is 20%, the Maximum tax rate should be twice that amount, or 40%.  (In a normal statistical distribution, the maximum is approximately twice the mean.)  The effective tax rate is the actual taxes due divided by the income. 

The 2020 ideal tax brackets which reflect the distribution of income are: 

Bracket	Lower Income	Upper Income	Marginal Tax Rate on Income Above the  Lower Income	Fixed tax	Effective Tax Rate Lower Income	Effective Tax Rate Upper Income
1	1	$53,450	14.7%	$-	14.7%	14.7%
2	$53,451	$106,901	30.7%	$7,865	14.7%	22.7%
3	$106,902	$160,351	36.6%	$40,682	22.7%	27.3%
4	$160,352	$213,802	38.7%	$99,335	27.3%	30.2%
5	$213,802	$267,251	39.5%	$182,164	30.2%	32.1%
6	$267,252	∞	40.0%	$287,827	32.1%	40.0%

The actual 2020 rates from the IRS according to those established in the Jobs and Tax Cut Act,  JTCA, are 

Bracket	Lower Income	Upper Income	Marginal Tax Rate on Income Above the  Lower Income	Fixed tax	Effective Tax Rate Lower Income	Effective Tax Rate Upper Income
1	1	$9,875	10.0%		10%	10%
2	$9,875	$40,125	12.0%	$988	10%	12%
3	$40,125	$85,525	22.0%	$4,618	12%	17%
4	$85,525	$163,300	24.0%	$14,606	17%	20%
5	$163,300	$207,350	32.0%	$33,272	20%	23%
6	$207,350	$311,025	35.0%	$47,368	23%	27%
7	$311,025	∞	37.0%	$83,654	27%	37%

The Marginal Tax Rates on income above the lower amount are comparable between the ideal and actual tax brackets.  The major difference between the two tables is the size of the tax brackets. They should be equal in a tax code based on income distribution.  There would be six tax brackets. The range of the tax brackets would be equal to the transient income as established by the distribution of income.  The actual ranges of income covered by the TCJA tax brackets are not equal and are much lower in the lower brackets.  Consequently the fixed amount (i.e. the taxes on the lower income in each bracket)  is lower for the upper brackets.  This results in effective rates that are far less than would be suggested by the income distribution. The upper tax brackets consequently have been paying effective tax rates that are much lower than would be suggested by the distribution of income. 

These lower than ideal effective tax rates have been in place since the Economic Recovery Tax Act of 1981.  If this was intentional, talk about a long con.  The inequality caused by that, and subsequent tax acts, may have been responsible for the growing wealth gap in the United States.  An income tax code should be based on the distribution of income.  In 1980, before that Tax Act was enacted, the transient income, T, the measure of the distribution of incomes, was only $39,622 in 2019 US Dollars .  A tax code which reflects the distribution of incomes at any T is shown below.  

Bracket	Lower Income	Upper Income	Marginal Tax Rate on Income Above the  Lower Income	Fixed tax	Effective Tax Rate Lower Income	Effective Tax Rate Upper Income
1	0	$T	14.7%		14.7%	14.7%
2	$T	$2T	30.7%	14.7%*T	14.7%	22.7%
3	$2T	$3T	36.6%	45.4%*T	22.7%	27.3%
4	$3T	$4T	38.7%	72.0%*T	27.3%	30.2%
5	$4T	$5T	39.5%	120.7%*T	30.2%	32.1%
6	$5T	∞	40.0%	160.3%*T	32.1%	40.0%

Adoption of new marginal tax rates may be a "Bridge Too Far" politically.  However adjustment of the ranges of income within each tax bracket might be undertaken which would more closely reflect the distribution of income.  The lowest tax bracket may not be necessary but it is retained here. The changes in the range of income in brackets effects the fixed amount, the amount due on income in the lower brackets, as well as beginning the highest tax rate at a lower income.  This lowering of the lower bound of income in the highest bracket actually has the effect of raising taxes for the current lowest income in the highest bracket because it increases the fixed amount due from taxes on income in lower brackets.  The proposed changes are shown below in red bold font. 

Bracket	Lower Income	Upper Income	Marginal Tax Rate on Income Above the  Lower Income	Fixed tax	Effective Tax Rate Lower Income	Effective Tax Rate Upper
1	1	$9,875	10.0%		10%	10%
2	$9,875	$53,450	12.0%	$988	10%	14%
3	$53,451	$106,901	22.0%	$7,402	14%	18%
4	$106,902	$160,351	24.0%	$19,161	18%	20%
5	$160,352	$213,802	32.0%	$31,989	20%	23%
6	$213,803	$267,251	35.0%	$49,093	23%	25%
7	$267,252	∞	37.0%	$67,800	25%	37%

The change in the tax bracket ranges, would lower the tax rate for the all incomes.  It would also lower the total amount of revenue raised by the income tax.  If the tax code is changed, it is suggested that marginal rates that more closely reflect the distribution of income should also be enacted.  As shown in the figure below, this would lower significantly the income tax rate for all those below approximately $140,000 while raising the tax rates for those with incomes above this amount.  However, these tax rates would more closely match the distribution of incomes.

The

Trust

 

Trust Me

You trust the teachers to teach your children
Trust the mechanic to build your car
Trust the carpenter to build your house
And yet you don't trust your brother at all

Trust but verify?

Regulations that require disclosure, such as Environmental Impact Statements,  weren’t adopted because they are fun.  Regulations that require disclosure were adopted because there was an absence of trust. It is like showing an ID to buy alcohol.  You are required to be a certain age to buy and consume alcohol.  A store clerk might not know you (or if they do, maybe they have to act as if they don’t know you, in order to treat every customer equally).  When you show your ID, the clerk trusts your ID and THAT proves your age.  If a customer uses a fake ID that is a criminal act by the customer, not the clerk.

Regulations are not adopted because of the people who we can trust.  We can be sorry that those people also have to go through the steps required by the regulations .  But there are those who we can not trust, who said they considered something but did not, or did consider it, but in a way that was not acceptable. They are why we have regulations that require full disclosure.  I wish we could trust everyone, but we can’t.  We can empathize with those who should be trusted, that they have to follow these disclosures, but they are not why the regulation were written. And in all likelihood, the ones complaining most loudly about the regulations are the ones who can not be trusted and why there are regulations in the first place.

If I don’t trust you, and you say that you should trust me, you could be lying. Ronald Reagan famously used the old Russian proverb,  “Trust but verify”.  If you trust Ronald Reagan, how can you then object to verification. Environmental Impact Statements are the verification that he required.

Dobbs vs. Jackson Women's Health Organization

 

My Country ‘Tis of Thee

My country, 'tis of thee,
Sweet land of liberty,
Of thee I sing;
Land where my fathers died,
Land of the pilgrims' pride
From ev'ry mountainside
Let freedom ring!

Is the freedom to have an abortion protected by the Constitution?

“Render unto Caesar the things that are Caesar’s, and unto God the things that are God’s”.  In the SCOTUS case concerning abortion,  the Supreme Court is NOT being asked to act as God, but it is being asked to act as Caesar.

IMHO, this opinion should not be decided on precedent.  It should also not rely on beliefs, no matter how popular.  It should not rely on whether the opinion might inconvenience any parties.  It should not rely on whether those actions were common law at the time the Constitution was adopted. It should rely on the US Constitution, and solely on the US Constitution, SCOTUS is NOT charged with being an activist who can invent rights not defined in the Constitution.

The Constitution defined that the people are its sovereign. That is what makes the experiment that began over 200 years ago so unique, that the subjects of a sovereign would BE the sovereign.   The subjects, the citizens of the States that were being United through ratification of the Constitution, did not ratify it without assuring that the Bill of Rights defined the rights of each person, to eliminate any confusion between rights of individual subjects and rights of the sovereign.  Those rights are enumerated to include, for the individual, freedom of speech, freedom of religion, freedom to assemble, freedom from unreasonable searches and seizures, and, especially pertinent in this case before SCOTUS, protection against actions by the sovereign unless the sovereign renders reasonable compensation.

When disputes arise between subjects of the sovereign, then the SCOTUS is charged with determining which subject’s rights prevail.  However the issue before the court is who is a subject.  In the Mississippi case, the state of Mississippi acting through its legislature, is clearly a subject. Those women who seek an abortion are clearly subjects.  Those women are carrying fetuses, and those fetuses may, or may not, be subjects.

The Constitution requires a decennial Census of its subjects to determine, among other things, voting representation.  The question of citizenship should thus be whether the Census, as required by the Constitution, considers a fetus to be a subject, i.e. a citizen.  Children are counted in the Census.  They are subjects, citizens, but do not yet have the right to vote.  Children who are born and die, between decennial Censuses are not enumerated, but they are still considered to be subjects, persons, because at the time of a Census they would have been enumerated.   The Census does not count fetuses.  Fetuses are children who have not yet been born.  SCOTUS has determined,  rightly IMHO,  that fetuses who are viable outside of the womb, are persons and have the same status as children who are born and die between decennial Censuses.  The question before SCOTUS is whether fetuses who are NOT viable outside of the womb are subjects. If they are not subjects, then laws giving special protections to those non viable fetuses, without compensation to the women who are carrying those fetuses, would appear to NOT be protected by the Constitution.

If the State of Mississippi required its citizens to take any action without compensation, and that action was not protected by the Constitution, it should be forbidden by the Constitution.  That the action is for non viable fetuses does not make that action Constitutionally protected, unless those fetuses also have rights under the Constitution. The Court has previously decided that, under the Constitution, those non viable fetuses have no protected rights.  I would hope that SCOTUS continues to uphold this principle.

The personhood of fetuses who are NOT viable outside of the womb is a matter of opinion and belief, e.g. a matter for God.  The status of those non viable fetuses with respect to the Constitution is the matter that is before the court.  Render unto Caesar the things that are Caesar’s.  Do not grant a right to those fetuses that is NOT listed in the Constitution. Unless there is a Constitutional Amendment which establishes that non viable fetuses are persons, the decision of SCOTUS should, IMHO, be clear. A decision by SCOTUS that a non viable fetus is not a person will not be popular with many. But just as paying taxes to Caesar was not popular,  the question is not popularity, but whether the issue is Caesar’s, i.e. the Constitution's, and not God’s.

Income Taxes

 

I Paid My Income Tax Today

I said to my Uncle Sam
Old Man Taxes, here I am
And he
Was glad to see me
Mister Small Fry, yes, indeed
Lower brackets, that's my speed
But he
Was glad to see me

The rate in a tax bracket is the marginal rate, not the effective rate.

There is a world of difference between speed and acceleration.  We understand that acceleration is important for sprints, but speed is important for marathons. And there is just as much difference between the marginal tax rate (analogous to acceleration) and the effective tax rate (analogous to speed). No one expects a National Association for Stock Car Auto Racing, NASCAR, vehicle to win a drag race against a National Hot Rod Association, NHRA, vehicle.  And no one expects a NHRA vehicle to beat a NASCAR vehicle at the Daytona 500.  The tax brackets are only a way to compute taxes.  The rates cited in those brackets are NOT effective tax rates.

If marginal tax rates were uniformly zero, there would be a flat tax rate.  This would NOT be a  progressive tax rate, which mathematically would be described as a convex function.  By contrast regressive taxes, which decrease with increasing income  mathematically would be described as a concave function.

Math is hard.  But the answer is not to make math fit our expectations. Votes to make Pi equal to 3, (Don’t laugh.  In 1897, the Indiana State Legislature considered such a law) because the value of Pi is hard to remember might be  tempting. But such a law would result in computing the circumference and area of a circle incorrectly.  The correct course should be to change our expectations to fit the rules of math, not vice versa. 

For example the marginal rate for the 2020 married filing separately tax bracket for incomes from $207,350 to $311,025 is 35%, but the effective tax rate varies from 23% to 27%. Mistaking the marginal rate for the effective rate could lead to mistakes in policy.

The effective tax rates are progressive, which is necessary but not sufficient in determining if they are equitable.  The effective tax rates should also reflect the distribution of income.  The US Census reports on the distribution of incomes by quintile.  The distribution of incomes appears to follow an exponential function.  The taxes, and thus the tax rates, should also follow this distribution.  If the mean tax rate, say 20%, is set then the maximum tax rate can be computed from this distribution of income. The formula for the taxes which reflects the distribution of incomes is

Taxes=Income*Maximum Tax Rate*(1-exp (-Income/(Transient-Income))) 

If the distribution of income exactly followed an exponential distribution (not function) then the transient income would also be the mean income.  In this were the case, then the median income would be would be 69% of the mean income.  The maximum rate is not higher than the mean tax rate, because there is a bias against those with higher incomes.  It is the inevitable result of a progressive tax system.  With a progressive tax rate, the only way the mean rate could be the same rate for all incomes, is if ALL incomes were equal to the mean.  The maximum tax rate is a consequence of all incomes not being equal and that there are high incomes and low incomes.  The greater the variance in income, mathematically, the higher the maximum tax rate must be.  As Willie Sutton, the bank robber, once said, he did not rob banks because he had a vendetta against banks. He robbed banks because that is where the money is. If taxes on the rich are high then that is because they are rich, not because the tax system has a vendetta against the rich.

Nature

 It's Nature's Way

It's nature's way of receiving you
It's nature's way of retrieving you
It's nature's way of telling you
Something's wrong

What is nature trying to tell us?

Nature is a strict mistress.  While humans may be able to choose a spectrum between User and Optimal solutions, chose a spectrum between Truth and Fantasy and choose a spectrum between Inclusion or Exclusion, Nature has come out very strongly for System Optimal solutions, for Truth, and for Inclusion.

Nature not only favors System Optimal Solutions, but its System Optimal solutions must be efficient AND resilient.  Texas might have thought that it had an efficient electrical system, but how did Texas like that the winter storm that Nature provided in February of 2021. Texas’s electrical system might have been efficiently System Optimal  as long as “normal” temperatures continued, but it wasn’t very resilient in the cold, was it.

Nature insists on Truth.  It does not treat liars very kindly.  Individuals can deny climate change all that they want.  There may have been species, that if they have been able, that would have denied climate change and yet still became extinct during the end of Permian mass extinction because  of climate change.  “And yet it moves.”  The Truth is the Truth,  deal with it.

Nature is very, very inclusionary.  It does not consider Caste and/or social status, even if humans may value them.  Former President Trump contracted COVID-19 just as readily as the lowest ranked person in society.  He was NOT excluded by Nature, even if he though he wished he had been.

While humans are free to choose where they fall on the Spectrum of a framework human behavior,  Nature, or if you are religious, God, seems to have already expressed choices.

Tax Brackets

Won't Get Fooled Again

Then I'll get on my knees and pray

We don't get fooled again, no, no

Have we been fooled in the tax rates?

A  change in the range of the brackets in the Tax Cuts and Jobs Act, TCJA, without changing the marginal rates in the TCJA, would lower the tax rate for most incomes. Incomes are not equal, but are distributed according to an exponential function.  Taxes should be expected to follow that same exponential function. The effective, not the marginal, tax rate is taxes divided by the income.  A flat tax rate assumes that all incomes are equal.  So country to popular wisdom, a flat tax is a communistic approach, not a free market approach.

Math is hard.  The Orange Menace’s son made the statement in the past that raising the average (i.e. mean) wealth raises everyone’s wealth because that is how math works.  It prompted a blog post from me https://dbeagan.blogspot.com/2018/08/wonderful-world-dont-know-much-about.html, because unless DJT Jr. was either hungover again in class at UPenn’s Wharton Business School and did not hear correctly,  this is different from the math that I learned, and used, as a graduate student down the street at UPenn’s Towne School of Engineering.  The statement is definitely false.  Whether it is false in a effort to deceive, or false because the speaker was ignorant, I can’t say, but the apple does not fall far from the tree.  The problem is that “Math is Hard” and people get the terms wrong, and people deal with linear equations better than with non-linear equations.

The tax code is one place where the difference between a linear and non-linear equation has dire consequences.  Because a nonlinear equation is hard to compute, when dealing with these equations, it is common to approximate the nonlinear function by a series of linear functions.  But you have to approximate correctly or it will not work correctly.

When approximating an exponential association, such as the tax rate, it is common to use a series of linear equations (e.g. tax brackets).  But math has rules. If you are approximating an exponential association, the range of those linear equations MUST BE EQUAL.  For example, if as in the TCJA, the top bracket is incomes over $539,000 ( $628,300 if married and filing jointly), then the range of the brackets should NOT be variable, but should be equal to the top range divided by the number of brackets minus one ( $89,833, or $104,717 if married and filing jointly).

 

The implication is that the constant term in the linear equation is lower for each tax bracket in the TCJA than it should be. I would like to assume that this was done from ignorance.  And this is the same ignorance that is shown when people are surprised that doubling the diameter of a cake quadruples the amount of a cake, not realizing the amount of a cake is a non-linear function of the diameter of a cake. But  this was done by the same “fine” individuals who also proposed the Texas Abortion Law, which was carefully crafted so that no government officials could be sued, and it has been going on for the last 40 years.   I have to conclude that the taxpayer is Lou Costello and the TCJA Tax Code authors are Bud Abbott, and those authors are taking advantage of poor Lou again.  https://www.youtube.com/watch?v=9udNrOh5DyA.

As shown in the figure above, computing tax brackets correctly will lower the effective tax rate for all incomes, but the lowering is proportionally larger for lower incomes.  This may mean also mean that marginal tax rates have to be raised in order to raise the same amount of total tax revenue, but  there are ways to do this that are  mathematically correct, and hopefully we have learned from our mistakes and won't get fooled again.

Distribution of Income

 

Good Morning Judge

I filed my income tax return, thought I'd saved some dough
I cheated just a little bit, I knew they'd never know
I got some money back this year, like I always do
They'll have to catch me before I pay Internal Revenue!

When you file, will there be the same flat tax rate in all income brackets?

A flat tax on income is socialist, if socialism is defined as everyone having the same income.  That is not my definition of socialism, but it is the definition of many.

The degree of the variation is a statistical measure called the..... variance.  If everyone had the same income, then the variance of income would be zero.  A flat tax rate, the same percentage of tax on everyone, also has a variance of zero.  If there is a distribution of income, then if there should also be a distribution of taxes on that income, then its variance could not be zero.

A uniform normal distribution is one in which the variance is 1.0, for example the familiar bell‑shaped curve. The phrase “Flatten the curve” became familiar during the COVID-19 pandemic.  It  means that the normal distribution of COVID-19 cases requiring hospitalization remained the same,  but its variance increased.  A normal distribution is one in which the median equals the median (where these values are also equal to a seldom used statistic, the mode). Flattening the curve is still a normal distribution but it was no longer a uniform normal distribution. 

A normal distribution requires the consideration of negative values.  It is common not to report negative incomes ( negative incomes could include donations, debt, etc. but those are not often considered to be income).  A distribution which does not allow negative values is the exponential distribution.  In this case the median does not equal the median, but the mean is a constant factor of the median.  In an exponential distribution, the mean is always 1.44 times the median.  The variance of an exponential distribution is by definition equal to its mean.

An exponential function is NOT an exponential distribution.

An exponential function is

a*e ^-bx

An exponential distribution is the special case where a=b, which is traditionally expressed using  γ, where the exponential distribution probability function is

γ*e^-γx

In an exponential distribution  the mean is 1/γ, the variance is also 1/γ , and the median is ln(2)⁄γ, or 0.69 * mean, or its inverse, mean = 1.44 * median. The variance of all exponential functions can be described.  It is at a minimum when the mean is the variance, which is the exponential distribution.

Any large collection of independent objects can be expected to follow an exponential function when their cumulative values are reported.  Individual incomes in the United States appear to follow an exponential function.  Prior to 1980, the distribution of incomes as reported by the US Census was highly correlated with the exponential distribution. These incomes were not equal.  If the taxes on this income followed the same distribution, it also could not be equal unless all incomes were also equal.  Allowing for a distribution of taxes, not a flat tax rate, considers this distribution of income.  A flat tax rate considers no variation in the distribution of income.  If individual incomes are not equal, then the distribution of taxes, which is what the tax rate is, should also not be equal.

Incomes in the United States prior to 1980 correlated well with an exponential distribution, especially at the higher incomes, and less well for lower incomes.  After 1980, the incomes follow an exponential function, but not an exponential distribution.  The variance in incomes are much larger than the mean income.  The variance in incomes increased between 1980 and 1990, and between 1990 and 2000. There was a set-back between 2000 and  2010, ( it is almost as if there was a recession during this period😏). However between 2010 and 2019 the increase in variance continued the previous trend.  The distribution of incomes have bent, i.e. the variance from an exponential distribution has increased. It has not yet broken yet, but how long is it healthy to continue this trend?