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?

Why?

 

Who Am I?

Who am I?
Can I conceal myself for evermore?
Pretend I'm not the man I was before?
And must my name until I die
Be no more than an alibi?

On the 200th post to this blog, it is probably time to explain the name.

I am a semi-retired traffic engineer/planner.  One of the questions that I am often asked to answer is  “ How many people would use a particular mode?” One mode is hitchhiking (which the profession would  euphemistically call a shared ride mode).  When hitchhiking  with an outstretched thumb, the question by the Driver to the Hitchhiker, if he intended to offer a ride would be, “Going My Way”.

“Going My Way” is also the name of a 1944 film that won the Oscar for Best Picture   It is the story of a Catholic parish priest played by Bing Crosby (for which he won the Oscar for Best Leading Actor).  Since I attended St Paul’s parochial parish School from grades 1 to 8, it is a safe bet that the nuns teaching at that school held this film and its sequel, “The Bells of St Mary’s”, in high regard. Consequently  I saw “Going My Way”  more than once.  That film also had the Oscar winning Best Song, “Swinging On A Star”.  Because I find it easier to remember a topic if it is associated with a song, I have tried to include some lines from a song before each blog post.

This blog post  has a song from Les Mis, and is dedicated to a former colleague, Kate Fox, whom I think of when I hear any song from Les Mis.

Distribution of Wealth III

You’re a Rich Girl

You're a rich girl, and you've gone too far
'Cause you know it don't matter anyway
You can rely on the old man's money
You can rely on the old man's money

How rich are we? And how rich should we be?

The United States is the wealthiest county on the planet. This is according to the Credit Suisse Global Wealth Databook for 2021 as reported in Wikipedia. Out of the 162 countries, or sub-units of countries, (e.g. Hong Kong and Taiwan are reported as separate sub-units of China), the United States is reported to have a wealth of 126 trillion USD, more than 30% of the world’s reported wealth, more than 168% of wealth of the second‑place country China, and more than 41 times the wealth of Russia. The country with the least wealth is São Tomé and Príncipe in Africa, but that country also only has a reported adult population of 104 thousand as opposed to the US adult population of 249 million, China’s adult population of 1.1 billion and Russia’s adult population of 111 million.,

Reporting the arithmetic mean of wealth per adult (national wealth divided by adult population) normalizes wealth by a country’s population. In this instance, the United States has a mean wealth of $505 thousand per adult, which is second place to Switzerland with a mean wealth per adult of $674 thousand per adult. However this same mean could also occur if all of the wealth is owned by only a few individuals. The median is the wealth at which 50% own more and 50% own less. The median wealth per adult in the United States is $79 thousand, which places it in 26th place, where the highest (first place) median wealth is Luxembourg with a median wealth per adult of $260 thousand. The mean and median wealth, when ranked, both seem to follow an exponential function, If this exponential trend continued, the first-place country should have a median wealth of $166 thousand per adult.

The distribution of wealth is often reported by the Gini coefficient, where a score of 100 indicates that all of the wealth is owned by one individual in a population. The Gini coefficient for the United States is 85.00 which ranks as 24^th place. When ranked, only two countries have a high Gini coefficient which does not follow the trend: Brunei with a Gini coefficient of 96.01 and Cameroon with a Gini coefficient of 94.30. The Gini coefficient does seem to show the distribution of wealth, but it does not give an expected normal distribution of wealth. It also shows the two most equitable countries, Iceland with a Gini Index of 50.9 and Slovakia with a Gini Index of 50.3, where 50 indicates an equal allocation of wealth throughout the population.

If the distribution of wealth followed a statistical normal distribution, the median would be equal to the mean. However a normal distribution must also allow for negative values, while wealth will only have positive values. Mean and median wealth appear to follow an exponential function which allows only positive values when ranked.  An exponential distribution is one where the median is 0.69 times the mean. This ratio of the mean to the median for an exponential distribution would be the inverse, 1.44, which is almost the ratio in Iceland and Slovakia.

If the linear trend between the 36^th and the 153^th ranked country continued, the expected ratio for the highest ranked country would be almost 4.0.  It is suggested that an equitable distribution for the United States thus might be when the median is 4 times the mean. This would suggest that the median wealth per adult, should be $126 thousand, which is $47 thousand higher than the reported amount. Those countries where the median income is less than this expected amount includes, not only the United States, but also Brunei, Bahrain, the United Arab Emirates, Brazil, Ukraine, Russia, Philippines, Lesotho, Laos, Yemen, Kuwait, South Africa, India, Zambia, Saudi Arabia, Nigeria, Botswana, Suriname, and Namibia. This may not be the best company to keep for an equitable distribution of wealth.

 

RINO?

 

Positively 4th Street

You've got a lotta nerve to say you are my friend
When I was down you just stood there grinnin’
You've got a lotta nerve to say you got a helping hand to lend
You just want to be on the side that's winnin'

You got a lot of nerve Lauren Boebert, Kevin McCarthy and Mitch McConnell!

Some bona fides first.  I was appointed by to a minor executive position by then Republican Massachusetts Governor William Weld.  My son’s youth soccer coach was the then wife of the Republican State Senator and Chair of the Republican Party in Massachusetts.  After leaving the legislature, her husband and I worked in the same building and I enjoyed chatting with him while we walked to catch the commuter rail.  Growing up I admired Republicans Ed Brooke, Margaret Heckler, Elliot Richardson, Margaret Chase Smith,  Everett Dirksen, Howard Baker, Nelson Rockefeller, John Chaffee.  Each of these individuals placed the interests of their country above their party.  While the Republican standard bearers have included such men of integrity as Theodore Roosevelt, Dwight Eisenhower, Gerald Ford, John McCain and Mitt Romney, the standard bearers have unfortunately also included the corruption of Warren Harding, the indifference of Herbert Hoover, “Tricky” Dick Nixon, the madness of Barry Goldwater, the voodoo of Ronald Reagan, and Donald “The Con(fidence Man)” Trump.  I realize now that had I been alive at the end of the Nineteenth Century, I would have been a Mugwump, an anti-corruption Republican.

When the Republican party was founded, its major issue was the noble ideal of the limitation, if not the abolition, of slavery.  As such it welcomed those self-serving former Whigs ( mathematically they would be described as User Optimalists), and the Know Nothing Party exclusionists who also supported abolition. After slavery was abolished, this led to the  internal  battle for control in the Republican party that has raged since that time and today is no exception.

The self serving and exclusionists are today in ascendancy in the Republican Party.  Those who believe in the importance of  integrity;  that as long as humans must run the government/system, there is a danger that those serving in the government would seek their own interests and not the nation/system’s interests and thus government should consist of the smallest number of individuals possible with the most constrained power; and that any actions by the government should be carefully considered such that good intentions are not overwhelmed by unintended consequences, are being labeled as RINOs, Republicans In Name Only.  Those being castigated are the only the ONLY Republicans worthy of the name.  It is those who are casting stones who bring disgrace when they call themselves Republicans.

The Distribution of Wealth II

I Have a Dream

And when this happens, when we allow freedom ring,
when we let it ring from every village and every hamlet,
from every state and every city,
we will be able to speed up that day when all of God's children,
black men and white men, Jews and Gentiles, Protestants and Catholics,
will be able to join hands and sing in the words of the old Negro spiritual:

Free at last! free at last!
Thank God Almighty, we are free at last!

We can not be free until, we all have an equal share.

For the 162 countries reported in Wikipedia using Credit Suisse’s Global Wealth Databook for 2021, the total number of adults reported are 5.05 billion and the total wealth is $416 trillion USD.  The mean global wealth is $82,306.  If this wealth followed a statistical normal distribution, the mean should be equal to the median.  However the product of the median wealth in each county multiplied by the adults in that country summed over all countries would require a global wealth of $786 trillion, so clearly the mean is not equal  to the median and wealth is not normally distributed  The country where the mean comes closest to the median is Iceland where the mean wealth is $337,787 and the median wealth is $231,462.  Iceland also has the second lowest reported Gini Index at 50.9 ( the lowest is Slovakia at 50.3).  The Gini Index is a statistical measure of inequality, where a score of 100 indicates that most of the measurement is due to one individual in the population.  The United States was reported to have a total wealth of $126 trillion, a mean wealth per adult of $505,421, a median wealth per adult of $79,274, and a Gini Index of 85.0. This is the 25^th highest Gini Index, the highest being Brunei with a Gini Index of 96.2.

Wealth is not reported lower than $0 ( technically negative “wealth” is debt, and would not be  counted as wealth.)  A normal distribution would require the allowance of negative values.  Wealth might follow another distribution for example an exponential  distribution.  In an exponential distribution the mean can not equal the median, but that distribution is closest to a normal distribution if the mean is 1.44 times the median.  The ratio of the mean to the median in the United States is the third highest at 6.38, the highest again being Brunei with a ratio of 7.63. Wealth in the United States is thus neither normally distributed, or distributed at an exponential minimum.

Wikipedia also reports countries by region.  It’s Northern American region includes only the United States and Canada.  (Mexico is assigned to its Central American region.)  Northern America is the region with the most wealth, and the highest mean wealth at $486,909, but the United States is responsible for 93% of that wealth. Canada has a mean wealth of $332,323 and a median wealth of $125,688. A region with a comparable mean wealth is Australia combined with New Zealand, which has a mean wealth of $465,680. However, the ratio of mean to median wealth in Australia and New Zealand is respectively 2.05 and 2.03.  Three regions comprising Europe (excluding Eastern Europe) have a wealth of $94 trillion, and the ratios of mean to median wealth per adult range from a high of 3.74 in Sweden to a low of 1.04 in Iceland.

The United States thus appears to have a less equitable distribution of wealth per adult: within its region, with a region of comparable mean wealth, or with regions of comparable total wealth.