Income Response to Tax Rates

Taxman

Let me tell you how it will be
 There's one for you, nineteen for me
  Cause I'm the taxman yeah, I'm the taxman

Taxes should be a way to grow the economy, not to  increase inequity.

No  one likes paying taxes.  Taxes are levied to raise revenue for governments. In the United States, the principal source of federal government revenue is the income tax.  However, the purpose of the income tax code is not only to collect revenue.  It is enacted to promote economic growth, while arguably not unnecessarily adversely affecting various economic sectors.  Income inequality is a measure of how the poor (lower income percentiles) compare to the rich ( upper income percentiles).  A proposed measure of income inequality is the ratio of Mean household income (i.e. total income divided by total households), divided by Median household income ( i.e. the income above, or below, which 50% of the households occur).  For a perfect normal distribution of household income, the mean and median would be the same. 

A measure of success of the income  tax code might be that total income increases, but the income inequity does not increase.  The Federal Reserve Bank of St Louis provides Mean and Median household incomes, as reported by the US Census.  The reported Mean and Median household incomes are shown in Figure 1.

Figure 1 Mean And Median US Household Income: All Years Current Dollars

If the goal of the Tax Acts were to increase economic growth, those Acts have fallen below an Compound Annual Growth trend line established by income from all years.  Also, from that figure, the  gap between Mean and Median household incomes has been increasing over time.

To account for inflation, the reported household incomes were adjusted by the Bureau of Labor Statistics Consumer Price Index, CPI,  to convert incomes to 1967 dollars ( any year could be used as an index, which would change the values on the y-axis, but would not change the data or curves because the impact of inflation would be the same.) These results are shown in Figure 2.

Figure 2 Mean and Median US Household Income, Adjusted For Inflation, By Tax Act

The major Tax Acts during this period are shown, which regress very well to the reported household incomes.  The analysis does not include the impact of the Tax Cut and Jobs Act of 2017 because it was signed in law in December of 2017 and not enough time yet has occurred to compute its impact on household income.  Shown in Table 1 is the Compound Annual Growth Rate, CAGR,  computed for the reported respective mean and median household incomes during these periods. If the intent of the Tax Acts was to promote economic growth, then arguably  growth has been less during each of Tax Act periods.  What has occurred is that the gap between mean and median incomes has increased during the period of these Tax Acts.

Table 1 Growth Rate During Periods Of Tax Acts.

	pre 1981	1981-1990	1991-2001	2002- 2018
Mean Income CAGR	2.30%	1.63%	1.93%	0.40%
Median Income CAGR	2.23%	1.21%	1.46%	0.13%

While the Tax Acts were adopted during, or immediately following, economic downturns, recessions, economic downturns, and recoveries have also occurred during periods with no changes to the tax codes.  The official National Bureau of Economic Research beginning and ending dates of recessions are shown in Table 2. There have been more recessions than there have been changes to the Tax Code during the reported period.  Based on the reported incomes, it is possible to recover from a recession without  any corresponding changes to the Tax Code.

Table 2 NBER Reported Recessions Corresponding to the Years In Figures 1 And 2

Beginning date	Ending date
1953-07-01	1954-05-01
1957-08-01	1958-04-01
1960-04-01	1961-02-01
1969-12-01	1970-11-01
1973-11-01	1975-03-01
1980-01-01	1980-07-01
1981-07-01	1982-11-01
1990-07-01	1991-03-01
2001-03-01	2001-11-01
2007-12-01	2009-06-01

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[1] https://alfred.stlouisfed.org/

Income Equity

A Bohemian Rhapsody

Is this the real life,
 Is this just fantasy?

Income equity is a real phenomena based on real data, not just the product of fantasy,

Many measures have been proposed to measure income inequality: the Gini coefficient, the Atkins coefficient, various percentiles of income, etc.  If Standard Deviations of household income were available, the Median, Mean, and Standard Deviation of those household incomes could be used to compute the Skew of household income compared to a normal distribution of household income.  The Standard Deviations of household incomes are not often reported, while the Mean and Median household incomes are commonly reported. Zimmerman[1] suggested comparing the Mean and Median household income as a measure of equity. 

The LIS Cross-national data Center in Luxembourg reports on various economic measures .  It reports Median and Mean household incomes for 51 countries during the period 1967 to 2016[2].  An Income Equity Index (Mean income divided by Median income) was computed from this data.  The results of this analysis are shown below.

  

Figure 1 Income Equity Index by Country

By inspection, an equity index of less than 1.2 appears to be common in most countries, particularly in the more developed countries.  If income followed a normal statistical distribution, the  Mean would be equal to the Median and the Income Equity Index would be 1.0.  However, this is only possible if negative incomes were also possible.  Since income less than 0 are not reported, an Income Equity Index of greater than 1 should be expected.

In most countries, the Income Equity Index is either decreasing or stable over the period of the LIS data. Only four countries have a forecast 2018 Income Equity Index greater than 1.2 where the Income Equity Index is also increasing over time.  In two of those countries, Lithuania and Romania, this forecast is based on only 2 years of data and the forecasts for these countries are not statistically significant.  The forecasts in the remaining countries, the United Kingdom and the United States are based, respectively, on 13 years and 12 years of data and are statistically significant. This historical data is shown graphically in Figure 2.

Figure 2 Income Equity Index: United Kingdom and United States

. 

For both countries, the largest and fastest increase in the Income Equity Index occurred during the period between 1980 and 1994 although the Income Equity Index is still increasing after this period. A common thread in both counties during this period is Arthur Laffer, who served as an economic advisor to both the Reagan and Thatcher administrations

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[1] https://fredblog.stlouisfed.org/2016/12/the-puzzle-of-real-median-household-income/

[2] http://www.lisdatacenter.org/data-access/key-figures/

Transit as a Public Good

The Best Things in Life Are Free

The sun belongs to everyone
The best things in life are free

Is transit a public good, or a private good?

Is transit a public good that should be provided to the general public?  This question becomes more important since transit is likely to be adversely affected by the COVID-19 recovery while at the same time it is essential for the commute trip of essential workers.

Economists have found it useful to categorize goods using definitions of rival, if some one uses a good then that good can not also be used by another, and  exclusive, a price can be charged for using that good.  Private goods are exclusive and rival.  I am charged for eating a piece of food, and if I eat that food no on else can eat that food.  Public goods are non-exclusive and non‑rival.  No one can charge me for basking in  sunshine and my basking in sunshine  doesn’t prevent some one else from basking in that same sunshine. 

Economists also categorize goods that are rival and non-exclusive as common resources, such as fishing grounds.  For example, no one charges for catching a fish,  but my catching a fish means no one else can catch the same fish.  Economists categorize goods as natural monopolies if they are exclusive and non-rival.  I can be charged for watching cable TV, but my watching cable TV does not prevent some one else from watching that same cable TV.

Source: https://www.reviewecon.com/rival-excludable

Transit is an example of a natural monopoly, in fact the original transit systems were formed as licensed private natural monopolies.  In my home of Massachusetts, the MBTA, the public transit authority, is a successor to the private Boston Elevated Company.  Natural monopolies are also categorized by having high fixed costs and low marginal costs.  The fixed cost of a subway line and its trains far exceed the marginal cost of adding an additional rider.  Governments grant a licensed monopoly to transit systems to protect that high fixed investment.

While transit is exclusive, in that while a rider is charged a fare for using transit, it is only partially non‑rival.  My riding transit does not prevent some else from riding transit, but the space in the transit vehicle itself is rival.  Movie theaters are another example.  A movie itself might be a non‑rival good, e.g. my watching a movie does not prevent someone else from watching that same movie, but the seats in the theater showing that movie are rival e.g. if some one is occupying a seat no one else can occupy that same seat.

The problem is treating rival and exclusive as an either/or proposition.  They are not like pregnancy. You can be a little bit rival, but you can’t be a little bit pregnant.

Transit itself might be a more like a public good.  While it is a natural monopoly, it is a public natural monopoly.  The fare that makes it a natural monopoly, exclusive, is a public choice, and most likely reflects political and not economic values.  Transit itself is non-rival; my using transit doesn’t prevent someone else from using transit, while the space on a transit vehicle is rival; if I occupy space on a transit vehicle no one else can occupy that same space.

Common Resources are regulated to prevent the “tragedy of the commons”.  Fishing quotas and licenses are imposed by governments to make that common resource more exclusive .  There is no economic problem with subsidizing transit and treating it more like a public good. The fact that transit has a cost doesn’t mean that it should be treated only as a private good or a natural monopoly.  The subsidy of transit for the commute of essential workers as a public good is a government, public, choice.

Price Inflation

The Happening

Riding high on top of the world, it happened.

Suddenly it just happened,

I saw my dreams torn apart

Something happened to prices during my lifetime. Rather than just being a cranky old man and complain about it, can examining the data suggest what happened?

Can you imagine a 5 cent candy bar? If you were born in 1951 like I was, you probably not only can imagine it, you can remember it. Before I entered college in 1969, prices were fairly stable. My first new car cost only $3,000. Something has happened to prices since that time. Looking at the data might help understand when, and why, something happened to prices.

The U.S. Bureau of Labor Statistics reports the Consumer Price Index (CPI) , which is often used to track inflation, from 1913 to the present. It is often indexed to a specific year. When the annual CPIs (with an index of 100.0 in 1984) are plotted, they take on a distinctive shape as shown below.

Doing a non-linear regression on that data, produces an equation whose values have a correlation of 0.9926 with the reported CPIs. The non-linear equation is essentially two straight lines with a transition between those lines somewhere between 1969 and 1975. Looking for a historical event that happened during that time period, that might have affected the CPI, and has remained in place since that time, suggests the Nixon Shock. In 1971, President Nixon ordered that the US Dollar, which was then the international reserve currency, no longer be convertible into gold. It had been not been convertible into gold for US Citizens since the 1930s, and this action seemed to primarily affect foreign governments, but that action remains in effect today.

If this was indeed the cause of the transition, this suggests that perhaps there are probably two transitions. One at the time of Bretton Woods Conference in 1944 when the US dollar (convertible into gold) was first made the international reserve currency. And then in 1971 when the US dollar remained as the international reserve currency, as it is today, but was no longer convertible into gold.

Fitting straight lines to the CPIs in each time period produces:

• A period before Bretton Woods, with virtually no CPI inflation
(an increase of 0.072 1984 CPI basis points per year. )

• A period between Bretton Woods and the Nixon Shock, where CPI inflation was modest
(an increase of 0.645 1984 CPI basis points per year) and

• A period after the Nixon shock, where CPI inflation was large
(an increase of 4.597 1984 CPI basis points year).

Using these three straight lines, you can compute values that have a correlation to the reported CPIs of 0.99931.

If you only look only at year to year inflation, which dropped from 11.0% in 1974 to 2.1% in 2017, you miss this underlying long term impact. The impact on inflation when a domestic currency is also used as the international reserve currency is known as the Triffin dilemma. https://en.wikipedia.org/wiki/Triffin_dilemma. An analysis of the reported CPIs, suggests that the dollar being the international reserve currency, especially when the dollar was no longer convertible into gold, has had a measurable effect, not just on the international economy, but on our daily lives.

The Difference between Means and Medians

Wonderful World

Don't know much about algebra,

Don't know what a slide rule is for

If you don’t understand math, then you may get talked into supporting some decisions that are not in your own best interest.

Teen Talk Barbie is right “Math is Hard”. But that doesn’t mean that you shouldn’t try to understand math. If you don’t understand some basic concepts of math, then you can get some unexpected results. One of those is that increasing the average, also known as the mean, does not make things better for the typical person. The average, mean, household income is total income divided by total households. The median household income, the income of the middle, is the income at which 50% of the households have incomes that are higher, and 50% of the households have incomes that are lower. When the median and the mean ( as well as another statistic called the mode) are the same, the name of that is a normal distribution. When their difference becomes greater, should that be called abnormal? To illustrate this, consider the Town of Duckburg, home of Uncle Scrooge McDuck.

In the town of Duckburg, 1,000 households have an income of $50,000 per year while Scrooge McDuck has an income of $5 million per year. The mean, average, income of all households is almost $54,945 per year, while the median, 50th percentile, income of the households is $50,000. The town is going to receive new income of $10 million per year but they have to decide how to divide this new income among the households in the town.

Scrooge says that his income is over 9100% of the mean income, so he should get most of that new income. However, he says that he wants to be generous, and suggests that he should only get 50% of that new income and the other $5 million should be shared among the rest of the households. This increases Scrooge McDuck’s income from $5 million to $10 million per year, while the other duck households increase from $50,000 to $55,000 per year. However, while the mean income increased by almost $10,000 to $64,935 , the median income only increased by only $5,000 to $55,000. The problem is that while Scrooge’s income was over 9100% of the mean income, it was only 9.9% of the total income of all households in Duckburg. To keep the income distribution the same, he and every other household should each only get a 9.9% increase in income. Not a 100% increase for Scrooge and a 10% increase for all other households. Since total income increases by 9.9%, if every household’s income had gotten an increase of 9.9%, including Scrooge’s, then the gap between mean and median income would not have increased.

Might giving most of the new income to Scrooge McDuck have been a good idea? Would he be more likely than most households to use that income to increase the economy, as supply side economics believes, where you accept becoming less equitable but possibly more productive? Maybe, but fans of Uncle Scrooge know the most likely outcome would be that Scrooge would only increase the amount of money in his vault, in which he will swim.

Truck Classification

The Blind Men and the Elephant

And so these men of Indostan, Disputed loud and long, Each in his own opinion, Exceeding stiff and strong, Though each was partly in the right, And all were in the wrong!

There is no single classification system that can be developed for trucks.

The poem the Blind Men and the Elephant is a humorous warning that it is not possible to establish an absolute truth based on limited observations.  The blind men in the poem base their understanding of the nature of an elephant on the things that they can actually observe, act like theirs is the only important observation, and then use that observation to get the nature of the elephant completely wrong.  

A truck is just as complex as an elephant.  If a vehicle is to be classified as a truck, and that truck was to be further classified into various types of trucks, the observations become important.  

Do you classify a truck based:

• On the weight of the truck?  And if weight, is it the weight at the time of the observation? Or is the maximum weight that can be legally transported?  Or is it the average weight per axle?
• On the number of axles and tires of the truck?
• On the body type of the truck?
• On the length of the truck?
• On the commercial markings on the side of the truck and/or its trailer?
• On the purpose of that truck’s trip?
• On the power of the engine in the truck?
• On the type of fuel powering the truck?
• On the contents of the cargo area of the truck? If the cargo contents, how is the cargo to be classified?  

These are not just idle questions.  Each of these observations has been made, and the use of them leads to different and potentially incompatible classification systems. Weigh in Motion (WIM) stations observe the weight of the truck at a moment in time that it passes through that WIM Station. Departments/Registries of Motor Vehicles (DMV/RMV) report the Gross Vehicle Weight (GVW), the maximum weight of the vehicle, cargo and passengers as specified by the manufacturer of the truck. Pavement engineers are concerned with weight per axle of various types of trucks.  FHWA in its Traffic Monitoring Guide (TMG) outlines a truck classification system based on the number of axles, tires and the general body type.  Some state DOTs classify trucks based on the length of the truck and its trailers.  Video or visual observations often classify a truck based on the marking on the side of the truck.  Commercial Vehicle surveys might be the only observations of the truck purpose, and then only for the sample of trucks that are surveyed.   

This can lead to classification systems that are incompatible.  Both of the trucks shown below have a body type of beverage trucks.  But the truck on the left would be classified by the TMG as a Class 5 (Single Unit with 2 axles and 6 tires), while the truck on the left would be a Class 8 (Combination Unit, one trailer; three axles in total).  And both trucks will have a different weight per axle depending on whether they are loaded or empty.

          

source: https://sites.google.com/site/coorslightmountainbikeyvh/

And this does not even get at the issue of whether ANY vehicles with a GVW less than 10,000 lbs should even be called a truck.  These light trucks are the subject of complex tariff systems.

(see http://www.npr.org/sections/money/2015/06/12/414029929/episode-632-the-chicken-tax,) The National Highway Traffic Safety Administration, the Federal Motor Carrier Safety Administration and the Federal Highway Administration may be too “chicken” to call light "trucks"  trucks.

To paraphrase Mark Twain, there is only One True Truck Classification System.....in fact there are several of them.  A truck classification system that focuses on fuel type won’t serve the needs of pavement engineers.  Nor is a fuel based classification system likely to collect the axle weight data that would make it possible to develop crosswalks between those systems.  It is probably unreasonable to expect to find a truck classification system that serves all needs.  Just try to find ones that are useful to you.

Traffic Congestion

Crosstown Traffic

All you do is slow me down
And I got better things on the other side of town

How is capacity determined in traffic analysis?

Congestion will slow you down.  The travel time in congestion is defined as a function of the capacity of a road.  The closer that the demand, volume, on a link comes to that capacity, the worse the congestion. However the capacity that is used in those calculation is often misunderstood.  If it were better understood perhaps no one would ask questions like “How can you even have a Volume to Capacity ratio that is greater than 1.0?”

Traffic flow theory says that traffic moves like a compressible fluid.  While my auto insurer of course doesn’t want me to compress my car, the compression as it is being used here, and by extension the capacity of that compressible traffic, refers not to the physical bumper to bumper capacity.  It refers to the operating capacity of the car.  And that operating capacity incudes not only the car itself, but also the spacing to the car ahead.  It is that spacing between cars that is compressible, not the car itself.

In a compressible fluid, the flow is expressed as the product of the speed and the density.  Because flow is typically expressed as cars per hour, and speed is typically expressed as Miles per Hour, this means density would have to be expressed in cars per mile.  The space consumed by an auto would be the bumper to bumper car length plus the spacing to the car in front, feet per car, or converting the units, miles per car. It should then be apparent that density of traffic as a fluid has to be the inverse of the operating length of a car, i.e. the bumper to bumper length plus spacing.

When I took Driver’s Ed, the rule of thumb for the safe spacing to the next car was a function of driving speed.  That rule of thumb from the safe following distance to the next car was one car length for each 10 MPH of your speed.  This has since changed to a 2 or 3 second gap, which says that the spacing between cars should be the length to travel those seconds at the speed of the car.  In any event both the old time rule of thumb and the newer gap time rules, make the operating length a function of speed.  If the bumper to bumper car length is 20 feet, and the operating speed is 70 MPH, then the space “occupied” by the car is 20 feet plus 7 car lengths, 70 MPH/10, or 160 feet.  The density would thus be 1 car/160 feet, or 33 cars per mile.  This means that the flow at 70 MPH and a density of 33 cars per mile would be 2310 cars per hour. This is just about the standard capacity in passenger cars for a freeway with a design speed of 70 MPH.

For the 2 or 3 second following rule you would get much lower capacities, but the Maximum Flow Rate its actually a transition between laminar and turbulent flow of fluid, which is way beyond what I wanted to discuss here.  So when the LOS is F and the Volume to Capacity, v/c, ratio is greater than 1.0, the spacing between cars is less than the one car length per 10 MPH rule.  Safety suffers, but this v/c ratio is still physically possible. The maximum density is of course one car length, but since that occurs at 0 MPH, the flow rate is zero anyway.