Monthly Archive: November 2014

Since Thanksgiving just passed us by, it might be worth talking a little about the historical roots and the economic lessons it affords us.

The usual interpretation for what the Thanksgiving holiday commemorates is that the Pilgrims, who came over from the England and settled the Plymouth colony, had a big celebration and a feast in the fall.  They were grateful for the bountiful harvest that they had obtained and they set aside a day in which to thank their God and to share their bounty with the Native Americans, who had helped them get established.

While accurate as far as it goes, the truth of the matter, free from the sanitary influence of Madison Avenue, is much more complex and interesting.  The majority of this information is available in William Bradford’s Of Plymouth Plantation. Bradford was the second governor of Plymouth Plantation and relates the course of its history from beginnings in Europe to the establishment and eventual prospering in the new world.

In order to set the stage, we need to examine the roots of what drove these people from England and made them think that the dangerous crossing of the Atlantic is was preferable to staying in Europe.   The founders of Plymouth colony were separatists from the Church of England and regarded the Anglican Church as still having too many ways of the Church of Rome and being too ‘popeish’.  Facing religious persecution in England, they first moved to the Netherlands in 1609.  But the culture was foreign and the long reach of England was not so easy to escape.

After 10 years, they resolved to leave for the new world and, early in 1619, these separatists, now come to be known as Pilgrims, received a land patent that granted them permission to settle in the new world.

The next question was how to finance the expedition.  They needed to get backing for the passage across the Atlantic, food for their members during the several months required to make the trip, and then supplies sufficient to build a whole new town for themselves and to sustain them until crops could be planted or some other sources of food be found.  Given the technology of the day, their relocation from Europe to North America is akin to picking up a modern suburban community and moving it to Antarctica.

The Pilgrims did find backers in the form of the Company of Merchant Adventurers of London.  The Merchant Adventurers were willing to provide the capital needed despite the very tangible risks.  These included the fact that Atlantic crossings often ended in disaster, that the colony could fail and be unable to send back any profit from the New World, and that the Pilgrims, despite their god-fearing ways, may simply choose to not honor their word and refuse to pay back their debt.

The Merchant Adventurers required that the colonists work ‘on company time’, basically 6 days a week, and that at the end of seven years, half of all their property would be surrendered to the company.  Thus from the beginning, Pilgrims were constrained to live under a communal arrangement of property.  That is to say that all of their efforts arranged for the common good.

After surmounting a variety of stumbling blocks, they finally set sail in the late summer of 1620 on the Mayflower, accompanied by their families and servants as well as by some people associated with the Merchant Adventurers (traders and the like, who were called  Strangers by the Pilgrims).  The ship struck land on the 11^th of November 1620, but the passengers found that they had sailed too far north from their original aim of Virginia and were near Cape Cod.

After some discussion, they resolved to settle in what is now known as Plymouth and to establish their colony.  It was late in the year, roughly the middle of December, when they had built shelters and finally moved people and cargo to land.  Many of them died during this time from what is thought to be maladies brought on by malnutrition (e.g., scurvy).

But surely, once they survived the winter, they would thrive.  Unfortunately, that wasn’t to be the case.  The year 1621 saw them barely meeting subsistence, and 1622 saw no better fortunes.  William Bradford, governor of Plymouth from 1621 to 1657, had this to say about the harvest in 1622 (page numbers refer to the PDF version available online)

In the beginning of 1623 Bedford penned:

and also

Clearly the Pilgrims were having a hard time becoming economically viable.  But why?  Well, they had encountered the Free Rider problem.  Since their fortunes were held in common (they all had to work to pay back their debts to the Merchant Adventurers), they had little incentive to take individual responsibility.

Given this economic arrangement, a Pilgrim could reason in the following way.  ‘It is in the interest of my neighbor to make sure our debt is paid back regardless of whether I work to do so.  Therefore, I will not work and my neighbor will cover for me.’  The problem with this logic is that each Pilgrim argued the same way, and no one worked industriously enough to make the colony prosper.

Finally, in 1623, the colony abandoned communal property and farming in favor of individual rights.  Bradford writes:

Note in particular, the passage ‘for it made all hands very industrious’.

Bradford then goes on to analyze the societal roots of what the colony had been experiencing.  Clearly, he laid the problem not at the foot of the debt, held in common by the colony to their backers, but in the colony itself.  He identifies how working in common was ‘found to breed much confusion and discontent’.  That the most able bodied young men complained [repined] that they had to ‘spend their time and strength to work for other men’s wives and children without any recompense’.

It is also amusing to note that Bradford takes time to mock the Utopian theory of common property found in Plato’s Republic as conceit.  A more detailed discussion of the debate about Plato’s Republic in Bradford’s time can be found in the article entitled How Private Property Saved the Pilgrims.

Bradford had an opportunity to oversee one of the most profound economic experiments of all history – not from curiosity but necessity.  What he found was that human beings function better and prosper when they are afforded private property rights and are allowed to keep the wealth they create.

One would have to be living under a rock not to know of all the debate that rages within the media and the halls of government associated with the Affordable Care Act (ACA).  In this post, I don’t want to weigh in that subject directly but I do want to explore a related topic – namely what is insurance.

The reason I think that is timely to do so is that there can’t be a reasoned (and reasonable) debate without being able to agree on what terms and words mean.  Zealots from all sides of the political arena start from the premise that “if you are not part of my solution you are part of the problem”.  Going hand-in-hand with this presumption of guilt for anyone not espousing their ideas is the presumption that their own use of words is the only correct one.  The more annoying of these even delight in conflating words and ideas if it suits their needs – having the ends justify the means.

Nowhere does this it-means-whatever-I-want-it-to-mean word usage seem to show up on the political landscape more than in the discussions of economics.  And within the subject of economics and its application to health care, no term seems to be as susceptible to vague interpretation as health care.  The problem is what we exactly mean by health care.  Is health care a type of insurance or is it something different?  And what exactly is insurance?

To attempt to explore this last question, let me first tentatively define insurance:

Insurance is the process whereby a group of people pool their resources together (voluntarily or by law) to mitigate a risk that results from incomplete information about who and how many will be adversely affected by the outcome that results if the risk is realized.

This definition may seem a bit more complicated than the Merriam-Webster definition ‘an agreement in which a person makes regular payments to a company and the company promises to pay money if the person is injured or dies, or to pay money equal to the value of something (such as a house or car) if it is damaged, lost, or stolen’ but they both convey the same ideas.  I’ll list those ideas and then explain them a bit with some examples.

The key features of insurance are:

1. Bad part - There is an event that presents an adverse outcome (injury, car stolen, house burned down, death causing the loss of my income, …)
2. If part - Uncertainty in whether the event will occur and to whom (if…)
3. Payout part - A pool of money that is used to partially or wholly correct the situation (money or payments)

To understand this definition in more detail let’s consider a very simple case.  Suppose there is a rare disease that affects only 10 percent of the population and which causes a long term disability where a person can’t earn a living for 10 months.  The situation can be presented schematically as

Now suppose that you are one of the people who could be afflicted.  How much money should you save to mitigate the risk?  Well, if you were mitigating this risk by yourself, the answer would be that you would have to save up 10 months of reserves (money, food, water, whatever) against the possibility that you would be the target.  If you cooperated with the nine others in the community, than each of you could save 1 month of reserves with the idea that all of you would contribute to the one who gets ill.  This savings for the possible use by someone else is called the premium.

On the surface, all of this should seem very familiar and quite obvious. There are, however, several sets of tricky questions with which one has to wrestle.

First, it is clear that the situation is clearly advantageous for the one who gets sick but is it advantageous for those who remained healthy? True they only had to save 1/10 of what they would have had to save otherwise but that 1/10 is now gone and they cannot use it unless they become sick.  In the case where each person mitigates his own risk, he is in complete control on how to judge that risk.  He can decide at some point to stop worrying about the disease and he can begin to tap into his reserves.  He can guess right or wrong, but he is the one making the choice.  In the case of the ten-person community, each person surrenders control of their premium.   Who then decides?  How are the decisions reached?  Since control is now surrendered, it often turns out that one or more of the healthy members regrets paying the premium, regarding it as a waste of resources.   How does the system work if too few people participate because they reason that way?  Should they be forced by law to do so (as is the case for car insurance)?

Second, is it always the case that exactly 1 person out of the 10 will get sick?  Generally, the rate of infection is an average measure with some outbreak having fewer victims and others having more.  How much should each member really donate to handle this uncertainty?   Who gets to hold onto the reserves should no one get sick?  How should the community divide the reserve if more than one member gets sick and there simply isn’t enough to satisfy the need?  Answering these questions and caring for the reserves became the responsibility of the insurance industry. They employ armies of statisticians, called actuaries, who try to set reasonable amounts for the premiums.  They also seem to employ armies of brokers for determining where the reserves go when not being paid out (e.g., where does the money get invested) and armies of lawyers to make sure only the minimum amount is paid.  How should the community as a whole regulate these armies?  What are the rights of the individual?  What are the rights of the firm?

Both of the previous sets of questions naturally arise from the basic arrangement of insurance as defined above and are worth debate.  But there is a third and trickier set of questions that are often posed that where the concept of the ‘if part’ is stretched outside of a decent boundary.  When these mental gymnastics are engaged, the term insurance becomes mangled and its meaning is broaden to the point where it becomes meaningless.

This situation occurs when the ‘insurance’ is used to mitigate an adverse outcome that is guaranteed to happen.  It is not a case of ‘if’ but of ‘when’.  As a concrete example, consider the question as to when members of our 10-person community will become hungry?  Clearly hunger is an adverse outcome (‘bad part’) that can be solved with an allocation of resources (‘payout part’) but is it a risk (‘if part’)?

If the community were farmers then the hunger question could be recast as a risk if the insurance where stated as ‘If a member’s crops should fail then that member would go hungry and crop insurance would satisfy a claim’.  But it is wrong to call protections against any occurrence of hunger an insurance.

Consider a car insurance policy.  No insurer includes items of standard maintenance like oil change, replacement of wiper blades, shocks, struts, and tires.  Even more ridiculous would be the expectation of an insurance policy that protects against running of gas - not in the sense of being stranded on the road - but in the simple and regular sense of having consumed gasoline in the course of driving.  Yet when applied to health care, insurance against 'if parts' (broken leg, chronic or critical disease) get lumped together with other things and the whole package is called insurance.  This muddies the water and prevents us as a society from allocating proper resources for the poor and needy.

Let me be clear, I am not against having societal protections against hunger or methods for making sure other health needs of the poor or disadvantaged are being met.  But it is disingenuous to call those protections a type of insurance.  Doing so seems to be a marketing technique that is designed to confuse two related but distinct issues in the minds of the electorate.  It also seems to me to be most advantageous for those companies offering these types of 'insurance'.

(The interested reader is encouraged to read about the distinctions between term life insurance and ‘whole life insurance’ and the debate on Wikipedia about whether it is better to call the latter by the term assurance.)

I was having a conversation recently with a co-worker who was lamenting that the lead on his project didn't find much value in my friend’s contributions.  It seems that the team lead is better on all the various technologies they employ.  I pointed out that even if that were true, which I doubt, my friend had an invaluable resource that no one could ever exceed – his time.  Every human on this earth has, in a normal day (i.e., one in which they are neither first conceived nor in which they die) the same number of seconds as everyone else.  This immutable fact of human existence leads to the idea of what economists call comparative advantage.

What exactly is comparative advantage?  It is best explained by examining a simplified version of my friend’s situation.  Suppose that we name my friend ‘F’ and his team lead ‘L’.  Also, let’s focus on two tasks that they each can perform and label them ‘A’ and ‘G’ (based on the actual tasks performed on my friend's project).

To understand comparative advantage, we have to say a little about how each of the persons working on this project employs their skills to perform these tasks.  When L says he is better than F, he can only mean one of two closely-related things.  Either he produces a better result in a fixed amount of time or he produces the same result in a shorter amount of time.

This balance between quality and time-to-complete is present in every daily activity where expertise is involved.  Do-it-yourself home projects are excellent examples where the weekend warrior spends two days trying to repair a sink or toilet when the same job could be done in a half-an-hour by a master plumber.

So why doesn't L just get rid of F?  After all, if L’s skill is analogous to the ‘master plumber’ and F’s to the ‘weekend warrior’ why even employ F?  This is where the time comes in.  Since L has the same amount of time available in a day as F, L can maximize the use of his expertise by relying on F to ‘take work off of his plate’.

Let’s make this more understandable by using concrete numbers.  Assume that L can perform task A in 0.5 hours and with a profit of $50, and task G in 0.3 hours and results in a profit of $20. Next assume that F can perform task A in 0.7 hours with a profit of $50 and task G in 0.4 hours with a profit of $20.  Note that in this example, I am imagining a situation where tasks A and G have to be done to a certain level of quality or no profit will result.  This is the usual situation when purchasing a good like a computer where the whole thing has to work (would you buy a computer that was mostly completed but was missing a hard drive?).   There are two final ingredients that have to be considered.  First, how many of tasks A and G must the firm of L & F complete?  Let’s assume that they need to complete at least 90 of task A and 80 of task G to live up to demand.  Finally assume that L and F are working a 40-hour work week.   I will only be examining a single week so I will not require that L or F work exactly 40 hours, but I will require that they stay within 0.1 hour (39.9 - 40.1) and I allow fractions of tasks completed. In a more realistic situation the output would be averaged many weeks and the fractions would disappear.  Let’s summarize the ground rules of our game in a little table.

Comparing side-by-side we can see that L is indeed better than F at both tasks.  That is to say that L completes both tasks faster than F for the same profit per task.

If the firm of L & F wants to maximize their profit (and who doesn't) the operative question is then:  what is the proper work load for L and F?

Let’s try a couple of examples.  Suppose L & F decide that since L is better at everything they should let him try to maximize the number of tasks completed.  It shouldn't be hard to convince yourself that the maximum number of tasks L can complete is 103 distributed between A and G as shown below (if he tries to do more tasks he has to do more on G leaving too little time for F to produce the remaining units to complete all 90 A tasks and 80 G tasks). The resulting work division is shown in the table below netting the firm a profit of $6,100.

Can their firm actually do better?  The answer is yes and it involves having L do fewer tasks, focusing solely on performing A tasks, which have the higher profit margin.  The maximum profit the firm can earn is with the following work load

which results in a net profit of $6,160 dollars.   Observe that in raising the profit of the firm, L actually drops his output from 103 tasks to 80 while F drops his profit from $2660 to $2160. In addition, L & F combined work 0.2 hours fewer. By allowing L to specialize, both L & F stand to make a larger profit than can be made otherwise.  And even though F is seemingly inferior to L in all regards, his ability to provide the invaluable resource that is his time allows the firm as a whole to earn more profit.  That is comparative advantage.

At this point there are two additional observations to make.

The first is that the example given above is particularly simple in that not only was L better than F at performing both tasks, he has an advantage over F in performing Task A that is greater than his advantage over F in performing Task G.  This advantage is measured as the ratio of L’s profit per hour to F’s profit per hour on a given task.  L earns $100/hr on Task A compared to F’s $71/hr giving an advantage of 100/71 = 1.40.  Likewise, L earns $67/hr on Task G compared to F’s $50/hr giving an advantage of 67/50 = 1.34.  The fact that L has the greatest advantage on the task with the greatest profit margin ($100/hr) is what makes the analysis of the maximum profit easy to do.

The situation becomes more nuanced if F can improve in his performance of Task A, completing it in 0.6 hours instead of 0.7.  In this case, L still has an advantage on Task A at a value of 1.2 but it is now lower than his advantage on Task G.  With F’s new found skill, the firm can not only earn more money, but they can do so by having L spread his efforts between G and A tasks.  A possible (not neccessarily optimal) work load is

which nets a profit of $6500 for the firm.  Note that L is still better than F in all regards, but L is not only doing more G tasks than before but his total number of tasks rises to 108 while F drops his task from 91.5 to 70.  Imagine now a real business with many employees and many tasks and you can see how complex it is to actually determine how to maximize business performance.

The second observation is that there is a human element to the problem of L & F that hasn't been addressed.  I posed a parenthetical question above when I asked who wouldn't want to maximize their profit.  Of course, in that context the profit was defined as dollars.  In fact, people define profit in all sorts of different ways  - job satisfaction, time off from work, lower stress, etc. – that make maximizing the outcome nearly impossible because of competing agendas and goals .  For example, it is possible that the firm of L & F is willing to forego some dollar earnings so that L & F can each share in the tasks being performed.   It’s for this reason that when this logic is applied in the broader context where L and F are human institutions (business, governments, or countries) there is a lot of friction in deciding what to do.

Is wealth created?  This is a question that, in some fashion or another, seems to occupy a lot of economic and political discussions.  Much of the rhetoric associated with taxes and income re-distribution is based on the idea that if Wall Street gains wealth then it does so at the expense of Main Street.  But is this really true?  And what is wealth?  Is it money?  Is it fancy cars and big houses?  Is it the 'good life'?  The questions abound. I'll try to answer the related questions 'what is wealth' and 'is wealth created' by asking a different, and admittedly more provocative, question.

But, before I do, I want to be clear that I am no fan of Wall Street.  Near the top of my list of reforms I would like to see enacted is the severing or curtailing of the special status enjoyed by Wall Street, and the cozy relationship it has with Big Government.  This relationship, which starts with Big Government having the power to pick and choose winners and losers based solely on the judgement of a small group of people, can and often does lead to cronyism, whereby Wall Street's winners reward government's pickers in lots of different ways.  I'll explore these rewards in future posts, but for now I just want to emphasize that I am not talking about wealth in terms of any 'Wolves of Wall Street' notion.

In order to address the question of wealth, I would like to pose a question that is a slight variation of a question I first heard posed by Prof. Timothy Taylor in his course Economics.  My version of the question is simple to state:

Take a few minutes to reflect on it before you read on.

There is, of course, no correct answer, but to help frame the question let's compare the lifestyles of the two groups in both 1914 and today.  To make things concrete, assume that we will compare lifestyles by three measures: money, possessions, and intangibles, where into the latter category go all the miscellaneous things that affect quality of life but which are hard to quantify.  Now let's talk about what life was like 100 years ago.

Consider first a typical member, let's call him Everyman, of the 99% in the year 1914.  How much money would Everyman be likely to command?  According to Mary Braswell, the average national annual income in 1914 was $577.  To get an idea of how much variation existed across the country, consider wages resulting from urban and rural employment scenarios.  First assume that Everyman was employed in New York City.  It was likely that his typical job would have been in construction as a bricklayer, carpenter, painter, etc.  His work week would have been 44 hours long with an hourly rate ranging from $0.50 to $0.75 an hour, resulting in a gross income of about $1500/year. In contrast, if Everyman worked on a farm, his wages would be a lot less (somewhere at about $300/year) as, presumably, were his costs of living.  A new car cost about $500, which is about 1 year's worth of income.  So, Everyman was unlikely to buy one without financing it or saving for years to do so. The cost of an average house was about $3500 or about 7 years of his income, again representing a substantial financial investment.  Everyman would have only modest spare time, little access to higher education, the fine arts, and ready entertainment, and he would be unlikely to travel often or far.  Correspondence between him and friends and family would be mostly by letter with days of delay between exchanges.

Next let's look at what it would be like to be in the 1%.  A typical representative of this group might be someone like George Eastman, a man who made hundreds of millions of dollars from his inventions and entrepreneurial efforts.  Located in Rochester, New York, the Eastman house is a huge mansion with large rooms, a conservatory, opulent chandeliers, regal staircases, lots of bathrooms, and more. The original house being considered too small, Eastman actually paid for it to be split and pulled apart and rebuilt with an insertion that provided even more room.  Outside of the 35,000-square-foot house, well-manicured gardens populated the 8-and-1/2 acres of land.  Eastman had servants, money, and resources to spend much of his time however he wanted, journeying often to Africa on safari.  As a captain of industry, he could obtain the finest things available in his time - cars, entertainment, fine clothes, luxurious trappings, etc.

Certainly each of us would want to be in the 1% rather than in the 99% in 1914, but would any of us be willing to move from the 99% in 2014 to become Eastman?  Consider all the things that we have as commonplace that Eastman, despite his millions, didn't possess.

We have access to much better health-care than Eastman did.  Vaccines for numerous diseases, such as polio, mumps, rubella, chickenpox, and measles, all found their birth in the 100 years between 1914 and 2014.  Smallpox and rinderpest have been eradicated.  Influenza no longer poses the huge threat it once did when it wiped out an estimated 50 to 100 million people in 1918.

The technology we take for granted wasn't even dreamed of by Eastman.  His trips to Africa took days of travel whereas we can jet to there in less than a day.  Cooking food in short order in a microwave oven provides us with a convenience no number of servants could have given him. Turning on the television for immediate entertainment, adjusting the central heating or air-conditioning for comfort, surfing on the internet for information, settling in to play a video game, the list goes on and on of the luxuries the 'poorest' of us has that Eastman didn't.

In the final analysis, the original questions of 'what is wealth' and 'is wealth created' can be answered as follows.  Wealth is not rightly measured in terms of money or possessions.  These things are only tools - means to an end.  The real measure of wealth is the amount of time we each have to better ourselves, to explore our existence, and to expand our personal horizons.  In this regard, how could any of us argue that wealth hasn't been created.  After all, the population in the country has more than tripled from 1914 to present but the vast majority of us have access to more time and opportunities to be ourselves than any other people had in the past.  We live with conveniences that even the highest of the 1%-ers of days gone by never enjoyed.  I can't speak for you, but I can say that, given the choice, I would rather stay in the 99% now, with all that that entails, than to have lived as Eastman did in 1914.  I can also voice an appreciation for what he and countless other entrepreneurs like him did to bring the wealth that we enjoy today to each of us.

Some much of the narrative that is offered on the economy is built on statistics.  And as often quoted there are lies, damn lies, and statistics.  One particularly annoying set of statistics rests on combining individual statistics by joining together (aggregating) statistics to tell a story that they don’t tell on their own.  This is at the heart of Simpson’s Paradox.

To illustrate the paradox consider a two demographic groups labeled ‘A’ and ‘B’.  Each is trying for a position at a large corporation ‘U’ with many divisions or departments.  Suppose that the hiring percentage for each group at the company is:

Can we conclude that the company discriminates against group ‘B’ in favor of group ‘A’?  At first glance, one may be inclined to say that ‘U’ clearly favors ‘A’ over ‘B’ and maybe has violated equal opportunity laws and is being unethical and unfair.

But suppose that we actually drill down to examine the hiring by division and that, for simplicity, ‘U’ is made of two divisions ‘S’ and ‘H’.  Also suppose that, upon request, the hiring percentages for the two divisions are:

and

At this point, we may be tempted to say that the company ‘U’ has cooked the books.  But a simple table shows that the statistics presented above can be understood very easily.  Again for simplicity, assume that 10 members of ‘A’ and 10 of ‘B’ apply for jobs but that 8 members of ‘A’ apply to ‘S’ and 2 to ‘H’ while the reverse is true for group ‘B’.

Note that by combining the statistics for ‘S’ and ‘H’ into one whole under ‘U’ the combine statistic tells a much different story than is told by tracking the two divisions separately.

The situation becomes more interesting when salary is factored into the analysis.  Suppose that each member of ‘A’ is paid on average $100K for his position in ‘S’ and that each member of ‘B’ is paid on average $125K for his position in ‘S’ and $60K for his position in ‘H’.  Members of ‘B’ seem to be doing quite well.  But when the statistics are combined into one roll-up, one would conclude that ‘B’s are paid only 92 cents for every dollar that an ‘A’ makes.

Okay, one may be willing to concede that the combined statistic doesn’t tell the whole story but one may object that there is still unfairness in the system.  After all only 4 members of ‘B’ have been employed whereas 5 of ‘A’ have been.  This objection can also be addressed by considering the simple modification of the results shown above.

Now ‘B’ clearly has the upper hand in employment not just at the division level but at the corporate one as well.  But if the same average salaries are used ($100K and $125K for ‘A’ and ‘B’ in ‘S’ and $60K for ‘B’ in ‘H’) and then all the statistics are combined into on measure, the story told is that members of ‘A’ are paid on average more than those in ‘B’.  In fact the margin between the average pay of ‘A’ and that of ‘B’ is now larger, even though more members of ‘B’ are now employed.

This is the heart of Simpson’s paradox.  What is not being accounted for is the reasons for why members of ‘B’ preferentially apply for employment in the lower paying jobs in division ‘H’ rather than for the higher paying jobs in ‘S’.

By now it should be clear that this situation has real world applications.  The most famous example of this type of situation that has worked its way through the courts is the case of the Berkeley gender bias case.

Other examples are the oft-quoted statistic that women make 77 cents for every dollar a man makes.  This statistic can be quite true and yet be quite misleading.  The common interpretation that women are being widely discriminated against is not supported by that statistic.  There are surely pockets of discrimination out there but more likely explanations are that women preferentially enter different fields (or that they interrupt their working years for various reasons, such as raising a family, which being a personal choice and one which I wish I could have pursued, is not addressed here).

If society really wants women to make on average the same as men, then steps should be made to address why so few women, comparatively speaking, enter high-paying STEM jobs.  This is where our focus should be and not on trying to fix what is mostly an imaginary problem caused by Mr Simpson and his paradox.