Author: Zachary Bartsch

The Tragedy of the Commons, or Lack Thereof

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In 1968, Garrett Hardin wrote an influential paper named “The Tragedy of the Commons”. It was published in Science and was kind of a big deal. The paper was about the problem of common resources that can be rationally over-used by individuals such that the resources are destroyed – making everyone worse off. The general idea is a great insight and we can see examples everywhere. People being loud in public spaces, odiferous foods microwaved in the breakroom, spoiled food that remains in the refrigerator. These are relatively innocuous. But more substantial parallels include dumping waste into common water sources, overfishing/hunting, or over-harvesting trees or scavenging in common forests.

The Original Problem

Harden was specifically concerned with human overpopulation. He wrote in the same vein as Paul Ehrlich, who published “The Population Bomb” in the same year. Harden explains that the universe, and earth specifically, only has so much matter and carrying capacity for humans. He left the limiting constraint open. Maybe there would be inadequate clean air, water, nutritious food, etc. The specific inadequacy doesn’t matter, they are all due to the finiteness of our world.

From Hardin’s perspective, there was no natural prophylactic that would prevent us from bumping into the natural and horrifying constraint that inadequate resources would impose. He thought that people would continue to reproduce at greater than replacement rates and death would ensue. He also astutely pointed out that if good people agree to limit their number of offspring, then we will be left with only bad people reproducing. They’d place everyone at risk with their irresponsible, though entirely rational, folly. He concludes that the only hope for humanity is a mutual consent to a coercive entity that would prevent this commons problem of over-reproduction.

The Typical Response and its Shortcoming

The most popular argument against Hardin comes from Julian Simon, who argued that humans are the source of innovation and ingenuity and that more humans implies more innovation. Against Paul Ehrlich, Simon famously bet that commodity prices would fall over the course of the 1980s, asserting that human ingenuity would increase abundance.

Putting the wager aside, Simon’s idea that humans figure out ways to make resources more accessible is entirely correct – except for when it isn’t. The Malthusian booms and busts in population and persistent subsistent income levels did occur historically. But it’s been a long time since then. For a few hundred years we’ve had increasing standards of living *and* an increasing population. There are exceptions. There’s been starvation in Venezuela, Cuba, Ethiopia, China, North Korea, and Ukraine. These countries were plenty populous with plenty of human minds to tackle the challenges of scarcity. More people = more abundance isn’t exactly what Julian Simon said, but it’s how a lot of people answer Hardin and Ehrlich’s predictions.

The Better Responses

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Fiscal Health & Divided Government

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For the past two years, we’ve had a unified government in which the Republican party has populated the White House and had majorities in both chambers of congress. Once the new legislators are in office we’ll have a divided government. That means that the political party controling the White House won’t also control the senate and house of representatives. In the spirit of saying something of substance, I want to know what the implications are for our fiscal picture.

One can measure fiscal health in many ways. Does a divided government bode well for shrinking the deficit? Rather than spit-ball about politics, I take the data since 1960 in one hand and a model in the other. See the end notes for model details.

Since 1960, the most popular form of government split has been a Democratic president and unified government, followed by Republican presidents and a divided government. Democrats have controlled at least one chamber of congress for 62% of the years. Do these splits matter for federal outlays, receipts, and the deficit? Since a unified democratic government was most common, I use that as the baseline fiscal case and compare the cases to it.

Below are the average impacts of government-party types on federal spending, revenues, and the deficit. The blanks are insignificant differences. On average, the only party split that results in less spending is a Democrat president with divided government. Those and unified Republican governments raise more revenue and reduce the budget deficit from its trend (there was a small decline in in discretionary spending at the start of Trump’s 2nd term with a unified government).  The bad news for deficit hawks is that Republican presidents with a divided government – the type that we’ll have for the next two years – perform poorly. On average, they reduce government revenue and increase the deficit. Again, all of this is ‘on average’.

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Random Sample Vs Sobol Sequence

Zachary Bartsch1 Comment

Say that you have a bachelor’s in finance, but that you’re not exactly a ‘math’ person. You know that diversification is good for reducing the volatility of returns, but the calculations are a bit mysterious to you. You know what the efficient frontier is, but its calculation is elusive. All is not lost! There are alternatives to the math: Sampling methods. By testing a few possible portfolios, we can get an idea of which one is the best fit for you. Here I’ll provide an example using 1) a simple random sample, 2) stratified random sample, 3) Sobol sequence, & 4) Scrambled Sobol.

I’ll use a two-asset portfolio here for ease. I assume that the portfolio includes no short or leveraged positions and that the asset weights sum to one. This is known as ‘long only’. The challenge is that we want a certain return-volatility profile for our portfolio, but it’s a bit hard to figure out what our options are. Luckily, both return and standard deviation (SD) of a portfolio are determined by the weights on the individual assets.

With a long only portfolio, all possible weights are uniformly distributed between one asset having zero weight and the same asset having 100% of the weight. Since the weights sum to one, whatever weight remains after the first asset is attributable to the 2nd asset. See the figure below. Unlike many distributions, we know exactly what’s possible for the weights. The portfolio expected return is simply the linearly weighted average and the portfolio variance is quadratically weighted. Return and SD equations are below.

The portfolio return is mathematically easy, since it’s just a linear average: more weight on asset A implies a rate of return that is closer to that of asset A. But the same is not true for SD, due to the covariance component. We can graph how both portfolio returns and SD are related to the asset weights below.

We already know that the possible weights are distributed uniformly (and so are the returns), but the possible SD are not distributed uniformly. Without the math, we want to know what our possible portfolio SD are so that we can determine what mix of assets is right for us. This example is a bit trite, but the gains occur when generalizing to many-asset portfolios. We can choose from a few methods for describing the correspondence between weights and the SD.

Method 1: Random Sample

The easiest thing to do is take a random draw of a few weights and calculate their associated returns and SDs. However, randomness also implies that we may get a set of points which are clustered together or that don’t sample the various nooks and crannies very well.  An example of a random sample is below, along with a line that connects the sampled options (I assume that we know the extrema weights: 0% & 100% values). Random sampling does an ‘ok’ job of choosing relevant portfolio allocations. But due to the random nature, substantial pieces of the actual SD menu options may be omitted. Sometimes the omitted portions are no big deal and other times they are – and which occurs entirely at random.  In the image below, the random portfolios left out the possible allocations that yielded the lowest volatility.

Method 2: Stratified Random Sample

The fact that the possible weights are distributed uniformly in weight-space is a big advantage. One way to constrain our sample of weights is to use a stratified random sample. In this case, we split the uniform weights into several equal intervals and then take a random sample from within each interval. This ensures that each interval’s characteristics are reflected, even partially, in the overall sample. The various shaded regions below reflect the regions from which a sample was drawn. While the regions are uniformly distributed, the random sample(s) within each region can occur anywhere within the region.

The green line implied by the sample is closer to the minimum SD, and the portions that have less weight on asset A are now less accurate (further from the dotted line). So, we gained some precision in some parts of the SD correspondence, but lost some in others. Loss is especially likely to occur near more jagged or irregular possible values. Since we don’t necessarily want the minimum SD allocation, using a stratified random sample is not always better than a simple random sample. But at least the maximum gaps between the observations are constrained. A simple random sample can detect local irregular shape sometimes, whereas a stratified random sample might always lack adequate resolution in a narrow interval.

Method 3: Sobol Sequence

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Disability: Income, Unemployment, & Education

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Let’s talk about disability. The American Community Survey (ACS) identifies seven broad categories, not including the baseline case of ‘No Disability’. I’ve written before about how disability designations are difficult because many qualifying conditions are a matter of degree. Surely you’ve met a person who is legally blind but can see *some*. How much sight ability can remain while still being considered blind? If a person can identify the sun’s location, but nothing else, then is that person still blind? Similarly, who’s to say whether some physical or cognitive characteristic is disabling? Why not enabling – depending on the task?

Wisely, the ACS side-steps this entire discussion and simply asks respondents whether they have “difficulty”.  We can be agnostic about the cause and degree while still trying to get at the heart of the matter. One downside is that people tend to have more difficulty as they age. Since that’s not relevant for earlier life economic outcomes, I only examine ages 24-45. Difficulty with “self care” is too small of a category in the 2024 ACS for the analysis here. Below are the other six difficulties identified:

  • Hearing Difficulty (n=6,609)
  • Seeing Difficulty (n=8,307)
  • Cognitive Difficulty (n=26,792)
  • Ambulatory Difficulty (physically getting around) (n=4,568)
  • Independent Living Difficulty (n=5,997)
  • No Disability (n=885,302)

We should say early on that many of the people who participate in “Deaf” (capitalized) culture do not consider deafness to be a disability and that any such suggestion is motivated by bias and hearing culture. I won’t engage with that here. But I can say that there is a long tradition going back through the 1800s that rejected alms-giving for deafness and instead supported independent living for deaf people. Historically, this manifested as outlawing panhandling while featuring deafness and rejecting government programs that provide simple transfers due merely to deafness. More recently, the push to reject the ‘disability’ label and its baggage has even been the motivation for some deaf people to oppose cochlear implants being covered by medical insurance. For ease, I’ll be using the colloquial terms for all of the above difficulties. Now that you have the greater context, let’s jump into the data (unweighted).

The baseline income chart is above. Given the above description, it should come as no surprise that deaf people have the highest average income among disability groups, conditional on employment. However, it’s also surprising that most of the above disabilities have incomes that I wouldn’t exactly call destitute. Many people who have a disability look much like everyone else. From an economic point of view, we all have a comparative advantage and it’s perfectly consistent with gainful employment and flourishing otherwise.

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Marriages By College Major

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[Edited to include divorces]

The American Community Survey (ACS) collects information on how many times people have been married.  Using the 2024 ACS, we can see how that changes across ages. Getting married is what we call an absorbing state. Once you get married once, you’ll never be married zero times again. So long as people get married across the age distribution, the proportion of never married people falls.

The same is true for getting married a 2nd time. Then, you’ll never have been married once ever again. While the proportion of people never married must shrink with age, the proportion of people married once can rise. If a few people get divorced or married a 2nd time, but an even bigger number of people get marred for the first time, then the group of people married only once can grow. The ACS stops measuring once someone has been married three times – then it’s “three or more” times. A subsequent divorce the universal absorbing state. Those people never go into another category.

The chart shows the proportion of people by age and the number of times that they’ve been married. Darker hues reflect divorces.* Importantly, this is the snapshot in 2024. So each age group is a cohort snapshot in time. That’s why the proportion of people in their 80s who’ve been married zero or one time is greater than people in their 70s. They’re a different cohort. When the now 80-year-olds were in their 70s, the sum of the blue and light yellow bars were larger than for more recent 70-year-olds.

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Degrees, Higher Degrees, & Higher Income

Zachary Bartsch2 Comments

I’ve discussed multiple times now how economics degrees are associated with higher income. One reason may be that it’s not the bachelor’s degree that’s doing the legwork, but rather the graduate degree. I examine that hypothesis here for the 25 most popular degrees in the 2024 American Community Survey.

The data identifies who has a bachelor’s degree and in what field. We also know whether an individual has a master’s or professional degree, or a doctorate. Unfortunately, we don’t know the field for the higher degrees. So, while we can say that 45% of Economics majors have a graduate degree, we can’t say that the graduate degree is in Economics. After all, plenty of people major in one thing and pursue a graduate degree in another thing.

Degree Types by College Major

Below is a chart that ranks the 25 most popular college majors and whether those graduates also hold a graduate degree. There are several patterns. First, the tier near the top of the chart shows more business majors tend to be terminal. Students majoring in communications, business, and marketing tend not to proceed to get higher degrees.

That contrasts starkly with the bottom tier of the graph where majors like Chemistry, Biology, Political Science, Math, and History all tend to have high rates of graduate degrees.  I’m not sure why this is. Maybe it’s because the skills are more research-oriented in nature and prepare those students well for graduate school. Other alternatives may be that the bachelor’s degree alone doesn’t provide much income or that a graduate degree results in a large proportional increase in income for those majors.

Economics majors are on the lower end in terms of the proportion with only a bachelor’s degree (55.5%), near the middle of the pack for proportion with a master’s or professional degree (39.7%), and have an average proportion holding doctorates (5.1%).

Because the numbers make it easy, I’ll pick on education majors a little. Given the high proportion of education and elementary education majors who have graduate degrees, there are relatively few of them who have doctorates. Other majors that have a lot of graduate degree holders tend to have more doctorates, but education majors in higher education are overwhelmingly people with master’s degrees. Given that many of them work for governments, I suspect that they often get procedural pay raises merely for holding a higher degree.

Income by Degree Type and College Major

Below is a chart that shows the average income among employed people by college major and higher degree. The highest-paying terminal bachelor’s and master’s degrees are both among Economics majors ($144k & $203k). A previous post showed that Economics majors had the highest overall income and here we can see that it comes primarily from the bachelor’s and master’s degree holders, while economics majors with doctorates earn the 3rd highest income ($208k) behind computer science ($247k) and electrical engineering ($238k).

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Race & Sex & College Major

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There are some stories that we tell. These include that we have increasing non-white and non-male participation in many college majors. Here I examine the 25 most popular majors in the 2024 ACS data and I split it up into older and younger cohorts, delineated by age 40 (unweighted).

Race

Below-upper is the distribution of race by college major for people older than 40 years of age, or who mostly graduated more than 15 years ago.  It largely conforms to my biases. There were a higher proportion of Asian people in the natural sciences and engineering, but also in Economics. I didn’t really have strong priors about the proportions of black people, but they composed the highest proportions in Criminal Justice, Business, and Liberal arts. Contrary to my expectations, Elementary Education had the highest proportion of white people. Below-lower is the cohort that is age 40 and younger. The entire distribution is  similar, but less white.

Some of the differences between the two groups are hard to see, so I’ve included those below. What are some general takeaways? 1) There are lower proportions of white people among all degrees. 2) There are higher proportions of Asian people in every field except mechanical engineering, which is unchanged. 3) Whether black people compose a greater proportion depends on the major.

In the younger cohort, black people are now a greater share of bachelor’s in chemistry, Fine Arts, Physical Fitness, Biology, and Liberal Arts. But black people also now compose lower proportions of people with bachelor’s in business management, Criminal Justice, and Nursing.

Interestingly, the whitest college major, Elementary Education, has experienced the least change in racial diversity and has had a decline in the proportion of black degree holders. Economics ties with Sociology with for the 4th lowest proportion of white people among younger graduates at 61%. Most of the criticism in economics has not been due to racial imbalance, but rather due to sex imbalances.

Sex

Because sex has two categories in the census data, I can fit everything into the single graph below. It illustrates the sex split by major among people older than 40 vs the younger cohort. The distribution mostly conforms to my priors. The biggest surprises to me among the older cohort are that Finance and Math were as popular among females as they were. Those are two fields in which I though men would compose a higher proportion, but Math is within a stone’s throw of an even split. Among the younger cohort of majors, the vast majority of degrees are more female now, though Economics is still around 2/3 male.

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Iso-Standard Errors & Unemployment By Major

Zachary Bartsch4 Comments

Say that I want to calculate the unemployment rate by college major. That’s easy enough – we just divide the number of unemployed people by the number of people who are in the labor force. Repeat for each major.  The 2024 ACS includes all the variables we need, including employment status by week, but here I just calculate the annual average. I’ll calculate unemployment rates using the unweighted observations because I want to make a separate statistical point about simple standard errors.

Sample weights aside, we have some basic data maintenance to consider. The sample sizes for each major differ. Some majors include more than 15k people, while others have less than 100. Which majors should I include? All of them?

It depends on how precise I want the estimates to be – how small I want the standard errors to be. Below is the basic equation for the standard error (SE). Maybe I want my standard errors to be no more than 0.1%, since unemployment rates are on the order of 1-5%*. Then, it’s just a simple matter of setting the SE equation equal to 0.001 and solving…. Except that there are two variables. Getting a SE of 0.1% depends on both the sample size and the observed proportion. So, a basic rule such as ‘include only majors with at least 100 people won’t quite achieve what we want since the whole point of the exercise is that we suspect that the proportions of unemployed people differ among majors.

In order to get an idea of how many observations we need conditional on the proportion, we can use a popular tool in economics. Basically, adding the prefix “iso” to any term lets us see how two (or more!) other variables matter for the value of the term. We have iso-costs, iso-quants, iso-Sharpes, iso-retirement payments, etc. Here, we can have an iso-standard error by graphing the sample size on one axis, and the proportion on the other. With the desired SE as a constant, we can rearrange the SE equation so that  the sample size and proportion variables remain. They’re isolated below – solving for sample size is much simpler.  

The above equations let us see all of the sample size and proportion combinations that yield an arbitrary standard error. We’re basically doing the first steps of what’s known as a power calculation. We’re setting up some guard rails before doing the analysis so that we know ahead of time whether we’d even be able to tell the difference between proportions with the sample sizes that we have. Below is the graph of the iso-SE to illustrate the sample size & proportion combinations that yield some target SEs. Pictured is the left side of parabolas. What does it tell us? It tells us that shrinking the target SE increases the necessary sample size at each proportion REALLY FAST.

Since the most college majors have a sample size that is well below 15k, we basically know ahead of time that we won’t be able to tell the difference between their unemployment rates if they differ by a mere tenth of a percent. Given that the national unemployment rate in 2024 was around 4% and around 2.3% for college majors, there’s not much room for error – literally. Everything looks the same when proportions are similar and sample sizes are small.

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Economics Major Income Premium

Zachary Bartsch2 Comments

I’ve written about Economics major incomes before. The consistent empirical fact is that they earn more than most other college majors. But why? My working theory is that’s it’s due to human capital differences.

Challenge 1: Top Business Schools

“The highest ranked business schools offer economics majors with various business concentrations instead of separate business majors. So, the high average income of econ majors is due to those top tier finance concentrations and the like.”

This challenge doesn’t hold water. If the high average income were just due to top performers, then omitting them would break the pattern of high economic major compensation. But it doesn’t. Trimming the top and bottom 10% of incomes for each major doesn’t cause economics to fall much in the ranking.

Challenge 2: Econ Majors Choose Higher Paying Occupations

“Economists aren’t especially productive. They merely choose higher pay occupations. Other majors could achieve the same thing if they wanted to.”

This challenge is partially true. Economics majors do choose higher paying occupations. The Bureau of Labor Statistics has an extensive list of occupation categories and codes that are linked to the American Community Surveys. I examine the broadest categories that have sample sizes of at least 40 for each economics and other majors.  The below scatter plot shows the relationship between average income by occupation and the proportion of economics majors who chose to work in those occupations. There is clearly a positive relationship. Economics majors do choose higher paying occupations.

But the claim about productivity isn’t quite right. If economics majors were just as productive as other majors within their occupational category, then they would earn around the average income within each occupational category. But they don’t! Below is a chart that plots the average income premium over non-economics majors within each occupational category (error bars are one standard error).  The occupations to the left are more abstract or even social in nature. That’s where economics majors earn their big income premium. Further to the right are occupations that are more ‘hands-on’. Economics majors earn about the same as non-econ majors in those categories.

The one interesting case is ‘Computer and Mathematical’ occupations, which are abstract in nature and yet economics majors have no better earnings on average. Those occupations have a higher than typical proportion of Computer Engineering, Computer Science, Computer Information Systems, and Mathematics majors. Given that those majors 1) also have training in abstract theory and 2) are highly specialized, it’s impressive to me that economists can keep up.

Additionally, economics majors are not uniformly distributed across occupational categories. They tend to pursue occupations in which they have an advantage as indicated by their wage premium. The below chart has the same horizontal axis as the one above and has more mass further to the left. A higher proportion of economics majors are in the occupations where they outperform others in the same occupation.

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