How Bayesians Read a Think Piece

How likely is it that an opinion critical of [topic] will get expressed by someone on the internet?

My good friend (call her Anne) texted me this week. Anne sent me a link to a blog that declared some of her preferred works of art (i.e. musicals) to be inferior. She loves art, so to be told that her tastes were not exceptionally good was disappointing.

In my reply I wanted to make sure that Anne wasn’t putting too much weight on this new evidence:

How should we incorporate blogs into our beliefs about reality? (I see the irony – I’m writing a blog right now.)

The non-technical summary: you should be skeptical of what you read online.

The technical summary: the fact that some writer said “H” on the internet, should make you only slightly more confident that “H” is true.

I can’t improve on the Wikipedia presentation of Bayes’ theorem, so I’ll just paste in:

Let’s consider the probability that it is true that Anne’s favorite musical is bad. We’ll call that hypothesis “H”. What’s the probability of H, given that one person wrote an article stating that the musical is bad?  

The evidence, E, is the article.

Instead of just evaluating whether the article is convincing or not, Bayesian inference requires that we consider

  1. Were we confident that H was true BEFORE seeing the article? Was there good data up until this point that convinced us H is true?
  2. If H is true, what’s the probability of this article being written?
  3. What’s the overall probability of this article being written, regardless of whether H is true?

The probability that musical is bad given that someone wrote an article saying so is :

P(H|E) = P(bad|article)

P(bad|article) = ( P(article|bad) x P(bad) )/ P(article)

The right side of the equation asks whether we are likely to see the article if the musical is bad. If the musical is actually bad, then we are likely to see it condemned in print. HOWEVER, if we had a prior belief that the musical is not bad, then the numerator gets smaller.

Finally, we consider the denominator, P(E) or the probability of seeing an article that is derogatory towards the musical. If that probability is high, then the probability of the musical actually being bad goes down.

Here’s how Anne should think:

P(bad|article) = ( likely that article will be written if bad x prior evidence suggests not bad) / snobby think pieces get written regardless

so

P(bad|article) = (big x small)/ big = small probability that Anne’s favorite musical is actually bad

You should be just the right amount of skeptical when it comes to internet content. Be Bayesian.

Only Real Quotes

I’m going to occasionally make cartoons of actual things that people have said. The real world can be very entertaining. I was a graduate student at George Mason University, so I got to take a class from Bryan Caplan.

He broke up his 3-hour lectures with Caplan-jokes. I only remember one. Maybe it stuck with me because of the funny voices. He was talking about happiness and consumption in the context of microeconomics. He impersonated a German philosopher debating a British philosopher.

This is an idea Bryan explores in a recent blog.

Do people do what makes them happy? What do we make, as economists, of people who claim that they want to write a novel but never do? If someone claims to prefer sad songs, can we really call them sad songs?

Next, here’s one from me and my son. I put his age on his cartoon shirt. I always ask him about the details of his day while I was away at work. He’s old enough to understand a little bit about how I spend my time, but sometimes I don’t get it right when I attempt two-way communication.  

Affording a second child

I have been reading Matt Yglesias’s book. I’m going to quote his podcast with Tyler here:

I also think that a lot of the way society is structured disincentivizes educated professional people from having a second or third child, even though it’s not that the objective financial cost of doing it is so high.
But you think about Democratic Party micro-targeting of everything. They’ll say, “Well, okay. If this little extra boost will help lift some people over the poverty line, we should do that. But if you’re making $140,000 a year, you don’t ‘need’ help with your childcare costs.” That’s how the people in the think tanks think.

Matt Y

On the margin, people who don’t live in poverty still feel financial pressure. They still worry about whether they can “afford” more children.

The following Facebook post stood out to me yesterday. I went to high school with this woman (call her Rachel). She teaches at a public elementary school in New Jersey. She is married with one daughter.

It sounds like Rachel wants another child, a sibling for her daughter. As a working mom, I can sympathize with her desire to not quit her job.

More answers from her peers include “I’ve been also looking for this answer. Anyone I know who has had more than one, one usually stays home and the partner works. I don’t know how people do it!” and “I have to say this month has been TERRIBLE! Paying $250 a month for my baby at daycare and then having my oldest there a few days a week bc my in-laws can’t handle zoom 😳 I’m literally working for health benefits.”

This response is probably from someone who is one stage of life ahead of Rachel, “It was hard but we lived off one salary till the kids were 5 years old. We didn’t go out or do much at all. Cost of daycare for twins was insane. Once they were in school most of the day I got my job…”

Matt Yglesias wants Rachel to have another child, and a third if she wants a “big family”. That’s not how we get to one billion Americans, it’s simply how we avoid population shrinkage.

I’ll probably deal with more of Matt’s ideas in future posts. Even if you disagree with all his policy recommendations, it’s a great book to get you thinking.

I did some quick Googling and it seems like Rachel’s job pays over $40,000 per year. It wouldn’t be crazy to assume that Rachel’s household income is “6 figures”. If their daughter is currently in daycare and they have a second child who needs daycare, then they could be looking at a daycare bill over $20,000 per year during the crunch time. That crunch time wouldn’t last very long, BUT that is a daunting bill to pay when you are also paying for rent and diapers and don’t want to eat beans every day. New Jersey has relatively high property taxes, rents, and daycare costs.

Abraham and Kearney on the Decline in Employment

Katherine Abraham and Melissa Kearney just published
“Explaining the Decline in the US Employment-to-Population Ratio: A Review of the Evidence” in the Journal of Economic Literature.

The unemployment rate measures people who are actively looking for work and can’t find a job. The authors are not examining short term fluctuations in unemployment (which shot up in pandemic times). They are looking at at long term decline in employment rates of working-age adults in the US. The trend began in 1999. Employment of adults in the US dipped after the Great Recession and still has not recovered a decade later. Less-educated males have experienced the largest drop in employment.

I’m reviewing the entire paper with my Labor Economics class. Most of what the authors talk about can be found throughout our Labor Econ. textbook, but I like using the paper to organize and motivate the collection of facts and theories.

Here’s a summary of their thorough examination of possible causes of the decline in working.

They estimate, drawing on other empirical work, that two factors have a considerable and measurable impact on the decline in formal employment. Import competition from China (the US changed their position on trade with China in 2000) and automation (industrial robots) both result in lower demand for US workers.

There are three contributing forces that the authors declare them to be minor casual factors. Increased receipt of disability benefits disincentivizes working, higher minimum wages results in less jobs, and the increased incarceration rate in the past few decades takes adults out of the labor force.

The paper is called “A Review of the Evidence”. The following is a list of factors that could in theory be responsible for the decline for working but for which data is scarce:
Lack of child care
Changes in leisure options (i.e. young men play video games)
Changes in social norms (i.e. young people can stay “in the basement”)
Increased use of opioids (could be a result of diminished job opportunities)
Rise in occupational licensing
Frictions or matching issues

All of those indeterminate items represent research opportunities.

The Powerful Allure of R0 < 1

I categorize this as “News”, because I don’t know if we will have enough posts on medicine to justify a whole category for Medicine. Because the coronavirus is affecting life so much, it’s well worth writing about currently.

R0 is the average number of people who will contract a contagious disease from one person with that disease. If you want, you can pronounce it “R naught”.


If R0 is less than 1, and stays that way for a while, the disease will disappear. That means that the virus can still be passed around between a few people (for example, if 1 out of 1,000 people forgets to bring a mask into the grocery store), but over time it will run out of targets and we will be done with this whole thing. If R0 is above 1, that means that a few cases produces more cases and eventually most people will get infected. Once you understand the potential of R0<1 it does become tempting to engineer a lockdown.


We understand the spread of the virus better than we did when lockdowns were first discussed in the US in March 2020. It’s not as simple as every infected person giving the virus to two new people. The way the virus spreads is often through “superspreaders” and superspreader events. That’s why so many large gatherings have been cancelled and continue to be cancelled. With this wrinkle in mind, there is still the overall R0 score of whether the virus is increasing or decreasing.

If you fail to stop the initial spread of the virus (R0 > 1) then a great many people can be infected and eventually the spread will slow simply because the virus is running out of hosts. One of the more controversial topics in Spring 2020 was whether “herd immunity” is or is not something we should want to achieve as a society.

One of the absolute best places to get virus news is MarginalRevolution.com. Today, Tyler has written a new post about herd immunity. I’ll provide some quotes. Much more at the link of course.

… these same herd immunity theorists tended to be less pessimistic than many of the mainstream forecasts…

Now, I don’t recall many of those theorists early on making a prediction about a specific number required for the herd immunity threshold to be reached.  Nonetheless, when deaths and hospitalizations collapsed in Sweden, London, and New York at about 20 percent seroprevalence, obviously it seemed that might be the critical level for herd immunity to kick in.

Then things started to go askew in the last few weeks.  First, it seems like a bad second wave came to an already fairly hard hit Madrid.  OK, you could say Madrid was never had 20% seroprevalence to begin with.  And then what appears to be a second wave has started coming to Israel, with rising hospitalizations.  Finally, it is believed that in Britian R equals about 1.7, and that a second wave of cases is on the verge of hitting London and Southeast England.

Tyler Cowen

Even though no one has all the answers, this is the conversation we should be having. In fact, I’m starting to wonder if we should make a Medicine blog post category.

It was just yesterday that the dreaded and long foreseen 200,000 deaths was confirmed.

The Problem of Paying Attention in Online Classes

Currently, I subscribe to Bloomberg Businessweek. Instead of ranking MBA programs, this year they decided to report on a survey of students about switching to online classes. (in the Sept. 21 issue)

Overall, the reaction from students has been negative. They believe an online MBA is not as valuable as the traditional in-person experience.

Something MBA students state, which I have already heard from my own undergraduates, is that it’s difficult to focus during online instruction hours. If your face isn’t being watched through your webcam, then it’s tempting to “multitask” and not pay attention to the professor. I feel the same temptation when I join online research seminars.

What’s the most sympathetic view of this situation? Doing your online classes “isn’t that hard”. I feel like the scold looking over my bifocals at millennials saying, “going to a dry cleaner isn’t that hard”. (We millennials cannot be bothered to go to a dry cleaner.)

Here’s my first and brief thought: College students today have been taught to use screens for recreation by their parents.

Parents put kids in front of screens to get rid of them. I get rid of my own kids by putting them on screens. I ensure that they are not watching something evil.

I hope parents are diligently ensuring that their preteen daughters are not chatting up predators. What responsible parents have been told is to try to limit total screen hours and also to try to keep your child out of the digital equivalent of dark alleys.

That kind of guidance doesn’t teach students how to use screens constructively. They are suddenly being asked by teachers to be constructive on the screen. Some of them can hack it. Some of them can’t. None of them were prepared for this.

Your typical 20-year-old college student today must have done well in traditional classrooms because they did, after all, get admitted to college. But when they were on their screens, they were scrolling and gaming and indulging their impulses. As long as they physically showed up to class on Monday morning and turned in enough homework assignments, no adult was going to make them do chores on screens.

Since screens are here to stay, we need a lot more research on how to raise humans who know how to be responsible on screens.

No answers came to me when posed this question to the hive mind:  

Thoughts on “The Social Dilemma” Documentary

I rarely watch things right when they come out. For once, I’m fairly current on something: the Netflix documentary “The Social Dilemma”.

Former employees of tech companies are using their talents to try to make sure that technology takes our society in a good direction. They appear to feel guilty for creating a product that is so fun it has become addictive.

They call attention to the negative effects of social media, which were difficult to foresee. The guy who claims to have created the Facebook “Like” button says that his intention had been to spread happiness. They didn’t realize that the lack of likes could exacerbate teen depression. They worry that in some cases it has even led to suicide.

They mention early on that social media has actually done some good. I know personally someone who was adopted from a foreign company and then reconnected with his birth family by searching his family name on Facebook.  That’s neat.

I think they underrate Facebook as a utility for adults. Parents are using Facebook to notify neighborhood residents of school fundraisers. Adults are using Facebook to sell used furniture.

Facebook is a place to turn for entertainment, but it’s really become more than that for my generation. We don’t have physical address books. We have a phone Contact list and we have our Facebook accounts.

Facebook is not the only service being scrutinized. Former employees of Google and Pinterest, among others, came forward to talk about how those services use customer data to sell advertisements.

One of the good points they make is that the algorithms that maximize ad revenue do not have user well-being in mind and can unintentionally lead to spreading false “news” stories. It’s important for users to know this. I am glad that more people are aware, thanks to the documentary.

The fact that radio is funded by ad revenue never caused us to shut down radio. Maybe it was always more transparent to listeners, and the fact that it is less individualized makes it feel less creepy.

Speaking of creepy, this documentary is creepy. It’s full of creepy music and long pauses in which your mind goes to dark places. They should have made it one hour instead of 1.5 hours. It was very manipulative, which makes sense because it was made by people who confess that they are professional manipulators.

My conclusion is that we should treat social media like alcohol. Most people can live with alcohol, but it kills. Every year, alcohol kills people. The US government estimates that alcohol kills 88,000 people every year in the US. We should be more careful with alcohol and we should all be more educated on the potential for harm.

Some people would be better off if we completely banned alcohol, but currently the strategy is to manage harm through EMTs and medical treatment. There are support groups for people such as Alcoholics Anonymous.

We think young people are more likely to hurt themselves with this dangerous item, so we restrict the sale to youth.

The internet can be very harmful to children and teens. It’s important to point out that respectable social media services like Pinterest are not the only places where kids can go. Kids and “screens” is a whole ball of twine. Regulating Facebook may actually do very little to protect children.

We can do a public health campaign, sort of like what’s going on with sugary sodas right now. I think this documentary is the beginning of a productive conversation.

It’s hard to say that I disagree with the conclusions of the filmmakers. I suspect that I do, and yet they mostly just tell stories and ask open questions and fidget quietly on screen. So, it’s hard to pin them down on precise policy recommendations. Although I resent having to watch them fidget for so many minutes, I also don’t want to sound ungrateful for the effort they made to raise awareness of an issue they feel strongly about.

Let’s have more documentaries, and more blogs, and more in-person conversations about how to make a better world now that the internet genie is out of the bottle. Let’s keep middle school students off of social media. It starts at home and in the neighborhood.

Can I Borrow Your Reference Point?

That is the title of a blog I wrote for a new publication Works in Progress.

I summarize an article I published in 2020 and relate it to the current polarized political environment, which is not an extension I made as explicitly in the article.

We often talk of a moral obligation to sympathize with others and “walk a mile in his/her shoes”. We do not often “walk a mile” in the shoes of our neighbors just to be nice, and we can’t even do it for money. In a lab experiment, I put people in an environment where they could earn money for accurately guessing what others did. I found that people tend to transfer their own reference point on to other people, which causes them to make bad predictions.

There is more at the blog. I end with a conclusion that some might say is too optimistic or too generous to the opposing side:

If people of opposing political persuasions spent more time learning each other’s life stories, then we would end up with a less toxic climate.

Two short polls on work habits

I ran two polls on Twitter about work habits. These are not scientific polls that are representative of the American public. The people connected to me on Twitter are mostly economists and data scientists. The strongest claim that I could make is that these results tell us something about the kind of professionals who check Twitter regularly. We are all working from home even more than usual because of coronavirus restrictions.

The first poll was about when and if people who are working from home break for lunch. I usually want to break for lunch at 10:30am but push myself to hold out until at least 11am. I wondered if there is anyone else like me.

The next week, I was reading about a new fancy software that helps you organize your own notes and writing schedule. I mostly write notes in Notepad, a text editor from the 1980s! Should I get with the times? First, I thought I’d ask my respectable friends whether they have bothered to schedule their writing times.

Most of them don’t schedule writing. So, I’m just going to stick with Notepad for now. I’m definitely open to the idea that I would be more productive if I worked harder on productivity. Maybe next year I’ll start doing every thing right.

Kids Helping with Chores and Adult Time Use

This past weekend, my 5-year-old son helped us clean the house. Tasks include emptying the dishwasher, picking up clutter ahead of the robot vacuum, and cleaning bathroom surfaces.

Here’s the advice I bet you have heard before: Get your child involved in chores by the age of 2. It will take more work to get them to help than to just do the job yourself. However, you want to raise a child who can help. It’s good for them.

Something I have my two year old do is sort clean silverware. She pulls spoons out of the dishwasher basket and puts them with the other spoons in our silverware tray that we keep in the drawer. Redirecting her and motivating her to stick with this task takes a lot of energy. It would be much easier to just do it myself.

[I am writing this from a perspective of a “suburban mom”. If you live in a tiny apartment or a big farm, then this might not apply to you at all.]

There are two benefits to having kids do chores with you that I think are underrated.

  1. Your kids have to be entertained, and we are all trying to limit screen time. My son spent at least 2 whole hours total this weekend cleaning. Those are 2 hours that I would have had to fill somehow. The “easier to just do it yourself” argument fails to take that into account. It’s true that I could have parked in him front of a screen while I did all the cleaning myself, but to me that would have presented an additional challenge of getting him off the screen. I use TV as a reward for when the cleaning is done. And then no one feels guilty about anything.
  2. It’s more fun to do chores with your kid. I can fold laundry myself, but if my kid is helping me, then it becomes quality time. As a working parent, I really value quality time. When you do chores together, you get to know each other.

Imagine that I spend 10 minutes folding laundry by myself and then I seek out my son for 10 minutes of quality time with him. That’s 20 minutes total. I could just fold laundry with him. If it takes 20 minutes, then the laundry is done and the quality time has been had. Will he spend most of his time rolling around in the clothes and whining that it’s hard to match socks? Sure, he will. But that presents opportunities for us to chat and overcome obstacles together. I could pay $1,000 for a white water rafting trip when all I wanted was some quality time and some obstacles to overcome. Folding laundry together is free. The only antic I will not tolerate is for the child to destroy a pile of clothes that I have already folded. Other goofy antics are allowed.

I understand that some of my readers outsource housework. I believe in the specialization of labor. More power to you. Some of my readers probably should be outsourcing more than they do.

My advice is, if you are doing thing like laundry and dishes and cleaning in-house, don’t do it alone. Getting your kids involved is less costly in terms of your own time than you might think.

Tip A: Do not expect your child to be efficient and hurry through their job. She might lie on the floor for 20 minutes before even starting. If you try to hurry kids you are setting everyone up for miserable failure.

Tip B: Be flexible. Technically, we are supposed to clean the whole house together on Saturdays. Sometimes the jobs bleed into Sunday if Saturday is busy. Sometimes I’ll do one task myself on Friday. Routine is helpful, but do what works for you.