Inflation: Not Merely a Monetary Phenomenon

Zachary Bartsch6 Comments

I’m a big fan of Milton Friedman. I’m also a big fan of easy-to-remember phrases that impart great wisdom. It honestly made me wince the first time I said the following:

“Inflation is *not* everywhere and always a monetary phenomenon“.

The reasoning is as plain as day. Consider the quantity equation:

MV=PY

For the uninitiated, M is the money supply, V (velocity) is the average number of times dollars transacts during a period, P is the price level, and finally Y is real output during a period. This equation is often called the “equation of exchange” or “the quantity equation”. Strictly speaking, it is an identity. It is a truism that cannot be violated. All economists agree that the equation is true, though they may disagree on its usefulness.

Inflation is simply the percent change in price. We can rearrange the quantity equation, solving for price, in order to see the relationship between the price level and its determinants.

P= MV/Y

What does this mean? It means that more money results in more inflation, all else held constant. It means that higher velocity results in more inflation, all else held constant. It means that less output results in more inflation, all else held constant.

Why would Milton Friedman say that inflation is always caused by changes in the money supply if it is clear that there are two other causes of the price level? When Milton Friedman said his famous quote, output growth was relatively steady. Velocity growth was relatively steady. For his context, Milton Friedman was right. The majority of price and inflation volatility was found in changes in M. See below.

Strictly speaking however, Milton Friedman knew better and he knew that the statement was not strictly correct. Friedman was a public intellectual and he was a great simplifier. He taught many people many true things. At the time, people were blaming inflation on a great variety of things: taxes, fish catches, and unions, to name a few. Arguably, Friedman got them closer to the truth.

Now, there are economists that are pointing to total spending as the driver of inflation. After all, both sides of the equation of exchange describe NGDP (a.k.a. – Aggregate Demand or Aggregate Expenditure). Replacing M and V in the equation with NGDP yields:

P=NGDP/Y

What does this mean? It means that higher NGDP results in more inflation, all else held constant. It means that less output results in more inflation, all else held constant.

But economists dismissing M in lieu of AD are committing the same oversimplification. Y can also change! Maybe economists figure that our recent history is full of relatively stable Y growth and that we ought not pay attention to it. And indeed, unsurprisingly, RGDP growth has been less than NGDP growth.

But what is driving the current bought of inflation?

Pardon the crude image. The pink lines are eye-balled trend lines on natural logged data for AD, Y, and P. Prices are up. Is it because of exceptionally high NGDP? Nope. Total spending is back on pre-2020 trend. Does Y happen to be down? Yep, it sure is.

Right now, assuming the previous trend was anywhere close to potential output, inflation is not being driven by excess aggregate demand. It’s being driven by inadequate real output. The news tells the story. There have been supply-chain bottle-necks, difficulty employing, lockdowns, and fear of covid. Right now we have an output problem and higher prices are a symptom. We do not have an aggregate spending problem.

PS – In fact, it is my belief that the Fed successfully avoided a debt-deflation aggregate demand tumble that would have been catastrophic. Inflation is expected when supplies of goods decline.

Weigh costs, benefits, and evidence quality

James Bailey1 Comment

Living means making decisions with imperfect information. But Covid provides many examples of how people and institutions are often still bad at this. A few common errors:

  1. Imperfect evidence = perfect evidence. “Studies show Asprin prevents Covid”. OK, were the studies any good? Did any other studies find otherwise?
  2. Imperfect evidence = “no evidence” or “evidence against”. In early 2020, major institutions like the WHO said “masks don’t work” when they meant “there are no large randomized controlled trials on the effectiveness of masks”
  3. Imperfect evidence = don’t do it until you’re sure Inaction is a choice, and often a bad one. If the costs of action are low and the potential benefits of action high, you might want to do it anyway. Think masks in 2020 when the evidence for them was mediocre, or perhaps Vitamin D now.
  4. Imperfect evidence = do it, we have to do something Even in a pandemic, it is possible to over-react if the costs are high enough and/or the evidence of benefits bad enough (possibly lockdowns, definitely taking up smoking)

Any intro microeconomics class will explain the importance of weighing both costs and benefits. But how do we know what the costs and benefits are? For many everyday purchases they are usually obvious, but in other situations like medical treatments and public policies they aren’t, particularly the benefits. We have to estimate the benefits using evidence of varying quality. This creates more dimensions of tradeoffs- do you choose something with good evidence for its benefits, but high cost? Or something with worse evidence but lower costs? Graphing this properly should take at least 3 dimensions, but to keep things simple lets assume we know what the costs are, and combine benefits and evidence into a single axis called “good evidence of substantial benefit”. This yields a graph like:

Applied to Covid strategies, this yields a graph something like this:

This is not medical advice- I say this not merely as a legal disclaimer, but because my real point is the idea that we should weigh both evidence quality and costs, NOT that my estimates of the evidence quality or costs of particular strategies are better than yours

Judging the strength of the evidence for various strategies is inherently difficult, and might go beyond simply evaluating the strength of published research. But when evaluating empirical studies on Covid, my general outlook on the evidence is:

Of course, details matter, theory matters, the number of studies and how mixed their results are matters, potential fraud and bias matters, and there’s a lot it makes sense to do without seeing an academic study on it.

Dear reader, perhaps this is all obvious to you, and indeed the idea of adjusting your evidence threshold based on the cost of an intervention goes back at least to the beginnings of modern statistics in deciding how to brew Guinness. But common sense isn’t always so common, and this is my attempt to summarize it in a few pictures.

Racial Gaps and Data Gaps

Jeremy HorpedahlLeave a comment

Are there racial gaps in the distribution of the COVID-19 vaccine? This is an important and interesting question in its own right. But I’ll talk about this question today because it’s an interesting example of how confusing and sometimes misleading data can be.

How do we answer this question? One is by surveying people. There are a number of surveys that ask this question, but a recent one by the Kaiser Family Foundation finds that among adults 70% of Blacks and 71% of Whites report being vaccinated. And given the sampling error possible with surveys, we would say that these are virtually identical. No racial gap! (Note: there was a racial gap when they did the same survey back in April, with 66% of Whites and 59% of Blacks vaccinated.)

But, surveys are just a sample, and perhaps people are lying. Maybe we shouldn’t trust surveys! And shouldn’t there be hard data on vaccines? Indeed, the CDC does publish data on vaccinations by race. That data shows a fairly large gap: 42.3% of Whites and only 36.6% of Blacks vaccinated. This is for at least one dose, and the percentages are of the total population (which is why it’s lower than the survey data). So maybe there is a racial gap after all!

But wait, if you look closely at the footnotes (always read the footnotes!), you’ll see something curious: the CDC admits that the race data are only available for 65.8% of the data. We don’t have the race information for over one-third of those in this data. Yikes! And given the exist disparities we know about in terms of income and access to healthcare, we might suspect that the errors are not randomly distributed. In other words, if there is probably good reason to suspect that Blacks are disproportionately reflected in the “unknown” category. But we just don’t know.

So what can we do? Since this data comes from US states, we can look at the individual state data and see if perhaps some of it is better (fewer unknowns). What does that data show us?

Continue reading →

China Cracks Down on Cryptocurrencies

Scott BuchananLeave a comment

The Chinese Communist Party (CCP) is all about control. In the well-known words of Chairman Mao:

Every Communist must grasp the truth, “Political power grows out of the barrel of a gun.” Our principle is that the Party commands the gun, and the gun must never be allowed to command the Party.

These days political power is linked to economic power and control of information, as well as raw military firepower. Cryptocurrencies have assumed financial importance and they entail information processing and tracking.

On the other hand, a key driver for cryptocurrencies is precisely to escape from the domination of big central authorities, such as the CCP. Proponents of crypto revel in the fact that anyone with a PC can get in on “mining” and that the crypto universe does indeed operate on the web as a largely democratized enterprise. Anybody can transact large sums with anybody, with a moderate degree of anonymity.

These two different visions of life collided on Sept. 28 when the Chinese government banned nearly all crypto-related transactions:

China’s central bank said on Friday that all cryptocurrency-related transactions are illegal in the country and they must be banned, citing concerns around national security and “safety of people’s assets.” The world’s most populated nation also said that foreign exchanges are banned from providing services to users in the country.

In a joint statement, 10 Chinese government agencies vowed to work closely to maintain a “high pressure” crackdown on trading of cryptocurrencies in the nation. The People’s Bank of China separately ordered internet, financial and payment companies from facilitating cryptocurrency trading on their platforms.

The central bank said cryptocurrencies, including Bitcoin and Tether, cannot be circulated in the market as they are not fiat currency. The surge in usage of cryptocurrencies has disrupted “economic and financial order,” and prompted a proliferation of “money laundering, illegal fund-raising, fraud, pyramid schemes and other illegal and criminal activities,” it said.

Offenders, the central bank warned, will be “investigated for criminal liability in accordance with the law.”

The Chinese government will “resolutely clamp down on virtual currency speculation, and related financial activities and misbehaviour in order to safeguard people’s properties and maintain economic, financial and social order,” the People’s Bank of China said in a statement.

Well, those are the bare facts. It’s good to know the CCP is so diligently safeguarding people’s assets and public order. And as noted, Mao’s successors would not naturally favor systems that allow people to just do what they want to do, free from guidance from the Party. But inquiring minds want to know or at least speculate further regarding the reasons for this move and its consequences.

Brian Liu and Raquel Leslie highlighted two other motivations for this crackdown. One motivation  concerns China’s desire to launch its own state-controlled digital currency. This will give the government heightened ability to track every single transaction by every single user. It would also provide China with a new means of exerting influence over other nations and corporations:

The ban comes as the People’s Bank of China (PBOC), China’s central bank, is piloting its own digital currency, the eCNY or “digital yuan.” Unlike private cryptocurrencies, the eCNY is issued directly by the central government and is being designed to provide the PBOC with near-real-time financial data on user transactions. Some observers fear that the eCNY will be used as a tool to strengthen the Chinese Communist Party’s domestic surveillance. Others worry that the eCNY will be used to retaliate against international companies that speak out on human rights issues. Fan Yifei, a deputy governor of the PBOC, announced last week that the eCNY has entered a “sprint stage” ahead of the February 2022 Winter Olympics in Beijing.

Another motivation may be to help prevent wealthy Chinese from taking their money abroad:

The crypto ban may also be intended to deter capital flight. Despite past crypto crackdowns and strict capital controls, wealthy Chinese have used cryptocurrencies to funnel more than $50 billion overseas in 2020. As China is in the middle of an economic slowdown that has been exacerbated by other regulatory crackdowns on the tech and education sectors, China may be redoubling its efforts to ward off skittish entrepreneurs from exporting their money overseas.

Will this crackdown fully succeed? Many observers doubt it. They think that people will find ways to do what they want to do, using platforms that are hosted outside China.

As for the digital yuan, well, it kind of goes against most of the reasons people have gravitated to crypto. It represents a move back to government control and surveillance. It is not really a “crypto” currency at all, but simply another form of regular money.  It could get traction, however, in international trade among countries who have reasons to try to escape from the current U.S. dollar dominance. Also, China could hand out its digital currency like candy to impoverished nations, to get them on board. Millions, maybe billions of people live without regular banking access, and so a medium of exchange and store of value that requires only a cell phone to move funds around town or around the world could be attractive. At any rate, count on China to make the digital yuan a big “thing” for international visitors due at the February 2022 Olympics.

The price of Bitcoin took this news in stride. It continues to bounce around in the same $40,000-$50,000 range that it has been in for the past three months. And being banned by China is not a death-knell for a financial entity.  Indeed, it could be a contrarian indicator. Consider that China has also banned Youtube, Facebook, Google, Instagram, Pinterest, and even (because of his uncanny resemblance to President Xi) Winnie the Pooh.

Grade inflation is making our students too risk averse

mdmakowsky1 Comment

Grade inflation in the US education system is a common observation, one that is, at least at the college level, largely undeniable. A couple recent interactions with students has brought it to the front of my mind again. When discussing their majors and what classes they were taking, there was considerable hesitation to take what were perceived as difficult classes. What I thought this called for, in the moment, was a bit of confidence building, for a professor such as myself to say “You can do it!”

It turns out confidence in their ability to learn the material was not the issue. What they were unsure of was their ability to get an A. No, to guaranteed get an A. It was the risk of a sub-A grade that concerned them (likely exacerbated by the fact that my university does not award + and – grades in undergraduate classes). So I went through my usual pitch:

You take 5 classes a semester for 8 semesters. That’s 40 classes. The cost of couple B’s or even a C will pale in comparison to the benefit acquiring more technical skills, which would pay out for a lifetime. A couple courses in computer science, econometrics and statistics, maybe real analysis for those thinking about a PhD in economics – these would all have huge payoffs. There was a problem with my logic, however, that quickly became apparent.

They weren’t sure what they wanted to do after their bachelors. They didn’t know what advanced degrees they might pursue, whether law or medical school was something they were interested in. What they did know, however, is that GPAs were really important. That students were applying to things they might be interested in, and doing so with 3.8 and 3.9’s. When they saw classes that regularly handed out C’s (not D’s or F’s mind you, just C’s), what they saw was pure downside risk. If they were great at something, no one would ever be able to tell. But if they weren’t, or if they had a bad day on a hard final exam, that it could close doors. What I inferred was that they were trying to maximize their expected outcomes, and in order to do so they had to minimize the number of hard classes in their portfolio. Each path had a handful of unavoidable hard classes, so to take a an additional hard class beyond the requirements of the path they chose was suboptimal.

I don’t know that they’re wrong.

I’ve told this story before. When I was considering getting a PhD in economics I planned on just going to my local school. I was visiting a friend on the opposite coast, though, and thought I’d stop in at a really good local school there. I met with the director of graduate studies in the economics department and was flatly informed that my application would not be read because my GPA (3.2, if you’re curious) was below their cutoff. I said thanks and left. It was some time later that it dawned on me that this was ludicrous. Did they simply never admit students from (the famously uninflated grades of) CalTech? Were they discriminating against math and engineering majors? Likely not. But this is deeper knowledge than that held by your typical undergraduate. All they know is the average admissions statistics and the implied (or in my case explicitly stated) cutoffs.

When we inflate grades and get rid of standardized tests, we put greater pressure on students to curate their education to expected grade outcomes and, more important, to minimize risk. There’s no upside to shining in a difficult class if the best 50% all get A’s. The signal value of success has been attenuated. The signal value of failure, however, has not just been left intact, it’s been heightened. There’s no positive variance to balance it out. There’s no way to be an excellent B+ student whose occasional C in risky classes are balanced out by some exemplary A’s. We’ve effectively raised the costs of taking challenging classes and in doing so discouraged students from acquiring the skills that are most rewarded in the marketplace.

The problem only becomes all the worse when we think about the cultural biases in the confidence we cultivate in different groups of students. If a deficiency in math and science has been low-key implied at every stage of your education, you’re that much less likely to incur the risk of “hard classes”. There’s much pearl-clutching over “everyone winning a trophy” and school being too easy from folks who walked to and from school through 12 months of snow, uphill both ways. Those arguments, which are often little more than a sort of grumpy money illusion, miss the real problem entirely. Undoing grade inflation to make school harder is like giving 7 points for every goal in soccer to make it more exciting.

The actual grades don’t matter. What matters is the the shape of the distribution of grades . If we bunch everyone in the A’s and then disproportionately select into institutions based on those grades, we’re incentivizing students to stay in the herd. To risk your GPA for the sake of hard classes is to risk being isolated. To risk being cutout by admissions committees trying to sort through 1000 applications, half of with have near-perfect GPA’s, and for whom the fastest way to make their workload manageable in an acceptable manner is cut out everyone with less than 3.7.

I’m not sure students are wrong in their grade-mongering. They got into college in many cases based on nothing but those GPAs. They’ll be able to go to grad school without taking the GRE. There will come a day, however, when the next step isn’t school, and after which no one will ever ask them their GPA again for the rest of their life. After which the only thing that will matter is what they know. And who will know more: the overconfident student of upper-middle class parents who graduated with a 2.8 BS in electrical engineering or the pragmatic student who curated courses to maximize their 3.7 GPA while preparing for the MCATS and medical school? I don’t know who will leave with more skills, but I also don’t worry about either. Who I worry about is the first-gen college student, the child of a working class household with a 4.0 BA and 4.0 MA in communications who, desperate to prove to others that they belonged in school, made sure to protect that perfect GPA at every turn. What have we done to ensure that they know enough when they enter the job market?

The high cost of day care and demographics

Joy Buchanan1 Comment

When I moved half-way across the country to take a new job, I had no local support system for my 2-year-old. Putting him in a full-time day care was the plan. I wanted a day care center with a good reputation that is located near work and home. My story, like so many others, includes phone calls and long wait lists. At first, it was hard to understand how I could be willing to pay for a service and it could just not exist.

Opening a large daycare center is risky. Who wants to take that risk? I joked that I’d quit my professor gig and start a daycare in response to the huge demand. Of course, I did not. Fortunately, I don’t live in one of the American counties that lost population over the past ten years.

The WSJ on demographics describes this situation in a shrinking county:

In Lincoln County, Kan., pop. 2,986, about 40 miles west of Salina, Kan., economic development director Kelly Gourley set out to build the county’s first day-care center not run out of someone’s home. A child-care shortage was making it difficult to work and raise children, she saw. The town’s handful of in-home daycares were the only options, and they tended to come and go.

Ms. Gourley estimated it could cost as much as a half-million dollars to build the facility, and she didn’t think it could weather fluctuations in demand. “In a rural community, you lose one kid and you might be in the red all the sudden,” she said. She shelved the plan and instead is working to increase the supply of in-home caretakers.

Allison Johnson, a 32-year-old nursing home speech pathologist, grew up in Lincoln County and hoped one day to have three children. She no longer thinks that is feasible after she had to wait a year to get an in-home daycare spot when her first child was born. Now she and her husband, who owns a residential-construction business, are trying to figure out how they would juggle having a second child.

Her father, a farmer, watches her son, now 2, when her in-home daycare provider isn’t available. But he and her brother are in their busy season, and “they’re not going to be able to do anything but throw him in the tractor.”

There are attractive economies of scale for day-care centers. This economic fact is part of the reason that young people are leaving rural areas, which in turn makes it harder for rural areas to support services for young families.

There has always been a huge amount of value created at home within families that is not fully captured by GDP. As more childcare is moving to the formal market, we are starting to see just how valuable those services are that used to be provided in the family.

Whatever your views on the matter, it’s not surprising that politicians are talking about subsidized day care.

Allowing for flexibility through policy moves like vouchers and de-regulating in-home daycares is important. Some communities can’t support a day-care center facility, like the one in this article. I think the if you build it they will come philosophy, if applied too widely, would be hugely expensive and not efficient. On the other hand, there could be situations in which more day care would be provided if the local government would take on some of the risk currently faced by entrepreneurs.

Markets in Everything for Christmas Decorating

Joy BuchananLeave a comment

Last year I blogged about a service to create your kid’s school Valentine’s cards.

Now, the temperature in Alabama has dropped to a chilly 71 degrees and the pumpkins are out. It’s time for parents to start worrying about who is going to create holiday magic at home.

You can pay someone to do this. An enterprising local has already posted this in a neighborhood group.

Creating holiday magic is a wonderful thing. There are huge positive externalities to even a simple string of lights around your front door. I love it. Creating the magic is also a lot of work. As someone who is forever swamped at work and has already booked three weekend work trips for Fall 2021, my willingness to pay for this service is positive. (I can’t afford this particular service, nor do I need my Christmas tree to look like the one in her picture.)

The rich have always had extra hands to manage their estates. I have a feeling that the percent of households for which this might be a paid service is expanding. There are women in the comments asking this crew to come over.

Social Security: Not a Great/Terrible Investment

Zachary Bartsch3 Comments

Upfront: I’m totally replying to a meme.

I sympathize with the sentiment of the meme. But friends of friends were quickly critical of it. Then I wasn’t sure what to believe. So, I crunched the numbers.

First of all, there is an inherent ambiguity in the meme’s claim, seeing as future tax rates, maximum taxable income, benefits, and plausible returns are unknown. But we can address the data so far. The meme is dated in 2019, but current data is even more charitable toward it.

What we know as of 2021:

The maximum annual benefit is currently $46,740. It was previously lower, but this is a charitable post.

We also know the historical tax rates and maximum taxable incomes. Currently, 12.4% and $142,800. YES, we’re about to assume that somebody met the maximum income criteria over their entire working life.

If someone worked for 40 years while making the maximum contribution each year, then they would have contributed $406,255.20. If we plainly calculate the rate of return on this amount, then we’d yield 11.5%, which is not too shabby ($46,740/$406,255.20). Of course, this is entirely unreasonable because the funds could have been earning interest in private hands during the contribution period. If the funds had been earning 5% throughout the entire period, then the 2021 value of the contributed funds would be $968,838.39. The annual benefit implies a return of 4.8% ($46,740/$968,838.39). Investing those funds in a private account that yielded 5% would have provided $48,441.92 per year, which is not a huge difference. In this light, social security appears not to be a terrible deal. Not as good as the private sector – but not far off.

Let’s be more charitable to the spirit of the meme. What about for 50 years of work? Then the total contribution would have been $423,905.38, yielding an implied return of 11%. Considering the time value of money changes the rate of return to 4.2%. Again, not terrible, but now noticeably less than 5%. If the funds had been invested at and paid out 5%, then the private annual benefit would be $55,846.56. In other words, the privately invested funds would have yielded an annual benefit that is 19.5% higher than what is currently paid. That is substantial. The social security investment is definitely not excellent.

How reasonable is the meme? Well, in order to get the $1.9M figure, interest rates would have to be 7.2% (assuming 50 years of work and that we don’t spend the principal). The concomitant annual retirement benefit would be $136,825.51 (Now that’s an exciting number). In order to get the $95k, we only need to assume 6.3% per year. The S&P 500 has yielded an annual return of 7.6% over the same period (not including dividends). The meme is reasonable. Not perfect. But not ridiculous.

One BIG caveat is that this entire analysis assumes that the employee could simply invest equivalent amounts if Social Security were abolished. This is very unreasonable. Currently, part of the contribution comes from employers. While employees would experience an increase in total pay if the taxes were abolished, the employer would also enjoy a lower cost of labor. Not all of the gains would go to the employee.  One could also argue that abolishing Social Security would improve growth and real incomes generally, but that’s a counter-factual beyond the scope of this post.

Here is the sheet where I show my work.

Tyler Cowen, Talent Curator

James Bailey1 Comment

Everyone else at EWED has been too classy (or earnest?) to post it, since it would implicitly be bragging.

But I’m home with a quarantined kid today and need the win. So here is biotech founder Tony Kulesa‘s article on how Tyler Cowen is the Best Curator of Talent in the World.

Highlights:

Tyler has identified talent either earlier than or missed by top undergraduate programs, the best biotech startups, and the best biotech investors, all without any insider knowledge of biotech. In comparison, Forbes 30U30, MIT Tech Review TR35, or Stat Wunderkind, and other industry awards that highlight talent are lagging indicators of success. It’s hard to find an awardee of these programs that was not already widely recognized for their achievements among insiders in their field. The winners of Emergent Ventures are truly emergent. 

What explains Tyler’s ability to do this?

1. Distribution: Tyler promotes the opportunity in such a way that the talent level of the application pool is extraordinarily high and the people who apply are uniquely earnest. 

2. Application: Emergent Ventures’ application is laser focused on the quality of the applicant’s ideas, and boils out the noise of credentials, references, and test scores. 

3. Selection: Tyler has relentlessly trained his taste for decades, the way a world class athlete trains for the olympics. 

4. Inspiration: Tyler personally encourages winners to be bolder, creating an ambition flywheel as they in turn inspire future applicants.

This seems right as far as it goes, and there is more depth in the article, but there has to be more to the story than we can see from the outside. Luckily Tyler has said he is writing a book on identifying talent.

The Half-Life of Policy Rationales

Jeremy Horpedahl1 Comment

Bryan Caplan recently wrote about public goods theory, how we teach it, and the unrealistic nature of how we classify goods as either/or, rather than on a continuum. I explored similar themes in a blog post that I wrote back in January, but Caplan brings up another important point about public goods theory that I forget.

In a short 2002 paper, and then in a 2003 book with the same title, Foldvary and Klein proposed the idea of “the half-life of policy rationales.” In brief, the justification for many market failure arguments is contingent on the current state of technology. They apply this to concepts such as natural monopoly and information asymmetries, but for public goods theory the most important application is to the concept of excludability.

Here’s the basic idea: it is costly to exclude non-payers for using some goods. If it is so costly that it would not be profitable for a private enterprise to produce the good in question, it won’t be produced privately. But it still may be efficient for government to produce the good, if the benefit from the good exceeds the cost of raising the revenue to pay for it (likely out of general revenue, since we have already admitted it is infeasible to charge the users directly).

But here’s the Foldvary and Klein point: all of the above paragraph is dependent on the current state of technology! Take roads for example. When you had to pay someone to physically take a few coins for a toll road, plus force all motorists to slow down to a complete stop to pay the toll, it was probably cost prohibitive to operate limited-access private toll roads. But technology changes. We now have the technology for electronic tolling done at highway speed (and even coin buckets were slightly faster than handing some dude your change). The argument for government provision of highways, which was strong when technology was ancient, is significantly weakened now that technology has reached its modern state.

(There may be lots of other reasons you think that roads should be publicly provided, such as equity, but these are separate questions and distinct from the argument made in standard public goods theory.)

Foldvary and Klein go through many more examples in their book, but we can already see the key insight. And I think this is extremely important for teaching public goods to undergraduates. It’s normal for us to say that goods are either excludable (in which private provision is best) or non-excludable (in which there is a strong case for some government intervention). But this either/or framing is wrong (a continuum is a better way to think about it), and crucially it can change over time depending on technological changes. Excludability is not some inherent feature of a good or service, it is a function of the state of technology.