YLL or VSL? Cost-Benefit Analysis in the Year of COVID

How do we conduct cost-benefit analysis when different policies might harm some in order to help others? This question has become increasingly important in the Year of COVID.

In particular, it is possible that some interventions to prevent the spread of COVID may save the lives of the vulnerable elderly, but have the unfortunate effect of causing other harms and potentially deaths. For example, increased social isolation could lead to increased suicides among the young (we don’t quite have good data on this yet, but it’s at least a possibility).

If you don’t think any public policies will reduce COVID deaths, then the post isn’t for you. It’s all cost, no benefit!

But for those that do recognize the trade-offs, a common way to do the cost-benefit analysis is to look at “years of life lost” or YLL. This is a common approach on Twitter and blogs, but I’ve seen it in academic papers too. In this approach, you look at the age of those that died from COVID, and use an actuarial life table to see how long they would have been expected to live. For example, an 80-year-old male is expected to live about 8 more years. Conversely, a 20-year-old males is expected to live another 56 years.

So, here’s the crude (and possibly morbid) YLL calculus: if a policy saves six 80-year-olds, but causes the death of one 20-year-old, it’s a bad policy. Too much YLL! (Net loss of 8 years of life.) However, if the policy saves eight elderly and kills just one young person, it’s a good policy. A net gain 8 years of life. (Of course, we can never know these numbers with precision, but that’s the basic idea.)

But I think this approach is fundamentally flawed. Not because I oppose such a calculation (though maybe you do, especially if you are not an economist!), but because it’s using the wrong numbers. Briefly: we shouldn’t value every year of life equally.

The superior approach for this calculation is to use an approach called the “value of a statistical life” (VSL). In this approach, we assign a value to human life (the non-economists are really cringing now) based on revealed preferences of various sorts. Timothy Taylor has a nice blog post summarizing how this value can be estimated, which is much better than how I would explain it.

In short, the average VSL in the US is around $10-12 million, depending on how you calculate it. You might be skeptical of this figure (I was at first too!), but what really convinced me is that you get roughly this number when you do the calculation using very different approaches. It just keeps coming up.

So how does VSL apply to our COVID calculation? What’s really interesting about VSL is that it varies with age. And not perhaps as you might expect, as a constantly declining number. It’s actually an inverted-U shape, with the highest values in the middle of the age distribution. Young and old lives are roughly equally valued! Once we realize this, I think we can see how the YLL approach to analyzing COVID trade-offs is flawed.

Kip Viscusi has been the pioneer in establishing the VSL calculation. If you’ve heard that “a life is worth about $10 million” and scratched your head, Viscusi is the man to blame. Over the weekend, Viscusi gave his Presidential Address to the Southern Economic Association (he actually delivered it in-person at the conference in New Orleans, but to a very small crowd since the conference was over 90% virtual).

As you might have guessed given his area of research, Viscusi used this address to estimate the costs of COVID, both mortality and morbidity (the talk is partially based on this paper). He didn’t talk much about the policy trade-offs, but we can use his framework to talk about them. Here’s a very relevant slide from the presentation.

Notice here we see the inverted-U shaped VSL curve. You may not be able to read it very well, but Viscusi helps us with a bullet point: VSL at age 62 is greater than at age 20. Joseph Aldy, a frequent co-author of Viscusi, has extended the curve even further up to age 100 which you can see in this column. Aldy and Smyth use a slightly different approach, but the short version is that the VSL for a 62-year-old is much greater than a 20-year-old (roughly double). The 20-year-old VSL is roughly equal to that of an 80-year-old.

So let’s go back to the above YLL calculation, which told us that if a policy intervention only saves six 80-year-olds but results in the death of one 20-year-old, it’s bad policy. Too many YLL!

However, using the VSL calculation, this policy is actually good, since 20- and 80-year-olds have roughly equally valued lives. The policy only becomes bad if it kills more 20-year-olds than elderly folks. This may seem strange, given the short life left for the 80-year-old, but it is where the VSL calculus leads us.

I will admit, this calculations are morbid in some sense. But we live in morbid times. Death is all around us, and we need to some clear method for assessing trade-offs. YLL seems like the wrong approach to me. VSL seems better, but if we take a third approach, something like All Lives Matter (and matter equally), we end up with the same calculation when comparing a 20- and 80-year-old.

In the end, we should also be looking for policy interventions that have low costs and don’t result in additional deaths. For example, I think there is now good evidence that wearing masks slows the spread of viruses, which will lower deaths without any major costs. But if we are going to talk about trade-offs, let’s do it right.

(Final technical note: there is an approach that combines YLL and VSL, called “value of a statistical life year” [VSLY]. Viscusi discusses VSLY in the paper that I linked to above. I won’t get into the technicalities here, but suffice it to say VSLY involves more than simply adding up the years of life lost.)

Third Quarter Check-In: COVID and GDP

How have countries around the world fared so far in the COVID-19 pandemic? There are many ways to measure this, but two important measures are the number of deaths from the disease and economic growth.

Over the past few weeks, major economies have started releasing data for GDP in the third quarter of 2020, which gives us the opportunity to “check in” on how everyone is doing.

Here is one chart I created to try to visualize these two measures. For GDP, I calculated how much GDP was “lost” in 2020, compared with maintaining the level from the fourth quarter of 2019 (what we might call the pre-COVID times). For COVID deaths, I use officially coded deaths by each country through Nov. 15 (I know that’s not the end of Q3, but I think it’s better than using Sept. 30, as deaths have a fairly long lag from infections).

One major caution: don’t interpret this chart as one variable causing the other. It’s just a way to visualize the data (notice I didn’t try to fit a line). Also, neither measure is perfect. GDP is always imperfect, and may be especially so during these strange times. Officially coded COVID deaths aren’t perfect, though in most countries measures such as excess deaths indicate these probably understate the real death toll.

You can draw your own conclusions from this data, and also bear in mind that right now many countries in Europe and the US are seeing a major surge in deaths. We don’t know how bad it will be.

Here’s what I observe from the data. The countries that have performed the worst are the major European countries, with the very notable exception of Germany. I won’t attribute this all to policy; let’s call it a mix of policy and bad luck. Germany sits in a rough grouping with many Asian developed countries and Scandinavia (with the notable exception of Sweden, more on this later) among the countries that have weathered the crisis the best (relatively low death rates, though GDP performance varies a lot).

And then we have the United States. Oddly, the country we seem to fit closest with is… Sweden. Death rates similar to most of Western Europe, but GDP losses similar to Germany, Japan, Denmark, and even close to South Korea. (My groupings are a bit imperfect. For example, Japan and South Korea have had much lower death tolls than Germany or Denmark, but I think it is still useful.)

To many observers, this may seem strange. Sweden followed a mostly laissez-faire approach, while most US states imposed restrictions on movement and business that mirrored Western Europe. Some in the US have advocated that the US copy the approach of Sweden, even though Sweden seems to be moving away from that approach in their second wave.

Counterfactuals are hard in the social sciences. They are even harder during a public health crisis. It’s really hard to say what would have happened if the US followed the approach of Sweden, or if Sweden followed the approach of Taiwan. So I’m trying hard not to reach any firm conclusions. To me, it seems safe to say that in the US, public policy has been largely bad and ineffective (fairly harsh restrictions that didn’t do much good in the end), yet the US has (so far) fared better than much of Europe.

All of this could change. But let’s be cautious about declaring victory or defeat at this point.

Coda on Sweden Deaths

Are the officially coded COVID deaths in Sweden an accurate count? One thing we can look to is excess deaths, such as those reported by the Human Mortality Database. What we see is that Swedish COVID deaths do almost perfectly match the excess deaths (the excess over historical averages): around 6,000 deaths more than expected.

Some have suggested that the high COVID deaths for Sweden are overstated because Sweden had lower than normal deaths in recent years, particularly 2019. This has become known as the “dry tinder” theory, for example as stated in a working paper by Klein, Book, and Bjornskov (disclosure: Dan Klein was one of my professors in grad school, and is also the editor of the excellent Econ Journal Watch, where I have been published twice).

But even the Klein et al. paper only claims that “dry tinder” factor can account for 25-50% of the deaths (I have casually looked at the data, and these seems about right to me). Thus, perhaps in the chart above, we can move Sweden down a bit, bringing them closer to the Germany-Asia-Scandinavia group. Still, even with this correction, Sweden has 2.5x the death rate of Denmark (rather than 5x) and 5x the death rate of Finland (rather than 10x, as with officially coded deaths).

As with all things right now, we should reserve judgement until the pandemic is over (Sweden’s second wave looks like it could be pretty bad). The “dry tinder” factor (a term I personally dislike) is worth considering, as we all try to better understand the data on how countries have performed in this crisis.

Two Papers on the 1966 Minimum Wage Increase

Continuing on the theme of last week’s minimum wage increase in Florida, there are two interesting papers recently accepted for publication that both cover the 1966 Fair Labor Standards Act. This law extended the federal minimum wage to a number of previously uncovered. Crucially, the newly covered industries employed a large number of African-American workers.

The two papers agree on some points, such as that African Americans saw large wage gains following the increase. But was there a disemployment effect? Here is where the papers differ.

Ellora Derenoncourt and Claire Montialoux’s paper “Minimum Wages and Racial Inequality” is forthcoming in the Quarterly Journal of Economics. Here is what they find: “We can rule out significant disemployment effects for black workers. Using a bunching design, we find no aggregate effect of the reform on employment.”

Martha J. Bailey, John DiNardo, and Bryan A. Stuart’s paper “The Economic Impact of a High National Minimum Wage: Evidence from the 1966 Fair Labor Standards Act” is forthcoming in the Journal of Labor Economics. They find “some evidence shows that disemployment effects were significantly larger among African-American men, forty percent of whom earned below the new minimum wage in 1966.”

So who is right? Let me clearly state here that both of these papers are very well done, both in their methods and in their assembling of historical data. But I think there is a key difference in the samples they analyze: Derenoncourt and Montialoux’s paper only includes workers aged 25-55. Bailey and co-authors use a broader age range, 16-64, which importantly includes teenagers (this is discussed in Section D of their online appendix).

Since teenagers and other young workers are the ones we suspect are going to be most impacted by the minimum wage (much of the literature focuses on teenagers), the exclusion of workers under 25 seems like a curious omission, and a reason I tempted to believe the results of Bailey and co-authors. But Derenoncourt and Montialoux do try to justify their choice of age group: 1. workers under 21 were subject to a different minimum wage; and 2. workers under 25 were subject to the draft for the Vietnam War.

So once again, you might ask, who is right? I will admit here that I don’t know. Standard economic theory suggests that disemployment effects will result from a legal minimum wage (I fully acknowledge the emerging literature on monopsony power, but I maintain this is still not the standard analysis), and especially so for teenagers and young workers. So I am skeptical of any analysis which excludes these workers, whatever other merits it may have.

Here’s my take: we probably can’t tell much about how the minimum wage will impact young workers today based on these studies. If Derenoncourt and Montialoux’s reasons for removing young workers are indeed sound, then we aren’t really testing the question most economists are interested in today (so I would caution against their attempt to apply the results to labor markets today). But that doesn’t mean these aren’t interesting papers to read on an important change in the history of minimum wage laws in the US!

Florida’s Minimum Wage Experiment

One of the more interesting results from last night’s election comes out of Florida: voters appear to have narrowly approved an increase of the minimum wage in stages to $15/hour in 2026 (Florida has a 60% requirement for ballot measures to pass, and the current vote total is just above that threshold).

Florida is not the first state to approve such an increase to $15/hour: 7 states have already done so, though no state is yet at that level. California will hit $15 first in 2022. Several US cities, such as New York and Seattle, as well as the “city-state” of Washington, DC are already at $15, but these are generally very high wage cities.

What makes Florida the most interesting of the states to try very high minimum wages is that Florida is not a high wage state. Once the minimum wage is fully phased in (in 2026), the minimum wage will be about 75% of Florida’s median wage (it was $17.23 in 2019). That’s much higher than other states: California will be the next highest at about 66%, with Oregon next around 64%. Oregon will be close to $15, but perhaps a little below, as they index their minimum wage for inflation.

(To make these estimates I am using 2019 median wage data from the BLS OES wage data and assuming 2% annual wage growth. This may not be exactly right, but it’s probably close enough.)

Also important to note in Florida: the median wage is not $17.23/hour all over the state. Several MSAs in Florida currently have a median wage at or even below $15 (Sebring, Florida is the lowest at around $14/hour). There will be some wage growth over the next 6 years in those areas, but still this means that the minimum wage will be applicable to roughly half the labor force.

That brings up another interesting legal question: will the minimum wage apply to salaried workers making less than $30,000 per year? The way the law is written, probably not, but logic would seem to dictate that it should. Otherwise, what’s to stop an employer from hiring an employee on a $2,000/month contract, equivalent to $12/hour for a full time worker?

The minimum wage debate among economists consumes a vast literature, and I am no expert on it, and will make no attempt to summarize it here. But Florida seems to be breaking new territory. My little state of Arkansas currently holds the “record” for a US state starting in 2021, with a minimum wage of $11/hour which will be about 67% of the median wage (and about 78% of the median wage in Hot Springs, Arkansas). Florida’s experiment will certainly give economists a new experiment to study.

Arin Dube, one of the leading researchers of the minimum wage and a strong advocate of raising the wage, suggested in a recent policy paper that a good minimum wage for Florida would be around $9/hour, given their wage distribution. That was in 2014 dollars, so we can roughly adjust that up to $11-$12 in 2026 dollars. Florida voters have chosen to go well beyond that recommendation.

Ice!

Continuing with our gift recommendations, Joy has asked us to recommend another gift besides a book (see my recommendation of The Pox of Liberty last week). I have one clear recommendation: ice. But not just any ice: clear ice.

Some of you might wonder what all the fuss about ice is. But if you have every been to a cocktail bar, you can clearly see the difference: clear ice just looks better. I won’t make any strong claim that clear is has better flavor. This value is primarily aesthetic. It’s a little indulgent. But it’s worth it. Since we’re all drinking more at home, recreating the charms of a good bar is half of the fun.

How do you get clear ice? You might find many suggestions on the internet, such as using distilled water or boiling your water. These don’t work. A few years ago, you only had two good options: buy a Kold-Draft machine for several thousand dollar, or get your ice out of a lake.

Thankfully today, there are many ice cube molds on the market that simulate the way nature makes ice: slow, directional freezing. The best one I know of is called True Ice, but you can find other similar molds. These are all around $40. Perhaps it is a bit much for yourself, but the point of gift giving is to find something the recipient wouldn’t have thought to purchase themselves, and they still enjoy. Otherwise, just give them cash!

And furthermore, while $40 for a mold that produces something your refrigerator already makes might seem silly, keep in mind that ice has a long history of being a luxury product. For fascinating history of the early commercialization of ice, read this article about Frederic “The Ice King” Tudor (for a longer treatment read The Frozen Water Trade).

Here are two cubes I made at home with the molds described in this blog post. Can you tell the difference?

Of course, I am assuming that you already have a basic 2 inch ice cube tray. If you don’t already, start with the Tovolo King Cube Mold before you really get into clear ice. These cubes are great for drinks that don’t need a clear cube since they aren’t clear themselves. They are also the perfect size for shaking cocktails.

And one last thing: fancy ice cubes aren’t just for alcoholic cocktails. Kids love them too. Put some plastic army men or other little toys in the ice cubes as they freeze, and they make great bath toys.

One final tip: if you pull an ice cube directly from the freezer and pour room-temperature liquid over it, the ice will break, ruining your beautiful creation. Set the ice out for about 60 seconds before pouring that delicious drink.

To Understand the Pandemic, Look to History (Economic History)

As the holiday shopping season gears up, Joy has invited us to suggest some books that you might give as a gift (or read yourself!).

I have one very strong recommendation: Werner Troesken’s 2016 book The Pox of Liberty. Unfortunately the publisher did not foresee the renewed interest in pandemics due to COVID-19, so you might have to settle for an electronic version of the book right now (though you might have better luck with the publisher than Amazon).

The Pox of Liberty – A Book Review By Dr. Price Fishback - Foundation For  Teaching Economics

Tragically, Troesken passed away two years ago. Many of us would love to hear his thoughts about the current pandemic. The beauty of this book is that we can still learn from him even though he is no longer with us, not only about pandemics of the past, but possibly with lessons for our current health crisis.

Troesken brings his broad knowledge of economics, history, and demography to examine the history of smallpox, typhoid fever, and yellow fever, as well as the policy responses. Broadly Troesken asks: why has the US historically been one of the richest countries in the world, yet so bad at fighting infectious diseases?

I won’t spoil the whole book, but he argues that the answer to both questions can be found in the US Constitution. The liberties protected in the Constitution allowed for the US economy to be among the best performing in the world, but made it hard for the federal and state governments to address pandemics. It’s a trade-off, or rather multiple trade-offs, as Vincent Geloso has put it.

We can see this clearly in the differences between the US and European responses to COVID-19: European countries were able to close their borders which spared many central and eastern European countries from the first wave of the current pandemic (though it does look like this may have been a temporary reprieve, as Czechia, Poland, and others are now seeing dramatic increases in COVID-19 cases). In the US, the virus has slowly spread from state to state, seemingly sparing no one in its path despite varying public policy interventions (including mostly unenforceable travel restrictions). We don’t know what the future holds for COVID, but the constitutional factors at play that Troesken described for smallpox 100 years ago seem to still matter today.

On a personal note, Troesken was a professor of mine in grad school (he spent one year at George Mason University, though most of his career was at Pitt), and he was a big influence on me, especially his teaching style. While I respected his work greatly, I was always puzzled by his interest in infectious diseases. What was the relevance of this topic for understanding the modern world? Well, in 2020, we all found out. And now we miss Werner even more.

How to Think About Inequality Data and Public Policy

Lately I’ve been thinking about the disagreements among economists about the extent to which inequality has increased in recent decades. I am facilitating a reading group at my university on inequality this semester with some great undergrads, so it has very much been on my mind.

With conflicting data showing different trends, how are we as economists to judge this? How can the general public even have a clue how to judge this?

You may have seen this chart before. It comes from an article in The Economist, which actually does a really good job of explaining the debate over the data if you know nothing about it.

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According to some estimates, the share of income going to the top 1% has doubled and is now over 20%. That sounds bad. Maybe we need some more redistribution. Maybe a wealth tax.

But according to other estimates, and taking account of our existing system of progressive taxes and redistribution, the share of income going to the top 1% has not risen at all, is only about 5%. Less worrisome. The existing system of taxes and transfers seems to be doing a pretty good job, or at least no worse than in the last 60 years. No need for a new wealth tax, etc.

So who is right?

Sorry, I don’t have the answer. I think I’m pretty good at digging into economic data (follow me @jmhorp on Twitter for an almost daily dose of data debunking!), but I am no expert in this area. There’s probably only a dozen economists that really understand this data and the trade-offs in different forms of measurement.

So instead of giving you the “correct” answer, I offer you a chance to reflect. Our temptation is to say the “correct” data is the one that comports with our political preferences. If you are a progressive, you probably think inequality is bad and getting worse. Piketty is your man. If you are more of a libertarian, you probably think it’s about the same as recent years. Auten and Splinter must be right!

Stop. And instead, consider how you might view the policy implications of the data you don’t like being the correct data. If you are a progressive, would you still think we need a wealth tax even if the Auten and Splinter data is correct? If you are a libertarian, would you still think things are just fine and maybe we should cut the top tax rate if it turns out that Piketty and co-authors have the real data?

If you answer is the same for the policy implications regardless of what the data say, you might want to check yourself. And if so, why are we even arguing about the data?

Perhaps your answer is “I might have the same policy answer regardless of the data, but there are people out there that are convinced by data.” I think that’s possibly reasonable, and I would like it to be true, but where are these people?

Perhaps the answer is “as a libertarian, I don’t care about inequality so long as the poor and middle class are also sharing in the gains.” Or “as a progressive, I will continue to worry about inequality until the top 1% only has 1% of national income.”

I think these are the normal fallback answers. But really? Libertarians: if the income of the top 1% doubled in a decade, but the bottom 99% increased by 0.5%, you would be fine with this, because at least no one declined? Progressives: you would really support increasing taxes on the rich, despite any downside to this, until incomes were exactly equalized?

Frankly, I don’t believe anyone really holds either of those extreme positions. So surely, the data must matter? We want some reasonably shared benefits from economic growth, but no one really demands that they be exactly equal, right?

So, consider your own biases. Don’t engage in motivated reasoning. And think through how your views might change if you are wrong about the data. Perhaps someday Mother Nature will reveal herself, we’ll have the true inequality data, and we’ll see if we were honest about our reflections.

Economic Research on Gender, Race & Ethnicity, and Inequality

How much research do economists devote to the topics of gender, race and ethnicity, and inequality? In a recently published article in Econ Journal Watch, Arnold Kling and I looked at articles published in the American Economic Review as well as the conference papers of the American Economic Association on this topics. We find that economists devote a large amount of space to the topics combined in recent years: over 10% of published articles and over 20% of conference papers. We also find that the share of research on this topics, as measured in these two AEA outlets, has been increasing over time (we go back to 1991, when the current JEL Code system was introduced).

Of the three areas we looked at, papers on gender saw the clearest increase, rising as both a share of published articles and conference papers. Published AER articles addressing inequality have also been increasing over this time period, though AEA conference papers on inequality have been stable. Both published articles and conference papers on race and ethnicity have been stable over the period we studied as a share of the total, though the absolute number has increased.

What is the significance of our results? Our main motivation was to challenge other economists who suggest, in various ways, that economists ignore these topics or don’t study them enough (for examples see these popular writings on gender, race and ethnicity, and inequality). Our research clearly shows that economists devote a good deal of attention to these topics, and for many areas it has shown a clear increase.

It is still possible that economists don’t dedicate enough time to these topics. We make no strong claim in the paper about what the correct amount of time for each topic would be. However, we do note the opportunity cost that comes with an increasing focus on these topics.

More importantly, those who suggest in public venues that economists ignore these areas are doing a disservice to all the scholars that have devoted their careers to studying these important topics and publishing their results in one of the top journals in the discipline. We have much more to learn about gender, race and ethnicity, and inequality, but dismissing the research that has already been done is unfair to a discipline that has increasingly focused on these areas.

OK, Millennial?

How do young people fare when it comes to household wealth? The recently released Survey of Consumer Finances from the Federal Reserve provides some insights. One major takeaway: the much-maligned Millennials are doing pretty good! Ernie Tedeschi created this informative chart on Twitter:

Looking at household net worth at roughly the same age, Millennials today have roughly the same household wealth as Boomers did in the past. And both of these generations beat the generation between them, Gen X, as well as the “microgeneration” creatively labeled Oregon Trail.

And it’s something of a running joke on Twitter, but I must add: Yes! It’s adjusted for inflation!

Part of this may be driven by the increase in dual-income households. Certainly that matters. While wealth data by number of earners is harder to track down, income data is more readily available. What if we look at single-income households? Millennials are still in the lead! (Once again, the chart comes from Ernie Tedeschi.)

And before you ask: Yes! It’s adjusted for inflation!

None of this means that Millennials don’t face challenges, including financial ones. This data is current through 2019, so 2020 will almost certainly make these numbers look worse, for a time. But all things considered and anecdotes aside, the kids today seem to be as well or better than past generations.

(Oh, and before you ask: Yes! It’s adjusted for housing, medical, and education costs! In fact, these three factors make up half or more of most inflation adjustment indices.)