The point of vanishing convenience

I don’t think climate change is a big deal. I don’t think it makes the top ten list of global problems, and I don’t think that we should do much to stop it. In fact, I think that we need to burn more fossil fuels than we do right now as it is the surest way to lift an energy-starved planet out of poverty. I know people say they disagree with me. Some even say we face a climate catastrophe that threatens us all with extinction. But when I look at how these climate change hand-wringers live, they act as though they are in complete agreement with me. Even more oddly, when you look at how I live, you’d swear I was the one who was the climate change hero trying to save the world. I guarantee that my carbon footprint is minuscule compared to just about everyone else in Canada. I don’t care how people live, and I certainly don’t care how others think I should live, but if you believe that the world faces a coming climate change induced extinction and you don’t even try to live like me, then you are worse than a hypocrite. Your convictions run only as deep as the point of your vanishing convenience.

The CBC recently ran a First Person piece by Heather Kitching. Heather says that the world faces a climate calamity, but finds it too difficult to cut carbon from her life given that she lives in Thunder Bay. Her main complaint is that EV car sharing isn’t available and that heating her home without natural gas is just too expensive. I am sure Heather thinks she cares about the world. She clearly wants to tell us about how much she cares and she wants us all to know how hard she’s working to do the right thing. A public confession of sorts, I suppose. But she hasn’t thought carefully about what she claims to believe. Consider this thought experiment:

Imagine it is WWII all over again. And imagine that you can save one Jew from the Holocaust. You have no ability to stop the Nazis or their evil machine, but you have the opportunity to save one human being. Now imagine that to save that person you have to move into a major Canadian city, rent a nice apartment (or buy a nice condo), give up car ownership, ride your bike all year long no matter the weather – hardly ever even taking public transit – and eat a mostly plant-based diet. If you live this way for the rest of your life, you will save one Jew from the Holocaust. Would you do it? If you claim that climate change is destroying the planet and there is nothing individuals can do about it, you’re wrong. You can live like me. At the very least you’ll be able to say, I couldn’t stop it, but I didn’t go along with it. And, you can say that in expectation my meagre contribution to the reduction of carbon in the atmosphere saved one statistical life somewhere on Earth over the next century. Maybe the great flood of 2087 in Bangladesh will be just a fraction of a millimetre lower because you spent a lifetime living a low carbon lifestyle. What’s more, is that as terrible and evil as the Nazis were, people like Heather claim climate change will be even worse – to their mind we face human extinction if we don’t do enough! Now, I don’t believe climate change is a threat at all so I don’t think that my lifestyle benefits anyone but me. But if you believe climate change is about to usher in an apocalypse and you go along with carbon burning because it’s convenient, that makes you a collaborator.

Me winter biking in Ottawa: A climate change hero or just a cheapskate?

What people like Heather from the CBC say is that they’ll help stop what they believe is the near certain death of humanity up to the point that it becomes too personally inconvenient. That’s her real confession. She could ride a bike all year long, even in the winter. I do so in Ottawa – and my bike isn’t even electric. She could section off living space in her home during the winter and heat her reduced living quarters with electric radiators. She doesn’t have to live in Thunder Bay if not contributing to climate change is that important to her. Now I don’t find Heather evil but I do find her dangerous. I believe she’s an honest soul who wants to be a good citizen. What makes people like her dangerous is that she doesn’t think. She falls prey to social desirability bias which leads to a world run by demagogues. Cost benefit analysis goes out the window in service of lofty ideals, opening the gates of hell for the demagogues to impose serious consequences including poverty and endless human suffering on the rest of us. (Peace, Land, and Bread anyone?) Heather shouldn’t feel bad about her carbon footprint. She should enjoy time with her girlfriend in her gas-powered car. Life is short enough as it is.

As for why I live in a box in the sky, with no car (I’ve never owned one), biking all year long, it’s not for climate change. It’s for time. By living this way I get time back for what’s important to me. I’m at work in 12 minutes, and on the tennis court with my wife in 15 minutes. And tennis is life to us. Everything I need is within a 25 minute bike ride and often within a 5 minute walk. And biking turns your legs into Sexy Flanders! My life isn’t for everyone. If you live on an acreage with a big pickup truck and ATVs, fill your boots – have fun! I’d love to have a beer with you. No one should have to live like me and certainly not for climate change.

Hallucinating with ChatGPT

Natural language generation has improved remarkably over the last decade and OpenAI’s ChatGPT showcases an unbelievable performance of state-of-the art systems. Like many curious people over the last month, I played with ChatGPT from time to time. It’s super impressive – it can create poems, write prose in nearly any style, and provide detailed answers to all sorts of questions. Oh, and it’s also an amazing bullshit artist and it will lie with abandon.

I decided to ask ChatGPT a specific question about particle physics that is a bit subtle but has a straightforward answer. ChatGPT’s response is stunning bullshit.

ChatGPT gets the first part right – the most common decay mode is to an electron, an electron antineutrino, and a muon neutrino. Now, the rest of the answer is completely wrong. First, the muon is kinematically forbidden from decaying into pions. The muon is simply not massive enough to do so. Second, even if the muon were massive enough to decay with three charged pions in the final state (like the tau lepton can), conservation of lepton number still requires neutrinos. Apparently ChatGPT has thrown lepton number overboard so that it can give me an answer!

The correct answer to my quetsion is: Theoretically yes, but hopelessly rare. No observation of muon decay without emitting neutrinos has ever been observed.

In the Standard Model (the theory of fundamental particle interactions) with massless neutrinos, muon decay must include neutrinos in the final state. The Standard Model with massless neutrinos conserves family lepton number and so neutrinos in the final state are required to conserve muon and electron number (a muon neutrino and an electron antineutrino). However, neutrino flavour oscillation observations tell us that neutrinos have very, very tiny masses. Extending the Standard Model to include neutrino masses allows for the muon to decay without neutrinos (for example to an electron and a photon) but at rates so extremely small that we have no hope of observing neutrinoless decays of the muon unless the Standard Model is further extended with exotic physics.

Ok, rather technical stuff. But where did ChatGPT come up with the idea of pions in the final state? Well, I asked it. And sure enough ChatGPT came up with references, including a paper in Nature from 1982 with claims of actually observing neutrinoless decays of the muon! Well, either I missed something during my PhD and postdocs (I have done a fair amount of work on supersymmetric extensions of the Standard Model with enhanced flavour violating decays of the muon) or ChatGPT is making stuff up. All of the references that ChaptGPT gave me are complete fabrications – they don’t exist!!

It turns out that natural language generation in systems like ChatGPT suffer from hallucinating unintended text. Its creative power, its ability to write poems etc., requires such an enormous amount of flexibility that ChatGPT seems to start making things up to complete an answer. I’m not an expert on natural language processing, but I know that researchers are aware of the phenomenon.

I happen to know something about particle physics so it’s not a big deal that ChatGPT fibbed to answer my question. In fairness, my question is a bit subtle (short answer is No with an if, long answer is Yes with a but). But imagine circumstances that are more important. How do you know if you can trust the answers? Asking it for reference doesn’t seem to help.

To me the lesson is that systems like ChatGPT are going to be ever more useful with the potential to make life much more convenient. But these systems are not a substitute for human cognition. For the teachers out there – don’t worry about ChatGPT writing your students’ essays, just check to see if the references exist!

Update (February 23, 2023)

I returned to ChatGPT last night, getting into a discussion with it about the top quark. ChatGPT continued to give insane answers about QCD, electroweak physics, and the nature of the Higgs sector. I thought I could get it on track if it would just realize that the muon’s mass is less than the pions. It produced this gem:

ChatGPT fails the Piaget test.

The Piaget test.

A chasing after the wind

As COP27 gets underway in Egypt, I am reminded of the remarks made by world leaders and politicians about what is allegedly at stake:

We are sleepwalking to climate catastrophe. In our globally connected world, no country and no corporation, can insulate itself from these levels of chaos.”  – Antonio Guterres, UN Secretary General

There’s one issue that will define the contours of this century more dramatically than any other, and that is the urgent threat of a changing climate.” – Barack Obama, former US President

My “Oh Shit” moment came early in my days as Environment Minister. We need to be absolutely clear-eyed about the accelerating climate crisis while using fear, anger & hope to activate us to do everything needed to ensure a safe climate.” – Catherine McKenna, former Environment Minister of Canada

These kinds of statements by world leaders, high level bureaucrats, activists, and former politicians abound in the media. The central message is that we must move heaven and earth within the current decade and beyond to avoid an absolute climate catastrophe. While these people might believe their rhetoric, the implications and logical conclusions of their statements are terrifying – they implicitly suggest a willingness, if not a desire, to torch liberal democracy while offering our youth nothing but a culture of nihilistic despair.

It is clear that climate change is not a massive world problem. The best economic estimates on climate change loss place the global GDP drag at about 0.15% per annum for the next 80 years if the world warms to the upper end of the IPCC forecast range. That is, if the world warms 5C by 2100, the world GDP will be about 10% to maybe 20% smaller than it otherwise would have been without climate change. As a comparison point, it means that climate change delays our well-being by about 10 to 20 years by the end of the century. It’s a bit like re-living the 20th century with a growth drag that puts the year 2000 at the level of the mid 1980s. Not great, but not quite the end of the world either. I explore the climate change story further in a previous post.

But let us suppose that you are unconvinced by the economic arguments and that you believe people like Catherine McKenna. Perhaps like her, you have had an “oh shit” moment too. In that case, you believe that climate change will make the world nearly unlivable if we don’t make significant changes to our economies right now. The problem now pivots: liberal democracies are slow and incremental with a focus on splintering political power, respecting individual autonomy, and building legitimacy through consensus. Parliaments, congresses, and executive branches face built-in constraints from divisions of power and the rule of law. Through centuries of experience and experimentation, our liberal democracies have given rise to the most successful and prosperous societies the world has ever known. But what if our democracies are too slow to satisfy climate change activists? Even worse, what if our democracies elect, at least from time to time, governments with a tepid view toward climate change mitigation? Seriously, between now an 2050 – the year we must, for some reason, hit net-zero emissions – what is the chance that Western countries will elect and re-elect governments that put climate change well down their priority lists? It’s certainly not zero. And if it is likely, what is the chance that liberal democracy over the coming decades can deliver on saving us from the climate catastrophe that activists tell us awaits?

Therein lies the rub. If activists can’t convince liberal democracies to move quickly on climate change by gluing themselves to famous works of art, setting fires at tennis matches, or making apocalyptic pronouncements at climate change conferences, the next logical move is an attack on liberal democracy itself. The unintended consequence of Catherine McKenna’s rhetoric, and people like her, is a deep disdain for democracy. If the electorate chooses wrong too often, changing the message from fear, anger, and hope to only fear and anger, what should we activate? In that eventuality, only benign authoritarianism can deliver us from the coming climate catastrophe. It’s not Donald Trump or “ultra-MAGA Republicans” I worry about, it’s the climate change catastrophe people who truly frighten me. The penny will eventually drop for them if they come to believe that our democracies can never bring the rapid change they think is necessary to save us from destruction. After all, what good is liberal democracy in a used up world?

In addition to sowing the seeds of authoritarianism, the climate change movement offers nothing but nihilistic despair to our youth. Again, let us suppose you believe the climate change message and that you know it is probable, if not likely, that we won’t do enough to combat climate change. The rational response to that belief is to hedge your life choices. What is the point in making long term investments in yourself with payoffs in a far off future that has a significant chance of never materializing? Why sacrifice the present and why bring another life into a world that has a large chance of being destroyed by inaction? Even if you think that our democracies will eventually choose well, you still must assign some non-zero probability that they won’t, and that non-zero probability should rationally inform your life choices today. It’s a bleak pessimistic worldview, and it’s wrong.

The climate change message terrifies me, not because of the climate change stories that will be told at COP27 over the next two weeks, but because it sets the stage for authoritarianism with all the confidence of religious zeal while simultaneously offering a philosophy of nihilistic despair to our youth. The desire to centralize power is as old as humanity itself; our liberal democracies help us resist that temptation. Let us hope that our democracy will endure the climate change activist tide.

Goodbye horses

The famous economist Thomas Sowell once wrote, “No race has a monopoly on high achievement and no race is incapable of producing high achieving individuals.” If we look across the arc of history, from the Chinese dynasties to the Indigenous peoples of North America, this truth is so plainly evident that it’s difficult to understand how eugenics programs ever gained traction. And yet today I read a CBC story, Ojibwe horses are endangered, that undermines the legacy of Indigenous ingenuity by building a narrative of mysticism while rejecting both science and history.

Prehistoric horses: Chauvet Cave paintings

The overwhelming consensus in the scientific community is that there were no horses in the Americas when Europeans made first contact. The vast majority of reputable sources on the evolution, domestication, and the history of the horse state that while horses existed in North America tens of thousand of years ago, they went extinct well before European contact and were only reintroduced after the arrival of Columbus. Genetic research shows that all horses in the Americas descend from Eurasian stock. Yet the CBC reports that the Ojibwe horse “lived around the Great Lakes long before European contact”.

Without question the Ojibwe horse, also called the Lac La Croix Indigenous Pony, is a national treasure fully deserving of protection. The breed nearly disappeared in 1977 and the Herculean preservation efforts since have given the breed a chance. The most remarkable fact is that the Ojibwe horse is a breed of pony matured by Indigenous people in Canada. Indigenous people used them in the bush along trap lines in Northwestern Ontario. As a breed, they are perfect for such conditions. Genetic testing shows that the Ojibwe horse originates from European introduction. Professor Gus Cothran, an expert on the genetics of horses says in Equine Monthly, “They are derived from horses that Europeans brought to North America. They did not originate in North America as a distinct strain of horse.” Research shows that the Ojibwe horse is a cross between the Spanish mustang and Canadian horses originally from France, but it was Indigenous people who created the breed.

Instead of doing research on the Ojibwe horse, the CBC simply states myths as facts. My guess is the CBC is trying to be sensitive to some Indigenous groups who insist horses in North America predate European arrival. (There are other groups in North America that insist on pre-contact horses, including some Mormons who wish to reconcile passages in their religious texts. I suspect that the CBC would be less generous entertaining Mormon narratives). By promoting mythical or religious beliefs to fact, the CBC not only undermines Indigenous ingenuity, but science itself. How does the CBC retain any credibility when confronting the anti-science crowd on climate change or vaccines when the CBC shows a willingness to behave exactly the same way with Indigenous issues? I find the CBC’s story on the Ojibwe horse disheartening – almost racist – because it robs us of the real story worth celebrating: Ingenious Indigenous people created a new breed of pony from European stock to fulfill their needs. It’s fine to discuss Indigenous beliefs, to create a greater understanding about rich Indigenous story telling, but it’s a form of neo-Lysenkoism to dismiss genetics to serve a political purpose.

Jared Diamond in his book Guns, Germs, and Steel, answers the question why the Europeans didn’t encounter a mirror copy of Europe in the Americas. The racist and terribly incorrect answer that has shaped so much of the awful history of this continent is based on racial superiority. But Diamond points out that the confluence of poor geography, and the general lack of domesticable plants and animals, such as the horse, meant that the flow of people from Europe to the Americas was always destined to go in that direction. The genetic potential of both peoples were the same, it was their unfair respective environments that set the course of history. The story of the Objibwe horse shows that if Indigenous people did have horses pre-contact, they would have created a plethora of breeds for every single need. And if that had happened, Columbus and Champlain would have faced Indigenous armies more powerful than the Huns – and perhaps during Indigenous first contact in Europe.

Thomas Sowell is right: No race has a monopoly on high achievement and no race is incapable of producing high achieving individuals.

A tale of signalling: post-secondary education and COVID-19 policies

A university education is not what it seems. The usual story, the one that makes us feel all warm and fuzzy, tells us that a university education – regardless of discipline – builds critical thinking skills, engenders a worldly view, and creates an informed citizen. We are empty vessels into which the fount of knowledge pours forth, filling us with enlightenment. Students graduate with skills that command a higher wage as they contribute more to society. But there is an alternative story that equally explains the facts. A university education is a signalling mechanism that does not pour knowledge into empty vessels, but instead sorts like jeweler’s loupe. Think about it. Most people can’t remember much of what they studied at university. In this story, a university education is a giant IQ test, coupled to a test of perseverance and conscientiousness. Students graduate with a signal that says they’re generally smarter than average and can put up with a lot of tediousness for years, and that’s exactly what an employer needs. Students who graduate had all the requisite attributes the day they entered university and the purpose of the degree program is to show the world they in fact have them. Who cares if you can’t remember the details of your liberal arts degree? Your employer certainly won’t. But your employer will care that they’re getting what they paid for – someone who can get a university degree. In truth, the human improvement and the signalling story are simultaneously true and the relative weight of each varies across degree programs. Bryan Caplan, an economist at George Mason University, has an excellent book on the subject, The Case Against Education: Why The Education System is a Waste of Time and Money.

CTV News London has an interesting story, A tale of two institutions: Western and Fanshawe deviate on return-to-school COVID-19 policies, that nicely illustrations the nature of signalling. Western University has opted to make COVID-19 boosters mandatory for all staff and students as well as to demand in-door masking at least until Thanksgiving. On the other hand, Fanshawe College will not implement masking or a vaccine policy this fall citing the Middlesex-London Health Unit. These two post-secondary institutions are in the same city (London, Ontario) with students of the same age. So why the difference? How is “the science” different at Western than at Fanshawe? Of course there’s no difference in the science, but the institutions fill subtly different roles in society. As a university, Western has a much larger signalling component in its diplomas than Fanshawe’s, an institution that operates more as a technical trade school. Students at each institution seek different products with different sensitivities to signalling, often coming from differing socio-economic circumstances.

Increasingly, adherence to high risk averse COVID-19 polices match political affiliation. Wearing a mask while riding a bike with no helmet – and I see this behaviour nearly every day in downtown Ottawa! – is a signal of political beliefs. We shouldn’t be surprised to see those institutions which trade in a signalling market, composed mostly of people from the urban upper middle class, will on average demand stricter COVID-19 policies two and a half years after the start of the pandemic.

Disclaimer: I attended Western for my undergraduate and I had an amazing time. It’s a great school and I learned amazing things from phenomenal minds. But I’m a bit weird. To me, going to class is a form of recreation, even a form of entertainment; it’s an end in itself.

Climate change mitigation: a solution in search of a problem

The new IPCC report is out this week and the Secretary of the United Nations has issued stern warnings and rebukes. The report’s co-chair James Skea of Imperial College London cautions that “If we continue acting as we are now, we’re not even going to limit warming to 2 degrees, never mind 1.5 degrees.” The authors of the new report argue that we need to halt all fossil fuel developments, and radically change our lifestyles including our diets to save the planet.

I accept the science. More precisely, I embrace the range of possibilities that the IPCC publishes based on the amount of global CO2 emissions and the likely effect on the atmosphere. But embracing atmospheric science is only a small part of the issue. What all the reports and commentary leave out are realistic cost-benefit analyses and the likely economic outcomes even in the upper range of warming forecasts. Of course the media does a poor job of highlighting the likely outcomes or placing them in proper context. Once we think about the outcomes it becomes clear that climate change is a solution in search of a problem.

Global GDP growth: the surest way to smash global poverty.

So, how can I believe the science but not the climate change mitigation story? First we need to be precise in our questions and goals. Clarity matters. Stripping away all the romance, the real question is:

If we want to spend tens of trillions of dollars today to make the world a better place in 2100, what is the most efficient way to proceed?

An answer to this question centers on three lines of reasoning:

1) Lifting worldwide GDP growth.
2) Avoiding a rare but potentially catastrophic possibility.
3) Protecting the planet’s biodiversity.

Implicit in the climate change narrative is the statement that climate change mitigation tops the list for addressing all three points. Let’s address each.

Lifting worldwide GDP

To begin we need a measure and a sense of scale. When comparing economic well-being, economists use GDP – the value created through production of goods and services. Of course GDP is an imperfect measure, but GDP and GDP growth correlate strongly with all the aspects of life that we consider important. We do not see a rush of immigration from countries or regions with high GDP to lower ones; it’s always the other way around. Since 1950, the planet’s GDP has grown by over a factor of 12. As a percentage of the population, fewer people live in abject poverty, lifespans are longer, health care is more readily available, infant and maternal mortality has plummeted. We are better connected, better educated, more fulfilled, more peaceful, and we are more productive than ever before. In short, the world has gotten an awful lot better for so much of the world’s population. Economic growth has been the key feature for shattering poverty. Nothing else comes close. Unfortunately we have a long way to go. There are many parts of the world where GDP growth has been tepid to say the least. On growth considerations, the germane question is:

If we want to spend tens of trillions of dollars today to increase the world’s GDP to the greatest extent possible by 2100, what is the most efficient way to proceed?

Not all countries have seen the same growth prospects and some countries switched paths over time. A great example of a path change occurred with China in the late 1970s. As China opened up and started to move to a more market based economic orientation, GDP per capita exploded. From 1990 to today, China’s GDP per capita has grown by more than 1,000%. When we think about poor countries and the lessons around economic growth, it’s hard to think about anything else! With China, we have a direct example from the last 30 years which shows what is possible by adopting at least some level of a market based economy. Going back to the end of WWII we have examples at least as impressive as modern day China such as South Korea, Japan, Singapore, and Hong Kong. If Africa took a similar trajectory to any of these examples, 1,000+% GDP per capita growth over the next 30 years is not only completely within the realm of possibility but could even be the most likely outcome. Think of a world in which another 2 billion people experience such economic growth.

Now let’s compare 1,000% GDP growth over 30 years to anything that climate change has in store. The best economic estimates suggest that at 6C of warming by the end of the century – the very upper end of the climate models – the world economy will be about 10% smaller than it otherwise would have been without climate change in 2100. Even if the estimate is wrong by a factor of 2, and the actual effect is 20%, the effect size of climate change is about 0.25% of GDP loss per annum! Climate change is peanuts compared to the variation in growth we see between countries which organize around markets and those which do not. So if we want to spend tens of trillions of dollars today with the goal of making the world a better place in 2100, would it not make more sense to use those resources to persuade as much of the world as possible to follow the success path of well known examples? It’s hard to believe that chasing 0.25% per annum growth level effects come out at the top of the list. Such small effects in our own GDP growth sit at the level of the inefficiencies in the Canadian tax code.

Avoiding Catastrophe

It’s pretty clear that if the path to a better world in 2100 is GDP growth, climate change is one of the last places to start – 0.25% per annum growth effects just don’t make the leap for us. But there are other concerns. Suppose that climate change triggers some presently poorly understood tipping point which catastrophically ruins the environment and makes the miracles of economic growth impossible. In that case, spending tens of trillions of dollars today on climate change mitigation might make a lot of sense. But now the question changes:

If we want to spend tens of trillions of dollars today to make the world safer by avoiding a potential yet poorly understood catastrophe by 2100, what is the most efficient way to proceed?

In other words, we seek to spend a lot of money today in a precautionary sense – buying insurance – so we can have a future with economic growth. To answer this question, we need to think about how climate change compares to other potential catastrophes. We are just coming out of a pandemic that in 2020 shrunk the world economy by an effect greater than 10 years worth of expected climate change damage. Now, imagine a pandemic much worse than Covid, or even much worse than the flu of 1919. A severe global pandemic could erase decades of economic growth almost overnight. But it’s not just pandemics. There are only seven principal cereal crops in the world of which just two, wheat and corn, make up over 60% of global production. Suppose that a serious blight or virus destroys much of the world’s grain output, something like the Irish potato famine but on a global scale. Global debt runs could ruin our economies and throw us into a worldwide great depression that lasts decades. And of course nuclear war always hangs over us like the Sword of Damocles, not to mention a comet or asteroid impact, a major volcanic eruption, the collapse of the Earth’s magnetic field…you get the point. There are many, many, low probable highly catastrophic possibilities to worry about all of which could in part be mitigated right now by tens of trillions of dollars worth of spending today. Where do we start? We can’t insure against all possibilities. To make the case that climate change is special, we have to show that somehow, of all the unlikely but horrible possibilities that exist, climate change makes the top of the list on a cost-benefit insurance basis. It’s hard to make that argument, but I have some limited sympathy for it. But to put catastrophic events in perspective, for at least the last decade governments have told banks and corporations to plan carefully around climate change exposure. Now imagine if a decade ago governments instead suggested that financial institutions and businesses put a potential pandemic at the top of their mitigation priorities. Perhaps Covid would have been handled much better. Stuff that really threatens us are events like Covid on steroids; real catastrophes come out of the blue, not something that gives a century of notice with gradual change.

Protecting biodiversity

Climate change mitigation seems like a weird place to start if we want greater economic growth or mitigation against rare but potentially catastrophic outcomes. But climate change might be special when it comes to biodiversity. Perhaps climate change will be so awful for the planet’s plants and animals that, while GDP will hum along, we will irreparably harm the biodiversity of the planet and eventually poison long term growth prospects. Again we need to think in terms of cost-benefit. The question now becomes:

If we want to spend tens of trillions of dollars today to ensure the biodiversity of the planet through 2100, what is the most efficient way to proceed?

The biggest problems around biodiversity are habitat loss and destruction by direct human intervention. The large mammals of Africa and Asia have nearly been hunted to extinction. Ocean life suffers from over-fishing. Direct human effects on the environment have so far proved far more destructive than the indirect effects caused by climate change. Even if we manage to get all of the Western world on electric cars by 2050, rhinoceroses and elephants will hover near extinction, if not already extinct by then, and another 30 years of over-fishing risks colossal implications for sea life regardless of a slightly cooler climate. I doubt our green infrastructure renewal will save even one giraffe or increase the length of single tuna fish. It’s not clear that climate change is the place to start if we want to protect the environment and biodiversity. Perhaps sectioning off large parts of the Earth as no-go zones for humans might lead to better outcomes. Returning to economic growth, it’s countries with high GDPs per capita that treat their environments the best. Thus a virtuous cycle of higher economic growth with increasingly cleaner environments may end up being the best way to protect the natural world. In that case, the pathway to rapid GDP growth could be the saviour of biodiversity.

Squaring the climate change agenda

Somehow the public has become captivated by an arbitrary, almost magical, threshold of 1.5C of warming with an implicit belief that the world will end at the 2C mark within a hundred years or less. Climate models make no such predictions. Worse, when experts do offer preliminary cost-benefit analyses, they often leave out the effects of human adaptation. Rising sea levels do not mean 187 million people will be displaced over the next century. Urbanization saw billions migrate to cities over the last 100 years. Patterns of human habitation will continue to change over the coming century. Humans live in extreme climates and elevations already, from the Sahara desert to nearly the north pole, from the Tibetan and Andes plateau to The Netherlands and the Mekong Delta. We have lived across this enormous variation for millennia. There is no model of climate change, even with 6C of warming by 2100, that has a level effect larger than the variation that already exists.

The more I think about it, the more I see climate change as a solution in search of a problem. Every time we rephrase the question to precisely address what we hope to achieve in the far off future, climate change does not seem to offer the leading solution. It’s hard to imagine how climate change tops the list for increasing economic growth, protecting us from a potential catastrophe, or sustaining biodiversity. Yes, climate change contributes in some way to all three of these lines, but it’s not leading order. It’s true that climate change is a classic example of an externality in which an unregulated market is unlikely to generate the optimal amount of global warming given the benefits from carbon intensive production that humanity receives. Spending something to mitigate climate change makes sense, but it’s not an all-hands-on-deck-or-it’s-the-end-of-the-world kind of problem and it certainly does not warrant anything close to the attention it receives. And if ultimately the political will is insufficient to address climate change in any substantive way, it’s not a big issue – we’ve learned to live with all kinds of externalities that are just too costly to address. We know how to adapt.

So if climate change represents a rather small or moderate externality, why does it attract so much attention? I am sure there are true believers who claim to “believe the science” and yet focus all their concern on highly improbable catastrophic climate change events as though those outcomes are the most likely to occur. But for others, I think climate change offers a seductive channel for capturing government power. Under the climate change lens, CO2 emissions are a form of pollution, creating an externality for government action to solve. But we have to remember that heavy direct government regulation of pollution is the backdoor to the government marshaling production. After all, pollution is a byproduct of production; you can’t touch one without touching the other. That’s why in industrial settings, economists argue for narrowly targeted pollution mitigation, often emphasizing indirect government involvement that relies on some form of market or price mechanism, tied to carefully delineated property rights and the rule of law. A government that shepherds a sea change of the entire economy through direct action and direct government participation – whether justified or not – ends up in the driver’s seat of the economy, deciding on what gets produced and who produces what. Regardless of intent, as President Eisenhower recognized over 60 years ago, that centralization of power is a danger to democracy and liberty. We face enormous institutional and political risks from the clarion call to centralize power to save the planet from what all reasonable estimates tell us is a rather small problem. But maybe that’s the point…

A pound of flesh nearest the heart

As we enter what are likely the end stages of the Covid-19 pandemic with the virus transitioning to an endemic state, our society has become angry and self-righteous, egged on by our political and chattering class. Pandemics at some point in their trajectory often find someone to blame. During the Black Death, the Jews made for an easy scapegoat, and in more modern times homosexuals served as the perfect minority to hate and blame during the beginning of AIDS pandemic. The pattern is always the same – find a group that nobody likes, claim that they are the party most responsible for the on-going disease, and then pour all of our hate and derision on them. Use political power to punish them and satiate the mob’s need for retribution. Today, with Covid-19, society’s scapegoat is the unvaccinated. Yes, people should get the vaccine; yes, they are safe and effective at preventing serious complications, especially for high risk populations, but a near religious fervor has gripped Canada in blaming the unvaccinated for our current woes with a near insatiable appetite to punish.

American political cartoon by Thomas Nast titled “The Usual Irish Way of Doing Things”, published in Harper’s Weekly, 2 September 1871. Anti-Irish sentiment ran deep in corners of North America during the late 19th century, fed and maintained by the chattering class. The ugliness of the mob.

The story sells itself. Unvaccinated people are much more likely to experience severe illness, hospitalization, or death, especially if they have comorbidities. Currently in Ontario about half of the Covid-19 ICU patients and one quarter of all Covid-19 hospital patients are unvaccinated even though they only represent about 10% of vaccine eligible citizens. Clearly the unvaccinated are highly disproportionate in their need for health care services should they contract Covid-19. Yet the unvaccinated are in fact scapegoats for much larger problems.

The vaccines are not particularly effective in controlling the spread of Covid-19. With the rise of the Omicron variant, Covid-19 is so transmissible that the argument for externalities completely falls apart. The Covid-19 vaccines almost exclusively provide their protection to the person receiving the vaccine, conferring negligible spillover effects in the form of transmission interruption in the wider community. Thus, the refusal to take the vaccine, however misguided, only hurts the unvaccinated person. Most professionals recognize the ineffectiveness of the vaccines to control transmission. Hence, even with 90% of eligible Ontarians vaccinated, we see tens of thousands of new cases per day leading to explosive exponential growth in the vaccinated population. However, politicians and the chattering class argue that the unvaccinated play a special role because they disproportionately place demand on the health care system.

To get a sense of our problems, we can look to our health professionals on the ground. An emergency room physician, Dr. Brett Belchetz, told Global News “We are looking at hospitals that are struggling to keep up and now you add in all of those extra patients…we are in a dangerous situation here. You see patients being treated in the hallway with regularity and often that is just a choice we have to make — provide no care or provide hallway care.” An anonymous nurse added, “the volume of patients is insane. We are so overcapacity.” Dr. Belchetz continued, “It doesn’t take a mathematical genius or an expert in health care to understand that having more people in the province, especially people that are older, that are sicker, with fewer hospital beds, is a recipe for hospitals to operate overcapacity. And not just overcapacity — dangerously overcapacity.” It gets worse, Michael Garron Hospital, formerly Toronto East General Hospital, has postponed seven cancer surgeries as a result of a shortage of beds in the ICU since December. Carmine Stumpo, vice-president of programs at Michael Garron Hospital, says it’s been a juggling act for surgeons, “So we work with our hospitals to ensure that sort of situation hopefully is completely avoided, but if it’s necessary it’s minimized.” Serious issues for sure but these are not stories from this winter or even last winter; they are from the flu season of 2017-18! Ontario hospitals have been in an overcapacity crisis long before Covid-19.

If all the unvaccinated had been vaccinated, Covid-19 would still be over-running Ontario’s health care capacity. Data on the comorbidity status of the unvaccinated is not readily available, but at least some of them would have still ended up in the hospital and the ICU vaccinated or not. Eliminating a quarter of the Covid-19 hospital cases in Ontario still leaves us terribly strained. Canada has one of the worst health care capacities in the developed world and vaccinating the last 10% of our population is not nearly enough to hold the ground against the Omicron wave. The unvaccinated are not the cause of hospital overcapacity but they allow our governments to distract us from their failure to build a robust health care system, and their additional failure to build adequate Covid-19 specific health care treatment capacity. Even though we have been trudging along with a broken health care system for decades, which Covid-19 has exposed for all to see, our political class can now just blame the Covid-19 unvaccinated. It’s an easy way out.

Blaming the unvaccinated is bad enough, but the Ontario government’s lockdown policies create a super regressive health care tax. The argument for lockdowns is that, at this point, they are the only way to protect our health care system. I doubt that the lockdown approach is correct, but even if it is, the people who pay for that protection are the working class who can’t find timely daycare for their children and who find themselves locked out of work. They pay the “health care tax” in-kind today, protecting the health care system, to make up for what wasn’t paid earlier. And all the while the laptop class enjoys full salary and the opportunity to work in their pajamas. We’re all in this together….yeah right we are.

How did we get here? Canada has large structural issues that are undermining our democracy and harming our institutions. These problems go well beyond Left vs Right or any political stripe. Our country has not properly addressed its regional composition either in the BNA of 1867 or the Constitution Act, 1982. Instead of a properly constituted federation in which representation by population is tempered by strong regional power, we have quasi-federalism or some kind of hyphenated federalism (executive-federalism, collaborative-federalism, shared-cost-federalism, fiscal-federalism, etc.) and in that regard governments responsible for delivering programs become increasingly divorced from the government that raises the revenue. By constitutional necessity, Canada leans on Ottawa’s spending power to address regional needs which has had the perverse effect of turning health care funding into a circus of side deals between the provinces and the federal government, not to mention the complexities of indigenous health care delivery. The locus of decision-making shifts like sand dunes across the political landscape, making it difficult for the public — and at times even Parliament itself — to hold the appropriate government and decision-making body to account. We have deep structural institutional and democratic problems in Canada which Covid-19 has laid bare through our health care systems. Blaming the unvaccinated for our difficulties in the current Covid-19 Omicron wave distracts us from the important work that lies ahead of us not only for our health care systems but for the health of Confederation itself.

Our experiment in national cruelty

As we approach the nearly two year mark since the start of the Covid-19 pandemic, I am shocked by my fellow citizen’s zeal in pouring cruelty, contempt, and derision on others. Perhaps I shouldn’t be shocked. Cruelty after all is the merging of joy and anger and its expression gives a deep sense of satisfaction to so many, especially when there is political hay to make.

Saturn Devouring His Son by Francisco Goya

The Covid vaccines are amazing. People should get them. The evidence shows overwhelmingly that they prevent serious illness and death, especially among the vulnerable. What the evidence also shows is that the vaccines are not particularly effective at preventing transmission. After a relatively short period of time, measured in months after full vaccination, waning immunity allows for substantial transmission even though the vaccines remain highly effective at preventing serious illness. In short, the vaccines work amazingly well on the most important dimension.

The logic behind vaccine mandates rests on the idea of spillover effects. For vaccines that interrupt transmission, known as sterilizing, your vaccinated neighbours confer protection on you. Vaccines with a sterilizing property create what economists call an externality – the problem that gains based on private decision making alone do not capture the full benefit to society. In such circumstances there is a compelling argument for some level of state coercion to force people to adjust their behaviour. It’s ugly but sometimes necessary. For me to be on board, I have to see that violence or the threat of violence is absolutely necessary to achieve actual consequences which pass a cost benefit test with flying colours. Solzhenitsyn warned us that unlimited power in the hands of limited people always leads to cruelty.

Across Canada people who choose not to get vaccinated stand in front of the pointy end of the state’s monopoly on violence. Some are losing their livelihoods, and all are restricted from full participation in society. Perhaps that level of violence could easily be justified if the vaccines were sufficiently sterilizing, but we know they are not. The vast majority of the benefit from receiving the vaccine accrues to the person who receives it. It’s hard to make the case for coercion in these circumstances.

Whatever one might think of the vaccine hesitant or resistant, these people have the courage of their convictions. I think they are mistaken, but they are clearly not cowards, they are not hypocrites or virtue signallers. Is there any principle in your own life that you believe in so strongly that you would be willing to sacrifice your livelihood, your career, and your social standing? If I’m honest with myself, I don’t know if I’m that brave. Few are.

Even if you come down on the side of vaccine mandates, that despite the small and diminishing spillover effect that the vaccines confer, you still believe that coercion is worth it, we should all show more compassion and understanding with the vaccine hesitant and resistant. We should use our monopoly on violence with great reluctance, with great sadness, and with as much empathy as we can give. I don’t see compassion in my fellow citizen or in the approach used by our politicians and leaders. I see contempt and cruelty applied with alacrity to those who won’t get vaccinated. It makes me sad to see how ugly we are. I guess Solzhenitsyn was right, evil really does pass through every human heart.

Update: January 1, 2022

Contempt and cruelty applied with alacrity.

COVID-19 spring redux: more cowbell

Although we’re more than a year into the COVID-19 pandemic, our ability to protect vulnerable people hasn’t improved much. On a medical front, we’ve advanced with better triage, better treatments, and now a vaccination program – but our public policy looks pretty much the same as it did last spring, expect in Ontario, this time with enhanced police powers.

Ontario is seeing a tidal wave of new infections. While new variants apparently increase risk among younger demographics, the 60+ age group and those with comorbidities experience the majority of the severe illnesses and deaths. Earlier this month, Dr. Micheal Warner pointed out that a person under 50 dies from COVID-19 in Ontario ICUs every 2.8 days. That rate among the young is higher than in the past, but with a current Ontario COVID-19 death rate of about 20 per day, that means about 60 old people are dying for every person under 50, who almost certainly has comorbidities. It’s pretty clear that COVID-19 and its variants are vastly riskier for the elderly and those with comorbidities. Unfortunately, our vaccination program has a long way to go to protect the vulnerable.

Since this pandemic began, our governments at all levels have focused on lockdowns, school closures, travel restrictions, and curfews as the primary mechanism to control COVID-19 community spread. For the last year these policies have shifted most of the suffering onto the poorest people in our society – our essential workers – who are employed in everything from meat-packing plants to supermarkets. Even the homeless haven’t escaped. In January, Ottawa homeless shelters paused intake due to an outbreak among residents and staff. Not only have the poorest faced the brunt of COVID-19, but the vaccination programs have had the greatest penetration with the well-off. For all the rhetoric and all the treasure we’ve spent, we have not protected the vulnerable.

Is this the best we can do?

Last spring, our governments implemented emergency measures in a state of overwhelming panic. This time around, we appear to be recycling the same emergency policy playbook, and in the process, discarding a year’s worth of hard won knowledge about COVID-19. Public Health Ontario has publicly stated that focused measures to protect the vulnerable are not possible:

While age may be the major driver of differential mortality risk, there are important equity-based considerations in understanding risk of dying from COVID-19 in non-elderly populations if public health measures were to focus on the risk to the elderly only….Public health agencies globally have supported the use of physical distancing measures and lockdowns to control community transmission of COVID-19, recognizing that high community transmission renders protection or shielding of higher-risk populations virtually impossible due to the connections within the broader community in which they live. Further, an approach to strict isolation of at-risk populations can also be considered inhumane and unethical.

I am not sure how Public Health Ontario comes to the conclusion that shielding higher-risk populations is virtually impossible, but it certainly points to a lack of creativity and no sense of resolve. The situation reminds me of the Berlin Airlift.

In 1948, as the Cold War was getting started, the Soviet Union prevented all surface traffic from non-Soviet zones from entering West Berlin. Stalin hoped to drive the Western allies out of Berlin, undermine the Marshall Plan for rebuilding the German economy, and place the Soviet Union as the dominant power in Europe. At the time of the blockade, West Berlin had about a month’s worth of food and fuel. The Soviets figured it was impossible to keep West Berlin supplied and the West would quickly capitulate. We didn’t. We organized an airlift that kept West Berlin provisioned for 15 months. In the end it was the Soviet Union that relented. At its peak, the airlift had a plane landing in Berlin every 30 seconds, planes filled with everything the city needed from coal to potatoes. Our response to COVID-19 looks nothing like this.

Constructing an optimal policy should use all available information. We know who the most vulnerable are: the elderly and those with comorbidities such as obesity, hypertension, and diabetes. We must use all we know about COVID-19, pandemics, and public health more generally. Two points stand out:

1) We now know that, for those over age 70, the survival rate from COVID-19 is approximately 95%. That is a terrible problem. For the vast majority of us who are at little risk, the survival rate is at least 99.95% and most likely higher. Comorbidities also increase risk. Healthy people under age 25 have a survival rate of effectively 100%. That is, the high risk group is thousands of times more likely to suffer a severe outcome. Given the extreme differences in survival rates between different population subgroups, it would be surprising if the optimal policy did not include that information.

2) As a biological fact, all pandemics end by herd immunity either by natural infection, vaccination, or some combination of both. The optimal policy that ends the pandemic gets us to herd immunity with the least total harm. Covid-zero is not possible with such a widespread pathogen and the social determinants of health stretch well beyond modern medicine.

Implicitly, our governments are telling us that the first point is irrelevant. They are saying that the optimal policy that offers the best protection to the vulnerable from COVID-19 is to treat the disease as though the risk of severe illness or death is exactly the same for all people in society. Our governments have said that for all the money we’ve spent and for all the economic burden that we have placed on our children and the least financially well-off in our society, there is little that we can do differently. In their view, our polices are close to optimal, and that our knowledge of who is most affected by the virus is of no practical significance for public health policy development. Is it really true that no other policy which uses this information is feasible, politically or otherwise?

The second point has become hopelessly and needlessly politicized. Herd immunity has somehow been equated to a political statement. It is not; it’s biology. As the Harvard epidemiologist Martin Kulldorff says, “it’s weird and stunning to have this discussion about herd immunity—flockimmunitet in Swedish. You wouldn’t have physicists talking about whether we believe in gravity or not. Or two airline pilots saying, ‘Should we use the gravity strategy to get the airplane down on the ground?’ Whatever way they fly that plane—or not fly it—gravity will ensure eventually that the plane is going to hit the ground.” However we get there, herd immunity is the only thing that will end the pandemic.

So what would an optimal policy look like?

First, anyone who is at high risk and who has to work in settings ripe for spread should immediately be put on long term disability that replaces their wage. We should not be sending pre-diabetic, hypertensive, heavy-set 50+ year-olds to essential workplaces. We need legions of young healthy people to step up, train quickly, and fill in. If 20 year-olds with minimal training – often less than a few hours in a Spitfire or a Hurricane – won the Battle of Britain, we can find a way to use our young healthy population to replace high risk workers in everything from meat-packing plants to hospitals. Second, for those in the high risk group who cannot self-isolate, such as poor elderly immigrants in multi-generational homes, re-purpose our hotels. Again, have legions of young and low risk people isolate with them, on rotation, to run operations. Ensure high levels of testing. For those who can self-isolate, our army of young people can still help by delivering groceries, medications, and other necessities. Third, let everyone else go about their normal lives to the greatest extent possible – especially children in schools. As we vaccinate our high risk population with an ever expanding vaccination program, and as the virus spreads among the low risk group, we will reach herd immunity and the pandemic will end. The current policy looks very much like let it rip in slow motion.

Perhaps these ideas are infeasible; perhaps our current policies of lockdowns and curfews are the best we can do. Maybe ideas like mobilizing our young is impossible. Maybe it’s too late. But I challenge anyone to rigorously show that we could not have done better or that we can’t do better now.

With bold leadership and a call to civic duty, our accomplishments during WWII and at the beginning of the Cold War showed how we can do great things under enormous stress, against terrible odds, at extremely high stakes. From the Dunkirk Evacuation to the Berlin Airlift, we never accepted the answer “it’s virtually impossible”.

We’ve been told that our civic duty is to stay home, wear a mask during essential trips, and wait for a vaccine all the while we push Covid-19 onto vulnerable essential workers and their relatives.

I bet we can do better. Let’s focus our protection.

Ontario ICU arrivals and departures as a Skellam process

Figure 1: Net daily change in the Ontario ICU census with Skellam inferred rates. The red lollipop points are days of net inflow and blue lollipop points are days of net outflow. The red ribbon and blue ribbons are the inferred daily ICU arrival and departure rates from the Skellam process. Lockdown imposition and lifting dates indicated.

As Ontario enters a new lockdown, the main concern is a potential overrun of our ICU capacity. A year ago, the Ontario government announced a planned major expansion of provincial ICU capacity, but, given our current limits, it appears that either the plan never came to fruition or that the efforts woefully underestimated possible COVID-19 ICU demand. The Ontario COVID-19 data portal gives the daily ICU COVID-19 census from which we can compute daily changes. As of April 4, Ontario has 451 ICU patients associated with COVID-19. The daily changes give us the net flow but the counting does not tell us how many people actually arrived or departed each day. When we see a daily uptick of 25 people, is that 25 arrivals with no departures or is it 50 arrivals with 25 departures? Both scenarios give the same net change.

Even though the COVID-19 data shows only the net change, we can infer the arrival and departure rates using the Skellam distribution. The Skellam distribution is the difference of two Poisson distributions, k = n_1 - n_2, given by the convolution with a negative sum, namely,

(1)   \begin{equation*} s(k; \mu_1,\mu_2) = \sum_{n=-\infty}^\infty\, p(k+n; \mu_1) p(n; \mu_2),\end{equation*}

where s(k; \mu_1, \mu_2) has support on \{\ldots, -2,-1,0,1,2,\dots\}, and p(k;\mu) = \frac{\mu^k}{k!}e^{-\mu} is the Poisson. The resulting distribution can be expressed in terms of the modified Bessel function,

(2)   \begin{equation*}s(k; \mu_1, \mu_2) = e^{-(\mu_1 + \mu_2)}\left(\frac{\mu_1}{\mu_2}\right)^{k/2} I_{|k|}(2\sqrt{\mu_1\mu_2}) .\end{equation*}

I take the daily difference in the Ontario ICU census data and estimate the Skellam distribution over a 21 day sliding window. The Skellam parameters are the ribbons in figure 1, smoothed with cubic splines with cross validation, and superimposed on the daily net flow. The red ribbon is the arrival process and the blue ribbon is the departure process. Each lollipop point is the net change in the ICU occupation on that day. In figure 2 I show a Q-Q plot of the Pearson residuals from the Skellam model – the model is a reasonably good description of the data generating process. In my analysis I use the R packages Skellam and mgcv (for spline estimation). For clarity, I indicate the lockdown imposition and lockdown lift dates. As of early April 2021, it looks like we are approaching an average of 50 admissions to the ICU every day with an average departure of about 40.

Figure 2: Regression diagnostics

Causation is hard to determine in regressions such as this model, but we see that after the lockdown date on December 26, 2020, the arrival rate quickly plateaued only to begin rising again near the end of the lockdown period. It appears that the lockdown this winter had the effect of tempering arrivals into the ICU. But as always with statistics, we need to be cautious about making causal statements. The arrivals in the ICU are from people who were infected at an earlier date, probably in the neighbourhood of one week earlier. Thus, we see that the arrival rate remains high from the beginning of the lockdown on December 26 through the end of December and early January. We should expect this inertia from infections that occurred near or before the imposition of the lockdown, although there is a distinct possibility that people started to change their behaviour before the lockdown date. But notice that the arrival rate begins to rise sharply almost exactly coincidental with the end of the lockdown on February 16, 2021. This observation suggests that infections were beginning to accelerate at least a week, maybe two, prior to the end of the lockdown. It appears that we would have seen a surge at some level in Ontario’s ICUs even if the lockdown had been maintained through the end of February or longer. Of course it’s quite probable that the resulting surge would have been smaller than the one we are currently witnessing, but to gain insight into such a counterfactual we need to know what caused the acceleration in infections prior to the end of the lockdown. If infections started to rise before the end of the lockdown, is it the result of the new more contagious variants? Is it lockdown fatigue? Is it spread among essential workers? Maybe it’s a combination of effects; I don’t know. Lockdown efficacy rests on that understanding.

Notice that the arrival process turned downward, or at least plateaued, about two weeks after the lockdown date of December 26, 2020, but also notice that the daily number of departures has been steadily increasing throughout the entire winter. Of course we expect that as arrivals increase, departures will eventually increase as well – everyone who enters the ICU eventually leaves. In a steady-state queue, the average departure rate will equal the average arrival rate. With time variation in the arrival process the departure rate will lag as the arrival rate waxes and wanes. It might be instructive to think about the average server load (ICU occupation) of an M/M/c queue (exponentially distributed arrival time, exponentially distributed server times, with c servers) as an approximation to the ICU dynamics. In an M/M/c queue the average number of busy servers (ICU bed occupation) is,

(3)   \begin{equation*} \bar c = \frac{\mu}{\tau}, \end{equation*}

where \mu is the arrival rate and \tau is the average service rate. For example, given an arrival rate of 50 people per day and an average length of stay of 14 days in the ICU, the steady-state average number of people in the ICU would be 700 patients, provided the number of beds (servers) is larger than 700. I don’t know if the length of stay has been varying over time. It would be great to do a full time dependent competing risk survival analysis on that data, but the steady rise in the departure rate that we see over the winter might indicate that the length of stay in the ICU has also been changing with the arrival rate. I don’t know.

There are a number of ways to extend this work. The estimator is crude – instead of a naive 21 day sliding window, it could be built with a Bayesian filter. The Q-Q plot in figure 2 shows that the naive sliding window generates a good fit to the data but if we want to back-out robust estimates of the timing of the infections associated with the arrivals, it might be worth exploring filtering. Second, it is possible to promote the parameters of the Skellam process to functions of other observables such as positive test rates, lagged test rates, time, or any other appropriate regressor and then estimate the model through non-linear minimization. In fact, initially I approached the problem using a polynomial basis over time with regression coefficients, but the sliding window generates a better fit.

Where does this leave us? The precipitous drop in ICU arrivals throughout the summer of 2020 with low social distancing stringency and no lockdowns, along with the steady rise in arrivals beginning in the fall, suggest that Covid-19 will become part of the panoply of seasonal respiratory viruses that appear each year. Hopefully with the vaccines and natural exposure, future seasonal case loads will occur with muted numbers relative to our current experience. Given that the largest mitigating effect, next to vaccines, seems to be the arrival of spring and summer, lockdown or not, the warming weather accompanied by greater opportunities to be outdoors should have a positive effect. Covid-19 cases are plummeting across the southern US states like Texas and Alabama, yet cases are rising in colder northern states like New York and New Jersey. While increased herd immunity in the US from higher levels of vaccination and higher levels of natural exposure must be having an effect on reducing spread, it really does seem like Covid-19 behaves as a seasonal respiratory illness. Hopefully we can expect better days ahead, but, in the end, it is very hard to maintain a large susceptible population in the face of a highly contagious virus that has already become widespread. Perhaps we should have been looking for better public health policies all along.