Dean Dot Dog

Exploring the Covid "Cost Mitigation Frontier"

August 25, 2020

The tradeoffs we face

We did a bad job closing the economy and we’re doing a bad job of “reopening” it. But for as much criticism as there’s been for the handling of Covid-19 at the national and local levels, it’s important to keep in perspective that the alternatives would be merely less worse: there’s no set of policies in front of us that doesn’t result in severe costs to lives and livelihoods. It’s like a major natural disaster has befallen us: as the category five hurricane makes landfall, setting out sandbags and boarding up windows certainly helps the situation, but we’re still getting hit by a hurricane. The pandemic threatens enormous costs in terms of physical suffering and deaths, but to mitigate it requires paying dearly in economic and social costs.

I believe part of the problem with our collective pandemic response has been a lack of ability to weigh these different types of costs against each other. To over generalize a bit: on one side are people who think any consideration for economic and social costs are dismissed as some kind of Wall Street neoliberal conspiracy to value profits over human lives and for whom only public health concerns exist. On the other side are people who defy even the simplest compromises, perhaps due to some magical thinking that if they don’t acknowledge the pandemic then it doesn’t exist, because considering the real human costs is too much to bear. Too many people are shouting about all or nothing behaviors: either the pandemic doesn’t exist and we should all hit the bars together and spit in each others mouths, or it does exist and a maximalist response is required no matter the cost.

Despite so much righteous talk of “there’s no trade off between money and lives”, there absolutely is a trade off between money and lives, and we need to get over the cognitive dissonance of holding both of these concerns in our mind at once. Yes, sending children to school together where they can spread the virus is very bad, but millions of kids missing out on early childhood education is also very bad. Yes, infections at food processing plants are very bad, but disruptions of the national food supply chain are also very bad.

In practice, we trade off money for lives all the time (“money” being used broadly as representing economic concerns in general), but it’s usually much more implicit, and therefore palatable. Consider the following proposition: each year, approximately 35,000 Americans die in motor vehicle accidents. Higher speed accidents have a much higher fatality rate, so if we capped the speed limit on every road to 25 mph we could certainly save a large portion of these lives. Or how about this one: shelter in place is reducing the spread of all infectious diseases, not just Covid. If we made stay at home orders permanent even after the pandemic is over, we could save some of those 60,000 Americans who die each year from the flu. While the cost/benefit of these proposals is obviously not justified, hopefully you can clearly see that there is indeed a cost, there is a benefit, and we can compare them against each other.

Many more hard choices lie ahead of us. How can we make sense of them? I don’t have anything to advocate for here in terms of specific policy proposals, but I would like to contemplate the general problem of how to make rational tradeoffs. Thinking back to when I was studying economics, there are a lot of frameworks there to draw on related to constrained decision making. Below, I’m going to explore a comparison between pandemic response policy and an economic model called the Production Possibility Frontier (PPF).

The PPF: guns and butter

Let’s start with a summary of the production-possibility frontier(PPF) model: in a world where you can allocate resources to producing good A or good B, there’s a “region” of possible combinations of A and B that you can make. The edge of this region represents the maximum possible production and, assuming that the more of each good the better, the “ideal” allocation will lie somewhere along this line—though where exactly depends on the relative value you place on A and B.

Production Possibilities Frontier

In the above example, taken from the linked Wikipedia article, we’re producing some combination of guns and butter. Point A is inside the production frontier and thus not Pareto efficient: we can produce more guns without decreasing our butter production, and vice versa. Point X is outside the frontier and isn’t a feasible choice given our current resources. Points B, C, and D lie on the frontier and represent maximal use of resources where we can’t produce any more of one good without sacrificing some of the other. Which one is ideal will depend on what our utility function for guns and butter looks like. If we suppose there were a breakthrough in butter production technology, that would push the frontier outward along the horizontal axis: for any given amount of guns, we can produce more butter, and some points that were previously off limits are now inside the possibility frontier.

The key points are:

  • Available tradeoffs between two quantities are represented as a set of points
  • Points inside the region are suboptimal and can be improved by moving towards an edge
  • While the optimal point lies somewhere on the region’s edge, which point is optimal is a value judgement

The CMF: R0 and unemployment

Now let’s start modifying the production-possibility frontier model for the problem at hand. In the traditional PPF model, we spend resources to produce something that we want, and the more that gets produced the better the outcome is. The problem of pandemic management inverts everything: we spend resources to reduce something we don’t want and the less the better. I don’t know if this alternative model has an actual name, but I’m going to call it the “cost-mitigation frontier” (CMF).

Here’s an example of what the modified graph might look like:

Cost Mitigation Frontier

Health costs are represented on the vertical axis, perhaps measured by R0, deaths, hospitalizations, etc. On the horizontal axis are economic and social costs from fighting the virus, such as unemployment, poverty, loneliness, etc. Yes, there are a lot of important details getting glossed over here: we probably care about how geographically concentrated hospitalizations are, whether some demographics are disproportionately impacted by unemployment, path dependency concerns, and the units aren’t very precise—but wave those details away for now. It’s okay if the model is kind of abstract.

Instead of wanting to expand outwards on the graph, we want to minimize costs by moving in towards the origin. Point A is a non-optimal point in the interior of the possibility region and X an unavailable point outside the region; which side of the curve is possible is flipped compared to the PPF. But like the PPF, points that are on the curve like B, C, and D represent Pareto optimal choices, each with different tradeoffs between health at economic concerns.

Should we chose point B (allowing a higher number of infections but limited economic impact), point C (perhaps an extended hard lockdown that stalls the virus in its tracks), or maybe point D (that’s somewhere in between)? That’s ultimately a question of values and not something that this model, by itself, can answer. But we can say for sure that we definitely don’t want to be point at A. And that’s probably closer to where we are today, suffering the worst of both worlds.

What does moving from point A to the cost frontier look like? We can think of implementing new public policies as taking a “step” from one point to another in the cost space.

Cost Mitigation Steps

Most policy changes will move us down and to the right, or up and to the left: we have to trade off some economic costs to make progress on the health dimension, or vice versa. Different policy actions will have different “exchange rates” between the two types of costs, which in the graph above appear as the slope between points. For example, moving from A to Z decreases infection rate a little bit but with a large increase in economic costs. A policy that moves us from A to Y1 looks like a much better move, since it gives a large decrease in infection rate with only a small economic cost. Z might represent “closing all restaurants” and Y1 “enforced mask usage in public indoor spaces”, for example.

Y1 dominates Z as a choice, because it’s better both with respect to health and economic costs. But is Y1 better than A, where we started? From the model’s perspective, it’s actually ambiguous. Whether this tradeoff is worth it depends on how we value health and economic costs, and people with different values (or in econ parlance, utility functions) might disagree on whether we should enact the policy that brings us from A to Y1.

What about moving from Y1 to Y2? This might be look like relaxing restrictions on low risk businesses, slightly increasing infection risk but having a large economic/social benefit. Like the move from A to Y1, whether Y2 is preferable to Y1 is ambiguous. But—Y2 is strictly better than A, our starting point! This is true regardless of what relative value you put on infection rates vs unemployment.

I think this is an interesting result: while there might not be a single policy action that could move us from A to Y2, a combination of policy actions, each with their own tradeoffs and perhaps controversial when considered by themselves, net out to a result that is an unambiguous (Pareto) improvement.

What’s the point?

All models are wrong, but some are useful

Obviously, there are a lot of real world concerns that are left out of this model. So what can we learn? Besides being a self-indulgent intellectual exercise, models are tools for creating new intuitions and conclusions from stated assumptions. The key takeaways that I got for exploring this model are:

Confront tradeoffs

We can, and must, weigh tradeoffs between health and economic concerns. Just knowing which activities are highest or lowest risk of spreading infection isn’t enough to tell us what should be permitted—we also need to consider the economic/social impact of those activities. Policy decisions should focus on the cost/benefit between these concerns, and it may be desireable to ban some low risk activity while simultaneously opening up a higher risk one, even though that appears inconsistent when viewed through just the lens of public health.

In other words, we should be ranking which activities we permit by which have the best “exchange rate” between health and economic costs. In other words, wear a damn mask.

Explore the cost mitigation frontier

In the model, we had a neatly drawn lines connecting our points that allowed us to precisely evaluate the consequences of different choices. But in reality, we can only speculate about the cause and effect of our actions.

A possible silver lining in the scattershot response America has taken to the pandemic, where each state and city is coming up with different rules for businesses and schools, is that it gives us an opportunity to run a thousand experiments to explore the shape of the cost mitigation frontier, learn about consequences, and make better policy decisions in the future.

(I’m really hoping that expecting us to learn from mistakes isn’t overly optimistic…)

Risks of one-shot policy evaluation

There are likely very few policy actions available that are Pareto improving; that is, even the best policy actions won’t be beneficial for everyone in every way. In addition to the tradeoff between health and economic concerns, in the real world some demographics might benefit from a policy while others aren’t affected or are even made worse off. Groups that are left out or harmed by a policy will (understandably) try to block it.

As we saw in the example above a combination of policies can theoretically net out to a generally beneficial result even if none of the individual actions do. If we’re evaluating whether we should move from point A to point Y2 that’s an easy sell, but if we’re evaluating each of the steps sequentially they may all get blocked by people who are concerned about the costs, and we aren’t able to make any progress.

This issue is actually general to all sorts of policy decisions, not just pandemic mitigation. Thinking through this has made me a bit more sympathetic to the big multi-faceted spending bills that go through congress and all the negotiation that’s involved there.

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