Good afternoon, everyone.
My name is Daniela Rus, and I'm the director of CSAIL
and the Deputy Dean of Research for the Schwarzman
College of Computing.
And I'd like to welcome you to this edition
of Hot Topics in Computing.
Today, I am delighted to welcome Professor Daron Acemoglu.
He is the Elizabeth and James Killian
Professor of Economics at MIT.
And in 2019, he was named Institute Professor.
This is the highest honor at MIT.
Now, Professor Acemoglu completed his PhD
at the London School of Economics.
And he was very young when he finished his thesis.
He was only 25.
I wonder if this is the youngest economist
to have ever received a PhD.
He lectured at the London School of Economics for a year
before joining us at MIT.
His research area is in political economy,
and he made numerous contributions
to this field, for which he was awarded the John Bates Clark
Medal in 2005.
This award is given to an American economist
under the age of 40 who is judged
to have made significant contributions
to economic thoughts and knowledge.
This is one of many awards Professor Acemoglu received.
He also authored hundreds of papers and two books
of which I would like to highlight the very influential
Why Nations Fail, which I read from end
to from cover to cover.
And I highly recommend in case you have not read it already.
And so with this, I would like to welcome Daron to tell us
about optimal targeted lock downs using a multi-risk SIR
where SIR is an epidemiological model that
computes the theoretical number of people
infected with a contagious disease in a closed population
Daron, take it away.
Thank you, Daniela.
Thanks for inviting me and thank you
for that very kind introduction.
It's a great pleasure to be here.
So this is joint work with my colleagues Victor Chernozhukov,
Yvonne Werning, and Mike Whinston.
And since time is short, and I would love to get feedback,
comments, criticisms, let me just jump into it right away.
So I presume you can see what I'm sharing.
Fine, it works.
I don't need to tell you about COVID 19.
Our whole way of life has been thrown upside down.
And one of the things that's very
interesting about this period is that we're actually
trying to do the science and the policy at the same time.
Trying to find out both about the epidemiological,
immunological aspects of the disease,
and how we deal with the social and economic aspects of it.
So even though it's a tumultuous sorry time
for most of humanity, it's also a time for us
to use our expertise and tools.
And at some level, there has been--
it's been a success because there has been
a lot of global cooperation.
But on the whole, I would say, we are still not successful,
even on the science part, because we don't understand
the pandemic very well.
And certainly, policy has not been very successful
in most countries.
In fact, we don't even understand the policy
So there is a lot to be done in terms
of contributing to this field.
And the reason why Yvonne, Victor, Mike, and I
jumped to this field into this area
is because we think that it's also greatly in need
of a multidisciplinary effort.
So this is an epidemiological problem.
Issues of herd immunity, mitigation, timing, immunity,
all of these we have to take from epidemiological data
But there are economic and mathematical computational
issues in terms of modeling, costs of lock
down, different types of social behavior,
and then, as I'm going to argue, it's
also an important computational problem
that you have to approach these problems--
modeling the various different dimensions
of heterogeneity with various quantitative tools.
And one of the things that we're going
to be bringing to the table here is actually
optimal policy analysis, which does require
some thinking and some extensions of existing
approaches, as I'm going to explain.
So one of the main starting points
for us is that, while several aspects of the disease
are still being investigated, one property of it
is very well documented.
It's an extremely asymmetric disease across age groups.
So if you look at mortality rate conditional on infection,
it's more than 60-fold higher for the over 65
group than, say, the younger group between 20 and 50.
If you go to even older age groups like-- such as 75,
it becomes two orders of magnitude bigger.
So this asymmetric mortality rate
requires the existing approaches to be extended in order
to look at the heterogeneous behavior
and heterogeneous regulations of behavior.
And that's where we come in.
So we're going to develop a simple multi-group model.
So multi-group models in epidemiology are not new.
But what has not been done before
is to actually explore optimal policy within this context.
So if you look at, for example, the famous Imperial College
Ferguson et al study, they have a very detailed structure.
But then, neither do they look at policies that differ by age,
nor do they look at optimal policies.
And as I'm going to explain later,
this actually has fairly major implications
for their conclusions.
So we're developing multi-group SIR model.
SIR standing for Susceptible Infected Recovered, or SBIR,
where you add the exposed group which
are asymptomatic for a while.
We do it both, but I'll just talk about the SIR here.
And the model is general, and can
be applied with multiple age groups as well
as multiple other characteristics
such as comorbidities.
But for this talk, I'm going to focus on three age groups,
young, middle aged, and old.
We're going to calibrate the parameters of this to COVID 19,
and we're going to compute--
characterize and compute optimal control models.
And one of my main emphasis, as the main emphasis of the paper,
will be to contrast targeting and no targeting.
No targeting we call uniform policies, policies
that apply to everybody.
Now, even policies that apply to everybody-- and I'll
come back to this in the US context, for example,
maybe de facto differential across groups.
But for to start with, I'm going to really look
at the uniform they apply to every group in society,
which is targeting differential policies for different groups.
And here is a high level summary of both our results
and our conceptual approach.
So our conceptual approach is built
on a very simple observation, of course,
that we are implicitly or explicitly trading off
deaths and output losses.
Both of those are excessive deaths.
Excess deaths over what would have
happened because of COVID 19.
And excess output, loss over what would have happened.
We are not-- as opposed to some other analysts or policy
makers, we're not in the business of telling society
where they should be.
But our approach is to say, we want
to characterize what's the menu of available policy.
So that's the first conceptual step.
So we're going to be characterizing what economists
would call Pareto frontiers.
So the thick line is the Pareto frontier
when you restrict yourself to uniform policy.
The origin, where you have zero excess loss
of output and zero excess debt, is where you would like to be.
But of course, that's not feasible.
So that convex-shaped black line curve
is showing you where you can be.
For example, if your values or your policymakers priorities
are such, you can choose the maximally feasible control,
which says, I'll take as much output losses as I want--
as you want, but I'm going to minimize that.
Or you can do some other combination.
And essentially, what I'm going to try to show you that when--
instead of looking at optimal uniform policies,
you look at optimal targeted policies.
You go to this dashed line.
So you can either save a lot of lives
or you can save a lot of output or a combination thereof,
and quantitatively these two curves are quite far apart.
That's the main-- those are the several main lessons from what
I'm going to talk about.
OK, some caveats, and then I'll pause for some questions,
and then go through the detail.
First of all, as I said, we are four MIT economists,
we're not epidemiologists.
We're going to be using epidemiological data.
But this is in the spirit of what
I said, there is a lot that we can all do together as computer
scientists, engineers, mathematicians, economists,
epidemiologists, public health specialists,
because I think this is a very multifaceted problem.
And just looking at it from the viewpoint of one discipline
is likely to lead to important omissions.
Worse, I think, even though epidemiologists
have done a great job, there is a huge amount of parameter
and outcome uncertainty here.
So in some sense, I think some of the early works,
like Ferguson et al, if they can be faulted,
they can be faulted for the great degree of certainty
that you can read between their lines.
That was completely unwarranted.
Even today, there is so much uncertainty
about what's going to happen in one or two months time.
And in fact, optimums, or policies, in some ways,
can be very sensitive to parameters.
I'll try to highlight that.
But some other aspects are extremely robust.
So in particular, the gap between
targeted and non-targeted policies is extremely robust.
And in what ways targeting policies improve over--
on target those uniform policies is extremely robust.
So but in that spirit of the understanding and recognizing
the uncertainty and the multi-faceted nature
of the problem, we are very open to comments , suggestions,
And I think the more people are thinking
about these issues, the better for our immediate
or even longer term future.
Daron, this is such an important topic.
And I just want to get clarification.
Does output loss mean economic loss?
And I'll be much more specific about what we
do once I introduce the model.
But yes, it's economic loss.
Now, there are many other social losses, some of them
having economic implications that we're not
going to feature in our model.
So people get bored.
People have psychological problems
because they're locked in.
And all of those things, we're going
to-- we're going to focus on some quantifiable-- easily
quantifiable economic aspects.
And I'll be very specific about that
when I go through the model.
So I think this is a good point for me to pause for a second
and see if there are any questions or comments before I
go into specifics.
We don't have any questions on the chat yet.
Please send your questions.
I just wonder while we wait for a few seconds,
how did you find the data that you needed in order
to reach this.
I'll be more specific about the data sources
when we come to the calibration.
But there are a lot of data out there.
Some of them we don't have access to.
Some of them we have access to, but we did not
choose our model to be as detailed as some of those data
But a lot of our data come from the Fergusons
report, which is very detailed, CDC, South Korea, and Italy.
And one more clarification, when you talk about targeting,
how do you target?
So I think that's a great question.
I'll come to that.
I think, first, let's look at what
we mean by the policies in the context of the specific model.
And then, I'll talk about the implementation, which
I think is definitely something that's not straightforward
But there are ways.
And we've thought about it.
We discussed them in our work.
Please go ahead, Daron.
All right, so here is the model in a graph.
So if you just take the top chart here,
the one that has ones and subscripts, that's
a representation of a slightly extended one group SIR model.
Everybody starts susceptible.
They may get infected.
So I'll explain how they get infected.
In the context of some diseases, they get infected
and that's it.
But for SIR-- sorry, for COVID 19,
there's a crucial difference.
You can have an acute case, where many
over 65 are having that.
Or a mild one.
So we therefore allow two types of infections.
We call them ICU and non-ICU.
So ICU one has an ICU need.
They may or may not get a bed, but they have an ICU need.
And then, the infected exit the infection state.
And they can exit then in two ways.
They can recover, or unfortunately, they pass away.
So the mild cases don't end in death, so they all recover.
But the ICU cases may end in death,
and that might depend on other things,
like the care that they take.
So what we are doing is that we're having multiple models.
And we are allowing network contacts between these models.
And the notation here is throughout standard.
S for Susceptible, I for Infected, R for Recovered,
and D for Dead.
And J is the total population.
So the standard SIR model assumes
a quadratic matching technology.
So it assumes that new infections is a function,
or is proportional to the number of susceptible times the number
of infected because the infected interact with the susceptible
and they bring the infections.
Now, whether that should really be quadratic
or some other functional form, we deal with that in the paper.
There are some issues with the quadratic.
It's not a better approximation.
But it doesn't really matter for any of our conclusions,
and so here we follow the more standard epidemiology
literature and stick with the quadratic.
But if you care about non-quadratic,
you should look at the paper.
But the key thing here is that, instead
of the susceptible in group J being just infected
by some monolithic group of infected populations,
they are infected by those in groups I, those in group, IK.
And the rate at which they are infected
depends on the interactions between these two groups.
So rho JK is the interaction between somebody from group J
and somebody from group K. And then, beta
is the rate at which conditional on interaction,
conditional on contact, we get infected.
And of course, to look at the total new infections
and group J, you need to sum over all the groups
with which an individual from group J can interact with.
But we're going to make this a little bit more complicated.
Because not every infected is going to be around,
and we're going to introduce lock down and slippages
from the lock down.
So let me give a little bit more of the math.
So we're going to have J groups.
Newly infected, they become a mild case with a probability
1 minus iota J, or a severe ICU case with iota J.
And the infections resolve at the rate gamma J.
And that resolution is itself either in death, delta JT,
or recovery, delta RJT.
We're going to model this delta DJT, the death probability,
is a function of the ICU capacity
because that's what the data from Italy
and some of the data from other countries
very strongly suggests.
This doesn't really matter for any other mathematical
So I won't belabor this particular point,
given that time is short, but I'll
come to it in the calibration.
Now, one important aspect is that, even though in the US,
we have done a horrible job with testing and isolating,
some of the policy tools and some of the social tools
are about social testing and isolating.
Some of that will happen naturally
because infected people will be in a severe state.
They cannot go to work.
So we model that in a very simple way.
A fraction tau J of the non-ICU because of contact tracing
isolation testing may not be in the infected pool.
And a fraction phi J of the ICU also are severely infected.
So they're not going to be lurking around
at work or at the shopping mall.
So the AIJ, which is therefore a composite of these rho iota J
phi J tau J, is going to be the fraction of the infected
who are not isolated, so they're going to be circulating around.
And then, one other parameter that, again, is important
is once you recover, can you be identified as recovered?
For example, by serological testing.
And the fraction of those that are identified--
so they can actually go back without infecting other people,
is kappa J, OK?
Now, the key thing for our model is the lock down.
So we're going to model lock down
with three key-- or four key parameters.
One is a policy variable, three of them are parameters.
First of all, the policy variable
is LJ, which is the fraction of group J
that are under lock down.
So they're not circulating around.
They're not going to work.
They're not going to shopping malls or to parks.
Now, we cannot shut down the entire economy,
so we recognize that by having an L bar J.
So L bar J is those who are in non-essential work.
If you locked down somebody, the cost
of that in terms of economic output loss, is WJ.
So that's going to be the output loss of the group that
can be indogenized.
But for now, I'll just take that as given
and we'll match that to data on wages in the calibration
But very importantly, lock downs are imperfect.
So you can have a shelter in place order,
but still deliveries will take place.
Some people will not obey it.
So you can close businesses, but some people
go and visit their neighbors.
So that's captured by this parameter theta J.
So therefore, when you have a lock down of LJT,
T is important here because you'll
see that optimal policy is strongly time dependent.
So that's one of the problems of Ferguson's analysis,
Then, the fraction of interacting infections
will be down from wherever it was to 1 minus theta JLJT.
If theta J was 1, then everybody you locked down
would be taken out of the infection.
But if theta J is say, for example, 0.75, for every four
people you look down, only three of them are effectively out.
One of them still circulates.
And then, the key is vaccine and cure.
So we assume that that arise at some time
T. That can be stochastic.
Let me take that in the calibration
to be 1 and 1/2 years just to show
you some of the patterns in the clearest way.
But whether it's stochastic or not
doesn't matter for the results.
Greatly, but its timing does matter
a lot, as I will try to highlight.
And of course, once the vaccine comes,
it's not immediately rolled out.
So those issues I'm not going to get to.
All right, so math.
So I have essentially summarized most of the model.
So put in a math form, this is where we were.
But now, new infections are not just SJ times interactions,
but it has two more components.
One is 1 minus theta JLJ.
So that's taking people out of the susceptible group.
The susceptible guys are not lurking around.
And second, inside the summation,
you have eta K 1 minus theta KLK.
So you see now what the quadratic matching technology
is doing, that lock downs are doubly affected because they're
taking people out both of the susceptible
pool and the infected pool.
And then, in addition, you have this eta K
here because some of the infections
are going to be taken out, even this is not for lock down, OK?
All right, so then, as I said, two objectives.
Lives lost, that's the number of deaths, and economic losses.
So economic losses explicitly is given
by this mathematical expression.
Let me give you what this mathematical expression stands
If you look at the first term, what it has
is that it has LJT times SJT.
So those are the susceptible people who could have worked
and are not working.
What are they losing?
They're losing WJ times 1 minus psi J. Why 1 psi J?
Because WJ is what you could have
produced if you went to work.
But if you stay home, you may still do what we're doing here.
We can do a less effective form of an in-person seminar.
So psi J is going to vary across group,
across sectors, et cetera, that can be incorporated for now.
I'm just not going to look at the sectoral version.
But that's where the economic losses come from.
The second term is similar.
It has the loss because of the infected people.
So you want to reduce infections also
because the infected people are not being productive.
The third term is because some of the recovered are also not
wanting to work so they cannot be identified.
And then the final term is that, if somebody dies,
all of their future contributions to productivity
So the economic term--
economic losses here already has some of the debts in it
because of this link between losing your future productive.
OK, and this was what I was showing you at the beginning.
This frontiers, you can think of them as economic losses--
minimizing economic losses plus some parameter times lives
And that parameter more or less corresponds to some economists
call statistical value of life.
But we do not take a position on the statistical value of life
because it's a complex ethical issue as well as one
where people disagree with.
So that's why we're going to look at--
we're going to look at the frontier in its entirety
for most of the talk.
All right, well, we could do some--
we do some mathematical analysis on this optimal control
But let me not present that because I
want to jump to the results and show
you a flavor of the results, and then open it up for discussion.
But before I do that, let me just make two comments.
One is that targeted policies is going to have two benefits.
And I think it's important to recognize both of them.
One is that you can lock down the more vulnerable groups
because infections are more costly for them.
That's a pretty direct effect.
But then there's a more subtle benefit,
which is that once you lock down the older group,
you can adopt different policies for the younger group.
And you can go for different types of immunity.
Herd immunity, based on a reduction in the susceptible
population or vaccine immunity.
And one way of seeing that is to look at this picture
here, which is like the phase diagram for a two group case.
The three group would be three dimensional,
so I'm not going to show you that.
So essentially, we start at somewhere near 1, 1.
And we're always traveling downwards.
Because a susceptible population is declining all the time
with people getting infected.
Now, how do we travel downward?
If you did nothing, and the infection
rates are the same across groups, which there's
some controversy on this.
But most of the evidence suggests
that heterogeneity is not only infection rate,
but what happens after infection.
Then, you will be following the 45 degree line.
The dotted line.
But policy means that you follow different trajectories-- curved
trajectories, different angles trajectories.
And then, where do these trajectories take you?
Well, the speed at which you travel is endogenous to policy.
And the difference between the qualitative nature
of the policies is that, if by the time
the vaccine comes you're still in the white area.
That's the waiting for the vaccine policy, which
means that you do not reach herd immunity
by the time the vaccine comes.
On the other hand, if you enter that green area that's, loosely
speaking, the base of attraction of infections going down
from there own.
So essentially, you're reaching herd immunity
that even if the vaccine doesn't come,
infections are going to fairly quickly disappear.
But where you enter into that green area matters a lot.
So the herd immunity that goes along the 45 degree line
is very costly.
But reaching herd immunity from other trajectories
may not be as positive, as I'm going to show you
All right, let me pause here before I go
into the quantitative analysis.
We don't have any questions on the chat right now.
So I suggest that you carry on.
I have a lot of questions
Sorry, Daron, but I suggest you carry on.
And we can [INAUDIBLE].
I'll carry on in that case.
So most of the parameters we use are standard.
I show you the data on the mortality rate.
Again, we could go more detailed there.
Of course, there's a trade off here.
We're going to contra compute optimal controls, which is not
the easiest thing to compute.
So if you 80 groups, then computing the optimal control
The contagion rate, the number that you
match for that is R0, which is the initial rate
at which new infections come relative to recovery.
So we target a rate of 2.4, which
is more or less the second wave of evidence from China.
I'm going to start with a uniform interaction structure,
rho equals to 1, just to show you what the differential lock
downs are doing.
But then, I'm going to show you this rho parameter calibrated
to the BBC pandemic project, which is the best
data available in our opinion.
The group sizes are from the US.
And the wages are, essentially, the same between young
and the middle aged, the two groups.
But the old have lower wages because they participate less.
So in the US, they earn about 25%
of what the young and the middle aged earn.
The hospital capacity, as I said,
we calibrate that to the Italy data.
So you can increase mortality by about 10%
when you exceed the ICU capacity.
Daron, can I ask a question?
We have a question about that.
And that is, how does the model handle the economic losses
from hospital capacity?
In other words, if a doctor is assigned to the intensive care
unit, that doctor can't perform other productive health care
And we know that so many procedures were canceled.
And only COVID patients were treated.
So as I said, there are many other social costs,
like the ones that you've mentioned.
So we're not incorporating them.
All of those can be incorporated.
And again, the model by Ferguson's, which
had 40 authors, are much, much more detailed
because they're written by the lab model.
And so those are-- they don't incorporate this.
But those are more natural models for them
to be incorporated.
We view ours as a mid-scale model,
or actually, a small model.
But some of those can be incorporated here as well.
But our point, as I said at the beginning,
is more like a conceptual one, is
to show you how this robust differential structure emerges.
So I'm going to try to emphasize that.
But those are all great questions.
Daron, another clarification question from the audience.
Is the Pareto frontier a 2D surface?
Yes, it's a curve.
But bends over.
So that I should have explained that, actually.
Since I was a little bit rushing.
The reason why it bends backwards
is because if you have a lot of deaths, that's bad for debt,
but it also has economic cost as I've explained.
Because people's foregone earnings in the future.
But let's see.
So the question is a little bit more detailed.
So since the output is economic cost
plus alpha times cost of lives lost,
don't take a stance on alpha.
Then would that Pareto front be two dimensional
or is it a curve?
Yeah, it's a curve in a 2D space because I've reduced everything
to two variables.
It's called chi in the model.
Different chis correspond to different points
along the curve.
So let me just quickly finish these parameters.
So as I said, low testing and isolation.
So most of the infected are lurking around
if it wasn't for lock down policy.
So eta J 0.9.
And then, so a key parameter here,
which we don't really know what it is.
There is no explicit data on this.
But on the basis of introspection, extrospection,
et cetera, we choose this as 0.75.
So which means that for every four people that you look down,
one of them is completely disobeying your lock down.
And then 30% of workers are essential.
So let me now show you the calibrated optimal policy.
So now, what I'm doing here is I'm
showing the empirical equivalence
that we compute with the optimal control algorithm
that I skipped.
But it's fairly standard optimal control
that we solve numerically.
The equivalence of the Pareto frontier.
The red one is the uniform policy.
And the green and the blue ones are the target policy.
But here, we are looking at two types of targeted policy.
Since we have three groups, the fully targeted policy
would target people in different groups differently.
But we also look at a semi-targeted policy
that doesn't distinguish the young and the old.
Sorry, the young and the middle aged,
it just distinguishes the old.
And as you can see, the green and the blue
are on top of each other.
So all of the gains can be obtained
by the very simple policy that treats the over
And I'll come back to that in a second.
But to show you what these curves mean,
let me now pick a point, or a couple of points,
and illustrate what the lock down pattern looks like,
and what it implies in terms of economic and public health
So let me take the red dots on the red frontier there.
So you can call that a safety-- focused strategy that says,
we're never going to tolerate anything
more than 0.2% mortality among the adult population.
That's pretty bad.
But still, one of the possible points you can predict.
Or you can be like some Republicans and say,
we're not going to tolerate more than some amount
of economic loss.
So say, for example, you can say you have
an economic-focused approach.
We say, no more than 10% decline in output.
So essentially, that's one year's GDP equivalent of 10%.
So what I'm showing you now are these two
policies, or optimal policies corresponding
to these two possibilities.
The top one is the safety-focused,
and the bottom one is the economy-focused.
A couple of important points.
First, you see that the lock down is fairly extensive.
So even close to 14 months, you have about 40% of the economy
under lock down.
That's the only way that you can limit COVID 19 that has
a very high infectious rate.
That's the only way without extensive testing
that you reduce spread of infections.
And its economic costs would be over 37%,
which means you're losing more than a third of one year's GDP.
And despite that, you're putting up with 0.2%.
If you went for the economy-focused one, that's
the bottom figure, you'll have a much shorter lock down.
The lock down completely ends in about seven months.
But as a result, you have to put up with over 1% fatality.
So these are grim choices.
Before I show you how they are improved
with a targeted policy, let me show you the reproduction
rate of the disease.
What you see with the reproduction rate
is actually a telltale sign of what's going on.
The safety-focused one waits for the vaccine,
whereas, the economy focused one goes for herd immunity.
How can you see that?
We could have seen that from the infection rate as well.
Just before the vaccine comes--
and that's why it's very clear to have a deterministic arrival
of the vaccine.
Just before the vaccine comes, you
start letting people out of the lock down.
You see that from the lock down policy.
Because once you know that the vaccine is going to come,
you're OK letting the infections build up a little bit
because the indirect effects of these infections
on the very large susceptible population is not there.
But because you don't have herd immunity,
you have this uptick in infections or the reproduction
rate starts increasing.
So if the vaccine didn't come, you
would have a huge second wave here.
But at the bottom here, you don't have that uptick
because you already reached herd immunity.
Because you've had infections peak here quite high.
And that spread the disease enough
that you've achieved herd immunity.
And that's why you had to put up with this relatively
high fatality rate.
All right, now, bottom line.
Big improvements if you look at semi-targeted policy.
So the optimal semi-targeted policy, if it's safety focused,
locks down the old for until the arrival of the vaccine.
And reduces the 37% losses to less than 25.
Say the same for the same mortality.
Or the economy-focused one reduces the mortality from over
1% to about--
to less than half a percent.
And the economy-focused one wants to use the older groups
labor force as well.
So once you have reached herd immunity,
you can actually let the old come out as well.
The herd immunity is not perfect.
That's why it takes a while.
But after that, you can let them come out.
So this is going back to my earlier figure.
You're going into the herd immunity region
in a very asymmetric way.
That's why you're saving a lot of lives,
but still letting the economy open up.
If you do fully targeted, now you
would treat the middle aged and the young differently.
But the gains are very small because the big gains
come from protecting the old.
So why is it that treating the young and the middle aged
doesn't matter that much?
Well, that's actually quite critical for understanding
why you're locking down the young and the middle aged here,
and why the gains are small.
The reason why you are locking down the young
here or here is because, even though you're
the older under lock down, if you didn't lock down
the young, because of the slippage due to theta being
less than 1, the old would still take the infection
from the young.
And that's very costly because the old are very vulnerable.
So that's why you lock down the young.
And now, you can see why it doesn't really
make a huge difference from a quantitative point of view
whether you lock down the middle aged or the old and young.
Because you're not locking them down to protect themselves.
You're locking them down to protect the old.
So it doesn't matter whether it's
the old or the middle aged, and that's
why semi-targeted policy does very well.
All right, you can choose other points on the frontier.
But quantitatively and qualitatively the features
are the same.
You either wait for the vaccine, or you reach
this asymmetric herd immunity.
And in both cases, you have huge gains
from being the targeted policy.
Now, you may say you're locking down
the old because the old don't contribute economically that
So here we allow the old to be heterogeneous themselves, old
retired versus old working.
And it doesn't really matter.
You want to protect both the old retired and the old working.
The main asymmetry here is in the epidemiological aspect.
The greater vulnerability of the older age.
So that's what this figures show.
Let me conclude because I want to open up for discussion.
We do a bunch of robustness checks.
I'm not going to go into them.
But I want to make just a couple of additional points.
One is that if you have testing and other social distancing
measures, for example, protect the nursing
homes by creating group distancing, the gains are huge.
You can reduce mortality by an order
of magnitude or economic losses by an order of magnitude.
So there's some important policy issues
that we have to talk about.
Second, I want to contrast with Ferguson et al.
There are many differences from Ferguson et al.
One difference that they emphasize
is that they have a hard ICU constraint.
So they say, we cannot have infections exceed a certain
And that's the reason why we're getting this
on and off policies of lock down, free up,
and then another lock down.
Well, it turns out that's not actually correct.
The reason why they're getting those second waves in Ferguson
is because they're looking at some optimal policy.
So they're looking at lock down and then no lock down.
But they're not looking at smooth policies that gradually
reduced the lock down.
So even with tight ICU constraints,
you may get a little bit of nominal tonicity,
but you never get a second wave like they do.
And that's what this figure here is showing.
And then, finally the thing that's rather important
is, of course, the network structure.
So here we use data from the best data
on this, which is much better than what's
available in the US, which is old
and not systematically collected, POLYMOD--
so the BBC pandemic project.
So when you do that, the most important aspect
is that each group interacts more within itself.
That's the pattern that the off diagonal year are lighter,
which corresponds to more intense activity.
When that's the case, the qualitative features
remain the same.
The quantitative gains remain the same.
But there are some interesting aspects that you get.
And the most interesting one-- and I'll
conclude with that, which is that now you
have another interesting non-monotonicity, which really
reveals the logic of these models.
So as you can see here, now the--
you released the oldest group from lock down.
And then, lock them up again later on.
Why is that?
The reason is because when the old interact within themselves,
once the infection rates among the old
are low, even when the infection rate among the young
is greater, you let them down--
you let them out because they're not interacting with the young
So that slippage that from the young,
they're getting the infection, is not a big deal.
So you let them out.
But once you let them out, they're
always going to get some more infections
because the infection has not been defeated.
But the quadratic says that infections are building up.
And at some point, they become very costly
and then you lock it down again.
So the non-monotonicity of this sort
is quite endemic in these models.
But critically, will not lead to second waves as in Ferguson.
Again, because you can manage it with optimal control policy.
All right, well since I've said a lot
about optimal control policies, and really
how parameters matter.
And here is the final thing I'm going to show you.
If you go to this website, and I can send you an email--
email this address to those who are interested.
You get a GUI where you can vary the parameters of the model
and see how the optimal controls and the quantitative gains
respond to different policies.
So this is in the spirit of allowing other people
to use these sorts of models.
And of course, they can be extended
in multiple dimensions, as I mentioned.
I'll stop now, and I look forward
to your comments and questions.
Thank you, Daron.
This is really powerful.
And so we have a number of questions on the chat.
If you have additional questions,
please send them to me or to Laura Ling on the chat.
And I will start with Fredo's question.
How predictive do we believe such a simulation can be?
My sense is that Ferguson was correct
about the non-intervention scenario, but quite wrong
about the effectiveness of the interventions.
Did they try to fit their intervention model
to what has happened so far?
And as I said at the beginning, there
is huge amount of uncertainty.
And one thing I did not show is that, if you
look at the early works, like Ferguson--
the Washington based-- I forget now the name
of the Institute's model.
There's another one in Europe.
And you look at their predictions,
their predictions are way off.
So every prediction that was made about COVID 19 is way off.
Why is that?
Well, there are a couple of reasons for why they're off.
First of all, they used the wrong parameters.
So I think there was a lot of uncertainty
about the parameters.
But even more importantly, and that's
why we need to look into these models from economics,
sociology, quantitative sciences,
is because social behavior is adaptive.
So even if you tell people--
and there's some nice graphs, but I didn't bring them.
Not our work, other people's work.
If you look at, for example, from data from OpenTable,
you see that in the US, people stopped
going to restaurants before governors locked down
When the governors looked down their state,
there's a further jump because not everybody was--
either cared about their own lives,
but the other things, of course, here you're
actually infecting other people.
So there is an element of how social regarding you are.
Because there's a negative externality when
you go and infect other people.
And the quadratic matching technology
is very important for understanding that.
But in any case, so you see that people
themselves were adjusting their behavior.
And for instance, with now with masks and so on and so forth,
that's really getting down to R0 the disease down.
So they didn't take that into account.
But they also did not use all of the correct parameters
for various different aspects.
And I guess, Ferguson et al would have a huge team there
updating their models.
Some other people may or may not be updating their model.
So I would not take any of the very specific
quantitative numbers seriously.
But what I've tried to emphasize are the general properties
that are very robust across different formulations.
So thank you for that.
Let me go to the next question from Windsor.
How can one deal with vulnerable communities that
are both poor and unhealthy, or do not have
proportionate health support.
Both lock down and opening up results in more deaths.
Right, so there are a couple of huge simplifications here.
One of them is that I have completely abstracted
from distributional aspects.
So the assumption here is, of course,
a completely counterfactual one, especially
in the US, which does not have a good social welfare state.
If you have the GDP, and then you redistribute the GDP.
Actually, given how bad the US social welfare state is,
US economic policies have been actually the only decent part
of the US policy response to COVID 19.
Unemployment insurance has been extended.
Various different other policies have made sure
that the most economically vulnerable have been protected.
But there are other issues here that you
want to go much more into the detail.
But another important dimension of heterogeneity
here is different areas.
The ICU capacity is very different.
And as you can see, the policy is quite sensitive to the ICU
So if you do that, the same policy should not
be used in Massachusetts as in Alabama, for example.
But obviously, that's where the political economy of it comes.
The practice is very different.
Many states that don't have the ICU capacity
have the very vulnerable population.
Not just because of economic poverty,
but also with comorbidities have adopted
the most insane policies exposing their populations
to the infections.
Actually, if you step back, in many ways,
US policy has been de facto--
the opposite of what we are advocating.
Because early policies way into the-- towards
the end of April via nursing homes, the oldest population,
was highly exposed to the disease.
Because anybody could go into nursing homes.
They had very low wage employees,
which were working in McDonald's and then going and working in--
without any check in nursing homes.
And even infected people were brought into nursing homes
so that their beds wouldn't remain
idle, which was sort of an insane
policy in the midst of a raging pandemic.
But in any case, so there was a lot of incoherent policy making
So let me go to the next question.
I have seen the argument in the context of simple SIR models
that strict lock down may be most valuable as we approach
the minimum threshold for herd immunity
because it prevents overshoot past that threshold.
I didn't see this come out in any of the optimal policy
examples you used as illustrations.
Actually, that's a great point.
I did not get into that.
So going back to the figure that I showed you
with the green triangle.
So that when you enter that area,
you actually travel in that area.
And that's the overshoot.
So the question is, how costly is that overshooting,
and how do you control it?
And so the reason why you don't need special attention to that
is because if you look at the optimal policy,
it induces a peak way before you reach the herd immunity area.
So by the time you get to the herd immunity region,
the pandemic is already decelerating.
So that's why you don't get into it with a very
high overshooting momentum.
But if instead you did completely uncontrolled,
so that the quadratic took you almost exponentially up,
then you would get into the herd immunity area
and you would travel way into it.
But optimal policy never does that.
So that's a great question.
All right, here's another question from the audience.
Roger had a question.
But, OK yes.
That was Roger's question.
That was Roger's question.
Thank you, Roger, for that good question.
Some of the optimal policies decrease the lock downs
and then increase it again.
Presumably, there are some large inertial effects.
For instance, lags between reducing lock down
and any economic increase.
Would modeling, though, substantially
affect the results?
That's a fantastic question.
So I have trumpeted the benefits of looking at optimal control
relative to the ad hoc policies ala Ferguson
et al, for example.
But I should have also been upfront about the shortcomings.
When you're dealing with complex social problems here,
and you cannot tell people, OK you're going to go down
a little bit and then you're going to go back.
So there are going to be delays.
There are going to be, perhaps, when
you use more complex policies, there will be more disobedience
to the policy.
I think all of those are great questions.
And one should really think about them.
We don't have a good lever for thinking
about how you can make these inertia things change,
or even find a way of quantifying it.
But what I would say is that, if you approach
this problem as an optimal control,
you can add additional constraints.
So for example, one constraint could be that instead of LJT
as I've formulated it, LJT itself
has to be a step function.
So it can jump down, but it cannot go down.
So it can jump down, and it has to remain steady for a while.
So those might be easier to implement, easier to explain.
So there are various ways in which you
can add additional constraints.
And at least our numerical algorithm
would work quite well here.
But again, if you want to increase the number of state
variables, then you might run into other numerical problems.
All right, another question from the audience.
Can you comment on policies for different geographic regions,
and possibly urban versus rural?
Great question also.
So the rho, which is the social interaction component,
is most likely very, very different
in urban versus rural area.
So the evidence so far from cross country and cross
counties that rural areas are generally doing well.
Better, well is not the right word.
Doing better because even without lock downs,
there aren't as many interactions.
If you don't have a public transport
system like New York or Massachusetts or London,
but even if you don't do any lock downs,
you're not going to get as many infections.
So those would immediately translate into very different
lock down policies.
In addition to, as I've pointed out, ICU capacity.
There is also a debate as to whether the beta parameter,
which is the infection rate conditional on contact,
is a function of geography.
Like for example, heat, the way that
droplets travel, and what--
the way that the virus is transmitted
may depend on other external circumstances.
But it's very, very poorly understood at the moment,
I would say.
Daron, we're getting close to the top of the hour.
So let me ask you a couple of broader questions.
What do you think MIT should do?
What does this policy--
how should we interpret the results
from this policy in the MIT context?
Well, I mean, I think MIT is a very different community.
So there are many more things that we can do as a community
that Massachusetts or New York can not do.
First of all, our students live together.
Live in confined places.
But they have less interaction with the broader
We are also a very well-educated group,
which we have great health care resources.
I would imagine-- I would trust that MIT students are socially
So they would behave in ways that, perhaps,
the average American would be harder
to convince them to behave in ways
that are more self-regarding.
And we can reorganize dorm, for example, so and others
are working on--
or the possibility of organizing students
in ways that you can minimize infections and do
I think all of those are things that we have to consider.
Well, the question that comes down to the following, OK?
We can all be extremely risk averse and say,
not on our turf.
And some governors may say that.
But of course, the cost of that is exactly
like you've hinted at, Windsor and others have hinted at.
The economic costs are very high,
and they also are very unequally distributed.
And if we have to open up to some degree, well,
if MIT cannot manage the opening up,
then how can high schools or elementary schools can?
So I think we are in a much, much better position in terms
of having a very well educated, very conscientious population.
Very predictable behavior in many ways.
And also we have great health care resources.
So I think there are a lot of things that we can do.
And again, this is something that resources--
intellectual resources from many disciplines
can help us navigate much better.
What is your most positive optimistic outlook
for the rest of the year?
I don't know, that's really hard.
I mean, I think I am really worried that the policy
failures in the US are going to continue.
And if they do, I fear that infections
being down where they are in places like Massachusetts
or California may not last.
And certainly, there are very different behaviors
across different states.
So there are a lot of concerns that would keep me up at night.
If I weren't so tired during the day.
Daron, thank you for being with us
and for sharing this amazing work with us.
I'm sure that many of the students in the audience
are inspired, and will love to continue to support and expand
But I would love to get additional questions
from anybody who's interested.
Thank you for hosting me.