(gentle music)
-[Viral Acharya] Good morning, everyone,
or rather good afternoon.
Welcome back to the
faculty insight series.
Today we have with us
Professor Thomas Philippon
from the Department of Finance.
He's going to talk to us
about optimal strategies
to mitigate pandemic.
Professor Philippon has been right
at the forefront of this research.
Within a very short period of time,
he has quickly identified how to use
some of the epidemiological
models and merge them
with some of the important
economic frameworks,
in order to get at some of the issues
of optimal mitigation strategies.
I would also like to put a plug in,
for Thomas' excellent book
that has recently come out.
It's called 'The Great Reversal'
and he talks about how free
markets in the United States
have likely given way
to greater concentration
and perhaps economic
rents for the incumbents.
He does it by contrasting
the American outcomes
to those in Europe.
It's a highly thought provoking book,
and I recommend all of you to
look at it in your free time.
Over to you, Thomas
we can take questions after
your presentation is done.
I'll curate them for you so
you don't have to worry about
the Q&A of the chat room.
- [Thomas Philippon] Well, thank
you all for being here.
I hope everybody is safe.
This is a joint talk with Callum Jones,
who is our former students and
now at the board of governor
in Washington, and Venky,
who is our colleague
in the econ department.
So as we already mentioned,
the motivation for us was
really to think about the way
of integrating the
standard model of epidemic
into a standard model of macro.
And thereason that
I think it's important
because the standard model of epidemic
allows you to keep track
of this in theory of how
the epidemic is evolving,
but it does not allow you to think
about the tradeoff between,
you know, economic and health outcomes.
So that's what we want to do.
So we want to do it in
a standard macro model
where people choose their
consumption and labor supply.
But of course, the key thing
is they understand there's an
epidemic going on therefore,
they understand that some consumption
and going to work and be
risky in terms of infections.
So what they can do is they can stay home.
That is they can reduce the purchase
of some goods and services,
they can stop traveling, they
can stop going to the store
at least not as often.
In terms of labor supply,
they can work from home, as well.
So we show that this is
actually an important factor.
And then the thing we
want to understand is,
first, what are people
going to do by themself?
And then the question is, Is that enough?
And if not, why, how
big is the gap between
what would be socially desirable
and what people would do by themself?
So when characterize the
private and social incentives,
and then we show that
the social incentives
are much stronger, and
much more front-loaded,
in fact, we can even find cases where,
the price incentives are perverse.
And then we'll calibrate
the model to get a sense
of how steep the trade-off is,
because that depends a
lot on the parameters.
So I'll get to that in one second.
But we find that the
private sector by itself
would have engineered the recession
of something like five or 10%
While, but they would have been
actually a very bad outcome
because the hospital system
would have collapsed.
And in fact, if you wanted to avoid that,
you had to push on the brake,
much earlier and more strongly.
And so the planner solution calls for,
a slowdown in economic activity
of something like 20 or 30%.
So, something like two or three times
more than the private sector.
So, let's try to
understand what's going on.
Okay, so the middle is two parts
or the paper has two parts.
One is the epidemic part the
other one is the macro part.
So the epidemic part is literally
the textbook, epidemic 101.
The simplest model you can
imagine, to model an epidemic.
Okay, so it's SIR, that's
the name of the model.
And it's, we just add a few things,
such as we try to distinguish
between people who are sick
and not sick among
people who are infected.
And then we'll talk about
congestion in healthcare later.
The first part of that
is the standard model.
So you can be susceptible
infected, or you can be neither,
which means that either you've recovered
from the infection or you've
died from your infection.
So the last two, recovered and dead states
once you get there,
there is no going back.
In this calibration, a
very critical question
for policymaker is whether
R is in the absorbing state
whether that we don't know yet.
But here I'm gonna assume it is.
So I'm assuming that
if you've been exposed
and you've recovered, then you
are not susceptible anymore.
Okay, so then the pool
of susceptible people
initially you can think
of it as it's everybody,
or mostly everybody or perhaps
everybody who is not a child.
So you could think of the
susceptible population as like
population between age 10
and you know, with no limits.
I think in the minor,
we're not going to make this
kind of subtle distinction.
So we're gonna imagine a situation where,
essentially everybody is susceptible
at time zero.
And then the number of
susceptible people goes down
as the number of infection goes up.
So the number of infections
is given this function,
beta e I S/N. So what is this?
So that's like a random matching model
with quadratic matching function,
which really means that it captures
the idea of random interactions,
not direct themselves.
So yes, it has four pieces.
Beta, it's a parameter that
is specific to the virus.
It's how easy is the
transmission conditional
on a given contact.
So for beta for us is essential parameter
that nothing can change.
What you can change is
e, which is the exposure.
You should stay home, if you wear a mask,
if you wash your hands all the time,
you're gonna lower e.
In the baseline SIR model, e is fixed.
It's like a number of people take.
Of course, in economics, the
whole idea is e is endogenous,
that's gonna be the key variable
that we want to understand.
So beta e is like infection rate
times the density of interaction,
and then you multiply by
the other matching part,
which is the number of
people who has infected, It.
So each infected, you can
think of it as everybody
who is infected.
So anybody who is in a category, It
is gonna meet e t people per unit of time.
So, et It, is the number
of meeting that involves
one of these infected people.
Now, some of the meetings
are gonna be with other infected people,
or with recovered people, in
which case nothing happens.
It's only the meetings that take place
with susceptible people
that can lead to an infection.
So therefore, you want to multiply, et It
by the share of infected
people in the population,
which is S/N,
N is just the number of
people at the very beginning.
So N is initial population.
S/N is the fraction of susceptible.
Okay so therefore, et It St/N,
is the density of meetings
between somebody infected and
somebody who is susceptible.
And then you multiply by beta,
which is transmission rate
conditional on the contact
and then you get the
number of new infections.
Okay, so that's the baseline model.
Notice here that it's
pure, it's perfect meeting,
so we don't assume that there's
different groups of people,
all of that could be extended
to multisector or multigroups.
But this is the simplest model.
The number of infected of
course goes the other way.
So, level infected today is the number
of infected yesterday,
plus the new infections that we saw
beta eIS/N, minus people
who leave the state,
the infected state
either because you recover,
that's gamma times I.
So gamma is the recover rate.
So we're gonna calibrate all
that at the weekly frequency.
So gamma is literally is the likelihood
that if you're infected today,
the likely that you're recover next week.
And to give you a sense, gamma
is of the order of one third.
And then, you have people who died.
So here we gonna distinguish among people
who are infected people who are sick.
Usually, that's the
cases that people report,
you know, like, a big
discussion was people
who are not symptomatic.
So you can think of one minus kappa I,
are the symptomatic ones,
and Kappa I, are the people who are sick.
And then delta is the death
rate condition on being sick.
Okay, so delta kappa is
going to be connected
to the case fatality rate,
which is the likelihood
of dying controlling
an active case, or detected case.
Delta kappa would be the
infection fertility rate,
which is conditional on being infected.
Okay, and then recover then,
and above that, of course,
they just accumulate
these functions, right?
That's the basic math.
So, from this model, you get
this kind of impulse responses.
So suppose you start with initially
0.1% of the population affected.
Okay, so Io/N times zero is 0.3
you see there was a tiny bit of infection.
It's not always, I mean,
0.1 is not a tiny bit.
It's like a significant number already.
Okay, so what happens when initially,
if you go back to my question,
when S is very close to one initially,
then this equation tells you that,
S declines exponentially
and I grows exponentially.
So the first thing that's
gonna happen is that,
the number of infected
starts to grow exponentially.
This literally is an exponential.
At some point, so this
is a stock of people
who are currently infected,
the stock of all the past infection,
minus people who have recovered or died.
And the number of new infected
so that the new infected.
In that the number of new
people who are infected
in that week, so it's only two weeks.
That takes up to 20
weeks in this calibration
and where 6% of the population
that's the fraction of
new new cases, Okay.
Now what happens here?
What happens here is that the
number of susceptible people
which is on the left here,
has dropped enough that the
number of new cases is lower.
Okay and if you think about
the math is pretty easy.
When S is equal to 1/R
where R is the basic reproduction number.
Then that's when you get
to pick of that curve.
So I think that
calibration was for Ro of 2
so therefore, you get
how herd immunity here,
when S is 1 1/2 roughly.
Okay, that's what happens.
Around week 20, only half of
the population is susceptible.
Therefore, you get this equation.
The number of new cases is
gonna become flat, Okay?
And then it's going to
start decreasing, Okay.
And then this is the number of people who,
that's the total number of
people who died in that line.
This last thing here is
the case mortality rate.
So this is, see this hump here,
it's because we're gonna assume,
this is like Italy if you want.
This is actually this
is literally calibrated
on Italian data.
This big spike here is
because this is what happens
if the hospitals get overrun.
So in the basic model, you
would set delta to a constant.
So that line would be totally flat,
it would be literally kappa
delta over rho kappa delta,
that would be just a flat line.
But if you think that delta is higher,
when hospitals are overrun,
then that's going to create
a higher fatality rate.
Because people are not treated properly.
And that's gonna be,
that increase that spike
is going to be higher
if the stock of infected
people is very high, okay?
Because then you don't have the capacity,
you don't have the number of ICU beds,
you don't have the number of ventilators.
So flattening the curve is useful
because you're going to
lower this spike here.
Okay, so that's the baseline.
Okay, so the first thing I want to do
is to show you the big issue,
which is the Parameter Uncertainty.
Okay, so the key parameter in this model
are beta, kappa, delta, gamma.
Beta is the transmission
rate of the virus.
Kappa is the number of
people who show symptoms.
So that's very ambiguous
because you have mild
symptoms, full symptoms,
I think for a normal model
you always think of Kappa
as people who have symptoms that are,
of course, people who need
to go to the hospital,
that's very clear that these
are very strong symptoms,
but also people who are really sick
that they feel like it's
very more than the flu,
I would call them as kappa.
So that's an important
number because in the data
some time we measure the symbol beta.
Delta is the death rate condition
on adding some symptoms.
So delta kappa is the
risk of dying conditional
on being infected today.
And gamma is the recovery rate.
Now gamma is actually the
one that's not too hard
to find the data,
I think the range of estimates for gamma
is much smaller than for
the other parameters.
Because once a case is diagnosed,
you can see you know, how
long it takes to recover.
And you know, that
number, there is a range,
but the range is relatively small.
So I think something like
one third per a week,
most people recover free,
if you're gonna recover,
you're gonna be recovered
within two or three weeks.
I think that seems to cover
all the reasonable cases.
The thing that's completely hard
to estimate is delta and beta, Okay.
So the infection fatality rate,
which is the one of the
key headline numbers,
is the risk of dying
conditional on the infected.
So for me, it would be
delta kappa over delta kappa plus gamma.
So, gamma is the thing that
pushes you the other way,
which is the recover rate.
Okay, so this is literally,
the fraction of people
who end up dying condition
of being infected today.
That number is very hard to estimate, why?
Because we don't know the
number of infected people.
Similarly, the basic reproduction number,
so when you when you hear
about Ro in the literature.
Ro is how many, what's
the number of people
that somebody who is infected today
would contaminate over
his or her lifetime,
if that person lived in a population
where everybody is susceptible?
So all you have to do is
to count how many people
they gonna meet,
and then they're gonna
transmit until they recover.
So that number would be beta
over gamma plus delta kappa,
that's the basic reproduction number.
Now initially, when we wrote
the first version of the paper
based on the data we found
from China and Italy,
we saw that the right number was that,
the infection fatality rate IFR was 1%
and that R was around two.
This was sort of the common
wisdom the way we read it
around like a month ago.
Today we know it's not true,
we know that the numbers are different.
And thatÕs good
news to some extent,
the best estimate we have
of the infection fatality rate is 0.5%.
So it's it's half of what we thought,
but Ro is much higher than we thought.
We thought it was around
two, in fact, it's 3.3.
So these are the numbers I'm gonna use
are from this disease study
in France by Institute Pasteur
where they calibrated
the model on French data,
city by city and also
together with the, you know,
the famous cruise ship where
everybody got sick and tested.
So that gives you enough
information to pin down
the history of range of
estimates, of course,
but much, much more precise estimation,
but we didn't know that at the time.
And so why is it so hard to
find out? So here's one thing.
So here, I'm showing you two infections.
We start with a very
low number of infection,
but I'm putting in two
different things one is,
so the red line, is the
the one that we thought
was the reasonable one a month ago.
So it's based on Ro of
two and an IFR of 1%.
So Ro are basic
reproduction number of two,
that means one person,
if you put one sick
person in a population,
she's gonna transmit to two
people in addition to her
before recovering, that's Ro of two.
IFR of 1% that means
condition of being infected
one person or people will die.
That's the calibration
we had two months ago.
Today, as I argued, the new numbers
point out that we should
really have Ro of 3.3
and IFRS of 0.5%
Can you tell them about?
Well, of course, if
you can test you would.
But if you can't test, then
you can't compute the first one
because the infection person
you don't know who is who is infected.
You're infected even less
susceptible you don't know
because you don't test.
So all you can can properly
are the really critical cases
or the number of death.
But look at these two curves,
see the red and the blue,
they are on top of each other
for the first four weeks.
So there is no way by looking at this data
to tell whether you are in the, you know,
very like quick condition
but not very deadly
or slow condition but very deadly,
because they're going to produce
the same number of
deaths at the beginning.
After a while, they're
going to start to divert.
Okay, so in the short term,
it's going to look like that.
In the medium term, if you have a high R,
it's like time is going
super fast, because you know,
the thing is spreading
so much more quickly.
If Ro is 3.3 and two, that
it's gonna peak much earlier.
In fact, the blue scenario
peaks after 10 weeks.
And the number of susceptible people
eventually drops to it's not exactly zero,
but it's very close to zero.
Why? Because so herd immunity
happens when SR is less than one.
So if Ro is 3.3, then that would
happen when S is one third.
So you can see here it
takes around 10 weeks,
around 10 weeks, S is around one third.
Okay, but then of course,
it keeps going a little bit.
So eventually, essentially, if Ro is 3.3,
and there is no intervention,
eventually everybody has
been exposed, pretty much,
which means that the death rate in a model
is gonna exactly 0.5%.
Now the red curve takes a
lot more time to play out.
Now, you would think, it
looks like the blue is worse.
But that's not true.
Because in the long term, of
course, the red line is worse
because he has a higher death rate.
So eventually the number of
people dying is much higher
in the orange curve.
So in fact, the orange is the most
scary scenario it plays out.
So, that's the one that I think
most policy makers had in mind
which is something which
is it might not spread
very quickly,
but it looks like it's very dead.
I think what happened is
we vastly underestimated
the number of people infected.
So we are, I believe we are
a bit more in the blue world
than in the red world.
All right, so that's kinda of,
but to do for you it's very hard to know
when you start, what are
the right parameters?
So now, I want to understand,
faced with this kind of risk,
how would a society react?
So I'm gonna bring in,
so now I'm gonna simulate
and the other numbers
that I believe are correct
based on today's data,
which is the number from France
or from the Institute Pasteur of study,
case of IFRS 0.5% and Ro of 3.3.
And then we're going
to calibrate something
on the case study to rate
when the hospitals don't get overrun,
that captures Italian data
and that's going to be a bit pessimistic
and it is this calibration
does not reflect
what would happen in the US
but it's gonna give just,
qualitatively it's the same of course
and it's gonna give you a
good sense of what's going on.
Okay, so what is our model,
well our model starts
from the baseline SIR.
So literally the SIR block is the same,
but then we add a model of behavior.
And the model of behavior
is straight macro.
So it's an optimizing
agent who looks ahead
and thinks about consumption and labor.
Okay, so maximizing utility is
connected to the upward row,
So here just to be clear,
we're going to assume
that there is a chance of having a vaccine
and no cure at the same time.
And if that happens, then
you go back to steady state.
So then this parameter row,
the discount factor is
actually gonna be very high,
it's gonna be something
like 25% or 20% per year,
because you pricing the
fact that there's a,
you know, 20 or 25% chance
that you're going to get a cure
in a vaccine per year, okay?
So it's going to be a bit
higher than the usual role
we have in mind.
Okay, and then the utility
is people like to consume
they don't like to, they enjoy leisure.
And then the key thing of
course, is they take into account
that there is a risk of
death and a risk of sickness.
So, if you are sick, so remember
Kappa I, people are sick,
and then you have a dis
utility of sickness Uk.
And if somebody in the household dies,
there is a dis utility Ud.
And this, 1 - d - Ki,
These are people who are healthy
therefore they can they
can work and consume.
So that captures is the cost of disease,
the cost of sickness
maybe also the fact that
it seems maybe if you if
you've been seriously sick,
there might be some
dominant effect actually,
the some data suggests that you're going
to recover the math,
common and damage.
So that would be like in the Uk parameter
and then the Ud parameter,
literally that's the statistical value
of life but that of course includes
the psychological cost
born by people who survive,
so that's gonna be a large number.
And then people will decide to work.
So there is a labor
supply only for one sick
and then we're going to assume
that there's a work-from-home.
So that is work-from-home
for us is a technology
that allows you to keep working
while not being exposed.
But it's going to be subject
to learning by doing,
which is the first week
is gonna be a disaster.
And then after a couple of weeks,
you gonna figure out how
to take care of the kids.
So my kids now are on their
computer all day so I can work.
And the school has become much better
at giving them you know,
instruction that they
can follow by themselves.
The parents don't have to be always behind
them to monitor them.
So this we think of learning by doing,
for businesses of course is figuring out
what can safely be done remotely,
like you know, investing
in the right software
for the conferences,
investing in the right.
I think a lot of it is safety
because many businesses who
run critical infrastructure,
they don't have the same
level of cyber protections
when people work-from-home.
So, they need to invest to ramp up their,
you know, IT system so,
people can work from home safely
in the sense of cyber risk.
All of these for me,
I think of it as learning
by doing which is,
initially it's a bloody mess,
but after a while people
figure out how to do it.
Okay, and then the key
thing is exposure et,
right at the end.
So, in the basic epidemic model
et, is a number or parameter
in the macro model et, is
the outcome of choices.
So, people choose how much to
consume and how much to work
and they understand there
is an exposure effect it.
So here et, is the sum of three parts:
one is social interaction,
not related to work, then
there is shopping, traveling,
so, consumption of goods and services.
And then those working Okay,
and then working is mitigated
if you work from home.
So m, is the mitigation from
working from home, Okay.
And that's it, and learning
by doing remodeling
the standard way,
which is the productivity
loss when you work from home
goes down when you practice.
Okay, so the math is
broadly straightforward.
And then we can simulate
the solution of the model.
So let me skip the calibration.
The numbers, the cleanup,
the range of these numbers,
where we don't know is the
parameter of infection.
Even surprising enough,
even the macro is actually
not that hard to get.
You get data on, what kind of up
or drop we see in China, in Europe,
it's very easy to get the right ballpark.
So I don't think there's that much
uncertainty about the lockdown.
But the biggest uncertainty
is about the parameter
that I showed you earlier.
So now am solving the model,
in the case of the
parameter that are today,
the ones that I think are correct.
So that's Ro of 3.3.
So what people do,
so blue is under the
exogenous infection model.
So that's the model that
people don't understand
that their behavior affect
their risk of infection
or they do, but it has no impact.
Okay, so that's the exogenous infection.
So now exogenous infection.
Nothing, their behavior
has doesn't change.
You can see exposure e, is blue is one.
So that literally would simulate
the model we saw earlier.
The tiny bit of change of labor suppliers
is because when somebody's sick,
people who are not sick
are gonna work harder to compensate.
That's why you have this
tiny bit of change here,
but they don't do it because they want
to change the infection
just do it because they want to make up
for the lost income
from people who are sick
that's this tiny change here,
but the exposure doesn't
change for the SIR dynamics
are exactly the one we saw earlier.
Now, if you don't have work
from home, this is the output.
The output would drop by about like 20%.
Because people would stop going
to work to a large extent,
and they would cut their
consumption to eliminate exposure.
So you would have a private recession
of something between 10 and 20%.
If you have working from home,
then what it does, is the
recession gets much milder, why?
Because you can cut your
exposure while still working,
it's still not as efficient.
So there's still a drop in output,
but it's much better
than not doing anything.
And so that allows you
to limit the drop in GDP,
and at the same time, decrease
your exposure more, Okay.
So that's what happens to the
exposure, that's the labor,
this is the working from home,
see the people working from home
peaks together with a crisis.
I'll show you something more
about the parameter because
I will get back to that
So, what's the impact?
Well, it bothers, right?
So the blue is the exogenous model,
and then the yellow here if you want
is the private residence
the private residence here cuts down
the number of infections quite a lot,
actually almost by half.
And the outcome is at the end of the day,
the number of people who end up dying
is maybe something like half
of what would have happened
if people didn't react
by themselves, Okay.
The problem is that the peak
infection is still very high.
Now these numbers are more
calibrated for like a big,
like infection that
starts relatively high.
So it's something you realize a bit late.
So that's more like for Italy.
Let's say that, at the
peak you have a maybe
20% of the population who is infected
and that means that even if not everybody
gets sick, of course.
There's enough people who are
sick and needs critical care
that the hospital get overrun
and you see the big spike
in the number of people dying,
because they don't get the care.
So the death rate is
higher than it would be.
That's because of the
congestion escalating
in healthcare system.
So, bottom line, people would do something
there would be a recession in any case,
but it will not be enough to
protect the healthcare system.
So now, what will the planner do,
the planner would do
something a bit similar
from private agents,
but he would do it more
quickly and more strongly.
So the planner, so the blue
is still the exogenous case,
but now, red and yellow are
the same exact technologies
so you have worked from
home technology or not,
but it's all from the
trustee of the planner.
So what you see, the
planner pushes on the brake,
much more strongly.
So now the recession is between,
instead of being around 10 to 15%
now it's between 20 and 40%.
Okay, so without work from home,
the planner would have to split
on the economy to like 40%.
With a work on from home,
it only slows down by about,
you know, 25%.
People in fact, in this economy,
many people actually work harder,
because working from home
is not that efficient.
And so to compensate,
you actually work more.
So the level of supply at home
is actually going up a lot,
total level of supply is still
going down because, you know,
people simply some just cannot work.
So of course, if you don't have the option
of working from home,
that's gonna drop,
but depend on users
working from home a lot,
because it knows that it's a
way of protecting the economy
and also it starts very early.
So the planner does what we did at NYU.
I think many universities
do the same, you know,
like the week before, spring break.
In fact, we started
teaching online with Zoom
even though we do didn't have to,
because we wanted to, you know
be ready for after the break
to be able to teach
right, we wanted to see
figure out the bugs early on.
This exactly is what I
mean by learning by doing.
And the planner does that,
the planner starts working
from home very early,
even though at the beginning
the peak infection is not there.
So, the gain in terms of
slowing down infection
is not that high at the beginning,
but the planner does start early,
because he wants to be ready,
for when the peak infection comes
and be efficient at working from home.
And then in terms of outcome,
the planner reduces the
number of people who end up
dying by another factor of two compared
to the private sector.
That can be that depends
on the parameters.
But roughly speaking, you
can think of it as you know,
if people didn't do anything,
the death rate would be very high.
Private response would cut that in half.
The planner would cut
that by another factor
of three or four or five,
depending on the exact parameters, Okay.
So that's the that's the key thing.
Now, why is that the
private sector response
is not strong enough?
Well, so, there are a
couple of key features.
The first one is, if you
think about the SIR model,
from the perspective of one
household, you take as given,
the key is that you take as given
what all are those people do?
So, when you think
about your own behavior,
you think about your own
the impact of your behavior,
on your risk of infection.
That's only half of the problem, Okay.
'cause the other half is
not you getting infected
but you infecting others.
So, literally if you have a
random matching search model
with a chaotic search.
Literally the planner has a multiplier
which is twice the private sector
because one thing with
relative aspect to one term,
but the planned takes
relative to the damn square.
So it's gonna be a two there.
So the planner is gonna have two
in all of its first order condition,
and on top of it the
planner is gonna be thinking
about the value of infection
over time quite differently
from the private sector,
and this is one, on the illustrate here.
So when you solve them in the background,
you have a bunch of value functions,
the value of being
susceptible S an infected I,
Okay, relative to recover.
So for these are negative
because it's better to recover.
But this is how they evolve.
On the left you have the equilibrium,
on the right you have the planner,
So what's so the equilibrium
Vi, is a straight line here.
This is actually always true.
This depends a tiny bit
on some of the small
details of preferences
but by and large, the i, is flat
as long as as the hospital
system is not overrun.
Because if the if the hospital
system is working properly,
then the risk of dying does not depend
on anything else people do.
So the value of being infected
is essentially constant over time.
That's what you see this
red line being constant.
What's the value of being susceptible?
Well, initially, it's zero here,
which means it's the same as
the value of being recovered
if there is no infection,
because if there is no infection,
there is no difference between S and R
'cause there is no risk.
The perverse thing is you see,
infection start at beyond one here.
So initially Vs, drops the private sector.
Vi doesn't change.
Because the risk you bear from
being infected doesn't change
whether as long as the
hospital system works on
you see that's a flat line anyway.
So the blue drops, the red doesn't move.
The blue minus the red shrinks,
but the blue minus the red
is exactly your incentive
to be prudent, right?
Because the incentive to be prudent for,
a bright private individual
is the blue minus red.
That's exactly what gives you incentive
to limit your exposure.
So what's very bad here?
It starts by going down.
And that's exactly the wrong thing, right?
It's going down, it would have
less incentive prudent initially,
and in fact, the worse the
epidemic, the less, why is it?
Well, it's because if
you think about your,
behavior as a private agent,
if the epidemic is bad,
and there is a high chance
you're gonna be infected
anyway, why bother?
Right? If the question is,
you gonna be infected today or tomorrow
or at some point, there
is not much difference
between being infected today
or being infected six months.
Okay, if the if you think eventually
you're gonna to be infected,
the reason to be careful are very small,
because you're going to
get it at some point.
Okay, so that's why you see
the blue curve going down.
And that's why the incentive
to be prudent are lower.
What about the planner,
when the planner agrees
that the blue curve goes down,
obviously, that's has to be true.
But the planner in the
first as you can see,
the red curve drops a lot, why is that?
Because the planner
computer for the planner,
this is the value of
somebody being infected.
That's the sum of this
one, which is the value,
because if I'm infected, I
can get sick or I can die.
But the planner adds to that,
the fact that if I'm sick,
if I'm infected, I can
infect other people.
So from the planner's
perspective, this drops a lot.
So the planner, in fact, blue
minus red goes up initially.
Okay, so the key thing here is that,
blue minus red goes down
for the private sector
but it goes up for the planner on impact.
Which means that if
you think about the gap
between what people
would do by themselves,
and what the planet would like them to do,
that gap, is going to be maximum
early on in the epidemic.
That's where there's a maximum tension
between what people want to do
and what the government
want would like them to do.
So all the particular economy issue,
all the issue of convincing
people to do the right thing.
It's all going to be very
acute at the beginning.
Now, there's even a case,
now to this the top line,
the top figures is when the
case where there is no risk
of the hospital being overrun.
Now, what if, okay, that's not realistic.
So what if we bring the Italian risk,
the risk that the health
care becomes overrun?
Does that help? No.
In fact, in this calibration,
it has the ultimate progress effect.
You see, it's still the
case that blue drops a lot.
So the key thing here,
you see is that the blue is below the red.
Now that's not a bug, it's actually true.
Why is that? Well, that's the
ultimate progress incentive,
which is if you think the hospital system
is gonna be overrun
in a few weeks, then in fact,
it might be a good idea to get sick today.
Because if you get sick today,
you're gonna be sick
before the critical mass
and therefore, you're
gonna get better care.
So in fact, in that case,
the private agent have
the opposite incentive.
There is no need to become sick quickly.
But that doesn't last of course,
because once the once
the hospital is overrun,
becomes very risky.
But that's to show you that, again,
what you see is this very
acute tension early on
within the planner and
the private outcome.
The planner, reacts the
way you would think,
which is if he knows the system,
the hospital system is fragile,
then he's gonna freak out
and Vi, is gonna drop even more.
And he's gonna have even more incentive
to impose a lockdown.
Okay all right that's it,
that's what I wanted to show you
just the key things are,
uncertain about the parameters
of the disease is that
to foster the issue.
That's why testing is so important.
Second thing is private
incentives are too weak,
and also the timing is wrong.
So you want to,
there's a need for a strong
intervention by the government.
The numbers that come out of the model,
if you're getting it right naturally,
are exactly in line with
what we've seen the data,
which is private response
into the range of five to 10%.
Optimal slowdown of the economy
in the range of, you know,
something like 30%,
which is pretty much what
we seen in Europe today.
Now, what about going forward?
The thing that's important is
that, this maximum tension,
where people don't have
private right incentive,
it gets better over time.
When the pool of infected
people is higher,
the risk is more present.
It's still true that the
planner would like people
to be more careful than
they would by themself.
But the tension is diminished.
So you can hope that the
exit from the lockdown
can be much more decentralized
than the lockdown itself,
because it's not the case
that you can fully trust
what private planner would do,
but you can trust them
to a much larger extent
than in the initial phase.
Thank you.
- That's great.
Thank you Thomas for a very
clear and excellent exposition
of such a nice building block to analyze
the optimal mitigation strategies.
Let me start with a
question by Yakov Amihud,
our colleague from the finance department.
Yakov's suggestion is that,
one can model the rising fatality rate
when hospitals are overburdened.
He refers to the models of
Carlo Favero at Bocconi,
who's calibrated it to Italian data.
The model is that there's
a constant fatality rate up
to the hospitals capacity
and rising rate thereafter.
- Yeah, that's
exactly what we do.
That's we use is we use his
numbers and his calibration.
- Okay, thank you
for clarifying that Thomas.
The next question is from David Yermack
And he's asking if you have compared
the recent hospital experience
in New York City and New Jersey
to what has happened in Italy
just in terms of anecdotal data modeling.
- So I saw
some people doing that.
And clearly in the hospital,
it doesn't look as bad.
It doesn't look like as of
now, as far as I can tell,
it doesn't look like the
congestion in hospital
and therefore the excess mortality rate
is as bad in the US or in any country
as it was in Italy or
Spain to some extent.
But there's a lot of disagreement exactly
ow to interpret the data.
So I think we, like countries we bought.
So, who gets to the hospital
versus who stays home?
It will feel important is
the Italian data is actually
the reports are conservative
the way they report.
So they count people who die at home,
people who die in hospital
and people who die in
retirement hospitals.
So the number would go
high because of that.
So if you want to do an
accurate to upper comparison,
you would really need to
add also non hospital deaths
and countries don't do it in the same way.
But I think my sense is even
if you do this adjustment,
it was still be much worse
in Italy than in the US.
- Thank you, Thomas.
There's a question again,
on the data itself from Larry White.
He's asking you to spell
out a little bit more
the fatality rate assumption that you have
for the reported cases for the US.
His quick calculation is that around
1 million infected in the US so far
with around 50,000 deaths,
and so he's estimating the
fatality rate to be 5%.
- Now, so the
number we use is 0.5%.
So that's conditional on being infected,
the likelihood that somebody would die.
But that takes into account
the fact that many people
who are infected don't know it.
So that's the critical thing
is sense that you can sort of count
number of the deaths right but you have,
very noisy estimate of people infected.
So in the US, I think the
number of were infected
is a guess.
So that's why the only
the data for that we use
from other countries.
The countries that have
more systematic testing.
- Let me let me
throw in one question
from my side Thomas, yes,
- Let me point at
this in the data the people
report two very different
number, CFR and IFR.
CFS is case fatality rate,
that is given that the
case identified as COVID,
what's the fraction of
people who end up dying?
And then IFR is out of the
total people who are infected.
The IFR, you never observe
you have to get it from,
you have to infer it.
CFR is based on actual cases.
So that's much higher, obviously.
So CFR it's probably, yeah, that much.
I mean, conditional on
going to the hospital,
the number of people dying
is probably like 10 or 20%.
Condition being either sick.
It's maybe two and a half percent.
Conditional being infected.
It's only half a percent, Okay.
- Yeah, and to just clarify
what Thomas just explained,
I think we have friends who are infected,
but we're not in the statistics.
And I think that's what
Thomas is referring to.
They're not in the cases
that are officially reported,
but we know that they have COVID symptoms
and they wouldn't be counted
in infection rate calculations.
Let me jump to a slightly
different question.
You hinted towards this at the beginning,
which is and Larry White
has also touched upon it,
So, clearly some of the parameters
such as the risk of fatality
upon being infected is highly different
based on very well
separable groups of people
say by age, for example,
this also relates to
those who are contributing
the most to economic activity
in terms of world contributions.
Of course, the elderly
might also be consuming
and therefore contributing
to economic activity.
So, have you thought about how one would
sort of rewrite these models
and what sort of externalities might arise
because some work that I
received just two days back
from Adriano Rampini was
essentially recommending
based on this observation that you know,
something like a separated lockdown
where you essentially have
elderly being quarantined,
and the younger being able
to work at their offices
may actually achieve
the efficient trade off.
And it's actually even efficient
from the standpoint of economic activity
as well as from the standpoint
of spreading of the disease.
- Yeah, so I
think that two different
question one is,
is it the case that any
optimal solution would involve
differentiated solution
by age or health studies?
I think that's the answer is yes,
there is absolutely no doubt
'cause there's so much heterogeneity
in the health risk between.
It's so nonlinear with age
that it's obvious that,
there is no sensible solution
that does not involve
discrimination along the age dimension.
I think that's kinda of obvious.
Now, then, whether it's strong enough
that there is a subset of
the population for whom
the private incentives
would be pretty much
aligned with the social incentive.
That depends all on the parameters.
You know, it's not impossible.
It's clearly possible for
people who are recovered.
So that's why there's
this issue of, you know,
if you know, you've been
exposed and you recover,
then you can get sick and
you can transmit that then,
in theory, you have zero externalities.
So you should have, you should just do
whatever is good for you.
I think that the, in Sweden for instance,
they have locked down the economy.
And they've advised I think,
older people to stay home
but it's not compulsory.
To to me the tricky
question there is really,
it is optimal, for sure to discriminate
along the age dimension.
And the big question is,
should that be a requirement or an advice?
I think that's a tricky question.
I find quite, I don't
know, I think it would be.
It would seem a little
bit too paternalistic
or too extreme for me that the world
would require older people to stay home.
You could advise.
Plus, if you think about it also,
older people, they are not the one
with the strongest externality
because they are very at risk.
And we're not so much,
we are worried about younger
people infecting older people,
well not so much the other way.
So, older people I don't think
that their externalities is very high.
So the case for making
something compulsory
for them is weaker.
The case for making compulsory
changes to younger people,
so they don't, infect the older ones
that one in that case is much stronger.
- Thank you Thomas,
Let me ask one other question.
You touched upon the model
uncertainty part of you know
how uncertain these parameters are,
and that seems sort of
really challenging issue,
even from a personal experience.
So clearly, having gone through,
say most individuals who have gone
through this over the
last two, three months,
have themselves been updating
their priors on, you know,
what they see as the spread of the disease
in their immediate vicinity.
You know, you look up the numbers
at the CDC or any other website.
One question I have is, could you,
is it possible that with some
sort of adaptive expectations
you know, individuals adapting
more to the recent outcomes,
that at certain,
stage of the curve you
actually get a reverse?
You sort of the externality
reverses, so to speak,
which is that precisely when
the curve starts declining,
because the recent past has
actually been pretty bad.
You get a fair bit of reluctance in people
to actually start consuming
and start actually relaxing
the lockdown on their own.
But, as in the early phase,
you have the externality that
that you were just mentioning.
- Yeah, especially so to me
the thing we're working on now
is to try to figure out,
how does the policy look
like under uncertainty?
And then you have two
types of uncertainty,
you have micro uncertainty
and macro uncertainty.
So you have, what will people
do if told them their status?
So in my model, maybe I
should make that clear.
Remember people don't
know, if they are sick
or you can only imagine the small fraction
of people in my world
who got really sick so that they know
that the symptoms they had
could it possibly be the
flu, and then they recover.
Then you can possibly assume these guys
know their status is recovered.
But I think that's a tiny
fraction of the population.
So it doesn't matter.
Most to all the agency
members, they'd have no idea.
They don't know, if they've
been exposed or not.
So I think that's the realistic benchmark.
So it's maximum uncertainty.
Now the question is,
suppose you bring in tests,
then what happens?
Is it good or bad?
Well, if it's a test of
whether you're infected or not.
It's not obviously good,
because people could have
the wrong incentives.
In other words, if you know you've likely
been infected already,
then you might be the one
who should go shopping.
Because you know,
that would not increase
the risk of infection
in the family that much,
'cause you probably have
been infected already.
So if your prior is somebody,
If somebody has been infected
or has a higher chance
because we never know,
then that might be the one
you want to send to the store.
And so in that case, giving
them more precise information
about the status could actually increase
the pool of infected people,
engaged in social interactions.
So now of course, if you can do a test
together with a quarantine mandate,
that's different because
then you don't have a choice,
you would like you do the
test if you come a positive
then you are required to
stay home for two weeks.
So that's kind of, so the
first thing you realize there,
is that a test should be together,
should be attached with some requirement,
because you cannot expect certain people
would make the right choices.
And if you look at countries that do that,
Korea, for instance, that's what they do.
Like if you've been tested positive,
you're required to and
they monitor your activity
and as a huge fine if you if you are found
outside your house
less than two weeks after a positive test.
So they don't trust how other people
who do it because of altruism
but that's probably true,
but I think it's, you know, on top of it,
they put some strong
punishment for not doing it.
Now, so that's the micro uncertainty.
And I think it's true
that exiting the crisis,
I totally agree.
Like we're gonna have
plenty of externalities,
plenty of aggregate demand issues,
local demand, all the
demands and staff like that
and people are gonna be
reluctant to start consuming,
the way they did if they
don't know their true status.
So I think in that case, clearly,
testing could have an impact on,
it would be like reducing uncertainty
and reducing precautionary savings.
So that would be like
a good macro outcome.
To me, the most important
thing with testing though,
is not the micro and suddenly
the macro uncertainty,
is the fact that you don't
know the state of the system.
And even today, we don't know
S in the US we don't know I,
we have some idea that maybe
20% in the in New York City,
but that's very like,
look at this publication,
as strong as they're they are not identic.
So, and as a policymaker,
that's the most important data you need.
So, to me the most valuable
part of having a test is that,
is to estimate the social distancing,
although, the precaution
that actually work.
Like you know, so the key thing would be,
say we'll reopen,
so, we gonna reopen the
school up to some age,
we gonna reopen the public
transport with some requirements,
we gonna tell everybody
has to wear a mask,
we gonna tell people
cannot have lunch together.
Maybe we'll have like 20 of
these policies like that.
And theyÕre all costly and we have no idea
which one has an impact
on the transmission.
So if we want to estimate,
what are the right policies?
Then we need to be able
to map these actions,
these policies into changes
in the infection rate
and you can't do that ,if
you don't have testing.
So to me, the most
important part of this thing
is that it allows you,
to keep track of what's going on,
so you can estimate which
policies are useless
and which ones are useful.
And even more importantly,
you can do risk management
because you need
an early warning.
And if you miscalibrated
your exit from the lockdown,
and then you thought that
masks were very efficient,
maybe they are not or something like that.
Then if you only have data
on the number of bad cases,
like I showed you earlier in the slide,
then that means it's going
to take two or three weeks
before you can before you become aware
that something is going wrong.
That's in three weeks in
this world is a disaster.
So we need testing because you need
to have real time feedback.
So you know that if you're lockdown,
if your exit is too quick,
and it's spreading more
quickly than you thought,
you need to be able to
figure that out in real time.
That I think is that by far
the most important policy or parameter.
-  That's great. Thank you, Thomas.
Unfortunately, we are just out of time.
So I'm not able to take the
last couple of questions
but Dick Berner has prefaced
this question by saying
a great presentation and I
want to say and call to that.
Thank you very much for introducing us
to the sort of very fascinating work
you're doing linking
epidemiological models to economics
and macrofinance work.
Thank you Thomas.
- Thank you.
- Thank you, everyone,
have a good afternoon
and stay safe.
(gentle music)
