 Okay, so I think we're ready to go. If you're ready, I am. I'll just start sharing and Very good. So Welcome everybody to the next ECB COVID-19 webinar today, it's our great pleasure to Welcome Martin Eichenbaum. He's a professor of economics at Northwestern University And he's a leading macroeconomist He has actually Produced already a paper on the pandemic and today he will give a sort of a macroeconomic perspective on the pandemic and I can take questions from you if you use your chat button and I also ask all of you to mute so that there is No background noise and with that over to Martin Thank you very much for the opportunity to speak to you It's a pleasure. This is a joint research project. It's a surgical rebello and the Matthias Travant who is a Young co-author that you should know about if you don't Let me begin to say that Obviously governments were all struggling with understanding the epidemic and trying to manage it and our basic tool I think when we all started off our Epidemiological models which are can be extremely useful and no question about it But there's an important caveat to their use that struck us as as macroeconomist Is that those models don't allow for the interaction between Economic decisions and rates of infection. So for example The epidemic naturally causes a recession as we'll see as people Shop and and work less to reduce the chances of getting infected. But of course The number of people that are working or shopping Influences the rate at which infections spread and those are effects simply not allowed for and in standard models Which can be very rich in other dimensions, but not on this one So in our model the way a macroeconomist thinks about Epidemic has both an aggregate demand effect and an aggregate supply effect So the supply effect is pretty straightforward an epidemic exposes people are working to the virus and People react to that risk very naturally by reducing their labor supply So that's the supply effect if you like, but there's also a demand effect Which is people the epidemic exposes people who are purchasing consumption goods to the virus and they naturally respond to that by Reducing their consumption. So both the supply and demand effects work together to generate a very large and in principle persistent recession Now with that said the there is a classic externality that arises when you think about an infection we call it is an infection externality Which is people are infected with a virus simply don't internalize the effect of their consumption and work decisions On the spread of the virus and I remember speaking to a journalist early on and he said oh, it's like pollution And I said that's exactly right as economists We understand that that externality and most of us are very comfortable with the idea of taxing such an externality So that leads to the question. Okay. Well, which policies should the government pursue to deal with that externality Well, you can break up Classes of policies we thought of and I'll give you obvious extensions that we're working on now The first I would say is simple containment and we model that in a variety of ways, but those are policies that reduce consumption and hours worked in ways that don't condition on People's health status or demographic status or things of that nature. So they're relatively brute force And in our model, you'll see they're effective But they're certainly very costly There's another class of Policies which I'll call smart containment which does treat people differently according to their health status and The way we analyze it. You'll see it's almost Aspirational in the sense that it requires to implement a great deal of a technology which quite frankly we don't have But it's so I really think of it as saying look if you have that technology is dramatically better than simple containment because you could basically Manage to deal with the epidemic without a severe recession and without a large number of deaths So it really says the returns to developing that technology extremely large We're currently working on an extension of the model that I'll talk about today Which allows for type 1 and type 2 errors both in testing for infections and for people that are recovered If there's time we can come back to that at the end Look we're going to use a pretty simple model because we started off on this and that means there's a lot of Important epidemic policy related issues that we're simply not ready to talk about yet. So for example Just plain humanitarian Issues like many people are losing their jobs and they're Constrained in their ability to borrow and for lots of reasons. We want to help them the the Liquidity issues, which of course the Federal Reserve has been quite terrific on and hopefully the ECB as well But I want to stress another thing that a CEO of a major bank and I were talking about and he said the way he thought about The the virus and policy was yes, of course, there's the short run effects But there's a bridge we need to somehow find a bridge to the after and the problem is we don't quite know how long the bridge has to be but there's an awful lot of human capital and firm capital that we don't want destroyed and We need to think of policies to to deal with that that's something I think it's easy We all agree on but of course and God is in the details and that's not what we're going to talk about today We also abstract from non virginities question Martin this is one question So far Seems to me that what you have in mind is a negative externality from the virus Is it possible that there could be a positive externality if it is indeed true as you were just saying that The virus may reappear. I mean we we sort of don't know and maybe is actually There may be there's actually positive externality by Everybody's staying at home if indeed that prevents us from having future outbreaks We sort of don't know how these curves Really look like right? What's the optimal? I think what it seems to me or what you're assuming it's that there is sort of a One-off shock Or not No, we will have an endogenous That is to say though. There'll be an epidemic. There'll be dynamics Certainly staying at home and social containment is part of what we call either simple or smart containment So I completely agree that we as we'll get to we get to the policy part We need to build up herd containment Well, you know absent a vaccine and now the question becomes what's the optimal way to do that and All the models that I'll talk about today I think share your intuition that we want people staying at home or minimizing their contact For a certain amount of period and so I certainly want to talk about all the issues that you've just raised So I don't think we disagree So maybe we can if that's okay circle back in just a few moments. Absolutely. Thank you Okay, the the robust central message Really that I want to stress is absent small action and the health consequences of the epidemic and Clever policy Get off as tolerable as possible from a social perspective Okay, let me tell you where we start off and by now that this is perhaps it was an obscure model the the classic sear On Craig Burnside many years ago use this model to talk about housing in which you talk about the way information is spread and and sentiment so we kind of knew the model and and Came about this horrible event I tried to apply it to study this event So this really goes back to a classic paper by Kermak and McKendrick and to stress they have Exogenous transition probabilities between Population some measure let's call it one for the sake of argument And we're going to divide the population into four groups. They're going to be Folks called susceptible. They haven't yet been exposed to the disease The effected there's a measure IT of those people There's a fraction RT that are recovered and sadly a fraction DT that are deceased now for today, I want to talk about The case in which people know their health status We have recently solved the model in which people don't know their health status And it turns out for the issues that I'll talk about today I have a graph at the end if people are very curious It doesn't make much of a difference for the set of issues that I'm talking about today for other issues it may So just as a polar case, it seems simpler to deal with everybody knows what they are although obviously in reality They don't I'm going to ascribe preferences so that we can be concrete I'm going to imagine the prior to the epidemic people are identical and they care about their consumption They're you know log CT and they dislike working and here's n squared t We we can make this much more realistic on a lot of dimensions, but for the main ideas this will be easy this household to emphasize a Capital physical capital it complicates the model We want this to be pretty painful for individuals cutting back work. And so for right now, we're going to abstract from capital And so people are going to have wage earnings They're going to have consumption and there's a question of how it is that the government is going to implement Containment policies, there's let me call it a mathematical trick that I associate with fari and warning who talked about capital controls And they imagined a shadow variable. Let's call it Mu CT which is sort of a quasi tax on consumption or a wedge on consumption The any proceeds from which are rebated to the household lump sum now to be clear That's not the way containment occurs So we also solved a version in which the government simply tells all people What their consumption would be and their hours work would be so there's no revenues There's no taxes and you get very similar results and again I'll actually show you that graph a little bit later on but for programming for right now Let me just think of mu CT as the containment rate and this is the the setting Very very simple model Consumption is linear it produced by a linear technology and a government has a simple budget constraint and that's that Since we wrote this paper people have allowed for lots of extensions of different consumption Etc. Etc. And and we've solved the model for a New Keynesian version of the model in which there's sticky prices I won't talk about that today because I truly don't think it's central to the issues for today This is an important slide because it really highlights in many ways what the value added if any of our paper is relative to the standard models Think of cap T as being the number of newly infected people in society The way the epidemiologists would have thought about this is that you have a measure of Susceptible people ST who meet with a measure of infected people and There are some parameter. Let's call it pie those meetings translate into New infections if you actually speak to the epidemiologist They're very very good about breaking this function into great micro details So you can talk about workers versus students etc So You know, that's a level of detail which we don't get into at this level But think of this is sort of non-economic interactions. It's sort of just exogenous Now of course in the real world people go to work, right? And it's a purposeful decision and so think of the total number of infected people IT and The total number of infected people let's call it the hours that they work So this is the measure of Infected people that the effective people that are at work If you're a susceptible person, you're working in s hours think of matching or meeting these people and those meetings translate into via this parameter a newly infected new infections We'll talk about the calibration a little bit But similarly on consumption There's going to be a variety of infected people who are Consuming so think of this as a total hours or measure of how much they're they're consuming and you as a set the susceptible people are meeting with And our shopping and you will meet with these people and that too will result in infections It's obviously true in the real world. There are different kinds of consumption activities Which are more or less time-intensive. So, you know, my son tells me going to a rock concert I'm too old for these things is much more time-intensive and there are more people Then other activities like take out food. So again, there are extensions of this model now, which allow for that kind of heterogeneity on Accounting so the number of susceptible people at time T is ST and new people will be infected So you exit from susceptible and you become from the stock Let's say you're becoming infected and so susceptible T plus one is susceptible T minus new infections The number of infected people at T plus one. Well, you start off with a certain number of infected people There will be new entrance of infected people How do people exit from? Infected state. Well, there's two ways. There's the good way the happy way There's some probability Pi are that you become recovered so that's what the R means and there's some probability Pi D that you Unfortunately pass away now. We've made this geometric it probably isn't geometric We can put in arbitrary probabilities and again today for simplicity. I'll just make these geometric this this will come back later when we talk about vaccines The number of recovered people at time T RT and you're gonna have new infected people a fraction Pi are of the infected become Recovered and so that's why this is T plus one and as an accounting matter. We have the number of deceased There's some stock of deceased individuals and Pi D of infected people die note one thing We are not allowing for which would be quite catastrophic in reality if it's true if People recover and can then become infected again That has very dire implications In in this model So we are not considering that possibility. We can put that into the model, but it was our judgment that That's not something we want to emphasize right now if it's really true. We are in not in good shape So Martin This is look again that was sort of what my Question was hinting at so yesterday. We actually had a very gloomy outlook painted to us by an epidemiologist Harvard University Who just published an article in science where indeed the prediction is that we should count on the current outbreaks and That immunity Builds up very slowly indeed over time and is not Permanent so in that sense There seems to be a lot of uncertainty around whether The one of lockdown is actually successful and is even the right thing to do It complicates matters quite a bit so this one I'm saying You know with pollution pollution is always bad in our models But in this case maybe depending on how these dynamics work out and whether people recover permanently or not sort of may may may you may end up in a much Worst state than what you have right now in the model, right? I so I would agree with that but be I would say that the the message of smart content Containment certainly will be important, but that will raise even more the stakes on what we call smart containment as a socially bearable way to deal with Infections, so I would you know, so maybe so I agree B I would say yes that even so that makes even more importance to this issue of smart containment So again, we'll come back to that because it's obviously a very very important issue. I don't disagree at all Okay in the model as you all know in these models you start with some seed a fraction Epsilon of susceptible people is infected It can be person-to-person. It can be zoonotic, which I gather is cross species. This is something my colleague Rubello taught me So there's Epsilon that are infected and one minus Epsilon are unaffected here for the heroics So we're assuming agents are aware of the initial infection It's not true and they understand the loss of motion governing population health dynamics, which is most certainly not true So robustness at a minimum becomes very important this kind of analysis This last bullet though. I think is definitely true For almost all of us, which is all agents will take as given Aggregate variables that is to say whatever I do. It's not going to affect how many aggregate infected people There are aggregate consumption of infected people and aggregate hours worked of infected people Okay Very quickly on the utility functions just so people understand the problems that in the basic model Let me and then I'll show you the complications in the simplest model the lifetime utility of a susceptible person What is that? Well, they have a period utility function. They care about their consumption their hours worked But from their personal point of view with some probability one minus tau they will not get infected They're not infected. They'll be susceptible and this is the value function of a susceptible person tomorrow With some probability, so they will get infected sadly and then they will have the value function of an infected person What do I as an individual perceive them my individual probability will become infected? Well, I may interact with an infected person and there's some parameter there If I go to work There's a bunch of infected people that are I might bump into that's this it and it and here's how much time I spend at work And this is this parameter governing that Similarly, if I go cons Shopping There's a bunch of people that are shopping if I go shopping. That's what the little C is that they may get infected Of course in equilibrium this little time my personal perception of the probability of them being infected is the same as The aggregate law of motion for the number of people getting infected So that's the the heroic rational expectations One thing that is true is that when I think of my probabilities I only think of The action that I take and how that affects that probability I do not take into effect how at each person doesn't take into effect How these aggregates are being affected by their individual actions. So that's the if you like the externality There's a budget constraint, which is straightforward So we have that Now if you're an infected person and this is important Martin certain to rub there are a couple of questions. Of course so Two related questions from from Gabrielle Perez-Cruz and Florian Hyder so How important is the assumption you're making that the probability of recovery is exogenous Shouldn't this depend on the number of people that we can absorb an intensive care And we'll just add another dimension to externalities and related to that it seems that Many of the containment policies were exactly motivated by capacity constraints in the health system is this unique This time and what does it mean for your model set? I absolutely agree and we do allow for that. That's what I meant by the simple model So I'm about two slides. I'm gonna get to exactly this issue critical issue of the health care system and overwhelming So just give me two slides, but a I agree be it's very important and see it's in the model And you know as far as generic epidemics, let me let me be eclectic on that I think this is such a massive infection that I don't know that I want to extrapolate You could imagine any widespread episode would threaten the health care system and it is very important So give me two slides and I promise you I'll get to there or a few slides But let's think about the infected people because there's gonna be a very important issue that comes up here and that is First people do care about their period consumption and work an infected person He may he or she may be infected next period And if they are how do you get? You're infected it means you got forbid you didn't die and you recovered So one minus pi r minus pi d you're infected with probability pi r. You are recovered. Okay Now what if you don't recover and you die? Well the standard assumption in the health literature is that the value of death is Zero or if you like the opportunity cost of living There is a very important issue which I'll come to which is Implicitly what is the value of life because that does affect people's decisions and of course policy We're gonna do it as you'll see later on for the standard US value Which is very arguable, but it's based on the micro literature people like kip fascusi and others It's about 9.2 million now this model doesn't have age Heterogeneity and so you're lumping together old and young people and so we're also gonna go to another extreme which emphasizes young people and think of the value of life as being 1.5 million and you'll see that some numbers change But nothing qualitative the way you vary that in this model is just by the discount rate You can basically control in terms of what does the model say the value of life is with apologies to the to the ethicist? by controlling beta Okay, we're also going to assume that people who are infected are not as he has not as productive at work and That's a subparameter fee. I of course in reality, there's two types of infected people They're symptomatic and asymptomatic and so we're going to calibrate this fee or think of this fee as reflecting an average between those people Recovered people are very simple. They're always recovered. So which was goes back to some point we raised before Here's their period consumption, but tomorrow they're going to be recovered for sure And so we just start the recursion that way The government's very simple They're basically in the in the simplest form of containment. They are handing out lump sum payments to all the different kinds of people in society. How do they get Stuff here. They basically get the containment tax if you like as I say that you I certainly don't want to take this literally And I'm very happy that the alternative way of modeling it gives us virtually similar results very similar results okay To the healthcare issue that the gentleman raised very important. We all understand that if the healthcare system Will deteriorate if substantial fraction of the population becomes infected So how did we model that? Well, a very simple way to model it is that the probability of death Is some say pi d but then is increasing in the fraction of the population that's infected So we have this non this convex function Which basically says the probability of death goes up and that's a stand-in for lack of ventilators for lack of beds, etc Etc. So this parameter as you'll see certainly has a very important effect on absolute consequences of the infection and and and Certainly policy in our model depends very much on that kappa Okay, we also are going to allow for treatments What are treatments? Well here We imagine that there's an effective treatment that cures infected people and it arrives with probability delta c per period Think of it as sort of calvo-esque Now we understand that in reality there's not as you know in reality We know that the treatments aren't going to happen for a while and then the probabilities are going to go up We solve the model have solved the model allowing in the other way This turns out to be prettier and easier to talk about so, you know, you can just govern Think of delta c, you know, if you want it to be once, you know They expected arrival time of two years one year three years that that's something that can be varied How would you modify the problem? Well, we're running a little short of time So let me just say if you're an infected person before you could either just get in You have to allow for The fact that the treatment arrives once a treatment arrives an infected person has effectively recovered So that's what this little red note on the far right hand represents This note is what happens when treatment doesn't arrive and it's just like we spoke about before So it gets more complicated with treatments Vaccinations which we're all very hoping for this is a vaccination against Infections and it too will arrive in a calvo-like way with probability delta v And again, one can feed in, you know, zero arrival rates for a year, which then go up dramatically That's just a model solution thing doesn't change anything first order. How does that change things? Well, it changes for the susceptible Right a vaccine isn't going to help an infected person. They unfortunately Can only be helped by treatment But a susceptible person now with probability delta v They're going to become like a recovered person because if the treatment if the vaccine is effective, that's it. You're done uh delta v One mind is delta v. You're just like you were before and you have to cycle through the normal state of affairs Let me briefly talk about parameter values because as we all know there is enormous uncertainty about many of the parameters And we kind of did the best that we could and tried to do as much robustness checks as possible So I'll just let me just say that This is a weekly model And in this initial attempt we said that it takes on average 18 days to recover Or die from an infection That's arguable. This parameter is quite important is important for Governing the time to a peak infection and a competitive equilibrium. So as I as If you like it's related to this this notion of aren't are not but Our initial thing was 18 We have I can tell you numbers later for peak infection time If it's five days, which uh, some people I think that's a little too up quite optimistic And we could talk about 10, but there's no discontinuity there Mortality rates very interesting and and difficult to measure. How do we do this? Well The best testing in the world so far has been south korea as far as we know or at least initially it was So we looked at mortality rates by age in south korea And then because we're americans, uh, we were thinking of america. We said well, what if Americans by age had korean mortality rates, but our demographic structure And when we do that we get a number that's roughly point five I mean you can argue it's point four, of course, and you can argue it's point six But our age adjusted mortality rates using south korean data is on the order of magnitude of point five Could this be wrong? Absolutely But we think it's still a reasonable number given the scientific evidence And then you can translate that into this parameter bearing in mind its weeks and bearing in mind this 18 number Uh, initial infected, you know, so with some seed, uh, we parameterized the cap the numbers a and theta a remembers productivity Thay is the disutility of labor So that before the epidemic people are working about 28 hours a week and they earn an average weekly income Of 58,000 divided by 52, which is the number for the u.s Very important beta point nine six to the one over 52. Why we choose that so that the value of a life Is 9.3 million 20 19 dollars in the pre epidemic steady state as I said that corresponds to what the epa and other u.s government agencies use Um, very important to vary especially in a simple model like this where we don't have heterogeneity with respect to age So I will most definitely I hope show you the numbers if this is 1.5 million and you'll see that Uh, the patterns are certainly the same if not the exact numbers Transmission function i'll be brief, but I owe you an explanation Here the the epidemiologists are very good about looking at different modes of transmission in respiratory diseases Right, so they'll look at a previous disease and say well, you know, how was it transmitted? And according to ferguson et al Um, about 30 occurs in the household 33 occur in the general community And 30 occur in schools and workplaces So the first thing we did was we said well, let's go look at this general community And ask how much time because it's not expenditures. It's time, right? So how much time in this category of general community services is devoted to consumption? So that gives us some knowledge about I'll show you how we impose the restriction On the fraction of transmissions in the workplace. We don't want to treat workers And students identically and the reason is that the epidemiologists tell us That the average number of daily contacts is much higher in school than in the workplace So we look at a weighted average of workers and students and get that information If you do that, then we're going to use three restrictions to pin down these three parameters pies The first is that evaluated at pre epidemic steady state values about one sixth of infections are going to occur via consumption That's how the numbers translate quite miraculously One sixth occur roughly in the workplace. Now we need one more restriction And here we decided to go to the lower end of a chancellor Merkel's scenario Which is a recall. I'm sure in the second week in march She in her speech said well, we think about 60 of the population Will either recover from the infection or die again This is an easy parameter to change and all the software is online And and we can talk about sensitivity to that particular parameter But if you think of the one six one six and sixty, we have three parameters and three unknowns We can back out the pies and that's how we transmit the transmission function Okay, so let's get to some results to make sure that we Martin, yeah, thanks before showing these fascinating results There are two more clarifying questions on the setup So one is where Carlos Montes-Galdón asking Whether the pi three in your s i r model Yes, it would also be affected by containment policies Uh, no, so that's that's an excellent, um No, in in fact the containment in our model is going to work through N through work and public consumption There there is we do not affect directly Pi we do not infect this third class of interactions And and that's why you may have to have a you'll see a quite a severe recession That's a very sharp question and and it's a good one We we uh, you could argue that, you know, maybe that's too too pessimistic, right? And that you could extend this to Somehow affecting the interactions that people have in a non-work and a non-consumption venue Really good question Yeah, that that was what the question was aiming at and the other question from klaus massouf is You mentioned heterogeneity between young and old How would the value of life in your model depend on remaining life expectancy without having the the virus Oh, absolutely. Well, so you you obviously well, so we can go to the micro literature and and here I want to be a little bit crass and you know, we're economists and With all the appropriate caveats to be to the ethicists In strict economic terms an 80 year old has less Well value of a statistical life than a 25 year old And so you have two choices then as a modeler One is to say like victorio's rule You simplify on a lot of dimensions about the dynamic choices of people and you allow for a lot of heterogeneity Right, that's one way to go. The other is what we've done in this initial draft Which is to say let's just say as a weighted average should we go with the younger person the older person The 9.3 of the government Is supposed to be a representative number but of course, you know, that's that Representative is always a difficult thing in these contexts That's why we went with the one five 1.5 million which would skew To the disease hitting disproportionately older people I think is is is the short answer to the question Is that okay? Yes, that's okay for now. Great. Okay. I don't agree. It will be better to have Uh, you know an overlapping generations model But you can imagine if you start to have substance now I'll come back to this age thing because it does matter a little bit for testing and and that's on in our ongoing work Okay, so let's look at I'm going to present the basic results I first want to show you a version of the model In which there's no medical preparedness. You can't overwhelm the system Then the no vaccinations and no treatments just so it's the simplest possible model to display what's going on What is first of all, what would an epidemiologist say? Well, you could think of what an epidemiologist said as doing is saying That people's consumption and labor decisions aren't endogenous So let's just fix them at their steady state value and see what effect that would have on the economy The key thing that I want to show you here is you would get um a Relatively um Uh, that's the dotted line and you would get a pretty big infection Right and many many deaths What does endogenizing? Oh, and by the way, you would get a very mild recession Uh, why do you get any recession? Well because a infected people as I said aren't quite as productive as Non-infected people so as more of the population gets infected they're less productive and unfortunately in steady state You will have deaths since that would affect total g consumption, but not per capita What is endogenizing work choices and consumption doing this model? well people are really afraid of getting sick and They're really going to cut back on their work and they're really going to cut back on their hours and notice How much bigger the recession is Uh, the solid blue line then Then the dotted line which is to say taking into account economics you get a much bigger recession What is the plus associated with this sharp contraction? Well deaths in the blue line are lower than deaths in the dotted line. So people are Willingly see it's a funny shock most shocks in economics. We like to think people like to smooth consumption Here it's just the opposite people respond to the shock by lowering consumption And so the average contraction in the simple model is about five and a half percent over the first year Which we initially thought was gee that seems big, but as you'll see well as you know Is kind of not maybe too small we can talk about that now You can imagine that Now the government says we just have simple containment policies and so we're going to impose one quote tax on consumption This is the pattern that the optimal containment policy would take It would initially be small which is not the prediction that we have because we don't have other the vaccinations in here You would basically initially there's not much of an externality Because there aren't many infected people in the beginning of the epidemic As the epidemic gets bigger you the externality gets bigger and so the containment gets bigger So that's why the rise in the dotted line and And notice that of course as you make the tax bigger you get a much bigger Falling consumption Notice that the the dotted line now is how the economy behaves under optimal containment much bigger Recession and also notice that the benefit is that you substantially reduce deaths Um Over time because you've contracted the economy more than the competitive equilibrium would have done on its own How would uh Adding a lower value of life affect things and obviously an important question So if instead of doing the exercise I just did for 9.5 million, I think and I did it for 1.5 million You can see a very similar pattern emerges uh, however, uh the Amount that you would intervene is lower Um Why because the quote value of the externality taking into account the value of life is lower But please note that you would still get you would still get a very substantial increase Um in the tax and a very substantial recession as a result of it All right, so but the numbers are smaller. You would still get 10 or about 6 year on year Uh under optimal containment Which is smaller but obviously still very sizable. So to emphasize lower value of life Being unreasonable you would still pursue qualitatively the same policy but to a smaller extent Now the gentleman that raised the question about medical preparedness Namely overwhelming the system. This is a pretty busy graph The blue the solid blue is the model I just showed you And now you can ask what would allowing for endogenous mortality rates do that is to say For allowing for the healthcare system to be overwhelmed The first thing that you want to see is that of course, um If I compare the red line to the blue, you have much higher deaths, right? It's precisely that people Are not our overwhelming this system in the way we've parameterized it and that translates into a much more serious epidemic in terms of health consequences What that also means is that you want much much more containment because now we have two externalities The first externality is just the infection. But the second is the externality on the medical system And so now we have a much bigger recession or substantially bigger recession Once the uh government or the the planner takes us into account Treatments is actually Martin sorry to interrupt There is a question on the first externality in figure three From florian hyder, so Who I understand correctly that in this externality I still work too much But why aren't people scared and in fact the externalities that I work too little It's related to luke's question. Is this a positive or a negative externality? Well, so let's go back to here. So let's first look at the competitive equilibrium Okay, so in the competitive equilibrium um, people definitely want to work less And they want to work less. But the question is how much less? Right, so it's not that you know, they definitely want to work less But not less enough because they're only thinking Selfish agents they're only thinking about the probability of they being infected But they don't think that if everybody thinks that way Right, they're not taking into account that the total amount of infected people Is increasing just think of it as pollution Everyone takes the amount of pollution as given or an optimal Tariff argument right each supplier of the good doesn't take into account that the country as a whole has some monopoly power So it's a very classic paguvian externality and the answer is yes They want to work less but not enough less Is that does that help clarify the the answer? Yes, of course. Thanks. Thank you Okay, so that's medical preparedness uh treatments treatments. Um There uh the the big difference between treatments remembers you're just curing infected people I won't say much about that It turns out that that the competitive equilibrium isn't very sensitive to that given how we parameterized it And of course you're gonna want it's it's actually quite similar to the argument for treatments are but vaccinations are important Why are vaccinations important? So if you look at the blue line, that's the the simple simple model and here you have vaccinations Notice that we have a different pattern here for optimal policy Before we had optimal policy starting off with a small tax and growing over time But with with vaccinations the the the planners the value of of delaying Um Deaths really goes up because if you can just get people to quote behave in the short run, you know The the calvo vaccine may arrive and that is obviously a social good. So here the planner starts with a very high Entainment taxi really wants people to stay at home and buy time for the vaccination to arrive So that's a different pattern than we got before And what if you put it all together? So now take the quote real model if you like Which is we have the medical preparedness? We have the vaccines and we have the uh the treatment Optimal policy looks like a combination of the things that we've seen you start high And then you get even bigger as the externality gets bigger What does that mean in terms of the contraction? Well, it's a big contraction in the model There's no question that you have a very sizable contraction in the first year But notice that the benefits in terms of deaths, uh, you have the dotted line is much smaller than the solid line So the basic Argument here is if you have to do simple containment You are are are going to want to have a severe contraction fortunately in the first Episode in the initial onslaught and it actually gets bigger over time and then you release Let me now go to um This is what you would do if you have a lower value of life Notice this is the big model with the lower value of life a similar pattern But a less severe contraction So you could well say that this is an overstatement of how big the contraction should be When you're calibrating say to the u.s. Numbers and if you go to a lower number like 1.5 million You would definitely want to start with containment. You will definitely want to have a recession But it will not be as large. It's roughly 10 contract in the first year Okay Martin on figure seven There's a question Since you don't include heterogeneity In the model in terms of young and old, but I mean you basically reduce the value of life, right, but uh question is Does this imply that your policy conclusion is biased against the interest of the young I used to get um Well, you want to be a little bit careful here because take take this one over here You're basically saying that the value of life is very much Skewed to well say it's skewed to younger people And because their quote lives are quote more valuable That's exactly why you want to have a big recession because you're rarely worried about them As you reduce the value of life and treat people in more like they're old Uh, you have less of a recession. So paradoxically a bigger recession is to save the lives of very valuable lives of young people No, it's a little bit of a paradox. Yeah, let's see a few words about um, um Early exit because and then I'll get to smart containment Um, we I I'm not a politician, but I am told that politicians Are keenly aware of the cost of the recession and are under substantial pressure to end containment early We can mimic such a policy in this model and say that look suppose you were a politician And uh, you exited After 12 weeks that is that's the uh, the uh, the red Well, here's red line is optimal containment. You're exiting after 12. You shouldn't be the dotted line is what you quote should be doing in our simple model Notice that what will happen are two things Let's look first at infection if you exit early You will get a huge shoot up in infections relative to what you would have had had you done the optimal policy Moreover, yes, you will get a v-shaped recovery in that initial period But as the infection goes up and you haven't had herd containment You're simply going to fall back into a recession again So early exit will get you if you like a short term high And unfortunately the cost will be more deaths ultimately And not Substant, you know, you'll get you will get a little more consumption, but but it's clearly I don't think worth it from the perspective of the model This row just says the longer you can hold off the politicians I don't want to be mean about politicians, but the longer you can hold off early exit the better So notice the the red And the dotted lines are closer. So the lesson is yeah, you can get a temporary kick, but it's it's not socially optimal What about starting late now by the way, let me just say if you Exit it say after the peak you would get the classic kind of pattern in the model that we saw in the black plague Sorry in the Spanish flu. There's a lot of interesting evidence across countries that you got, you know Dips and then big infection rises again And then here we just get an acceleration because where we ended We could have ended over here and then you would have got a resurgence This is just the cost of starting late and all I'm going to say about that is If you start late, you're really going to have to slam the economy once you start Right, if we had started earlier, we would not have had to have such severe containment policies As this red line depicts over here here. You're starting very late in the infection There's a raging infection and you just have to send everybody home and the economic consequences are extremely severe Okay, I want to end with smart containment because I've been relentlessly gloomy and I think we all need a little bit of Something to look forward to The the problem that I just solved amounts to a Either think of it as a Ramsey problem Where you have one tax instrument or a social planning problem Where you impose the constraint that consumption and work for everybody is exactly the same Let's imagine for just a moment that you had the technology and the ability for social planner Who could choose consumption and hours worked for people based on their health status To be clear. I know we don't have that but suppose we did I want to call that smart containment as opposed to what we just looked at Well at the beginning of the epidemic, what would be the the the criterion function of this planner? Well, there are no Uh recovered people, right? They're only infected and they're only susceptible people and these are the two weights infected and susceptible And he or she would want to maximize this this value function Now what are the constraints of the problem? Well, there's the transmission function the laws of motion for the population The lifetime utility of infected recovered People as well as the lifetime of susceptible people. But here's the critical thing The planner internalizes all externalities. So there's no quote pollution or optimal tariff externality He or she every time they make a decision. They internalize all the externalities We do need to make a choice about How do we think of consumption of infected people? I'll show you two solutions. One is if you think that the infected have to go shopping And more humanely, we're going to imagine in the second scenario that we can somehow just drop food off In their homes without a danger of contagion So first, let's look at what happens If you have to If infected people go shopping for themselves the answer is We hardly have a recession at all. Look at aggregate consumption. It's tiny. It's less than one 10 It's what one tenth of one percent roughly. And why is that what's underlying this? If you start this off early, what you do is you take the infected people And you quarantine them. That's it Then all the recovered people Are absolutely free to go work because they know the infected people are quarantined Everybody's free to go consuming because they know the infected people are quarantined. They're not in the general population So notice that the infection The the what's happened to the infected is well, it's it's it's going down very smoothly There's no peaks and basically they're recovering or god forbid dying And the infection and so total number of deaths now These are very different numbers that we saw under either smart containment or the competitive equilibrium Now to do this, you know, and this is almost a mathematical quirk You would have the consumption of the infected people be very very low It wouldn't be zero because it's log c. So the marginal utility of consumption goes to infinity And it would be quite tragic So you can resolve the model under the assumption that yes, we can somehow get food to Infected people, which you know somehow we can think of different technologies for doing that And what would you do? Well, then basically, uh, you would their consumption would be quite similar a little bit lower Uh to susceptible people and infectable. It wouldn't be identical, but it would be reasonably similar and we wouldn't be accused of being inhumane Um, and uh, we would just say look you guys are infected. You have to go home Um until you recover or you pass away That would be uh notice how dramatically that policy Would change the trade-off between economic costs And if you like health costs measured say by deaths Now, what's the problem with that? I mean, you're all obviously onto this in reality We have one class of tests for infected people Whether you're infected or not a different class about whether you're covered one one person either asked are you covered forever? Well, the recovery tests now that are being developed measure Uh, I believe it's called antigens. Just how how recovered you are Um, and there is also the issue of type one and type two errors for the different kinds of tests so The kinds of issues that we're raising or modeling now are allowing for people not to know their health status Or there to be a test of Different types of alpha one and alpha two and to say what would you do in the beginning? Of an infection as opposed to in the United States, unfortunately We're going to start off with serious testing well into the infection Right, so the question is would you really take you know? Suppose you started with 30 of the population infected How would you treat that versus a very small infection when you knew for sure one percent? Perhaps we're infected Anyway, let me stop there and simply say Uh, that there is this uh clear trade-off with the kind of policies We're entertaining now between the cost of a recession the health benefits And what I take to be the hopeful point here where we should be really focusing perhaps The science is building up our our ability to test and track which I gather the Germans are doing Um and having the capacity to to to implement To implement the results of those tests. So I'll stop there and just take questions Thank you martin Um So, uh, there's one question from mikaela lansa um In the model without smart containment. So let's assume that that is still out of reach for now um I mean, are we right to say is he right to say that politicians who face elections soon are the most dangerous I mean, maybe and maybe I can add to this isn't there sort of another very Dangerous externality outside the scope of your model. But if you think globally, isn't there an international externality? So from a so global social welfare point of view And don't we need to find ways for all politicians globally to be patient? Well, I agree. I mean, I so a I agree. I mean, I'm not a political scientist, but um, Clearly short termism It can be enormously costly if if you know, we in this country are facing an election in november um At the closer we get to november the close the larger the temptations to uh do early exit from optimal policy Now I I don't know what the right way to deal with that other than to educate the public um But it seems that the the repercussions of that for other countries are enormous and So sorry, you mentioned like korea germany. They seem to do everything right, but it's uh It's kind of all in vain if uh, you're the only one doing that, right? Well, it's certainly right that if the united states, um slips into Second recession because of early exit the repressions just from a strict I'm not so much worried about health because the europeans always say look you guys just can't come in planes But the economic damage to europe because the policies on our part Are undeniable So yeah, I mean, I think it's incredibly, you know, i'm canadian and uh, so I live in the united states, but canada Pierre elia trudeau one said in the 70s when the elephant gets a cold and sneezes the mouse when the elephant sneezes the mouse gets a cold so that's very much true for canadians and uh It's not quite the right analogy for europe, but there's no question that there will be implications for you Well, at least we know what to do about a cold this one. It's indeed seems more Fricky well martin, um time is up and we thank you very much for this beautiful paper and great presentation um a lot to chew on for all of us and um I Let me just say I wish you the the best of luck, you know, both personally, but as policymakers. This is an incredibly challenging time You know both I certainly the fed and I believe vcb have done a tremendous service in terms of liquidity and calming financial markets and wise heads, uh Will hopefully give wise advice to our politicians will be wise enough to take it And that's why we reach out to you and others and the indeed it's uh, it is more difficult to do this from your Home office rather than being all together with way of managing. Well, I look forward having beer in frankfurt with all of you in the future