 Today, we are very pleased to welcome Dirk Kruger, who is a professor at Economics at UPAN. He doesn't need an introduction, he's a leading macroeconomist, very well known to us, and today he will be talking about macroeconomic and redistributive effects of this crisis. So over to you, Dirk. Okay, thanks a lot for having me. So I'm hopefully have, at this point, shared my screen and you can see my slides. So what I want to do in the next minute is to essentially do three things. I want to talk about the epidemics from a broader perspective and then talk about one concrete project that I have together with Andy Glover, Jonathan Heathcote and Victor Riosroll. And at the end, I want to briefly mention a project of Mind That Builds on the paper by Eichenbaum, Rebello and Trump Bundt that you might have seen in the last week and give my take on that as well. And when I talk about the specific project on healthless wealth, I will try to do this on a fairly bird's eye view. A lot of the details are in the paper. I included a lot of the details in the slides, but there's quite a few slides I won't be talking about because of time, because of time constraints. So when I think about the recent COVID-19 crisis, I would identify three main areas or dimensions of the crisis. First, there's the health crisis. And I will show you some data on daily deaths and cumulative deaths. Then the wealth part of the title has to do with the real economy. What happens to GDP and unemployment? There are the numbers that we have are much more speculative, but I would like to give you those speculative numbers just to put into perspective of just how severe the crisis is and could be. And then there's an element that has to do with banking, finance, sovereign debt, and public finance, which is, I think, fascinating, super important. But I won't be talking about today. So if we start from the health dimension, so in this talk, I will use the words corona crisis and COVID-19 interchangeably. But it's important to keep in mind that COVID-19 stands for coronavirus disease 2019. That is the disease caused by the virus, sometimes known as novel coronavirus. As of this morning, I looked at the numbers from Johns Hopkins University. There's about 2.75 million confirmed cases. My view is that the number of cases is much, much larger than that. And there's more than 191,000 confirmed deaths worldwide associated with the COVID-19 virus. Let me just give you a sense of how large this is, depending on the area that you're talking about. So the next three slides are taken from a fascinating paper by my colleague Jesus Fernandez-Villaver and Chad Jones. And what they are doing is they take a very standard model from the epidemiology literature called the SIR model, which I will talk about in greater detail later. This is a model that basically models people as being in one of three health states. S stands for susceptible. So these are people that are currently not infected, that have not had the virus, and therefore are in principle susceptible for receiving the virus. I stands for infected. So these are people that currently have the virus and can spread it to others. And R stands for recovered. So these are people that had the virus, have recovered from it and are not currently infectious. And R could stand for either people that have recovered successfully and are immune to the disease. Or it could be people that had the disease and had died from it from the perspective of the SIR model that makes no difference because both recovered as well as that are absorbing states. And for the evolution of the epidemic doesn't make a difference whether you covered from it or not. So what Jesus and Chad did, they take this model, make it flexibly parameterized and estimated for different regions of the world. Just to be very clear in that paper, there's no economics in that paper. It's a purely statistical paper trying to estimate the best fit on the data. Their view as well as my view in this talk is that the hardest data that we have on the virus are death data. So rather than looking at active cases, they only look at data on deaths. And if you do this for New York City, you get what's on the slide currently. They use data up until April 12th, try to fit this SIR model through the observed daily death data. And what you see is that initially the virus has exponential increase in death numbers around here. According to their predictions right now around, we are at the peak of the daily death numbers and then the death numbers will be coming down. How fast they will come down, that depends on different parameter values. But the idea is that currently in New York, we are around at peak death numbers, perhaps slightly to the left of the peak. If you do this, for example, for Italy, Italy is faster ahead in the epidemic. So there you can clearly see that the number of daily deaths in Italy has been trending down. And again, depending on assumptions on what you do about further social distancing, on how quickly you open up the economy, the predicted further deaths by this SIR model looks like that. Just to give you a perspective, what does that imply for the total number of deaths in Italy going forward? You get estimates that look like this. So this is the date. So right now we are around here. And this is the cumulative death per million of people. So this is 300, 400, 500. So depending on precise parameter values, the prediction is that Italy will end up in the number of death of about 400 to 500. I think this morning, according to Johns Hopkins, the number of deaths in Italy per million inhabitants was 424. And depending on the prediction, you're going to land somewhere between 450 and 500 per million people. So that's about 30,000 people death from the corona crisis. So this is a massive health crisis. It has inflicted many, in fact, all countries around the globe. One way to further look at just how severe this is is to plot on the x-axis the days since the first death and on the y-axis of the cumulative death per million. This is a log scale. So going from here to here doubles the number of cumulative deaths. And what you see is that for many countries early on in the epidemic, you basically get a situation where every two or three days, the number of death people doubles. And then, of course, all the effort is about flattening this curve, which, for example, South Korea, which had very rapid growth of early deaths, has then successfully done. This is the Hubei province in China. And these are some European countries with very rapid death per days and recent flattening of the curve in Italy and Spain, maybe less so in France and the UK and the like. So this is the health dimension of the crisis. It's a very large crisis. It has inflicted all major industrialized economies. And it has a massive death toll. Now let me turn to the economic dimension of the crisis, which with some delay is perhaps equally severe. And the remainder of the talk will really be about the tension between what do we do in order to fend off the health crisis as opposed to the economic cost that such measures have been entailed. And my particular spin on this will be to argue that the benefits from curbing the health crisis, the benefit from mitigation efforts, the benefits from shutting down parts of the economy down, will very largely accrue to older populations, whereas the main cost of the mitigation efforts will mainly be formed by younger people actively in the labor market. So that's why you need both the health dimension, which I've now talked about. And now let me turn to the economic dimension. The economic dimension requires very high frequency data. So this is going to be quite a bit more speculative. I focus here on the United States. I'm sure there's very good data for European economies. I mainly will talk about the United States. And I think our data situation is probably worse than that in Europe. So let me show you one picture that I think has really made people freak out. So this is new unemployment claims over time. So you can see new unemployment claims in the great recession. If you look at the peak of the great recession, we had about 656,000 new unemployment claims in March 2009 at the peak of the great recession. So this is a four-week moving average. And then here towards the end, so these are the most recent data. And here we go to a situation where new unemployment great claims on average for the last two years to the last data is April 11th, are in the order of 5.5 million, or another number that you might want to keep in mind, about 24 million new unemployment claims and last for four weeks alone. So this is a massive collapse of US labor market. Now, the next official number for the unemployment rate are not due until early May. But there's a very nice, very recent paper by Big and Blandon, what they have done. They have basically conducted an internet survey that tries to, in terms of survey design, trace the CPS. And according to their estimates, by mid-April, their estimates of the current unemployment rate in the United States currently based on their survey. And that certainly consistent with new unemployment claim is that the unemployment rate in the US is already in the order of 20%. And there's a paper by Faria Akastru from the St. Louis Fed that uses this 20% number in the estimate of what might be the fiscal policy consequences of that. Now, these are not hard data yet. For official unemployment rates, we have to wait until early May. But if I were to have to have a guess of how severe the economic crisis already is in the labor market, I think a 20% number is quite plausible, could well be higher. So this is substantially larger than what happened in the Great Recession. And we are in great depression of the early 1930s territory when it comes to the unemployment rate. So this is a very massive, massive event. If you think about how large could be the GDP decline in the second quarter, where we essentially shut down large parts of the economy. Again, this is very speculative. But if I read reports by Goldman Sachs, it should be Morgan Stanley. I think drops in the order of between 20% and 35% are certainly in the realm of possibilities. So on one hand, you have a major health crisis with a substantial number of deaths. I will show you later data that suggests that the deaths are very concentrated among the older population. On the other hand, you have a collapse in economic activity that is unprecedented in many countries for data after World War II. And it's certainly on pace to look like the great depression of the early 19. So what I want to do in the remainder of the talk, and this is now based on a recent paper that I have with Jonathan Heathcote, Andy Glover, and Victoria O'Srill. And I should say that Andy Glover and Jonathan Heathcote, their employer are the Federal Reserve. It's the Federal Reserve system. So nothing that I will say here reflects the official policies or opinions of the Federal Reserve. So what we basically do in this paper is we take the health crisis as given. We built a very simple model of the macroeconomy and then ask, taking as given what the U.S. did up until April 12th, what should we do from this point on in terms of what share of the economic activity should we lock down in what sectors and how long should we maintain this partial lockdown and when should we try to come back to normal in terms of economic activity? I think that's a very relevant question because that's precisely the policy debate that's currently being led in the public discussion at least in the U.S. And in terms of the model structure that is being used here, it's really in a very fundamental sense. It has a health block and epidemiological block that's based on the standard SIR model. So I wanna talk a little bit about the sausage-making of this SIR model to give some context. And then that model is merged with a very simple macroeconomic model where the extent of economic activity is basically determined by two things. How many people are healthy enough to work and how many people are allowed to work as opposed to be shut down by government mitigation policy. I will then try to bring that model to the data and make sure that that model represents the actual situation on April 12th of the U.S. economy reasonably well. And then I will ask a simple question. On April 12th, you can play policymaker and you can ask how long should the economic shutdown still last and what part, what share of the economy should be shut down? And as I said, how long? One policy option is one that was clouded initially by the president. Say we wanna open on Easter, let's just remove all restrictions. That's one benchmark policy. The policy that's currently in place to the best of our interpretation shuts down 50% of the non-essential sector. So the sector that is non-essential for providing healthcare, food supply, and so forth. And that will last maybe until June 30th. And then we will ask the question, okay, from a perspective of social welfare where I have to tell you what exactly social welfare is. How much should we open up and how quickly should we do that? And as I said, the main theme of this entire talk is that there's gonna be very substantial disagreement depending on whether you're an older citizen, mainly subject to massive health risk from the crisis, or whether you're a young worker working in a non-essential sector, that's currently to be shut down where your employment and income of earning opportunities are basically disappearing and where you yourself, you're subject, of course, to the health risk, but all the data suggests us that directly you're unlikely to become sick. And even if you do become sick, it's very unlikely that you might die from the virus because you're young. And then at some point towards the end, I will say, what's potentially missing in the simple model that you might want to model more directly. So of course, I'm open to questions at any time. But so as I said, the broad research question, what is the appropriate economic policy response? The specific question is, how extensive should micro-economic shutdowns be? When should they start? When should they end? And the key point of the paper is that there's a very large distributional aspect from this policy debate because the main beneficiary of the policies are protecting the old from getting the virus and potentially die being bought by young, still economic reactive individuals and especially those that work in sectors that are deemed non-essential and therefore potential and potentially subject to a shutdown. If you think about sectors like hospitality, restaurants and the like, these would be the primary sectors that are affected by this shutdown. So what we, as I said, what we do in this project, we start with a basic epidemiological model, integrated into a macro model where economic activity depends on the degree of a shutdown and the degree to which people are sick or not. One key aspect is that those people that are not allowed to work any longer, they have to receive transfers from the rest of societies and we assume that those transfers are costly because you have to raise revenues, say with distortion or taxation to transfer to those individuals that are banned from pursuing the economic activity. And then we analyze the combination of optimal shutdown and redistribution policy and the catch interaction between these two policy goes like that. If you do more shutdown, you're gonna have more unemployed people from the sectors that are not allowed to work anymore. In order to make that palatable for society, you need more distribution. You have to provide these people with higher unemployment benefits. But if it's costly to raise the revenues to provide people with these transfers, then the appetite of doing mitigation becomes less severe and that interaction might mean that you do less mitigation, less shutdown than otherwise, where redistribution concerns are not on the table. So relative to say a representative agent model where the benefits and the costs they are evenly distributed because you have to transfer resources to the people that are laid off. And if these transfers come with excess burden of taxation, you might do less mitigation than you otherwise would do in a representative agent model where redistribution is either off the table or is costless. And I will try to demonstrate that in as we go along. Let me just make sure that I'm okay with time. So if there's no question, then what I want to do now is I want to briefly talk about the basic epidemiological, the SIRR model that many of you might have seen, but I think it is important to understand sort of the basic sausage making of that model. I will focus on the intuition and not go through this precise math, but I think all of us that have sort of been thrown in terms of research into this topic. I think the first thing that we have tried to learn is how this basic epidemiological model works and where it might potentially be have to be extended in order to make it palatable for economic analysis. Because you might ask, look, we're all economists. Shouldn't we all believe in specialization of labor should we not let the epidemiologists work on that part? And we should sit at the sidelines and not worry about that. I will argue that economics has something to contribute. But for that, I think we have to understand where exactly I think the interaction between the epidemiologists and the economists have to lie. Okay. The basic SIR model. And as I said, the pictures that I showed you on the health side, on the health side from Fernandez, Villarvera and Chad Jones basically took that model and estimated a fairly flexible version of that model with actual data. So now I will provide you with a sort of underpinning model that basically these guys have estimated and also the underlying model that many of us that have worked on this recently have used. For example, the Eichenbaum Rebello and Trabant paper is very much built upon that model. So let me try to explain how that model works. So this is a model that is cast in continuous time. Marty and Sergio and Matthias used a discrete time version of the model, but it works, of course, completely equivalently. So the idea is normalize the population size to one, ignore the fact that there's population growth. This is a model about a very short run. An individual can be in one of three health states. You can either be susceptible, meaning you don't have the virus, but you can potentially get it. You can be infected, meaning you currently have the virus and you can transmit it to other people, or you can be recovered, which might mean that you have had the virus and you have gone through it and now you're immune. The underlying assumption is that once you've had the virus, you're immune to it, or you might have died from it, in which case you obviously also cannot transmit the virus any longer, and big S, big I, big R, these are the population shares in these states. At the beginning of the epidemic, nobody is recovered, nobody has worked through the virus. There's a very small fraction of the population that is currently infected, and that might come from China in the case of the United States, or this might come from transmissions from animal. Absalon is meant to be very small, which means that the initial share of people that are in a susceptible state is basically equal, A equal to one, and then the smallest meant to describe the dynamic of the epidemic as it unfolds. And under the hood, there's three differential, or in the case of I can bomb et al. In this screen, time three difference equation that describe how the number of susceptible, how the number of infected, and how the number of recovered people will evolve over time. The dot in front of the top of the variable means the time derivative. So this is the change over time and the number of susceptible, the change in the number of infected, the change in the number of recovered people. And so the key two equations and the key two parameters are given here. So the number of susceptible people, those that are not infected is reduced over time and the number of infected people is increasing over time according to the following logic. This is the number of susceptible people. This is the number of infected people. So if you want the product between the two is the number of meetings between somebody that is infected and somebody that is not infected has not been infected, but it's also not immune. And then at intensity beta, these meetings create new infections. So the number of susceptible people is shrinking at this amount. This is the number of meetings S times I and beta is basically the intensity at which infections transmit from the I people to the SP. So this term is negative, meaning the number of people that have not had the virus is shrinking over time. Where are these people going? Well, these are exactly the new infections that increase the number of infected people. So the number of infected people increase because there's new infections and the key parameter that drives how many more infections we have is this parameter beta. On the other hand, there's now an outflow of people from the infectious state into the recovered state where these are the number of people that are currently infected, a shared copper of them recovers, which either means they had the virus, they worked through the virus and they are now immune to it and healthy or they might have died from the virus. So the second key parameter here is copper. So that's the intensity with which you recover. One over copper is the expected time length that you spend in the infectious state and are able to infect other people. So the two key parameters is the intensity with which you spread the virus to other people. If you are infected and copper, where one over copper is the expected time length that you spend in the infectious states. So these are in the very basic model, the two key parameter that you have to get a handle on that will tell you how this epidemic unfolds. In fact, what is really key, and I will show you to show that to you in terms of the basic math, is the ratio between beta and R because remember that one over copper, that's the expected time that you spent in infectious states, times beta, that's the intensity with which you transmit the infection. So R zero, which has, you know, it's a famous number, has a name basic reproduction number. That's the expected number of infection generated by one person that is infected. And to first approximation early in the epidemic, that's the number that you want to get a handle on how large is that, the largest is this number, the more rapidly the virus, the virus spreads. And what I would say, what I would say, and I would say that on the next slide, what really economics has to contribute is, you know, if you're an epidemiologist, it's clear that you wanna figure out how big is R zero. And you want them perhaps think about, you know, how is that R zero perhaps changing over time? I think the main insights of all the models that economists have recently constructed is that this R zero, especially because of the parameter beta, this beta is not a policy invariant parameter, but that's exactly where economic mitigation, economic activity affects this beta with the ideas that the more economic activity you have, the more infections per infected people you're gonna have, the largest beta. So clamping down on economic activity will reduce this beta and maybe the biggest contribution that these recent economic models with an epi part half is to try to get a handle on how big is the derivative of beta with respect to economic activity. That's exactly where the interface between health and epidemiology on one hand in economics is on the other hand. Just to give you sort of a basic idea of how this works. Before you move to this part, I have a clarifying question. So it seems that these models treat recovery and death as identical, but death shrinks the size of the population while recovery does not. So absolutely, so on the next slide, I will actually break them up and then in our economic model, that is precisely one of the factors. So we will actually argue that this SIRR model for our purpose is not quite rich enough. I will break it up a little bit and one of the things that you have to do in the ritual model is to break up this R into a share of people that do recover and a share of people that actively die because they recovered people. These are the perfect guys that you want to send back to the labor market if you know who they are. Whereas the dead people, of course, you cannot do that, but from the basic mechanical evolution of the epidemic itself, it doesn't really matter whether the recovered people recover and are dead or are recovered and they're healthy under the assumption and that might be an assumption that might not be a great assumption and there's a lot more research to be done that the recovered people are in fact immune to the disease once they have recovered, right? So what I'm saying is that from a basic epidemiological point of view, it doesn't matter from an economic point of view, it hugely matters and we will integrate that distinction into our economic model very much because it makes a huge difference, absolutely. Yeah, I meant it more from a mathematical point of view that in the differential equation, the third one, it says everything is normalized, size population one. Actually, aren't these models sort of assuming that the death rates are sort of relatively small so that you can approximate it with this equation? Yes, that is certainly true. I mean, so early in the epidemic, death rates are zero but even at the height of the academic epidemic, we're talking about at most perhaps, that's my hope, 30,000 deaths in Italy relative population of 60 million. So this is probably not a bad assumption but both recovery as well as death from the perspective of the model are absorbing states since there, I mean, if you see where R comes back, R never feeds back anywhere here. So the feedback is not there. Now, if you think that, you know, how many people died, that might affect the birth rate and therefore population growth. Then of course, this is not the accurate model but as long as recovery, both healthy recovery as well as death are absorbing states for these differential equations that really doesn't matter whether you're dying or not. For the economics, obviously it does but not for the dynamics of the system. So let me talk briefly about how about the beginning of the academic epidemic. So you can take this equation and divide it by I, then you get the growth rate of infections and that's given by this, but the early times of the epidemic, in the early periods of the epidemic, the number of susceptible people is close to one because number of infected people close to zero. So to a first approximation, early in the epidemic, the growth rate of infection is beta minus copper because the number of susceptible people is close to one and the change in the number of susceptible people which is given by this term is close to zero because the number of infected people is very small. So in the first, say 10, 15, 20 days of the epidemic, you can think of this as close to zero. You can think of this as close to zero which means that the growth rate in the early epidemic is just given by how many people are a new person infects minus the recovery rate and therefore early in the epidemic basically the number of infected people evolves as an exponential function. The exponential function is this term which means that whether the growth rate is positive or negative, exclusively depends on this R zero, this basic reproduction number, if that number is bigger than one, you get an exponentially growing number of infected people. If it's smaller than one, then the epidemic never gets off the ground. From the epidemic, how rapidly the epidemic evolves depends exclusively on this number R zero and that's why the focus on this R zero is so important. I would say, as I said before, the main contribution of economics is to point out that beta might not be policy invariant, it might not be invariant to social interactions, of course, and of course the epidemiologists understand this and it might also not be invariant to economic activity and the key aspect of all of this research is some time to come to grips to the fact of how strongly does R zero depend on economic activity through this parameter beta. The other thing that you can do in terms of very basic math is you can ask away, this is a very short run, the upshot of this equation, forget about details of that. Early in the epidemic, you can expect exponential growth of infections and the speed of that growth is basically determined by beta or that basic reproductive number and that's why people are so obsessed trying to figure out how big that really is. Is it three? As early research on China suggests and how quickly does it come down, has it come down below one where it means that the epidemic is subsiding. Also can ask it, what happens on the long run? How many people get never infected and how many people will get the disease and how many people will die? I would say at the end of the day, there are people that never have been infected. S star solves this, it's mathematically, it's a transcendental equation that has a unique solution somewhere between zero and one and the number of people that had the disease at some point is one minus S because in the long run, there won't be any infected people left. Well, this is the number of people that at some point have had the disease. Let's take the assumption that there's a constant case for adulterate, a certain share of people that have a disease die new. You can actually calculate from that very simple formula, the share of people that at some point have had the disease, a fraction new of them die. Best estimates suggest that for old people that fatality rate is quite substantial, perhaps in the order of one to 2% for people above 65, for young people that number is fairly small, perhaps one 10%, so if you give me the total number of people that at some point during the epidemic have been infected, that's R-star, then I can tell you the total number of people that will die from this epidemic according to the simple model. And the number of people that at some point during the epidemic will have had the disease is one minus the number of people that will never have had the disease. And according to this model, this solves the simple equation. If you really wanna have a dirty first approximation, you give me that basic reproductive number. And if that number is not too far away from one, then as a first approximation, this is the share of people that never had it. So if this number is two, if each infected person infects two additional people, then the share of people that will never have had the disease in the long run is 50%, the number of people that at some point will have had the disease is also 50% and the number of dead people will be say take two tens of 1%, so 0.2%, multiply that by 50% and that's your best prediction of how many death people that people you're gonna have as the epidemic evolves, but that might take quite a while. So the number of death that we currently observe is only a very imperfect approximation of that. So the nice thing about the SIR model, this is all analytically tractable and you can make predictions under the assumption that this zero is a fairly constant parameter and that you have a precise estimate of what this R zero is. Bottom line that R zero is a super important, what does economics have to figure out? How strongly does this R zero respond to economic activity? So this is all broad reading of epidemiology from my perspective, from the perspective of our paper, I'm getting late. This is not quite fine enough. Our paper we basically say, well, the simple model has only infected people, but it makes a huge difference whether these people are infected, but they have the infection, they have the virus, but they don't have any symptoms. They are asymptomatic. So in our paper, what we basically do, we take the infected and we break them up in three states. Those that have the virus, but they don't have any symptoms, which means they might not know about having the virus and the key aspect of these asymptomatic is these guys still go to work if they're allowed to. They go shopping and they transmit the virus at the workplace, at the store and at home because they are symptomatic. Nobody knows that they have it, maybe not even themselves. Then there's a group of people that have the virus and they have developed some flu-like symptoms. We call that F. And then there's some people that not only have flu-like symptoms, but they have become severely sick and they have to go to the emergency room. We call them E. So we basically take the SIR model and make it into a safer SIR model. We're safer, simply stands for susceptible, asymptomatic, flu-like symptoms, emergency room, and then recovered. And among the recovered as looks at, one should split up those people that have recovered and those people that have died. So in our more evolved model, the worst case disease progression is that you start not having the virus. You go to work or you go shopping. You get contaminated with the virus. You become infected but asymptomatic. You still happily go to work. You don't have any symptoms. You're still happily go shopping. Then if you are unlucky, you develop symptoms. You don't go to work anymore. You might have other people go shopping for you. That changes your infection, the spread with which you spread the disease. Then if you are unlucky, you develop really severe symptoms. So the transition from year to year, mainly old people, young people can happen too, but it's unlikely. And then if you're really unlucky, then you die. But at any point in this chain, there's a good chance that you will recover. And the way we model is that the recovery rates are very strongly H dependent because actually the transition between susceptible and infected but asymptomatic don't vary all that much by age. According to our reading, in fact, young people are more prone to getting the disease. But then the transition between having symptoms, having very severe symptoms and potentially dying, these probabilities are much, much larger. Old people. So what we do, we basically take this model but enrich it into this safer model. That includes these three stages of being infected. And again, the key difference is that the guys that are asymptomatic, they have the virus, they can spread the virus. But since they don't have symptoms, they continue to go to work. And it's exactly that. These are the people who are on targets. Meaning these are the people that are locked down from a policy that says you can't go to work because you might spread the virus. You don't know it. We don't know it. But your economic activity is being reduced because you're infectious and infect other people. Into this basic epidemiological model, we have an economic very stylized. So let me just give you the very basic bare bounds of the model. In order to study redistribution, we have three types of people, young and old. Work anymore. But they are very susceptible to condition on getting the virus dying. Then there's two groups of young people. Young people either can work in a basic sector, which we think of as healthcare food production. That's a sector you cannot shut down. It's central for economic survival. And the young people in the basic sector, they always work and they are not subject to a shutdown. And then there's young workers working in the luxury sector, restaurant, entertainment and so forth. This is a sector that in terms of production looks very similar to the basic sector, but the government can go to that sector and shut down a fraction M of that sector. So only a fraction one minus M of that sector is producing. So I'll put in the luxury sector is all the people that can work because they are either not infected or they're infected but don't have symptoms or they have recovered. So this is a group of people that are not having flu-like symptoms and are not in the emergency room. So these are the people in the luxury sectors that don't have symptoms either because they're not infected yet. They are infected, but they have not developed symptoms or they are recovered. So this is the number of bodies that in principle could work. Then the government shuts down as a part of that sector with the share M. So one minus M is output in the luxury sector. Output in the basic sectors, all the bodies working in that sector that can show up for work. Total output is then given by the sum of the two. Perfect. One key assumption is that people in the basic sector have to work in the basic sector. People in the luxury sector have to work in the luxury sector. There's no substitution. And the key part where the government shutdown comes in it shuts down part of the luxury sector which has two effects. It reduces output and it sends a share of these workers that in principle could work. It sends them home. Why would the government potentially do that? Because it exactly is these people, those people that have the disease don't know about it are symptomatic. They are super spreaders of the disease. And since you don't know who these people are one way to curb the infections from these people in part of the sector. Now, of course in an ideal world if you have large testing, what would you do? You would test a bunch of these people without symptoms try to distinguish between those and especially between this and those. And once you know that these are people that don't have symptoms but they already have had their disease those you send to work and those guys you keep them at home but without effective testing one very, very core substitute is to send one minus M of these people home in order to avoid the spread of the virus. The economic mall then says, okay we have sent a part of... There, sorry, one other question on this. So the young are more prone to contagion that that's also a key assumption for some of the policy prescriptions, right? Yes, it is the case that the way contagion works you can either transmit the disease in the workplace you can work it while consuming you can do it through social transactions and then if you happen to be in the hospital you can transmit it to the nurses and the assumption is not that the young are are exhaustionously more transmitting but since the young go to the workplace and since part of the transmissions happen in the workplace the young are more at risk of transmitting the disease to other people just simply because they are more at risk getting at that work whereas the old people they are not currently working and it's not that there's anything that is special about the old it's just that they don't have as much production activity and therefore less prone of infecting other people conditional on receiving the infection of course the old guys are much more likely to develop severe symptoms and dying from the disease and that's something that we'll try to calibrate some more. Yeah, so I understand I'm just asking this question because I don't know about the US but at least in Europe there's a lot of talk discussion around some of these care facilities, these old people's homes where so if you have all the old locked up in one place then maybe this is a kind of a strong assumption and maybe I mean I think your model can speak to it but you probably come down at a very different policy prescription right because then all the forces pull in the same direction so I think where this is where this is perhaps two causes the situation so there is I think it starts with the young people the young people are more prone to getting this then they go to visit their parents especially if they are asymptomatic they don't know they have the disease they visit their parents they infect old people and then there's a little bit of a feedback from old people to young people and I think that transmission from old to the young if you could insulate the old more effectively and if you could institute a policy that says the young people cannot visit the old people because you lock them in facilities and you don't allow visitation of course that would be a very effective way to curb that transmission back and when we bring our model to the data one thing that seems very clear there must have been something really massively happen in the US around mid-March where there are zero numbers that initially according to our judgment was very high it must have fallen quite substantially according to our reading of the evidence and I think this is a very effective way where we realize old people in nursing home they are very prone to getting this they are very prone to what's dying you basically wanna separate them from the rest of society and by doing so it very much slows the transmission of the disease, absolutely. So just to complete the economic part of the model so then there's basically two types of policies that the government has it can control how much of that luxury sector to shut down but then you have a bunch of workers that in principle could work but can't earn income because they're shut down so the second part of economic policy is redistribution there's two groups of people essentially those that continue to work and earn income and then those people that are shut down from working and earning income so you have to give them transfers so CN is the amount of consumption that the people that currently do not work receive how does that work? These are basically direct transfers through unemployment benefits from the working people to the non-working people and one assumption is that that act of transfers is costly meaning if you wanna transfer $1 from workers to non-workers because of distortionary taxation and center of reasons it's gonna cost you $1.38, 30 cents of extra cost to make that transfer because of incentive costs and so the play the interplay between these two policies is how much mitigation do you want to do? How much you wanna do it? How much of that sector you wanna down? Then you know that the more you shut down the more people you have to which you have to transfer transfers are costly and that will reduce your appetite to do towards doing mitigation in the first place relative to a world where everybody is identical representative agent we don't have this concern about redistribution so at the end of the day our economic model is basically an optimal policy design problem that asks how much do you wanna shut down? When do you wanna stop? And how much transfers do you wanna give to those people that are not working and there's this feedback loop between those between the degree of mitigation and the degree of transfers because transfers are costly and therefore that reduces the government's appetite for these transfers. Okay, so I'm gonna talk about the details of the model and in fact, I think given the time I probably don't have time to talk about the calibration in great detail but let me just mention there's a bunch of parameters in these models what do we think is really important? To a first approximation what is really important is what's the main benefit of these shutdown policies? Well, you save old people from dying in these type of models you have to take a stance on how much is that worth? How much is it worth to keep old and you know, jack to this from an ethical perspective that economists think about the value of life and put some number on how valuable it is to keep people alive but if you wanna talk about optimal policy there's no way around quantifying how valuable is it to keep all people alive? Agencies for example in the US that quantify what is called the valuable statistical life because if you want to evaluate environmental projects you want to ask how much is it worth to save an extra life through environmental production? So these government agencies have to come up with numbers. If you take their numbers the value of life is quite high let me translate that a little bit maybe if you take the number from the Environmental Protection Agency of the US at face value it is corresponding to a flow value about $515,000 or about 11.4 times end consumption so that's how much it is worth protecting one extra year of life to take a stance on that so this is one important parameter the other thing that is super important so we tend to rub each time on this there's actually a question on this kind of related to this value of life of course what you're talking about here sort of from the perspective of society as a whole the question is what would happen if young people would be altruistic versus the old value of the life of the old so it's slightly different how would that be? Numbers because I will look at sort of social welfare which is the weighted sum of the welfare of these three groups effectively we have three groups, right? We have old people, we have young people in the basic sector we have young people in the luxury sector one thing I will ask suppose the old guys were dictatorial and they can determine and this is sort of a world where either the old people have all the say or the young people internalize utility of the old people by being altruistic so I can show you relative to utilitarian social welfare function how much more mitigation you would do and how much longer would mitigation occur so I will show you exactly those numbers so to first approximation if the old guys are dictatorial I don't think the old guys are dictatorial at all this is an approximation to a world where you value the old directly and you value the old through the lifetime you told you of the young because they're like their parents and they're really important in these type of exercise and we struggled quite a bit with it it's to come to grips of what I will hear called initial conditions our thought experiment is you sit here on April 12th and now you have to decide how much longer to do shutdown how large should the shutdown be you have to get a sense on how does the world look on April 12th and the key unknown is how many infected people do we have that are asymptomatic that can transmit the disease but they don't have any symptoms now again if you have great testing if you could test the entire population this would not be an issue but currently it's certainly in the US we have no idea how big this number is so what we try to do is we are going to say and this is broadly summarized on this slide if you wonder if we take as hard facts the number of deaf people and maybe even that is severely underestimated but on March 21 there were 300 on April 12th this exploded to 22,000 and what we are saying is that what does what do the basic transmission rate these basic reproductive numbers have to be to rationalize a world where initially we have very small number of death then this explodes but it explodes within within a matter of three weeks the number of death explodes so you have exponential growth but at the same time the number of daily death is not all that high and this leads you basically to a view of the world that says on March 21 that are already infected that but are asymptomatic so to the best of our estimate on March 21 you have about 5.5 million of people that are already infected but don't have symptoms much, much larger than the caseload of people that are officially at that age infected and have the symptoms and when you look at these death rates and you try to come to grips with that that tells you that initially these infection rates must have been really, really high leading to a lot of deaths on April 12th but on the other hand this must have come down very dramatically and we interpret this as the outcome of social distancing efforts by governments voluntarily social distancing by people and economic shutdown that exactly started around that time where states basically shut down the economy so a drastic reduction in this basic reproduction number that makes it such that you have a ton of people that are already infected leading to deaths three weeks later because it takes a while for people from infection of asymptomatic asymptomatic state to the death state but at the same time the number of daily death is not all that large and that can only be consistent with the data if the number of new infections starting around this time has been reduced very, very substantially meaning the number of newly infected infections must have come down very dramatically we think it's under one and again, where does that come from social distancing as well as partial shutdown of the economy then let me just give you a few numbers because I think I should wrap up so basically we look at three time paths of mitigation policy our thought experiment is whatever got us to April 12th that's what it is on April 12th the policy maker has a choice to make of how much is that 50% of the non-essential sector is shut down that's about 27% of the overall economy that's certainly consistent with the 20% 25% unemployment rate that I've shown you at the beginning so policy one is open up at Easter that's what the president said at Easter we open up open up anything from April 12th on no further economic mitigation social distancing people still do what is privately optimal in terms of social distancing but no economic lockdown that's one policy the baseline policy is not that our baseline policy is to keep the current lockdown measure in place up until June 30th and again the magnitude is that shuts down about 27% of the economy or 50% of this non-essential sector and then we will say okay what is optimal where I will look at optimal by saying weighted sum of lifetime utilities of these three groups the old guys the young guys in the sector that will never shut down and the young guys in the sector we have a 57% problem or you're a widow and you got shut down and you can't work any further so let me show you what happens then so let me first focus on these two policy the baseline and opening up on Easter this basically shows the number of daily deaths under these two scenarios so this is the baseline scenario where right now in the US we're about at let me immediately go to the number of deaths the baseline scenario says around now we have about 2,500 daily deaths in the United States under this baseline scenario where 50% of the non-essential sector is shut down you keep that shut down until June 30th then you lift it and what you see is the number of daily deaths will increase and before it comes down so the observation here is that daily deaths are about where they are right now under the baseline policy you keep the lock but it's still stubbornly high you remove the lock down you're gonna get a rebound of the virus and it's gonna take quite a while for these daily deaths to come down to zero certainly by the end of the year this is not completely done if you're wondering how many people are in the emergency hospital and how many emergency spots do you have this is about consistent with being almost at capacity in terms of the emergency room what would have happened suppose you open up at Easter this is the counterfactual scenario of opening up at Easter the number of deaths would be multiplied by three the emergency room would be overrun and part of the number of deaths that we simulate come from the fact that you're gonna get a big spike in the demand for emergency hospital and our assumption is once you are at capacity the death rate of having more people in the emergency room that you can handle spikes from a pure health perspective this is a disaster you're gonna get 6,000 deaths per year on the other hand the epidemic can fall much more quickly and you go to zero death much more rapid this plot basically shows that two-thirds of all the deaths are concentrated among the elderly one of the ones that are 65 years and older and again baseline and if you would have opened up at Easter a big problem with opening up at Easter you're gonna kill a bunch more old people because those are the guys that are more severely dying you can calculate the total number of deceased people under the baseline scenario where you open up on June 30 on the scenario where you open up at Easter and what I would think is as optimal which I will argue is somewhere in between but close to the baseline scenario of keeping it up until June 30 if you wonder what's the gap it's about 200,000 additional deaths coming from the fact of relative to keeping lockdown until June 30 so the number of cumulative deaths that you avoid if you keep in the lockdown longer relative to opening up at Easter is about 200,000 extra death and the number of and this corresponds to about 0.1% of the population so under the baseline policy we're gonna have about 0.1% of the population dying eventually from this virus opening up at Easter that goes up to about 0.2% in the optimal policy this is about 1.13% How about optimal policy? Suppose you ask the old how much mitigation you wanna have the result is even the old would say 0.5% might be a bit too high so current mitigation policy is perhaps too extreme and why would the old say that? Well, because the old understand that it's gonna keep you safe but it affects consumption and since consumption has to be financed by transfers from the rest of the economy part of the economy shut down even the old would say current mitigation is probably too severe but crucially, the old would say let's keep it for much longer let's keep it say until the beginning or the end of August before we wind it down because that will minimize the epidemic and that will minimize the number of death if you ask the luxury workers those workers whose sector is shut down way less shut down and want to have it revoked much more rapidly why is that the case? Well, they also understand more mitigation leads to less health transitions it leads to less death among them because they get infected by working but on the other hand they also they are very strongly severely affected economically now they do get transfers from the rest of the economy but since transfers are costly their consumption drops very substantially and this reflects the fact that true they're gonna get unemployment benefits but unemployment benefits do not replace nearly the income that they would have earned if the sector has not shut down so these are the old these are the young in the luxury sector if you take away the average what we think is optimal that's the blue line the blue line says how much should you shut down the economy? According to a utilitarian social welfare function I'll be currently due but you should keep it for longer towards July and August because that will basically avoid this expansion I mean, if you get the shutdown and then remove it end of June you get this rebound of the virus if you keep it longer the blue line is optimal that rebound is being avoided and if it's not costly to transfer if there's no death rate law shift optimal mitigation up then you do more of it that's to be expected because that just means that it's easier to transfer to the old it's easier to transfer to the people that get mitigated therefore being unemployed by being shut down out from the from the luxury sector is not such a big not such a big deal the last thing I wanna show you the welfare gains or losses from these policies are very asymmetric basically along the optimal policy utilitarian weighted sum of lifetime utility the old guys very strongly favor that policy it's 1.1% of lifetime consumption young guys especially those in the luxury sector they are fairly ambivalent between a policy that it has a partial shutdown on a policy that opens up on Easter and it's clear why because these people on one hand they do value the fact that they're gonna die less likely by being infected more likely if the economy is opening up at Easter but on the other hand their consumption takes a strong lick the basic effect is they are basically indifferent between opening up at Easter or opening up optimally according to this blue line guys in the basic sector for them it looks a bit more a bit better because they are not as severely affected in terms of their consumption and the old as I said they're the main beneficiaries of that policy because it effectively keeps them alive if you actually just ask the old what is their preferred policy much more mitigation you're gonna get larger welfare gains for the old obviously their preferred policy and now the young guys in the luxury sector amend the preferred policy by the old which is extended lockdown for a long period of time they actually find that less appealing than an immediate revocable of the shutdown at Easter they suffer from that debate so if you wanna tell a political economy story of the current protest at the state capitals in the United States about opening up the economy you say look you guys, you politicians, you're old you like those policies to protect the old people you have implemented a policy that is welfare reducing for us because we get shut down we rather wanna open up the economy immediately so there's very strong redistributive consequences between the old and the luxury workers in the sun of the young that are mitigated that are mitigated through the economy these numbers become even larger if redistribution is costless because then they do more mitigation so let me just conclude here the main results seem to suggest that relative to what we currently have in place you wanna have substantive shutdowns but perhaps at the lower level so maybe the sounds are too severe but you wanna have them for longer certainly until the end of the summer the welfare gains from the shutdowns are very unevenly distributed large for the old, much smaller for the young and if redistribution is less costly you want to do more of mitigation clearly the results are sensitive to parametrivolacy especially the value of life and Luke already has asked one such question if you increase the value of life you wanna do more mitigation if you reduce the value of life you're gonna do less obviously it's very sensitive to how big is our zero how quickly that's the disease spread without any mitigation effort and it's very sensitive to the probability conditional on contracting the virus how likely you are to die now on one level and let me conclude with this slide so what is this model about it's a fairly elaborate model of the epidemic it's some very cost description of economic policy so the government is fairly involved here what is perhaps missing is that here private agents don't do all that much they don't have that many margins along which to adjust their private behavior and that is of course potentially important so for example if you have strong incentives to adjust your savings behavior Kaplan, Villalante and Mall have suggested that that leads to very asymmetric effect between those guys that have very little assets and those guys that have a lot of them and let me conclude by saying that here our assumption was there's people working in one sector the luxury sector that sector gets nailed people get mitigated and there's not too much they can do about that and then there's some people working in the basic sectors the basic sector you cannot shut down maybe the basic sector is also one where infections are not all that large suppose people can actually adjust their economic activity towards the sectors that are less infectious then that is very important and just to end with that you might remember the paper by Aikenbaum, Rebella and Trabont where they're basically a representative of agent model with one representative sectors and they say without any mitigation effort you're gonna get this massive consumption recession and you get this massive increase in the number of dead people you might remember that plot from their presentation suppose you allow people to adjust across sectors and sectors are heterogeneous with respect to how infectious they are because some sectors you have to work your way your sectors food delivery at home giving seminars from my office suppose there is substitution ability in a paper with Harald Ulrich and she from the University of Singapore we played that out and just the substitution possibilities across sectors in a basic Aikenbaum or Rebella Trabontomy once you allow people to substitute and you have some plausible elixir of substitution across goods what you're gonna get you're gonna get a consumption recession in the bench where elixir is fairly high instead of 10% you get a consumption recession of one and a half percent and then instead of having an epidemic much more mitigate and why because people individually rational adjust and go to sectors in terms of their consumption and work that are less prone towards infections and if that elixir of substitution is very large and if people practice some social distancing according to our estimates the epidemic never gets off the ground so this is a little bit the Swedish solution if you have strong incentives and strong mitigation forces from private behavior it might be the case that that is so strong that the epidemic is mitigated in its infancies so this would be our optimistic view of the Swedish solution but it does require very strong private incentives it does require very strong substitution possibilities and it does require perhaps a government that coordinates on these substitution possibilities so it's not saying the government should stay out and Chicago style, nobody should intervene but it should perhaps mean that the government should coordinate private actions towards sectors that are less infectious Many things Dirk for this very rich presentation you have been very generous with your time we basically have run out of time, big time there were a few more questions but fortunately we don't have time for those I did want to, if I may impose on you with a last question since you are one of the world's leading public finance experts I know that that was outside of the scope of your talk today which has sort of ended a little bit on a note that's why I thought I would ask you since what's very nice about these heterogeneous models is that you see these transfers between the young and the old and that is also the political economy very much so what a sort of, in a few sentences sort of a big message you would have for us on the public finance front since we also discuss these issues with fiscal authorities on a daily basis Yeah, so I mean I think from the perspective of the model so here the transfers between the young and the old have to come out of current output so I mean the obvious next step would be to think okay let's do that partially with government debt and of course governments around the world do exactly that if you want to evaluate that I think the next step would be to embed that into a full overlapping generations model where there's future generations and part of the burden will be pushed for future generations now in our essential world basically think of the young as not only about the current young but the young people having children and valuing future generations as well so this basic trade-off with government debt could be represented between the old and the young and the clear, default less obviously the old want to have this type of policy in place being financed with public debt whereas current and future generations so you look, you know, you're gonna settle us with tremendous amounts of public debt and we might not want to like that so it's clear that you wanna do public debt and the redistribution consequences are not so much between the young and the luxury and the young in the basic sector between the old now and future generations and that's why I've started working on that because I'm very concerned about future generations partially because part of the lockdown and that's not here at all is, you know I have three kids at home they're not good to school they don't learn anything I mean they have distance learning but that's sort of more or less useless what's gonna happen to their human capital accumulation, what happens to long run growth at the same time where we have an explosion of public debt now I think that using public debt with a crisis is very much what you should be doing in terms of smoothing but the long run effect on future generation that is absolutely there you need an overlapping generation model to model it it's very much, I mean certainly on my agenda and Alex Ludwig who's here in Frankfurt and myself we are starting really very much trying to work on that because that is absolutely crucial I mean my view is that right now the world is burning groups with a very short run the long run is all about public debt and human accumulation for the young generation and that's the next generation of the models Thank you for that Dirk so we will be looking forward to that work from you we'll keep an eye out for that and maybe be in touch on that again so for now on behalf of the ECB thank you very much for making some time in your schedule I know it's early still there so enjoy the rest of your day Let me just one last remark so the two papers I talked about they're on my website if you have any questions I will happily answer any emails so you know where to find me and I'll happily share the slides as well as those papers with you if you want to disseminate them in any way so you know I'm not running from any questions by running out of time I'm happily answering any of those that your economists, your staff, any of you might have and thanks for having me and giving me the opportunity to speak to you guys Thanks for your generosity