 Let me first wish you a Happy New Year, fuel of opportunity, of course, and new stimulating scientific ideas. We had, at school, last month's discussion with Arnaud Fontané in a workshop quite similar to season one. Arnaud Fontané is from the Institute of Pasteur, and we were talking about the perspectives of the pandemic and more especially on the perspective of the Omicron. Unfortunately, things happened as anticipated by scientific and by Arnaud with a variant which is much less lethal, but much more contagious than the former variants. Today, we organize a scientific with Toulouse School of Economics and more especially with a shared risk value and market and a workshop on long-term care and aging. The share between SCOR and supported by SCOR at the Toulouse School of Economics is a long-standing share because it begins in 2007, and he has, therefore, a long tradition, more than quite 15 years, and it has been very fruitful. And on the side of SCOR, we have been very, very much satisfied by the activity and all the ideas we have been able to share thanks to the academics and which have been feeding the business. I will leave there after, Stéphane Wilder, present press with more precision the avenues of the research. We agreed on for the coming years. But let me say that long-term care and aging is a very hot topic currently in advanced economies. These topics are even more challenging as we don't know so much on these topics. It's a new experience by him in many dimensions. Many proposals, political proposals, have been put forward that seem to ignore the basics of behavioral theory and empirics of aging. At the same time, issues lament the lack of demand for long-term care products while government are committed for long to provide such products but not have done anything at least in France, for example. The workshop is organized around the keynote and the presentation of five scientific papers. Let me just a few words on that. Firstly, his important keynote, Pierre Pasteur from the University of Lege gave us an overview of recent research on long-term care. I think it's very important for many persons coming from the business to have an overview because it is what they are lacking of. Then, Olga Strelik from the University of Göttingen, if they have good understood, will look more in the detail of his care, the expenditures and the elasticity to the increase in life expectancy while Clara Kantav, the Toulouse Business School, will consider a theoretical bio-dining model with gender differentiation and therefore include the consequence of gender in the results of the model. Tatiana Korichkova from Korkoria University in the US builds on an equilibrium model for nursing care market that aims to quantitatively evaluate the effects of long-term care policies, which is important for businesses and also for civil servants. For those who are connected and are civil servants, this is very important. While Mathieu Lefeuil from Ex-Marseille School of Economics checks a very hot topic currently, especially in France because of a public debate on the subject on whether nursing home were lending themselves to excessive, excess mortality. Jean-Marie Lozakma from the Toulouse School of Economics shows that when singles and couples coexist, gender neutrality limits for distribution, in fact, and he will detail in which conditions. I hope you will enjoy this workshop and let me thank the Toulouse School of Economics and the Toulouse School of Economics Chair for having organized it and all the speakers. And I give now the floor to Stefan Wilneuve, who leads the Toulouse School of Economics Chair on risk value and market. You have the floor. So thank you, Philippe, thank you. So I'm a Stefan Wilneuve professor of mathematics at TSC. My field of interest is about stochastic modeling, stochastic control, finance, mathematical finance, and I am in charge with Christian Golié of the chair. So let me quickly take the floor to give an overview of the chair to those who have only vaguely heard about it, okay? So let me share some slides in order to be, I think that I can share this, yes. So my, as Philippe said, it's a long-standing relationship. So 2007, 2008, it depends on the time of the call. I do not remember exactly when the first contract, but it's around that date. And the idea is to support theoretical and applied research on the market, insurance market, risk management and a lot of questions about sharing risk. So our mission is really having a role of helping score to understand how risk can transform influence decision-making. So it's a general assessment, but if you want to have some idea about what we are doing, we have an annual report about the work we are doing under the agit of this chair available on our website at this address. And this annual report summarizes our activity in terms of paper. And I like the main events like this workshop or any relationship we have with the score teams. So especially with, we have several contribution with several leaders on the score. And I will be more specific on this by describing the topics on this chair. So it is just a summary. I won't be long because we are all in passion to listen to the speakers. So let me give you just three points. The first one is about behavioral economics. We are very, very interested in that new trend in economics. So question like do markets and courage and ethical behavior are very interesting for us. There is another big, big challenge about the green investments so everybody knows. Global warming is a big challenge and we are working our own have for instance how to quantify the risk premium associated with the uncertainty associated with the criteria. So generally we depart from the standard risk versus return problem by adding a third component. And the last bullet is about health, economy and aging. And because this is a today's topic, I will leave to Pierre the floor to present it to give us an overview and I will be very short on this on that aspect. So I hope that you have a better idea of what we are doing at TSE on research about general risk market, risk sharing, regulation of markets, health, economies and really, really I insist if you want to have I think the most information are in the website. So it's a pleasure if you are free and I will be happy to share and your comment if you have any. Okay, so Pierre the floor is yours. Thank you Mr. Fad. And I will stop to, if I am able to do this, I will stop to share my screen. So where it is, if I do that, yes, that's okay. Thank you. Thank you. Good afternoon to everyone. So you can see what I'm going to talk about. It's a quick survey of some recent work on the economics of long-term care. Next please. Well, as you know, long-term care concern people who depend on health to carry out daily activities. It deals mainly with nursing care rather than with healthcare. However, over the last decade, sorry. Over the last decade, improving longevity and medical progress, for example, towards cancers has led an increase in clinical diseases and thus to dependence requiring both nursing and healthcare. So I will give you an overview of some recent work. Most work is empirical or based on calibrated simulations. Here, I'll focus mostly on theoretical contributions but which crests which are based on that empirical work. Next please. Next, sorry, I'm not in control of my slides. That's why I have to say the outline. First, I will give some evidence. Then I will turn to the three main actors of long-term care, the family. I will give the motives behind the family head and the collateral effects of family assistance. Then I will turn to the market, the so-called LTC insurance puzzle and then the rules of reimbursement. And then finally, I will look at the role of the state. Basically, I mean, I will deal with very shortly on the issue of optimal policy given family head and insurance market. And I will say a few words about some political economy models. Next please. So the background, so long-term care needs are increasing rapidly. The financing course source, well, if I give you an odd of pocket, I will give you some rough estimation. You have the family support, the public and the private support. We get that kind of allocation. You can see that the long-term care is basically a finance or provided by the family unlike, I mean, the pensions and healthcare which rely mostly on the state. So it's quite different. In looking at that kind of allocation, which is, as I say, I mean, 3D and back of the envelope estimation, we have to distinguish between provision and financing. For example, we can have a public financing and a public and a private provision. So the distinction has to be made. Next please. First, the family, the main helpers. The main helpers are the spouses and the children and mainly the wives and the daughters. In a recent paper, it has been shown that there is such a thing as a blood and gender bias. What do we mean by that? It means that by blood, we mean that the children will have their parents more easily than their in-laws. And by the gender bias, we mean that a daughter will help her mother more easily than her father. And we can show that such a gender bias and blood bias prevails in all European countries. What are the motives behind the aid to the dependent? Traditionally, we think that people help their parents out of altruism. It has been shown that altruism is just one of the motivation behind aid. There are two other motivations which are as important. First is the exchange motivation. I mean, you help your parents, but in exchange, you expect them to take care of their grandchildren. And also, I mean, they provide you some intervivous transfers and ultimately some bequests. So there is a quid pro quo type of contract within the family. And then there is the family norm, which depends clearly on the culture. And it's not surprising that in the patriarchal culture, as the one which still prevails, I mean, the women are participating more than men in that kind of process of family solidarity. We have shown indeed that the norms are playing a very important role. And why is it important? It's important for two reasons. First, I mean, the type of the effect of public policy will be different according to the norm. Public policy, for example, will have a coordinate effect on family solidarity in case of altruism. But in the case of the family norm, you will not find that kind of coding or the effect. Also, the effect, the collateral effect to which I'm going to turn now is going to depend on the type of motif. That's why it's very important to sort out those motifs. Next, please. There are indeed problems with the family, what we can call the collateral effects of family assistance. It has been shown that family care can have a number of negative effects. First, on the career of helpers. Quite often, women have to stop working or they have to move to a part-time work to help their dependent parents. But more important, informal care has a lot of negative effects on the health of the carers. And it has been shown that the social cost of these effects is as important as the social cost of the dependent, the dependence itself. So it's quite important. Another issue is the choice between staying home and going to a nursing home. I mean, this is a very difficult choice. It's quite important. As you will see in the paper presented by Matthew, countries don't behave the same way towards that issue. There are countries where nursing home tend to be more, if I can use the word deadly or lethal than others. For example, I think we will see that countries such as Belgium, Germany, France tend to be less, their nursing home seems to lead to death more often than staying home. So I mean, it's quite important. There is a recent book in France. I mean, some of you know about it called The Foss Wire, which show that indeed, I mean, those nursing homes can be not very friendly to say the least. Next, please. No, I move to the market. There's a real puzzle in the way the market behaves. The question is, we noticed that we have a very thin market for a risk which seems to be perfectly insurable. It conserves everyone and is quite measurable. And so that's why do we have such a thin market? I mean, that market is so thin. In the US, where the market is the most developed, it concerns only less than 10% of total long-term care spending. And in other countries, it's even below. In some countries, I mean, the market is, the long-term care insurance market is inexistent. There are various reasons for that puzzle. Let me list them and discuss them. First, they are the high prices, very costly. It has been shown that the loading costs are very high, particularly for men that has been shown by several papers by Braun and Ficklestein. Also this, and that can be explained by the adverse selection. In fact, it has been shown that the individuals have a better information than the insurance agents have better information on their probability of getting dependent and also on the possibility of getting some help from the family. And given that asymmetric information, we get precisely, I mean, the adverse selection, which leads to high prices. The family also play a role of substitute and that has been labeled the intra-family moral hazard by Paulie, the point is the following. Parents prefer to have the help of their kids than to go to a nursing home. They know that if they take an insurance, it will be tempting for their kids to send them to a nursing home because that will be less costly. So by not buying, purchasing a long-term care insurance, they get a guarantee or more guarantee to get the help from their children. Another argument is so another factor is the fact that in all countries, you have some social assistance for low income people in a certain way, I mean, the government is playing the role of a good Samaritan. And that leads the people, not only the poor but also the middle class to try to get that kind of social assistance and therefore they don't buy the insurance they could buy otherwise. For example, it can be shown that the 20% of Medicaid expenses, which is the US social assistance for long-term care, 20% of Medicaid expenses, I think concern people, middle class people who could very well buy, purchase a private insurance. Another factor is the fact that the rules of reimbursement are not terribly attractive. I will turn to that point in the next subsection. There is also the fact that the state, the UTG stay dependent. It has been shown that it's, there is a possibility that the marginal UTG of income would decrease with the severity of dependence, which means that the dependence will not be anymore an insurable good. Then there is, there are an array of behavioral biases. One of them is ignorance, ignorance about the risk of dependence, ignorance about the cost of dependence. There is also myopia, which comes from a sort of duality. People tend to prefer instant gratification over long-term welfare. And that leads them not to buy any insurance. Finally, I mean, there is the fact, I mean, that people don't want to think about what's going to happen when they get older. I mean, there's a sort of denial, a denial of death. There is a denial of dependence. And that's another reason why they don't buy purchase insurance. Next, please. Then I would like to say a few words about the rules of reimbursement. There are two types of, two main rules of reimbursement. One of them is a reimbursement of long-term care expenses. So it means that the actual cost of care is going to be reimbursed. But that reimbursement is limited. There's a ceiling in the amount of the benefits in the length of reimbursement. For example, in the U.S. where that rule is applied, it's quite often most insurance policies have a ceiling of two years, which means that after two years, I mean, you have to end up going to Medicaid or you have to finance your own dependence. The alternative is a cash indemnity long-term care. You get a sort of lump sum amount. It can be on a limited amount of time or it can be forever. That's more practice today. I mean, that kind of lump sum payment. It's used in the French market and the U.S. are using it more and more. But when you look at these rules of reimbursement, you understand that they are not terribly attractive for a lot of individuals. Why? Because there is no protection and it's a too long and costly period of dependence. For the insurer, it limits the uncertainty of long-term risks. But that's for the insurer. For the insurer, there is that problem of limited reimbursement period or the limited amount of reimbursement. Next, please. I show you here some data coming from the U.S. which shows the length of dependence for people who are above 65. You can see that for men, there are 9.8% of people who will be dependent for five and plus years. Women, there will be almost 18% who will be dependent for more than five years. That's quite a lot and it shows why a limited reimbursement period raises some problems. It has been shown by several authors that in fact it would be more efficient to turn to a policy, insurance policy, which would include a deductible principle that has been shown to be an efficient way of insuring individuals by Kenneth Harrow a long time ago. Concerning the Lumpson formula, it has been shown by Kremer et al. that it can be justified on theoretical grounds when you have the support of the family. Next, please. Let me turn now to the state. When we look for some countries here, I just choose three countries and I look at the cost of aging as a percentage of GDP, the cost of aging for the state. Basically, it means that if I take Germany in 2019, Germany devoted 1.6% of GDP to long-term care. If you put pensions, health, and long-term care together, it was 19.3%. You can see the same figures for Spain and France. When we look at, we try to forecast that. By forecasting, I mean you take some reasonable demographic and economic forecast and then you take the unchanged policies and you can see that spending is going to increase from 1.6% of Germany to 1.9%. The increase is not that big. It's a bit bigger for France. Does that mean that we should not worry? We should be careful because that means unchanged policy and we know that the current public support for long-term care is not sufficient. It's very likely that if there is a demand for more coverage, there will be a need for more spending. Next, please. The question is why do we need public intervention? After all, we always have to raise the question why do we need the government? There are two reasons. One of them is a redistributive reason when individuals differ in wages but also in survival and dependence probabilities. It's very important that we can expect that the government has to intervene. At one point, people thought that it would be enough to have an optimal income tax to do the business but it can be shown that given precisely that we have such an heterogeneity across individuals, it does not suffice and a social insurance is socially desirable. One other reason is that we have market and family failures. There are a number of models which look at the optimal design of public policy for different settings as to the behavior of families in the market. In all these models, and I will not be able to cover all these models, but the basic structure of these models is that we have a government which behaves as a Stackelberg leader which takes into account the responses of both the market and the family. Next, please. I give you here a list of eight different models. There are much more models than that which take into account certain types of features of either the family or the market. For example, we have the uncertain family aid which means that you cannot always be sure that you will get some help from your kids so it is a sort of uncertainty on whether your kids will help you. The reasons why they would not help you are numerous. It could be purely demographic or it can be economic. There are many reasons, but it is an uncertainty which we cannot ignore. There is also the fact that the market has a very high loading cost. Then there is the issue of strategic exchange. Here we have a family in which you have exchange between the kids and the parents, which can be exchange of money or exchange of time, but those exchanges can be purely non-strategic or strategic, but anyway it is going to affect the way the public policy is going to be designed. When instead of altruism the family aid is motivated by a norm that is going to change also the nature of the optimal policy. The gender issue is quite important as well because just to give you an example we know that women help more than men and also women live longer than men, so that has to be taken into account when deciding the policy. The opportunity cost of labour, the fact it's clear that helping parents is easier or let's say more attractive for people with low income, labour income that for people with high income and that also you can in designing the optimal long-term care policy it's important to take that into account that the low income individuals, families are going to help in time and the high income people are going to help their parents, dependent parents in cash. Variable altruism, I just mentioned that and then we have the fact that the risk of dependence and the risk of survival are different and they are not correlated with income in the same way. Next please. So I mean a way of distinguishing the different models existing the prevailing models is to look at the case where individuals are identical and the case where they are not the same. And I will give you just an example of those models. So in the case of identical individuals the choice between private and social insurance is going to depend on the respective loading cost or on the reimbursement rule and it hinges also on the reactive behavior of the family and for example this is a type of model which has been developed when family aid is uncertain and opting out is enforced there are cases where the market cannot own best social insurance also when the market reimbursement rule is limited and social insurance with deductible can be shown to be efficient in the line of a raw steering. Next please. No turning to different individuals. Social insurance aims at some redistribution and its role will depend on the correlation between dependence risk and income and income and given that the correlation between dependence risk and income is negative whereas the correlation between survival probability and income is clearly negative it can be shown that the case for a long-term care social insurance is much stronger than that of public pensions. So these are just examples of the existing models. Next please. A few words on the positive models because so far I've looked at a government which maximized some sort of welfare function but I look at models where the long-term care would be decided through a voting process and there are two types two interesting topics which have been analysed one of them deal with the reasons which explain why it might be possible and even desirable to let part of the middle class to apply to LTC to long-term care social assistance so to a certain extent in a certain way we can say it's too bad that the middle class is using the resources which should be targeted to the poor but at the same time to let part of it use those resources can be desirable from a political economy viewpoint because that would mean that there would be enough political support for a long-term care social insurance. The second type of model it's just to show that the social long-term care insurance can be supported by voting even when you have a private long-term care insurance. Next and finally I will stop here I will say that there is a clear need to build a bridge between those theoretical studies and the rich empirical work the presentation I just made you can get here you can find it on the paper with Justina and myself that's all thanks and I don't have time for questions Emmanuel so thank you Pierre do we have questions questions, comments yes yes I have two just two question or remarks to Pierre the first one is Pierre said there is in the cash and dignity model of long-term care there is a problem of too long period of long-term care but to my knowledge it's not such a main problem the duration of the long-term care is not a big problem with cash and dignity insurance what is a problem with cash and dignity insurance is much more inflation that is most of the insurance don't cover the risk of inflation and what people cannot anticipate is exactly inflation it's my first remark and question to Pierre the second one is the question of the public system there just presented some arguments in the defense of a public system the problem is that with long-term care the management of nursing home with the public authorities is relatively difficult and all the more because the demand is very diverse the public administration is good at presenting one solution fits all but it's not adapted for diversified offer and what we know from our experience is that for older person nursing home is relatively differentiated by families and they have very specific needs they want to provide to their elderly and it is not exactly the same whatever the level of income the demand is not homogeneous by level of income to remark and question in fact let me quickly answer those two questions the first one I agree with you the lump sum type of reimbursement has no time limit the question as I said was not very clear but I wanted to say for that kind of reimbursement the issue is that it's not big enough it's much below what it costs so totally concerning the other question it's an important question because it's true that in our theoretical model we are unfortunately very simplistic and as I said earlier very important distinction between financing and provision and I think basically we assume we look at the financing issue more than the provision and there is very little work about the provision of nursing homes and nursing services and it's more for the industrial organization people than for public economists but it's a big issue and we don't make the distinction thank you another question I have a quick question for you I would like to return to the entragenerational agency as I understand maybe I'm wrong parents don't buy insurance because they anticipate family support yes so is that bad it is bad for welfare so if such family support or if that is bad how do you fight against that agency problem can you force the senior parents to not do anything to not wait about family health it's a tricky issue it's not the fact that they don't expect they want to force their kids the problem with family health is that at first sight it looks like a good thing in the solution the kids are happy to help their parents and parents are happy to be helped by their kids but as I said when you look at all the collateral effects particularly in the case of severe dependence I think we should be careful help is not always a good thing because the effect after the when the parents pass away the damages are huge and you can see the amount of depression and all sorts of I think also that the more tricky stuff is that when you have three brothers and sisters in the same family which one is in charge of the parent which is sacrifice because it's more blood out between brother and sister than between parents but that changes a lot across countries thanks to share which is a panel on elderly people in Europe we can see that the role of the family and the type of arrangement among kids varies quite a lot in other countries but that's another issue OK so if we have no more questions I propose I would like to thank again Pierre for this nice overview nice general presentation and the floor is our next speaker will be Olga Astrolik from Göttingen who will speak about the optimal demand for care and so before you start Olga I have to apologize because I have to teach at 3A so Emmanuel can you share the session just after yes I can thanks a lot and then I would like to inform you of a change Mathieu Lefevre and Chiara Kanta have switched their slot so Chiara fans will therefore have to stay longer to hear Chiara but just after the talk of Olga Mathieu Lefevre is the Mathieu presentation OK so thank you so Olga the floor is yours all right so thank you for inviting me and to being interesting in our work can I share my screen let me see can you see this yes OK so this is John with your harness this is Timur Trimborn and it's about long-term care in this kind of continuous time life cycle models who we are usually working with and I think I don't know need so much often motivation for this crowd and maybe also not in introduction we had the keynote lecture but let me just emphasize one thing here with this picture which shows health related expenditure by age in the US this is also not our work but from Dinaadi and co-authors but what we usually do in our models is kind of we fit here rising health expenditure with age and then we make predictions with the models and policy conclusions and all kinds of stuff and when we match this to the data we are quite happy and then we continue but almost always it is overlooked that this the composition here of the expenditure and from a perspective of their function they are very different because kind of only the darker part here is kind of serious health expenditure in the sense of preventive and curative expenditure treatment if you wish and the light gray stuff is long-term care expenditure and the kind of fascinating thing here is that all this increase with age of expenditure is driven by long-term care expenditure and the other is basically flat after a certain age and maybe it goes even down a bit so which means that if we lump this all together and then act as if all of this expenditure would be kind of the normal expenditure for treatment there is a big mistake and in this in this model I'm presenting we kind of repair it so we would like to take into account this different function so we have medical care expenditure to care or to prevent health deficits and long-term care expenditure to help for the daily routine to help with activities of daily living instrumental ones for that being so these have totally different functions in the model and then also potentially for the predictions that you get out of it and the main question is I mean you can answer a lot of questions perhaps but for now what we do with the model is how do these different forms of expenditure respond optimally to increasing income and better technology and the idea is that an individual in a younger generation faces the same constraints but he probably has higher income and gets a better medical technology and what does it do with this total expenditure and the composition of the expenditure and this we think is interesting in its own right but it is also kind of there's an interesting ambiguity here because we actually don't know a priori what will happen with long-term care expenditure because we have two effects that counteract each other as the guy gets older he lives a longer part at old ages where he is potentially dependent on long-term care but he is also healthier that's the main reason why he became so old so at every age he is healthier and thus is less likely to need expensive long-term care and everywhere we don't know what effect it dominates and how much and we try and answer with an economic life cycle model of ageing so where we this is not about general equilibrium and public policy it's just one guy, an average American later on and his decisions over the life cycle are distinguished between these two forms of care-related expenditure in particular with respect to what happens with the composition and the absolute level of these expenditures and as a sideline this is also maybe interesting in as a contribution to the so-called red herring hypothesis I don't know whether you heard of this but cycle antiques are kind of obsessed with this and it's emphasized a lot that this whole idea that his expenditure rises with age and thus there will be more health and people get older because it doesn't depend on age it depends on nearness to death and we think that with our model here we can actually speak to this hypothesis and investigate whether and to which degree it holds true or not in our setting but I also want to use this forum for this opportunity to spread the gospel and make some advertisements for the health deficit model because that's the general framework that we use and this is intended to replace the Grossman model and the Grossman model is this framework that was in use for 40 years or 50 or 60 years of age and I think it's wrong so in the Grossman model people accumulate health capital big age that's the change of health capital over time and that's a depreciation rate and the assumption here is basically if you look at it for example the one with the greater age with more human capital the healthier guy loses more health capital gets less healthy sooner than the healthy guy and that's simply wrong if you ask medical scientists or gerontologists or other people they say no this is not how it is the opposite is true so then we just start from the opposite and say no no people do not accumulate health capital as they grow older but they accumulate actually health deficits and the more health deficits you have the faster is the speed at which you get new ones and this is how gerontologists basically think life works pretty sad but this is kind of consistent with observations and the little age are then health expenditures which you can slow down the accumulation of health deficits or here you can invest into your health capital another problem with the health capital is that nobody knows what it is nobody you cannot communicate with medical scientists or other people outside economics but also not with normal people and after tonight I visit my old father and when I ask him what's your health capital and have no clue but when I ask him what are your health deficits he will listen to me and say do you know that I'm suffering from this and this and that and he knows his deficits perfectly as does his doctor so we can have a language to understand each other and measure health deficits well there we rely also on gerontologists that suggest to measure it with the health deficit index and this is just a relative number that counts the present of health deficits in the person from a long list of this list of 30 or 40 health deficits that are present in the person and then if you look at this on average these are very systematically accumulated as we get older in an exponential fashion actually we get roughly 3-4% more health deficits from one birthday to the next so it's kind of an exponential accumulation of health deficits and of course there is a lot of individual level but if you look at the average guy it looks or representative individual it looks deterministic so here we kind of use these ideas in such a health deficit model to implement personal care expenditure and then calibrated also using insights from these authors and our own empirical studies and fit the model to the data and then kind of use it for counterfactual experiments and in particular for today on the effect of income and technology on long term care expenditure that's basically the idea so how does this work so I happily noticed in the introduction that there are also mathematicians in the audience so I don't want to bore you with formula but at least I know that there is no problem to get understood so should I defer it's just because it's about the deficit versus health versus capital distinction or should I postpone to the end perhaps I don't know whether I am yes but if it's necessary to follow it's not necessary to follow during the talk this is just experienced utility from consumption which is then but only experienced at a given age when the guy survives and survival depends on this health deficit the frailty index and then this is all discounted to the present and at big T life is over for sure so survival and lifespan are endogenous and depend on health deficits and then we have a normal instantaneous utility function that people maximize and then here you see this if you ignore the last two terms you have this exponential accumulation of health deficits over life natural aging but then with health expenditure you can reduce it and with decreasing returns to expenditure measured by gamma and this A this will also be one of our parameters for our experiments is this level of medical technology how efficient it is to reduce health deficits 200 years ago this was probably close to zero but then there is also long term expenditure and so this and the idea is when you do medical expenditure health deficit accumulation is reduced survival is higher and life expectancy is greater but long term expenditure has a totally different purpose it doesn't increase life expenditure or survival it is just essential for activities of daily living but when you have more health deficits you increase the probability that you need long term care that's the P and you increase of long term care or yes or the magnitude of long term care expenditure but this is not at all instrumental for being healthier that's just of getting only for getting around and then there's this budget constraint where people get wage income and later pension capital income here only from annuities for simplicity they spent on consumption on medical expenditure and then long term care and these are the two prices P and Q of these activities and then the individual has this problem to maximize and expected lifetime utility subject to these two dynamic constraints the costs of long term care and initial conditions the initial health and final health and initial wealth and final wealth so this is a free terminal time problem and the problem of optimal control can be solved with standard methods and then from the first order conditions you get a everybody in the audience knows this Euler equation or Ramsey equation for consumption growth that also comes out of this life cycle model that says how does the individual want to allocate consumption expenditure over time so nothing new here but then we have also health expenditure and Euler health equation if you wish which gives you the growth rate of health expenditure and if you just ignore this big last time for a moment you see that it depends on the difference between the interest rate and the natural aging rate and if the interest rate is larger than the natural aging rate it makes sense to have health expenditure later in life it's a very simple rational for increasing health expenditure past but then we have this long term that doesn't appear in the kind of normal health deficit model which is all driven by long term care and if you look this effect in parentheses it's positive because this is how the probability of receiving long term care goes up when you health deficits increase and how the level of expenditure increases when health deficits increase and how survival declines as health expenditure increases so this is all positive but the multiplier front is negative because that's the shadow price of health deficits and since health deficits are bad by design they contribute negatively to the objective function so this is negative and reduces the slope but we don't know yet by much by how much but if you if you come back to the initial thing and we want to know why is this no longer increasing so maybe then the intuition is here it is reduced because of the last term here because health long term care kind of becomes more important as individuals are older and thus they shift more of their other health expenditure to younger ages and thus the slope of this expenditure gets flatter that's the idea here and then we calibrate the model with the survival function probability for long term care and level and these are all dependent on health deficits not on chronological age and then we fit but how do the functions look like the parameters well to get the parameters we know how deficits evolve with age from the papers from Mitnitsky we take this pass and then we determine the slope of the function and its location such that when we fit in deficits by age into deficits by survival we get survival by age and that's the normal survival function which we then compare with data from mortality or what not and the dots are the data points so this is kind of this familiar survival function but survival doesn't depend on age it depends on this is already here an outcome it's a survival depends on health deficits and similarly for the probability to receive long term care we fit in health deficits into this unknown association between long term care probability and health deficits and this is a prediction how long term care probability is associated with age which we then can again confront with the data so this is all data for an average US American who is 20 in the year 2012 and then we calibrate all the other parameters then we have all the other parameters and some of them we just said and the others we jointly estimate with some targets one is to get the life expectancy of this guy right then to get medical expenditure at four different ages long term care expenditure at two ages so here are the externally set parameters you see this first five I already showed you how they were obtained from these functions here so these are already from there and we have initial deficits decreasing returns of health expenditure the wage of the guy interest rate prices are all normalized and the replacement rate for pensions and then these are all the unknown parameters which are then estimated and some of them are just latent and some of them are not to make out of them but for example this mu natural rate of aging that's actually measurable in the data and this is what we it fits very well to what Magnitsky and co-authors have measured for in this situation which is close to one which is also kind of assuring and then this is the prediction here so this is medical care increasing with age but then flattening at the later ages the dots are again the data and this is per user long term care but not everybody needs long term care and the time pass of per capita long term care which increases much more steeply and corresponds to the graph from the introduction and here are the health deficits that the guy develops as he ages so now that's the model now to the experiment what happens to the medical technology and income improve let's first consider medical technology so the idea here is that we increase the A and just to figure out by how much we say by how much would A increase if the medical technology increases by 1% per year so here's the answer so the blue lines are the same and the red dashed lines are now the response to this improved medical technology more health expenditure and thus at any age there's the probability to depend on long term care declines thus also the because people are generally healthier at any age also the long term care expenditure declines at any age and thus as a combination of the two per capita health expenditure declines as well even stronger so that's not kind of relevant for the individual because the individual looks at expected long term care expenditure so and this is perhaps the most interesting figure here in the lower left panel which is inverted U shape so if it is first increasing because it is more likely to receive long term care as the guy gets older but then it is declining because it becomes less and less likely to survive to these old ages in which eventually becomes the dominating effort and then you see if the red curve would be perfectly overlapped with the blue curve then we would find support for this red herring hypothesis then it would be just irrelevant for long term care expenditure how long the guy lives but it isn't so this shifts so but maybe not so much as expected and then that's the final experiment here so look at the absolute numbers the numbers behind the figure so this is this increase of medical technology by 10 per 1% per year then expected long term expenditure increases by roughly 4% compared to our benchmark calibrated individual but medical expenditure increases by much more so that's kind of the takeaway here so that the share of long term care expenditure or the ratio between long term care expenditure and medical expenditure actually is quite heavily life expectancy increases naturally and the last here is the elasticity by how much increase by how much increases long term care expenditure when life expectancy increases by 1% and I don't have time to go over all the other experiments here we have other technology improvements here we have income and the numbers are slightly different of course it matters how great the change is but look at this elasticity here it's basically always the same 1.7 and you can see that this is expected expenditure but relevant for life cycle decisions is the discounted expected expenditure that the guy faces now when he is 20 and makes his life cycle planning and this is lower this is around 1% rule of thumb 1% more long term care expenditure for every percentage increase in life expectancy that the model predicts there's a problem with the model because empirically as you probably know a long term care expenditure increases much more heavily empirically it increases roughly in sync with other care expenditure whereas our model predicts that the ratio should actually decline when this guy makes optimal decisions so that's kind of interesting food for thought I would say because if it is actually much more steeply increasing that must be for reasons outside the model pretty likely compositional effects through demographic change but also maybe some of the mechanisms that Pierre emphasized in his talk but I think I'm already a bit over time and that's it for now thanks a lot Olga for this very nice talk question yes you can Olga I'm a bit puzzled by the first graph that you show I mean when you start yeah because I mean I was always first I mean I'm puzzled by the fact that you take the age and in 100 are you talking about the average individual because we know that that's part of the big puzzle we know that most health care occurs two years before death and given that we have individuals who die at different ages we should not have the curve you have there I mean we should have health spending going up quickly before death but here we don't know what time we are dying because you give us an average so in fact you are it's so very clear the issue you are dealing with yes I agree but this is kind of not our figure so this is from Dinadi, French and other famous American economists and they this is kind of standard to look at the data expenditure by age and not at expenditure by distance to death that's also kind of the argument of the red herring hypothesis that for expenditure it should matter how close you are to to death and not how old you are and in principle we see this here because so the red guy here in this experiment you get 2.3% more life expectancy since the guy is roughly 80 on average you get 2 more years but but the curve so there are two movements the curve shifts out basically you can interpret the same expenditure 2 years later as I did during the talk when you are at this age the probability that you have the expenditure declined so in this kind of figures we take this into account but I completely agree with you that in the introductory figure it kind of can be misleading but that's the way how stuff is presented so the first question I had two questions maybe I asked the more important one so I didn't see aren't you implicitly assuming a value of being alive so I didn't with the CS functional I think you were using for utility if you have negative values or if you have values beyond one you can actually die and shorten their lives so did I miss something or do you put something in the utility or here we don't need it because this is always positive so you're not using CS you're not using power utility we do but this guy gets so where do we have the utility function I mean for the beyond one in the empirical range you have a negative sign for sigma greater one no I subtract one here okay but then it still depends on the scale yes but the scale is high enough the scale is high enough but to get rid of it you can just add a number here this could be something which is hard to explain but would be the value to be alive as you said we could add it and then set it to zero in our calibration that's perhaps better intuition I could add here a constant but we don't need it it can be zero but it drives people's choices since we don't have it it drives not people's choices maybe sorry I'm one of the co-authors maybe I can add something here it is actually like to fit the value of life the monetary value of life we would actually come to the conclusion that this is zero because the lifetime utility as we presented here without the constant already delivers the value of life and the utility function here is never below zero if you check it then that's fine that one is making the assumption here so the value of life of this guy of the calibrated individual is 9 million which I think is quite well with the kind of statistical value of life okay Grigory last question thanks a lot thanks Olga I was quite convinced by your defence of health deficit models thanks a lot for your talk I had a question about the modelling of time in the model when there is a health deficit it pushes the survival probability down so it makes people impatient more rapidly and I see that the model delivers very nice results in terms of calibration but my question was what about the results we could get if we were assuming a kind of less straightforward I'm not sure that the person who has deficit necessarily becomes more impatient I mean something else in a way we could say in the model it is conflated with the biological discount factor so I was wondering whether you were considering other calibrations with less automatic updating of the survival function but you already have nice results without that I know you Grigory I think there is also a clever comment so actually I thought about this but never did it so far the idea is in reality I strongly believe that survival probability depends on the health deficits that the guy has but when he makes his lifestyle plans he could choose something else for example he could think that it depends on chronological age or make some other mistakes so I think this is actually a relevant issue to say that people make actually don't, are not able to assess this probability correctly and then implement it in their life cycle decisions and then kind of their life cycle plans are made on the wrong facts and then it's interesting what happens then but I know a paper that discusses this in a totally different context but I never tried it out here okay thanks a lot Mathieu, the floor is yours thanks a lot Olga I need Olga to finish to share the screen in order me to share mine okay where it is okay is it okay can you see my slide yes it's okay so thank you for the invitation to present this work today so this is a joint work with Xavier, Sergio, Pierre and Jérôme who are all at the University of Liège and I think they all are also present today so if any questions I cannot answer they could maybe help me so the paper deal with the nursing homes and the mortality in the nursing homes the starting point of our studies here has been this recent debate that we have had about the number of deaths of COVID-19 pandemic in the nursing homes if we look at some of the numbers about the COVID related deaths in a few European countries there are some figures that show that about for example in Spain 66% of the total COVID related deaths was actually from nursing home residents and these kind of numbers also are found in France and in Germany with 50% and 35% and related these COVID related deaths in nursing homes there was quite a large discussion in the public debate and in the news of course about the possible of course low quality of care that could explain that these elderly actually died quite a lot in the nursing homes and the numbers is the kind of disparities that we observe among these European countries in terms of this number of deaths of the percentage the mortality rate I would say that we observe nursing homes with quite differences between European countries that questions actually the quality and maybe the institutional features of these nursing homes in Europe and as Pierre mentioned it in his presentation it means if you do not doubt we have some journalists from the Journal Le Monde in France that this week released a book about these all PR nursing homes that actually cast some doubt actually about the care in the nursing homes and of course these possible higher mortality or lower health status of the nursing home residents could be a problem actually if these mortality is due to the to the own characteristics of these nursing homes if the cause actually is the structure or the organization of the nursing home that means that we should maybe do something in terms of public policy these numbers about the deaths in nursing homes is also important regarding the long-term care policy that means all the decisions that we could have about how we should organize long-term care how we should deliver it and of course how we could finance it and also the question is all about the role and the substitution possible between the informal care and the formal care okay so this is where our study takes place because when we look at the literature about the nursing home with two strands of the literature one that has been dedicated to the choice of housing at all dates we have some quite many studies to estimate what are the drivers the determinants of the elderly choosing to go or not into a nursing home and usually what they point compared to the prices of course it's also the role of these activities of daily living limitation the assets or the income of these elderly the partnership meaning do they have some partners or no that could take care of them if they have some limitation but also they also they often point out the quality as determinants of a choice of a nursing home by quality I mean quality of nursing homes as measured by some resources aspect and regarding this quality there are also some studies that have tried to identify possible factors of mortality within the nursing homes we recite a few one in the slides and what they show this kind of study it's of course the role of mobility and limitation but also the quality of the nursing homes the big problems we have found in this literature is that often these studies are let's say affected by endogeneity issues and so we lack of causal evidence and this is where basically our paper takes place actually our studies we try actually using data from the the survey on health aging and retirement in Europe to estimate if being in a nursing home leads to higher mortality this is obviously done with some data that I'm going to present to you that took place before the COVID-19 pandemic and in order to try to conclude and I will try to convince you that we conclude on some causal evidence we use a propensity score matching method to compare in the terminology of this method some treated individuals who are actually elderly living in a nursing home to some untreated individuals who are living at home and what we observe is that after controlling for the determinants of entry into a nursing home the difference in mortality can be attributed somehow to the way these nursing homes are designed and organized or saying differently to the quality of head and service that we could find at home compared to the nursing homes and how the results are just anticipating a bit our results what we what we find it's that there is an overall in our sample of European data negative impact of being in a nursing home on life expectancy but these overall impact is actually driven by some differences among countries we find that in central and eastern countries of our sample we have this significant negative effect of being in nursing home on mortality which is not the case in northern and southern country finally looking at these results we try to identify actual differences in terms of the quality of this care facility and to see if we can explain these results by some mechanism that we find in the data let me just say because I'm not sure that I will have much time to present it that we also try to basically go a bit further in terms of sensitivity analysis and our results are quite robust to some violation of the conditional independence assumptions I will be back to this in a minute okay so let me maybe first start by introducing the data and giving you some descriptive statistics about the questions we are interested in so we use data from we use four ways from this survey the way the waves 4 to 7 why so we start from wave 4 because this is when the survey starts to include nursing home residents okay and we concentrate we focus on a sample of individuals age 65 plus that have at least one limitation in the activity of daily living that means that we concentrate on individuals that actually has already some limitation could lead them to go within the nursing homes we keep the people for whom basically we can observe the place of residence and a time T which is a wave and we can observe for them their status meaning being alive or that the next wave so in T plus one that means that we have eliminated some observation for which we do not have of course we also eliminate countries for which there were too few observation in the sample regarding the nursing home residency but overall our study is based on about 30,000 observation for 13 countries which is quite a thing a nice sample if you want to know a bit more about that I could show you the detail of the sample and so what we have what is the dependent variable that we are looking at that means that we observe the status of residents in one wave and we look if this individual is still alive in the next wave that means that we compare the mortality between wave four to five five to six and six to seven for the analysis I'm going to present here we have pulled all these transitions together to get a nice sample of transitions so just to show you a bit what we observe in our data you have the table that show you for the 13 countries in our sample and you can see that we have organized the sample such as basically identifying what we could call the northern country the central country the southern country and the eastern country from the sample and we have the mortality rates according to our transition between one wave to another according to the full sample and then differentiating to the residency basically what is interesting first of all of course is that we observe quite its originality in terms of mortality rate in our sample according to the countries but also these differences are quite interesting when we look at the difference between being in a nursing home or not actually because we can observe that in almost all countries of the sample there is an excess mortality of those in nursing homes compared to those in our home this last column show us this mortality ratio which is the ratio between the two mortality rates which is bigger than one for most countries except for Italy but I can go back to this later to explain maybe the reason for that of course looking at that is interesting you could say oh it seems that the people in nursing homes are earlier than those who are still at home but of course the population within these two types of residencies can be different that means that the people in nursing may differ from the people staying at home in terms of health of course but also age, marital status wealth etc etc and this is where we try to introduce our propensity score matching method because we need to control for the possible simultaneous determination of health and housing of course and this is true because still looking at our data our 13,000 observation we can actually observe that when we look at some important statistic descriptive statistics if we compare these in nursing homes to those who are staying at home we observe that actually in terms of age the population is different that means that those who are in nursing homes are older than those who are at home on average and those who are in nursing homes are mostly single we observe also that those who are nursing homes in our sample are more time coming from the first teresile of wealth etc etc which means that the two samples are quite different actually the sub samples and this is why we try to introduce this propensity score matching methods in order to control for the possible selection bias and to observe the both these kind of statistics and characteristics that we observe between the two sample the two group let's say like that of our sample and so what we do, what I'm going to present to you now is that we use this propensity score matching methods in which we're going to consider those who are in a nursing home as being the treatment groups according to the common terminology of this method to those who are at home which will basically constitute our control group and what we try to do with this is to match every individual that we observe in a nursing home to individuals living at home who actually has the same or observable characteristics and doing this it allows us to condition, we think, insufficient observable information to obtain a kind of counterfactual that we do not have by looking simply at the difference between these two groups and then that means that the difference in outcome that we could observe, the difference in terms of mortality rate that could observe between within this matched pair can then be attributed to the treatment, I mean being in a nursing home so that's the very important hypothesis that we are doing to do this estimation which is the conditional independence assumption we assume that controlling of this on a set of observable characteristics the mortality of the individuals in the control group and in the treated groups are independent of the residence status once actually we then have control for that, okay and in order to do this estimation so we use of course the density matching if you know a bit about this matching method we are not going to match individuals according to all the sets of observables that seems important to explain the choice of being in a nursing home so not but we use a density score that we obtained through a probability regression but we use a density to go into a nursing home according to some important variables that explain that two groups are a bit different and these balancing variables that we use in the analysis are here, we use of wave to control for the fact that we have different waves in our sample but also gender, age, the partnership status the wealth, the number of the limitation the fact of having at least one child and the fact of suffering for at least two chronic diseases so that means we have tried to introduce most of these important determinants that have been pointed out in the literature that I was cited before about the determinants of going into a nursing home okay so that's the methods and how we implemented basically, okay so let me say two last things about it before presenting you the results according to these propensity score matching methods we do it for the whole sample with the 13 countries we do it also for each country separately that means it's going to be also interesting in terms of results we separate each country and we do the analysis within each country in order also to look at some differences in terms of the effect of these two countries what we have done with these propensity score matching methods of course it's to be sure that the estimation achieved the right balance on covariate between the treated and the controls unit and starting from that we have matched all observation according to a kernel matching algorithms if you know a bit about propensity score matching method we need to match these individuals from the two groups according to different algorithm we use in the main analysis the kernel matching methods but let me tell you that if you are interested in our results are really robust to using other matching algorithm like the nearest name matching method without replacement and the radius and stratification matching methods with a replacement and here we use the kernel matching methods okay so maybe let me show you the result because I think this is what we have here is the average treatment effect on the treated so that means this is basically what is the effect of the nursing home on mortality after controlling for all these important determinants of being in nursing homes and what you see is that for the overall sample of analysis that we have we have a positive and very significant results at 1% here that basically show us that being in a nursing home increased by 10% the probability of dying so the mortality rate which is not that low because in the whole sample we observe about 20% of mortality in our sample of data taking into account all the individuals which would correspond to 50% increase of the mortality rate which is quite a lot what is interesting also is when we look at our estimation by country separately because if you see that country pops up in our results the first one it seems that in the central countries and especially in Germany in France, Belgium and Luxembourg, Switzerland we observe this positive effect, we find it also in the two eastern countries of our data we do not find the same kind of positive and significant effect when we look at northern country and southern country which just start to question a bit maybe what I was saying in our introduction, maybe that those countries in the way they organize their nursing homes, the long-term care policy regarding the use of nursing homes by residents and the quality of these nursing homes are actually different and this could actually explain that we observe the diverging results I will go back to that at the very end of the presentation I just want to go maybe because I see that the time is running on a second aspect you maybe tell us, yes of course but I'm not sure this conditional independent assumption which is central to our analysis the fact that we assume that after having control for the observable to which we have access the mortality between the two groups can be dependents of these resident status and it's true that we can question it we implement a simulation strategy in order to see how results are actually robust to some deviation from this CIA, this conditional independent assumption what we do is following the strategy that has been developed by Ichino Edalina in their Journal of Labour Economics 2008 paper we assume that this conditional independent assumption is not satisfied with the observable we have access but would be, if we could observe another variable of course an additional binary variable there would be such that we could simulate these potential co-founders adding it to the covariate and then comparing the results obtained with and without it that means that by comparing these two we can see that the baseline results, the results I just presented you would be robust to some failure of the CIA so without maybe spending too much time on that the assumption that we do here is that the CIA only holds given our set of observable X and this unobserved binary variable U and the whole question here is that this U should then be a treatment and the outcome what could be this unobserved variable for example in our controls we do not have access to the informal care and maybe that receiving some numbers of hours of informal care would affect the probability to go within a nursing home but would also affect the status of the residents so we could try to simulate how this additional unobserved variable could affect the result and especially how it affects the probability of mortality which is what we call the outcome effect here and also the probability of going to the nursing home which would be the selection effect so the whole questions now just to finish and I presented you the sensitivity analysis the whole question is how we can simulate this unobserved variable and how we can use this one of the covariates as you know and I'll propose there are two ways two to approach to do what one would be to pick the parameters of the distribution of these unobserved variables similar to the one we observe in the empirical distribution of the important binary covariates that we still introduce in our analysis the second approach would be to choose the parameters of the distribution it kills literally the average treatment effect that we observe it would drive the ATT to zero and still if we can do that we can compare the results and if those results are very unlikely that means that the exercise that we are doing here supports the robustness of the estimates so just quickly the results what I can tell you first of all if we try to do what we call we found a like simulation that means if we try to simulate this unobserved variable as the distribution we observe for being a woman or having at least one child or having at least two chronic disease or having a living partner we still find ATT that are really similar to what we observe in our main analysis so let me adding these unobserved variable doesn't kill our results we again based on that measure outcome effect and selection selection effect that are a bit different to what we they're a bit different according to the kind of distribution we have but nothing really much thrilling I would say if it's lower than one it means that it decrease the probability of a higher mortality if it's bigger than one here it increase the probability that you go within a nursing home and say that now the second exercise it's with the killer confounder so here we have show you for example do not pay attention because I do not have much time to this DNS parameters but basically what we do is we try to kill the ATT so you see the ATT is going towards zero and when we are able to have one unobserved variable that is such that it would basically pull our result towards zero the selection effect and the outcome effect that we have are so high compared to what we observe above that are very unlikely because that means that it would affect the probability of going into a nursing home almost 60 times more than what we observe with a simple simulation still the same with this outcome effect you see it with double or three times higher so that means that they are very unlikely so that we can trust our I would say that our main results are robust to any violation of the of the CI now the last things just to finish my presentation because I think this is probably one of the important results so far of this paper how can we explain these cross-country differences that we observe in mortality between the countries you could say maybe that the population who are in nursing homes in Germany or in France are totally different that the same population in Italy and Spain you could say that our different systems of health which would be important to explain this diverging mortality but we control for the health status we control for the chronic disease we control for the limitations in our analysis so what's left maybe that our this is the assumption we are making in this paper maybe that there are differences in terms of long term care between this country that can explain it in our analysis we do not have micro data on care in the nursing home for the residents that we observe in the share but if we try to relate of course our results to some figures so macroeconomic figures I would say about the formal long term care it shows quite interesting evidence so as I say it we do that being careful about issues of reverse causation and just without concluding on any causal effect we just try to identify some mechanism that should be of course investigated in the future to relate the long term care policies in this country to the results we have in our analysis and what we observe in this is quite huge table it's some interesting things first of all it seems that in the countries in which we observe significant effect of being a nursing home on mortality there is quite of a mix of lower spending public spending in terms of percentage of GDP in long term care also there is quite low number of long term care workers for 100 individuals age 65 plus and also a quite high share of for-profit nursing home compared to these other countries that means that if you look at this continental and eastern countries we can see here that the share of profit or healthcare is quite high compared to the people we see also that regarding the spending the Nordic countries have quite a high spending in terms of percentage of GDP for the nursing home and also looking at the informal care here we observe two things that are interesting in the southern country they have a really high share of informal care that provides at least 20 hour per week in the Nordic country they have a very high share of population providing informal care even if they do not provide that many hours compared to the southern country but it means that it seems that the way the informal care is organised here is more like a mix of public and informal care and here in the southern country a quite high share of informal care while it's not the case in our central and southern countries so these kind of results were totally descriptive of course firstly give us a kind of insight of what we could look for or what we should investigate a bit more in order to understand how we result so just to conclude before letting you know sometimes for the questions what we show in the paper is something that is interesting is that we have these differences among countries in terms of mortality rate in a nursing home such it seems the central and eastern country show in the same words as what Pierre mentioned earlier deadly nursing homes and actually these results can be related not causally but related to some country specific features of the long term care we observe that the higher mortality country have lower and resources and we also observe maybe the role of the for-profit sectors that I would say need to be investigated especially regarding as I said in my introduction this recent evidence that has been shown in this very nice I guess very nice book but very interesting studies by journalists in France about these or PR nursing homes so that's it thanks a lot Mathieu for this very nice talk questions comment two minutes of question if you want yeah maybe Mathias you have questions yes I have a question I like very much the way you try to with this new method to account for these unobservables that might be confounding I was thinking about another thing and I would love to see and I think that's like a more traditional way to do it is probably just to show how big is the effect just unconditional and then at the observables you have and see how much goes away and how much is still left do you have a graph like that no I don't so yeah no I don't if you put in ADLs right then a lot disappears of the initial stuff right I'm sure but what you mean is that doing not doing is trying to do a matching we don't just do how much higher is mortality in nursing homes without controlling for anything then add ADLs then add the 2D seizes and then see how much it goes down and sort of gives you an intuitive sense of what you're after I mean your method is a lot more fancy and looks beautiful it seems convincing to me but I would find that interesting and that's a good suggestion and we should do that of course yeah thanks I don't know if there is another question so yes one quick question can you be sure that the people who kind of left the sample are actually dead because they could have left for other reasons like refusing to answer because they could have left for something okay so let me maybe if I'm not totally right I think that Jérôme or Xavier could answer because they know really well what we use is what they call the end of survey questionnaire that means that in share what they do when people disappear they try to identify basically if there is because of attrition over deaths because the share survey is a share in which we have some interviewer who goes in the household asking questions to the individual so it's not an online survey we know directly if the people are dead or not and we know usually from which can death they actually are dead but we know exactly if they are dead or not and not if it's attrition or not so we know that that's the most moving rate that we have in the data okay I propose a little break and a break of 15 minutes okay okay thanks a lot Tatiana are you ready yes I'm ready you're ready thanks a lot thank you for your participation and the floor is yours all right thank you Manuel for inviting me and hello from Canada so this is a joint work with Minj and Lee at Carthon University and it's entitled long-term care choice and equilibrium implications for public policies so our work is motivated by the high demand for long-term care which I don't need to convince you it's high over 70% of individuals will need retired individuals will need long-term care over their lifetime and half of them will use paid care paid care is expensive whether you use nursing home or in-home care if in-home care is used extensively it can be as expensive as nursing home and public long-term care services and support programs and then the US the largest such program is Medicaid which is targeted in the poor, it's an in-tested program that covers both in-home care and nursing home long-term stays individuals who are more disabled have no spouse, live alone or who reside in nursing homes are more likely to be Medicaid and another part of motivation comes from US nursing home industry which is largely run by a private sector, it's a large industry with big revenues and over half of its revenue comes from Medicaid which reimburses nursing homes at a rate below the private price and the rest of the payment most of it comes from private individuals from a paid out-of-pocket the competition is limited on this market because individuals don't travel too far to find a nursing home so given that Medicaid plays a big role on both sides of the market on the household side and nursing home side and for both types of care nursing home care it seems logical to ask but when we analyze policy it's important to take into account decision-making on both sides of the market and that's where our contribution will be we build on two kinds of literature on the demand literature there's a large demand side literature studying household decisions for long-term care and public policy analysis but that literature usually takes the supply side there is a supply side literature that studies nursing home optimization but it takes the demand for nursing home in a reduced way so what we do is to combine these two bridge these two literatures and model both life cycle optimization with old age risks for long-term care choices they choose between in-home care and nursing home and this allows us to obtain a micro-founded demand for nursing home care and then nursing homes absorb this demand and decide price intensity of care and the number of beds and this determines the cost and intensity of nursing home care which then in turn affects household decisions and the density of nursing home care we discipline our model that rich micro evidence on long-term care with much patterns of long-term care usage by health, wealth and family status using HRS data on both extensive and intensive margin and Medicaid recipients use observations on the nursing home market then we study effects of long-term care policies in particular we look at Medicaid generosity and subsidies to in-home care we look at allocation of care, cost and intensity of care and make conclusions about welfare effects now I will briefly present the model of long-term care choice in equilibrium now it's a big, large dynamic model I will give you some intuition using a simple model so there are two types of market players there retired households, there are two overlapping generations of those they are heterogeneous face old age risks, demand care and there are nursing homes in on the local market who produce care and face identical cost structure there is government that subsidizes both households and nursing homes we abstract from private insurance here and focus on symmetric Nash equilibrium on the nursing home market so households are heterogeneous in age, wealth, income health and family status and they face uncertainty about their health which could have high and low need for care if the health is bad and family status which may change because spouse may die and child might be available or not the households value consumption of goods care and bad health states and requests they make saving consumption and care decisions and they solve their life cycle dynamic optimization problems which I will skip here I will not give you the bellman equation which is huge as far as long term care choice is concerned individuals choose between in-home care and nursing home care in-home care modeled in somewhat reduced way individuals face marginal cost of care which is lower if there is a healthy spouse or a child nearby available they decide how many hours of care to consume and if there is no family available these individuals face fixed cost of care for nursing home care they just choose whether they enter or not and they take intensity and price as given because it is decided by nursing homes there is Medicaid available for the poor eligibility decided by income and assets tests and there are consumption floors that take and account various exemptions depending on household status and the coverage is in terms of number of hours it's the same except it's lower for in-home care and the low need for care low activities of daily living status as a result so this plays an important role caring for such individuals in nursing homes is more expensive so here is a simple model this is just a static simple model of the choice of long term care just to introduce the intuition so these indifference curves show individual preferences over non-care consumption and care intensity of care I think of hours of care there are two budget sets budget lines drawn for two types of individuals this one the green one is without family the blue one is with family so the individual family can afford more care because he faces a lower price of home care in home care so if the individuals choosing home care care hours would be given by this point and the optimal consumption would be given by points C S and F nursing homes provide a relatively high level of care and you can see that the single individual is willing to pay this price this is individual wealth by the way pay this price and go to a nursing home with this high level of care high utility however individual without a family would choose to obtain care at home however when medicaid is available if consumption flow is high enough and this individual qualifies for medicaid we see that even individual with family will choose to go to a nursing home because he is made slightly better off there with this high level of care and he only has to give up that much wealth so that's basically the idea and if we look at the entire distribution of households with different levels of wealth we can show that everything else is the same just the wealth is different the choices of individuals will break into these four regions the poorest individuals will choose medicaid then somewhere in the middle of the wealth region individuals will choose nursing home and otherwise they will receive that many hours at home using home care now this figure is drawn it's a snapshot for a given quality given intensity of care given price of nursing home as we change price of nursing home stay and intensity of care these cutoffs will shift and we can derive the demand for nursing home aggregate demand for nursing home and medicaid for private individuals and medicaid demand for nursing home we then go to nursing home problem when nursing homes maximize the revenues that comes from private beds M which are sold at price P medicaid beds which are compensated by the government rimburs by the government at rate M below this price and they face some costs like the intensity of care total number of beds nursing homes take decisions with respect to price and intensity of care of other nursing homes as given and decide their own price and intensity of care as to maximize the revenues and as I said we focus on a symmetric now I will say just a few words about data and parametrization because I want to allocate most of the time to talking about our experiments because I think that to hear people probably know very well the data on long term care patterns so our data comes from health and retirement studies and we look at both intensive and extensive margins of care so there is a lot of research and research by wealth and income quartiles health status measured by activities of daily living and family status and also medicaid so we break down this usage by all these dimensions just to give you an idea little snapshot of some of the statistics. So if you hear the dark area represents individuals in the nursing home, lighter areas, individuals in home care. So you can see that highly disabled individuals receive care both in nursing home and at home. As well when we look at the Medicaid recipients, there are individuals, there are about 60% of individuals in nursing home who are on Medicaid. There's also a substantial number of individuals quarter who are receiving home care at home and also are on Medicaid, financed by Medicaid. Now in terms of nursing home market, there is, so this data comes from Pennsylvania State Department. So individuals usually don't, 90% of individuals don't travel more than 23 kilometers to find the nursing home. So that gives us some geographical area of 24,070 plus individuals. A quarter of 80 and over individuals need long term care and what 20% of those go to nursing homes. This market covers 11 nursing homes. There are about 105 residents in each nursing home, 60% of them are on Medicaid. The price of a nursing home is $85,000 a year with 2,000 hours per individual, per resident per year and Medicaid reimbursement rate is about 90% of the private price. So we take all those observations to calibrate the whole number of parameters in this model. But as I said, I would like to focus on policy experiments here in the time allocated. So we'll consider two experiments here. One is more generous Medicaid. This is a typical experiment you see in the demands inside the literature that models household decision about long term care. And then we introduce another experiment a subsidy to in-home care for individuals without family support. We look at steady states and compare effects within without nursing home response to learn to what extent it's important to model the supply side. We look at location of care and the welfare. Obviously we are not counting in tax distortions, but some of our conclusions go through even without this element. So we measure consumer surplus as lump sum wealth compensation at the age 70. All right, so the first experiment, more generous Medicaid. So this, we have variations of this experiment, but this is the one I'm gonna show you where consumption floors are increased by $3,000 a year across the board for all types of individuals. Of course, the direct effect is there are more individuals who will choose to go on Medicaid, more eligible individuals and more individuals will prefer Medicaid now because it's not such a deal anymore. And that applies to both in-home and nursing home care. Now there is also an additional indirect effect and that's where our paper contributes as that now nursing homes face a higher demand for Medicaid from Medicaid residents. The response is to take advantage of this high demand and to actually increase intensity and price of care. They kind of need to increase the price of the increase the intensity of care. What that does is attracts more Medicaid residents and also this is done at the cost of losing some private residents who move away from more expensive nursing homes to private in-home care. So if you look at this movement, obviously Medicaid, the direct effect comes, hits the poorest individuals. So we look at the bottom half of the wealth distribution, there's a lighter bars. So these individuals leave private in-home care and go to Medicaid in-home care and Medicaid nursing home. This is the direct effect when we keep the price and the intensity of care provided by nursing homes is given. Now when nursing homes are allowed to respond, they increase the quality of care and as a result, these individuals strictly prefer to go to, from the bottom half of wealth, they strictly prefer to go to nursing home Medicaid because it's now better quality of care. They'll go to Medicaid in-home care, not so much. In addition, the private payers who go in the nursing home don't like this higher price, even though there is also higher quality, they leave nursing homes for private in-home care. So this relocation turns out to be important. So if you look at the welfare effects here, consumer surplus obviously increases, but increases way more if nursing homes are allowed to respond. However, Medicaid expenditures increase even more. So overall, and this expenditure increases driven by this large increase in Medicaid nursing home expenditures. It is large as it is, but when nursing homes respond, it increases even more. So overall, this is a bad policy and we show that supply side reaction here is important, that this increase in Medicaid claims by nursing homes is making it really bad and private payers actually lose here. Then the second experiment is in-home care subsidy. It's motivated by the fact that there is a high fixed cost of in-home care that somebody has to take care of the house. So I sure estimates that's about $20,000 a year. So we conjecture that this high cost of in-home care creates a barrier to their in-home care use. So we propose to consider a subsidy either as a direct cash transfer or cover a fixed number of hours of basic custodial care. And this policy, we consider uniform eligibility for any individual without family support. So there's no means testing here. So how does this work? So this is again, this is the individual who has this amount of wealth, omega, has to pay fixed cost of in-home care if he wants to receive care at home. And his budget set and the preferences determined is optimal choice of this in-home care. If nursing homes provide this high intensity of care and medicaid is sufficiently generous, this individual will prefer to go to a nursing home on medicaid. Now we introduce a subsidy that has half of this fixed cost. So now this individual's budget set expands. He can achieve this utility given by the blue line and you can see that now he's strictly better off at home on the subsidy rather than going to nursing home receiving this high level of care. So that's the idea on the demand side. Now how does this play out on the supply side? So this is a snapshot of the entire market suppose that wealth is the only source of heterogeneity across individuals. This is a simple model illustration. So this is initial allocation of care. Now as medicaid, also as we introduce the subsidy, obviously in-home care becomes more attractive and some individuals leave medicaid for private in-home care. A number of individuals leave nursing home, private nursing home, and go for private in-home care with this subsidy. But now nursing homes respond because as they face higher competition and they compete with each other too for this smaller pool of customers. So their response is to reduce the price to 80K, $80,000 a year and reduce intensity of care as well. So this reduction in price allows them to bring some of the private payers back into the nursing home. However, this reduction in quality makes a lot more individuals leave medicaid because it's no longer such a great deal to be on medicaid in the nursing home. Because remember these individuals who are medicaid only care about quality of nursing home because they don't face the price of the nursing home bed. And we show that they, so this affects a substantial this is what drives the final result. So here's the consumer surplus, obviously increases they're getting this subsidy. But interestingly, medicaid expenditure is actually declining overall. So the policy costs nothing. How does that happen? If you look at medicaid expenditures, they of course medicaid is giving all these transfers they accounted for, they're not means tested but as we said, uniform transfers to single individuals but their nursing home expenses fall dramatically especially if we consider response of nursing homes. The in-home care expenses fall too but not so much if we account for nursing home expense. And so this transfers, so actually this fall in nursing home expenses outweighs the increase in transfers. So the takeaway is that this is a good policy. There are the uniform eligibility means that there are very few distortions. It's easy to implement, it pays for itself no extra taxes necessary. So we don't need to take into account those taxes when computing welfare benefits. Care allocated more efficiently when consumers face the marginal price. Supply side reaction is important and we do think that this high cost of fixed cost of in-home care creates a barrier for using this care. So the conclusion is we built an equilibrium model of long-term care choice with decision makers on both sides of the market. The model generates whole range of long-term care patterns observed in the HRS, the much the distribution of hours of care, patterns of nursing home usage by ADL status and family status and by income and wealth. With much Medicaid rates for in-home and nursing home care, we show that in-home care subsidies achieve a more efficient distribution of care at no additional cost to the government. And the key to this result is that consumers may face marginal price of care unlike for the means tested Medicaid. And that's important to take into account the supply side response when analyzing long-term care policies, even if this policies only target the demand side. So that's it. I have three minutes remaining. So any questions, I guess? Thanks a lot. I have a question. Yes, Pierre? Yeah. You heard before that in France, I mean, there is a scandal about abuses in nursing home and abuses exist also in the US. It's well known. So the question is, how can you account for that in your model? Because clearly, abuses come from both a market and a state failure. The state failure is because the regulation does not work well. And the market failure, it's the fact that there is no good control on the quality because of asymmetric information. So my question, do you think that you can take into account the risk of abuses in your model? So, Pierre, this is a very good question. In fact, so this is a first step, right? They've just brought in nursing home decisions into the market. But we assume that all nursing homes are homogeneous. They face the same construction, everything. There is perfect information everywhere on both sides of the market. Now, you're right that these things happen. And so what we are thinking about extending the model to heterogeneous nursing homes, first of all. So these nursing homes still have to compete, right? And it would be interesting to model private information about the quality of care they deliver. I think this is all on the agenda. I agree that's important. It should be taken into account, definitely a good point. And so it is on the agenda. Yes, this is kind of like a first baby step toward that. But you're right, this is exactly why we want to model nursing home decisions because we want them to respond to government policies. And it's important to know how these government policies can affect their decisions, even if the government does not have perfect information about everything that happens in the nursing home. But you're right, yes, it should be done. Thank you. Thank you, Pierre, Mathias. Ah, yeah, I had a question. Yeah, first impressive that you model both sides of the market, that's really quite amazing. I had one question. So that's this one fascinating graph where this OOP in home care, the green area. So I can't hear you. You disappeared, I can't hear you. Did I press something? I couldn't hear what you said. Sorry, I can't hear you. Your headphones, maybe something, did you? Ah, sorry, can anybody else hear? No, no, we cannot, I cannot hear him actually. You cannot hear. No, I can't hear, no. Sorry, I'm sorry. Maybe you can type your question. Okay, anybody else? I have a stupid question, but in the demand side to obtain your graph, you assume individual preferences, I suppose. Yes, yes. And they depend on only two goods. So here, there are, okay, so where is it? So there are two, this is a simple model, right? This is, so the full model is dynamic model that there are. There is non-care consumption, just regular consumption. There is consumption of care in bad health states and there are big risks. So that's it, yeah. But there's no leisure. Yes, yes, I understand the graph of course, but to derive your result, you have no assumption on the instantaneous utility of... Oh, no, no, what can I say? Is it too good for you have... Oh, no, no. So I... I cut... We calibrate, so there's this parameterization section. I, maybe I should not have cut it so short. I thought I would run out of time. But yeah, there is a whole set of observations here on non-care usage patterns that allow us to pin down these preferences. And it's a discrete choice model. There is a preference shock that determines individual choice of care. So observationally identical individuals will choose different types of care as it is with what we see in the data. So yeah, there is pattern, there's a wealth and income shapes of this usage of home care or nursing home. So this is all... That evidence allows us to pin down the preference parameters. So Medicaid, the CPC allows us to pin down this consumption floors that take effective exemptions into account. So the... Yeah, no, no. There is a model has lots of parameters actually. And all that evidence is used and there is some extra evidence that we used to validate the model. Okay, thank you. You can read the question of... Okay, my tears. Yeah, can you hear me now? I can hear you now, yes. Okay, so that's really fascinating that you have the green area embracing the blue nursing home area. And I was asking myself, is that driven by the symmetric Nash equilibrium assumption? And wouldn't we expect that in reality some nursing homes have incentives to cater to lower care needs? For example, by assisted living. So I understand it's very hard to do in your model, but yeah, so we're going to hear your thoughts on that. So I didn't quite get it. So you're asking... So you're focusing on symmetric Nash equilibrium, right? So that forces everybody to offer exactly the same amount of care in the nursing home. Wouldn't we expect in reality that some people here try to cater and to do some assisted living with lower intensities of care to capture a different market? So we check for deviations from this Nash equilibrium and it's stable. It's... Really, okay, good. Yeah, yeah, yeah. So there is no incentive for these nursing homes, for some nursing homes to deviate. Yeah. Okay, last question, Olga. You last question. Yeah, so I mean, you probably selected this policy experiment because they are relevant for the US, but they are also, I guess they are clearly second best policies. And then the question is, what would be kind of the first best policy in this setting? Yes, another good direction for the next step. Yes, optimal policy would be very interesting to analyze. And there you might want to ask a question, who is it, should we provide the care, should we separate this private residents from Medicaid residents? You could go that way too, change the structure for nursing homes and maybe provide different level of care there. I don't know, there are many dimensions for the optimal policy to go to, but yeah, it's also on the agenda. So that's right. So this is kind of, so the first experiment, its purpose is to basically tie to the household literature that focused on this type of policies and show how it is different in our setup. Once you take into account nursing home response, but yeah, the next step definitely, optimal policy would be very interesting. Thanks a lot, Tatiana, for this very stimulating talk. And now Kyara Kanta from Toulouse Business School. The floor is yours, Kyara. Yeah, let me just, should I share, right? Can you, so can you see my screen? Can you see my slides? Can you hear me? The problem is that I don't see anything. Okay, so first of all, thank you very much for inviting me and for everybody in the audience that would bear with me. So this is a fully theoretical paper. So, and it's about the gender gap informant care and how policies should take it into account and it's going to work with him and with the TSE. So this is quite preliminary. So, well, any feedback is most welcome. It's the first time I'm presenting this work. So, well, here I will not spend too much time defining long-term care and trying to motivate why long-term care is interesting to study, do it to be studied. And so in general, well, we have seen it before, it represents significant financial risk and most, the main provider of care is still the family. So this was also shown by Kelle this morning, earlier this afternoon. And when you look at the differences, so you're actually the family, by family we mean spouses, but also children. And so typically when you look at children, so we're going to talk about children in this paper, the daughters and daughters-in-law have been shown to provide more care than sons. So there is a lot of evidence about that. And yes, so this is so much the case that, well, in a paper about dementia, both another say that basically the best long-term care insurance is a conscientious son, by the way this works, let me not say, is a conscientious daughter. So, so basically why do we might have, why do we have maybe daughters being more involved? Well, first of all, we might have norms, well, societal norms, family norms, and also lower the market opportunities for women. So if women have lower wages, they might also have a lower opportunity cost of providing more care to their parents. And of course, it's just many, the fact that daughters provide more informal care, the biggest provider of informal care, after spouses, is that, well, these daughters will receive probably higher gifts and requests from parents, there is some evidence showing that, but also they will work less. And as Piera pointed out in his presentation, there is a psychological burden and a lot of hidden costs with the provision of care, so that basically the fact that women provide a lot of care might actually not only exacerbate labor market gaps, gender gaps, but might also have impact on the mental health of women. So, all this, all this should be taken into account by long-term care policies. So if you think about this gap in provision of care, for instance, you see right away that whatever the government decides to do for long-term care might have an impact on this gap of informal care provision. For instance, just setting public transfer that are conditional on informal care provided by the family, well, this transfer may actually exacerbate this gender gap in provision, there is a paper about Norway by Jakobsson et al that actually, well, basically reports the fact that social, basically social workers, when deciding how much public care should be assigned to different dependent people, they take into account whether there are some, there are some family members that can help them. But then if these family members are disproportionately women, then basically provides the, and then the social, and these people, well, basically people with daughters, they have some caregiver at home and then they receive less public care, this might even exacerbate this gender type of provision because if the state decides not to step in, daughters might be even more, even more, might be even more obliged or might be obliged to provide to step in. So in such a context where you think that not only that there is this problem of dependence that we have pointed out throughout the afternoon, but in addition to that, there is also, there are also symmetries related to the gender of the children, for instance, then the government might have different roles when designing, might think about different objectives basically when designing long-term care policies. So the first one is obviously providing insurance against dependence and this role makes sense when private markets, for a number of reasons that were already mentioned earlier on, private markets are absent or very thin. So this is one of the roles of long-term care, but if there is this gender gap, then the government, the policy might also redistribute the cost generations, might have an impact on the distribution of surplus between parents and children. And also, of course, across different families which might differ across the gender of the children that might provide help. So families with daughters will be different from families with son for a number of reasons, but also because, and in particular, families with daughters might have families with daughters that might receive more informal care. So this is basically the situation we have in mind and our question is what is the optimal policy in such a context when families differ in the gender of their children and daughters for reasons that I will explain later, which kind of reasons we take into account and daughters provide more informal care. So what do we do exactly? We consider a cooperative intergenerational family model. So in the spirit of primary industry in 1993, and we have children basically that provide care and receive transfers from parents. And the decision about the intensity of informal care and the transfers, intergenerational transfer, are taken cooperatively and the parents and children are assigned some virgin weights that are given. And we abstract from the family norms, well, the bargaining weights might capture some family norms, but we abstract from the society norms that are, for instance, put forward in the 2020, we really look at the social norm. So female daughters provide care because they want to fulfill some social norm. So we abstract from these like spillovers or externalities effects. Daughters in our model differ from sons because they have a lower bargaining weight within the family and also lower job market opportunities by, let me say, lower job market opportunities could just mean lower wages. We assume that informal care and intergenerational transfers are observable and contractible by the government. So the policy can be conditional on the level of the policy that is put in place might be conditioned on informal care and transfers. Well, you can discuss about this assumption. So what we have in mind is a bit like the Norwegian case where basically the transfer from the government where social workers can somehow observe whether there are caregivers and what they can provide in terms of informal care and they decide about the public transfer or public provision accordingly. And we will focus on two policies and try to compare them. At least we started to compare them. Attending policies or policies that is generally specific. So we offer some public transfers to dependent people and these transfers depend on the gender of the children. And then we're looking at gender mutual policies. So policies that are not conditioned on gender. For a number of reasons, you might not have gender dependent policies in particular political reasons. So when you cannot actually condition your policy and the gender, what is the optimal policy in that case? So these are the two policies that we have. And since I always tend to speak too much, I want to give you a preview of the results. So first of all, we look at the last affair. So not very surprisingly. So what happens within the family? So the decision is within the family and we compare boys and families with daughters and with sons. And we see that transfers increase in the bargaining. Transfers to children increasing the bargaining weight and decreasing the labor market productivity. And daughters always provide more informal care and they're always worse off than sons. So they might receive a higher transfer. It's not really safe, it's ambiguous in a model, but they might receive a higher transfer in exchange for more informal care. But this does not compensate them fully for the extra informal care they provide. Then we look at the tagging policy. We show that it can be centralized for its best. So in the first best, we have pulmonary distribution across all dimensions, across states and across generations and across families. And the instruments we need are transfers to dependent people. So basically social long-term care insurance, some transfers from young parents. So this would be like the social insurance premium and some transfers also to children. I will say more later. And we find that of course, children have a lower bargaining weight. So for instance, if daughters have a very low bargaining weight, then transfers to their dependent parents should be subsidized. So transfers from their dependent parents should be subsidized and informal care should be taxed. So you should discourage informal care from daughters with a very low bargaining weight while you should incentivize transfers towards these same daughters. And then we turn to the gender neutral policy. Not surprisingly, this policy is only second best. That does not allow us to achieve the first best because now we have some empty constraints. We need to offer the new policy must be incentive compatible. So now we can only reach the second best and we find some distortions both in transfers and informal care. And I will say more later if I have time. So just briefly about the model. So while we have taken in previous presentation, there were many more questions, but if there is some question about the mechanics of the model or presentation please I can take now. So each parent has one child of gender I, either the daughter or a son called daughters by the substrate G. We design daughters by a substrate G and sons by a substrate B, girls and boys. So basically here we have each elderly person has only one child, which can be their daughter or child. So we only have two types of families, the one with one daughter or the one with one son. And parents have an exogenous income why when young? So they live two periods. They, when they are young, they receive an exogenous income, which is the same for every parent. We don't have it originating income in the income of parents. They save a certain amount K and are dependent to an old with probability Pi. So any case of dependence they will get some informal care A, like A and they might make a transfer cow to their child. So maybe it's clear if you look at it this way. So when young parents basically they consume their exogenous income minus their savings and then when they all with probability one minus Pi, they are healthy, they are non-dependent and then they consume their savings. If they are dependent, they consume their savings, they receive some help from their children. And in this case, they also make a transfer to their children. And we assume that the marginality consumption is higher in the case of dependence. This ensures that there's some need for insurance. And then we assume that basically the benefit that the monetary equivalent of the informal care is increasing and concaving informal care. So this is pretty standard in this type of model. And then we look at, we have the children which just decide how much time they allocate to informal care. They have one unit of time and they just allocate between labor and informal care. And on the labor market, they get a wage and this is the first difference between boys and boys, between daughters and sons. Daughters have a lower wage than sons. So the expected utility of the child of gender I is just, well, the probability power of the parent is dependent, so the child receives a transfer and exchange he or she reduces labor supply by A, the level of informal care. And with probability one on spike, the parent is non-dependent and then the child just consumes the wage, works the whole time and consumes the wage. So as I said, we consider a cooperative model. So the family maximized jointly. Jointly maximized awaited, awaited average of the utility of the parent and utility of the child. And alpha represents the weight that is given to the utility of the child and one minus alpha will be the weight for the parent. So again, we assume that daughters are different from boys in the same dimension, in the sense that girls, the daughters have a lower bargaining power within the family than girls. So maybe they're lower. So in principle, daughters have a lower bargaining weight so this might capture some norms, social norms in a little bit now, what it is used for. So what we find here, basically the family maximizes this object with respect to informal care and transfers and intergenerational transfers. So the optimal level of informal care just equalizes the marginal benefit of informal care, gamma prime, AI, and the marginal cost, which is the opportunity cost for the child, which is WI. This level of informal care does not depend on the bargaining weight, it's only on the weight. So this is actually the efficient level of informal care. We see that this is the first level of informal care. It's just marginal and then it's equal to marginal cost. And there is a reason for the family, the jointly not to basically maximize the pie in its respect. And we find of course that since daughters have a lower wage, they also will provide more care. They have a lower marginal cost of provision. And the optimal transfer will satisfy this condition. This condition basically tells you that the marginal utilities of the parents when dependent will be equal to the marginal utility of the children in case of dependence only if the half is equal to one half. So for instance, if the children have a higher weight than their parents, then in the objective function of family, then the marginal utility of the parents will be higher than the marginal utility of the children. And this is important for comparison to the first best. So basically find that informal care decreases with the child's wage, but does not depend on the bargaining weight. This is what I already said. And also what we find is that the transfer to children now decreases with their wage and increases with their bargaining weight. So this is again very intuitive, but this makes a comparison between the transfer to boys and the transfers to sons and the transfers to daughters is ambiguous because daughters have a lower wage. So this goes for a higher transfer, but they also have a lower bargaining weight which goes for a lower transfer. So the comparison is ambiguous. What we can show on the other hand is that daughters are always worse off than sons. So basically VC is always lower for daughters than for sons. So even if the transfer to daughters is higher than the transfer from boys, even in this scenario, this is not enough to compensate for the higher informal care that they provide. So when we look at the first best, well, the difference between what the family does and what the social planner does is that the social planner basically max is utilitarian and is the same weight for every generation and for every family. So the social planner just maximizes the sum of the families with girls and boys which are the same, they are the same, they are 50-50 in the population. And basically the sum of this utility which attributes weights one half to the utility of the parents and the children. So in the first best, well, we don't introduce any sensation, but basically what we've had is that the marginal utilities are equalized across families based on new natures and generations. So the marginal utility should be constant in respect of whether you're a son, a dependent elderly or a dependent or a non-dependent elderly or an infant. And in the informal care, we get this expression that we're equal to gamma prime which is the same as in the last year. So the trade-off is actually the same as I already anticipated. So let me go move on to the first policy we analyzed. The first policy we analyzed is a tagging policy. So where we have gender-dependent transfers and what we consider that's actually decentralized. So the transfers we need to decentralize the first best are transfers, are a set of transfers to dependent parents. So we would have transfer, we call them TS, transfers to the C, TS, which is dependent on the gender. So we have a fact with A and it is potentially a function of informal care and transfers. And then we would need the transfers to children on a non-dependent parents. They are the ones that do not receive any transfers on their parents. So the policy includes the optimal policy should include some transfers to non-dependent to children that do not have their parents, as their parents are healthy. And then we have some transfers to or from young parents. So this is T1, T in first period. And also this is gender-dependent and on the gender also on the child. It potentially depends on the gender of the child and then potentially because I will show you that we find that this, that we don't need any effects for gender-dependent for all transfers. And they potentially depend again on the informal care and intergenerational transfers. So this basically is equivalent to a policy where the government that care transfers and encode this lump sum transfer, TS, LH and T1. So just here basically I wanted to have this because to show you how this transfers basically play in the utility of the parents. So basically we would have a transfer for parents in young age, T1. This looks a bit like a premium, an insurance premium. And then parents, sorry, this is basically the parental issue goes here. And then when sick parents, they get, when sick, when dependent parents, they get TS. And when you look at children, they get LH, when the parents are healthy, they get the transfer LH. So this is basically what I wanted to show. And of course, savings, we assume that savings are still chosen freely by the family. So what are the results for this policy? So we find that a gender-specific transfer to depend. So the first best that can be implemented by a gender-specific transfer TS to dependent parents. So this is, we can interpret it as a long-term care benefit and this benefit has to be a function of A and Tau, or both. And then there should be a gender-independent Lanzan transfer for young parents. So basically an insurance premium, which is uniform. It doesn't need to be gender-specific. And then we find a gender-specific, and then we still need a gender-specific transfer to children of healthy parents because they do not receive family transfers. So we cannot, I mean, in order to ensure that we get to the first best consumptions, meaning that they get the same marginal utility in both states of the world, we need some transfers. And the first best, we show also, by the way, that the first best can be decentralized by union instruments, but I will not enter into this. So what is more interesting is, so basically we have Lanzan transfers in the first period which are totally independent from the gender and from the transfers and care. Of course, they were in the first period, so this is practical. And then we have transfers to children that only depend on the gender. They do not depend on the care and on the Tau. So what depends on informal care and the Tau would be this gender-specific transfer. So the transfer will be conditional on how much informal care parents receive and how much they transfer to the achievement. And actually we find that the marginal transfers look like this. So the derivative of the transfer with respect to informal care, like this would be this. And this in the first line is in the marginal transfer with respect to intergenerational transfers. And what we find is that, for instance, you see that here, if alpha is greater than 1-up, if children, so maybe not, if alpha is smaller than 1-up, so if the child is lower by gaining weight than the parent, this expression is positive. So we should subsidize transfers at the margin, while if alpha is smaller than 1-up, we should tax informal care at the margin. So the idea is children with a lower by gaining weight are kind of exploited by the parents. So in order to establish some equality for generation, we need to subsidize transfers and tax informal care. And the opposite is true if the children have a higher bargaining weight. So all this is related to paternalism. So the parents and children consumption levels are weighted differently by the family and by the social family. So we need to distribute these youth across generations because basically the social family doesn't benefit the utility in the same way as the family. And then just to conclude on the last policy we consider, we consider gender and neutral policies. So all this is very nice. So all this tagging policy leads us to decentralization of the first phase, but very often these gender-specific policies are not feasible politically in particular. So think about, I don't know, different, for instance, pension rules and how they are often, how they, well, for instance, how they have been kind of ruled out by the European Union. So what the best you can do in this case if you cannot do a gender-specific policy, you can offer a menu of contracts and then let families choose. So in order to differentiate, to still be able to not to pool of girls and families with sons and families with daughters, the best you can do is to offer a menu and make it in terms of compatible so that families with daughters will choose a different policy than families with sons. So we can show that when we look at the first best implementation, so the policy I just presented, if you let families choose, all families would select the policy designed for families with daughters. So basically what we have is the only binding I could constrain that it's the one of families with sons. So families with sons would like to mimic families with daughters and this is also intuitive because the families with daughters are pure resources and daughters earn less on the labor market. So what the government wants to do intuitively to distribute from families to daughters to families with sons and when you look at incentive compatibility constraints under the first best policy, sons would like to mimic girls. Sorry, families with sons would like to mimic family with daughters. And so we have the same problem as before for the government except that now, well, except that now we have incentive compatibility constraints here which is incentive compatibility constraints of the boys. We want the boys to act like boys, and we don't want boys to act like girls and take the policy designed by girls. So I say boys and girls, but the families with sons and families with daughters. So what we find is to leave the last part. So what we find is that the first best solution of course cannot be implemented here. Informal care will be distorted the output for families with daughters. There will be the usual result of no distortion at the top for the informal care of the sons, but there will be a distortion up for families with daughters. So we will have basically more informal care than in the first best. Remember this was the same as the last affair. So basically daughters will have provided more informal care than in the last affair under the solution and the intuition is just to relax. And the reason why you do that is to relax is because families with sons who actually not mimic families with daughters. And the last interesting point is that we find that the optimal gender neutral policy still provides full insurance against risk of dependence for both generations. Okay, so if you look at the first part of the sense there is a full insurance against risk of dependence. However, so they managed to move basically their imaginary behavioral consumption but the allocation of those generations is now distorted. So the transfer intergenerational transfers are not the first best transfers and they are distorted for both the sons and the daughters. And this is because in both cases the children and parents have different revenue weights than in the social worker function when they have the same revenue weight. So what we find is that when sons have a higher weight than their parents, so if alpha for sons is greater than one then parents of sons will receive a lower share of the surplus in the first best and parents of daughters will receive a higher share of the surplus in the first best. So you will tilt the transfer so that the families with sons will prefer, so families with sons will go for the policy design for sons. You distort the transfers to give more surplus to the sons and these families value more utility of the sons they will like that. And you distort the transfers for daughters so that you give more utility to parents of daughters and the families of sons do not like it because they give more value to sons. So here there is a trade of basically between paternalism and incentive compatibility, okay? So providing incentives and relaxing anti-constraints is not fully compatible with paternalism. So you would like to equalize marginal utility for functions across generations, but you cannot do it because this is wouldn't be entirely compatible. So I think I more or less on that. So we find that daughters are always worse off than sons in the less affair. I think this is an interesting result of the less affair. We always find that the daughters are worse off. So they're never compensated really moderately by, in such a model for their extra effort. And the policies depending on gender caregivers can redistribute not only across rates of the world but also across generations. And gender neutrality basically uses the type of redistribution, in particular the distribution across generations and that in particular it hurts families with daughters and implies more informal care by daughters. Then what we would like to do for future research versus the very simple model, we don't consider private insurance market. So the next step would be to introduce private insurance. Maybe starting with some fair insurance to basically see what happens. There will still be a role for the government and but it would just be more about redistribution across generations and families and probably the role of the government in terms of providing insurance would be less, would be less time. So I'm going to put you down. Thank you Chiara for this nice talk. Question or comments? Yeah, can I ask a question? Yes, you can. Yeah, you're the chief. No, I'm not the chief. Well Chiara, my intuition is that the government should try to encourage the son to help their dependent parents and discourage daughters to do that. I mean, to try to reach a better balance in informal caring between genders. And the reason is that because of the collateral effects of caring, I mean, that would be fair. Do you have that kind of result in your paper? Yeah, so it was, it creates to this in the sense that so here it is a little bit mitigated by the fact that we, I think we have a lot of instruments that we consider, but if you just look at about this, so you can take care in part, you can take care of your distribution between daughters and transfers, direct transfers. But probably it is also captured by this. So we show that basically what the dependent parents should get when they are dependent from the government is, for instance, if you take daughters, if daughters are very low bargaining weight in the family. So you would find that the transfers to daughters should be subsidized when their informal care should be taxed. Okay, so this goes exactly in your end. So this is strongest for the children in general that have low bargaining weight. So we have that, so we, I think that if we didn't have our transfers to children, LH, which allows us to redistribute nicely in a more direct way between daughters and sons, I think the results would probably go, I mean, there would probably be more action here. But yes, I would say, for instance, here, it would be your intuition in this model if daughters that have bargaining weight, that is higher than their parents, while sons have a bargaining weight that is higher than their parents. But so this is captured a little bit by the bargaining weight. And in a way, whether you want to subsidize or tax informer care depends on how big is the bargaining weight of the child. If this bargaining weight is low, you want to tax informer care exactly, and this would be a factor of your intuition, I guess. Thank you. Olga? Yeah, so intuitively, I thought the gender abandonist says would be much larger within families. So when I would set up a model, I would say if I have a family with a girl and a boy, and then there's bargaining between the girl and the boy, who does the care, the gender imbalances would be much stronger. And the question is just, why didn't you choose this setup? Is it too obvious or too difficult? No, I mean, it's, well, we simplify, yeah, we looked at the simplest way that, so this way, you get very easy comparisons. So you don't have extra factors for gaining within the family, but of course it will be very interesting to consider. And then you would consider, I think it could be also a natural way to go, to consider basically four types of families, two daughters, two sons, no, three types of families, daughter, son, son, and daughter, son, and then maybe start from there. So this is a very good suggestion. And the reason why we did that is that it was just natural, I don't know, it was more, it was simpler. It's just reason, but it would make a lot of sense to look at this, but there will be more action in a way, because then there will be some daughters from daughters to sons, and then here you would have more complex functions for the quality, because depending on what you do with both your daughter and your son, the transfer from the government should depend on what you do really between the family, with both children. But yeah, it's a very good point. If I can just intervene, you are right, but I'm not sure if it would change a lot, actually. I record my paper with Francesca and Kerstin, where it's a completely different setting, because we don't have differences in bargaining ways, but we have a social norm. But there actually, we do have either two daughters, two sons, or the mix of the two, and actually the funny thing is that this makes things very complicated, and one of the referees told us that, well, this is really nonsense, you should really concentrate on families with one child. And he was actually basically right, so he or she. So you are right, this would make things picture, but I'm not sure if it would change a great deal in the result, as long as we maintain the assumption of overall bargaining in the families, but I'm not sure, so anyway. It's an interesting question. We should have a discussion about that. I think also it changes a bit, it would make heavier our informational assumptions, because to make the policy, you would need to make the policy based not only on the overall informal care literacy, but also on the, can you observe really whether the informal care receipts are provided by doctors or sons? So here it makes things easier in our model in terms of informational data. Even if your model is static, have you an intuition of the impact of your gender specific policy on labor market and on the wedge gap between a daughter and soon? So, okay, let me think about that. So in fact, if I think about, well, now I'm thinking about the first best implementation basically, and then well, in the second best you will have some sort of, but as long as you manage to, as long as you tap informal care, you should push really, I mean, as long as you tap informal care for women, for instance, then you should be able to push more women to the labor market. So I would expect a lower gap in terms of participation. When it comes to the wage, we haven't modeled it at all. So you would need what you would need probably some education as well. You change that, change the program to your own, you change that, change the productivity of women on the labor market. So I'm not sure. No, I don't have a good intuition. But if women are well overburdened wages, I guess they would get less education on their young ones and then lower wage. Because in the reality, but I don't know, but in the reality, it seems to me that the non-feasibility of gender-specific policy come from a pressure of labor of, I don't know the word in English. It's from the patronage side that it blocks. That is to say that they are afraid that if it was too favorable to women, they would find themselves with a labor market that is not the one they want. Okay, so this would be the employers. So the employer's lobbying that is often against this kind of gender conditional policies because they are afraid that this would, well, basically make women more, so this would make wages go up. That's what they're afraid of. Frankly, I don't know. In this case, right, or that's basically what you are, but so they could be more bargaining power-specific workers, but I don't know, yeah. Well, can you help me? Yes, please help me. Yeah, okay, but I'm not sure because you see, we find that if care of daughters is distorted upwards, so which would, I guess, decrease their labor supply. So you would rather expect their, so if you take into account the effort on the labor market, which, yeah. Let's see, okay, let's see. But anyway, wait a minute. Oh yeah, no, it's good. It would decrease their labor supply so the wage may actually increase, yes. But there are an impact on the difference of wage between man and woman. Yeah, you're right. You change the difference. And in your model, all is based on this difference, not on the level of wage, but on the difference between these two. But it's another question. And you're right. Not in your model. This is interesting, we should think about it. You're correct that I was reversing the sign, but you're correct that this was probably increased women's wages, so making a gender neutral. So this would, but we will, it's an interesting suggestion, we will look at this. So, thank you. With pleasure. You're welcome. Thanks a lot, Chiara. The last paper is not explicitly long-term care, but it's on longevity on a hot issue in French because it's on the design of retirement system. Then Jean-Marie Lozak-Meur, the floor is yours, Jean-Marie. Jean-Marie is up here. I cannot hear you, too. Yes, we don't hear you. Excuse me, is that okay? Is it okay now? Yes, it's okay. Yes, it's okay, Jean-Marie. Sorry for that. Yeah, it's right that this paper does not deal directly with long-term care, but it's about retirement policies so that longevity here will play a big role. And there are a few common points with the last presentation is that we take gender seriously into account and the other one common point is that we share one co-author and the other co-author is also Italian. Okay, but this is a paper about retirement system and especially with... Excuse me, Jean-Marie. It was just for... It's not very important, but Francesca is the first author on the paper, so not that. Yeah, because her family name is Kantar. No, Francesca by Gottsey. B comes before C. Oh, that's right. Yeah. So you mix up between the Italians. So not all Italian women are alike. So Francesca, not just to point out that this is a mistake. So Francesca is the first author of the paper. So yeah. Okay. So this paper is about gender wage gap as the last paper, but we also speak about longevity gaps and their impact on the optimal retirement system. So let me introduce you briefly to things you know already, I guess. There are two gaps when considering gender. One gap is longevity gap. We know that women die earlier than women. So this difference has been decreasing over the last decades, but well, it continues to be quite significant. If you look at the OCD countries, we can observe that women's life expectancy at birth is actually around four to six years that of men. On the contrary, there is also wage gap in the sense that men have a higher wage in general and women in this time taken in the European Union are earning 15% less than men when considering the wage per hour. Okay. So we studied this. We take this into account and study their implication for this design of pension system that will be represented by net benefit rule, which is a function of retirement. Okay. So we'll distinguish our result with different social objectives. Take simply the utilitarian one. Okay. This will lead to, because of the gender wage gap, some redistribution from men to women. Okay. Longevity gaps will not play a role here if we are purely in a utilitarian framework. Why that? It is because for a given per-period consumption and the same retirement age for a utilitarian government, giving $1 to one or the other has the same social value. Okay. But we will study the case where there will be aversion towards life expectancy or lifespan inequality in the sense that we will have a concave transformation of lifetime utility. So that the direction of redistribution will be ambiguous in this case. Okay. We have additional complication. So the first one is that we, in the paper, study the case where individuals may be single or live in couples. Okay. So that the rules will be different here, depending upon the marital status of individuals. And again, as in the last paper, we will take gender neutrality into account. Okay. Because the optimal rule, as in the preceding paper, is likely to be gender specific. Because if we observe gender, you observe one more characteristic so that the policy will be more efficient by definition. But we will impose gender neutrality as an additional requirement. So of course, a simplistic interpretation of gender neutrality here is that would be, well, we have a uniform system of retirement and that's it. Okay. So that's a very simple answer to this question. Here we add up the most sophisticated approach in the sense that the menu of contracts, which will be a retirement age and pension rules, okay, will be a self-selective, okay. And more formally, gender neutrality here will be equivalent to say that gender is not observable. Okay. Yeah. So let's move quickly to the model. So we have a very simple model where the utility of an individual, okay, is a VT at time T at HD, okay. Which is simply the utility of consumption at date T minus the digitality of labor. And here labor will become as ages increase, the digitality of labor will be large, okay. So we take a discrete approach, okay. So that per year, for example, the labor supply will be constrained to be zero or one. So here we will say one, okay. And which means that the utility per period will be the utility of consumption at date T minus the digitality of labor until the age where you retire, the retirement age is denoted two, okay. And after retiring your utility per period is simply the utility of consumption, okay. We will assume that there are perfect capital markets and certain lifetimes, okay. Just to be simple and to concentrate on simple heterogeneity stuff. So it means that the level of consumption will be equalized in all periods so that the life cycle utility can be representative here. The utility can be described by this equation. So it's a life span T, capital T, times the utility of consumption minus the digitality of labor where two is the retirement age, okay. And people will be characterized by two parameters. One is the per period earnings, okay. So that lifetime labor income will be this per period earnings times the retirement age. And TC will be the lifetime consumption. So here subscripts J will refer to the gender and I will be used to describe whether there is indeed really a single or living couple. Okay, so we assume that, well, as in reality men and women populate society in equal proportion and can be divided between being singles or living couple. Okay, so the wage gap will be such that, okay, the per period earnings of the female will be lower than the one of males, but women will live longer so that the lifespan of female will be larger than the lifespan of men. And we assume that the utility when dead is zero. And we will assume that the social planner observes gender, marital status and retirement ages, but not individual per period consumption, okay. So that we will study contracts defined by retirement age and net pension benefit that is retirement age. So pension P, so P will represent the pension benefits minus the contribution you made during working. And this will be contingent on the marital status and gender when possible, okay. And we will implement this by a net pension rule depending on the retirement age taken by the individual. Okay, so in a few words, what happens if in a laissez-faire economy like that? Well, we know that for singles, per period consumption for male will be higher than the one of females. Especially because of the fact that male have higher earnings. And well, we don't know whether women or men will retire. We don't know whether women or men will retire. We don't know whether women or men will retire. We don't know if female will retire before men or the contrary, but because of substitution and income effects, okay. But as usual, we assume that substitution effects that dominate income effects so that male will tend to retire later. For the couple, what happens in a laissez-faire? Well, the total income of the family will be equally split between the two members of the couple, but men will retire later than their spouses. And this is independent of the form of utility function because consumption will be the same. Okay. So what happened in the first best economy here? So we have a social welfare function which is a concave transformation of individual utilities whether they are single or live in town. Okay. And this is a kind of social welfare function and this transformation will be increasing and concave. Okay. So that you can model utility, a pure utilitarian government by V equal to zero. Okay. And in this case, in the first best, you will have some redistribution across groups only with different income. Okay. Which means that male, there will be a redistribution between, from male to women. Now for V greater than zero, there will be concern for distribution across groups with different lifespan. So that in this case, redistribution will be ambiguous. Okay. So basically that's that's a result during the first best. Okay. On one side, if we consider only singles, we have redistribution from male to female. Okay. What counts here is the level of earnings of men which will be lower than that of women. And if we are in the pure utilitarian setting, then we'll have redistribution from men to women. However, when a version to lifespan equality, inequality is taken to account, this redistribution may be reversed. Okay. So if we consider couples, we'll have that redistribution will be from male to female, together with the fact that female will take their retirement before the one of the men. And basically that's a less effort solution. Okay. So no government intervention here will be desirable. However, when we introduce some degree of inequality with respect to the lifespan, then we may have some redistribution from women to male and we'll end up with a solution in which female will retire later than men. Okay. Now what's going on with gender neutrality? This will complicate the, of course, the allocation and this will limit the physical redistribution. Basically we'll have some, to add some constraints which are incentive compatibility constraints. Okay. We will not be able to condition transfers depending on the gender. Okay. So he will have a bidimensional heterogeneity, which is the way the earnings, annual earnings and lifespan. Okay. So that no general single crossing property can be established so that either, for singles, either one or the other of both IC, incentive compatible constraints will be binding. Okay. So for singles here, these constraints say simply that women do not mimic the contract offered to male and the second here constraint is exactly the opposite, is that male do not have an incentive to claim the retirement age and the pension benefit offered to women. Okay. This will be similar for couples except that here, distribution will not be easy to do because, because basically spouses will equally split their income including pension. Okay. And this equal. Okay. So that the government cannot undo this. So what happens if we consider the second best setting will have different cases for singles will have a different cases possible according to which what the type of incentive, the compatibility constraint is binding. However, if you look at the paper in our calibrated simulation the constraint saying that male do not have to mimic the allocation given to female will be binding. Okay. Which basically means that you will have to offer some male, some informational hands so that gender neutrality here will impair single women. For couples, well, the first best allocation will be incentive compatible as long as the first best solution is characterized by the fact that women retire earlier than men. Okay. So, which is the case if inequality aversion to inequality in lifespan is small enough. However, in on the contrary, when you want in the first best that the female retire later than men, then the second best will involve the same retirement age for the two members of the couple. So many will have a uniform here solution. Okay. So here gender neutrality will impair male spouse. Okay. So let me conclude my presentation was fast. Okay. I know I'm still, I'm still on time. So our theoretical analysis here is completed in the paper by a numerical simulation based on the calibrated model. Okay. And it illustrates our analytical result and and give some numbers to the one derived in the paper. And it especially quantifies the size of the overall welfare cost imposed by society by imposing gender neutrality as well as its impact on the different segments of the population, male, female, singles and spouses. And also in addition, we also consider the more realistic case where singles and couples coexist. Okay. I think that the main takeaway of this paper is that the gender neutrality here will hurt the gender towards whom the distribution is targeted. In particular, it impair single women and male spouses while it largely benefits to single men. Okay. That's it. Just on time. Thanks a lot, Jean-Marie. Questions, comments. Ah, welcome. Politically, is it really, so Olga, sorry. Yeah. So this is very interesting, but I'm just wondering whether the results are driven by the assumption that lifespan is given because men could use income transferred to them to live longer and wouldn't this then kind of work in the opposite direction? You would mean that lifespan is endogenous here? Maybe I misunderstood, but I thought it is given in your model. Yeah, it is given, yeah. But if it wouldn't, if it would depend on expenditure, then it's no longer obvious that you should distribute away from men, or? Well, it would be the same for women, so I don't think that it would change the results, maybe. Yes? What makes you say that life expectancy would depend on the transfers? So is there any evidence where I don't know the empirical literature well, but is there any evidence that higher pensions lead to longer life expectancy? No. No, I thought at the contrary. So if, let's say, if a constant share of income is used for, let's say, healthcare and life extension, then a man lives considerably shorter, then couldn't it be worthwhile to transfer income to them because then to make them live longer? Yeah, we have to think about this, but I don't see exactly how this would work in practice because I'm not sure if... Well, I don't know how desirable would be this policy because it would mean that also you transfer money from women to men, so in this case you will decrease the lifespan of women by raising... So I'm not sure that this policy will be desirable even in the purely and you're delaying this. But if I understand Jean-Marie, in your paper, longevity is exogenous. Yeah, yeah, yeah. Okay. If it were endogenous, things would be different. Okay. And the objective function would be crucial. Yeah, of course. Yeah, sure. We agree. That's good. I mean to end the session. Do you know any paper who looks at endogenous longevity? Oh, yeah. In a theoretical, okay. Paper of Pierre. But we can't look at all that. Some paper of Pierre on Gregory... Okay, yeah, okay. Can you send this to me? Yeah, I would like... I don't know this literature well enough, so sorry. So I would be interested in seeing this. I slide it under your door in a few moments. Yeah, but... But as it's a literature with Pierre and Gregory, I'm not sure it goes under your door because it's still very thick. Okay. No, but Pierre can... Gregory can send it to me by mail. It would be easier. Because... So... Okay. I would like to... to thank all the speakers. I have just one remark on the last question. Yes, Philippe. If you allow me, it's very, very brief. The fact if longevity is endogenous, nevertheless, probably when considering the point which has been made by... by... ...Zachmer, the timing of both problems are relatively different. Because the consequence on longevity will be very, very long-term, while the consequence on... on redistribution and etc. will be probably medium-term and not as much long-term as for longevity. And therefore, we have a transition path which probably is more complex to design. Mm-hmm. Yeah. Thank you, Philippe. Okay. Then, I would like to... to thank all the speakers and all the participants for this very, very stimulating session. I think, of course, the score, the foundation score. And I want to thank Florence and Valérie for their remarkable work, their organization skills are a considerable asset for the Toulouse School of Economics. Yes. If you want to conclude, or, Philippe, if you want to conclude, the floor is yours. Maybe a few remarks before Pierre because Pierre has to conclude it is. But I would thank also all the... the speakers and also all the participants for their question. And I think it's very highly stimulative. There are empirics and theorics of something to provide to us and we have to think about it even on the side of the business because the problem you have been arising, for example, the last question is a tremendous question when managing an insurance company. And, of course, we will discuss with Tess if we can, of course, the workshop by providing the discussion and all the pictures. And I don't know if it is possible to have the presentation made also public, just the question will be probably raised on the whole side because we want all this kind of document to be as much as possible public. But, of course, if you think that your research is not sufficiently advanced, then it will not be possible. But I leave the floor to Pierre. Well, I don't need the floor. Let me say that after having heard these six fast words, I must say five. Fascinating. I can't say six. My feeling is that there is much to do. We still have much to do. I didn't listen to himself. That's why he says five. He wasn't listening when he was talking. It's the reason why I can't say six myself. Thank you, Philipp. I can count on you. No. I think that one of the big issue I'm sorry to come back on that is the issue of abuse. I mean the quality. And by the way, I think we should look not only at the abuse in nursing homes, but there is also abuse in families. Because when you have subsidy transfer to the family, I mean there is a lot of strategy which can end up keeping the dependent person in a closet and the rest of the family benefiting from the transfers. I mean that's not unusual, unfortunately. And the question is how can we get a good regulation process to try to control abuse both in the nursing and in families. And maybe Pierre differentiating nursing home which are profitable and non-profit nursing home because we are in a sector where both are operating and relatively dynamic and therefore if something is possible also on that point it's interesting then we can look at what competition is providing and then what profit is providing or not providing. Okay. So I think we should stop here. Thanks to everyone and see you next time. Thank you very much and goodbye. Thank you to the organizers for the conference. It was great. Bye bye Tatiana. Bye bye.