 Okay, good afternoon. This is a paper on making the poverty line dependent on the reference group. There's some illustration. Before I forget, let me mention that I have three quarters, two people from the Indian statistical institute in Kolkata, Satya Shakravarti and Nashi Keta Shatopadyai, and a former student who's no teaching at IEL University. Well, after Maria knows the talk, I don't have to convince you that relative and absolute income are important. And the purpose of this paper is actually, there is a similar distinction. You have absolute poverty line usually in developing countries, and you have relative poverty line in richer country. And after what we heard from Mariano, there is certainly a case for assuming that the poverty line should have both an absolute and a relative aspect. And what we do in this paper, we derive axiomatically a poverty line which we'll obey these two assumptions. I will not go into many detail concerning the axiomatic derivation. I'll give you the intuition. And before that, although Mariano talked about reference group, I'll give you some survey of recent work on the importance of reference group. And then I'll do this axiomatic presentation, and at the end I'll give you some result of our empirical application. Okay, now as it appears here, certainly, choosing a poverty line has a lot of impact from a policy point of view. As you know, the World Bank in 1991, following some work by Martin Ravallon and Datte in Vandevallet, had fixed the poverty line, an absolute poverty line of one dollar. And later on, a few years later, other work by Martin Ravallon, Chen and Sangrola, decided that the poverty line, absolute poverty line should be $1.25. Just to say a few words for those who are not familiar with these papers, how did they get to $1.25, very simple? They took the national poverty line in various countries, relatively poor countries, obviously using a purchasing poverty exchange rate, that they regressed on the log of per capita expenditure. And what happened, they got a line which was a regression, now if you want a kind of, which was flat up to some level of per capita expenditure, and then it was rising. So as a point where it was flat, that gave them the idea that this should be the poverty line, so it used to be $1, then it's $1.25. Though there's been some criticism, some serious criticism of, as they approach, you can read it in Angus Deaton presidential address to the American Economic Association in 2010, and where he gives a lot of example which showed that this approach is somehow problematic, he made some proposal, but I do not have time to go into details. So, as I said before, we want to take the idea that a poverty line should have some absolute, as well as some relative aspect. And the way we do this, and you will see it when going a little bit into the demonstration, is that we actually, we compare two situations. Okay, let's assume we have an individual who is just at the poverty line, whatever the poverty line is, and he doesn't take it to account other people's income. So he has some utility which he derives from his absolute income, which is a poverty line. And we compare this situation with another case where we assume the individual is again at the poverty line, but is also influenced by some referencing. And we will assume that in the post case, the level of utility is the same, and we will derive as a consequence a way to define the poverty line. So that's your general idea, and you will see the details later on. Now, as was mentioned before, we, the importance of relative income is a relatively old tradition. Mariano mentioned the famous citation by Carl Marx and the Houses, the work by Duesenberry. Yes, there is also a long, relatively long literature, more, centered more on the idea of relative deprivation. It started with the post-poverty work of Rensimand on deprivation 66, and then you have several other papers which took, which extended in a certain way, the early work of Rensimand. Okay, so let me just say a few words for a few minutes on the idea of reference group, because it is one of the key aspects of our approach. Now, some of the ideas that I will mention quickly now have been already mentioned previously. So there are several ways of defining a reference group. The first, one possibility is to consider a reference group, people who, you know, who work with you or something like this, you know, and you, in the paper by Claudia Sienic in 2009, you have this kind of approach. Clark and Andrew Clark and Oswald define the reference group of a worker as the income of employees who had the same age and level of qualification as a worker and were doing the same kind of job. Other studies look more at the characteristic, okay? And the trusting work by Adafi-Rere Carbonell, where the reference group of people who have your age, your level of education, your region of residence, a little bit similar to what Mariana presented previously. Some other people define a reference group or reference income as the average income of individual of the same race in the cluster and district where the individual survey live. This is a paper by King Don and Knight. Now, as far as the direction of influence, you know, how do other people's income influence me? Well, usually the emphasis is on status, which as was mentioned previously by Mariana with other people, if my reference group income increases then I will feel not so good as before. And this is mentioned and previously tested in several paper by Claudia Sienic, 2000, and Clark and Sienic. But I wanna talk about another effect which until recently was really only theoretically presented by the wisdom of testing. This idea which goes back to a famous paper by the late Albert O. Hirschman, who is a technical appendix by Michael Rothschild, as a story is as follows. Albert O. Hirschman would be teaching in several universities, his life career was teaching, was working at Harvard and he got stuck in a tunnel in Boston. So there were two lines that were stuck and suddenly the line next to him was moving and his line was not moving. And he says he didn't feel bad because his idea was if this line is moving, I will soon also move. And so he felt good about it. And that gave him the idea of the tunnel effect. What is the idea that when other people's income increases, well, you may eventually expect that your own income will increase. And this is a significant effect. So that was a nice idea, which was not tested, but it was recently when a few years ago tested by Claudia Sinek in two paper. And there is some evidence that this effect exists also. Obviously, the status effect is important, but this exists also. Some more, a few additional work, which you have on the parallel impact of your own income and rising reference income, like in the previous paper we had. For example, Knight and Corsair looked at subjective well-being in China and in their regression they introduced a dummy variable indicating whether the household income was much above, above, below, much below the village average. And Andrew Clark and Corsair reported a regression where the dependent variable refers to the satisfaction with income and the result is interesting and to compare with your finding by Iano. It then appears that the coefficient of own income is about three times as high as that of self-reported reference income and of opposite sign, obviously, even when the variable measuring the comparison intensity of the individual that is how important it is for the respondent to compare our income with that of other, is introduced. So this was really just to show you that there is a rising literature stressing the impact of the reference income in a recent paper, Bernard Manprach you know, tried to convince people that it is very important to collect information on the reference income. Okay, so let's now present a little bit of a formal framework. We will have actually a narrative and a multiplicative form and this idea appears already in the paper by Clark and Oswald. Our idea is that the individual utility is increasing and concave in absolute income but it is decreasing and convex in the reference income. Okay, I gave you already before the general idea that we compare two situations when one, when my utility depends only on my own income, the absolute approach if you want and one where my utility depends also on other people's income. Now what is interesting is that we prove that whether you take multiplicative or additive form which means we can assume that what's important is the absolute gap in dollar between my reference income and my income or you can assume that what's important as far as reference income is, is a ratio between the reference income and my income. What's interesting, whatever you assume two possibilities, obviously we are not, it's not the same demonstration and even not the same axiom but we always get the result that a new poverty line taking into account both the absolute and the relative income becomes a weighted average of the given poverty line, the absolute poverty line and the reference income and we can give a nice interpretation to the weights. What is also attractive is that in fact the results we get we can show that it corresponds by choosing correctly the weights to, for example, if we take the EU standard where the weight is 60% of the median income or the mean income and we'll see in a second just to remember right now or a proposal made by Tony Atkinson, Francois Bouillon, 2001, we can show that these are particular case of the results we did. All right, so a little bit of mathematics without going into too many detail, let X and M be respectively the absolute income and the reference income of individual. We can call M this reference income as a kind of positional good if you want. M could be the mean, the median income or whatever you consider reference income and we assume utility X of M which is it increases in X but it in the concave, it is concave in X but it decreases in M and other things come and it is convex in M. All right, these are quite standard assumption. What's the idea? Why do you have this convexity and this negative income in M? Not only when the reference income increases, my income doesn't change, I will feel worse but when it increases even more, I will consider that it becomes more and more difficult to reduce income and that's why you have this convexity. All right, so let's first, the first case is when I assume that the way I look at the reference income is by looking at the difference in dollar term between the reference income M and my income. So the utility function like this, sorry, a utility function like this, my utility depends on my income as well as the gap between my income and the reference income because the reference income is higher than my income because we focus on poverty here, obviously this is going to be negative. Now what action do we propose? Two actions, very simple. The first one is we have called linear translatability and it says the following things. If you add the same amount in dollar to my income and to the reference income, then my utility following this increase in the income of the reference individual and my income, my utility will increase by some perception, by some share K of this additional income, okay? So the idea is that since I'm the equal, equal of the absolute reference income, the relative status remains the same because X minus M didn't change, X plus C minus M plus C doesn't change, but my income increase, so individual utility should increase. And this axiom assumes that that utility doesn't increase necessarily by the full amount but by some percent. The second axiom is linear homogeneity which says that if you multiply my income and the reference income by some constant C, then the utility will be multiplied by some constant C. And then we prove that given these two axiom, I don't enter into the proof. Actually I would not be able because I'm not a special axiomatic, this is by the field of two of my co-authors, those who work at the Indian Statistical Institute, then you can prove that the utility is written as a weighted average of my own income and the reference income with the constant A being negative. And actually it corresponds somehow to the, an ID which was already put forth in 1998 by Clark and Oswald, the idea of additive comparison model. Now, how do we get your result? Now we'll assume a situation where I do not take into account other people's income. So I only take into account my own income and let's assume my own income is on the poverty line. Then I just, if I take into account other people's income I will get this level of utility. If I do not take other people's income into account I will have this utility and then when I equalize both utility I end up, it's easy to show and I don't know, that my, the new poverty line should be a weighted average of my original poverty line when there will be an absolute poverty line and the reference income and the weight can be easily computed. Obviously the higher this weight use the more weight I give to absolute income and that's why it can be considered obviously as a policy parameter that policy maker can choose. Let's go quickly to the other possibility with Clark and Oswald for the ratio comparison model which means that you take into account the reference income by comparing, by looking at the ratio of your income and the reference income. So we write the utility function in this way, utility function of the function of my income and of some function of this ratio and you do the same procedure. You compare situation where you ignore the reference income and the situation where you do take it to account in both case you assume you are the poverty line, the poverty line when you Z zero when you have only an absolute approach and the poverty line Z one when you have take a relative approach. The axiom we make are the axiom, the following axiom, linear homogeneity which says that if you multiply the income and the reference income by a constant C then your utility will be multiplied by constant C when you have two other assumptions which are more technical assumption, normalization, continuity and we do the same kind of demonstration as before. We equalize the utility in both cases, okay? So this is a case where I do not take into account the reference income or I say that the reference income is my own income, the poverty line Z zero and the other case and you can prove that at the end the poverty line which will not be the same as in the case on the additive model but the poverty line again when you have a reference income will be a weighted average of the poverty line which you assume when you have only an absolute poverty line and the reference income. All right. So, and here you have the formulation, you know, where the European Union assumes that the poverty line is 60% of the median. Here you have the weight that you should take if you wanna get the EU poverty line and Atkinson and Bourguignon made another suggestion and here's the weight to get the Atkinson-Bourguignon poverty line. All right, a few minutes, a few words of empirical application. We worked with agent data in various countries. We assume that the reference income by lack of information was either the median or the mean and we assume, you know, we applied our result that the poverty line taking to account both absolute and relative income should be a weighted average of the absolute poverty line and the reference income and we call this kind of poverty line an amalgam poverty line. As weight, weight of the absolute income, we chose one which is the situation you have today when you take a dollar, a dollar 25 as poverty line in developing countries, but we also try to find out what would be the impact on poverty if the weight is 90%, 66% or 5%. Now the data we had included all the information on the D side, so we had only 10 income, you know, the distribution of income in various countries, we had only 10 data, but we extended this by trying, by applying two technique, a one which was proposed a long time ago in 73 by Nanakakwani and Ripesh Poder, which is a regression where you regress the height of the Lawrence curve on the cumulative population share and another which is a technique which was proposed at Wyder by Tony Sharks when he was the head of Wyder and my Guanghua one when he was working at Wyder and I don't have time to enter into this technique but it allows you to create a lot of observation on the basis of observation. So let me just give you two, three minutes. You know, what will be the impact on the percentage of poor and also on the number of poor when you adopt our proposal. So I give you results just on some country like Bangladesh, for example, the absolute poverty line, assuming $38, which is $1.25, there a day then you have 43% of poor. So that's actually, now if you took the Amalgam poverty line that we proposed, you have quite an increase, a little bit less than 10% in the number of poor if you go from 100% to 50%. In Cambodia, you have a much greater increase. This is when you do the weighting with respect to the median but we have also a result when we take it with respect to the mean. Obviously, because usually the median is smaller than the mean, you're gonna have a higher impact on poverty. If you take China, here's a difference between rural and urban China, here the impact is very important. With the tradition, absolute poverty line of $38 and assuming the reference income is immediate, then if instead of giving all the weight to the absolute poverty line, you give it only a 50% when you're gonna have a tremendous increase percentage of poor from 29 to 40% with the Kacuani-Poder approach, 21 to 36% with the Sharks and Man approach. And in urban area, you didn't have any poor in 2009 with the absolute poverty line and you have 26 or 21% and similarly with the mean. We have also data on India. In India, the jump is somewhat less important in the rural area from 66 to 42 or 34 to 42. In urban, you have a bigger impact, all right? And here are the results you can look at since the paper is on the website. So with this, let me just conclude that this is the first time a proposal has been made to axiomatically derive a poverty line which will depend both on absolute income and on the reference income. And we have shown, I didn't show you this table. You can take a look. I'd be also computed the impact as far as the number of poories. And in some cases, you have a tremendous impact. Let me just, oh, sorry. If you take a case of China, for example, rural China, sorry, I don't have it here. Okay, here it is, sorry. Rural China, you can see that the number of poor increases from 142 million to 251 when you take the median as reference income, you can take a look at the other one. That's it.