 Well, hello. I'm not going to talk about what the paper is about for the first few seconds. He's going to put it on, but I was going to discuss something related to the other three papers. First of all, we're talking about inequality in those three papers. And I think it's very important to understand what inequality really is. What inequality really is for almost every measure we would ever use is two income standards. What an income standard is, it's a way of summarizing the entire distribution in one income, one number, one EDE in Atkinson's terminology. And what happens is that you have one of these income standards that looks out of the right eye, so it focuses on higher incomes. A second income standard focuses out of the left eye, and that looks at lower income standards, lower incomes. So in the case of the Gini coefficient, it's the mean and what's called SEN's measure or welfare measure, which is moving toward a Rawlsian approach. Or you might in fact even use the mean against the lower 40% mean, which is now being used by the World Bank as part of their measures of progress. But it's always a pair of such income standards. So therefore when you look at inequality, you already have the mean income in it, typically as one of the two standards for most measures. And so if you're running regressions, my main question is how does whatever it is you're looking at impact differentially the upper mean, the one that's focusing on the right eye, and the lower standard, which is focusing from the left eye. And it's that difference that the factor affects the one standard differentially than the other is changing inequality because every inequality measure looks at a ratio of these two indicators. I thought I'd start with that since few people have talked about fundamental measurement issues in inequality, and I think it's useful to do so. In my cross-country regressions I've done it once, I made use of that. So now let's go down to what this paper is talking about. It's poverty actually, but it's poverty the intersection with a form of inequality. And so all of this was started when Sabine Alkar came to a talk of mine and said, you know, what you're doing could be turned into multidimensional poverty. I said I couldn't believe that. You can't measure multidimensional poverty. You can't measure multidimensional inequality. It's too hard. She convinced me otherwise. And so the result of that has been a whole lot of measures that have been applied in probably about 40, 50 countries with about 10 of them taking it on as their official measure. So this stuff has hit big time in terms of what countries are doing because they feel that they can actually do something better about policy and the poor by knowing what dimensions people are deprived of and focusing on those dimensions to make things happen for the poor. And since our measure is a measure of priority, it says, you're deprived in a few things and you're deprived in a few things, but you're really deprived in a lot of things. You're multiply deprived. We're going to focus on you. You're the poor. That's our target. So you can then see what dimensions they're deprived in and go after them. So let's go ahead and get back to the paper itself and see if I can get this to turn. Move, shake, do something. I think I've ruined it. I don't use these computers, I'm afraid. So could you help me make sure that I don't screw it up? And then I should press on the side here going to the right, right? I just make a touch, sorry. There we go. There's two forms of technologies for measuring poverty. One of them is called unidimensional, like income, $1.25 a day. It has identification, who's poor, aggregation, how much poverty is there. All approaches to measuring poverty have that sort of structure and has developed in this 76 paper. But what's different about unidimensional compared to the other is it has one single variable, like calories, which I used in a paper that I had in 1984 on unidimensional poverty, and otherwise it has measures that have been kind of constructed into one dimension from many dimensions. So when you can do that, use unidimensional approaches, but sometimes you can't. And when you can't use unidimensional approaches, is when the variables themselves don't really mix well. There's no way to do the apples and oranges here. Or perhaps you can do the apple and oranges, but policy says I'm not interested in the apples and oranges all piled together. It's India and half the kids are malnourished. I want to see why. Let's look at the income or the consumption related to food. Maybe that holds some insight and we'll keep it disaggregated. There's been a lot of demand for this stuff and it's been coming from governments and from international organizations, NGOs and so on, and there's been a ton of measures that have come out. Problem is that very few of them are inapplicable where you need them most. When you have ordinal data or qualitative data or categorical data, because most of the other dimensions are not nice like income and you can do cardinal stuff with them. No, instead it's quite crude, those data. And secondly, the measures themselves that are used or come out of that literature are often very crude in and of themselves. They're their headcount, which doesn't satisfy what I call dimensional monotonicity. If you're a poor person, you're deprived in an additional dimension, you should have more poverty should be the result of that. It shouldn't just be ignored by the measure, but the headcount ignores it. There's also the type of identification whose poor is very non-discerning in many cases. It's a union-based approach that says if you're deprived in one dimension, heck, you're poor. Well, that isn't very useful, everyone's poor. If you go to data in all kinds of places, the numbers are 80%. Latin America, it's crazy. But yet, if you use the other extreme, you have few people poor. So what? Something has to come in between those two extreme cases. So there's been a new methodology introduced by myself and my co-author, Sabina Alkar, at Oxford. And it has as an identification approach a so-called dual cut-off. You have cut-offs in each dimension and then another cut-off that says, hmm, if you're deprived enough or multiply enough, chop, you're considered to be poor. So that's the identification. The second is the aggregation. And to do that, we use some kind of an FGT or some other sort of measure. In this case, we look at the adjusted head count ratio. M0, I'll mention that in just a second. So it addressed the problems that were in the literature before. We can apply this directly to any ordinal data, the really crappy data. And we did with the DHS. It also is not that crude, really, because you do observe when people become more deprived, a poor person becomes more deprived, poverty goes up. You're measuring the breadth of poverty. And as they add another dimension, they have more breadth. It also has a fairly discerning identification in that you're looking at a cut-off that isn't saying all or virtually none, some. It's an intermediate approach to identifying who's poor and prioritizing where action should take place. And it satisfies really cool properties. When I say cool, I mean these are the properties that have led to a whole lot of analysis out there, at least the top one. Subgroup decomposability of the FGT indices. That's what made those things used everywhere for measuring poverty because you could disaggregate them according to groups and target different groups. In fact, Progresa was originally targeted using those things, the FGTs, because they were decomposable. The paper that Santiago Red and Levy wrote was based on decomposable poverty measures, those. So the second one, however, is what's new. Breakdown by dimension after identification. It means that you can conceptually look at each dimension of poverty and you can construct some sort of a function on each dimension and say, ooh, there's the contribution of that dimension to poverty. Come on over here, over there. There's a lot of implementations of this. The multi-dimensional poverty index of the United Nations appears every year in the Human Development Report. Official poverty measure of Mexico, Colombia and now another 10 countries are implementing it right now. The Gross National Happiness Index uses this as the way of looking at its measure of flourishing, one minus the measure of deprivations, if you will, of poverty, and the Women's Empowerment and Agriculture Index by USAID and a bunch of other folks uses the same structure. So there's one big critique of this. At least it was made by a few people. Hey, this isn't sensitive enough. This measure, this adjusted head count, isn't sensitive enough to inequality within the poor. Okay, and so I said, well, what types of inequality could we have? We have a comb type of inequality, sort of like a generalized Lorenz idea with many dimensions. That's one approach. Or you could have the Ackerson and Bergen-Yohan approach, sort of positive correlation along the various dimensions. If we all, if I have more goodies and you have much less goodies, then that's more inequality. So those two types of inequalities among the poor could be incorporated. The problem is actually our measure satisfies what properties there are, like those, right? Because they're all weak. They never specify anything strictly. And so our measure actually satisfied it. The change in the distribution didn't change our measure. Hence, it satisfies the weak property. And there are others that we have constructed, in fact, in our paper, that satisfied both of those, or one of them. But it turns out that those sorts of measures are not useful with ordinal variables. So we're back in the conundrum. If you try to incorporate inequality, it seems like there's a problem. So this paper asks, hmm, can M0, the adjusted head count ratio, be altered to obtain a measure that, a method that's both sensitive to distributions among the poor and applicable to ordinal data? And I'll say one more thing. Maintains its breakdown. The answer is, well, the first two is yes. It's really easy to construct these things. And I hope to explain it to you in very simple terminology. But essentially, you start with an inequality measure that is transfer, you know, is adhering to distribution sensitivity. It pays attention to inequality among the poor in terms of income. So it's a unidimensional measure. Apply it to a particular distribution that I'll create from the multidimensional setting. And when you apply that, you will get the second form of inequality in the measure itself. It's a trivial matter, so that critique is not relevant, at least in some sense. It's easy to extend M0 to obtain such measures. So that's relying on an intuitive transformation from unidimensional to multidimensional measures. And it offers, this approach, offers insights as to what M0 is all about. But here's the kicker. When you do that kind of stuff and try to incorporate this form of inequality into the measure, you lose this great property, this decomposable property, the breakdown property by dimension. And that is where so much of the interesting policy has been coming from in the application of this measure. So the question is, you know, is there any multidimensional measure that's sensitive to the distribution of deprivations and also has that property? The answer is no. It's an impossibility result which we've proved. You can have one or the other, but not both. And so therefore we would go back to M0 and say augmented by other indicators that will help you understand the inequality. That's the outline. Now I've probably run out my time, so I can't really talk about outline. Traditional framework of sand, who's poor, how much poverty? Typically uses, the first step uses the poverty line, typically. An early definition was, you're poor if your income is below or equal to the poverty line that was sent, and then it was clearly a better way of saying strictly below. Example, look at the income distribution there. 7, 3, 4, 8, poverty line is 5. Who's poor? Well, these two guys. So there's the identification. What do you use for aggregation? You use some poverty measure, right? Formula aggregates to the poverty level. You can use watts, sand, FGT index. There's the typical FGT. Forget that. Let's look at an example. It's a lot more fun. Essentially FGT can be calculated in three seconds. Here's a poverty line. There's the distribution of underlying the people who are poor. Therefore this is the deprivation vector saying who's poor, who's not. Take the mean of that vector, that's the head count ratio. Look at the normalized gap vector which takes the poverty line minus the income of the poor person, puts it over the poverty line. Four-fifths would be that second person. Each person has some shortfall, average the shortfall. Of course, zero for non-poor people. That becomes the so-called poverty gap measure, HI. And then finally, if you square those normalized shortfalls, why would you do that? Square that to get this, square that to get that. Well, look at the ratio. 4 to 1 versus 16 to 1. It emphasizes the people who are really poor. Take the mean. You get a measure emphasizing the really poor folks. That's called the FGT measure and it's been used quite a lot as well. Properties. There's tons of properties. I don't have time to go through them but they're all good. A poverty line actually in this case has two roles though. And this is one of the kind of aspects of this paper that's quite different. A poverty line has two roles. One of them is to find out who's poor and the other is to use as a standard to compare the shortfalls. And so we want to separate those two roles and that's what we do. So in some applications it may make sense to do this, particularly let's say ultra-poverty measurement. You say, who are the ultra-poor? Are you going to lower the standard that you're using to measure how poor they are just because you need to identify who they are? So you have $1.25 and you really want to get down to the lowest people earning less than 50 cents a day. But why do we then lower the standard as we measure the distance from the standard to where they're at? No. We'll keep that distance. We'll keep the original standard but identify who's poor using the cutoff, the pi i, the standard used to measure is pi a. And this can be used in other examples as well. So we have a broader class of measures with two cutoffs. Well, one standard, one cutoff. And I show you how you can then turn around and use this to construct and measure poverty in an example. With the usual things, you'll have a different cutoff which identifies only this person as being poor. But how poor is that person is still four-fifths. Right? So that's what's going on here. God bless you. All properties are easily generalized to this environment. The usual unidimensional poverty measures just generalized easily. The idea of the poverty measurement is that it allows flexibility at targeting the group below the poverty cutoff while maintaining the poverty standard and hence the measures you've been using at the higher amount. This is very helpful for ensuring that when you have the very different types of poor people that you are doing things for them appropriately to who they are and I see the green. So how do you evaluate poverty with many dimensions? There's a ton of approaches that have been used. All of these previously were pretty impractical, I would say. I think so. Let me outline what we have done so you can see. We have something called a dual cutoff identification. A person who is multiply-deprived enough is considered to be poor. Here's an example to show you how this can be constructed. Income per day, schooling, self-reported health. Right-hand side is whether you have access to a particular service. Here are cutoffs. Very natural, $13. It's close to U.S., by the way. Well, it's a little bit low but that's good enough. Twelve years of education in this example. Your poor or fair health entitles you to be deprived in that dimension. If you don't have access to the service then you're below one and that would lead to zero and hence you're called deprived in that case. Who's deprived? Put the lines underneath. How much? So who is poor? That's a different group, right? Because you're not just talking about people and then the deprivation. You're trying to identify from this matrix of who is deprived who would be considered to be poor. Well, this person might be. I don't think so. That one probably is. This one's not. So what we do is we take some cutoff say K equals 2 for this example. Chop. Everyone who doesn't have many deprivations is not considered to be poor and this person is one of those examples so goodbye deprivation we don't pay attention to you. We can also do an example which goes beyond to the kind of FGT indices we won't do that here. Properties satisfied are very nice. Note, the poverty measures that use higher alpha the ones that I just ran by don't satisfy our denality. Let's forget about them right now. Here's what the adjusted head count ratio does. It takes and looks at the head count ratio. It's a half here because these two persons qualify but also looks at the share of deprivations that they're suffering here. Two out of four. Four out of four. Average them to get an average share A. That's three out of four. Multiplies it times the head count ratio to get three eighths. That's what we have here. But another way of doing it is to take that sensor matrix and do its average. Add up the total entries in it. It's six. How many entries are there? Sixteen. Three eighths again. That's our measure which can be by the way replicated and done with various values instead of equal values. Now we have equal values but this could be two and this could be what would be the equal share for those. It would still apply. We could do the same exact thing. Properties are nice. Okay. There's all sorts of properties. I'm not going to get anywhere to this discussion as I thought I would just keep going and get to the main thing. What I wind up doing is turning the matrix around and looking at achievements attainments as it turns out instead of deprivations. So where I had a one before I now have a zero where I have a zero I have a one. And then I count up those attainments four, two, zero, three. It's just the opposite, isn't it? That's what we had before. And that becomes the distribution equivalent. And now I apply poverty measures to those things. And the first example shows that we well the second example shows that we get the alkyr foster multi-dimensional measure by applying a poverty gap where the poverty standard we're using to measure how far you are from the top is d itself the number of dimensions we have and the cutoff that we use to identify for it is a cutoff that's below that. We get the multi-dimensional and it's just a gap. So you get the same properties as gaps have in this measure. If we go to example four it produces Mexico's structure that they use for the national multi-dimensional poverty measure. They do so because their poverty gap measure doesn't have a difference between the two income the two cutoffs and the standard. But instead they're the same. And so it has a rather different way of constructing it and you can work through these two examples at another time. Okay, so the properties of these M's the multi-dimensional poverty measures that are produced by unidimensional measures it turns out follow exactly what the unidimensional measure satisfy. If the unidimensional measure satisfies monotonicity you get my so-called dimensional monotonicity and if it satisfies transfer then you get so-called dimensional transfer which I was talking about being sensitive to the kinds of correlating types of switches or movements of goods from one poor person to another which stresses more inequality or less inequality. But at what cost you can construct all of these measures you'd want but at one cost give me about one and a half and then I will go. This is the crucial property it turns out there's a theorem that says there is no symmetric multi-dimensional measure of any type not even those that you construct using that way or any others you could put together that would satisfy both dimensional breakdown and this type of correlational inequality period it just won't work and the proof comes from a lovely little paper by Pot and I ready and a couple of other folks but we have our own proof so that's the impossibility conclusion it's easy to construct measures satisfying dimensional transfer but at a cost you lose this key element of the toolkit and you're out of luck so what are you going to do instead maybe you'll use other measures don't know that's it I'm done thank you very much