 Rwy'n credu wedi'i gael gyda'r byddau eich ganddeithasol ac distributedeithio ac o deitio'r llwyddo iawn. Rydyn ni wedi'n credu iawn chi gyda ffroedd. Rydyn ni wedi'i gilydd mewn clywedau a y sgwpeth yw y pethu ar-gweithio. Rydyn ni wedi'n credu ei fydd eich gŵr arbeithio. Rwy'n credu eich gŵr o'r ysgwpeth eich gŵr i wedi'r gwyll â ch частоr ac mae'n siarad iddyn nhw'n fawr yn gweithio. ac mae'n credu yn yma yw gweithio. Fy enw i'n cael ei fod o'r gweithio, hynny yw'n dweud o fyw yn gyfwyrdd yn y roi'r cymdeithas yn meddwl cyhoedd o fuddiol, a'r fuddiol fel Cronig a wnaeth yn fuddiol? Felly yn ymweld o'r fuddiol mae'n meddwl cyhoedd o bwysig ac yn ymdweud i'r fuddiol a'i fuddiol o'r fuddiol o'r fuddiol? Yn rhan o'r cymdeithas, yna'r fuddiol yn cyfwyrdd Cronig o problemi yn fwywyd, yn y pwyllt, ac yn y pwyllwyr, oedd o'r ffordd, o'n fwyfyd, fel cael ysgol o resid yn ei fuddo i'r fwylltu yn mynd yn oed, ac oedd yn prysgol i'rdymu. Roedd hynny'n gwneud gofio i chynnyddio i'r pwyllwyr i Lloedau Pwyllwyr ein bod ym ni'n bach o'r rhagel i amdanofod mewn prysgol i ddod â'r ddaf, a'i ei ddysgu i ddod â'r ddau gade i'r dyn� anders ddaeth sy'n ddigon i'r ysgol ar y ddysgu. Felly mae'r frysg gyda leol o ffordd o tanig o ddeimlif wherebyau. Rydym ni engagements ac mae'r dyn nhw'n edrych ar y ddeimlo i gyd ymgyrchu a'r ddigon o ran ychydig a chydig o hefyd o hyd o osu ddiddordeb, mae'r osu ddiddordeb yn digon o gydig o hyd o osu ddiddordeb, a gydig o'u bydd wedi rhoi allan o'r ddiddordeb o'r ddiddordeb. byddai y gall Cymru i gyfysgol ymgyrch yn cael iawn. Felly, rwy'n mynd i fod yn cyfor'r cyfrifolau. Yn y dyfyrdd i fynd i fynd i'w byn yn yr ystyried i'w bod gyfriedd yn gyfrifolau yn cyfrifolau fewn i'w cyfrifolau sy'n gennym. A'r ystyriedu polisi nifer oedd yn olygu'n ei amgylcheddoeth. Mae cymru yn gwybodaeth llunyddol yn y bwysigol iawn yn ei gilydd gyda—— i sicrhau i ddydigol iawn, a'u llyfr o uniladau o'r cyfrifolau pobリ hynny a oedd yn trefnio'r fforddau sydd y bydd yn elefnod oes ar y cyfnod. Mae'r cyfnod oes cyfnod arfer o'r cwrs o'r cyfnod. Mae'r cyfnod o'r gyflwyno yn 2,000 oedd y cyfnod yma gyda'r gwahanol i'r cyfnod yn gwneud iddo i'r cyfnod a'r gwahanol i'r cwrs ac mae'n wneud o'r rhan o'r pryd i'r cyfnod yw'r cyffredin, ond mae'n gallu rhan oedd yn llwyth gynnig o'r cwrs ac yn gyntaf i'r gwahanol i'r cymharae i'r dyn nhw i'r ddweud y dyn nhw'n hynny. Felly, na ydych chi'n ddatblygu nad yw'r prif o'r cilio cyffredin a fydd yn cymryd yn cyfryd ar gyfer rhan i'r gweithio ymwynt i'r prif o'r cyffredin a'r cyffredin i'r cyffredin i'r cyffredin o cilio cyffredin. Felly, rydyn ni'n cythigio'r cyffredin, felly rydyn ni'n cyffredin ar y cyffredin, ac mae'n gyflwyno iddyn nhw'n cyffredin ar y cilio. Er fyddwch ei wneud, mae'r rhaid o bwysig wedi'i ddweud yn fawr o ddweithio. Mae'r bwysig yw'r cwmiad yn gyfnodol yn dangos hefyd, ond yna'r bwysig yn cael ei ddefnyddio eu ddweud yn gyrwg ar fawr o'r ddweud. Mae'r cwmiad yn eithaf i ddweud i ddweud i ddedigogungu ddweud, I'm proposing yet another measure to add to that literature and saying, well maybe this new measure kind of combines those properties that we want a chronic poverty measure to have. So the key perhaps, I don't know if failings is quite the right word, but the key gaps if we're thinking about the properties that are appropriate for measuring chronic poverty, it's either thinking about discontinuities in the ordering embodied by those measures or measures that i gynnwys yw'r gwybrel yma ychydig. Rydych chi'n gwybwch ar y mynd, nid yw hwn i leidio'r gwybrel tai'r cyffredin cyffredin, ddiwedd yn sicr cyffredin cyffredin cyffredin cyffredin, wedi'u gorbl o ddweud ar gwaith, felly mae bwysig hwn ymlaen chi'n gwybrel cyffredin cyffredin. Yn gyfrinsbryd datblygu dda nhw yw dechrau cyffredin cyffredin cyffredin cyffredin cyffredin ar gyfer gael cyffredin a gwahanol cyffredin cyffredin ryeirwch i nifer y cyfnodau creu bronchii. First of all, I characterise a general class of measures then I choose a function within that class that captures the properties the time after that I think are critical for measuring chronic poverty. Then, finally I apply that to data from Moorilya Theopia and have a look at comparison of chronic poverty in different villages. Ac wnaeth gael y cyfnodau'r gwahoddau cyfnodau yn gweithio'r Llan-Jelann yn y methu yn benedig. Mae hynny'n gweithio'r hynny'n gweithio a'r hynny'n gweithio'r gweithio'r cyfnodau. Yn gyfodd yma'r prifs, rydyn ni'n gweithio'r cyfnodau yn ddod o ddod o'r prifs o'i gwaith ac yna'r prifs hynny'n gweithio'r gwaith, yn gweithio'r cyfnodau ac mae'n gweithio'r prifs yn gweithio'r cyfnodau. First of all, I'll go as quickly as I can through the kind of quite analytical, characterising the general form of poverty measures that are appropriate when we're aggregating information about individuals over time and aggregating over individuals as well. So just quickly defining some notation here, I'll just go through this very quickly. It's very, very standard, pretty much shared by all of the papers in this literature. So I'm assuming that I've got an indicator of well-being for each individual eye in each time period T, and for now I'm going to assume that that's kind of a real valued indicator. It's not really a real value, it's kind of some real number multiplied by some unit of measurement, and that's, I'm assuming, I don't want to get too much into the debate about what does cardinality mean in this context and so on. Think of it as a cardinally measurable indicator of well-being, if you like. So I've got a variable population size, and I've got a fixed number of discrete time periods, and this is very important. I'm assuming that the indicator of well-being that I have for each individual is comparable across different individuals, and it's comparable across time periods. So perhaps if I'm using household survey data, then I'd want to be looking at a per adult equivalent, and I'd be wanting to deflate over time if it's income or consumption in order to ensure that comparability. And so putting together all the possible profiles of individuals' well-beings at different points in time, I get this big domain, which is going to be the domain of the functions that have my poverty measures. And so what we're really thinking about is a poverty measure, it's a function that acts on a matrix of well-beings for different individuals at different periods in time. So each of the rows in this matrix represents one individual, and if you look at the different numbers going across that row, that's the trajectory of well-beings that that person experiences over time. And when I say well-being, that's kind of shorthand for some measurable indicator of well-being, and I don't really want to go too much into the philosophy of what that means at all. You'll see later on that I might use a consumption expenditure measure. So I'm interested in intertempo poverty measures when I'm basically summarising all of the information in that matrix into one real number that tells me how much poverty or how much chronic poverty is experienced by that group of people whose information is in that matrix there. OK, so just to kind of create a framework and restrict the class of measures because at the moment the measures could be any function at all, I want to introduce a couple of fundamental ethical principles. So these should be familiar if you know any kind of social welfare measurement or poverty measurement. So first of all anonymity or symmetry, I'm treating each individual in exactly the same way. And also what Foster has called subgroup consistency, which as many of you will know links very closely to the idea of separability across different population subgroups and is going to give us a nice consistent measure as we divide up into different groups of the population. And then I'll also introduce another perhaps not quite so fundamental property, the population size neutrality, which is basically equivalent to replication invariance. And what I'm saying there is that the total population size does not intrinsically matter. Now that's actually something a completely different set of issues that I don't want to explore here. We're thinking about kind of the value of life and death and what if you are so poor you do not survive. So those are really, really, really important issues, which I'm just completely ignoring for now and maybe that's further work to explore those better. So what about anonymity? Well in these two societies here we have the same number of people and we've kind of rearranged the characteristics or in this case the trajectories of well-beings experienced by those people, the different people. So you see we had two red trajectories there and two red trajectories there, one blue, one blue, two green, two green. So it's different people but they're experiencing the same trajectories of well-being. And so the basic idea is that the poverty in this society is going to be exactly the same as poverty in that society. So hopefully there are no objections to that, although perhaps it's not quite as innocuous as it seems because if I really do impose that assumption, I'm saying that the information that I have in this individual per period well-being measure actually kind of contains all of the information that's relevant to thinking about the well-beings of those people so far as I'm measuring chronic poverty. OK, so if I have information on many dimensions and so on and so forth I'd actually need to include all of that and even environmental kind of contextual kind of information. I'd need to include all of that into these individual per period measures. Subgroup consistency, I don't want to spend long on this hopefully but just the idea there is basically so if there is less poverty in society Y compared to society Z, and then I change in some kind of subgroup of that society, can you see at the top, I've changed the pattern? Well I'm saying now that there is still going to be less in Y than Z and can you see that underneath the line, I haven't changed at all what's going on. So we've got consistency if I do totally in the other way round, sorry, I was just looking, you can see these diagrams especially, I've been looking at these diagrams in two lines. OK, so what's my saying, there's less poverty in Y than Z, so can you see if we compare the two societies above the line they're identical but you see that the characteristics are different in Y and Z. So if there's less in Y than Z here, there's also less in Y than Z here and can you see we're comparing exactly the two things there but we've changed for both of those societies what's above the line. And that's still the case even if we don't just change the kind of the pattern of characteristics for the people above the line, we can even change the number of characteristics. So basically I'm saying that when I compare these people to these people, what's going on in the rest of the society so long as it stays the same in the two that I'm comparing, I'll have a consistent comparison of poverty there. I don't want to explore that any further right now, there are interesting questions associated here but basically this probably makes sense if we're thinking about a kind of absolute measure of poverty, less so if we're thinking about a relative measure of poverty. So let's continue to think about an absolute measure of poverty, that's pretty fundamental and then population size neutrality, well simply if I increase the size of population but don't change anything else then I'll evaluate the two societies as having the same amount of poverty. So very similar to the idea of replication invariance and probably essentially equivalent to each other. Okay so putting all those together I know that my poverty measure is going to have to have this functional form that we've got here and so what am I doing? Well first of all I'm taking this function small p, it's a function of the trajectory of wellbeing for an individual and then I might want to do some transformation of just kind of arbitrarily decompose the function into two parts there and then I'm taking the arithmetic average over individuals and then I might well want to do another transformation. The two transformations are both strictly increasing so they're ordered preserving and at the moment this p function can be anything I would like it to be. I'll obviously restrict that quite a lot more in a second. So same function there again, so this p function is a function of the trajectory of wellbeing for one individual and so represents an ordering of the space of possible trajectories of wellbeing. And so those fundamental principles that I introduced a moment ago basically mean that my poverty measure has to induce an unambiguous ordering of the set of possible trajectories and that's really useful because now I can continue and think about what does that ordering look like in order to be appropriate for chronic poverty measurement. I'm just going to take a quick detour before I do that. Oh yes, it's not really restricted at the moment but it needs to be an ordering that's representable by a real function but that doesn't cause us too many problems at all. So if you just look at the structure of what's going on here, first of all we're aggregating over time for each individual. We might then do an order preserving transformation. We're then taking that average in order to aggregate over society and again we might do another order preserving transformation. So before thinking a bit more detail what do we want for this little p? Let's sort out the G and the F and now we can kind of have a useful trick here. I'll go very quickly through this because you can read the paper if you want more details. But the idea is basically if we restrict attention just to trajectories in which every individual experiences the same constant level of wellbeing. Different individuals might have different levels of wellbeing but each individual is just experiencing constant wellbeing. Then this looks an awful lot like static unidimensional poverty measurement and that problem has been solved. We have a literature ready to use there so we can kind of exploit that analogy. So introduce standard properties that we know from the static poverty measurement literature. Now we're just looking at those profiles that consist of trajectories of constant well-beings. So that's just kind of analogies of those standard properties that we know from the static literature. And I'll add another technical property in there that I don't want to worry about too much but basically will mean that I can do a useful trick in a second. And what can I say? Well I can actually, it looks a bit more complicated but I can tie down the form of my measure quite a lot more. So this is really, really quite general. Let's choose something a little bit more specific. So the thing to point, the thing to imagine, we've still got the same function P here and then we're saying that each of these trajectories we can find a constant wellbeing equivalent for that trajectory kind of given the ordering there. So we don't need to worry about the whole trajectory, we just need to worry about the constant wellbeing equivalent. So those are the C's in there and this looks like a static poverty measurement problem. And so we can read the literature on that and like is pretty standard in the applied academic literature now, we could choose the poverty gap squared measure, foster growth or better. So let's stick with that poverty gap squared in order to do the social aggregation and that means that the measures we'll come up with will be directly comparable to other poverty measures that are based on this poverty gap squared thing. So now all we need to worry about is how are we aggregating over time. Okay so that's in four minutes what I needed to cover. The first thing to think about is I've imposed the poverty gap squared form of the measure and so now I've still got, it's still a very large class of measures, a very large family of measures that are available to me but they all look like that. So that's the variable thing in there, it's the form of that little p function in there. Now all of the measures in this class will give you exactly the same value of poverty, the profiles in which everybody's experiencing these constant levels of wellbeing. And it makes sense if everyone's just having constant not fluctuating levels of wellbeing, it makes sense to think that poverty in that context is entirely chronic. So then this gives us a really nice way to decompose. We can say that if we have a measure of total intertemporal poverty we can just take the difference between the total measure and the chronic measure and that gives us a decomposition into chronic and transient components. That makes a lot of sense because all of these measures completely coincide. We didn't need to use the poverty gap squared form, we could have used another sensible static poverty measure and done exactly the same thing but for now we're using poverty gap squared. So what do we need to do? We still need to determine the form of the little peak. What can we do here? So just quickly have a look at how Jalon and Rivalion did that. For the form of the little p they basically looked at poverty gap squared. They just looked at average levels of wellbeing. So you might have a fluctuating trajectory and they just averaged out of those fluctuations. That maybe doesn't really fit with the concept of franicity. So let's think a bit more about the properties that we want to represent franicity. For monitonicity first of all if a poor person has a reduction in wellbeing in any period we want their poverty to increase. That's straightforward, all the measures in literature share that. What about continuity? Well I would argue even though this is not shared by many of the measures proposed in the literature I would argue that if you don't have a continuous measure you can get some really perverse orderings of trajectories that don't fit with our kind of intuitive notions of which trajectory is more poor or less poor than the other. Now I want to impose an assumption of continuity here. So some of the measures in the literature are definitely not continuous. What about something really specific to chronicity, the idea of chronicity? We want our measure to be duration sensitive. So the longer someone spends under the poverty line the more poor they are. So again some of the measures proposed have that property and some do not. And then something a little bit more subtle but which maybe also makes a lot of sense if we think about chronicity as kind of persistence. That periods under the poverty line or further under the poverty line have a bigger effect, a bigger negative effect if they're closer together than if they're further apart. So again some of the measures in the literature have that property but not others. And the thing is that none of these measures combines all four of these critical properties. So we have a project which in two minutes we will complete. So some of the measures may be because they're not duration sensitive or they don't have the contiguous property. They might be more appropriate for measuring the total amount of poverty over time rather than chronic poverty per se. So now I want to construct a measure that combines the appropriate properties and I'll pull it out of a hat and here it is. It's a bit of a mess and this is where I'm still working to try and characterise a general class and messing about with different functional forms that might look a bit more elegant than this. Anyway, let's just have a quick think about what's going on here. What we're doing is taking a kind of geometric averaging over, not quite geometric averaging, over kind of subsets of the entire period and then going over the whole period. So I assert that that satisfies my properties and I'll just show you quickly some isoquance of taking slices through that function to get some idea of what's going on and you'll see that there's an asymmetry in here so I'm thinking imagine here three time periods, one, two and three isoquance with X1 and X2 and I'm slicing through at different values of X3. So this is where X3 is equal to zero. We've got really, really kind of low wellbeing in the third period and then the second and then kind of less low and then finally less low and if I have one minute left I can quickly show you some numbers applying this to data from the Ethiopian Rural Household Survey and looking at different villages or different peasant associations within that survey and I think there might be people in here that know a lot more about this data than I do. So I'm following Dirklaun Krishnan and Porter. May I take 20 seconds? Thank you. So I'm following, there's been an awful lot of poverty analysis already conducted with this data and so I'm using the consumption aggregates that are deflated and per adult equivalent that have been used for most of the poverty analysis that's been done here. What do I get? An awful lot of numbers. The ones to look at, these are the different villages. If you look at the final two columns you'll see the decomposition into the percentage of poverty that's chronic and the percentage that's transient. Now this is the Jalan Ravallion decomposition. You'll see that basically the amount of poverty is very, very, very low except for in a couple of the villages that makes a lot of sense. If you know this data set you know that there's a lot of kind of vulnerability to shocks. There's lots of transience, there's lots of changes over time going on. So when we average we tend to kind of wash out the chronic poverty a few households are always poor. If you carry on and look then at the new decomposition the pattern's an awful lot different. Most of these percentages of chronic poverty are around about the 20, 30, 40% miles. So we're actually picking up a lot more proportion of that poverty as chronic and perhaps we can be more confident in what those numbers mean because we've seen the properties that that measure has and so I think that's it basically. So there remains still work to make the measure maybe a bit more elegant and characterise more general class there. Thank you.