 So I'm going to talk today about estimating utility consistent poverty lines and focus on Mozambique and maybe some for Tanzania. I'm going to be a little more methodological, but I wanted to just also, as you co-mentioned, we have the GAP project, and this fits in with that. And really the big motivation for the GAP was, you know, what's going on in Africa. And then we had some operational focuses or folk died. And one is that relative prices are important. And we're going to, I think, talk about that in this session. And this is both across space and through time and over the income distribution and where different people have done. The second, as you was mentioning, is this need to triangulate and understand outcomes and look at different results. And finally, looking at monetary and non-monetary measures. And here I'm just going to be talking about relative price differences and how we cope with them within a survey and what that might mean. So I'm drawing from some work that's published in the EDCC. And as you was mentioning, this approach has now been applied in various ways. We tried to do it consistently, but it's hard to be completely consistent in different settings in each of the Ghana various countries. So there's some utility to getting this presentation out of the way. So we're going to look and take the case of Mozambique. And one of the features of Mozambique, which is common in a lot of African countries, is it's big. This is a long way. So this, if this, you know, for, this is a couple of thousand kilometers here. And it's very diverse. There's a lot of different types of consumption patterns going on. Different relative prices, different cropping practices. And so on and so forth. And how do we handle that? How do we come to cope with that in a poverty measurement sense? And when the sort of the first poverty assessment was being done sort of Mozambique just after the Civil War was complete, there was the notion that we need to have different poverty bundles. That we need to have multiple bundles across space because these consumption patterns differ fairly dramatically across space. And so that's what they did. And they're not the only ones that have done this. Papua New Guinea, Egypt, Tanzania, some variations in Burkina have been worrying about these differences. And so that's what was done. And it was done with 1996, 97. Household survey, there were 13 spatial domains applied to cost of basic needs approach in each domain. And Mozambique was a poor country at that time. About 70% of the population poor with some other things. Now, we're going to kind of move into what was done in 2002, 2003 and look at some of the choices and what they meant and what it meant with respect to relative prices and so forth. This was done again in 2008, 2009. But the 2002, 2003 serves as a good example. And basically, we had two choices, which is kind of on this bottom line here. And we have the easy choice and the hard choice. And the easy choice is we take the 1996 bundles and we price them in 2002 and we have a new poverty line and presto were done. And this is great because it takes about two days. And it's simple and it's easy to understand. And the hard choice is, well, we're actually going to go and get new quantities. And this could be more difficult, takes more time and there's various concerns. And so this is basically our choice. And obviously, the first thing we did was the fixed bundle because that's nice and simple and easy to explain and easy to do. The disadvantage is that it's ignoring substitution effects. If prices are changing, we're not going to capture that. Obviously, the bundle is fixed. And basically what this means is if we were here, our poverty bundle in a too good world, we're sitting here on this utility level and then relative prices change and people start to consume up here, if we just price the same bundle, we get a higher poverty line and we're overestimating poverty. That's the essential issue. So we want to stay on this, we want to be utility consistent staying on this utility level. So if we go ahead and we just take the fixed bundle, we get a decline in poverty of about 7% nationally, which is okay. And so then we start to worry about, are these substitution effects important and is something else going on? And the first thing to do is go and check whether there actually are major changes in relative prices, because if there's not, then we don't have to worry about it so much. And it turns out that there are substantial changes in relative prices and in the bundles. So in 1996, 97, food aid in the form of yellow maize was a major consumption item, almost all over the place. By 2002 through 2003, it's almost gone. You can't even find it in the survey. So things happening there. And how large are these potential substitution effects? And one way to do that is to just sort of, I mean, we often say suppose, with a fixed bundle it sort of says suppose preferences are Leontief, right? But we can suppose preferences are called Douglas. They're not, but we can see what it does. And so then we identify the utility level and we can, through cost mean, go ahead and get a new poverty line via the prices. And what happens if we do that? Well, if we do that, then we actually get a national poverty rate of 52%. So instead of a decline in poverty of seven, we get a decline in poverty of 17, 10 percentage points more. And so potentially these substitution effects really are quite important. So now we're at the point of trying to come up with a new bundle. And this is good in that we get to accommodate potential changes in consumption patterns. But difficult because we want our bundles to give us a similar level of utility or the same, ideally. But we don't observe utility, so how do we do this? And the way, so basically this is the issue. We're gonna estimate a new bundle. We wanna be here, but we might end up here or we might end up here and we wanna know if we're far off or not. And so to do that, we're gonna make recourse to reveal preference conditions. And we can do this through space and through time. And basically what we're gonna do is we're gonna say, well, assume these bundles give the same level of utility. And if they do, then these things should apply. So through time, if I've got a 2002 bundle here priced at 2002, prices, if this bundle gives the same utility as this bundle, I'm now in 2002, I face these prices, I chose this bundle, why? If it's the same, gives the same level of utility, well, because it should be cheaper. I can go the other way. I could say, well, back in 1996, consumers chose this bundle at those prices. They could have chosen my 2002 bundle. It was there. Why didn't they do it? Well, at 1996 prices, it cost more. The same applies on a spatial basis. If I'm in one region facing my regional prices, I have other bundles available to me. I could have purchased Region B's bundle. Why did I purchase this particular bundle? Well, because it gave the same level of utility and was cheaper. So this is sort of the very simple, something that we can apply that rationalizes preferences across these bundles and keeps us utility consistent. And these tests are easy to apply and they fail absolutely all over the place. It's difficult to make them work. So we have kind of a desire to have bundles that change, but we have real difficulty making them sort of satisfy things that we really want to be true, namely that revealed preference conditions are satisfied. So in this, we have lots of potential bundles, but only six mutually consistent pairs. In other words, establishing on the spatial side both sets of revealed preference conditions. So now, in a sense, we're kind of stuck. And what we've posited here is that we're actually in a actually familiar situation in empirical work. So here we are. We've done our best to estimate bundles. We've done our best to make them have the same level of utility, but they don't. And so it's inconsistent with what we require to be true, but we're not the first person to run into this. I guarantee you that every time the national accountants estimate their national accounts right off the bat, they do not satisfy all of the macro-consistency constraints that we know must be true. In physics, we have applications, image processing others, where there's some fuzziness that needs to be dealt with. And the way that we deal with it is through some information theory. Five, okay. So the intent is to give away of extracting the most convincing conclusions implied by given data and any prior knowledge of the circumstance. So what we're gonna do is we're going to try to adjust our bundles such that we arrive at something that satisfies revealed preference conditions, but we wanna retain the information that we have from the survey. And essentially the problem looks like this. So we have, this is the budget shares in our new bundles. These are what we're adjusting. We're gonna adjust the shares, we're gonna adjust the content of a bundle, but we're gonna try to stay entropy close or to these flexible shares. We wanna satisfy revealed preference conditions, some accounting and calorie requirements. What we're basically saying is choose new baskets that preserve to the greatest degree possible the information inherent in the original bundles shares, but that satisfy revealed preference conditions and other needs. And this works quite well. We get a nice clean matrix. And this then gives us, once we have this fairly easy to calculate a new poverty rate of around 54, which is what we've gone with. We do this also in other places. We've done it in Tanzania, nine regions. Whoops, got it in the wrong order somehow. Again, many failures have revealed preference conditions in the orange of failure, but not difficult to rework for 2000, 2001. When we do this, we actually end up very close to what the Tanzanian official numbers are. They're using Fisher price indices. It's giving us a similar kind of result. The national level result, that's just a leveling result. It's kind of a happy coincidence, but the similar pattern is a result of similarities in the methods. So the conclusion is that it's desirable. Or actually, someday you're gonna have to change a bump. I mean, we're not gonna keep the 1996 Muslim beacon consumption profile in perpetuity forever for measuring poverty. We have to deal with this somehow, some way. And so these revealed preference conditions are appealing for looking at this. And this entropy adjustment procedure we think is attractive. And it's important. It's not something you apply right off the bat. It's your last resort, once every other source of information has been exhausted. So that's what I wanted to talk about. Thank you. Okay, thank you for that.