 Okay, thank you. So I'm gonna talk about poverty decomposition by regression. So I think many of you already know what poverty decomposition is, but basically the idea is to attribute observed poverty changes into components of interest. So the most sort of popular way is to decompose observed poverty into growth component and redistribute redistribution component, which includes data rebellion and other decomposition methods. And this provides useful information on the sources of poverty change. And in this kind of study, most studies basically fix everything other than one and let one thing change, okay? So all these studies use this move one thing at a time approach and most existing decomposition methods as a result of this failed to satisfy what I call time-reversion consistency and sub-periodativity. So what do these things mean? Well, time-reversion consistency basically says the following. Suppose that you travel from time t0 to t1, you are a time traveler, and then you decompose observed poverty into whatever components. You do the reverse travel in time and each component has to add up to zero if you go there and come back, okay? And this requirement seems to be quite natural to me but these methods do not satisfy. Sub-periodativity says that if you go from t0 to t2 and t2 to t1 and you do the decomposition, each component must add up. That is, so let's say you look at growth component, growth component from t0 to t2 and t2 to t1 must add up to growth component from t0 to t1. And this basic property is again failed in most of the existing methods. So in a different paper, I propose a decomposition method based on integration. So if you think about the property of integrals, it's quite easily see that sub-periodativity and this time-reversion consistency is maintained. So I'm going to do something similar but here I want to develop a method that is based on regression. And this method is potentially useful because we can look at how covariates affect poverty. So you may be interested in the impact of policy or changes in education level and so on and so forth. And here I consider a general class of additively decomposable measure including FGT measure, what's measured, Chocobarty measure and so forth. But for the sake of simplicity of the presentation, I focus on poverty gap but in the paper, I pretty much deal with a very general class of additively decomposable measure. So I'm not going to show you many equations. Instead I do a very graphical presentation. So let's say you have covariates on the horizontal axis. On the vertical axis you have consumption per capita. The red line is the poverty line. And let's say that this line represents the relationship between covariate and let's say consumption per capita. Now suppose that this is the initial X and Y and poverty gap in this graph is represented by this distance, yeah? So pH is zero means that poverty gap in the initial period. Now suppose that X increases, Y also increases, poverty gap also increases. And here I assume that this line is fixed, okay? So I'm dealing with an obvious case. What? Decrease. Sorry, decreases, yeah, sorry. Poverty gap decreases. Okay? So in this case, you know, the change is completely due to the change in X. So this is a very obvious case, nothing, but this is an instructive case. So let's think about the case where actually this line changes. Suppose that the line changes from here to here, okay? Poverty gap decreases from PG zero to PG one. How can we decompose this thing? Okay, so we can think of certain scenarios. Suppose that X changes first and B changes second, okay? Under this assumption, we are basically thinking about this trajectory. You fix B first and let X change and then B changes. If you think about a decomposition like that, then this is a change due to, sorry. This part is a change in PG due to X, and this part is a change in PG due to the slope coefficient. Of course, you can change the sequence of the change in B and X. Suppose that B changes first, then this is a change in poverty gap due to the change in slope, and this part is a change in poverty gap due to the change in X. So if you do this decomposition, X component is larger and B component is smaller, okay? So what this clearly shows is that both components depend on the path of change. So with that additional information, to me, a smoother path, instead of just going like this or going like this, would be more appropriate, and perhaps not like this, okay? So what would be the reasonable path to think, okay? So here we are going to make this assumption. So X is linearly changes and B linearly changes. If you have additional data, you can calibrate this, but I think this is more reasonable than assuming that X changes first and B changes second, or B changes first and X changes second. And under this assumption, actually the change is quadratic. If I just have shown this picture, you might have thought that linear change is reasonable, but it's not. The reason is that if the slope is going up, you would expect that Y would be changing, Y would be changing faster towards the end of the time period if you believe that X also changes linearly. Now, under this assumption, you can calculate the contribution of B and X. This is a very simple algebra. So let's see how these formula relate to the graph that I have shown earlier. So actually, under the assumptions that I have shown, the change will be like this, okay? And X half is the value of X at time t equals 0.5. And this level of Y is actually smaller than the average of Y zero and Y one in this graph. Okay, that's not generally true, but under the assumptions that are shown there, this is true, okay? Now, suppose that this dashed line is a line that has the same intercept, but coefficient of the average of B zero and B one, you can, let's say, and this one obviously goes through X half and Y half, push it down, okay? And then you have a parallel graph here. In this picture, you can see that this is a component, X component, and this is a B component. So what does this mean exactly? Well, this distance is the X one minus X zero times half of average of B zero and B one, okay? So that's the X component. And this distance is equal to this distance, okay? Which is just changing Y due to the change in slope at the middle, okay? So this is how it relates. Now here so far, I have completely ignored the existence of residual, okay? So I have been looking at a particular person, but usually when you have a real data, you don't have an exact line like this, okay? If you fit the line, there will be an error. So how do we deal with it? Okay, so again, I can deal with it in a similar way. I assume that error changes linearly, and with this, I can actually decompose into the changes in different components, including the intercept, slope, changing covariate, and error term. And here, the covariates do not have to be just one variable, there can be many variables, yep? Now, one question you might have is that what do you do if you have poverty rate, okay? It's discrete. So it doesn't have all the nice properties. So I'm still sort of experimenting, but one thing that I'm doing right now is to use expected poverty. I just run regression and look at the poverty expected poverty rate, as opposed to observed poverty status. Okay, so now let me move on to the application part. So I apply this method to Côte d'Ivoire and Tanzania. For Côte d'Ivoire, I use CILSS, Côte d'Ivoire Living Standards Survey for 85, sorry, 86, 87, and 88. This is a rotating panel. So half of the observations in 85 and 86 is a panel. Half of the observations in 86 and seven is panel and so forth. And in Tanzania, I use a Tanzania National Panel Survey for 2089 and 2010-11. And I use households that didn't split up or do not have missing data for our purpose. And in the earlier version, I used everything, but I decided to focus on rural areas. So the number of observations are actually smaller than these. Okay, so here are the results for Côte d'Ivoire. How do I, how do you look at this? So this is say, let's look at this. So this is a distance to the closest market. So because of the change in X, poverty gap has decreased by 0.39 percentage points. You also have this B component because the slope is also allowed to change. So 0.71 percentage points increase in poverty gap due to the sort of structural change. So I have all the things. And the constant is of course zero by definition because X doesn't change. And so this part is the part that can be explained by this decomposition. But of course, because of the presence of the ipsum term, I have this part that is due to residual. So if this part is very big, this is not, decomposition is not very useful. So unfortunately for the years 85 to six, the decomposition is not particularly informative. But for other years, the covariates can capture the changes in poverty in a reasonable way. And between 87 and 88 in particular, we find that the change in the distance to market has helped to mitigate the actual poverty increase that was observed. Okay. This is the result for Tanzania. So the decomposition works well because the residual term is really small here compared with observed change. And I think this is a good example of sort of agricultural development here. So people are exiting from agriculture, which contributes to poverty reduction. And also the gap between non-agriculture and agricultural sector has diminished. So as a result, there is a total of 1.07 percentage point reduction in poverty due to the change in agricultural households status. Okay, so I may be going a bit too fast actually. And during the study period, market access didn't affect poverty much. So here I look at distance to the market and this really had a very small impact on poverty. Distance, yeah. Sorry, this is in kilometers, sorry. So this is the distance of the village that the household is located to the closest market. And it can be zero if the market exists within the village. Yeah, okay. So I developed a method of poverty decomposition based on regression. And this method satisfies time reversion, consistency and sub-period additivity. And you can think of it as a sort of, you know, Oaxaca-Blinder kind of decomposition applied to poverty. Although it's not exactly that, but it has a flavor of that because they have regression model. And I want to argue that this method is complementary to randomized control trials because this can be applied, exposed, you know. So long as you have data, you know, you don't have to design experiments, and this is much cheaper than obviously running, you know, a randomized controlled trials. So if you want to assess policy, if you have a policy variable at the household level, you can do this decomposition and see the contribution of policy to poverty change. This decomposition analysis may help researchers and policy makers to understand the important sources of poverty change. Now, as you may have noticed, you know, this is done for panel surveys. And I have tried cross-sectional models. I can, you know, make much stronger assumptions and do a decomposition, but so far I haven't been really, you know, successful in getting compelling results. So I, at least for this version, confine myself to the panel model, okay? Thank you very much. Okay, okay, so I guess, you know, the application part is, can be improved. I guess the data is, you know, because the panel, the timeline between the panel is a bit short, which means that many of the X's actually don't change. So I thought about a lot of candidates. So if you have, you know, if you know of any data that is more appropriate for this kind of method, I would love to know. I really much, very much appreciate your inputs for the ideas of, you know, better application. I'm not trying to sell that this is the best application that I can think of. Okay, thank you very much.