[MUSIC] In the next slide, we provide you an example of these data envelopment analysis technique for the index of human well-being. As you will see in this table, we find a lot of weights that are equal to 1 and that are equal to 0. Let me just go to the next slide, where we go to the so-called technique, budget allocation process. A budget allocation process is a technique that basically consists in selecting a group of experts and giving them a budget, an artificial budget. And then you ask the expert to votes, to give this budget, to spread this budget around different weights of different partial indicators. According to the budgets, they are deciding to expend in any of the weights or in any of the partial indicator, we will get the weights. Of course, in this slide we represent, or we write down for you the phases of this budget allocation process, but they are quite natural. What are the advantages of this technique? The advantages is that this technique is based on expert, and somehow it gives some legitimacy to the policy-maker precursors. To the people who are designing the composite indicators, because it's based on experts' opinions. What are the disadvantages? The disadvantages are mainly these ones, also. Then we have expert, that somehow they might confuse urgency with importance. And then other experts are probably too local, and they might decide on local basis. So basically then, this would make a problem. And finally, please remember the arrows in possibility theorem. We might find some inconsistencies, also, in the final decisions. Okay, going now to the next slide, we are going to talk about the, what we call analytic hierarchy process. This is another way to select the weight, and it's basically based on taking pairwise subjective comparisons of indicators. So we take a target, we choose the one that has to be approached by the composite indicator, and then we take the partial indicators. And we compare them partially pairwise, two by two, with respect to this composite indicator or this target variable. The one that exhibits better, or approximates better the composite indicator is the one that gets the better weight. Of course, the drawback we get with this type of pairwise comparison is that many times, we get inconsistent results. That is, it's very difficult to be able to order, based on pairwise comparisons, the weights. What are the advantages, we can find them in the next slide. The advantages are basically that transparency, and the fact that it's also based on expert. These are respect inside the pairwise evaluations, and therefore it is not relying on technical manipulations. Okay, in the next slide, we are going to talk about price-based weights. In a previous section of this course, we called your attention by the fact that we related the choice of the weights with the marginal regression of substitution between partial indicators. As you probably remind on this time, we highlight that from economic theory and from utility maximization problem. We remember that the equilibrium condition was that the marginal relation of substitution between two goods should be equal to each relative prices. So somehow, since weights are a function of this marginal relation of substitution. We can find analytic relationship between relative prices and relative weights for two different partial indicators. That's clearly the intuition that is behind this type of techniques. And it basically consisting of assigning prices to, or that weights should reflect prices. Or in some cases, shadow prices if real prices are not available. In the next slide, we talk about stated preference weights, this is a very standard technique. And we wouldn't like to spend too much time on it, so please have a look to the corresponding slides. And let me just end up by the hedonic weights. Hedonic weights are basically a way to choose weights that is well-spread around, and technically very commonly used by experts. Hedonic weights basically means to approximate the composite index, the target we want to take, through endogenous variable, through a variable Y. And then we try to explain this variable Y through a linear combination of the different partial indicators. The regression coefficient of this regression is going to be or are going to be the weights, conveniently normalized. So basically, it's a regression-based approach. What are the drawbacks of this hedonic price selection technique? The main drawbacks are basically those related to the regression techniques. That is, first, if the partial indicators are highly correlated, the weights are going to have a lot of variation. And secondly, the problem can be that the endogenous variable, the Y variable we want to explain, and that needs to be close to the composite indicator, is not available. [MUSIC]