In this paper, we follow this second approach. We define first what we call a Composite Welfare Indicator (CWI)<sup>4</sup> at the individual level and then aggregate this individual welfare indicator across individuals as we would do with standard uni-dimensional poverty measures. Therefore, the multidimensional question is treated at the individual level with the construction of the CWI while aggregation at the societal level can follow standard procedures used for uni-dimensional indexes.

The second question of weight is complex and largely unresolved. When we aggregate different welfare dimensions the question is whether each dimension should have the same weight or different weights. Should, say, illiteracy be given the same weight as malnutrition? Some authors have preferred to attribute equal weights to different welfare dimensions. In this case, the problem of weights does not arise as all dimensions are attributed an equal weight (usually one). Other authors have made an effort to attribute different weights to the different dimensions according to various criteria. For example, some authors have imposed arbitrary weights on different dimensions based on economic criteria or simply normative considerations. Some use hybrid approaches where weights are attributed to differentiate income and nonincome components but then equal weights are used for non-income dimensions. Other authors have tried instead to use surveys that ask questions to respondents about the importance of different dimensions and used answers to these questions to attribute weights to dimensions. Another stream of literature tried to seek weighting schemes based on expenditure patterns or other behavioral patterns measured in observed variables. Decancq and Lugo (2010) have reviewed these different approaches to weighting schemes in multidimensional indices of poverty and classified these approaches in no less than eight different categories.

Another approach that has been recently explored with the measurement of multidimensional poverty is a weighting scheme based on factorial or Principle Component Analysis (PCA). The idea is simple. We can consider welfare as a complex and unobserved multidimensional phenomenon that we want to estimate based on a set of observed proxies of welfare. We are searching therefore for a latent variable and our objective is to use and aggregate what we consider as possible dimensions of welfare in a way that they can represent satisfactorily the unobserved complex welfare indicator.

The natural choice for exploring latent variables is a PCA type of analysis. In addition to considering multidimensional poverty as a latent variable, this technique is particularly appealing because it provides weights for each dimension based on the covariance matrix of the _rXc_ matrix. Therefore, the weights are implicitly determined by the procedure and based on the correlation system of all variables vis-à-vis the latent multidimensional variable. PCA type of analyses are particularly indicated for continuous and

> 4 Unlike previous studies, we refer to the composite indicator as „welfare‟ rather than „poverty‟ indicator. That is because the composite indicator applies to poor and non-poor and is therefore a „welfare‟ indicator.

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