How multidimensional is welfare? A sparse principal components analysis

This paper attempts to measure the dimensionality of welfare by using Principal Component Analysis (PCA) with sparse loadings, which combines PCA with regularization techniques, and uses nonlinear PCA techniques to handle mixed type data. Assuming that welfare can be represented by a subspace of a given data set, the hypothesis of multidimensionality of welfare states that more than one interpretable dimension is necessary to describe it. An empirical application to Argentina’s Permanent Household Survey shows the limitations of PCA and the advantages of PCA with sparse loadings in determining the relevant subset of variables for assessing welfare. I find such subset among 126 mixed type variables, which could be useful for implementing shorter surveys. I conclude that welfare is multidimensional, but there is room for dimensionality reduction: with three sparse principal components, it is possible to explain 20 % of the variance using only 35 % of the variables, and 30 % of the variance using half of them. With a single sparse principal component, it is possible to explain 20 % of the variability in welfare using half of the variables.