Multidimensional Poverty Frontiers: Parametric Aggregators Based on Nonparametric Distributions

We propose a new technique for the estimation of multidimensional evaluation functions. Technical advances allow nonparametric inference on the joint distribution of continuous and discrete indicators of well-being, such as income and health, conditional on joint values of other continuous and discrete attributes, such as education and geographical groupings. In a multiattribute setting, "quantiles" are "frontiers" that define equivalent sets of covariate values. We identify these frontiers nonparametrically at first. Then we suggest "parametrically equivalent" characterizations of these frontiers that reveal likely, but different, weights for and substitutions between different attributes for different groups, and at different quantiles. These estimated parametric functionals are "ideal" in a certain sense which we make clear. They correspond directly to measures of aggregate well-being popularized in the earliest multidimensional inequality measures in Maasoumi (1986). This new approach resolves a classic problem of assigning weights to dimensions of well-being, as well as empirically incorporating the key component in multidimensional analysis, the relationship between the attributes. It introduces a new way to robust estimation of "quantile frontiers", allowing "complete" assessments, such as multidimensional poverty measurements. We discover massive heterogeneity in individual evaluation functions. This leads us to perform robust, weak uniform rankings as afforded by nonparametric tests for stochastic dominance. A demonstration is provided based on the Indonesian data analyzed for multidimensional poverty in Maasoumi & Lugo (2008).