On Exact Statistical Properties of Multidimensional Indices Based on Principal Components, Factor Analysis, MIMIC and Structural Equation Models

Abstract

Recent empirical literature has seen many multidimensional indices emerge as well-being or poverty measures, in particular indices derived from principal components and various latent variable models. Though such indices are being increasingly and widely employed, few studies motivate their use or report the standard errors or confidence intervals associated with these estimators. This paper reviews the different underlying models, reaffirms their appropriateness in this context, examines the statistical properties of resulting indices, gives analytical expressions of their variances and establishes certain exact relationships among them.

Keywords: Principal components, Factor analysis, Structural equation models, Latent variables, Human development

JEL Classification: C03, C43, I32, O15