Simultaneous confidence bands for growth incidence curves in weighted sup-norm metrics

Abstract

ABSTRACTThe so-called growth incidence curve (GIC) is a popular way to evaluate the distributional pattern of economic growth and pro-poorness of growth in development economics. The log-transformation of the the GIC is related to the sum of empirical quantile processes which allows for constructions of simultaneous confidence bands for the GIC. However, standard constructions of these bands tend to be too wide at the extreme points 0 and 1 because the estimator of the quantile function can be very volatile at the extreme points. In order to construct simultaneous confidence bands which are narrower at the ends, we consider the convergence of quantile processes with weight functions. In particular, we investigate the asymptotic convergence under specific weighted sup-norm metrics and compare different kinds of qualified weight functions. This implies simultaneous confidence bands that are narrower at the boundaries 0 and 1. We show in simulations that these bands have a more regular shape. Finally, we evaluate real data from Uganda with the improved confidence bands.