Kernel Density Estimation Based on Grouped Data: The Case of Poverty Assessment

Abstract

Kernel density estimation (KDE) has been prominently used to measure poverty from grouped data (Sala-i-Martin, 2006, QJE). In this paper we analyze the performance of this method. Using Monte Carlo simulations for plausible income distributions and unit data from several household surveys, we compare KDE-based poverty estimates with their true and survey counterparts. We find that the technique gives rise to biases in poverty estimates the sign and magnitude of which vary with the bandwidth, the kernel, the number of data-points analyzed, and the poverty indicators used. We also demonstrate that KDE-based estimates of global poverty are highly sensitive to the choice of bandwidth. Depending on the choice of this parameter alone, the estimated proportion of '$1/day poor' in 2000 varies by a factor of 1.8, while the estimated number of '$2/day poor' in 2000 varies by 287 million people. These findings give rise to concern about the validity and robustness of kernel density estimation in poverty analysis.

Keywords: kernel density estimation, income distribution, grouped data, poverty

JEL Classification: I32, D31, C14, C15