Comments on: “Single and two-stage cross-sectional and time series benchmarking procedures for small area estimation”

<Para ID="Par1">We congratulate the authors for a stimulating and valuable manuscript, providing a careful review of the state-of-the-art in cross-sectional and time-series benchmarking procedures for small area estimation. They develop a novel two-stage benchmarking method for hierarchical time series models, where they evaluate their procedure by estimating monthly total unemployment using data from the US Census Bureau. We discuss three topics: linearity and model misspecification, computational complexity and model comparisons, and, some aspects on small area estimation in practice. More specifically, we pose the following questions to the authors, that they may wish to answer: How robust is their model to misspecification? Is it time to perhaps move away from linear models of the type considered by Fay and Herriot (J Am Stat Assoc 74:269–277, <CitationRef CitationID="CR4">1979</CitationRef>), Battese et al. (J Am Stat Assoc 83:28–36, <CitationRef CitationID="CR1">1988</CitationRef>)? What is the asymptotic computational complexity and what comparisons can be made to other models? Should the benchmarking constraints be inherently fixed or should they be random?. Copyright Sociedad de Estadística e Investigación Operativa 2014