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Discussion of "Single and Two-Stage Cross-Sectional and Time Series Benchmarking Procedures for SAE"

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 U.S. 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 (Battese et al. 1988; Fay and Herriot 1979)? 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?