Overview
William E. Griffiths is an econometrician at the University of Melbourne, known for Bayesian inference in regression models and applied demand analysis. His 2002 conference paper with Ma. Rebecca Valenzuela developed an all-conjugate three-block Gibbs sampler for multi-set SUR models with cross-set coefficient restrictions, applied to Australian household equivalence scale estimation and Merino wool cost function estimation.
Key Contributions / Features
- Bayesian SUR MCMC chapter (Griffiths 2001): comprehensive treatment of the M-equation SUR model under the noninformative prior |Σ|^(-(M+1)/2); three MCMC algorithms — joint Gibbs(β,Σ), equation-by-equation Gibbs (βᵢ|β₋ᵢ ~ multivariate t with vᵢ=T-Kᵢ df), and Metropolis-Hastings random walk; extensions to inequality restrictions (truncated MVN for β|Σ), nonlinear SUR (M-H required), and missing data/Tobit; predictive pdf f(y*|β,y) ~ multivariate t with v*=T-M+1, averaged over MCMC draws; applications to wheat yield, translog cost, and nonlinear expenditure functions
- Multi-set SUR Gibbs sampler (Griffiths-Valenzuela 2002): three-block all-conjugate sampler for Yh = ZhΘh + Xhη + eh with separate Ωh per set and common η across all H sets; extends Percy (1992) and Chib-Greenberg (1995b) single-set SUR Gibbs to the multi-set case
- Pooled-GLS Block 3: η | rest ~ N(W⁻¹Q, W⁻¹) where W = Σh Xh′(Ωh⁻¹ ⊗ I_Mh)Xh — aggregates cross-equation information across all H sets simultaneously
- ELES equivalence scales: 5,532 Australian households, H=8 demographic types, 11 commodities; first child raises two-adult household budget ~23%; estimated on SHAZAM
- Sample size requirements for SUR (Griffiths-Skeels-Chotikapanich 2001): showed standard requirement T ≥ max(M, k_max+1) is incomplete; Theorem 1 (two-stage FGLS): T ≥ M + ρ − η where ρ = rank of combined regressors and η depends on regressor overlap; Theorem 2 (ML/Bayesian): T ≥ M + ρ, always more stringent when equations have distinct regressors; Bayesian Gibbs sampler fails silently for undersized samples
Related