Zellner’s idea of combining several equations into one model to improve estimation efficiency (Zellner, 1962) ranks as one of the most successful and lasting innovations in the history of econometrics. The resulting seemingly unrelated regressions (SUR) model has generated a wealth of both theoretical and empirical contributions. Reviews of work on or involving the SUR model can be found in Srivastava and Dwivedi (1979), Judge et al. (1985), Srivastava and Giles (1987), and Fiebig (2001). It was also Zellner (1971) who popularized Bayesian inference in econometrics generally and described the SUR model within the context of Bayesian inference. However, at that time, convenient methods for deriving or estimating marginal posterior density functions and moments for individual SUR coefficients were not generally available. Subsequently, analytical results were derived for some special cases (Drèze and Morales, 1976; Richard and Tompa, 1980; Richard and Steel, 1988; Steel 1992) and importance sampling was suggested as a means for estimating marginal posterior density functions and their moments (Kloek and van Dijk, 1978). More recently, the application of Markov-Chain Monte Carlo (MCMC) methodology to Bayesian inference has made available a new range of numerical methods that make Bayesian estimation of the SUR model more convenient and accessible. The literature of MCMC is extensive; for a general appreciation of its scope and purpose, see Tierney (1994), Albert and Chib (1996), Chen et al. (2000), Chib and Greenberg (1996), Gilks et al. (1996), Tanner (1996), and the chapter by Geweke et al. (this volume). For application of MCMC to the SUR model, see, e.g., Percy (1992, 1996), Chib and Greenberg (1995), Griffiths and Chotikapanich (1997), and Griffiths et al. (2000).