  In this paper we consider the simulation-based Bayesian analysis of
stochastic volatility in mean (SVM) models. Extending the highly efficient
Markov chain Monte Carlo mixture sampler for the SV model proposed in Kim et
al. (1998) and Omori et al. (2007), we develop an accurate approximation of the
non-central chi-squared distribution as a mixture of thirty normal
distributions. Under this mixture representation, we sample the parameters and
latent volatilities in one block. We also detail a correction of the small
approximation error by using additional Metropolis-Hastings steps. The proposed
method is extended to the SVM model with leverage. The methodology and models
are applied to excess holding yields in empirical studies, and the SVM model
with leverage is shown to outperform competing volatility models based on
marginal likelihoods.
