Approximate Bayesian Estimation of Stochastic Volatility in Mean Models Using Hidden Markov Models: Empirical Evidence from Emerging and Developed Markets

The stochastic volatility in mean (SVM) model proposed by Koopman and Uspensky (J Appl Econ 17:667–689, 2002) is revisited. This paper has two goals. The first is to offer a methodology that requires less computational time in simulations and estimates compared with others proposed in the literature as in Abanto-Valle et al. (Q Rev Econ Financ 80:272–286, 2021) and others. To achieve the first goal, we propose to approximate the likelihood function of the model applying Hidden Markov Models machinery to make possible Bayesian inference in real-time. We sample from the posterior distribution of parameters with a multivariate Normal distribution with mean and variance given by the posterior mode and the inverse of the Hessian matrix evaluated at this posterior mode using importance sampling. Further, the frequentist properties of estimators are analyzed conducting a simulation study. The second goal is to provide empirical evidence estimating the SVM model using daily data for five Latin American stock markets, USA, England, Japan and China. The results indicate that volatility negatively impacts returns, suggesting that the volatility feedback effect is stronger than the effect related to the expected volatility. This result is similar to the findings of Koopman and Uspensky (J Appl Econ 17:667–689, 2002), where the respective coefficient is negative but non statistically significant. However, in our case, all countries (except Peru and China) presents negative and statistically significant effects. Our results are similar to those found using Hamiltonian Monte Carlo (HMC) and Riemannian HMC methods based on Abanto-Valle et al. (Q Rev Econ Financ 80:272–286, 2021).