Session 4: Bayesian Econometrics
Chair: Sune Karlsson
David Gunawan: An Efficient Pseudo Marginal Method for State Space Models
Abstract: Pseudo Marginal Metropolis-Hastings (PMMH) is a general approach to carry out Bayesian inference when the likelihood is intractable but can be estimated unbiasedly. Our article develops an efficient PMMH method for estimating the parameters of complex and high-dimensional state-space models and has the following features. First, it runs multiple particle filters in parallel and uses their averaged unbiased likelihood estimate. Second, it combines block and correlated PMMH sampling. The first two features enable our sampler to scale up better to longer time series and higher dimensional state vectors than previous approaches. Third, the article develops an efficient auxiliary disturbance particle filter, which is necessary when the bootstrap filter is inefficient, but the state transition density cannot be expressed in closed form. Fourth, it uses delayed acceptance to make the make the sampler more efficient. The performance of the sampler is investigated empirically by applying it to Dynamic Stochastic General Equilibrium models with relatively high state dimensions and with intractable state transition densities. Although our focus is on applying the method to state-space models, the approach will be useful in a wide range of applications such as large panel data models and stochastic differential equation models with mixed effects.
Abstract: This paper extends the existing fully parametric Bayesian literature on structural VAR models with stochastic volatility (SVAR-SV) by introducing an innovative Bayesian semiparametric framework to model high-dimensional time series of financial returns. A Bayesian nonparametric (BNP) approach based on a Dirichlet process mixture is used to flexibly model the returns distribution by also ac- counting for skewness and kurtosis, while the dynamics of each series volatility is modeled with a parametric structure. Our hierarchical prior overcomes over- parametrization and over-fitting issues by clustering the coefficients into groups and shrinking the coefficients of each group toward a common location. An efficient Markov chain Monte Carlo sampling scheme is designed to perform inference in high-dimensional settings and provide a full characterization of parametric and distributional uncertainty. The proposed semiparametric approach is used to investigate returns predictability of the financial series.
Kitak Kim: A Stochastic Volatility Model with Markov-Switching Skewness: Bayesian Inference and Applications
Abstract: In this paper, we propose a stochastic volatility (SV) model with split-normal errors, the skewness of which follows a first-order Markov-switching process. The goal of this Markov-switching skewness SV (MSSKSV) model is to accommodate a time-varying property of skewness in financial asset return series and detect possible regime shifts of skewness in real data. Such modification of the standard SV model comes with a great advantage that it is possible to estimate the SV using one-block Gibbs sampling method, lowering a computational burden to a significant degree. The state variable in each period is sequentially simulated through Hamilton filtering and backward recursion. For model comparison, we discuss a plan to compute BIC of the proposed model using auxiliary particle filter (APF) method. Our posterior sampling algorithms exhibit reliable performance in both simulated and real data. The posterior inference on each parameter is precise on average in simulation study, and the BIC of the true model is relatively lower than that of the constant skewness framework. Empirical applications indicate the existence of negative skewness in error terms for a normal era of world major indices, which is in accordance with previous studies arguing left fat-tails in aggregate returns. During market crash periods, on the other hand, negative skewness in the return distribution vanishes away and aggregate returns enter the regime of symmetric normality. We demonstrate there is a promising evidence implying stock market turmoil like the global financial crisis (GFC) and Covid-19 pandemic corresponds with increased size of the SV, rather than diminished level of skewness in returns.
Aubrey Poon: Efficient Estimation of State Space Mixed Frequency VARs: A Precision-Based Approach
Abstract: State-space mixed-frequency vector autoregressions are now widely used for now- casting. Despite their popularity, estimating such models can be computationally intensive, especially for large systems with stochastic volatility. To tackle the computational challenges, we propose a novel precision-based sampler to draw the missing observations of the low-frequency variables in these models, building on recent advances in band and sparse matrix algorithms for state-space models. We show via a simulation study that the proposed method is more numerically accurate and computationally efficient compared to standard Kalman-filter based methods. We demonstrate how the proposed method can be applied in two empirical macroeconomic applications: estimating the monthly output gap and studying the response of GDP to a monetary policy shock at a monthly frequency. Results from these two empirical applications highlight the importance of incorporating high-frequency indicators in macroeconomic models.