My current research focuses on developing time-varying large Bayesian VARs for forecasting and structural analysis. For beginners in this area, my book chapter on large Bayesian VARs (with examples and code) might be a good place to start. Below I organize my papers and current projects around two themes.
Hierarchical Shrinkage Priors
Large VARs have a lot of parameters, and the key to make these VARs work is the use of appropriate shrinkage priors. I have developed a few flexible hierarchical shrinkage priors that are easy to use and forecast well.
1. Chan (2022) proposes a new asymmetric conjugate prior for large Bayesian VARs. Unlike the standard natural conjugate prior that rules out cross-variable shrinkage, this new prior allows the user to shrink coefficients on lags of other variables more aggressively than those on own lags. In addition, the marginal likelihood under this new prior is also available in closed-form. It thus makes choosing lag lengths or optimal shrinkage hyperparameters easy (e.g., by maximizing the marginal likelihood).
2. Chan (2021) introduces a new family of Minnesota-type adaptive hierarchical priors that captures the best features of two prominent classes of shrinkage priors: global-local priors and Minnesota priors. Like the global-local priors, these new priors ensure that only 'small' coefficients are strongly shrunk to zero, while 'large' coefficients remain intact. At the same time, these new priors can also incorporate many useful features of the Minnesota priors, such as cross-variable shrinkage and shrinking coefficients on higher lags more aggressively.
Time-Varying Parameters and Stochastic Volatility
For small VARs, it is well established that various forms of time variation like time-varying parameters and stochastic volatility are empirically important. My coauthors and I have designed a few flexible VARs and the associated estimation algorithms that are scalable to large systems.
1. Chan (2023a) develops an efficient Bayesian sparsification method for large hybrid time-varying parameter VARs with stochastic volatility. The new method automatically decides, for each equation, whether the VAR coefficients and contemporaneous relations among variables are constant or time-varying. Using US datasets of various dimensions, we find evidence that the parameters in some, but not all, equations are time varying.
2. Chan (2023b) estimates 3 types of stochastic volatility models for large Bayeisan VARs, including common stochastic volatility, Cholesky stochastic volatility and factor stochastic volatility, and develops Bayesian model comparison methods to select among them.
3. Many popular multivariate stochastic volatility models used in empirical macroeconomics are not invariant to how the endogenous models are ordered. Chan, Koop and Yu (2021) show that this ordering issue becomes more serious in large VARs. We propose a specification that is invariant to ordering. In a macroeconomic forecasting exercise involving VARs with 20 variables we find that our order-invariant approach leads to the best forecasts and that some choices of variable ordering can lead to poor forecasts using a conventional, non-order invariant, approach.
4. Chan (2020) introduces a family of large VARs with flexible covariance structures, allowing for non-Gaussian, heteroscedastic and serially dependent innovations. In particular, the version with a common stochastic volatility and t-distributed innovations seems to be able to handle the large outliers due to the COVID-19 pandemic.
5. Chan, Eisenstat and Strachan (2020) develop a large time-varying parameter structural VAR where the VAR coefficients and the multivariate stochastic volatility are formulated as a singular state space model. This singular state space model reduces the dimension of the state vector and implies a a factor-like structure, which makes the model more parsimonious and easier to estimate.