Large Bayesian VARs Research Articles

A Macroeconomic View on Banks’ Deposits after Monetary Interventions

Abstract We study the evolution of bank deposits in response to monetary policy shocks. The objective is to assess whether a significant deposit channel, that is, an outflow of deposits when monetary conditions tighten (Drechsler et al. 2017), emerges at the macro level. The analysis relies on the estimation of a large Bayesian structural VAR for the USA, and monetary policy shocks are identified with Arias et al. (2019)’s method. We find some elements of the deposit channel, but our results suggest that its relevance for the transmission of monetary policy at the macro level is limited.

Applied Forecasting of the US Economy with Covid Volatility in Large Bayesian VARs

Applied Forecasting of the US Economy with Covid Volatility in Large Bayesian VARs

High-dimensional conditionally Gaussian state space models with missing data

We develop an efficient sampling approach for handling complex missing data patterns and a large number of missing observations in conditionally Gaussian state space models. Two important examples are dynamic factor models with unbalanced datasets and large Bayesian VARs with variables in multiple frequencies. A key observation underlying the proposed approach is that the joint distribution of the missing data conditional on the observed data is Gaussian. Furthermore, the inverse covariance or precision matrix of this conditional distribution is sparse, and this special structure can be exploited to substantially speed up computations. We illustrate the methodology using two empirical applications. The first application combines quarterly, monthly and weekly data using a large Bayesian VAR to produce weekly GDP estimates. In the second application, we extract latent factors from unbalanced datasets involving over a hundred monthly variables via a dynamic factor model with stochastic volatility.

Conditional Forecasts in Large Bayesian VARs with Multiple Soft and Hard Constraints

Conditional Forecasts in Large Bayesian VARs with Multiple Soft and Hard Constraints

Comparing stochastic volatility specifications for large Bayesian VARs

Large Bayesian vector autoregressions with various forms of stochastic volatility have become increasingly popular in empirical macroeconomics. One main difficulty for practitioners is to choose the most suitable stochastic volatility specification for their particular application. We develop Bayesian model comparison methods–based on marginal likelihood estimators that combine conditional Monte Carlo and adaptive importance sampling–to choose among a variety of stochastic volatility specifications. The proposed methods can also be used to select an appropriate shrinkage prior on the VAR coefficients, which is a critical component for avoiding over-fitting in high-dimensional settings. Using US quarterly data of different dimensions, we find that both the Cholesky stochastic volatility and factor stochastic volatility outperform the common stochastic volatility specification. Their superior performance, however, can mostly be attributed to the more flexible priors that accommodate cross-variable shrinkage.

Large Time‐Varying Volatility Models for Hourly Electricity Prices*

AbstractWe study the importance of time‐varying volatility in modelling hourly electricity prices when fundamental drivers are included in the estimation. This allows us to contribute to the literature of large Bayesian VARs by using well‐known time series models in a large dimension for the matrix of coefficients. Based on novel Bayesian techniques, we exploit the importance of both Gaussian and non‐Gaussian error terms in stochastic volatility. We find that using regressors as fuel prices, forecasted demand and forecasted renewable energy is essential to properly capture the volatility of these prices. Moreover, we show that the time‐varying volatility models outperform the constant volatility models in both the in‐sample model‐fit and the out‐of‐sample forecasting performance.

Fast and Accurate Variational Inference for Large Bayesian VARs with Stochastic Volatility

We propose a new variational approximation of the joint posterior distribution of the log-volatility in the context of large Bayesian VARs. In contrast to existing approaches that are based on local approximations, the new proposal provides a global approximation that takes into account the entire support of the joint distribution. In a Monte Carlo study we show that the new global approximation is over an order of magnitude more accurate than existing alternatives. We illustrate the proposed methodology with an application of a 96-variable VAR with stochastic volatility to measure global bank network connectedness.

China’s government spending and global inflation dynamics: The role of the oil price channel

This paper explores the international spillover effects of China’s government spending onto global inflation dynamics and the role of the oil price channel in the transmission process based on a monthly dataset covering 20 OECD economies spanning from January 2000 to September 2021. Based on the estimation results of Large Bayesian VAR models this paper provides three novel findings to the literature. Firstly, China’s government spending expansion significantly raises the CPI of most OECD economies. Secondly, the oil price rises significantly in response to China’s government spending expansion and magnifies its spillover effect on global CPI inflation. Thirdly, the effect of the oil price channel on the international transmission of China’s government spending to the global inflation dynamics crucially depends on the oil import dependence rate and the energy subsidies of the shock recipient countries.

Asymmetric conjugate priors for large Bayesian VARs

Large Bayesian VARs are now widely used in empirical macroeconomics. One popular shrinkage prior in this setting is the natural conjugate prior as it facilitates posterior simulation and leads to a range of useful analytical results. This is, however, at the expense of modeling flexibility, as it rules out cross‐variable shrinkage, that is, shrinking coefficients on lags of other variables more aggressively than those on own lags. We develop a prior that has the best of both worlds: it can accommodate cross‐variable shrinkage, while maintaining many useful analytical results, such as a closed‐form expression of the marginal likelihood. This new prior also leads to fast posterior simulation—for a BVAR with 100 variables and 4 lags, obtaining 10,000 posterior draws takes less than half a minute on a standard desktop. We demonstrate the usefulness of the new prior via a structural analysis using a 15‐variable VAR with sign restrictions to identify 5 structural shocks.

Model-based approach for scenario design: stress test severity and banks' resiliency

After the financial crisis, evaluating the financial health of banks under stressed scenarios has become common practice among supervisors. According to supervisory guidelines, the adverse scenarios prepared for stress tests need to be severe but plausible. The first contribution of this paper is to propose a model-based approach to assess the severity of the scenarios. To do so, we use a Large Bayesian VAR model estimated on the Italian economy where potential spillovers between the macroeconomy and the aggregate banking sector are explicitly considered. We show that the 2018 exercise has been the most severe so far, in particular, due to the path of GDP, the stock market index and the 3-month Euribor rate. Our second contribution is an evaluation of whether the resilience of the Italian banking sector to adverse scenarios has increased over time (for example, thanks to improved risk management practices induced by greater awareness of risks that come with performing stress test exercises). To this scope, we construct counterfactual exercises by recalibrating the scenarios of the 2016 and 2018 exercises so that they have the same severity as the 2014 exercise. We find that in 2018, the economy would have experienced a smaller decline in loans compared to the previous exercises. This implies that banks could afford to deleverage less, i.e. maintain a higher exposure to risk in their balance sheets. We interpret this as evidence of increased resilience.

Minnesota-type adaptive hierarchical priors for large Bayesian VARs

Large Bayesian VARs with stochastic volatility are increasingly used in empirical macroeconomics. The key to making these highly parameterized VARs useful is the use of shrinkage priors. We develop a family of priors that captures the best features of two prominent classes of shrinkage priors: adaptive hierarchical priors and Minnesota priors. Like adaptive hierarchical 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. We introduce a fast posterior sampler to estimate BVARs with this family of priors—for a BVAR with 25 variables and 4 lags, obtaining 10,000 posterior draws takes about 3 min on a standard desktop computer. In a forecasting exercise, we show that these new priors outperform both adaptive hierarchical priors and Minnesota priors.

A Large Bayesian VAR of the United States Economy

We model the United States macroeconomic and financial sectors using a formal and unified econometric model. Through shrinkage, our Bayesian VAR provides a flexible framework for modeling the dynamics of thirty-one variables, many of which are tracked by the Federal Reserve. We show how the model can be used for understanding key features of the data, constructing counterfactual scenarios, and evaluating the macroeconomic environment both retrospectively and prospectively. Considering its breadth and versatility for policy applications, our modeling approach gives a reliable, reduced form alternative to structural models.

Stablecoins and Cryptocurrency Returns: Evidence From Large Bayesian VARs

We study the cross-sectional interdependence between returns on cryptocurrency pairs and deviations of Tether USD from its parity to the U.S. dollar. Methodologically, we propose a large-scale Bayesian Vector Autoregressive (BVAR) model which features a global-local shrinkage prior for cross-pairs return correlations. Empirically, we show that deviations from the USDT/USD parity significantly and positively correlate with future returns on cryptocurrency pairs, conditional on both aggregate and asset-specific trading activity. A simple long-only rotational investment strategy which exploits the exposure to the lagged USDT/USD deviations outperforms out-of-sample passive benchmark investments in Bitcoin and a value-weighted market index.

A large Bayesian VAR with a block‐specific shrinkage: A forecasting application for Italian industrial production

AbstractThis paper proposes a Bayesian vector autoregression (BVAR) model with the Kalman filter to forecast the Italian industrial production index in a pseudo real‐time experiment. Minnesota priors are adopted as a general framework, but a different shrinkage pattern is imposed for both the VAR coefficients and the Kalman gain, depending on the informative contribution of each variable investigated at frequency level. Both a time‐varying and a constant selection for the shrinkage are proposed.Overall, the new BVAR models significantly improve the forecasting performance in comparison with the more traditional versions based on standard Minnesota priors with a single shrinkage, equal for all the variables, and selected on the basis of some optimal criteria. Very promising results come out in terms of density forecasting as well.

Efficient selection of hyperparameters in large Bayesian VARs using automatic differentiation

AbstractLarge Bayesian vector autoregressions with the natural conjugate prior are now routinely used for forecasting and structural analysis. It has been shown that selecting the prior hyperparameters in a data‐driven manner can often substantially improve forecast performance. We propose a computationally efficient method to obtain the optimal hyperparameters based on automatic differentiation, which is an efficient way to compute derivatives. Using a large US data set, we show that using the optimal hyperparameter values leads to substantially better forecast performance. Moreover, the proposed method is much faster than the conventional grid‐search approach, and is applicable in high‐dimensional optimization problems. The new method thus provides a practical and systematic way to develop better shrinkage priors for forecasting in a data‐rich environment.

Macroeconomic forecasting with large Bayesian VARs: Global-local priors and the illusion of sparsity

A class of global-local hierarchical shrinkage priors for estimating large Bayesian vector autoregressions (BVARs) has recently been proposed. We question whether three such priors: Dirichlet-Laplace, Horseshoe, and Normal-Gamma, can systematically improve the forecast accuracy of two commonly used benchmarks (the hierarchical Minnesota prior and the stochastic search variable selection (SSVS) prior), when predicting key macroeconomic variables. Using small and large data sets, both point and density forecasts suggest that the answer is no. Instead, our results indicate that a hierarchical Minnesota prior remains a solid practical choice when forecasting macroeconomic variables. In light of existing optimality results, a possible explanation for our finding is that macroeconomic data is not sparse, but instead dense.

Weigh(T)Ing the Basket: Aggregate and Component-Based Inflation Forecasts for the Euro Area

We compare direct forecasts of HICP and HICP excluding energy and food in the euro area and five member countries to aggregated forecasts of their main components from large Bayesian VARs with a shared set of predictors. We focus on conditional point and density forecasts, in line with forecasting practices at many policy institutions. Our main findings are that point forecasts perform similarly using both approaches, whereas directly forecasting aggregate indices tends to yield better density forecasts. In the aftermath of the Great Financial Crisis, relative forecasting performance was typically only affected temporarily. Inflation forecasts made by Eurosystem/ECB staff perform similarly or slightly better than those from our models for the euro area. JEL Classification: C11, C32, C53, E37

Fast and Accurate Variational Inference for Large Bayesian VARs with Stochastic Volatility

We propose a new variational approximation of the joint posterior distribution of the log-volatility in the context of large Bayesian VARs. In contrast to existing approaches that are based on local approximations, the new proposal provides a global approximation that takes into account the entire support of the joint distribution. In a Monte Carlo study we show that the new global approximation is over an order of magnitude more accurate than existing alternatives. We illustrate the proposed methodology with an application of a 96-variable VAR with stochastic volatility to measure global bank network connectedness.

Scenario Design for Macro-Financial Stress Testing

The goal of this paper is to provide a possible empirical approach to ScenarioDesign for selecting a stress scenario on international Macro-Financial variables. TheScenario Design framework belongs to the class of Second Generation Stress Tests andis composed of a few building blocks. First, multiple scenarios on the risk factorsare generated simulating a Multi-country large Bayesian VAR. Second, we take theperspective of a representative investor who aims to select a severe yet plausible scenarioon a set of systematic risk factors following a factor investing strategy. Moreover, wecompare the stress scenarios selected under different approaches to measure plausibility(the Mahalanobis distance and Entropy pooling under subjective views with a cleareconomic narrative). Finally, we compare our Scenario Design approach to an historicalscenario approach in terms of its ability to select a stress scenario in the eve of a rareadverse event like the COVID-19 pandemics. We give evidence that our frameworkis suitable for the selection of a proper forward-looking severe yet plausible Macro-Financial stress scenario.

Minnesota-Type Adaptive Hierarchical Priors for Large Bayesian VARs

Large Bayesian VARs with stochastic volatility are increasingly used in empirical macroeconomics. The key to make these highly parameterized VARs useful is the use of shrinkage priors. We develop a family of priors that captures the best features of two prominent classes of shrinkage priors: adaptive hierarchical priors and Minnesota priors. Like the adaptive hierarchical 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. We introduce a fast posterior sampler to estimate BVARs with this family of priors - for a BVAR with 25 variables and 4 lags, obtaining 10,000 posterior draws takes about 3 minutes on a standard desktop. In a forecasting exercise, we show that these new priors outperform both adaptive hierarchical priors and Minnesota priors.