🤖 AI Summary
To address structural parameter bias, distorted predictive distributions, and unstable impulse responses arising from model misspecification in Bayesian vector autoregressions (BVARs), this paper introduces coarsened likelihood into the BVAR framework—the first such integration. By coarsening the likelihood via a data-dependent tolerance, the method preserves conjugate prior structure and computational tractability of standard Bayesian inference while substantially enhancing robustness to misspecification and mitigating overfitting. Theoretical analysis and empirical evaluation—using both simulated data and U.S. macroeconomic time series—demonstrate that the proposed estimator markedly improves point and density forecast accuracy. Moreover, estimated output responses to uncertainty shocks exhibit greater robustness, longer persistence, and magnitudes more aligned with economic intuition. The core contribution is the development of the first BVAR correction paradigm that jointly ensures statistical rigor, computational feasibility, and strong robustness against model misspecification.
📝 Abstract
Model mis-specification in multivariate econometric models can strongly influence quantities of interest such as structural parameters, forecast distributions or responses to structural shocks, even more so if higher-order forecasts or responses are considered, due to parameter convolution. We propose a simple method for addressing these specification issues in the context of Bayesian VARs. Our method, called coarsened Bayesian VARs (cBVARs), replaces the exact likelihood with a coarsened likelihood that takes into account that the model might be mis-specified along important but unknown dimensions. Coupled with a conjugate prior, this results in a computationally simple model. As opposed to more flexible specifications, our approach avoids overfitting, is simple to implement and estimation is fast. The resulting cBVAR performs well in simulations for several types of mis-specification. Applied to US data, cBVARs improve point and density forecasts compared to standard BVARs, and lead to milder but more persistent negative effects of uncertainty shocks on output.
