Large structural VARs with multiple linear shock and impact inequality restrictions

We propose a high-dimensional structural vector autoregression framework that features a factor structure in the error terms and accommodates a large number of linear inequality restrictions on impact impulse responses, structural shocks, and their element-wise products. In particular, we demonstrate that narrative restrictions can be imposed via constraints on the structural shocks, which can be used to sharpen inference and disentangle structurally interpretable shocks. To estimate the model, we develop a highly efficient sampling algorithm that scales well with both the model dimension and the number of inequality restrictions on impact responses and structural shocks. It remains computationally feasible even in settings where existing algorithms may break down. To illustrate the practical utility of our approach, we identify five structural shocks and examine the dynamic responses of thirty macroeconomic variables, highlighting the model's flexibility and feasibility in complex empirical applications. We provide empirical evidence that financial shocks are the most important driver of business cycle dynamics.