Large structural VARs with multiple linear shock and impact inequality restrictions

We propose a high-dimensional structural vector autoregression framework capable of accommodating a large number of linear inequality restrictions on impact impulse responses, structural shocks, and their element-wise products. Combining impact- and shock-inequality restrictions can be flexibly used to sharpen inference and to disentangle structurally interpretable shocks through sign and shock constraints. To estimate the model, we develop a highly efficient sampling algorithm that scales well with model dimension and the number of inequality restrictions on impact responses, as well as structural shocks. It remains computationally feasible even when existing algorithms may break down. To demonstrate 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 settings. We provide empirical evidence that financial shocks are the most important driver of the dynamics of the business cycle.