(Almost) Recursive Shock Identification with Economic Parameter Restrictions

We propose to estimate the parameters of a vector autoregressive model under the restriction that economic theory is not violated, while the shocks are still recursively identified. We use an augmented Lagrange solution approach, which adjusts the coefficients to meet the theoretical requirements. In a generalization, we additionally allow for a (minimal) rotation of the Cholesky matrix. Based on a Monte Carlo study and an empirical application, we show that the "almost recursive identification with parameter restrictions" leads to a solution that avoids an estimation bias, generates theory-consistent impulse responses, and is as close as possible to the recursive scheme.