Principled Identification of Structural Dynamic Models

Abstract

We take a new perspective on identification in structural dynamic models: rather than imposing restrictions alone, we optimize an objective. While definitive structural identification ultimately requires exogenous economic insight, a weighted correlation-maximizing objective yields an Order- and Scale-Invariant Scheme (OASIS) that selects the orthogonal rotation most aligned with designated target variables. In traditional SVARs, these targets are the reduced-form innovations, making OASIS a natural reference rotation. We show that recursive Cholesky identification is a constrained version of the same objective and that OASIS is systematically closer to perfect correlation, closing roughly twice as much of the gap as recursive orderings, both theoretically and empirically. The same framework also provides a principled estimation strategy for Proxy VARs (IV-SVARs), where the weighted criterion is essential for resolving overdetermination in multi-proxy systems while symmetrically accommodating proxy leakage. Revisiting 22 published SVARs, we find that reduced-form innovations are typically only weakly correlated, helping explain the historical robustness of recursive schemes. Applying OASIS to seminal proxy applications, however, reveals economically important leakage across shocks and shows that accounting for such leakage can materially alter substantive conclusions.