An empirical assessment of the influence of informative rotation prior in the sign-identified SVAR model

In the sign-identified Bayesian SVAR model, the standard setup usually postulates a Haar prior for the rotation matrix. However, the rotation matrix does not enter the likelihood, and its prior is never updated by data. A key implication is that the Haar prior rotation matrix can be unintentionally informative about posterior inference, despite having no relationship with economic interpretations or data. We show empirically how Haar prior rotation matrix could affect the results in the context of two well-known models: Baumeister and Hamilton (2018) and Peersman and Straub (2004, 2009). For both models, the histograms of accepted impact responses are shown to reflect closely the histograms of accepted rotation matrices. Although sampling uncertainty is updated by the data, it barely contributes to determining the set of accepted impact responses compared to the uncertainty about the rotation matrix, explaining why the histograms between the accepted impact responses and the accepted rotation matrices are similar in shape. To a lesser extent, the influence of the rotation matrix is carried over to subsequent responses where additional sampling uncertainty arises. Our results reinforce the argument that the rotation prior can affect the distribution of accepted responses, possibly leading to erroneous inferences.