Max-Share Misidentification

Valid max-share identification requires necessary and sufficient conditions that are hard to satisfy in practice—the target variable's response to the target shock must be (i) orthogonal to its responses to untargeted shocks and (ii) larger than combinations of those responses. We theoretically characterize consequences of local and global violations to these conditions. In practice, the weight max-share places on an identified untargeted shock can be obtained by projecting the response to that shock on the max-share response. Empirically, the TFP news and business cycle shocks identified by Kurmann and Sims (2021) and Angeletos et al. (2020) are, respectively, at least a third and a quarter contaminated.