Variance-Maximizing Identification and the Plague of Confounding Shocks

This paper examines the vulnerability of variance-maximizing identification, specifically the Max-Share estimator, to biases arising from confounding shocks. We show analytically that Max-Share tends to recover a hybrid of structural disturbances rather than the dominant long-run shock of interest, even when the target shock clearly drives low-frequency variation. To address this weakness, we propose a band-limited frequency-domain estimator – the Limited-Spectral approach – which isolates low-frequency dynamics and reduces contamination from higher-frequency shocks. Using a transparent two-shock model, we characterize the confounding mechanism and document its implications through Monte Carlo experiments. We further show that, while Limited-Spectral improves identification of low-frequency shocks, variance maximization in the spectral domain can still face difficulties at business-cycle frequencies when multiple structural shocks overlap.