Problems related to confidence intervals for impulse responses of autoregressive processes

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Lag Selection in Subset VAR Models with an Application to a U.S. Monetary System (2000, methodology): “To illustrate how these subset strategies can improve results from impulse response analysis, we use a VAR model of monetary policy shocks for the U.S. economy.”
Local Projection Inference Is Simpler and More Robust Than You Think (2020, background): “First, the condition can fail when some linear combinations of the variables exhibit no persistence (Benkwitz et al., 2000). Second, in the presence of (near-)unit roots, certain linear combinations of the autoregressive coefficients are necessarily super-consistent (Sims et al., 1990). This comprom”
Structural vector autoregressive analysis for cointegrated variables (2006, unknown): “…bootstrap methods generally do not overcome the problems due to zero variances in the asymptotic distributions of the impulse responses and they may provide confidence intervals which do not have the desired coverage level even asymptotically (see Benkwitz et al. (2000) for further discussion).”
Delta-method inference for a class of set-identified SVARs (2018, background): “Our main assumption is less demanding than the asymptotic normality of the reduced-form impulse-responses in GMS17 (see Kilian (1998), Benkwitz, Neumann, and Lütekpohl (2000)).4 2.2.”