Small sample confidence intervals for multivariate impulse response functions at long horizons

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Structural Vector Autoregressions: Theory of Identification and Algorithms for Inference (2010, unknown): “…is more serious for small-sample inference because classical bootstrap procedures or Bayesian Monte Carlo Markov Chain (MCMC) methods require expensive random samples of the structural parameters (Kilian, 1998; Geweke, 1999; Inoue and Kilian, 2002; Geweke, 2005; Pesavento and Rossi, 2006).”
Local Projection Inference Is Simpler and More Robust Than You Think (2020, background): “Wright (2000) and Pesavento and Rossi (2006, 2007) construct confidence intervals for persistent processes at long horizons h = hT ∝ T by inverting the non-standard AR limit distribution, but these tailored procedures do not work uniformly over the parameter space or over the horizon.”
Simultaneous Confidence Regions for Impulse Responses (2009, methodology): “These approximate multivariate Gaussian results and the Wald principle are also useful in anchoring structural identification of the system.”
Oil Prices, Exchange Rates and Emerging Stock Markets (2011, unknown): “…to vastly different impulse responses.24 Third, unit or near-unit roots and cointegration in the VAR can lead to inconsistent impulse responses at longer horizons when the lead time of the impulse response function is a fixed fraction of the sample size (Phillips, 1998; Pesavento and Rossi, 2006).”