This paper by Christopher A. Sims and Tao Zha examines the theory and practical behavior of Bayesian and bootstrap methods for generating error bands on impulse responses in dynamic linear models. The authors find that Bayesian intervals have a stronger theoretical foundation in small samples, are easier to compute, and perform similarly to the best bootstrap intervals by classical criteria. Bootstrap intervals based on the simulated small-sample distribution of an estimator without bias correction perform poorly. The paper also discusses the incorrect use of standard algorithms for Bayesian intervals in overidentified models and provides a correct method for constructing Bayesian intervals in such cases. The authors emphasize the importance of Bayesian posterior probabilities over classical confidence levels, especially in nonstationary models, where asymptotic normality assumptions break down. They provide computational exercises to demonstrate the performance of different methods and conclude that Bayesian intervals are relatively straightforward to compute and well-behaved, making them a valuable tool for econometricians.This paper by Christopher A. Sims and Tao Zha examines the theory and practical behavior of Bayesian and bootstrap methods for generating error bands on impulse responses in dynamic linear models. The authors find that Bayesian intervals have a stronger theoretical foundation in small samples, are easier to compute, and perform similarly to the best bootstrap intervals by classical criteria. Bootstrap intervals based on the simulated small-sample distribution of an estimator without bias correction perform poorly. The paper also discusses the incorrect use of standard algorithms for Bayesian intervals in overidentified models and provides a correct method for constructing Bayesian intervals in such cases. The authors emphasize the importance of Bayesian posterior probabilities over classical confidence levels, especially in nonstationary models, where asymptotic normality assumptions break down. They provide computational exercises to demonstrate the performance of different methods and conclude that Bayesian intervals are relatively straightforward to compute and well-behaved, making them a valuable tool for econometricians.