Working Paper: CEPR ID: DP4536
Authors: Elena Pesavento; Barbara Rossi
Abstract: Existing methods for constructing confidence bands for multivariate impulse response functions depend on auxiliary assumptions on the order of integration of the variables. Thus, they may have poor coverage at long lead times when variables are highly persistent. Solutions that have been proposed in the literature may be computationally challenging. The goal of this Paper is to propose a simple method for constructing confidence bands for impulse response functions that is not pointwise and that is robust to the presence of highly persistent processes. The method uses alternative approximations based on local-to-unity asymptotic theory and allows the lead time of the impulse response function to be a fixed fraction of the sample size. These devices provide better approximations in small samples. Monte Carlo simulations show that our method tends to have better coverage properties at long horizons than existing methods. We also investigate the properties of the various methods in terms of the length of their confidence bands. Finally, we show, with empirical applications, that our method may provide different economic interpretations of the data. Applications to real GDP and to nominal versus real sources of fluctuations in exchange rates are discussed.
Keywords: Impulse Response Functions; Local to Unity Asymptotics; Persistence; VARs
JEL Codes: C12; C32; F40
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Existing methods for constructing IRFs (C51) | Inaccurate results (C83) |
| Reliance on auxiliary assumptions about the order of integration (C22) | Misrepresentation of the persistence of shocks (E32) |
| Proposed method based on local-to-unity asymptotic theory (C29) | Better coverage properties at long horizons (C41) |
| Proposed method (C59) | Confidence bands that asymptotically contain the true IRF (C51) |
| Proposed method (C59) | Improved performance for horizons greater than or equal to 10 (C69) |
| Proposed method (C59) | More accurate confidence intervals for IRFs (C51) |