Working Paper: CEPR ID: DP7266
Authors: Lutz Kilian; Yun Jung Kim
Abstract: It is well documented that the small-sample accuracy of asymptotic and bootstrap approximations to the pointwise distribution of VAR impulse response estimators is undermined by the estimator?s bias. A natural conjecture is that impulse response estimators based on the local projection (LP) method of Jordà (2005, 2007) are less susceptible to this problem and hence potentially more reliable in small samples than VAR-based estimators. We show that - contrary to this conjecture - LP estimators tend to have both higher bias and higher variance, resulting in pointwise impulse response confidence intervals that are typically less accurate and wider on average than suitably constructed VAR-based intervals. Bootstrapping the LP estimator only worsens its finite-sample accuracy. We also evaluate recently proposed joint asymptotic intervals for VAR and LP impulse response functions. Our analysis suggests that the accuracy of joint intervals can be erratic in practice, and neither joint interval is uniformly preferred over the other.
Keywords: bias; confidence interval; impulse response function; joint interval; local projection; vector autoregression
JEL Codes: C32; C52; C53
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| LP estimators (C51) | greater bias (D91) |
| LP estimators (C51) | higher variance (C46) |
| greater bias (D91) | wider pointwise impulse response confidence intervals (C46) |
| higher variance (C46) | less accurate pointwise impulse response confidence intervals (C51) |
| bootstrapping LP estimator (C51) | exacerbates finite-sample accuracy issues (C51) |
| bias-adjusted bootstrap method for VAR models (C51) | outperforms LP confidence intervals (C51) |
| joint confidence intervals for LP and VAR methods (C32) | can be erratic (E32) |
| LP method's excessive variability and bias (C51) | less preferable than VAR methods (C29) |