Discussion Paper Details

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Title: Do Local Projections Solve the Bias Problem in Impulse Response Inference?

Author(s): Lutz Kilian and Yun Jung Kim

Publication Date: April 2009

Keyword(s): Bias, Confidence interval, Impulse response function, Joint interval, Local projection and Vector autoregression

Programme Area(s): International Macroeconomics

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 JordÓ (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.

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Bibliographic Reference

Kilian, L and Kim, Y. 2009. 'Do Local Projections Solve the Bias Problem in Impulse Response Inference?'. London, Centre for Economic Policy Research.