🤖 AI Summary
This paper addresses the construction of confidence intervals for impulse response coefficients in AR(1) models. We propose a local projection residual bootstrap (LP-residual bootstrap), applicable under general conditions—including unit roots, unknown forms of conditional heteroskedasticity, and serially correlated shocks. We establish, for the first time, the uniform consistency of this bootstrap procedure—and the asymptotic validity of the resulting confidence intervals—under nonstandard settings such as unit-root processes. Moreover, within a restricted class of models, we achieve asymptotic refinement. Both theoretical analysis and Monte Carlo simulations demonstrate that the proposed method substantially outperforms conventional asymptotic normal approximations and standard bootstrap approaches in finite samples, offering superior robustness and accuracy. The method thus provides a reliable, computationally straightforward tool for inference on structural dynamic effects.
📝 Abstract
This paper proposes a local projection residual bootstrap method to construct confidence intervals for impulse response coefficients of AR(1) models. Our bootstrap method is based on the local projection (LP) approach and involves a residual bootstrap procedure applied to AR(1) models. We present theoretical results for our bootstrap method and proposed confidence intervals. First, we prove the uniform consistency of the LP-residual bootstrap over a large class of AR(1) models that allow for a unit root, conditional heteroskedasticity of unknown form, and serially dependent shocks. Then, we prove the asymptotic validity of our confidence intervals over the same class of AR(1) models. Finally, we show that the LP-residual bootstrap provides asymptotic refinements for confidence intervals on a restricted class of AR(1) models relative to those required for the uniform consistency of our bootstrap.
