The Local Projection Residual Bootstrap for AR(1) Models

This paper contributes to a growing literature on confidence interval construction for impulse response coefficients based on the local projection (LP) approach. We propose an LP-residual bootstrap method to construct confidence intervals for the impulse response coefficients of AR(1) models. The method uses the LP approach and a residual bootstrap procedure to compute critical values. We present two theoretical results. First, we prove the uniform consistency of the LP-residual bootstrap under general conditions, which implies that the proposed confidence intervals are uniformly asymptotically valid. Second, we show that the LP-residual bootstrap can provide asymptotic refinements to the confidence intervals under certain conditions. We illustrate our results with a simulation study.