Simple robust two-stage estimation and inference for generalized impulse responses and multi-horizon causality

TL;DR

This paper proposes a new two-stage estimation method for generalized impulse responses that improves accuracy and robustness over traditional least squares, especially in non-stationary data and large horizons, with applications to economic causality.

Contribution

The paper introduces a novel two-stage estimation and inference procedure for GIRs that enhances efficiency and robustness, avoiding serial correlation corrections and accommodating growing horizons.

Findings

Outperforms LS in simulations

Robust covariance estimates improve inference

Reveals short- and long-term effects of economic uncertainty

Abstract

This paper introduces a novel two-stage estimation and inference procedure for generalized impulse responses (GIRs). GIRs encompass all coefficients in a multi-horizon linear projection model of future outcomes of y on lagged values (Dufour and Renault, 1998), which include the Sims' impulse response. The conventional use of Least Squares (LS) with heteroskedasticity- and autocorrelation-consistent covariance estimation is less precise and often results in unreliable finite sample tests, further complicated by the selection of bandwidth and kernel functions. Our two-stage method surpasses the LS approach in terms of estimation efficiency and inference robustness. The robustness stems from our proposed covariance matrix estimates, which eliminate the need to correct for serial correlation in the multi-horizon projection residuals. Our method accommodates non-stationary data and allows the projection horizon to grow with sample size. Monte Carlo simulations demonstrate our two-stage method outperforms the LS method. We apply the two-stage method to investigate the GIRs, implement multi-horizon Granger causality test, and find that economic uncertainty exerts both short-run (1-3 months) and long-run (30 months) effects on economic activities.