On the relationship between Jorda?s IRF local projection and Dufour et al.?s robust (p,h)-autoregression multihorizon causality: a note

The main objective of this research note is to establish a link between the local projection (LP) approaches of Jorda (2005), Kilian and Kim (2011), and more recently Plagborg-Møller and Wolf (2021), Li et al. (2022) and the multihorizon causality analysis of Dufour and Renault (1998) and Dufour et al. (2006). Our detailed review of these papers with particular attention to Jorda?s local projection methodology make an enlightened comparison with Dufour et al.?s generalized causality methodology which is based on the (p,h)-autoregression concept. In particular, we highlight the fact that Jorda?s approach relies on standard Cholesky decomposition to compute the IRF while we use the GIRF?i.e., the Koop et al. (1996) and Pesaran and Shin (1998) generalized impulse response function (see also Warne, 2008)?to make this comparison more reliable and in line with Dufour et al.?s robust methodology, which also refers to GIRF coefficients. Dufour et al.?s methodology does not require orthogonalization of the disturbances. We therefore call their method ?the Dufour et al.?s GIRF??a new type of GIRF?that, unlike the usual IRF which is for horizon h = 1, is for any horizon h ? 1. We also highlight the fact that our multihorizon causality test based on the (p,h)-autoregression relies on Monte Carlo simulation, which can greatly improve test level in small samples, alleviating substantially the variance problem observed in the literature. As shown in Li et al. (2022), while LP is less biased than VAR OLS methods, there is a serious variance problem that makes the LP method quite erratic. Our Monte Carlo simulation method seems therefore quite well adapted for tackling this issue, improving LP or our (p,h)-autoregression method sufficiently to make it reliable in small samples. This multihorizon causality test that we develop and apply in this paper, and the empirical evidence we present shows that it is reliable when applied to classical monetary causations.