Danne (2015) VARsignR: Estimating VARs Using Sign Restrictions in R

Summary

This is the vignette for VARsignR, an R package that identifies structural shocks in vector autoregressions using sign restrictions. Rather than imposing zero (recursive/Cholesky, short-run, or long-run) restrictions to pin down the structural shocks, sign restrictions require the impulse responses to have theory-consistent signs — a set-identification approach. The package implements four established procedures: Uhlig's (2005) rejection method, Uhlig's (2005) penalty-function approach, the Rubio-Ramírez–Waggoner–Zha (2010) rejection method, and Fry and Pagan's (2011) median-target method. The document explains their usage and the technical details, bridging the gap between the software and the underlying papers. (MPRA Paper No. 68429.)

Key Claims

• Why sign restrictions. A reduced-form VAR cannot be structurally interpreted without extra restrictions; the traditional zero/recursive restrictions (Sims 1980; Blanchard–Quah 1989) are often inconsistent with theoretical models. Sign restrictions (Faust 1998; Canova–De Nicolò 2002; Uhlig 2005) instead constrain only the signs of selected impulse responses, which many models agree on (e.g., a contractionary monetary shock raises the policy rate and lowers prices and output).
• Set, not point, identification. Sign restrictions do not deliver a unique structural model but a set of admissible ones; inference summarizes the whole set, which raises the question of how to report and compare draws.
• Uhlig (2005) rejection method. Draw candidate orthogonal rotations of the reduced-form shocks, compute their impulse responses, and keep only draws whose responses satisfy all sign restrictions (over the imposed horizons); the retained draws form the posterior over admissible models.
• Uhlig (2005) penalty-function approach. Instead of accept/reject, choose the impulse vector that minimizes a penalty for violating the sign restrictions — selecting a single impulse vector rather than a set.
• Rubio-Ramírez–Waggoner–Zha (2010) rejection method. An efficient way to draw the orthogonal rotation matrices (via QR decompositions of random normal matrices), improving on ad-hoc rotation schemes for sign-restriction identification.
• Fry–Pagan (2011) median-target method. Because reporting the pointwise median impulse response mixes responses from different admissible models, Fry and Pagan propose selecting the single draw whose responses are closest to the pointwise medians — a "median-target" model that is internally consistent.

Concepts Introduced or Extended

• Sign Restriction Identification
• Structural Identification

Entities Mentioned

• Christian Danne

Quotes

"VARsignR identifies structural shocks in Vector Autoregressions (VARs) using sign restrictions. It implements Uhlig's (2005) rejection method, Uhlig's (2005) penalty function approach, the Rubio-Ramírez et al. (2010) rejection method, and Fry and Pagan's (2011) median target method."

My Take

As a software artifact this vignette's value is accessibility and comparability: it puts the four canonical sign-restriction algorithms behind one interface so a practitioner can actually run them and see how much the answer depends on the method. The two most conceptually important distinctions it surfaces are (i) rejection vs. penalty — a full posterior over admissible models versus a single selected impulse vector — and (ii) the median-target fix for the fact that pointwise-median impulse responses are not a real model. It complements the theory pages: sign restrictions are the main alternative to the zero/recursive and long-run restrictions catalogued in structural identification, and the natural companion to monetary-policy-shock work where the sign of the interest-rate/price/output responses is exactly what theory agrees on.