43: Reducing Dimensions in a Large TVP-VAR
Joshua C.C. Chan, Economics Discipline Group, UTS Business School, University of Technology, Sydney, Eric Eisenstat,University of Queensland, Rodney W. Strachan, University of Queensland.
Date of publication: March 2018
Working paper number: 43
Abstract: This paper proposes a new approach to estimating high dimensional time varying
parameter structural vector autoregressive models (TVP-SVARs) by taking advan-
tage of an empirical feature of TVP-(S)VARs. TVP-(S)VAR models are rarely used
with more than 4-5 variables. However recent work has shown the advantages of mod-
elling VARs with large numbers of variables and interest has naturally increased in
modelling large dimensional TVP-VARs. A feature that has not yet been utilized is
that the covariance matrix for the state equation, when estimated freely, is often near
singular. We propose a speci cation that uses this singularity to develop a factor-like
structure to estimate a TVP-SVAR for 15 variables. Using a generalization of the re-
centering approach, a rank reduced state covariance matrix and judicious parameter
expansions, we obtain e¢ cient and simple computation of a high dimensional TVP-
SVAR. An advantage of our approach is that we retain a formal inferential framework
such that we can propose formal inference on impulse responses, variance decomposi-
tions and, important for our model, the rank of the state equation covariance matrix.
We show clear empirical evidence in favour of our model and improvements in esti-
mates of impulse responses.