Reducing Dimensions in a Large TVP-VAR

This paper proposes a new approach to estimating high dimensional time varying
parameter structural vector autoregressive models (TVP-SVARs) by taking advantage 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 modelling 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
specification 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 efficient
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 decompositions 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 estimates of impulse responses.