The graphics presented in this website are computed from the impulse response functions derived from a set of 90 bilateral sign-restricted vector autoregressive (SRVAR) models covering all pairwise combinations of 10 European countries: Austria, Belgium, France, Germany, Ireland, Italy, the Netherlands, Portugal, Spain and the United Kingdom
The models are estimated on a dataset spanning 498 weeks over the period January 2006 to July 2015
In the SRVAR framework, one first estimates a reduced form VAR model which captures the dynamic relationships in the data. One then generates a large set of observationally equivalent structural representations of the reduced form model (i.e. all of the structural models imply the same reduced form process)
Each of these candidate structural models is then tested to see whether the impulse response functions that it generates satisfy a set of inequality constraints defined with respect to their signs
All of the candidate models that satisfy the sign restrictions are retained; the rest are discarded -- inference then proceeds using the set of retained structural models
Our SRVAR models are estimated using Harald Uhlig's pure sign restrictons approach in MATLAB. Our estimation code makes use of several scripts written by Ambrogio Cesa-Bianchi as part of his excellent VAR Toolbox 2.0
The estimation of so many sign-restricted VAR models is highly computationally demanding. We use MATLAB's Parallel Toolbox to estimate multiple models simultaneously. In addition, our codes are designed to be distributed over multiple computers in a cluster-computing environment. Even so, each individual sign-restricted VAR model must be estimated on a single CPU so there are limits to the gains from parallelisation
A rigorous technical discussion of our estimation framework including details of our identifying sign-restrictions can be found in the paper