Andrea Renzetti, Department of Economics, Alma Mater Studiorium Universit`a di Bologna, Piazza Scaravilli 2, 40126 Bologna, Italy.
Forecasting with the TC-TVP-VAR
Response analysis at the ZLB with the TC-TVP-VAR
Starting from:
we can write the TVP-VAR in static compact form as:
Suppose we want to specify independent RW stochastic processes for all the coefficients in Φ as:
This is just another way of writing:
The integrating constant of the Normal-Inverse-Wishart prior
Considering the three first blocks we get
The marginal likelihood is given by:
Following the same steps as in (Giannone et al. 2015) it can be re-written as :
The competing models in the out of sample forecasting exercise in Section 3 are
• A constant parameters VAR with flat prior.
• A constant parameters VAR with Normal Inverse-Wishart prior.
• A TVP-VAR model
The VAR with Normal Inverse-Wishart prior is given by:
The model is taken from Del Negro et al. (2015) and it is a version of the popular medium scale New Keynesian model in Smets et al. (2007). The set of log-linearized equilibrium conditions of the model is